Klaus: EU climate measures a tragic mistake

Click the picture for AFP's summary of the Handelsblatt's interview with Czech President Václav Klaus.

Full interview in German

Why it was wrong to cut the rates

Eight days after the Big Ben lowered his defining interest rate by 0.75 percentage points, they subtracted extra 0.5 points, ending at 3.0%. The sum, 1.25 percentage points in 8 days, is unprecedented. Even after the 9/11/2001 attacks, the interest rates were only lowered by 0.5 percentage points.

The interest rates in the U.S. should have been higher by 3-5 percentage points during the last 5 years or so. Let me sketch several general reasons why it was wrong for the Fed to reduce the rates so rapidly and why it is generally bad for the Fed to maintain low rates and to allow the U.S. currency to weaken.

Regulators should regulate fluctuations

As we have discussed repeatedly, markets have the tendency to amplify various fluctuations. The herd mentality of the investors is one of the reasons. Such economic cycles may lead to crises. These things are natural but if they are excessive, they are unhealthy. If the central banks and federal bodies are supposed to do something, they should try to make the behavior of markets more constant, not more violent.

So they should act as a kind of negative feedback. They should never try to overreact. They shouldn't try to overcompensate an effect by another but stronger effect or amplify the overall havoc on the markets.

Now, most slowdowns are preceded by various unsustainable bubbles. In many cases, various equity prices grow faster than certain sustainable rates. While the growth may be trusted in the short run and many people earn cheap money from it, it is very clear that eventually, it must stop or collapse. The dot com bubble and the housing bubble of the last decade are two recent examples.

In my opinion, responsible officials should try to regulate these movements already when they are going up. They might want to say what prices and their time derivatives they consider reasonable and try to influence and calm down the psychology of the markets. Some price dynamics is clearly unsustainable. For example, if housing prices increase by 10 percent every year while wages only grow by 5 percent or less, it is not hard to see that houses are rapidly getting increasingly unaffordable. Constant affordability essentially means the same average growth of the housing prices and wages.

Still, it is not unusual that the housing prices sometimes increase by 10 percent for a couple of years. However, it is then obvious that these prices must sometimes also drop by comparable fractions. If the authorities didn't act to slow down the excessive increase of prices, they shouldn't act against their drop either. A further drop in housing prices by 20-50% is pretty much unavoidable and responsible people shouldn't pretend that it is not.

Now, a decreasing feeling of wealth surely reduces consumers' spending which might be considered a bad thing by some people. But the very same sentence also holds in the opposite direction. Increasing home prices are (or were) artificially increasing consumption above the rate that would exist if the housing prices were increasing sustainably. I feel that too many people want to see only one side of this coin (and many other similar coins). If they become financial government officials, they inevitably lead the economy to an unsustainable behavior that must obviously end up in amplified cycles and deeper crises.

Inflation and exchange rates are more robust measures of the proper value of money

Finally, all central banks look at inflation because inflation is always and everywhere a monetary phenomenon. The Federal Reserve in particular emphasizes the economic growth. It uses lower rates to stimulate it when the growth slows down. I think it is a wrong perspective.

While lower rates do stimulate the economy, they also lead, to one extent or another, to many other effects, including higher inflation, weakening currency, increasing spending, increasing debt. I think that the primary goal of the central banks should be to keep the value of money constant.

In the past, the value of money was determined by the gold standard, by the ultimate "constant" precious metal. However, gold doesn't play such an important role today. Neither does silver, the second candidate for a "prototype" of value. In fact, the gold/silver price ratio has been dramatically fluctuating during the last two centuries. A much more robust definition of the value of money involves all possible products that people buy.

The inflation rate measures how the value of money with respect to the basket of actual consumable things changes every year. This number should be kept more or less constant because price stability defines the equilibrium of supply and demand for money.

The GDP growth depends on many other things - for example the weather in agricultural countries - and there exists no principle that would dictate that this figure should be constant. Also, stock prices are derived quantities that determine the ability of companies to create values under certain (and changing) circumstances. Again, there is no a priori reason why these things should be constant. But a non-constant value of the money - with respect to things that people actually need - is simply a bad thing.

Irresponsible behavior should be punished

We have discussed the issue or moral hazard many times. Once again, irresponsible behavior must be punished. If someone takes a risk and makes a profit, it must also be possible that sometimes the risk works against the person and leads to a loss. If the government or the central banks save the speculators - both rich as well as poor ones - in such a way that the sign of the speculators' profit is always positive, it leads to increasing speculation, less stable markets, and less efficient markets where people effectively insured by the government earn cheap money for activities that are not useful for anyone (except for the person who makes the money).

The Fed shouldn't be a slave of the Wall Street. The decisions of the Federal Reserve influence many other types of people - such as U.S. students who must now pay a lot of money abroad. The bankers should be independent from all pressures of limited subgroups of the population or the economy.

Strong dollar policy is beneficial for the U.S.

The strong dollar policy has been a very good policy for the U.S. and if someone openly or secretly believes that it is not the case, he or she is extremely wrong.

First of all, a strong dollar has been one of the major reasons that is (or was) making American economy, science, and technology superior. A stronger currency means higher salaries - when converted to another currency - and higher salaries attract skilled workers and increase the competition. All these things increase productivity and related observables.

It is an effect that we also know from individual countries. For example, Prague is able to concentrate skillful, hard-working, smart people because it has a richer local economy than the rest of Czechia. The causal relationship goes in both ways. The local economy is strong because there are lots of hard-working people who have something to offer and they are there because the local economy is strong and offers them high salaries.

If the effect of concentrating people worth high salaries diminishes, the comparative strength of the city or the country diminishes, too. What do I want to say? For example, the U.S. still may have about 3 times higher salaries than the Czech Republic if measured by conversion (but 2 times as measured by the PPP). Will this ratio of 3 or 2 persist? I think that the answer is No unless the U.S. restores the strong dollar policy. If it doesn't, the average salaries in both countries will eventually coincide - just like the average IQs (98) and other objective quantities describing the economical environment in both countries coincide.

Once again, the currency strength has a profound impact on the attraction of brains and qualified workers in general. The competitive edge of a country largely depends on these things.

Relationship with trade balance

Moreover, America has a significant trade deficit. While it is true that a weaker currency could reduce it, it takes some time. In the short run and medium run, it is much easier to reduce it by a strengthening U.S. dollar simply because the imports become cheaper in the U.S. dollars and imports are more important for the overall calculation than exports because they are larger (because of the trade deficit).

I think that a weak currency significantly helps the trade balance only if the country already has a significant surplus (an example is or was China). For countries with a large trade deficit such as the U.S., a weak currency may make the balance even worse and the last 6 years demonstrate this fact pretty clearly.

On the other hand, there is nothing wrong about having a large trade deficit for many decades because the growth of the economy - and population - of different countries may simply differ for whole centuries. There would be nothing surprising about the U.S. economy growing, building, and importing more than the Japanese economy simply because there is more space in the U.S. for people, their houses, and their new companies.

I want to say one more thing: a strategic, political observation. Friends of the U.S. are much more likely to hold the U.S. dollars while the U.S. enemies have a much higher probability to bet against the U.S. currency. By weakening the currency, the Fed effectively helps the enemies of the U.S. financially while it punishes its friends. It is a very bad evolution for the American (and not only American) strategic interests.

Fast rate cuts create the feeling that something really serious is going on

Another observation is so obvious that I will only dedicate two sentences to it. Fast rate cuts create the impression that the U.S. economy is in a serious trouble and such an impression has the ability to transform itself into reality. Such a dramatic behavior repels all kinds of investors, especially the international investors who are influenced not only by the prices of U.S. stocks etc. denominated in the U.S. dollars but also by the value of the U.S. dollar.

Americans borrow easily and they need higher rates

Finally, America should have higher rates than many other countries simply because the Americans are clearly not shy to borrow money. After all, their self-confidence in borrowing money is one of the driving forces behind the trade deficit. This comment is another reason supporting the thesis that lower interest rates "help" to increase the trade deficit.

If I summarize, I think that the importance of one causal relationship - between interest rates and the stimulation of the economy - is being heavily overestimated because of some flawed, Keynesian thinking while many other, more important relationships and principles are being largely neglected. When you think about all these things, you will see that the bankers are creating at least as much damage as they help.

And that's the memo.

Brian Cox and Leonard Susskind on String Theory & Supreme Master TV

Part II: Extra Dimensions (and Susskind's DNA/compactification landscape analogy)
Our Universe Among Others I, II, III (22+24+19 minutes with Susskind; subtitles in 12 languages, saving of our planet by becoming a vegetarian, spirituality, and God's direct contact to An Inconvenient Truth is included in the Supreme Master Television's powerful package) :-)
Brian Cox channel

Well, I think that Brian Cox clearly doesn't get certain elementary subtleties and the spiritual agenda of the Supreme Master TV program (owned by Ching Hai, an apparent god whom I've never heard about) is more entertaining than insightful but I think that all the programs are pretty catchy and pleasing and whenever they talk about science itself, it makes sense.

Half-centennial snowstorms in China

BBC, NASA

Transport chaos is inevitable. Thanks to Willie Soon!

Cosmic strings seen in the CMB at 2 sigma

Today's news about cosmic strings start with

PhysOrg

where they wrote a story called "String Theory Gets a Boost" about a preprint that was recently accepted to

Phys. Rev. Lett.

even though careful readers of the arXiv have known it nearly for a year as

astro-ph/0702223.

Quite a long time for the "speedy" PRL. In the paper that has collected 25 citations so far, Neil Bevis, Mark Hindmarsh, Martin Kunz, and Jon Urrestilla statistically investigate the cosmic microwave background. They try to parameterize it by two models. One of them is based on ordinary inflation - what matters is the scale-invariant spectrum - with an adjustable power law tilt. The other has cosmic strings included.



By looking at the l=10 spherical harmonics, they argue that the relative contribution f_{10} of the cosmic strings is optimized for fitting the data at f_{10}=0.11 plus minus 0.05. So it is not zero and the strength of this statement is approximately two sigma. Well, that's not a terribly strong signal but it is justifiably enough for some people to find it intriguing.

I am somewhat skeptical about this kind of an argument because it reminds me of various "proofs" of anthropogenic global warming: you can't match the curves with the first naive natural model you write down and if you add men to the naive model, you do better. Well, it is not too surprising. Two-sigma signals are guaranteed to be almost everywhere and a model with additional parameters - (almost) whatever they are - is guaranteed to fit the data more accurately than a more robust and simple model. Of course, if this were a 5-sigma signal, I would be more afraid to make such a statement but with 2 sigma, I have enough courage to do it. ;-)

The work is surely interesting but the results so far are uncertain enough to allow me to stick to my subjective and purely theoretical 15% probability estimate that cosmic strings exist and will be reliably observed (or produced) by 2100.

What I would find more convincing would be if a cosmic-string model were able to fit the data better than a cosmic-string-free model with the same number of parameters. For example, if you showed that a model with a fraction of cosmic strings and a fixed tilt is more accurate than a model with an adjustable tilt and its time derivative (or scale derivative) or whatever new additional but "conventional" parameter is useful to reduce the errors.

Couldn't this become a standard technique - in all scientific disciplines - to decide about the relevance of a very new effect previously unused to match the data?

Abdus Salam: a birthday

Abdus Salam, the first Muslim and the first Pakistani Nobel prize winner, was born on January 29th, 1926. What was his main goal? Well, let me speak himself:



See also 35-minute interview with Abdus Salam (start with the last one and continue to the left; Salam superenthusiastically celebrates string theory from around 4:45 of the part 2/4; at the beginning of 3/4, Salam has a funny description of Edward Witten) and dozens of other videos.

As you can see, he had pretty much the same goals as other great and passionate theoretical physicists and he has made a substantial contribution towards this goal.

Family & short bio

His father was an educational bureaucrat in a poor rural district but learning and piety have had a long tradition in their family. I guess that you understand that one of the advantages of the Muslim background is that I don't have to describe the job of his mother in detail. ;-)

He was a stellar student and studied in Lahore, Pakistan and Cambridge, England - where they remember him as a great cook. He founded the school of theoretical physics in Trieste, Italy and finally he created a very lively group at Imperial College, London.

His PhD thesis already contained important results in Quantum Electrodynamics. At that time, he was already famous.

Back in Pakistan & beliefs

With a doctorate, he returned to Pakistan to teach in Punjab. But he was disappointed to find out that it was impossible to establish a powerful research group in that country. On the other hand, he was pretty influential as a policy advisor for their government.

Salam has been a devout believer in the Ahmadiyya Muslim Community. If you don't know, this Ahmadiyya stuff was politically incorrect in Pakistan so the word "Muslim" was later erased from his grave and Salam's name couldn't appear on his own postage stamps.

Nevertheless, when he was alive, he was convinced that Islam and science could not be separated and he wanted the Muslims to become leaders in science. Even during the Nobel ceremony, Salam quoted some verses from Quran that apparently promote scientific curiosity, if you interpret them in a certain way.

Achievements

Salam was one of the folks who proposed to describe neutrinos with two-component spinors and realized that parity violation inevitably follows.

More importantly, he constructed the electroweak theory with the right U(1) gauge group included in it and gave it its name: "electroweak". He shared the 1979 Nobel prize with Shelly Glashow and Steve Weinberg. The theory easily predicted weak neutral currents and W,Z bosons that were observed four years after their Nobel prize.

Salam always realized the important role of symmetry - especially unitary symmetry - in physics. This concept has led him to study grand unification and, more characteristically, to co-father the not-quite-grand-unified Pati-Salam models. He was among the first people to predict and calculate the proton decay rates. Salam has also contributed to the superfield & superspace description of supersymmetric theories.

He has dealt with renormalization of meson theories and helped to integrate gravity into effective field theories in the modern way - as just another tensor field. He was clearly a very modern particle physicist believing in a kind of religion that looks somewhat less modern to me.

Islam and science

Finally, I want to ask this question myself: is Islam compatible with science? If you need a binary answer, it must be Yes. And many of us know very smart and productive Muslim physicists. Salam's picture of a unified theory being identified with a part of Allah is arguably a coherent one. ;-)

On the other hand, I have some doubts whether Islam encourages one to go through the kind of critical thinking and comparisons of alternatives that are so essential at many points of the evolution of science. According to Islam, things must be in harmony and even if they are not, the believers are strongly pressed to pretend that they are.

That's a counterproductive pressure in about 50% of cases or so and it may slow science down. In my opinion, it would take at least millenia for the modern science to develop if the whole world believed in Islam. I might be wrong but at least, you should admit that the data from the history give a certain asymmetric boost to my statements.

Moreover, I guess that generic Muslims - one billion of people - wouldn't subscribe to Salam's understanding of the relationship between physics and faith.

See also Steven Weinberg on religion and a fresh interview with Sheldon Glashow where they talk about Abdus Salam, among many other topics.

Observing cosmic strings via the stretched hydrogen line?

Science Daily,
PhysOrg,
Wired Science

inform us that a group at University of Illinois has proposed a new method to search for signatures of cosmic strings in the skies. The project is based on the 21-centimeter Hydrogen line.

Recall that the Hydrogen line arises from transitions between two nearly ground states of the neutral Hydrogen atom that are split by the so-called hyperfine structure: its origin is in the interaction between the spins of the electron and the proton. The two states, distinguished by different total spins, differ by a very small energy whose corresponding photon has frequency of 1420 MHz or the wavelength of 21 centimeters.

A direct transition between these two states is highly suppressed and almost certainly unobservable in the terrestrial labs (the rate is less than 3 emissions per 10^{15} seconds). However, there is a lot of Hydrogen in the Cosmos so this 21-cm line is easily observable. However, the radiation whose wavelength is 21 cm today is not what the people want to observe.

Instead, they want to focus on the radiation whose wavelength was 21 cm right during the decoupling era. By the expansion of the Universe, the wavelength is now closer to 20 meters and they would need to build a network of powerful radio telescopes and try to see something. I might misunderstand something, but I wouldn't expect this stretched spectral line to be too sharp.

Such signals, if observed, could nevertheless not only identify the inhomogeneities caused by cosmic string networks - that are unobservable in the normal CMB spectrum - but even determine the string tension and perhaps some other features of such cosmic strings hypothetically imprinted into this portion of electromagnetic radiation. Note that cosmic strings appear in various unified theories, starting from grand unified theories and ending with superstring theory itself: cosmic strings can literally be fundamental strings from string theory stretched into astronomical distances.

It looks as a rather interesting and unexpected experimental idea that should be looked into very seriously. Such possibilities highlight that creative people may often solve questions that look too difficult at the beginning. They also emphasize how incredibly idiotic are the aggressive crackpots' proclamations that modern theoretical physics in general and string theory in particular is untestable.

Anthropocene: a postmodern geological period

This article is about the geological epochs. Paul Crutzen, a Nobel prize winner, has been promoting the notion of a new, recent geological period started in the 19th century, the so-called

Anthropocene.

The beginning of the year 2008 brought us two new papers defending this concept: see some news from Australia. It is almost certainly becoming a topic of serious discussions between the people who have the power to modify textbooks. I mostly think that the idea is silly. But let us begin with some basic facts describing the eons, summarized in the (hopefully) most transparent way you have ever seen:

• Hadean (eon): 4.6-3.8 Gyr BC, named after Hades, a Greek god of the underworld
• Archean (eon): 3.8-2.5 Gyr BC (also "prahory" or "urhills" in Czech), divided to these eras:
• Eoarchean: 3.8-3.6
• Paleoarchean: 3.6-3.2
• Mesoarchean: 3.2-2.8
• Neoarchean: 2.8-2.5
• Proterozoic (eon): 2.5-0.54 Gyr BC (Rodinia supercontinent, oxygen created, preparing for complex life, also "starohory" or "old hills" in Czech)
• Paleo-: 2500-1600 Myr
• Meso-: 1600-1000 Myr
• Neo-: 1000-542 Myr
• Phanerozoic (eon): 542 Myr BC - today (Greek for "visible life"):
• Paleozoic (Greek for "old animals"; also "prvohory" or "Primary"): 542-251 (Cambrian, Ordovician, Silurian, Devonian, Carboniferous, Permian)
• Mesosoic (dinosaurs and reptiles; also "druhohory" or "Secondary"; Greek for "middle animals"): 251-65 (Triassic, Jurassic, Cretaceous)
• Cenosoic (mammals; Greek for "new animals"): 65 Myr BC - today:
• Tertiary ("třetihory"): Paleogene: 65-23 Myr BC:
• Paleocene, Eocene, Oligocene
• Neogene: 23-today
• Tertiary: Miocene: 23-5.3 Myr BC
• Tertiary: Pliocene: 5.3-1.8 Myr BC
• Quaternary: Pleistocene: 1.8 Myr - 9600 BC
• Quaternary: Holocene: 9600 BC - today

Note that Tertiary covers both Paleogene as well as a part of Neogene while Quaternary ("čtvrtohory") roughly coincide with the broader human race. Now, there are hundreds of other facts that the mankind has learned that you might expect me to reproduce here. But I won't. Let me focus on more general facts.

Each geological eon, era, or period is associated with some geological events as well as with some epochs in the evolution of life. But because all of them are geological periods, it should be the rocks that determine the natural boundaries.

Continental drift and the creation of various mountains and other huge structures belong to the defining events of the geological classification. Life is added as a cherry on a pie. Its fossils are confined within the rocks.



Journey to Prehistory ("Cesta do pravěku", Karel Zeman, Czechoslovakia, 1955): brontosaur in Mesosoic

If we look at very ancient eras, it is clear that our time resolution diminishes a little bit. For example, the Hadean lasted nearly for one billion of years and it has no official subdivisions. The fact that the recent subdivisions are finer has two major reasons:

• subjective ones: I mean our inability to learn the distant past in detail
• objective ones: I mean the fact that the events on Earth are speeding up

I guess that the objective aspect dominates in the very recent periods. In principle, we can measure time rather accurately even for events that occurred tens of millions of years ago. But we simply don't divide those events to as short periods as one million of years or thousands of years because we are not aware of too many dramatic events that occurred a long time ago.

It is not just that we are aware: many of us are convinced that the frequency of events worth human attention was limited, indeed.

Life occurred rather quickly after the Earth was created. While there has been a lot of rather sophisticated life on Earth in Phanerozoic, it doesn't mean that there was no life in the previous eons. In fact, you can find life not only in Proterozoic but even in Archean.

Consider modern life with internal membranes in cells and cytoskeleton, those that usually have the nucleus. These life forms are called "eukaryotes". Well, what is the evidence for the oldest eukaryote? It wasn't found by your humble correspondent but it was found by Jochen Brocks, his former roommate, and it probably lived 2.7 Gyr BC, in Neoarchean.

That's when the Earth was roughly 50% younger than today.

Only in Phanerozoic, in about the most recent 10% of the Earth's life, we could see abundant life forms around. And only in Cenosoic, the most recent 1% of the Earth's life, there have been mammals around. In the most recent 0.1% of the Earth's history, we saw some kinds of humans around. The white race as defined by the SLC24A5 mutation has only existed for the last 0.0001% of the Earth's history.

Things seem to be speeding up.

Well, it is plausible but unlikely that a similar acceleration occurred in the past and dinosaurs or other distant cousins were driving their SUVs around - before they were destroyed. Let us assume it is not the case and the Quaternary is the first geological period when the evolution of intelligent life forms started to speed up exponentially.

Fine.

But now the main point. With all my admiration for the unbelievable progress that life has recently made, I think that we - the mammals, humans, or whomever you want to include - have a very limited impact on the features of our planet that geologists will be able to study in the year 10,000,000.

I think that the notion of an anthropocene is arbitrary, its beginning is ill-defined, its justification is not really based on geology, and one could invent even newer, more recent eras associated with another kind of human progress.

Note that according to the classification above, we already live in Phanerozoic as well as Cenosoic as well as Neogene as well as Quaternary as well as Holocene. Holocene, the shortest period, approximately coincides with the existence of oldest civilizations as we know them. Do you really want to add Anthropocene to the list?

I don't see too many qualitative geological events that occurred in the last 200 years but that would distinguish us from the ancient Greeks or Romans. Honestly speaking, I consider myself to be much closer to some old people in Greece or the Roman Empire than most politically correct loons who live in the "Anthropocene".

Will we also have to add Microprocessorocene, Multiculturalismocene, or something else? Please stop this insanity. Create new mountains. If you can't do it, please wait until Mother Nature does it for you. Then you can start a new era. ;-)

50 years of LEGO & Józek z bagien

Koukejte vycouvat (Ivan Mládek)

0:41 Back your car ... out of here
I've been here long before you.
Don't ask me to get upset
at you....

0:50 I waited until the Sir
creates some space for my car.
I wanted to put my car
there. Everything's behind me.

0:58 You seem to pretend that you don't hear me - bah bah baah.
Okay, so you may want try to leave - bah bah baah.
When you return your car will be given - bah bah baah
a scratch from a penny or a nickel - baah.

1:15 When the man left the place
we got some time for a revenge.
I walked around his car with
a quarter dollar coin.

1:24 But he was lurking [behind the corner]
waiting how I would behave.
He walked across my roof
and ruined my [lovely] car.

1:32 I had no longer mood for his jokes.
I saw darkness in front of my eyes.
I kicked both head-lamps away from his car.
The bodies were atop of one another.

1:48 And so a head physician from a hospital with a math professor
were rolling on the road without any fuss.
Both older men as soon as they were arrested
rightfully have earned almost the same sentence.

Songwriter, composer, and comedian Ivan Mládek has been one of the heroes of my childhood and I still enjoy his work (as I told him a month ago during a Christmas party; he was also a classmate of President Klaus). He has written hundreds of funny songs and I have memorized most of them. However, "Koukejte vycouvat" (Back Your Car Out Of Here) above has been one of my favorites. For amateurs, I find the LEGO videoclip by Mr Big Stalk and Mr Little Stalk (Košťál and Košťálek) rather impressive.



Another huge hit was "Jožin z bažin" (Josh from the Swamps), the Lumo #1 hit of 1978 and 1979, that I also offer you in a LEGO version; see also a videoclip with Ivo Pešák's Parkinson with Polish subtitles. Right now, thirty years after it was written (for one bottle of alcoholic beverage), it is becoming a successful hit in neighboring Poland and the YouTube video in the previous sentence has over 1 million of Polish visits. Another million has visited copies of the same video. And it is number one on Polish radios; see Polish TV.

I don't fully understand the dynamics behind this development but the Poles must find not only Ivo Pešák's dancing but also the Czech language very funny, maybe even more funny than the Polish language is for the Czechs.

Ilulissat glacier: global warming started 269 years ago

Click to zoom in.

Note that the retreat of ice in Ilulissat, Greenland (satellite) has been pretty much uniform and monotonic and began at least 165 years before Henry Ford established his company.

Thanks to iLoveMyCarbonDioxide.COM.

Alexander Cockburn: A Short History of Fear

Alexander Cockburn has written a book combining Stephen Hawking with Michael Crichton, A Short History of Fear, to be released in April. But already now, in

Spiked,

he describes how the warming church has almost crucified him.

Also, he argues that global warming in general and Al Gore's activities in particular are politically driven and caused by failures of previous left-wing ideologies (he says that the remaining ashes of socialism have themselves turned into a degraded Malthusian outlook, even in Europe) - these Cockburn's ideas sound just like Václav Klaus - but he adds a characteristically left-wing comment that this program can't help to realize the leftist dreams because it will be no one else than the corporations and evil capitalists who will benefit from the fear. ;-)

Well, I tend to agree that the people who benefit are evil even though their identification with capitalism or corporations depends on your conventions. At any rate, I agree with the liberal pundit that it is wrong for various non-profit organizations to have lunches paid by indulgences and it is wrong to promote nuclear energy by global warming fears even if - and even though - nuclear energy is a great thing.

Cockburn paints peer review in the real world as a method to form biased cliques of friends that fight against the unexpected and undesirable. He writes about the political implication of climate alarmism for the third world (e.g. green ideological problems with the new cheap Indian car) and about the self-righteous intimidation he has been subjected to because of his previous blasphemies.

Let me offer you one of hundreds of similar stories of your humble correspondent. A nice former senior ex-colleague of mine was spending some quality time with Naomi Oreskes and he had the interesting idea to put us in touch to discuss the climate. Unfortunately, she first saw my page debunking her paper that had argued that 100% of papers support the "global warming consensus" and she sent me a testimony of hers in the Senate, expecting that it would settle all my questions.

So I sent her a detailed technical analysis of her well-known controversy with Benny Peiser: what points of Peiser's criticism were incorrect and which of them were correct and why etc. She clearly had no idea about the actual literature about the climate and the proportion of papers of various kinds.

On December 12th, 2006, I finally received the following e-mail:

If you are not persuaded by fifty years of scientific work, including by some of the leading geophysicists and atmospheric chemists of our era, then nothing I can say will change your mind, and I apologize for taking your time.

That was an OK e-mail. However, what was less OK was the list of recipients: copies of this e-mail were sent to two senior ex-colleagues of mine whom I knew very well. Incidentally, this technique has been used not only by Naomi Oreskes. Years earlier, an e-mail from Michael Mann (or Stephen Schneider?) was also sent to Daniel Schrag and a few other Harvard alarmists.

If this were not a flagrant case of intimidation, what would be one? Imagine that a senior white male right-wing professor would send such a letter - indicating his foe's incompatibility with the scientific community - to his junior female left-wing colleague, while copies would go to her senior right-wing white male colleagues. A new world war could possibly begin and the white male perpetrator would have to resign with the whole hierarchy above him that was unable to stop this shocking case of discrimination. ;-)

Of course, I didn't get intimidated that easily, so my equally polite - but probably unexpected - answer was as follows:

Dear Prof Oreskes,

thank you very much for your apology although the reason why Prof [1] and Prof [2] have received a copy of this e-mail remains unknown to me.

Sincerely Yours
Lubos

Yes, it seems I wasn't persuaded by self-described authorities and the permanent repetition of some people's favorite talking points; only scientific arguments would matter in my case. Moreover, I have never considered geophysics and atmospheric chemistry to be among top scientific disciplines with the brightest people. ;-)

She was explained these things pretty clearly. And indeed, it has worked in this case. The crackpot has simply shut her mouth and I haven't heard from her again. So even though she was using some of the classical totalitarian tricks to impose her favorite ideology on others, she was not among the worst ones.

Joseph Louis Lagrange: an anniversary

Joseph Louis, comte de Lagrange, an eminent mathematician and a tragic figure, was born on January 25th, 1736, in Turin as Giuseppe Lodovico Lagrangia. His father was a rich manager of the funds of the Sardinian royal army.

He only began to be interested in maths at the age of 17. However, two years later, he wrote a letter to Euler in which he solved the isoperimetrical problem (finding a curve minimizing [thanks, Carl] the perimeter, given a fixed area inside; the solution is clearly a circle but he gave a proof) using variational calculus. Let us say it bluntly: he used a kind of Lagrangian approach. ;-)

Euler and Lagrange: the leaders

Leonhard Euler, a fellow string theorist, instantly understood that Lagrange's methods were important. Euler generously withdrew his own, more primitive paper about similar issues, allowed the young Italian guy to take the full credit for his discovery, and even invented a catchy name for Lagrange's techniques. Lagrange instantly became a celebrated mathematician: only Euler was above him.

Despite Euler's generosity, we still usually talk about the Euler-Lagrange equations that physicists usually derive from "delta S = 0".

Other achievements

At the age of 22, Lagrange established a society that later evolved into the Turin Academy. During this period, he published some papers. One of them found an error by Newton in acoustics. Another paper solved the transverse vibrations of a string, making Lagrange another 18th century string theorist. Add some extra work on physics of sound, probability theory, recurring series, and variational principle.

Later, Lagrange explained why we still see the same side of the Moon. He studied a lot of details in celestial mechanics and reinterpreted Newton's mechanics in the abstract Lagrangian fashion that later became crucial for Feynman (and Dirac) to discover the path integral approach to quantum mechanics.

Lagrange also coined an "infinitesimal" approach to calculus - one that directly assumes the existence of infinitesimal numbers and avoids epsilons and deltas - but his approach was heuristic at that time and was only recently made rigorous (and has previously led many sloppy people to errors). He was a perfectionist teacher and typo-free author of papers.

Many things are called after him, including Lagrangian mechanics, Lagrangian, Lagrangian point, Lagrange multipliers, Lagrange polynomials, and at least five theorems: a theorem about the order of subgroups, the four-square theorem allowing all integers to be written as a sum of four second powers, a theorem about the number of solutions mod p of algebraic equations in number theory, inversion theorem calculating Taylor expansions of inverse functions, and reversion theorem for expanding functions given implicitly.

Health and family

Lagrange's health was never great and the mental part of these difficulties helped him to die at the age of 77. Also, he tried one unhappy marriage, just to be like others, and another happy marriage with a young woman who was feeling very compassionate for him.

L' équation Bogdanov

Le secret de l'origine de l'Univers?

(The Bogdanov Equation: the Secret of the Origin of the Universe?)

Presses de la renaissance,
240 pages, 140 x 225 mm,
ISBN-10: 2750903866,
ISBN-13: 978-2-7509-0386-2

Click the picture to buy it for EUR 19, passwords from amazon.com probably work

Table of contents (why you should learn French)

About the author
Preface by Clovis de Matos, ESA
Introduction

1. The great mystery of the origin

• Towards the Big Bang
• The mystery of the zero point

2. A brief history of physics

• Is there a center somewhere?
• The apple and the Moon
• Heat, entropy, information
• Information theory
• Liquids and fields
• Relativity and quantum mechanics
• Wave mechanics
• The uncertainty principle
• Relativity
• General relativity
• Black holes and expansion
• Putting fields and quanta together

3. The last dream of Einstein

• Quantum gravity: a modern puzzle par excellence
• Gravitational singularities
• Quantum gravity: open questions

4. Strings and membranes at the Planck scale

• What to do?
• Problems with the "atoms of space"
• Additional problems
• Black hole entropy
• All roads lead to string theory
• The birth of string theory
• The first superstring revolution
• The second superstring revolution
• The last decade
• Holography
• Matrix theory
• Landscape

5. The Bogdanov methods to solve the puzzle

• Fluctuations at the Planck scale
• Topological field theory
• Chern-Simons theory
• Fluctuations of time at the Planck scale?
• New subtleties near the time zero
• Quantum groups and noncommutative geometry
• Space, time, temperature, and complex signatures
• Real and imaginary time
• Quantum foam
• Symmetries and conservation laws
• Supersymmetry and supergravity
• Possible repercussions of the fluctuations in the telescopes
• Bogdanovs' tale about creation: summary

6. Strange adventures of the Bogdanov twins

• Unexpected thesis defenses
• A brief history of their adventures
• How physicists evaluate ideas
• Groupthink vs individual appraisal of science

7. Tomorrow and beyond

• Three realities
• Cosmological code
• Complex and imaginary time
• The moment zero and information
• A homework for experts

Conclusions
Glossary
Bibliography
Index

Unfortunately, I can't write more here, for example the equation itself and whether it is correct. The reader will hopefully understand. ;-)

J.K. Rowling also didn't explain her readers on her blog whether Harry Potter was just injured in the last, 7th book and whether the injury hasn't been painful for 19 years after the fight. :-)

A bright independent reader has actually read the book and understood the message. Thanks, Marc!

Majorities in spacetime

Thomas Dent has asked the following interesting question:

Given that we agree not to use an assumption of 'typicality', is there any reason to discard a cosmology where the overwhelming majority of brains are Boltzmann brains? (And the majority of stars, planets, galaxies etc. are also Boltzmann-stars, planets, galaxies...)

The short answer is No. Here is my longer answer.

Dear Thomas, I don't understand what one can possibly mean by an "overwhelming majority of something in a cosmology". I only know how to measure majorities of people or brains or other objects or creatures who live or exist at the same moment (a thickened slice of spacetime), who interact with each other, and who have some enforced equality or a similar mechanism that makes counting of majorities relevant.

If you want to compute majorities in spacetime as opposed to space, what is it supposed to mean? You face exactly the same problems as with the problematic notion of "typicality" in spacetime because typicality and a membership in a majority is really the same thing.

These majorities are ill-defined

Do longer lives matter more than shorter lives? Do you double-count brains that have been transplated into a different body (if the readers kindly allow me to avoid reincarnation)? Do you discount future votes by a discount rate or, on the contrary, increase their impact because they will be smarter, more sensitive, and more important than the contemporary brains? How do you count majorities if the number of brains is infinite - which is clearly a possibility in a temporally infinite universe?

Do you grant full human rights, including the rights to vote, for the Boltzmann brains even though the circumstances of their birth are much more morally problematic than those of generic bastards and their DNA probably deviates substantially from anyone whom we have ever called a brother or a sister, for that matter? How will the future Boltzmann brains defend themselves against the Boltzmann racists such as your humble correspondent who consider them to be a worthless piece of biological junk rather than subjects that determine majorities? Are you ready to impose and advocate intertemporal Boltzmann political correctness? ;-)

Whatever your answers are, how do you determine that they're the right answers while other answers are wrong? What is the physical meaning of such bizarre rules and calculations of majorities in spacetime? Why should physics care about such rules? How can the rules of mechanics and field theory co-exist with metaphysical laws that are built upon "majority" labels? What is the (acausal) mechanism that allows majorities in the future to beat or overshadow minorities in the past and decide about their fate or the fate of their Universe? Isn't it really obvious that such an action can't exist because of the basic principles of causality?

I think that any statement involving majorities of anything in spacetime has exactly zero physical meaning, so the answer to the question above is that if something holds or doesn't hold for such a bizarre "majority", it means nothing whatsoever for physics. There is absolutely nothing wrong with a theory or a cosmology only because it leads to some bizarre (or socially undesirable) "majorities" in spacetime, probably dominated by some future configurations of matter, and there exists no rational reason why "we should be them".

Many two-headed gay canibals

To see how the "majority" reasoning is absurd, let me ask you about the following gedanken experiment. Imagine that the mankind survives for millions of years and there will be quadrillions of people living in the Milky Way during those later times, most of which will be two-headed gays and canibals. Does it mean that something is morally wrong with our world or a theory that describes it? How could you blame our civilization, our Universe, or the laws that describe them for something that happens or doesn't happen in the distant future? Or do you think that, assuming their existence, these future two-headed gay canibals could change our current gay marriage or agricultural laws just because there will be so many of them? Or do you think that there exists some a priori metaphysical yet rational method to prove that the sketched future is logically impossible or, on the contrary, logically inevitable? You can't be serious.

Whether quadrillions of canibals or Boltzmann brains evolve in the year 1,000,000 or not has absolutely no implication and cannot have any implication for our behavior today and for our rational decisions about the validity of theories that describe our Universe. Only the presently available observations, possibly encoding past events, can influence our decisions and arguments whether individual theories are valid. These relevant effects are called "evidence" and legitimate "evidence" must be something that already exists today, not something that could hypothetically emerge in the future.

Let us insist on causality...

These things may evolve or not but it is a dynamical question that is only relevant for the future, not for the present or our explanations of the past. Any other answer would be acausal and logically absurd because if one admitted a role of the future events for physics such as cosmological evolution, it would also lead to causal loops, i.e. essentially closed time-like curves. Still, it is exactly one of the kinds of absurd and flawed reasoning that the anthropic people misdo on a daily basis.

Future is only constrained by the present and the laws of physics, not by universal metaphysical bans

The future of our Universe can involve an empty de Sitter space (the most likely choice), the Big Crunch, trillions of cycles of a cyclic Universe, Boltzmann's brains, or anything else that the actual laws of physics will lead to. There can't be any inconsistency about the physical laws (or, on the contrary, a selective advantage of certain universes) just because they lead to one particular kind of future or another. The future is allowed to be whatever it will be according to the laws of Nature.

The free-will theorem makes this conclusion particularly clear because the physical systems in the future "freely decide" what to do and the probabilistic predictions of quantum mechanics are the only constraint they must respect. In particular, the future coincidences cannot determine or influence the "prior" probabilities that were deciding about the evolution of anything in the past.

For example, if the climate alarmists are right, and I have no problems whatsoever to think about such far-fetched gedanken experiments, a foreseeable future of life on Earth involves either a cataclysmic warming or a new, carbon-regulating, global totalitarian system (they prefer the latter choice even if the former one were impossible). Does it mean that such a dark future proves that our Universe is cosmologically inconsistent? Is there something wrong with physical laws just because they predict something in the future that we don't like for existential reasons? Does God decide for abortion once She calculates that the distant future of Her Universe looks bleak?

Or are the mechanisms of supersymmetry breaking leading to a very rich Africa in 2050 (that earns a lot of money from the African gravitinos) more likely to be true than the mediation scenarios that keep Africa poor?

I find it obvious that as long as our reasoning is rational, respects causality, and avoids wishful thinking or an implicit or explicit God who is protecting us not from logical inconsistencies but from bad luck, as measured by human emotions, the obvious answer to all four questions is No. These kinds of future, however unattractive for a human, don't mean and can't mean that a physical model is inconsistent or unlikely. And a rosy future doesn't mean that the corresponding model is preferred.

Because of the very same reasons, one can't "derive" the opposite conclusion, namely that the civilization must end soon and only a few more billion people will be born, otherwise we wouldn't be typical. In reality, whether the mankind is going to kill itself or not will depend on the future decisions of people and on the future external physical circumstances, not on a metaphysical, spacetime-wide counting of typicality.

Please, let's not use the speculations about the distant future to determine what could have happened in the past. The past may influence the future but the opposite type of influence is not possible because the events in the past depend, via the laws of physics, on the data in even more distant past, not on the data from the future. Allowing the influences to propagate in both time directions would immediately imply logical contradictions that are familiar from cheap and not-so-cheap movies about time machines.

And that's the memo.

RSS MSU corrections & record cold temperatures

First, you should know that John Christy and Roy Spencer (UAH MSU) have identified an error in their competition's data (RSS MSU). You should notice that two climate skeptics have actually made some data look warmer than previously reported. Would the champions of the global warming alarm ever actively identify an error whose correction would cool down the Earth?

The corrected RSS MSU results are approximately 0.1 °C warmer for 2007 than previously reported and they are closer to UAH MSU and articles such as one about the very cold year 2007 will have to be corrected. See the link at the top of that page.

Independently of that, HadCRUT's station-based data show that December 2007 was the coldest month of this century so far and 2007 was the coldest year i.e. the "eighth warmest year" after remaining years of the 21st century and 1998. Paradoxically enough, HadCRUT3 makes 2007 look cooler than the satellite teams.

Recently, during the last two days or so, record cold temperatures were recorded in

• Oregon
• Washington State
• South Carolina
• Iowa (record snow)
• United Arab Emirates
• North India

and other places. Near-record low temperatures are seen in nearby regions such as Wyoming, Canada, Pakistan, North Carolina, and others.

Bike speedometer: 20,000 km

A cold January is not the most likely month for such "anniversaries" but statistics happens:



I bought the BC 500 speedometer in Summer 1995 or so and it has measured kilometers on two continents. If I were riding my bike along a geodesic instead of those small gravitational quantum loops, I could have arrived to the antipole of Pilsen (1000 miles Southeast from New Zealand). But the puzzle is: what will happen with the number above after another kilometer? It will either

1. display 20,000 even though the space for the digit "2" seems somewhat constrained
2. display 19,999: it will be stuck
3. display 0
4. display 0,000
5. display "Error", "infinity", or another special message
6. something else

Paul Langevin, David Hilbert, Hideki Yukawa: birthdays

Paul Langevin was born on 1/23/1872 in Paris. Because he was a rather important representative of French science and a science official, great physicists have encountered him at many conferences. Langevin was also a leading figure who promoted relativity in France.

The modern interpretation of diamagnetism and paramagnetism in terms of electron clouds asymmetrically or anisotropically located within atoms is due to Langevin. In statistical physics, he wrote down the Langevin equation describing Langevin dynamics. The simplest example is Brownian motion in a potential: Langevin's equation is then Newton's equation of motion with the classical potential term, a friction term, and a noise term. He also designed some ultrasound-based technology based on the piezoelectric effect (previously demonstrated by the Curie brothers) to locate submarines during the war but when the gadget was ready, the war was over.

It is a matter of rumors whether Langevin was ever dating Marie Curie. However, there is no doubt that his granddaughter and her grandson are married to each other today. ;-) Langevin was an outspoken opponent of Nazism and was removed from his chair by the Vichy government and returned there in 1944. He died in 1946.

David Hilbert was born on 1/23/1862 in Königsberg, a Russian island in Prussia. He was one of the most important mathematicians of the late 19th and early 20th century.

There's a lot of things he has done - the Hilbert space, 23 Hilbert's problems, Einstein-Hilbert action, ... Let me omit his name in each entry of this list except for the first: Hilbert class field, cube, curve, function, inequality, matrix, polynomial, series, spectrum, symbol, transform, arithmetic of ends, axioms, basis theorem, constants, irreducibility problem, Nullstellensatz, hotel paradox (where you can always add one more guest), theorem (in differential geometry), theorem 90, syzygy theorem, -style deduction problem, -Pólya conjecture, -Schmidt operator, -Smith conjecture, -Speiser theorem, principles of theoretical logic, and others.

Hilbert believed Cantor's big program of formalizing mathematicis and proving every theorem and he was religiously saddened by Gödel's results. Camille Jordan has also said that the proof of the Hilbert Basis Theorem was theology, not mathematics.

His contributions to general relativity remain questionable but I tend to think that he arrived at the desirable result kind of independently. But I also think that Einstein couldn't really plagiarize Hilbert because it would be rather difficult for Einstein to understand Hilbert's formalism. Hilbert has said that "physics is becoming too difficult for the physicists". He proposed to measure the importance of a scientific work by the number of earlier publications rendered superfluous by it. ;-)

Hermann Minkowski was Hilbert's best friend but Hilbert was surrounded by a lot of great minds in Göttingen. Emmy Noether had problems to be hired because they didn't have restrooms for women. Hilbert famously said "Meine Herren, der Senat ist doch keine Badeanstalt" (the faculty is not a pool changing room).

Hilbert has never tried to solve Fermat's Last Theorem, claiming that one needs three years to study at the beginning and he didn't have enough time to waste for a probably failure. Nevertheless, he once gave a talk about "the proof of Fermat's Last Theorem". His talk had nothing to do with it and he explained that the title was only prepared for the case that the plane crashes.

At an engineering convention, engineers worried that Hilbert could insult someone because he didn't think much about the engineers. He replied: "Don't worry. How could I possibly offend anyone if engineering and mathematics have nothing in common!" :-)

Hideki Yukawa was born in Tokyo 101 years ago, on 1/23/1907.

In 1935, he published his theory of mesons as particles that inspire the strong nuclear force between protons and neutrons, via the Yukawa potential (A.exp(-kr)/r, the 3D Fourier transform of A'/(k²+m²)). In 1947, the pion was observed and two years later, Yukawa could grab the first Japanese Nobel prize. Yukawa also predicted K-capture, i.e. absorption of an electron by the Hydrogen nucleus.

He has been the member of all kinds of societies and editorial boards. Yukawa fought against nuclear weapons, too. He died in 1981.

India: three meters of snow

Cold wave intensified and ten feet of snow have killed soldiers etc. in India, bringing the toll to 137.

New Kerala

To avoid similar problems, the Indians should sell the remaining stocks and pay a few trillion dollars to cool the whole planet by 0.001 °C and please the God of climate change. ;-)

A new crisis: disappearing dirt rivals global warming as an environmental threat

At least

Seattle Post Intelligencer

says so. The effect used to be called erosion and it has been fought against for decades but now it has become a new result of cutting-edge science because urban-based journalists have no idea about the actual environment.

In this case, it seems easier, more meaningful, and cheaper to please Gaia. You don't need to stop using fossil fuels. Just switch to "no-till farming" that used to be called "chemical farming" but the adjective "chemical" recently became politically incorrect because it masks the opinion that chemical farming is more "natural" than the till farming. ;-)

Farmers have been doing it for decades, anyway. It is them who should know what is good for their business, isn't it? I guess that this problem won't be covered in the media because it is not interesting for urban politics.

Lev Landau was born 100 years ago

Recently we wrote about a physicist who died exactly 100 years ago, namely Lord Kelvin, and a physicist who was born exactly 100 years ago, namely Edward Teller.

Lev Davidovich Landau belongs to the second category because he was born on January 22nd, 1908 into a Jewish family in Baku, Azerbaijan, Russian Empire, to become the most stellar Soviet and Russian physicist of his century.

Another ordinary prodigy

As in many other cases, he was a child prodigy. At the age of 13, he completed his high school. Because he couldn't enroll in a university, he at least did two schools in Baku simultaneously. In 1924, he moved to the physics department of Leningrad University where he graduated three years later, at the age of 19. He received a doctorate two years later, at the age of 21.

Two more years later, the Rockefeller Foundation teamed up with Stalin's government and allowed him to visit Göttingen, Leipzig, and especially Copenhagen: Landau always considered himself to be a pupil of Niels Bohr. In 1930, he became a friend of Edward Teller, among others. Landau traveled to Cambridge and Zürich before he returned to the Soviet Union, to lead theoretical physics in Kharkov, Ukraine.

Physics Today: a family portrait of Lev Landau by his niece

The Landau school

One of his mottos was versatility. His students had to pass the "theoretical minimum" that covered all aspects of theoretical physics and only 43 candidates ever passed. I pretty much agree with this philosophy and I would say that I have passed an equivalent of it. In this way, the students may become more than narrow specialists.

Mr Jozef Kvasnica, an old physicist we knew from Prague when I was an undergrad, studied in the Landau school and he was a source of humor as well as interesting stories about Landau. For example, when Kvasnica first arrived to the institute, he met a janitor or someone like that in the corridor.

The janitor, while cleaning the floor, already informed Kvasnica that they had tough tests and just for fun, he gave Kvasnica these tests to solve them. We were explained that Kvasnica succeeded and the janitor turned out to be, of course, Landau himself. :-)

In Kharkov, Landau started to write his ten-volume Course of Theoretical Physics with Evgeny Mikhailovich Lifshitz, his friend and former student. Decades ago, I studied these texts and liked them a lot. They're very well structured into sections and each of them has a well-defined result. Recommended.

Incidentally, Landau didn't have too much respect for bad physicists, as the following true and cute story about a predecessor of Lee Smolin shows:

In the Physical Technical Institute in Kharkov where Landau was working some time, there was one vain and mediocre but prolific physicist who made his research mostly by the method of plagiarism. One day he received a telegram which said that he is nominated for Nobel prize and therefore he should prepare a corpus of all his papers in the typewritten form in two copies (by the way, it was before the era of computers) and submit them to the head of Department of Theoretical Physics (which Landau was) with deadline of April 1st.

The poor man lost his mind and did not pay attention to the dubious date. He began to feel very important and stopped to say "good-day" to his old friends. He accomplished the great task of typewriting the corpus in time and laid it on the Landau's table only to be met by the question: "Did you really believe that Nobel prize could be given for this trash?"

As you can see, Landau was not too different from Wolfgang Pauli. So what happened when these two guys met? Well, you know Pauli...

Landau who treated everyone else as a fool found his match in Pauli. After explaining his work to a skeptical Pauli, he angrily asked whether Pauli thought that his ideas were nonsense. "Not at all, not at all," came the reply. "Your ideas are so confused I cannot tell whether they are nonsense or not."

During the Great Purge, he was arrested in an NKVD prison in 1938-1939 for 367 days, instead of those 10 years he was supposed to waste as a potential German spy. Pyotr Kapitsa finally wrote a letter to Stalin, personally vouching for Landau's behavior. In 1962, Landau's car collided with a lorry. Landau's importance was so high that the Soviet officials instantly brought an airplane with a top brain surgeon from the imperialist U.S. Nevertheless, Landau's head and mind never quite recovered and he died six years later.

Landau has never cared about politics much but the following authentic exchange with the notorious agronomist Lysenko, a darling of the communist party, at the session of the Soviet Academy of Sciences is very funny:

When Lysenko's report was over, Landau asked: So, do you argue that if we will cut off the ear of a cow, and the ear of its offspring, and so on, sooner or later the earless cows will start to be born? - Yes, that's right. - Then, how do you explain that the virgins are still being born?

If you really need a hint to get the point of this sensitive joke, supplement the last question from Landau with "even though we f*** them generation by generation". ;-)

Landau's ranking

Landau liked to rank physicists on a 0-5 logarithmic scale.

• 0: Newton
• 0.5: Einstein
• 1: Bohr, Heisenberg, Dirac, Schrödinger; Bose, Wigner
• 2: Landau (initially 2.5)
• 4.5: David Mermin (who wrote Homage of a 4.5 to a 2)

Achievements

Landau's achievements cover many areas of theoretical physics. For example, his 1962 Nobel prize was awarded for his theory of superfluids, relevant for Helium II (He 4), that he wrote down as early as in 1941, together with an explanation of the roton spectrum.

Well, he has done many important things earlier and many more things later. Concerning the first category, he discovered the density matrix approach to quantum mechanics in 1927, independently of Felix Bloch and John von Neumann.

In 1930, he has figured out the right quantum theory of diamagnetism for materials whose magnetic permeability is smaller than one (a kind of imperfect superconductors), something that is relevant whenever there are no stronger effects such as paramagnetism and ferromagnetism inside the material. As an undergrad, I didn't want to like condensed matter physics too much but I simply liked these kinds of derivations.

Landau added a calculation of antiferromagnetism in 1933. At the same time, in 1932, he worked on astrophysics and independently derived the Chandrasekhar limit on stellar masses. To make the story even more impressive, he also developed a theory of adiabatic energy transfer in nuclear and atomic collisions in the same year.

Second-order phase transitions

Landau has developed a theory (or "the theory") of second-order phase transitions. Recall that this terminology due to Ehrenfest indicates that the first derivatives of the free energy with respect to thermodynamical variables are continuous (for example the derivative, called the density, with respect to the chemical potential, unlike in first-order phase transitions such as melting of ice caps where the density jumps) but the second derivatives have a discontinuity (things like the heat capacity change in the transition and really have a singularity over there).

The key observation is that these phase transitions involve a symmetry breaking. Typically, the high-temperature phase preserves a symmetry but the low-temperature side breaks it. Qualitatively, the free energy depends on an "order parameter x" as

• A (x,T) = x⁴ + K(T) x².

I have suppressed the dependence of A on other variables. But what is important is that even if the coefficient K(T) depends smoothly on temperature T around T equal to the critical temperature, the physics will not as long as K(T) changes the sign.

If K(T) is positive, you see that the minimum of A(x,T) is at x=0. The system will sit at x=0: this corresponds to an unbroken symmetry. On the other hand, once K(T) becomes negative, typically for T cooler than the critical temperature, A=0 at x=0 becomes a maximum rather than a minimum. Instead, the system will choose the minimum with a negative A(x,T) at a nonzero value of the order parameter x: this corresponds to a broken symmetry.

Particle physicists know the potential very well from the Higgs mechanism. The politically correct, anti-Slavic terminology for this potential is the "Mexican hat potential". However, the historically correct name of the potential, taught across the post-socialist Eurasia, is the Landau buttocks.

You can check that the shape looks appropriately and that Landau's insights pretty much include everything that was later used to break the electroweak symmetry: Landau's buttocks are the most important ingredient in Weinberg's toilet, as Sheldon Glashow calls the so far unobserved sector of the Standard Model. Landau was extremely good in figuring out some qualitative features of the behavior of various systems - or "emergent phenomena", if you wish - which are usually relevant at many places of science.

Landau-Ginzburg models

A related insight that rapidly followed his theory of phase transitions was their 1950 theory of superconductivity in which the electromagnetic U(1) symmetry is spontaneously broken (higgsed) by a vacuum expectation value of a charged field (corresponding to a collective wave functions of the Cooper pairs, as understood later by BCS).

Potentials for such a charged field occur at many places of physics. For example, many non-geometric and string-size compactifications of extra dimensions in string theory are described in terms of Landau-Ginzburg models and their generalizations. I am talking about theories that flow to the minimal model CFTs and that can be combined into the Gepner models, among other theories.

Landau pole

All these insights lie at the core of theoretical physics where theoretical condensed matter physics and high-energy physics are both excited by their relevance. Even closer to the standard particle physics is the Landau pole; I wrote most of the Wikipedia article, much like the core of hundreds of similar examples.

Already around 1954-1955, Landau realized that the inverse squared electromagnetic coupling was, at least at the one-loop level, a linear function of the logarithm of the energy scale. It was therefore a running coupling and Landau could determine the slope. For QED, the quantum effects make the interaction stronger at higher energies. At some exponentially high energy scales, much greater than the Planck scale, the inverse coupling drops to zero and the ordinary coupling thus diverges.

Even though the higher-loop effects could lead to unexpected conclusions, the U(1) gauge theory almost certainly breaks down at this point and an embedding of the gauge theory into a more UV complete theory (such as a grand unified theory) is desirable. The point is referred to as the Landau pole even though some physicists, especially condensed matter physicists, often like the term "Landau ghosts". Note that in certain conventions, the inverse squared electromagnetic coupling is the coefficient of the photonic kinetic term i.e. the squared electromagnetic field in the Lagrangian. As the coupling formally gets negative, the photon propagator becomes a (wrong-sign) ghost field.

Plasma physics

In 1936, Landau worked out a transport theory in plasmas. He returned to similar topics a decade later. Landau damping is the exponential decrease in time of the amplitude of longitudinal space charge waves, found in 1946. It prevents an instability from developing. A proper technical derivation of the effect depends on contour integration but Wikipedia offers you a vague argument involving surfer dudes.

In 1953, Landau generalized Fermi's model and constructed a relativistic hydrodynamic model for particle production in high-energy collisions. In 1956-1958, he presented his theory of Fermi liquids.

Neutrinos

In 1957, Landau proposed a two-component theory of neutrinos and CP conservation in weak interactions, independently of Lee, Yang, Salam, Marshak, and Sudarshan. Two laters later, he worked out the analytical structure of singularities in scattering amplitudes. We have mentioned a lot of stuff, so the following quote by Landau finally starts to make a lot of sense:

Wir Mathematiker sind alle ein biszchen meschugge. (We mathematicans are all a bit crazy).

Lev Landau was a genius and I propose to upgrade him from 2 to 1.5 if not 1 on the Landau scale. ;-)

And that's the memo.

Carbon regulation vs millions of jobs

While many places on Earth recently witnessed the coldest days in many decades, many not quite reasonable people continue in their crusade to regulate the world's carbon cycle in order to "fight climate change".

While the U.S. department of energy argues that the U.S. won't follow Australia and regardless of the winner of the 2008 elections, it won't join Kyoto, several more "progressive" regions of the world prefer a less reasonable approach.

A powerful German energy lobby group has calculated that certain new rules proposed by the EU could increase the costs of the carbon trading scheme 18-fold and make things more expensive for Germany by EUR 17 billion. They see the European industry in danger, following their calculation assuming a EUR 30 price per ton.

Meanwhile, the current EU ETS price of carbon emissions is between 1 and 2 eurocents per ton. ;-)

Food fights between the EU members are beginning and Germany expects that one million of jobs may be lost as a result of the new scheme. Steelmakers and representatives of other industries argue that if this lunacy is going to continue, they will simply leave Europe.

Moreover, Japan is wise enough to propose 2000 as the new reference year, instead of 1990, to determine future emissions according to a successor of the Kyoto treaty. This fact also makes the situation more difficult for Europe.

One of the main reasons why Europe has been so supportive of these schemes is that they were pegged to 1990 and Europe's CO2 production actually dropped during the 1990-2000 decade. The reasons had nothing to do with global warming - see e.g. Communism, capitalism, and environment - and Europe could simply benefit from being already below the 1990 numbers.

I personally think that if a regulation scheme would have to be adopted - which I don't believe to be the case - it would be more fair if a later year were chosen as the reference year. With 1990 as the reference year, many regions of the world are being punished for their growth in the 1990s while Europe is irrationally rewarded.

One sixth of Britons, close to a 10-year record, suffer from fuel poverty (more than 10% of income spent for utility bills). Green energy policy is one of the underlying reasons of this bad trend.

Thanks to Benny Peiser.

André-Marie Ampère: a birthday

André-Marie Ampère was born on January 20th, 1775, in Lyon, France, to a family of a rich and smart merchant and a pious mother. He was a child prodigy who lived in a nearby burg. André-Marie was able to resum long arithmetic series using pebbles and biscuits before he knew the figures.

His father wanted to teach him Latin but it was realized that the boy prefers maths and physics. Nevertheless, André-Marie had to learn Latin soon, in order to read the papers by Euler and Bernoulli. ;-)

Love and faith

In 1796, he fell in love with a very religious woman, Julie Carron, who was from the working class and they married in 1799. However, two years later, he moved to Bourg, to earn some money for the family as a professor, leaving his ailing wife and son (later, French philologist Jean-Jacques Ampère) in Lyon. Sadly, she died in 1804 and his heart was broken forever. Exactly when she died, he copied a touching verse from the Psalms and started to read the Bible and the Fathers of the Church more regularly.

When he was 18, he quoted the following three events as the key to his life: his first holy communion; the reading of "Eulogy of Descartes" by Thomas; and the taking of the Bastille.

Electrodynamics

Jean Baptiste Joseph Delambre was impressed by Ampère's probabilistic analysis showing why the gamblers always win in the long run and he made sure that Ampère stayed in physics. What did Ampère do on September 11th, 1820? No, he didn't fly into the World Trade Center and he didn't defend his PhD thesis. Instead, he heard of Hans Christian Ørsted's strange new phenomenon: a magnetic needle moves when there is a voltaic current nearby.

It took him one week, until September 18th, to write a nearly perfect paper about the phenomena that was more general and to present it to the Academy. His work also showed that parallel wires with currents attract or repel each other and the full equations followed abruptly. Just to remind you, during the following years, he made some experiments and realized that

∮ B.dl = ∫ J.dS

the contour integral of the magnetic field B around the wire is equal to the total electric current through the loop. You have to respect the right hand rule. Both sides of the equation are dimensionful and you may guess how the unit is called: one ampere.

In differential form and SI units, the law says that

curl B = μ₀J + ε₀μ₀ ∂E/∂t.

I didn't want to confuse you so I have also added the displacement current (the time derivative), the only real contribution of James Clerk Maxwell to the individual Maxwell's equation.

Note that Ampère's law was the first quantitative law describing a relationship between electricity and magnetism. Faraday's electromagnetic induction experiments came 11 years later, in 1831. So Ampère is the man who really started to study electromagnetism as a theory. Moreover, he gave us one more gift related to this important discipline: he gave it its seemingly modern name, electrodynamics.

Summary

Ampère died in Marseille and is buried in Paris. He was a very amiable and child-like character, a teacher and an Inspector-General of the University, but he has also established electrodynamics as a theoretical discipline and wrote sophisticated essays on calculus, curves, light, zoology, psychology, and philosophy of science and knowledge.

Numerical BFSS matrix model & black holes

Press releases can occassionally be useful.

Japanese KEK

has pointed out a work of the kind I always wanted to do.

Jun Nishimura et al. (Phys Rev Lett)

have numerically calculated the properties of non-supersymmetric D0-like black holes in the maximally supersymmetric BFSS matrix model. The most difficult part is the strong coupling that is relevant for the Schwarzschild black holes which is what the D0-branes become.



They have used powerful computers and flexible algorithms to optimize their calculation and the resulting energy-temperature relation agrees with gravity even at strong coupling and even though the agreement cannot be guaranteed by any supersymmetric non-renormalization theorems because the whole setup breaks supersymmetry. Of course, I have never had any doubts that it would work but it is cool that one can actually do it. They can now literally calculate how the black holes are composed out of stringy objects.



Their calculation is not a lattice gauge theory approach but rather a sophisticated Fourier expansion over time with the Polyakov lines used as the key order parameter whose nonzero vev at all temperatures shows that supersymmetry removes the phase transition, as expected (in contrast to a purely bosonic model).

I completely missed the paper when it appeared in the summer - otherwise it would have been included in 2007 in theoretical physics.

Sunyaev, Kontsevich, Witten share Crafoord prize

Half of the USD 500,000 total award goes to Rashid Sunyaev (middle) and two quarters go to Maxim Kontsevich (left) and Edward Witten (right), respectively. Congratulations. Click the picture for more details.

Physics World

Bayesian inference

Two years ago, we discussed the Bayesian reasoning in a critical light:

Bayesian probability I, II

I have emphasized that the Bayesian probabilities are subjective in character. They depend on the precise evidence that one uses in his reasoning. It is meaningless to calculate Bayesian probabilities too accurately or claim that science has calculated one of them to be 90%. For example, if a report says that the probability that most of the 20th century warming was caused by man-made CO2 emissions was determined by science and equals 90%, it proves that the authors are just parrots who don't know what such probabilities mean. Why?

If someone's probability that the statement is correct really equals 90%, it means that the person thinks that a better scientist who could actually choose and analyze better and more extensive evidence more carefully would end up saying that the probability of that statement is 100% (with probability 90%) or the probability of that statement is 0% (with probability 10%). The precise figure of 90% is just a subjective result and a temporary state of affairs. The only reason why it is not equal to 0% or 100% is that the question is not settled. Some people can't distinguish subjective psychological conclusions from objective science.

Goal of this text

But it turned out that there exists another problem. Other people, and sometimes it is the same ones, also don't know how to look for their own subjective opinions and probabilities rationally. Bayesian inference is a good method to separate assumptions from results and to provide us with a solid methodology to use evidence and arrive at reasonable conclusions about the likelihood of various statements.

So even though nothing changes about my criticism of subjective probabilities, I will dedicate a special positive article to Bayesian inference and shed some light on its relevance for the naturalness problem, anthropic misinterpretations of the landscape, retrodictions, and thermodynamics.

Several related previous blog articles about this topic are:

Retrodicting the past
Myths about the arrow of time
New York Times about reincarnation

Articles on this blog criticizing the anthropic reasoning are far too numerous to be listed. Try the landscape category.

Bayes' formula: its meaning

Rev. Thomas Bayes (1702-1761) was more than a Presbyterian minister. He was also a mathematician who gave us a useful formula how our psychological probabilities should be refined if we obtain some new evidence. I recommend you this Wikipedia article for a pretty clear explanation. Nevertheless, I give you mine, too.

In this formula, we investigate different, complementary (and mutually incompatible) hypotheses H_i to explain some phenomena. Before we obtained the new evidence, we had some idea about their likelihood (from previous evidence, from the testimonies of our favorite and wise friends, or from some laws of physics such as the Hartle-Hawking state, if you wish). These subjective probabilities P(H_i) are called the priors. If you like to think in terms of physics, the initial conditions of a physical system are the best example of such hypotheses: each initial state is a hypothesis H_i. Bayes' formula is then a method of retrodiction.

If we don't know anything about the validity of the theories at all, the priors should give a chance to every qualitatively or macroscopically different hypothesis to survive (e.g. 1/N). You shouldn't kill a theory by choosing a ridiculously small prior just because it has a low entropy or a small number of extraterrestrial aliens etc.

Suddenly, we observe some evidence E to occur. In the case of retrodiction, E is a particular feature of the final state that we observe - for example the whole macroscopic or approximate description of such a final state. We use this final state to deduce the initial state. In exact, microscopic physics, there would be a one-to-one correspondence between initial and final states. But if we only know some partial (e.g. macroscopic, in the thermodynamic sense, inaccurate, or otherwise incomplete) information about the final state, it is impossible to uniquely deduce the initial state, not even its basic macroscopic properties.

Predictions become irreversible and retrodictions follow different rules, ideally the rules of Bayesian inference. Because this kind of reasoning inherently depends on the priors, there will always be an uncertainty in any kind of retrodiction.

Because rationally thinking people want to avoid the base rate fallacy and they care about the evidence, their guess about the probability of different hypotheses (or initial conditions) is influenced by the evidence. The probability of a hypothesis after we obtained evidence E, namely the so-called posterior probability P(H_i|E), written down as the conditional probability of H_i given the evidence E, will be different from the prior P(H_i). But how much it will differ?

Bayes' formula: a derivation

First, assume that every hypothesis H_i either claims that the evidence should occur, i.e. the conditional probability P(E|H_i)=1, or it shouldn't occur, P(E|H_i)=0. How does the evidence that E has actually occurred influence the probabilities?

Well, it's easy in this case. We simply eliminate the hypotheses that have been falsified, i.e. those H_i with P(E|H_i)=0 that predict that the evidence E shouldn't occur. Note that all your knowledge of dynamics and Feynman diagrams is only used to calculate the conditional probabilities of evidence E in a hypothesis, P(E|H_i). That's where all the dynamics is hidden.

But when E is observed, we shouldn't change the ratios of probabilities of the hypotheses that have survived because all of them passed equally well. So we must only renormalize all of these probabilities by a universal factor independent of the particular hypothesis H_i, a factor chosen to guarantee that the sum of P(H_i|E) over i equals one. The correct formula is thus:

P(H_i|E) = P(H_i) P(E|H_i) / P(E)

where P(E) is the normalization factor equal to the sum of P(H_i)P(E|H_i). Note that with this factor, the sum of the posterior probabilities P(H_i|E) equals one. Also, this number P(E) is equal to the weighted average of the conditional probabilities P(E|H_i) of the evidence E over different hypotheses. It is naturally weighted by the prior probabilities of these hypotheses which is why it is natural to call it simply P(E), the so-called marginal probability of seeing the evidence E.

Check that the formula has all the desired properties. If a hypothesis H_i predicts that E shouldn't occur, i.e. if the conditional probability of E given H_i, namely P(E|H_i)=0, then the posterior probability of H_i will also vanish. The hypothesis has been falsified. For the hypotheses where P(E|H_i)=1, we see that P(H_i) and P(H_i|E), the prior and posterior probabilities, only differ by the universal normalization factor which is what we wanted.

In reality, hypotheses often imply that the evidence E isn't sharply predicted or sharply impossible. Instead, a hypothesis H_i can predict E to have a probability P(E|H_i) between 0 and 1, given e.g. by the expectation value of a projection operator for the evidence E in quantum mechanics. It is natural to make the posterior probabilities P(H_i|E) linear in the conditional probabilities P(E|H_i). In other words, we can use the displayed formula above even if the conditional probabilities are generic numbers in between 0 and 1. Then it is the real Bayes' formula.

Everything clear?

Avoiding repeated evidence

You might ask why the relationship between P(H_i|E) and P(E|H_i) is linear. Well, the choice is natural because you can imagine that H_i is divided to equally likely "subhypotheses" H_ij, some of which (i.e. for some choices of j) have P(E|H_ij)=0 while others have P(E|H_ij)=1. In this setup, P(E|H_i) is the proportion of the subhypotheses H_ij of H_i with P(E|H_ij)=1. With this interpretation, the continuous Bayes' formula may be derived from the formula where P(E|H_i) are only allowed to be 0 or 1, assuming that you will choose the prior probabilities P(H_ij) of the subhypotheses to be independent of j.

But the question why the relationship is linear is a good one, anyway. For example, if someone incorrectly uses the same (or not at all independent) evidence E to refine his probabilities of hypotheses twice or thrice, he could end up with a quadratic or cubic relationship.

If someone uses the evidence 2500 times, as the IPCC does, the relationship will be a power law with the exponent equal to 2500. Posterior probabilities calculated in this way will effectively set the probabilities of all the theories H_i except for one that maximizes P(E|H_i) equal to zero. But such posterior probabilities are, of course, completely wrong. The corresponding logical fallacy that pretends that one or the most likely alternative (even among many) must occur is called the appeal to probability and it is the most frequent argument in all kinds of alarmism and paranoia. The correct relationship must be linear and only independent evidence may be used to refine the probabilities of hypotheses in the Bayesian reasoning.

(Global warming alarmism also uses many other kinds of logical fallacies such as argument from precedent - comparing the current climate with some events in the past -, fallacious slippery slope, the fallacy fallacy, bare asserion fallacy, the informal fallacy, if-by-whiskey fallacy about the quality of life in a warmer world, and dozens of other fallacies: see the list. But we don't have space here to cover all of them.)

Asymmetry of H and E

As we have repeatedly discussed in the articles about thermodynamics, H is not a mirror image of E in this framework. Well, let me be more careful. It is true that Bayes' formula can be written in the following H-E symmetric form,

P(H_i|E) / P(H_i) = P(E|H_i) / P(E),

which is why you should believe that its essence kind of remembers the underlying H-E symmetry that becomes the time-reversal symmetry if we use the formula for retrodictions.

However, the interpretation of different objects in the formula above is asymmetric. For example, the conditional probability P(E|H_i) is a sharply calculable prediction of the hypothesis H_i for seeing evidence E, for example the expectation value of a projection operator representing E in quantum mechanics (or a sum of squared amplitudes) with H_i as the initial state. It has an objective and unchanging meaning. On the other hand, the posterior probability P(H_i|E) is a subjective probability of a hypothesis after we have taken some evidence E into account. It has no objective or eternal meaning, especially because it depends on the priors P(H_i).

Most importantly, P(H_i|E) is not equal to P(E|H_i) even though some people incorrectly think that time evolution is time-reversal-symmetric even when the information is incomplete: this assumption would imply that the two quantities should be equal to each other, much like the squared absolute values of the inner products of "evolved initial" and "final" states in both orders. But they are not equal. The mistaken belief that they are approximately or exactly equal is so widespread that it has a name: it is called "the conditional probability fallacy". Mathematician John A. Paulos explains that the mistake is often made by highly-educated non-statisticians such as doctors and lawyers (and cosmologists such as Sean Carroll).

Analogously, P(H) and P(E) play a different role, too. P(H) is purely subjective - or it depends on previous data that have nothing to do with the new evidence E - while P(E) depends both on the subjective likelihoods of H_i as well as calculations of the evidence E in the different hypotheses.

The purpose of this short section was to repeat that retrodictions in physical theories are not canonical, unlike predictions. They always depend on priors. Once any kind of incomplete information occurs in your discussion - e.g. if you only study the system at the macroscopic level - retrodictions follow very different rules than predictions. That's why high entropy may be predicted in the future but not in the past. The people who still don't get this basic asymmetry are probably just too zealous or too stupid.

Bayesian inference and naturalness

But I also want to discuss other topics related to Bayes' formula. We will dedicate a few paragraphs to a simple question, namely the interpretation of naturalness. Naturalness in particle physics says that dimensionless parameters in the Lagrangian are expected to be around one. Is it a universal law of physics?

No, it is just a psychological expectation. Consider the QCD theta-angle. We know that a shift by 2.pi is physically inconsequential which is why the QCD theta-angle is a priori a number between 0 and 2.pi. If we don't know anything, we should assume a uniform probability distribution for this parameter.

Is such an assumption canonical? Nope. It is just a guess. For example, you could also think that a power of theta, not theta itself, has a uniform distribution which would be equivalent to a different distribution for theta. In this case, a uniform distribution for theta itself sounds more "intuitive" because it measures the volume on a moduli space once theta becomes a modulus but there is no hard proof that it is the correct one. Equally importantly, different sensible distributions that are uniform in simple functions of theta lead to the same qualitative conclusions.

What conclusions? Well, if we assume the prior probability P(H_i) to be uniform - in this case, we must clearly use a continuous setup of Bayes' formula where probabilities P(E|H_i) and P(H_i|E) become densities and sums over i must be turned into integrals over theta - the probability that theta is gonna be smaller than 10^{-9} is clearly smaller than 10^{-9} (over two pi). Even with slightly different distributions, the probability will be very small.

So we should be surprised. Of course that there is no contradiction here if theta is measured to be smaller than 10^{-9} as it indeed is. But the surprise strongly suggests that the prior probability is probably unrealistic. In other words, there must be some other, so far unknown and not quite random physical phenomenon or phenomena (for example, a new substructure of the particles and their quantum fields or a new symmetry that implies new cancellations, at least approximate ones) that make small values of theta (or zero) more likely. Once you understand these phenomena (perhaps axions, in this case) more correctly, your expectations for the distribution of theta will obviously change. If you are lucky, the strong CP-problem - the puzzle why is theta so surprisingly small - will evaporate.

Once we understood inflation, the huge size or mass of the observable Universe in Planck units also became less mysterious. There are many examples of this kind. Science is about making surprises less surprising, after all.

Incidentally, in the case of the theta angle, we seem to know that the anthropic principle can't be enough to show that theta is very small because life could probably exist for large theta, too. If someone claims that the anthropic principle clarifies all unnatural puzzles and hierarchies in current particle physics, this observation of mine pretty much falsifies his statement. The anthropic principle is not enough to make all small numbers sound natural. It can constrain others. But is it unexpected that some quantities are constrained by life and others are not? Can the tautological fact that a correct theory of the Cosmos must be compatible with life be used to derive anything non-trivial about the Universe? Which things can be derived and which things can't? How many of them should be derivable (clearly not all of them)? How do you decide in which of them the anthropic explanation is enough and which of them should get a better one? Is there any rationally justifiable answer here?

I am not aware of one. The statement by Nima et al. that the dimensionful parameters of the Lagrangian are more affected by anthropic arguments than the dimensionless ones is the closest thing to a rationally semi-justifiable observation I can think about.

Bayesian inference and the anthropic principle

Bayesian inference allows us to sharply distinguish what is our assumption - the prior probabilities - and what is actually being deduced from some evidence E. Some people use seemingly rational proportionality laws that they present either as results of some evidence E - which they are clearly not - or as justified priors - even though there exists no rational justification for such priors. These mistakes have been pointed out and corrected by many people, for example by Hartle and Srednicki in Phys Rev D, but many people still don't get it.

The first logical fallacy is called the "selection fallacy" by Hartle and Srednicki and it involves counting the more or less intelligent observers, the density of life, or counting the vacua in a class of stringy compactifications in order to find out which kind of background is more likely to describe the real Universe, assuming that we are "typical representatives" of a class. People often say that a class of stringy vacua is likely to be correct because it has many elements. Others say that universes with a high expectation value of intelligent observers or a higher density of life per galaxy are more likely.

Are these things scientific? In other words, do they follow from Bayesian inference?

For example, let us consider the most important example in which the existence of humans is the evidence E from the formula and we use it to refine our subjective probabilities of different stationary points in the landscape. Some people argue that the theories with a (very) large portion of the Universe occupied by intelligent life are (strongly) preferred. Is that true?

To answer this question, we must be very careful what E actually says. The evidence we have says that at least at one point of this observable Universe, there exists a human civilization. More concretely, the available evidence doesn't say that at a randomly chosen place of this Universe, one finds a human civilization. This is a very important subtlety. ;-)

Why is this subtlety so confusing? Because we may say that our planet is located at a random point of the Universe - a sentence that sounds correct and almost equivalent to the previous one. But the meaning of the word "random" is different than it was in the previous paragraph. The people who don't distinguish the role of the adjective in these two contexts are, in fact, making the very same error as the people who don't distinguish predictions and retrodictions.

When we say that our planet is located at a random place of the Universe, it means that we are not aware of any special properties of our Galaxy or the region occupied by the Solar System. If you pick a random galaxy and a random star in it, you end up with stars that are pretty similar to the Sun. That's why the sentence "We live at a random place of the Cosmos" is kind of correct.

But you don't end up with the Sun itself (you shouldn't forget to randomize your random generator!) which is why the sentence "At a random place of the Universe, you find humans" is obviously wrong. Random stars in random galaxies usually don't have life on them and even if they do, the creatures don't look like us. If there were humans with TV antennas orbitting nearby stars, we would have already detected many of them.

So it is very important to notice that there is no evidence behind the statement "At a random place of the Universe, you find humans" because in this sentence, you allow the other people to run their random generators and look at their random places. They will find no life over there. If you want to use life as evidence to refine your ideas about the validity of different theories, you must formulate E more carefully.

Once again, the justifiable statement is that "At least one star in the Universe is orbitted by a planet with humans". Furthermore, you may add another justifiable observation that the lively star looks much like many other stars. If a hypothesis H_i seems to predict that there are humans somewhere in the Universe, it doesn't matter how many civilizations or how high density it predicts. It simply passes the test.

If you deal with a theory of a multiverse or a class of string compactifications, which involve more or less well-defined sets of stringy backgrounds in both cases, the corresponding hypothesis really says that "Our planet lives in the universe that is correctly described by [at least] one vacuum in the corresponding set of vacua."

Again, this is the hypothesis we are testing. If you use the existence of life to decide which class of compactifications is more likely, the only thing that matters is whether at least one vacuum in the class is good enough to admit life similar to ours. Once a class of vacua passes the test, it just passes.

Whether life of our kind is predicted in a large percentage of the compactifications or a small percentage of compactifications is clearly irrelevant. If you go through the exact formulation of the hypotheses and evidence and use the correct Bayes' formula, you will see that I am right and the anthropic people are simply making a mistake. Their reasoning was too sloppy. There is no mystery here.

So why do I like heterotic vacua?

You might say that if I deny that an observed property of the Cosmos should better be generic in a promising class of vacua, I also undermine a reason why I believe that the heterotic vacua - that can pretty simply and naturally give the Standard Model gauge group within a grand unified framework - are more likely to be correct than the type IIB flux vacua. Some vacua in the type IIB set will have these properties, too, and I just said that one was enough. So isn't it a tie?

OK. So how do I formulate my thinking in the Bayesian framework? In this case, it is all about the priors. I simply believe that there exists a cosmological mechanism that makes "simple" vacua, with a proper definition of the word "simple", more likely to result from a cosmological evolution and more likely to survive various instabilities, inconsistencies, and dualities that will be discovered in the future. Or perhaps, a new theory of initial conditions will assign simple vacua a greater weight. Simple vacua are preferred much like low-lying states of a cool enough harmonic oscillator. Because of this reason, my prior probabilities are concentrated around the "simple" representatives of various compactifications, for example the heterotic compactifications with small Hodge numbers or braneworlds with small numbers of branes or small fluxes.

In the type IIB set, my prior is mostly located at too simple flux compactifications that simply do not give us the correct gauge group or the correct fermion spectrum. With this kind of reasoning, I end up thinking that the heterotic vacua that predict a pretty good physics "without much work" and with "specially looking manifolds" are actually more likely to be true than numerous vacua that are more generically incorrect. But I also realize that this conclusion depends on my prior belief in some kind of simplicity of the world, in Nature's tendency to choose special compactifications.

Constraints from a small cosmological constant

The cosmological constant is observed to be something like 10^{-123} in the Planck units. This observation is the main empirical evidence used to defend the anthropic ideas. Using Bayesian reasoning, does the small cosmological constant actually imply that we must live in a vacuum inside a dense discretuum i.e. a huge landscape of possibilities?

As usual, the answer depends on the priors. First, let us assume that the cosmological constant in any realistic, supersymmetry-breaking vacuum must be a random number whose distribution is peaked somewhere around the Planck density. Then, it is indeed unlikely for a string compactification to generate any region of space where the cosmological constant would be so tiny. The probability that at least one place or bubble has the right cosmological constant approaches one as soon as you consider an ensemble of 10^{123} vacua or more. That's why the anthropic people like the large landscape.

Imagine that you only consider a small set of candidate vacua, for example the 10+10+10+10 most beautiful heterotic, Hořava-Witten, G_2 holonomy, and F-theory vacua. What does the observed cosmological constant - the evidence E - tell you about the probabilities? Well, indeed, the uniform priors would imply that the tiny observed cosmological constant would make it unlikely for one of these 40 theories to be correct.

However, my prior is not uniform. I think that there can exist many potential mechanisms such as the cosmological seesaw mechanism that make small values of the cosmological constant pretty natural. I am not certain about the existence of such a mechanism but I assign a non-negligible probability to its existence. This nonzero probability therefore influences my (inaccurately known, in this case) conditional probabilities for various theories to generate various values of the cosmological constant so that a small cosmological constant is simply not astronomically unlikely anymore: there is a finite "tail" near zero. With these assumptions, I don't need a huge set of possibilities.

What I say should have been expected. Whether or not you need a huge landscape depends on your beliefs. If your priors reflect your belief that there can't exist any mechanisms or alternative calculations making small lambda likely, a huge landscape of 10^{123}+ vacua is almost necessary. If you believe that there is a chance that a more detailed calculation can actually show that the cosmological constant likes to be small, the huge landscape is not needed.

If the correct answer is that there are way too many vacua and we live in a rather generic one, it still doesn't tell you much about other questions. For example, even if you know that the cosmological constant (or the number of dimensions of space) has an anthropic explanation, it is no free ticket for the anthropic explanations to spread.

Whether or not the strong CP-problem is explained by having many vacua is a new question, unrelated to the cosmological constant. And the answer to this question is almost certainly that the right explanation is non-anthropic, e.g. axions. These answers - whether the anthropic explanation is relevant for some question - primarily depend on something else than the universal, religious power of the anthropic principle. Quite on the contrary, these answers depend on the existence of deeper and more accurate explanations for the individual features of the Universe. Every physically independent question is a new one.

Life should be likely: but how likely?

You often hear that theories that predict that our life is more likely are more acceptable than the theories that predict that our life is much less likely. Indeed, this is a correct principle. In Bayes' formula, the theories that probably lead to life have a higher value of P(E|H_i), where E stands for life, which increases P(H_i|E), too.

However, once again, you must be very careful what the probability P(E|H_i) means. It is the probability that life E emerges somewhere - in at least one region - in the observable Universe predicted by the theory H_i. If your theory H_i predicts that a huge fraction of stars have life, it doesn't increase its posterior probability P(H_i|E) simply because the high density doesn't matter since there is no evidence for such a high density! One lively planet is good enough. You can't choose a probability P(H_i|E) greater than one.

If you imagine that a theory predicts a spatially infinite Universe, you could protest that such an infinite Universe will inevitably generate humans somewhere and my prescription assigns an unfairly high probability to such a theory. You might think that such a theory should be punished for predicting a very low density of life. I disagree. One planet predicted by such a theory where the phenomena look just like the phenomena observed from the Earth and follow the same patterns and relationships is simply good enough for the theory to pass the test of life.

In this context, you should notice that a theory that produces Boltzmann's brains in a spatially and temporally infinite Universe may also pass the test of life but it fails other tests. Indeed, life can emerge somewhere in a spatially and temporally infinite Universe in the form of Boltzmann's brains. So the conditional probability P(E|H_i) where E is life and H_i is a theory with the infinite Universe is equal to one and the theory is not punished by the observed existence of life at all, whether or not the theory predicts burning stars!

On the other hand, the binary fact about the existence of life is not the only evidence that can be used to refine the probabilities of various theories. Additional evidence implies, among billions of other things, that the observations E_2 from many telescopes are consistent with an ordered Big Bang cosmology. The probability of such an outcome predicted by Boltzmann's brains is something like exp(-s) where s is the number of data points ever measured in science. ;-) It is this evidence - the observed order of the real world that seems to make sense - that effectively rules out Boltzmann's brains as a correct explanation. But the observed existence of life itself is simply not constraining enough to do so!

Some people might just correctly want to punish Boltzmann's brain theories but they don't determine the correct reason why we know that these theories are very unlikely. The reason is not the known existence of life or a low density of life predicted by those theories but the observed order of our empirical data that is predicted to be very unlikely by every Boltzmann's brain theory.

Summary

Everyone is recommended to learn the formulation and a proof of Bayes' formula and use them carefully whenever there is a controversy about the calculation of some probabilities, especially if the differences between the opinions of people about some probabilities become exponentially huge and whenever there is a dispute about the difference between assumptions and the insights obtained from the evidence.

Once you do it, many arguments may be shown to be simply wrong while others might be shown to be nothing else than an encoded version of the author's preconceptions, preconceptions that are supported by no evidence. Technically, the latter mistake is based on choosing exponentially small priors for sensible (and probably true) theories.

Conclusions that the young Universe had to have a high entropy; that a scientific theory predicts that we should be Boltzmann's brains; that classes of vacua are better if they produce bigger Universes with denser life or if the class of compactifications are very numerous - all these conclusions may be sharply identified as results of faulty or sloppy reasoning, incorrect versions of Bayes' formula, misinterpretation of the hypotheses or the available evidence, or illegitimate choices of prior probabilities that suppress the correct answers a priori.

Let's avoid these mistakes, please.

And that's the memo.

Bonus: craziness of Bousso et al.

While Hartle and Srednicki are not only right but also win the citation-count battle in this typicality discipline, there are still people who disagree with their (and Bayes') obviously correct rules.

For example, Bousso, Freivogel, and Yang argue on page 1 of their bizarre paper about Boltzmann babies that Hartle and Srednicki's rule that we are not allowed to assume our civilization's typicality implies that we can't deduce anything from our predictions and that science as we know it is impossible. In other words, the anthropic principle is a pillar underlying all of science. Wow. ;-)

In their thought experiment, a theory T1 predicts the electron in your lab to have spin up with probability epsilon (much smaller than one) while T2 predicts spin down with probability epsilon. If you measure the spin to be up, T1 is pretty much falsified while T2 is confirmed.

Bousso et al. claim that one can't make this conclusion in the Hartle-Srednicki setup. Why? Because - hold your breath - we should actually compute the probability that the spin is up in at least one laboratory of the Universe predicted by T1 and this probability is not epsilon but X = 1-(1-epsilon)^L where L is the number of labs in the Universe and this number X is effectively equal to one for very large L, leading to the opposite conclusion than the correct one.

The conclusion by Bousso et al. is of course complete rubbish. When T1 predicts P(up)=epsilon, it is a probabilistic prediction that applies to every single lab in the Universe with the same initial conditions. It holds for typical labs as well as atypical labs, labs led by men and women, liberals and conservatives. In fact, the free will theorem guarantees that the electrons randomly decide according to the statistical predictions and they are not affected by the lab in which they live or any of the data in its past light cone: you can't really divide the labs to typical ones or atypical ones because all the electrons are free and their random decisions are unaffected by their environment (e.g. hidden variables that are thus forbidden).

By the way, it is useful to have many labs or many copies of the experiment if you want to measure the probabilities more accurately. Bousso et al. argue that according to the Bayesian reasoning, having many labs makes things less conclusive which sounds as a complete madness to me. I don't even know what confusion leads them to this conclusion so I can't discuss it. But having many labs is a different topic and I want to talk about the single-lab setup only.

When you say that T1 predicts P(up)=epsilon in your lab, you don't need to be making any assumption about your lab whatsoever, except for the assumptions and initial conditions that were used to calculate the result. The theory has already made the prediction for P(up) and it was epsilon. The statement that "at least one lab in the Universe saw the electron spinning up" is a completely different statement than the statement that "the electron in your lab - or any other one concrete lab - is spinning up". Raphael et al. seem to mix up these two different statements.

What does the evidence in the two cases actually say?

Because I don't genuinely believe that they're so confused that they don't distinguish these two clearly different statements, I think that the reason of their confusion must lie elsewhere. I think that they actually misunderstand which of these statements has been empirically justified in the two situations (spinning electron vs life in the Universe).

If we measure the spin to be up, we have actually proven the statement that "the electron spin in our particular lab is up". More concretely, it is the same lab for which we have defined the initial conditions. Quantum mechanics was able to link the initial state of this particular lab with the measurements of the spin in the same lab. It doesn't matter which lab in the Universe it was. The important thing is that we are still talking about the same lab.

If Raphael et al. use the initial conditions in the lab No. 2008 and use quantum mechanics applied to T1 to deduce that at least one lab in the whole Universe will see spin up with probability epsilon, they are just using quantum mechanics incorrectly. If they use some combined average information about all labs in the Universe and deduce something about a particular lab, they are making a similar mistake. If they use the same lab both in the initial and final state but they end up with the probability 1-(1-epsilon)^L, they are making a mistake, too. The laws of the realistic quantum mechanical theories are local and only allow us to predict the measurements in the same lab whose initial conditions had to be inserted to the machine to calculate the theoretical predictions. And such a result is independent of other labs and their number.

But the situation with the counting of life on planets (or in the universes) is different. Should an easily acceptable theory predict many planets with life? The answer is a resounding No, as explained above. Where is the difference from the spinning electron thought experiment? The difference is that the possible hypotheses or initial states that we are comparing in the case of life are no longer the initial states of a single lab or a single planet but the possible initial states of the whole Universe.

The whole Universe has no special relationship with any of its planets. So there is a dramatic difference here. In the case of the electron, we have measured the spin to be up in the same, special, marked lab whose initial conditions were used to derive the prediction. T2 correctly predicted the spin to be probably up but the probability was a conditional probability given the assumption that the same lab had certain initial conditions.

On the other hand, in the case of the planets in the Universe, we observe life on at least one, arbitrary, unmarked planet of the Universe but this planet is in no way connected with any special region of the Universe included in the initial conditions or in the defining equations of the theory and the corresponding probability of life is not really a conditional one.

So when we observe life, we observe "life on at least one planet", while when we observe the spin up, we observe "spin up in exactly the same lab whose initial conditions helped to define the very problem". In other words, the quantifiers are different. In the case of life, the empirical evidence only implies that "there exists" at least one planet with life. In the case of the spin, the empirical evidence implies something different and kind of stronger, namely that "in the same particular lab that was talked about when we defined the initial conditions of the problem, the spin was up".

In the case of the electron, the initial state of the same lab was a part of the conditions in the conditional probability P(up|conditions) predicted by T1 and this fact makes a huge difference. When we make the theoretical calculation of the observed existence of life, we mustn't make any a priori conditions about the planet where the life would be going to be observed: the probability is not really conditional.

If you wanted to defend the statement of Raphael et al. about the typicality of life, you would need a different sort of empirical evidence. You would need to show that there is life on every or almost every planet of this Universe. You would need evidence that our Universe has the property that when you start with a planet, you end up with life with a high probability. Or you would at least need to show that the density of lively planets is high. This is tautologically the evidence that you need to argue that a theory should better predict many copies of life in the Universe and we obviously don't have any such evidence because we only know one lively planet so far.

To understand the difference between these two things is a kindergarten problem that a kid should be able to figure out in a few minutes. Nevertheless, Raphael, despite his bright mind, has clearly been struggling with this triviality for years to no avail. It seems kind of amazing and Bayesian reasoning indicates that because he couldn't have figured out these basic things for years, it is unlikely (P < 1/(365 x 5)) that he will do it by tomorrow. But I still hope he will! ;-)

New York Times about reincarnation in cosmology

Dennis Overbye

had an entertaining article in the New York Times about some cutting edge cosmology. Its scientific content is bizarre but I think that Overbye faithfully reproduces the actual discussions between theoretical cosmologists - including the most famous ones - and the ideas that they are currently thinking about. Yes, it seems that many of them are losing their minds.

Below, in this essay originally posted on January 16th, I will show that even though the silliness has many forms, most of it is a result of one very concrete flawed assumption about the priors.

First of all, the article talks about Boltzmann's brains.

Recall that Boltzmann half-jokingly argued a century ago that if the Universe exists for an infinite period of time, it is likely that all finite-volume configurations of matter are likely to be repeated infinitely many times (unless the matter density decreases too quickly). The configurations include your brain that spontaneously emerges, with the usual memory and its content, from the middle of some galactic gas. It is unlikely but if you wait for an infinite amount of time, such things do occur.

Some people have seriously claimed that it is thus infinitely more likely that your brain in its current state that you experience didn't occur as a result of an ordered evolution starting from the Big Bang and continuing with human evolution and with love affairs of your parents. Instead, it is more conceivable for it to be a random fluctuation emerging from a complete chaos. Such a brain without its proper context and history is referred to as Boltzmann's brain or a freaky observer.

But are we Boltzmann's brains?

Needless to say, the argument above is completely wrong and I think that every sane person must know that it is wrong. How did we end up with the statement that Boltzmann's brains are more likely than those that have evolved from the Big Bang? Well, we have obtained this answer because we have assumed it from the very beginning. We have assumed a particular "Bayesian prior" making configurations that appear many times much more likely.

Sensible vs absurd priors

However, such a prior is completely irrational. An event or an explanation doesn't become more likely just because it is repeated many times in a hypothetical universe or multiverse. While Joseph Goebbels or the champions of global warming alarmism can make the gullible people think that a statement is more likely if it is repeated 100 times, the actual likelihood doesn't change.

Balanced priors

Once again: we must repeat it many times to make it true. ;-) If a theory predicts an observed event to be repeated many times, it doesn't make the theory more likely than if it predicts one copy of such an event. We only observe the event once and the theories that predict it at least once pass while the theories that predict that the observed phenomenon shouldn't exist fail. But no theories "pass trillions of times".

Why? I could simply say that probabilities can't exceed one. But we may be more detailed. Let me talk in terms of Bayesian inference that is a kind of useful framework for these qualitative discussions. Bayesian inference is a process to refine our idea about the perceived probabilities of different hypotheses. How do we refine them? First, we start with a prior probability: our idea what the probabilities should a priori be. The prior is the most controversial part of the Bayesian inference. But a correct prior assigns comparable probabilities to qualitatively different explanations and theories.

If one hypothesis may come in a quadrillion of forms while another hypothesis is essentially unique, you shouldn't treat the forms as equally good. You shouldn't think that the theory with a quadrillion of forms is a priori much more likely while the unique theory is nearly hopeless to start with. After all, you could always design quintillions of modifications and deformations of any hypothesis to give it a stronger voice. Such a procedure must obviously be forbidden unless we want the degeneracy to inflate and our reasoning to get out of control.

Wrong "proportional" priors lead to dozens of myths

Nevertheless, the mistake above is what many people are doing all the time. For example, the mistake leads some people to believe many kinds of myths, including the myth that

• a lie repeated 100 times becomes the truth. This is the conclusion of the zealous people who promote the "consensus science" where "scientists" repeat the same sentences after each other, convinced that it makes them more likely. If two arguments are not independent at all, they must be counted as one argument
• the most likely arrangement of the Universe at any moment, including its birth, is a highest-entropy state. This conclusion blatantly contradicts the second law of thermodynamics according to which the entropy in the past should be, on the contrary, small. The conclusion is a result of an irrational preference of high-entropy states, something that can be dynamically justified in the case of predictions for the future (as we explain below) but something that is absolutely unjustified and flawed for statements about the past
• we must be typical observers. Clearly, there is no reason why we should be typical observers. A theory that predicts that we are much more typical observers is not much more likely. After all, the best theory should predict that we are insect because insect on Earth is more numerous than mammals. Hartle and Srednicki gave a cool example why this "democratic reasoning" is absurd: it would make a theory that predicts trillions of exotic extraterrestrial organisms virtually falsified - because such a theory would "predict" that we should be them but we are not - even before you observe whether these extraterrestrial forms of life exists. Such a reasoning is logically wrong. A theory simply cannot become more likely or less likely just because it predicts a statement whose validity has not yet been empirically verified (in this case, the existence of extraterrestrial life of some kind) - no Bayesian inference can be made in this case - while the believers in "typicality" irrationally think that the theory without those "Jovian creatures" becomes much more likely
• a class of string-theoretical vacua with a very large number of elements is much more likely to describe the Universe than a class with a small number of elements that are either unique or almost unique.

As you can see, most of the diseases of the contemporary intellectual world, from global warming and other types of "consensus science" to the anthropic principle to Boltzmann's brains to reincarnation, have a common root. This common root is very silly and it violates all rules of logical inference as well as common sense. But it is very widespread.

Sean Carroll and the cosmology of an egg

Sean Carroll is quoted as saying his favorite childish comment that when he is breaking an egg, he is doing cosmology. I think that the mistake in his reasoning has been explained in so many complementary ways and so clearly, most recently in my Myths about the arrow of time, that even kindergarten kids should begin to get it. Sean Carroll doesn't.

The weird statements that we should be typical; we should be Boltzmann's brains; we should be or shouldn't be reincarnated (a new discovery of Andrei Linde to be discussed below); we should have a higher entropy in the past than what we have today, and so on - all of these statements are simply examples of a wrong choice of priors or a wrong logical inference. People end up with these strange things as a result of a sloppy thinking that assumes that some probabilities are proportional to something even though there is absolutely no rational reason for such a proportionality law.

Neither of the correct answers to these questions depends on any details of your cosmological model. The second law of thermodynamics and the breaking of an egg is a result of general statistical features of a large number of microscopic objects such as atoms and it has nothing whatsoever to do with cosmology. In fact, macroscopic quantities inside an egg are almost exactly uncorrelated with any details about the egg a nanosecond earlier: all patterns are being destroyed very quickly. The independence of an egg's fate on the details of the Big Bang 13.7 billion years earlier is expo-expo-exponentially accurate.

After Sean Carroll argues that he is doing cosmology by breaking an egg, Jeff Harvey of University of Chicago gives an apt reply. He says that this is the difference between cosmologists and particle physicists. Why? Because when particle physicists like Harvey are breaking an egg, they are not doing cosmology but preparing a breakfast.

I am usually preparing a dinner when I am breaking an egg but it is enough for me to be in the same universality class as Jeff Harvey. The properties of an egg including the thermodynamical ones are based on the behavior of atoms and ensembles of atoms. They can be (and, in fact, they have been) derived from local physics but not from cosmology. The predictions of these derivations have been successfully verified and all features of the assumptions behind these derivations may be seen to be irrelevant because the result - for the strength of time-reversal-symmetry-violating processes - is much more robust.

For example, the assumption of "molecular chaos" is just a matter of convenience that simplifies our calculations. Other assumptions about the microscopic structure of your material in the initial state lead to results that are practically indistringuishable from others after a tiny fraction of a second.

Andrei Linde and reincarnation

The most revolutionary new idea along these lines is due to Andrei Linde and Overbye dedicates the last paragraphs to this idea. Linde thinks that the computations of the likelihood of cosmological models will be dramatically influenced by the question whether you have been reincarnated. He argues that many cosmologists are not brave enough to talk about this important physical question. ;-)

Well, unlike others, I am surely brave enough to talk about these things but I am less certain that Andrei Linde will be satisfied with my correct answers.

If I understand well what he wants to argue, he probably wants to say that a human being that has been or will be reincarnated many times is either much more typical or much less typical and the probabilities associated with him or her (or the universe where he occurs) should dramatically change or drop. I don't even know which way his argument is supposed to go but it is wrong in both cases.

Kucinich for president

Instead of full-fledged reincarnation of soul, let me talk about something more graspable, namely identical DNA codes. Imagine that Dennis Kucinich has such a special attractor DNA code that it keeps on repeating many times. The Earth has seen thousands of such identical Kuciniches and it will probably witness many more. So far so good.

You want to calculate something about Kucinich, for example whether he will be elected the U.S. president. Some people could say that because the Kucinich DNA is repeated many times, it is just much more likely that a person with the Kucinich DNA becomes the U.S. president than a person with DNA that doesn't like to be reincarnated. And no person with the Kucinich DNA has been elected so far so he is almost certainly the one. Hillary has therefore no chance because she hasn't been cloned in the history.

Is it true? Is the likelihood that Kucinich is gonna be elected close to 99.99%? I hope not!

If you actually look how the real world works, bizarre coincidences such as the existence of thousands of Kuciniches in the history is completely irrelevant for the election process. The president will actually be chosen by the voters and their odds don't reflect the repetition of the Kucinich DNA in the history. They depend on entirely different things which is why the chances of Kucinich are virtually identical to the chances of all other similar folks, even those dwarf-morons who don't suffer from reincarnation.

Even the identical nature of particles in quantum physics has physical consequences only because of subtleties of quantum physics. For example, scattering amplitudes are obtained by summing over all histories. If we are not allowed to sum over all histories, e.g. in classical physics, we can't really make particles identical.

If someone changed Kucinich's reincarnation into a major political question, it could indeed influence the elections. Kucinich would win some votes of (superstitious) voters and lose some other votes of (equally crazy) voters but these changes wouldn't follow from some exotic counting of reincarnated souls or DNA codes. They would be caused by confusion and superstition of confused souls and minds of American citizens - both reincarnated as well as (the most typical) non-reincarnated. ;-)

Even if reincarnation were true in some sense, it simply doesn't control elections or any other physical phenomena that we normally care about. Politics has been separated from reincarnation long before the state was separated from the church. And physical phenomena at different length scales are also mostly separated from each other: that's why nuclear physics doesn't depend on biology and breaking of eggs doesn't depend on cosmology. Saying anything else is an extraordinary - because apparently manifestly wrong - statement that would require extraordinary evidence.

Humanrightism and democracy

The people who build on typicality, democracy between observers, and similar flawed concepts simply don't understand why seemingly similar things hold in the cases where they hold and why they don't hold elsewhere.

For example, we can show that a body of gas tends to evolve towards the most typical states of highest entropy. But why is it so? It is because there is an actual mechanism that makes this happen: the evolution itself. If the gas evolves for a long time, it chaotically tries all configurations with the same values of conserved quantities and spends roughly the same time in each of them, as a detailed analysis of the evolution implies. The most generic ones will thus dominate in the future. The process is called thermalization.

But this argument certainly can't be applied to the distant past or the beginning of the Cosmos because the beginning of the Cosmos didn't chaotically evolve from something else. There was no thermalization before the Big Bang, almost by definition. The typical chaotic configurations are only obtained in the future because there is a mechanism that makes microstates "equally powerful" in an ensemble: a random evolution that takes a long enough time to kill any initial patterns and easy-to-see correlations.

Analogously, some people assume that each observer (or each stationary point in the landscape) should have the same "voice" in some decisions and calculations of probability, in analogy with a democratic society. But why do most people have the same rights in our society? Because we have written down some laws that are being, at least partially, enforced. This is what allows various majorities to control the main policies in various countries. If the laws were not enforced, there would be no physically meaningful equality. In fact, some of us remember that various people who are considered equal today were not considered equal in the past. The conventions, laws, and constitutions have changed.

In the future, progressive politicians can make the voices of bugs equal to the voices of humans and insect will control the immigration policy across the world. We are not yet there and it is legal to spray out mosquitos whose immigration is not convenient enough for our human minority. Thanks God.

Analogously, there is no actual mechanism that makes the "voice" of a terrestrial human being (or a flux vacuum) be equally loud as a "voice" of a hypothetical citizen of Jupiter (or a heterotic vacuum) which is why all arguments and calculations based on the assumption that terrestrials and Jovians are equal (or individual flux vacua are equally likely as individual heterotic vacua) are just unjustifiable, stupid, insane fantasies. In physics papers, they are just bad science. No such interplanetary or interuniversal thermalization has been seen or demonstrated. Most likely, it cannot exist.

People are only equal and people only have their human rights if there exists a framework that enforces these principles. There exist almost no rules of this kind that you could rely upon in Iran. You might be dreaming about them and think that they are good but they are not true in the real world. And there exist no rules whatsoever that would defend your rights on Jupiter. Because these mechanisms don't exist, you shouldn't be thinking like if you assume that they do exist.

In politics, the active defense of the idea that human rights exist even without mechanisms to enforce them is referred to as humanrightism. It is incompatible with realistic politics of a country in the real world. A country can only promise those rights to the individuals that it is able to enforce. By the way, it costs some money and effort.

Summary

I think that if someone offers you some bizarre statements such as those that depend on our typicality, statements that the arrow of time was directed in the opposite direction 5 minutes ago when the eggs were unbreaking, that the reincarnated people are very politically powerful or, on the contrary, hopeless politicians etc., you should ask the person to tell you how he calculated the odds.

In principle, the person should be able to present his or her argument in the framework of the Bayesian inference. He should tell you what his priors are - i.e. to reveal his assumptions - and what observations he has used for the logical inference.

If his Bayesian priors are such that the probability of "almost certainly correct" or "sane" or "reasonable" alternatives are exponentially suppressed, you may tell the person that he is only ending up with bizarre answers because he is already assuming them and excluding the correct answers from the very beginning.

Sean Carroll thinks that the arrow of time should be the opposite what it was 5 minutes ago because he irrationally overhypes high-entropy configurations in the past in his priors which is simply irrational and wrong. High-entropy states in the past are not more likely and there is no sensible reason to think that they are. Retrodictions follow different rules than predictions. Andrei Linde might overhype or suppress the role of reincarnated people, and so forth.

Once you convince the person to adopt sensible priors - that give each qualitatively different hypothesis a comparable chance to live - you should also make sure that the Bayesian inference is correct and follows Bayes' formula. The refined probabilities will never depend on the number how many times an event or a person or a brain or a similar stringy background is repeated. The Bayesian inference simply doesn't allow you to do such things.

Equally importantly, the Bayesian inference can only be made if you actually have some new (direct or indirect observational) evidence that can be compared to your hypotheses, not just a new calculation of the predicted number of Jovian creatures - a number whose correct value in the real world can't actually be measured at this moment. It is impossible to decide which among two otherwise equally robust and consistent theories is more likely without comparing them to some empirical evidence.

Restoring sane conclusions

Once you agree about this basic logic, all the absurdities discussed in Overbye's article and elsewhere will simply go away. The entropy in the past was much smaller than it is today. This statement may be shown by many observations that are consistent with this hypothesis, making it increasingly likely - via the logical inference - that the hypothesis is correct.

Also, the hypothetical reincarnated people won't be discriminated against but they won't have special rights either.

You will be able to see that we are almost certainly not Boltzmann's brains. How can I show it? Well, the theory that we are Boltzmann's brains predicts that the individual events in our memory shouldn't seem to fit together: they are probably chaotic. The theory predicts that the past as reconstructed from our freaky memory doesn't make much sense. On the other hand, the hypothesis that our brains have evolved from a rather ordered evolution predicts that up to some mistakes of the brain, our memory should make sense.

And it mostly does.

If you compare the predictions with reality and make one step of Bayesian inference, you will see that the hypothesis assuming an ordered evolution becomes more likely than it was a priori while the freaky theory becomes less likely (since the conditional probability of order given the assumed freakiness is small). Because you can make many observations of this kind that are more or less independent, you can show that the probability that we are freaky observers is smaller than any reasonably positive number you can think of. There is actually a lot of evidence that we are not freaky observers.

There is no evidence that we are freaky observers: the only way how to argue that we are freaky observers is to choose priors that assume that we are freaky observers and all justifications of such priors are irrational, based on non-existent and wrong proportionality laws. Laws that someone wants to believe because of some bizarre metaphysical reasons but laws that haven't been successful in science.

You will also see that neither of these conclusions depends on any details of your cosmological models as long as the cosmological model is consistent with the present as we observe it and the cosmologists who want to study cosmology by breaking eggs or talking to their deceased relatives are simply being dumb, at least at this particular moment. Once again, you will see that physical phenomena at different scales are largely separated from each other. Breaking eggs is about condensed matter physics whose effective laws may be determined by a careful research of molecular physics but whose features are unaffected by climatology or cosmology.

The information about breaking eggs won't actually help you to decide about the type of the cosmic inflation used in our Universe or anything of the sort. When treated properly, every good enough cosmological model predicts that eggs break and they don't unbreak. They pass (P=1) and none of them passes "trillions of times more". The breaking eggs won't tell you whether you have been reincarnated and messages from your other cloned souls won't inform you about the radius of extra dimensions. And most - but not quite all - other things that follow from common sense will be confirmed by rigorous calculations, too.

And that's the memo.

Annapolis, Maryland: a protest against global warming

Click the picture for more information and one more picture from the funny rally. These warriors are lucky that they don't have to protest in Russia where temperatures will drop to minus 67 degrees Fahrenheit at some places.

Hat tip: Drudgereport

In Afghanistan, 200 people and tens of thousands of sheep have died from an extraordinary cold snap that pretty much influences the whole Middle East.

Heidi Fleiss will open a wind-powered brothel for women. ;-)

Galileo vs Benedict XVI

The Holy Father was expected to give a speech at the Rome University that would start the new academic year. As

Tommaso Dorigo

describes, the Pope eventually cancelled his visit after a protest of 67 professors, led by Emeritus Professor Marcello Cini, who didn't like the fact that in 1990, Cardinal Ratzinger supported the following quote by Feyerabend:

In the age of Galileo the Church showed to be more faithful to reason than Galileo himself. The trial against Galileo was reasonable and just.

Galileo at the process of the Inquisition

I recommend you to click the picture above and read a page that tries to defend the Church against Galileo. For example, it mentions the opinion of Italian journalist Vittorio Messori:

Galileo was not condemned for the things he said, but for the way he said them. He made statements with a sectarian intolerance, like a ‘missionary’ of a new gospel …. Since he did not have objective evidence for what he said, the things he said in his private letters to those men [of the Roman College] made him suspect of dogmatism supporting the new religion of science. One who would not immediately accept the entire Copernican system was ‘an imbecile with his head in the clouds,’ ‘a stain upon mankind,’ ‘a child who never grew up,’ and so on. At depth the certainty of being infallible seemed to belong more to him than to the religious authority.

Also, Galileo is criticized for the fact that the boundaries between religion, philosophy, and science were fuzzy in the 17th century. I doubt it was Galileo's fault and I don't really care whether Galileo's teaching was a new religion, new philosophy, or new science. I think it is much more important that he was right and his wisdom turned out to be essential for the development of our civilization. I happen to care about the fact that Galileo was infallible in the fundamental questions, unlike the religious authority. This fact introduces a certain asymmetry and the asymmetry might lean to the opposite side than the side that Vittorio Messori would like.

Note that Galileo Galilei's description of the crackpots of his time is almost identical to your humble correspondent's favorite words about the contemporary heirs of the Inquisition - I mean the imbeciles who irrationally criticize string theory today and who are trash upon mankind and childish simpletons who haven't grown up. Well, let us admit that great minds think alike. ;-)

Analogously, Vittorio Messori's criticism of Galileo who "didn't have objective evidence" is almost identical to proclamations of individuals such as Peter Woit. Tiny minds think alike, too. :-)

With all my respect to the Pope's intellect, his conservative values, hypothetical links to the Creator ;-), and the traditions and security he represents, I think that Galileo's approach was indeed a new kind of reason and a new religion that we call "science" today. Science as outlined by Galileo was a new religion and it is a good thing, too. The obsolete religious bigots who were so colorfully and so rightfully criticized by Galileo always behave in the same way. They haven't changed much.

And that's the memo.

Ice caps in the crocodile empire

This weekly dose of peer-reviewed skeptical literature about the climate looks into Science magazine:

Isotopic Evidence for Glaciation During the Cretaceous Supergreenhouse

André Bornemann and eight co-authors investigate whether there were ice caps in the Turonian, a warm period roughly 90 million years ago that lasted for 4 million years.



The tropical sea surface temperature constantly exceeded 35 °C, more than by 10 °C warmer than the current temperatures, and crocodiles used to live in the Arctic region.

However, new data involving the Oxygen 18 isotope indicate that during this era, there was a roughly 200,000-year-long period when the Antarctic ice cap did exist and it was about 50% of its current size. In contradiction with the common assumptions, 10 °C of global warming is apparently not enough to prevent ice sheets from growing. See also

CCNews
Daiji World
The Telegraph

Needless to say, such a finding implies that the estimates of possible sea level rise - even in the case of hypothetical insane alarmist warming - would have to be scaled back a lot.

Greenland melt: natural rates

Let me add one more new article. In Journal of Geophysical Research, Petr Chýlek and three co-authors argue, among other things, that the Greenland melt is now actually slower than it was in the 1900s, 1930s, 1940s, 1950s, and 1960s. The available data see no signal - a man-made deviation from the normal natural rates.

Rain in Israel

You may also want to know that a study showed that the Israeli precipitation rates remain essentially unchanged in the last 60 years, despite occassional vague fears that global warming might be changing precipitation patterns.

Water cycle driven by plants

One more comment. Paul Ferguson and Ján Veizer argue in Journal of Geophysical Research that the water vapor fluxes are largely controlled by plant breathing (60% in average), especially in regions with limited vegetation (70%) which might be surprising. Abiotic evaporation is a small portion of the cycle. Forget about CO2 or temperature as the primary direct driver of water feedbacks. If you were ever computing the evaporation in the water vapor feedback that may amplify the greenhouse effect and you thought that the evaporation of H2O was controlled directly by temperature, you probably overestimated this positive feedback amplifying the warming effect of CO2 by a factor of three.

Thanks to Benny Peiser.

Edward Teller: 100th birthday

Exactly 100 years ago, on January 15th, 1908, Edward Teller was born into a Jewish family in Budapest, just like his right-wing comrade John von Neumann four+ years earlier.

Budapest is the capital of what European country?

When he was young, he had to witness a lot of revolutionary mess in Hungary which made him realize that both communism and fascism were dangerous crap. His PhD thesis under Werner Heisenberg in Leipzig was one of the first accurate solutions of the H2+ ion.

Friends & leaving Germany

George Gamow and Lev Landau became his friends in 1930. Teller's friendship with Czech physicist George Placzek was very important for his interests in nuclear physics. For example, Placzek arranged a summer stay in Rome with Enrico Fermi for Teller.

In 1933 he managed to escape Germany. Teller spent some time in Britain and Denmark (with Niels Bohr). He married Mici Harkanyi, a sister of his friend. Their son born as Raymond Joseph Teller (now just Teller) is a magician. In 1935, Gamow drafted Teller to the U.S. He did all kinds of molecular quantum physics but once fission was discovered in 1939, his interests focused on nuclear physics.

The Manhattan project and beyond

Teller was somewhat upset that Hans Bethe and not him was chosen as the director of the theoretical division of the Manhattan project. Because he was also bored by the ordinary fission bomb, he refused to calculate the implosion of a fission bomb and pursued Fermi's rough idea of a "Super" which is how he called the Hydrogen bomb. They had to find someone else to calculate the implosion: it was Klaus Fuchs, a skillful physicist who later turned out to be a Soviet spy. Not too great a job, Edward. :-) Nevertheless, Teller has made some contributions clarifying the implosion mechanism.



A two-minute interview with Teller about Roosevelt, Hitler, and freedom

Teller was overly optimistic about an obsolete type of the H-bomb in 1946. But in 1950, after the Soviets succeeded in creating a fission bomb, Truman ordered his scientists to develop the fusion bomb. Teller returned to Los Alamos. Teller was surrounded by pessimistic scientists who would think that the fusion bomb was infeasible - a fact that apparently drove Teller up the wall.

The H-bomb finally works

After some wrong designs had been shown flawed, Edward Teller and the Polish mathematician Stanislaw Ulam proposed the Teller-Ulam design in a paper. And it worked. Teller argued that Ulam has made no contributions and that Ulam didn't even believe the content of the paper. Others dispute this statement. Teller wanted more money for military research (especially the theorists) while Bethe didn't. So Bethe emphasized that the H-bomb was due to Teller's ingenious mind, not a result of funding. ;-)



In this fun and musical 3-minute documentary about the very large bomb, they also say that the rough idea about the combination of fission and fusion bombs was due to Ulam. It was actually Fermi's idea.

The details of the design remain classified as of 2008. Many historical questions, e.g. whether Andrei Sakharov et al. created the Soviet H-bomb independently or whether they analyzed the fallout from the U.S. explosion, remain uncertain, too. In 1955, Teller was effectively forced to publish an article called "The work of many people" in Science in order to calm down his jealous colleagues. Later, he described the article as a "white lie to soothe ruffled feelings" and claimed full credit for the invention.

The Oppenheimer controversy

His tension with various scientists escalated already in 1954. In his testimony about Robert Oppenheimer, Teller said that he believed that Oppenheimer was most likely loyal to the U.S. However, he was asked whether Oppenheimer was a security risk. Teller said that Oppenheimer's decisions were confused and complicated and public matters should better rest in other hands. Teller said many good things about Oppenheimer but he also recommended not to grant clearance to him.

The authorities agreed with Teller who became a pariah in the scientific community and a darling of the conservative politicians and pundits in the U.S. and Israel (via Yuval Neeman). It seems clear today that Teller wanted to sink Oppenheimer and become the U.S. nuclear boss instead of him.

The 1960s and later times

In the 1960s, Teller tried to work on supersafe nuclear reactors and fought against proposed nuclear test bans. He was inventing various peaceful projects based on nuclear explosions - building harbors or extracting oil. He was named Director Emeritus of the Livermore Laboratory and a Senior Fellow at the Hoover Institution.



In 1979, Jane Fonda (pictured), Ralph Nader, and similar anti-nuclear fanatics made Teller suffer a heart attack because he had to undo the damage they did on the public perception of the nuclear technologies which was a lot of work. In the 1980s, he was a big champion of Reagan's star wars. After the collapse of communism in 1989, he was excited about the developments in Hungary. In 2003, two months before he died in Stanford, Teller was awarded with the Presidential Medal of Freedom by George W. Bush.

Students

Edward Teller's most famous student was Chen Ning Yang, a co-father of Yang-Mills theory, Yang-Baxter equation, and the Lee-Yang parity violation. At the age of 82, Yang learned mirror symmetry because his new fiancée was 28. ;-)

Climate change

In the essay about John von Neumann, we discussed his projects to artificially warm up the Earth by a few degrees by coloring the polar ice caps which might be great for life on this planet. Like most great minds, Edward Teller was a climate skeptic, too. In 1997, he wrote that the jury was still out whether the greenhouse effect contributed to warming. But he proposed a simple solution that would only cost USD 1 billion a year, roughly 500 times less than Kyoto-protocol-style approaches. Click the previous link to learn more.

Eskimos upset about U.S. green groups

Reuters

The Canadian Eskimo organizations fundamentally disagree with the U.S. green groups' tactics to use polar bears as hostages in their disgraceful attacks on the administration of George W. Bush. And so does The Reference Frame.

The Eskimos whose average IQ is estimated to be between 91 and 98 - nearly reaching the average U.S. levels (the relevance of this comment is explained in the 5th fast comment or so; I kindly ask the obnoxious PC crowd to shut up) - criticize the environmental groups and the U.S. media for their black-and-white presentation of a problem that actually has many levels.

The green and journalistic simpletons often present the polar bears as animals going extinct because of climate change and sports hunting. In reality, the polar bear is a very important subsistence, economic, cultural, conservation, management, and rights concern for Inuit in Canada, as explained by Mary Simon (picture), the boss of Inuit Tapiriit of Canada group.

The population of polar bears is about 25,000 (two thirds of them in Nunavut i.e. Canadian Arctic) and tends to be increasing. During the year ended on June 30th, 2007, 498 bears were killed in Nunavut. The figure includes 120 animals shot during sports hunting (the recreational "athletes" have to pay CDN 30,000 a piece): the rest is covered by the native inhabitants.

Via Marc Morano.

Kurt Gödel: an anniversary

Background and countries

Kurt Gödel (4/28/1906) died in Princeton 30 years ago, on 1/14/1978. He was born in Brno, Moravia, Austria-Hungary to a family of a textile industry manager and automatically became a Czechoslovak citizen in 1918 when the monarchy split apart. At that time, Brno had a slight German-speaking majority - today the percentage is around 1% or so.

Talented in languages but speaking almost no Czech, he felt like an exiled Austrian in Czechoslovakia. Let's admit that various ethnic groups had worse feelings and not only feelings in Greater Germany in the course of the history. At the age of 23, he chose to become an Austrian citizen. Nine years later, when Hitler annexed Austria, he became a German citizen. After the war, as a founding member of the IAS, he became a U.S. citizen.

Schools and research of completeness

At the age of 18, he entered University of Vienna, intending to study theoretical physics. He also attended (and thought about) courses on mathematics and philosophy and a lecture by David Hilbert in Bologna transformed Gödel into a full-fledged logician. His PhD thesis defended in 1930 proved Gödel's completeness theorem i.e. the provability of all true assertions in first-order logic.

One year later, he proved his more famous theorem, namely Gödel's incompleteness theorem. Every consistent axiomatic system that is strong enough to include arithmetics of positive integers allows the existence of true statements that can't be proven (first theorem). And the consistency can't be proven either (second theorem).

The unprovable statement from the first theorem is a technically encoded statement saying that "I am unprovable within the system". It can't be false because if it were false, it would be provable (because it says it is unprovable). And provable assertions would have to be true. Being true and false at the same moment would cause inconsistency, in contradiction with the assumed consistency.

So the statement is true but unprovable within the axiomatic system. The only reason why I could have proved that the statement was true is that I used physicists' logic that is more powerful than any system of axioms of a narrow-minded mathematician. ;-)

See: Dangerous Knowledge (+), a 10-minute BBC document about Kurt Gödel. If you like it, try the whole 90-minute documentary including many more mathematicians.

I can also sketch the proof of the second theorem. Why cannot the consistency itself be proved in the system? Because it turns out that one can also translate the statement of the first theorem itself, "there exists an unprovable true assertion in the system", into the language of the given axiomatic system: one can formalize it. In this context, let us call the assertion of the first theorem "p". Above, I've explained that "p assuming the consistency" was not provable in the system, just by extended meta-tools. But the proof of "p" itself can be formalized, as a tedious analysis of the methods of the first theorem shows, and demonstrated as equivalent to "p is unprovable". In other words, "consistency implies that p is unprovable" is provable. But because "p is unprovable" is not provable, it follows that it must be the consistency that is unprovable. ;-)

Philosophical impact

This ended dreams that many of us have had at some point in our lives that one can design completely rigorous axioms for all of mathematics where all statements may be either proved or disproved. In the college, people would be telling us that these results have had far-reaching consequences for philosophy. Of course, I thought that theoretical physics has had much more dramatic consequences for philosophy than logic can ever dream of. But I must confess that as I studied these results due to Gödel in detail, I had to admit they were damn interesting and surprising.

Incidentally, I used to attend courses by Prof Petr Vopěnka (pic) in Prague (it was in this mathematicians' building on the Lesser Town Square, directly connected to the famous church). He was quite a character among the teachers. In the Czech context, he was a relatively achieved set theorist. He was also a former post-Velvet-Revolution minister of education - a source of many stories he told us - and probably the first Czech politician who advocated the dissolution of Czechoslovakia.

America and algorithms

In 1933, Gödel first visited the U.S. and met Albert Einstein who became his friend. Many decades before the official birth of the discipline, he studied algorithmic complexity and NP completeness, as his letters sent to John von Neumann recently emphasized.

He also worked out the consistency of the axiom of choice (it is possible to choose a set that contains exactly one element from each set from an infinite collection of non-empty sets) and the continuum hypothesis of Georg Cantor (there is no set with more elements than the integers and less elements than the continuum) and their unprovability within the conventional systems of set theory axioms.

Axiom of choice vs nice Lebesgue measures

Yes, they are actually unprovable from the other axioms. While most mathematicians prefer to believe that they are true, there also exist pretty good reasons to declare them false. For example, you can't prove that there exist sets without measure in measure theory without the axiom of choice.

I dare to say that I would find it "prettier" to have an axiom that every set of real numbers is measurable than to have the axiom of choice. Choosing representatives from an infinite collection of sets without any rule is unphysical and you can very well say that it is impossible because you won't ever need such an infinite election process in practice. On the other hand, it is physically attractive not to have pathological unmeasurable sets of real numbers.

The very notion that it is up to you whether these axioms are true or not is kind of revolutionary. Who would have thought that these seemingly objective questions about the Platonic world of mathematical structures - such as "Is the axiom of choice true?" - depend on your preferences!

In 1940, Gödel began to use the power of "models" - collections of easy-to-imagine, constructible sets where the validity or invalidity of various axioms may be seen - to further investigate the consistency and independency of various axioms.

Existence of God

In the 1970s, the last decade of his life, he proved the existence of God - He who has all positive properties - using the template of St Anselm and especially Gottfried von Leibniz. The proof is wrong because of the uncertainty principle, among other reasons. Gödel assumes that a union of positive properties is positive, too.

However, it's not the case. If God has a well-defined location, it's good because He is oh so sharp. If He has a sharp momentum, it's also good because He has oh so clear direction. But if He has both, then He is an idiot who misunderstands quantum mechanics which is bad. ;-)

Closed time-like curves

Gödel studied paradoxes outside mathematical logic, too. He learned general relativity and constructed solutions for rotating universes that would allow time travel, something that made Einstein doubt his own theory. Gödel's rotating universes embedded in string theory are T-dual and therefore equivalent to Penrose's pp-waves.

Kurt Gödel has suffered from poisonining paranoia throughout his life. He would only eat if his wife Adele tasted the food for him. Exactly 30 years ago, she was absent for a while and he starved to death. He was 30 kilograms when he died.

Snow brings peace to Baghdad

Kid and smile...

Romantic snow videoclip

For the first time in more than 60 years, snow visited the Iraqi capital on Friday (see current weather there). Two fronts peacefully met in Baghdad and people rejoiced while the U.S. troops celebrated it with impolite words.



Young girls in the park...

If you're an Iraqi citizen searching the Internet whether it is a sign from God, the answer is Yes. Snow is an omen of peace. Snow should become the Iraqi minister of information.

FoxNews videoclip
New York Times (with a video)
Blog Search
YouTube videos

You should finally show the world that you are better than the U.S. liberals and thank George W. Bush and the U.S. troops for the freedom they brought you and the potential they unleashed: Allah has already thanked them.



She won...

Thanks to Yaksman.

Bonus: Northern Saudi Arabia shared the cold experience with Baghdad, with snow cover, speedy winds, and livestock freezing. It looks as their coldest winter in 20 years. Children as well as teenagers were building snowmen and some of the bravest ones even snowwomen.

Afghanistan buried a hundred of people who have frozen. Israel Electric may plan some rolling blackouts during the record demand caused by the deadly freezing winter.

Music and race: Antonín Dvořák the negrophile

Robert Schwartz and independently Jorge Pullin kindly sent me a pretty interesting article by Joseph Horowitz, an artistic advisor to orchestras:

New World Symphony and Discord

It describes the relationships between race and music in Boston and New York at the end of the 19th century.

Czech composer Antonín Dvořák was assigned the task to create the American national music. He was impressed by many things in America but he decided that the "negro melodies" such as "Swing Low" and "Deep River" were the "future for American music". He thought that the black themes would penetrate into classical compositions while jazz became a completely new genre but his prediction was nontrivial anyway.

In Boston, Dvořák's opinions were politically incorrect because the blacks were "not inherently musical" according to many powerful figures over there. For example, a very influential Harvard professor argued that blacks and whites were different species. Dvořák was labeled a "negrophile". Also, critics in Boston newspapers routinely and "scientifically" described Dvořák's and Tchaikovsky's music as "primitive" and "barbarian". In New York, however, the people who thought that the blacks were "inherently musical" were stronger and created a much better environment for Dvořák.



The New World Symphony back in Vienna

One can see that Antonín Dvořák always cared primarily about music and the pure excitement from it but the environment full of snobs and political preconceptions influenced him anyway.

The 21st century

In some sense, I feel that during the decade in the U.S., I encountered less American culture - including jazz - than what we are normally exposed to in Central Europe. For example, a party on Thursday was in the style of Chicago of the 1930s, gangsters blackmailing bankers, shooting, prohibition, jazz, Chicago the musical (e.g. the Czech version of All That Jazz that I've only known since they preloaded it on an MP3 player I bought), roulettes, and shooting contests. I don't remember things like that from America. The closest thing of this kind I remember was a jazz evening with Natalia Saulina and Chris Beasley. ;-)

Weather, climate, and noise

Gavin Schmidt and Stefan Rahmstorf discuss the difference between the weather and the climate and the relevance of noise. There are many correct things in their text but there is a lot of naivité in it, too.

They present the observed temperatures as the sum of an underlying trend - something that they count as the climate and that should probably be dominated by greenhouse gases - and a random noise that is called the weather. The weather controls the short-term behavior but it averages out if you consider a long enough period of time: they mention 15 years as the period where you start to see the "climate".

This could be a good enough approach to get a rough idea about the weather, the climate, and their difference but their naive model is simply not good enough a starting point for a proper understanding of 21st century climate science. There are many reasons - some of which are related to each other - that we will discuss in detail:

1. The actual "long-term" climate is not composed of one effect, as they seem to incorrectly assume, but hundreds of effects that operate at all conceivable time scales from seconds to billions of years.
2. The long-term effects do not contribute a linear function to the temperature and other quantities. Instead, many long-term effects are oscillating or even periodic.
3. There is no sharp boundary between the short term and the long term. A choice of such a boundary is a pure convention and one must always be aware that there exist "faster" as well as "slower" effects that influence reality.
4. For every animal, man, or nation, it is actually the local weather that is more relevant. The local temperature is much more wildly oscillating with time than the global average which really means that the weather is always more important for every animal, man, or nation than the long-term averages. The long-term behavior is only interested for a very specialized group of experts - or for chronic bureaucrats - but not for reasonable policymakers or ordinary people.
5. The averaging both over space and time can increase the "signal to noise ratio" but such an averaging is never perfect. Observed changes over long periods of time that may be comparable to one century can still exhibit trend-like patterns that are nevertheless a result of noise.
6. Even areas that are smaller than the surface of Earth and time periods that are shorter than a century may be large enough for the hypothetical noise to average out. It means that a disagreement of reality with a long-term large-area model prediction for whole continents or 30-year-long intervals may still be able to falsify the model or at least provide us with strong circumstantial evidence that it is incorrect.
7. When they talk about noise, they clearly imagine some kind of non-autocorrelated noise in which the temperature anomaly for one day is uncorrelated to the anomaly from the previous day (or year compared to the previous year). In reality, the "noise" always has some autocorrelation, regardless of the time frame we use for averaging, and it is important to know the color of the noise.
8. They assume that the "trends" and "noise" must simply be added. However, this linearity doesn't hold too accurately in Nature, especially because the character of the noise - the weather - may also be changing with the "trends". This fact makes it harder to properly separate these two.

Let me now discuss these points one by one.

Effects and time scales

Their picture of reality is truly simple: the temperature is the sum of an underlying, nearly linear warming trend caused by CO2 and a noise called the weather. They are not interested in the weather and they think that they don't have to understand it: we will return to this assumption later. But once they average the weather out, they parameterize the result as a trend.

But that's not what the result looks like in Nature. Even if you subtract all short-term phenomena whose duration is shorter than 15 years, you don't end up with anything like a linear function. Both observations as well as a good theoretical perspective shows that there are many other things, too.

Most of these effects are oscillating, not monotonic

The solar activity oscillates in the 11-year cycles that are modulated by 200-year cycles. The circulation of oceans periodically brings warmer and cooler water to different places and it is a mixture of waves and chaotic evolution with durations between years and thousands of years.

Add all the Milankovitch cycles, continental drift, bubbling of the Solar System through the spiral arms of the Milky Way that is known to modulate the weather through the cosmic rays, and epochs in the life of the Sun. All these things matter. The temperature in reality is a mixture of periodic as well as aperiodic, oscillating as well as monotonic, easily calculable as well as unpredictable curves with all kinds of frequencies you can think of.

Even if you decided that the concentration of CO2 is the main thing you want to follow, its profile thousands of years ago was significantly influenced by outgassing from the oceans (that drove it from 180 ppm to 280 ppm and back) and in the future, the concentration of CO2 will depend on future technological breakthroughs or, less optimistically, the desires and successes of power-thirsty megalomanic loons who would like to control the life on Earth. Linear functions are not good enough.

No sharp boundary between weather and climate

The Gentlemen at RealClimate.ORG try to implicitly convince the readers that 15 years is the time scale where averages of the weather become the climate. But it is very clear that this boundary is nothing else than a convention. If you disagree, try to offer a calculation of the figure 15 years. You won't find any.

Moreover, their convention is not the standard one. Atmospheric scientists would usually define the climate from 30 years, not 15 years.

Such a sharp or approximately sharp separation would be useful if there existed a dominant time scale above which certain difficult "fast" phenomena would cease to exist. But no boundary of this kind around 15 years exists in Nature. For example, it is not true that the temperatures during one year are uncorrelated to the temperatures of the previous year.

Let me explain why. The weather is not just something that changes from one week to the next. The weather is also dictated by El Nino and La Nina patterns and weather scientists must be interested in these things. The typical average duration of an El Nino regime is something over 2 years. It is therefore more likely that the ENSO contribution to the temperature during a year will coincide with the previous year than the probability that they go in the opposite direction.

If you disagreed with this conclusion because you imagine a different frequency of ENSO regimes, you won't disagree with the same conclusion in the case of the Pacific Decadal Oscillation (PDO) that also influences the weather but that takes a decade or much more (50 years) to switch to the opposite regime. Will your definition of the weather try to average over the regimes of PDO?

If it will, it won't be terribly useful for predictions of anything during a typical human life span because the weather at the 50-year scale will still be affected by these oscillating things. If you won't try to average over the influences of PDO, your understanding of the weather will have an intrinsic error because you will be forced to neglect it: PDO is a part of the weather that is slower than the weather should be.

The actual weather is more important than the climate

The members of RealClimate.ORG correctly say that the variations of the local temperature are much more violent than the variations of the global mean temperature. Look at a graph of the global mean temperature. It looks pretty wiggly, not as a linear function. But if you think about the people in Prague, they are actually influenced not by the global mean temperature but by their local temperature. Since 1775, it looked like this:



The end of the 18th century was pretty warm, the 19th century was cooler. But the 20th century was again warmer. The graph shows the average annual temperatures but frankly speaking, real people are living real lives and they are affected by daily temperatures. The temperature jumps and drops by 5 °C or so during the day (day vs night) and an additional cycle comparable to 10 or 20 °C is added during the year (seasons). Even the global mean temperature is warmer in July than January by about 4 °C because the land's fluctuations exceed those of the oceans and most land is on the Northern Hemisphere which is why the (rich) Northern Hemisphere dictates the sign to the world. A seemingly subtle geometric asymmetry between the South and the North can generate a huge global difference between the seasons.

If you think about it and look at the graphs, the change of some carefully smoothed out 10-year average by 0.3 °C per 50 years - most of the life of a human being - is completely irrelevant for the life or people in Prague in comparison with the fluctuations described a minute ago.

Moreover, the underlying 0.3 °C warming is only calculable globally. Prague is smaller than Earth and the slope of the trend will be affected by much wider error margin. I was talking about people in Prague but I hope that the readers understand that the same conclusion holds for people in any town or village in the world: it holds for all people.

There are no people who live in the average of a decade and there are no global people - except for those who can travel wherever they want and who can thus easily compensate any change of the weather. At any rate, no people can be even able to honestly "feel" the underlying changes and trends - except for people who like to fool themselves. And even if someone were able to feel the trend, there would still be a long journey from a "feeling" to actual "damages". If you feel a little bit of speaker's methane in a seminar room, you're usually pretty far from being suffocated. ;-)

Averaging is never perfect

Some laymen (and even poor-quality scientists) think that if they create a graph of x vs. y and the correlation is nonzero - if there is some increasing or decreasing underlying trend in it - it means that they have discovered an important signal from God or Nature that must be taught and used by the society. Some scientists, especially those who promote the climate alarm, like to abuse this irrational feeling of the laymen.

In reality, the correlation coefficient never ends up being exactly zero. Even if the data were random and uncorrelated, it would not be exactly zero for a finite number of points. But besides "clean" random noise, or "cosmic variance" if you wish, there can also be a lot of hard-to-predict low-frequency contributions in the datasets such as the Pacific Decadal Oscillation discussed previously.

You are almost guaranteed to see some trends, either increasing or decreasing, in any temperature graph you look at. It is unlikely for someone to obtain exactly zero for the slope of linear regression. Having any nonzero slope can never be a rational reason for alarm. And obtaining the warming sign of a trend more frequently than the cooling sign - or the other way around - is not a reason either. It is the normal state of affairs.

Continents and medium term matter, too

The champions of climate hysteria often like to dismiss any disagreement of their model with somewhat detailed observations as nothing else than noise. For example, Antarctica has been gaining mass recently. Some alarmists will tell you that it was just a fluctuation. Others will tell you that this change is actually confirmed by their best models.

These answers completely contradict each other but the advocates of these two viewpoints never argue with each other even though they like to consider their answers to be important and the question to be settled. Why don't they argue with each other? Because they don't really care about answering scientific questions. They care about silencing climate realists and about the promotion of their favorite policies of regulation. From this "key" point of view, both contradictory answers are equivalent.

In reality, Antarctica is a large enough region and 30 years is long enough period of time for models that are sometimes used to determine our policy for the year 2068 to predict nontrivial things about the weather trends in Antarctica since the late 1970s. If the models can't do it, it's too bad because the verification of any model or theory must always be based on an extensive enough set of numbers - i.e. on high-frequency and/or local observations.

If you have a model that fails to predict a hemisphere (or 30-year trends), it is very hard to convince a rational person that once you jump from the hemisphere to the whole Earth (or from 30 years to 60 years), all the errors of the model inevitably evaporate. The relative error margins may drop by the square root of two in both cases but this change can't really change the "everything is noise and nothing needs to agree" situation to the "everything is perfectly accurate and trustworthy" situation.

The smaller regions we consider, the more legitimate it is to say that what we see is just noise. For example, the record low sea ice area in the Arctic in 2007 was arguably an example of weather. On the other hand, we don't have to talk about the Arctic or Antarctica. Instead, look at the hemispheres. In the last 30 years when the temperature was measured with satellites, the trend on the Southern Hemisphere was about 3 times slower than the trend on the Northern Hemisphere.

That means that even if you take regions that are almost as large as the Earth - namely one half of it - and time intervals that are as long as 30 years, the "noise" is at least as large as the "signal", assuming that there should be any "signal" (global warming) at all. And this huge noise survives despite the long time interval and despite the average over the whole hemisphere. The noise in Prague or any other place is actually much much larger than the noise associated with a hemisphere. The warming trend is clearly negligible.

Switching from the hemispheres to the whole Earth or from 30 years to 60 years only changes the matters a little bit, by the factor of the square root of two. Moreover, it is really the hemispheres and individual years that matter for living creatures and nations.

Color of the noise

Schmidt and Rahmstorf as well as many others often think about the weather as about noise with no autocorrelation. The temperature anomaly on Sunday has the same chance to be positive and negative regardless of the temperature anomaly on Saturday. The temperature anomaly in 2008 is uncorrelated to the temperature anomaly in 2007. But as we have explained, it is certainly not true.

The temperature difference between two moments separated by a short time interval is likely to be small because the temperature is a continuous function of time, after all, and its characteristic size scales up as a power of the time interval. The critical exponents are very interesting to study and good climate models should also be able to reproduce the critical exponents observed in reality: the existing climate models usually don't do it correctly.

You should imagine the temperature graphs to be somewhat similar to the Brownian motion: the shorter intervals you look at, the greater warming trends per decade you extract from them. The same thing holds for "random trajectories" in Feynman's approach to quantum mechanics: the random trajectories are equivalent to Brownian motion, after all.

The longer intervals you study, the more accurate cancellations take place and the smaller trend you are left with. In reality, the actual power law has a different exponent than the exponent found in the Brownian motion. But just like in the Brownian motion, the climate is able to accumulate a significant deviation from the "classical expectation value" over time even though it is not really infinite as the Brownian example would lead us to believe.

Imperfect decoupling of noise and signal

Finally, the RealClimate.ORG ideologues like to present the underlying climate trend and the noisy weather as two uncorrelated terms: the observations are simply the sum of these two.

This linear expectation is the first one we consider but there exist good reasons to think that this approximation is simply not good enough. For example, the observed warming at nights and winters seems to be faster than the observed warming during days and summers: the differences between day and night and the differences between summers and winters shrink. And if you care, flowering orchids don't really care about the night temperatures, so they are not too affected by global warming. ;-) It is clearly an example of a non-linearity. Incidentally, this observation is also a reason not to take the greenhouse explanation too seriously because the greenhouse explanation effect should work uniformly 24 hours a day and 365.25 days a year.

While the linearity is a good starting point, one must be very careful about similar assumptions. As a minimum, a scientist should realize that he is making an assumption and that every assumption of this kind can be wrong. He should try to check and clarify many other details. He should never be satisfied with superficial and naive models of reality such as those presented by Gavin Schmidt and Stefan Rahmstorf.

And that's the memo.

STRINGVACUA for Mathematica

James Gray, Yang-Hui He, Anton Ilderton, and André Lukas have created a package for Mathematica that analyzes potentials in N=1 supergravity (usually convoluted ratios of polynomials in fields), their critical points, and constraints necessary for a low-energy model to generate semi-realistic vacua.

Tutorial: preprint (PDF)
Installation instructions
Download

The system can filter vacua according to their number of flat directions (for example, you can suppress all non-stabilized vacua) or according to inequalities imposed on field values and it determines the number of negative directions etc. Non-perturbative i.e. non-polynomial (usually exponential) terms may be added and represented by dummy variables.

Buy Mathematica 7.

Donald Knuth: 70th birthday

Gustáv Husák, the last communist of Czechoslovakia, would celebrate his 95th birthday today. Before the Velvet Revolution, this anniversary would be written in calenders. ;-)

However, today we are free to celebrate the 70th birthday of someone else, namely Donald Knuth, a professor emeritus of computer science at Stanford and the author of TeX, METAFONT, and the shape of every character in the Computer Modern typeface family.

Congratulations!

Knuth systematized the techniques for the analysis of complexity of algorithms and he has written - and is still writing - many books and papers about it. But theoretical physicists and mathematicians primarily know him as the father of TeX. Many of us have written dozens or hundreds of papers and books using his typesetting system. I've known several people who viewed TeX as a religious symbol of perfection. People who prayed to TeX.

The approach of Donald Knuth himself, who is a Christian, is not too different. The current version of TeX is something like 3.141592653589793238462643383279 and the newest version of METAFONT, a vector system to draw letters and fonts, approaches "e" in a similar fashion. Moreover, Knuth pays one hexadecimal dollar (USD 2.56) for a typographical error or a mistake found in his books. The Wikipedia page about him has collected many more jokes like that.

The very idea of TeX as a generalization of text with added commands and symbols is a cousin of many other frameworks in the contemporary computer industry, including HTML and XML. The output of TeX looks great. At the same moment, I feel that the features of the system are somewhat technologically limited and the exact science community could try to switch to something more modern, and something more compatible with the internet browsers, search engines, symbolic computational software, and communication gadgets.

Is there someone as brave as Donald Knuth in the world to develop a new up-to-date system to deal with text rich in mathematics?

California: big brother will control your home temperature

It sounds as a joke but it is probably a serious proposal (PDF). The California Energy Commission is going to decide whether the Californian utilities will control heating and air-conditioning in your house and all other buildings with a radio-controlled thermostat:

NC Times

The mechanism would apply in "emergencies". For example, during a heat wave, it would guarantee that the citizens of California can't really use air-conditioning. ;-) Air-conditioning will only be possible if the temperature around is already the optimal one.

In Ontario, as Tim Patterson reports, a similar policy already works on a voluntary basis. You save CAD 25.00 on your electrical bill if you allow the big brother thermostat in your house.

Well, there can be cases when such extreme measures may avoid blackouts. But I think that one could still find more market-friendly solutions of such situations. For example, electricity-powered transportation could switch to fossil fuels, much like other places where this switch is possible. Also, the price of electricity could be variable and jump whenever it is necessary. But forcing all citizens to buy and have a gadget in your home that is controlled by someone else seems a little bit too much.

An even better solution might be to build some new power plants, for example nuclear ones.

And that's the memo.

Thanks to Marc Morano.

Three quadrillion lawsuit

The Katrina victims have sued the U.S. and its engineers who designed the levees for more than USD 3 quadrillions - USD 3,014,170,389,176,410 if you care.

MSNBC

The U.S. would have to pay the U.S. GDP for 250 years. The amount is approximately equal to the total product of mankind in the world between homo erectus and 2008. If the amount is paid in pennies, the coins would reach 150 times to Saturn and back.

There are a few hopes for the engineers. One of them is that someone figures out that the quadrillionish plaintiffs are insane and must be medically treated. Another chance is a new hurricane that will kill all of them. At any rate, I think it is very clear that the levees were not delivered with these full guarantees and relatively ordinary people such as fallible engineers simply can't be responsible for events that are so much more powerful than a few human beings. Even if you slash the amount by three or four orders of magnitude, you would still have an absurdly high amount.

Many people - but not all of them in the Gulf of Mexico - have surely suffered but it is unacceptable to transform their suffering - one that was caused mainly by Mother Nature - into a huge financial tragedy for additional groups of people or profits for other folks who don't deserve them.

The levees at least have some rational core. However, CNN Money informs about possible lawsuits against a toymaker and cruise operator for "not telling enough about their contribution to global warming". Unless it is going to be swiftly and universally accepted by lawyers as a fashionable postmodern insanity, this tendency poses a real threat to the judicial system and the global economy.

If you want to know one more example of the recent madness, read what project "Dr" Richard Somerville, a member of the losing debate team of the alarmists, is considering:

"I think a dramatic shocking surprising climate event that is unambiguously due to global warming may be the only thing that motivates people and governments."

Well, before Mr Somerville is executed for threatening the civilization, he should pay millions of dollars to Michael Crichton for shamelessly stealing the idea of a vast ecoterrorist attack described in "State of Fear".

Hat tip: Anthony Watts

Why is the greenhouse effect logarithmic?

Steve McIntyre at climateaudit.org is trying to locate the provenance ;-) of the logarithmic formula for the greenhouse effect. Instead of joining him, let me post my explanation why I personally think that the idealized greenhouse warming is a logarithmic function of the concentration under semi-realistic idealized assumptions. This posting is a technical supplement for

Dynamics of greenhouse effect
Sublinear CO2 climate sensitivity

Let us first notice that as Wikipedia explains, Svante Arrhenius published a paper in April 1896 that attempted to quantify the warming caused by "carbonic acid" (the term was used even for CO2 itself at that time). And he abused the effect to incorrectly explain the alternation of ice ages and interglacials (the reasons currently believed to be relevant are the Milankovitch cycles i.e. fluctuations of the geometry of Earth's orbit and axis and perhaps some waves inside the Sun).

Because this blog likes to offer you the original sources, here it is:

Svante Arrhenius: On the influence of carbonic acid in the air upon the temperature of the ground (PDF, 1896)

I admit that I am impressed by this paper. It is as technical and as detailed as the fourth IPCC report except that it was written by 1 man instead of 2500 people and it was written 111 years earlier. Much like the IPCC, Arrhenius obtained something comparable to 5 °C for the climate sensitivity and just like the IPCC, his numerical result was wrong. The only difference from the IPCC is that climatologists already agree that Arrhenius' results were wrong.

A footnote on page 238 contains logarithms but it doesn't talk about the CO2 concentration. Instead, you must go to the top of page 267 which says:

... Thus if the quantity of carbonic acid increases in geometric progression, the augmentation of the temperature will increase nearly in arithmetic progression. ...

This rule - one that Arrhenius only deduced "experimentally" on page 266, without a derivation - says that the warming in Celsius degrees is proportional to the logarithm of the ratio of the initial and final concentrations:

Delta T = alpha log(C/C0)

That's why it is slowing down as the concentration increases, much like the effect of 10th painting of your bedroom. And that's also one of the reasons why our worries should be diminishing even if the CO2 production stays constant. The logarithmic formula guarantees that even though we will probably produce substantially (twice or thrice) more CO2 in the 21st century than we did in the 20th century, it will contribute - via the greenhouse effect - roughly the same amount to the warming.

Clearly, the law is not completely universal. It breaks down for very small C because the logarithm would otherwise go to -infinity. For small C, the correct relationship becomes asymptotically linear: each molecule of CO2 causes pretty much the same warming if you only have a couple of them. Phenomenologically, the linear increase for small C and the logarithmic law for the large values of C is often interpolated by a function that is also quadratic in the middle but it is just one of possible conventions for curve-fitting. Another popular function is

Temperature = Temperature₀ + ln(1 + 1.2 x + 0.005 x² + 0.0000014 x³)

where "x" is the CO2 concentration in ppmv. This formula works pretty well up to 1,000 ppmv.

However, the asymptotic logarithmic behavior for large C is more than a convention. It can be derived as a result of an idealized calculation that is relatively realistic - a kind of calculation that theoretical physicists, especially condensed-matter physicists, should like. One reason for the logarithm could be found if we were looking how new spectral lines and their "wings" become relevant for the absorption. The old lines eventually get saturated but the total greenhouse warming never quite stops because new spectral lines emerge: it just slows down. However, below we focus on a different effect related to the lapse rate that, I believe, is dominant for the dependence of the greenhouse effect on the concentration.

The setup

If the sensitivity with respect to the CO2 doubling is 1 °C, the warming obtained from each multiplication of the CO2 concentrations by a factor of "e=2.718..." should be around 1 °C / ln(2) = 1.44 °C. That's the quantity that we would like to derive here.

Consider the Earth with CO2 only. The density of CO2 decreases exponentially with the height, being proportional to the Maxwell-Boltzmann factor exp(-height/height_0) where height_0 is something over 5 kilometers, I don’t know exactly, for CO2. The precise number doesn't matter for the qualitative result.

This exponential decrease is a standard result of college thermodynamics, coming from the maximization of entropy of a gas given a conserved energy. Fellow readers can remind you about the derivation of the result from statistical physics if you need it.

Lifting the tropopause

Now, if you increase the total concentration of CO2 e-times, the level where the concentration is equal to a reference value, say C_r, increases exactly by height_0 in the direction up. I conveniently choose C_r to be a representative for the concentration above which the whole atmosphere may be considered transparent for the infrared radiation we consider, with some accuracy. The height where this concentration is C_r may be referred to as the tropopause, the boundary between the troposphere and the stratosphere above it. It is somewhat fuzzy but I can choose a convention about the percentage how transparent it should be, and then the tropopause will be a well-defined sharp shell. For example, define the tropopause as the plane such that the whole atmosphere above it only absorbs 10% of the black body radiation corresponding to the temperature of Earth.

The fun is that the behavior around the tropopause is pretty much universal, regardless of its height. The other assumption I need to use is a pretty much constant lapse rate - the decrease of the temperature with the height above the Earth. This is another law I need to assume, with all disclaimers about its inaccuracy etc. The lapse rate law holds because it is a form of the adiabatic law.

So if the multiplication of the total CO2 volume by "e" lifted the tropopause by height_0, the temperature at the tropopause dropped additively by the "lapse_rate times height_0". Because the lapse rate is about -5 °C per kilometer, you will get approximately 25 °C decrease of the tropopause temperature from multiplying CO2 by "e".

A linear decrease of the temperature means that the radiation that is emitted by the tropopause decreases by a linear term, too.

Now, I must impose the overall equilibrium of incoming and outgoing energy in order to balance the Earth's energy budget. So if the tropopause radiation dropped by a certain amount E and the incoming solar radiation is unchanged, the radiation directly from the Earth surface must increase by E to compensate the drop from the tropopause, which means that the surface temperature must increase by a linear piece.

Putting the arguments together

So if you combine all these things, you see that a geometric increase of the total CO2 volume - and I could have divided the e-folding into several smaller fixed percentage increases - means a linear increase of the surface temperature. This conclusion is valid assuming that various linear relationships mentioned above hold.

So the lapse rate should be pretty well-defined i.e. constant between the old and new tropopause; the change of the percentage of the energy emitted by the surface vs tropopause should be much smaller than 100%; the predicted change of the temperature should be much smaller than the absolute temperature of the surface, and several other limiting assumptions that you might realize should be satisfied, too. Then the linearizations mentioned above are legitimate.

Don't forget that the logarithm of a power is still proportional to the logarithm so the logarithmic shape for high enough concentrations is probably more robust than you might a priori think.

With the assumptions listed above, and they are kind of - although not perfectly - satisfied for the doubling from 280 to 560 ppm of CO2 as one can check (the temperature change comparable to 1 °C is much smaller than the 300K absolute temperature, the percentages change from 92:8 to 95:5 or something like that is relatively small), the Arrhenius' law is a law. It is all about the Maxwell-Boltzmann distribution, the lapse rate, and the black body law. A geometric/exponential increase of the concentration moves the physical phenomena linearly in altitude and makes standardized linear contributions to various terms.

A rough numerical calculation

Let us try to end up with the 1 °C sensitivity. First of all, as we have already suggested, fundamental physicists respect "e" and not "2" as the right base of exponentials and logarithms so the goal will be to show that multiplying CO2 volume by "e" will warm up Earth by a certain amount comparable to 1 °C / ln(2) = 1.44 °C. Let’s see how close to 1.44 °C for this e-normalized climate sensitivity we can get.

With the e-multiplication of CO2 (between 1800 and 2150 or so, assuming fossil fuels to go on), the tropopause shifts by height_0 = 5 km, the temperature at the tropopause drops by 25 °C. If the tropopause and the surface were emitting 50% of the radiation each, then the surface would have to warm up by 25 °C: with this change, the decrease of the thermal radiation by the cooler troposphere would be compensated by the increase of the thermal radiation from a warmer surface. However, 25 °C would indeed be a pretty high, catastrophic e-sensitivity. Fortunately, the surface emits a vast majority of the radiation, so a small increase of the surface temperature is enough to compensate the small cooling at the tropopause.

Assuming the average percentage composition of the radiation from surface vs tropopause to be 94:6, you see that the Earth is 17 times more important than the tropopause for the energy budget. So you need to change the Earth surface temperature by 25 °C / 17 in the opposite direction to compensate them which is 1.47 °C. A pretty good agreement. OK, I cheated a bit by saying that the effective distribution was 94:6 but what is important is the framework of the calculation and the qualitative logarithmic form of the result. You may try to put better numbers into it if you want to improve it.

You should also think how you could properly incorporate heat convection and some basic influence of different forms of water in the atmosphere.

Climate models: gullibility vs cynicism

Finally, I would like to write a few sentences about "what is known". Although the derivation above is a caricature primarily designed to understand some qualitative features of the greenhouse effect and make some order-of-magnitude estimates, I am convinced that the contemporary climate models should be able to get the right results for the flow of radiation and its absorption and emission by CO2 at different altitudes (unless all of their creators are doing something really silly). For example, the phenomenological formulae written above were constructed to agree with the climate models.

In my opinion, doubts about the climate models only start to be legitimate once we include clouds, precipitation, turbulence of both the atmosphere and the ocean, and other "non-uniform" and "time-dependent" features of the climate.

Davide Gaiotto: Killing the two-headed monster

Edward Witten has proposed his AdS/CFT dual of pure gravity in three-dimensional anti de Sitter space.

In the bulk, pure gravity looks as simple as you can get. However, the boundary CFT was conjectured to incorporate what is arguably the most complex symmetry group in mathematics, namely the monster group.

In the usual AdS/CFT fashion, the central charge of this CFT increases with the curvature radius of the AdS3 space. The central charge can be written as c=24k. A known theory exists for k=1 but for higher values of k, it was not known whether a CFT existed and whether it was unique. More precisely, we are looking for an extremal CFT which is a CFT whose lowest dimension of a non-identity primary field is k+1, the highest value of the lower bound that general rules of CFTs can allow. All these non-identity primary fields are then good enough to be identified with BTZ black holes.

Matthias Gaberdiel proposed a conjecture based on an analysis of some data about the CFTs. One of the key implications of his conjecture was that the CFTs with k=42 and higher do not exist. It would look like the size of the AdS3 space could not exceed 42 units if you required pure gravity in the bulk.

The new paper

Davide Gaiotto

argues that the Gaberdiel conjecture banning high values of k is wrong because a simple power of the monster module is a counterexample. (A refined version of the Gaberdiel conjecture involving "irreducible" CFTs has not yet been falsified, I think.) But he offers a much more fascinating claim about the extremal CFTs with monster symmetry:

The k=2 i.e. c=48 theory already doesn't exist.

While the monster group CFT exists for k=1, already the doubled "size" of the AdS3 leads to contradictions with axioms of CFTs and the structure of the conjectured monster symmetry.

Gaiotto's strategy

Which contradictions? Davide doesn't use any other methods than the axioms of CFTs themselves: his approach is based on conformal bootstrap. The monster group has nearly 10⁵⁴ elements so Davide is essentially going to build the twist fields for each element in this rather large set. It's not an impossible task because the answer only depends on the conjugacy class and there are 194 conjugacy classes of the monster.

He starts with the 2A conjugacy class and determines the lowest dimension of the twist field in the appropriate sector. The twisted partition sums are certain hauptmodules and the coefficients in them are incompatible with the positivity and integrality properties of the CFT combined with the information from the OPE of the two 2A twist fields.

Message

Unless there is a mistake in Gaiotto's analysis, the main lesson is clear. You must allow the proper laws of mathematics to determine what theories can exist and what theories can't. And the proper laws of mathematics are the full microscopic laws, in this case the stringy laws describing the boundary CFT.

The existence of the k=2 theory may be motivated by heuristic albeit controversial, loop-quantum-gravity-like "gravity as a gauge theory" arguments, the picture looks complicated enough to avoid obvious contradictions, the CFT has Edward Witten's signature below it - but one (or at least Davide) may still prove the theory doesn't exist if he looks carefully enough.

What is the actual structure of the AdS/CFT for pure AdS3 gravity? Well, it might be that the theory exists for all k but most of them don't have the monster symmetry; they can still be extremal. However, it looks somewhat strange that a bigger AdS space should break the symmetries of the smallest one. Alternatively, the pure gravity in AdS3 with k=2 or higher k (and its dual CFT) might simply be non-existent.

Barack Obama loses SmogMaker 2007 award

Barack Obama has won the Iowa caucus. But during the following day, he also won something equally important. A well-known radical environmentalist blog, DeSmogBlog, named him the SmogMaker of 2007.

How did Obama deserve it? Well, Jim Hoggan has explained that the Democratic voters have the right to expect a leading liberal candidate to be as extremist environmentalist loon as the editors of DeSmogBlog themselves. So Barack Obama was a huge disappointment for them. The targets that Obama proposes were not dramatic enough. Furthermore, Obama tries to help the coal industry which is not so shocking because it is a pretty important industry in Southern Illinois.

DeSmogBlog has figured out that Obama was looking like George Bush Lite (not to be confused with Busch Light). It would be much better if Obama were looking like Václav Klaus Hard, but for a Democrat, being George Bush Lite is good enough. ;-)

However, DeSmogBlog's soulmates at Climate Progress, together with George Moonbat and a few other thinkers of the sort, have criticized the award, claiming that DeSmogBlog was owing three apologies to Barack Obama. Climate Progress argued that no one else than George W. Bush has the right to grab the award as long as he lives in the White House. The criticism has had a big impact on DeSmogBlog. They first wrote:

... If Barack Obama offers any convincing counterpoint on his coal position, we'd be happy to "strip him" of this award. In the meantime, our position stands: he's spinning the American people on this issue.

However, a few days later, DeSmogBlog apologized the SmogMaker 2007 and stripped him of his title. The life of the moonbats is often entertaining.

Well, I think that Obama deserves the prestigious award and the mad guys at DeSmogBlog have no right whatsoever to steal the award from him. Barack Obama should sue them.

And that's the memo.

Black hole: flash

... full screen ...

Wikia search: a bizarre Google killer

Jimbo Wales has just released his

Wikia Search

that is supposed to be a Google killer, combining the advantages of Google-like search engines with the virtues of Wikipedia.

So far I would bet the ranch against the success of this product. For example, you want to know something about Edward Witten. So I suppose that you must first click at "Science & Nature". In the right upper corner, you may type "Edward Witten".

The first hit is the Uncyclopedia page of your humble correspondent, a semi-witty page full of typos. The second page is another Uncyclopedia web page about the Protocols of the Elders of Zion where Witten appears together with Adolf Hitler, Jesus H. Christ, Uri Geller, and Henry Kissinger.

OK, maybe I used a totally wrong website. So I eventually found a page with a more Googlish design,

alpha.search.wikia.com.

If you try to search for "Edward Witten" here, the first hit is an unexpected 14-line Spanish biography of Witten, the second page in the list is a home page of your humble correspondent's Czech translation of "The Elegant Universe" by Brian Greene, and the following three hits are dedicated to random programs at the IAS, KITP, and Oxford.

At this moment, the search engine is clearly unusable but the question is whether it can be refined to become a serious competitor of the conventional search engines. I don't quite understand how the human members of the social network behind Wikia are supposed to influence the hits. But frankly speaking, even the very fact that the algorithm is not clear indicates that it won't become a method that will use millions of people's work to improve the results.

Without this work, it is hard to imagine how a superior outcome could ever be achieved. But once again, the success of Wikipedia was unexpected for many people, too. We may also be surprised in this case. Nevertheless, at this moment, I feel that Jimmy Wales has completely misunderstood the real power and essence of the objective ranking algorithms behind Google and why these algorithms are better than recommendations of a few random biased individuals who are simply not enough to keep the most relevant pages at the top of the respective lists.

If the volunteers are expected to modify the rank of individual pages, I am afraid that the hits would eventually be contaminated by organized cliques of morons. For example, about half a million of imbeciles visit dailykos.com every day. An article on that Nazi hate site would be enough to convince Wikia members who also read dailykos.com to promote a bad page about a right-wing guy or a flattering page about a left-wing jerk. These undesirable tendencies are partially suppressed at Wikipedia because the editors are kind of responsible for their edits. It is just hard to see how can one enforce any verification of responsibility of editors for their ranking of tens of millions of pages.

Don't get me wrong: human editors could improve the hits, if they were smarter than the impersonal mechanisms behind Google. But the average internet users are clearly much more stupid than the Google's impersonal mechanisms and it is the average users who would eventually control the hits. The comparison is analogous to the comparison between direct and representative democracy. The representative democracy also contains the virtues of competition that makes it possible for the elected officials to be much better than an average citizen. Direct democracy - and the Wikia Search - kind of directly puts the average person's opinions at the top which might be too little to make a new search engine useful.

2007 warmest year on record? Coldest in this century

An error in RSS data has been identified by John Christy and Roy Spencer, competitors from UAH... It may influence the text below.

2007 remains the coldest year of the century according to HadCRUT3 weather stations.

One month ago, we noticed that November 2007 was the coldest month since January 2000. Well, the RSS MSU satellite data prepared by remss.com show that December was even cooler. The December anomaly was -0.046 °C, compared to -0.014 °C in November. That means that December 2007 was also cooler than the average December from 1979. Moreover, we can finally complete the ranking of the years!

Let me start with forecasts in the mainstream media.

In January 2007, we were informed that 2007 was either likely or certain to surpass 1998 and become the world's warmest year on record by most media, including:

Reuters
AP & Foxnews
IHT
BBC
MSNBC
CBS
USA Today
The New York Times
The New York Sun
The Washington Post
National Geographic
CBC
The Guardian
The Independent
China People Daily
ABC Australia
Discovery Channel
Science Daily
Met Office

as well as virtually all other media you know. They justified this statement by referring to scientists who have combined greenhouse gases with the observed El Nino. Many sources, such as the New York Sun, even gave you the probability that 2007 would be the hottest year as 60 percent. They immediately added that this should "add momentum for the next phase of the Kyoto protocol", a comment that clarifies what is the actual goal of many of the people who study these questions professionally.

In the middle of the year when it started to be clear that the prediction was bogus, Phil Jones (Reuters) changed his mind only infinitesimally. It would be the second hottest year, he said. These big-shot agenda-driven scientists never have the courage to say that they were simply wrong.

Reality: thermometers

However, the greenhouse gases are not too important and El Nino was replaced by La Nina. As a consequence, RSS MSU data for the lower troposphere (graph, more graphs) show that 2007 was the coldest year in this century so far. In alarmist jargon, it was the ninth hottest year on record: the most recent year was cooler than all other years in this century as well as 1998 (by a whopping 0.41 °C) and even 1995 (do you remember Summer Nights 95?). According to different datasets (HadCRUT3, UAH MSU, NOAA), the year is going to be approximately the 8th (HadCRUT3, final) or 7th (NOAA) or 6th warmest year. UAH reports 2007 as the 4th warmest year (on 1/7/2008: final, just by 1 millikelvin warmer than 2006) but it is probably because of the diurnal drift that has recently become obvious (see also World Climate Report). When it is corrected, it is likely that UAH will be rather close to RSS.

GISS became a kind of exception (1/8/2008: final) because the 2007 temperatures exactly matched those of 1998, their 2nd or 3rd warmest year (as James Hansen said a few weeks ago, with 2005 being their hot king) - but it is still very far from the hype about the hottest year. Your humble correspondent is not the only one who believes that the satellite measurements such as RSS, UAH are more accurate than GISS, HadCRUT3. It just happens that HadCRUT3 is closer to RSS than UAH to RSS, as far as the recent rankings go.

Commercial: Where did global warming go? (Boston Globe)

The RSS MSU linear trend extracted from the 1998-2007 interval is -0.48 °C per century of cooling! Numerically, it's almost the same trend that we assign to the 20th century but with the opposite sign. The RSS MSU data imply that 2007 was 0.12 °C cooler than the already cool year 2006. Other teams will generate qualitatively compatible results but substantially different numbers, raising doubts about the reliability of the temperature measurement even in the modern era.



Figure 1: Global cooling. Nine hottest years on record as shown by the RSS MSU calculations, from the hottest year 1998 to the coolest year 2007.

The choice of 1998 as the beginning of this graph is, of course, a P.R. trick to make the trend look as cooling as possible. If someone chooses e.g. a year in 1970s - the coldest year in the last 70 years - as his beginning, it is a P.R. trick, too, even though the goal has the opposite one. Certain qualitative conclusions simply depend on these choices and one must be careful about this fact. Similar issues are also discussed in the fast comments. Moreover, I only included the last 10 years for efficiency because typing three times as many numbers to the Excel file would be rather tiresome. Incidentally, if I wanted to demonstrate recent global cooling, I could have been even tougher and show you 36 months since January 2005, including the linear regression:



Figure 2: Global cooling 2005-2007. The trend is over 15 °C of cooling per century. ;-) Also, the trend is accelerating: for the 12 months of 2007, a similar linear regression gives about 35 °C of cooling per century. :-)

Let me emphasize that if someone thinks that the "ninth hottest year" is still hot, it is of course an irrational reaction. The global mean temperature is a continuous function of time and is auto-correlated. It follows that a short time after what has been identified as the hottest instrumentally measured years, we can't abruptly return to years as cool as 1850 or 1660. The laws of mathematics just make such a possibility extremely unlikely.

Let me offer you a metaphor. Imagine that all newspapers in the world would cite "experts" and predict that Nico Rosberg would almost certainly win in the Formula One 2007 season. However, the first three drivers would be Räikkönen, Hamilton, and Alonso while Rosberg would be ninth. Would the readers appreciate the "expert" who would just decide that Rosberg was the best guy? It would be an entirely foolish prediction. Why is the climate so different?

Ramifications

Do you expect the media listed above to apologize for the misinformation they have printed? Do you think they will tell their readers and audiences that they have made a mistake and reported scientifically unreliable and unlikely propaganda created by political activists and hacks such as Phil Jones? Do you think that they will promise us that they will be more careful in the future and avoid this kind of hype? If you do, you haven't understood what religious bigotry and special interests really mean. Most of these people are either lunatics who pay no attention whatsoever to reality, the actual data, or serious science, or corrupt people who greatly benefit from this big-scale misinformation and propaganda.



Figure 3: RSS MSU temperature anomaly for the lower troposphere (the layer near surface, description) in deg C, 1998-2007.

Here is the Google Docs spreadsheet with the complete 1998-2007 monthly data of RSS MSU and nearly complete data from four other teams (HadCRUT3, UAH MSU, GISS, NCDC NOAA) that will release their December data in a few days or weeks. You may also download the Excel file. The World Meteorological Organization publishes their data as an average of HadCRUT3 and NOAA: you can do the math to predict their results, too: for WMO, the year will be either 7th or 8th warmest year.

Phil Jones et al. now forecast 2008 to be even cooler than 2007 (sanely, due to La Nina that will strongly affect at least the 4 following months) but they present this prediction as perfectly compatible with "underlying global warming" that is not "waning" in any way, despite the observed cooling. It seems obvious that the mysterious "underlying" numbers are more important for them than the numbers that are being actually measured.

Now they bravely forecast that 2008 will be in the "top ten" of the warmest years. This developing story about global warming reminds me of the joke how the socialist Czechoslovakia tried to catch up with the capitalist world. In the late 1940s, it was "úspěch" (success). In the 1950s, it was "spěch" (hurry up). In the 1960s, it was "pech" (bad luck). In the 1970s, it was "ech" (whoops). In the 1980s, it was just "ch" (ps). Fortunately, 1989 was the end of the story.

SSRC Florida: Lasting cold era ahead

The Space and Science Research Center, an independent scientific research facility located in the nice building above in Orlando, Florida, has just announced

... press release ...

that it has confirmed research of NASA solar physicists. There are significant changes occurring on the solar surface. A decrease of the solar activity between 2010-2020 will lead to "solar hibernation" with the coolest temperatures reached around 2031, they say.

John Casey, the director, has "verified the cycles to well over 90 percent" and the new cold era is supposed to be a reflection of a 200-year cycle. Last time, during the 1793-1830 Dalton cycle, the reduced solar behavior cooled the planet. Now, I don't think that you should take the press release too seriously but it is fun anyway.

Notice that the first sun spot of the solar cycle 24, sun spot 980, may be starting to emerge.

Hat tip: Marc Morano

Lev Aizenberg: I disproved Riemann's hypothesis

Update: The paper was withdrawn by the author.

Lev Aizenberg had a highly provoking 6-page-long paper yesterday:

Lindelöf's hypothesis is true and Riemann's one is not, PDF

The proof of the negation of Riemann's hypothesis is presented as a corollary of a possible proof of Lindelöf's hypothesis that essentially says that the Riemann zeta function on the critical axis grows slower than any power law with the distance from the real axis.

Aizenberg strengthens Lindelöf's hypothesis and claims that zeta(sigma+it) goes like O(log(t)^1/4), with a coefficient allowed to be sigma-dependent, for every 1/2 < sigma < 1, a statement that contradicts older papers that assumed Riemann's Hypothesis to hold.

It's not even clear to me whether Aizenberg would receive a megadollar for such an unexpected proof if it wer