## Thursday, February 13, 2014 ... //

### Universe is maths, but only some maths is relevant or true

Max Tegmark of MIT has released his book, Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, a month ago and it just appeared in the Kindle edition, too.

I won't write a full-fledged review, especially because the book looks way too similar to Brian Greene's The Hidden Reality. Greene's latest major book talks about "parallel universes of all types" we find in physics and the most speculative ones, simulated universes and the universe of the mathematical totality as promoted by Tegmark, were described in the last chapters of Greene's book.

Off-topic: Dominique Gisin (Switzerland), a particle physics fan, visited CERN to see how the protons are accelerated to 99.9999% of the speed of light. This CMS enthusiast who thinks that ATLAS sucks in comparison has used the know-how to accelerate herself while downhill skiing in Sochi. Congratulations to the gold medal! She shared the medal with Tina Maze, Slovenian skier and piano player who must have been trained by ATLAS. Click the photo for more info.

Tegmark introduces the reader to some basic physics – including quantum mechanics and cosmology – and then begins to discuss inflation. He is led to define "Level N parallel universes" with different values of the integer label N.

Ultimately, he claims that the world isn't just described by mathematics. It is mathematics. And he tries to deduce some far-reaching consequences of this claim.

Tegmark is clearly a mathematical Platonist, and so am I. Mathematics exists independently of the humans. Humans are actually discovering (pre-existing) mathematics rather than inventing it. Mathematicians – and physicists – are therefore more analogous to Christopher Columbus than to Thomas Alva Edison. The newly found mathematics may appear in front of the human eyes for the first time but at least if it is important enough, Nature or the "mathematical wisdom of the world" knew about it before the discovery.

I actually think that most mathematicians consider themselves Platonists like Tegmark does (and I do). There are surely exceptions, e.g. Brian Rotman who reviewed Tegmark's book for The Guardian. I just think it is silly to make a big deal out of it because the Platonism doesn't really mean anything tangible. It is a philosophical way to think about the "place where ideas live". Moreover, neither Tegmark nor your humble correspondent "invented" this philosophy. Perhaps Plato did. ;-)

In 1998, a senior top physicist at Princeton (whose name I will keep confidential) informed his younger colleague, an otherwise mainstream-oriented cosmologist Max Tegmark, about the following insight (via e-mail):

Your crackpot papers are not helping you.
He or she clearly meant all these "Level N bullshit universes" that Tegmark had already been emitting for quite some time. The times have changed and it's plausible that the senior physicist is no longer courageous to publicly point out that Tegmark's papers are crackpot papers. Well, TRF isn't under this pressure by the crackpot movement so it is still perfectly OK – even now, in 2014 – for you to point out that Tegmark's papers are crackpot papers. ;-) And if you look at the most recent one, Consciousness as the state of matter called perceptronium, you will both laugh and agree that Tegmark as an individual writer of papers is a kook.

Is Tegmark right? Well, his propositions primarily lack any beef.

Is reality just "described" by mathematics or "is it" mathematics itself? I don't mind if you say the latter; I have said it many times myself. The objects we actually perceive obey some rules that are mathematical, so in this sense, any question about the real objects' behavior is equivalent to a question about their mathematical description. So the real objects are isomorphic to the mathematical concepts or structures, so it doesn't really hurt if you identify them. As long as you care about the derivation of the true statements, you may say that the real objects are the same things as the mathematical structures that represent them.

Fine. But that doesn't mean anything.

Even if you identify the world with the "totality of mathematical objects and structures", you won't be able to answer particular physical questions, like whether mammograms save at least a thousand of American women's lives a year. Or any other question, for that matter. Both answers, Yes and No in this case, may be given a mathematical representation and may be connected with additional mathematical structures and their networks and relationships. However, only one answer – in this case No – is the right one.

Off-topic: my ex-colleague Subir Sachdev talks about AdS/CFT applied to condensed-matter physics, his primary expertise.

So one may imagine a "totality of mathematical laws, objects, structures, axioms, lemmas, and proofs" but it's still true that only a part of this megaverse is relevant for Nature around us. Mathematics is really the "glue" that connects some mathematically represented "objects" with others – by links that are of mathematical character, too. Much of the power of mathematics is really hiding in the "patterns of the links", in the glue and its detailed distribution. But when we say statements about physics or the real world, we need some particular mathematical links – and mathematical objects connected by these links – that may be glued to the objects in the real world. They're very special animals, relatively to the unselective "total world of all mathematical concepts".

So only some candidate physical theories may be relevant for the Universe around us. They must be quantum theories which are relativistic at the same moment and which contain some spectrum of particles and forces whose existence is demonstrable. There may be other conditions, too. This is an extremely different set from the universal "set of all mathematical objects".

Off-topic: a crow solves an 8-step puzzle I still have trouble to comprehend. ;-) Hat tip: Peter F.

In physics – and in all of science – we are looking for the truth by falsifying i.e. eliminating conjectures that disagree with the empirical evidence. So in physics, a conjecture really has to be kind of mathematical to be considered in the first place. But it's not enough for it to survive. It must also survive tests – comparisons of its predictions with some empirical data, with some observed properties of Nature around us.

This process may be shown to prove that creationism, the phlogiston, loop quantum gravity, geocentrism, causal dynamical triangulation, local hidden-variable theories, spin foams, the luminiferous aether, Alain Connes' noncommutative theory of the particle spectrum, de Broglie-Bohm pilot wave theory, Ghirardi-Rimini-Weber collapse models of quantum phenomena, and millions of other potentially mathematical thoughts that people have invented over centuries are simply wrong. It doesn't matter that they belong to some abstract, all-encompassing world of mathematical objects or structures or propositions. The claims about the real world based on them are wrong. In a similar way, whole portions of otherwise totally legitimate mathematics are wrong "even as a starting point" to do physics – Cantor's diagonal tricks, Gödel's theorems, denial of the existence of Feynman's path integral, and so on, and so on.

The reason why Tegmark tries to "radically enhance" the mathematical Lebensraum that is identified with the physical world look utterly incomprehensible. But this enhancement is anti-falsification and therefore anti-science in effect if not in intent (thanks for the linguistic construct, Larry). I think that there can only be one "big reason" why one would want to "resuscitate" all the parts of maths that don't seem relevant or right for physics – that have been eliminated as a description of physics. The "big reason" is the desire to deny that they have been falsified; to deny that it's right for physics and science to discriminate empirically valid or viable mathematical structures from the... challenged ones that are still waiting for their success, if I am allowed to copy a politically correct description of the word "losers" from one commercial promoting expensive enough cars. :-)

And if you want to suppress this discrimination of right and wrong theories, Max, then it's too bad because this is really the defining property of the scientific method. Science doesn't necessarily say that certain mathematical concepts and structures "don't exist anywhere"; it just says that they should be used (at least) less frequently than others whenever we talk about Nature unless we want to be wrong!

Because Tegmark effectively throws away the scientific method – the falsification of the wrong ideas – it is not surprising that most of his comments about the impact of his largely fairy-tale "parallel universes" on observable questions are just wrong, and demonstrably so. I have written too many blog posts that rather surgically isolated the flaws in the reasoning based on the multiverse or anthropic paradigm and I feel it was a waste of time because the human stupidity clearly cannot be eliminated, anyway, so I decided not to write anything like that again.

Your musings may be as good as important and correct physical theories from the viewpoint of the indiscriminate realm of all mathematical structures, Max; but they're not equally good from the viewpoint of science. Your crackpot musings may be helping you to sell books but they are not helping you you to improve your credibility as a scientist among those who actually have a clue about the field, Max.

#### snail feedback (129) :

Physics contains no errors of derivation. It has forever suffered errors of assumption. That is why we perform heretical experiments - and have trash barrels

Given Ptolemy, curve fit astronomy. No – Copernicus. Given cartography, curve fit Euclid. No – Bolyai. Given cyclotrons, curve fit Newton. No – SR. Given Mercury’s orbit, curve fit Newton. No – GR. Given helium’s emission spectrum, curve fit Bohr. No – QM. Given the Dirac equation, curve fit proton magnetic moment. No – quarks. Given spiral galaxies, curve fit the Tully-Fisher relation. No dark matter – Milgrom acceleration. Given Yang and Lee, curve fit vacuum mirror symmetry toward hadrons. No – trace vacuum chiral anisotropy toward matter measurable with geometric Eötvös experiments.

Reality is not administrative triumph of Aristotle over Galileo. Reality is theory free of empirical failure. When theory fails, physics must look orthogonally elsewhere, not curve fit. A black swan in Australia is not a parameterized Northern Hemisphere white swan.

Hear hear! But things are about to change ;-)

LOL, I like the combination of adjectives "stupid, man-made" as if they were nearly synonyma.

Flight is great but I would like to disappoint you by pointing out that the spaceships that flew to Mars couldn't have used wings because wings depend on the air. Instead, they used utterly unnatural, stupid, man-made devices such as rockets.

Sorry for having crippled your belief system so much.

Well, if you define "beauty" as the ultimate ugliness that is ready to be mindlessly adopted in the name of the defense of the old order against new heretical revolutions – in your examples, quantum theory and relativity – and if you define "reasonable things" as the contrived models stubbbornly proposed to fight against all principles that Nature is rather directly showing us, then they were beautiful and reasonable, indeed!

Dear Luboš,
very interesting opinion! Thanks again. For sure I hate bureaucratic tricks :-) and I don't want to question your "moral assessment"... but at least some physics believe in the *physical* Church-Turing thesis
( http://arxiv.org/pdf/1102.1612v1.pdf )
and other ones think that there could be a *Gödel undecidable* problem in real physics like the answer to a simple question: ‘will the orbit of a particle become chaotic ?’ (... from page 13 of http://arxiv.org/pdf/physics/0612253.pdf )

Dear Giulio, thanks for your interesting thoughts.

To be sure, most problems - differential equations or analogous problems - cannot be solved analytically in terms of elementary functions, and not even "not so elementary" functions.

However, if you phrase a completely well-defined physical question like "will the evolution be chaotic", I am sure that none of them may be undecidable. After all, they may really be solved by catching some qualitative properties in an accurate enough numerical simulation.

It was my fear of over diagnosis that stopped me going for mammogram and breast exams too ! Where is Gordon? I chose homeopathy instead :).

When I was nearing menopause I wanted to look into hormone replacement therapy, and for that you need a doctor. I used to go to a good gynecologist, but he was so good that his time was taken over by women trying to conceive and I believed his time would be better spent there. I tried a friend's gynecologist, and he examined me and found by palpitation the same remnants of infections during breast feeding that the previous doctor had seen. He said : to be sure, go and have a mammogram at XXX medical center.

So I went. It was the first and last one.. a) it hurt very much because my breasts were small and b) the specialist doctor there looked at the mammogram and said "hmm, I see this and that shadow but it is better that you discuss it with your surgeon".

The minute I heard "surgeon" I took it for a one way road to over diagnosis ( I had great trust in my first doctor ).

So I went to my sister's homeopathic MD and now take a little pill every morning and that's it. I am now 74, if I reach 80 that will be fine. We will all die one day and something will be written on the death certificate.

Dear Lubos,
I still don't get. You have a question, let's call it Q. The question can be checked by experiment. In the case of SETI the question is whether we are able to catch a message from aliens. Now you say, well, is Q true or false? Then you say, nobody knows either way. let's check. That for me is the very definition of science. Choosing a good question Q and deciding whether you have the right tools to answer it can make the difference between good and bad science. But that's it.
I fully agree that making physical contact with those aliens may end up very badly. I was just thinking about point in time when we receive the first signal and said that it would be important. But yes I would link some positive excitement to this event. I would agree that the risk of answering that message should be carefully evaluated depending on the content of the message, from where it comes, whether they can detect our TV signals anyway etc. Probably it would be too tempting to answer though.

"Tegmark is clearly a mathematical Platonist, and so am I. Mathematics
exists independently of the humans. Humans are actually discovering
(pre-existing) mathematics rather than inventing it."

Yes! Me too. I annoys the crap out of me when people try to say mathematics is just a human construct.

On the other hand, I also agree with you that Tegmark draws from this a total non sequitur.

http://space.mit.edu/home/tegmark/mathematical.html

Dear Lubos, probably no ET has been detected because they don't use EM waves to communicate ... most likely, advanced civilizations use teleportation of signals ( http://pra.aps.org/abstract/PRA/v89/i1/e012311 ) ;-)

In the most ideal society there is a device that recognizes the distinction that the DNA has markers that can be treated and until that time is reached, even one life is worth saving. Anybody who sacrifices a life, because consensus can't be reached about recognizing the architecture of the individual cancer diagnosis, not one of those treatments or advice to not have a mammogram can be fended off with statistics.

Horgan failed here and does not know his science. He does not say what needs to be told about those markers. Emotion has nothing to do with it and neither does politics.

Rockets are ok for transporting objects through space, but not as good as planets (or perhaps comets as you alluded to a few days ago)... nature wins again... :-)

Enough of this... I think we get each others points and I have other things to do. Have a nice weekend!

Lubos boldly asserts: “Mathematics exists independently of the humans. Humans are actually discovering (pre-existing) mathematics rather than inventing it.” One easily visualizes him in climbing harness scaling icy walls on the wind swept lofty peaks of ST, here and there flipping a prettier piece of shale to find his math inscribed by Nature. He states: “I just think it is silly to make a big deal out of it because the Platonism doesn't really mean anything tangible.” I agree heartily, but perhaps it does matter in some small way in that it could be a pointer into the nature of consciousness.

Just as the realization that atomic particles and the devices used in there investigation were inextricably linked was absolutely central to the formulation of QM, it may be that our mathematics is inextricably linked with our stream of consciousness viewed as a mapping from or, pace Thomas Metzinger, a representation of the neurons constituting our minds. No sane individual doubts reality’s causality, but the “logic” represented in our minds by this causality in no way exists in the real world as anything other than an ephemeral: a 3D array of dynamic binary registers (our brain) creating the representation in our minds that we call “logic” is what actually exists in cold, hard, absolute empirical reality.

Sartre, that most incoherent of philosophers, actually said something meaningful (at least to me) along these lines: “the consciousness saying “I think, therefore I am” is not the same as the consciousness doing the thinking”. Such temperance leads one to take applied mathematics as a supplier of quantitative models, where accord with empirical data becomes the final, and only, arbitrator of truth, and one must be happy with this. To expect more as in “the precise form of physics” may be a bridge too far (think of technology’s advance yielding data from which Le Verrier extracted Mercury’s perihelion precession, leading to GR, leading to ST, leading to …).

Haha ;). This is from Quine's 48 'on what there is'. To cite a pre-'two dogmas' Quine on the relationship between mathematics and physics is not quite unlike citing a 10 month old Quine on potty training. 'Quine was against defecating on the toilet'; you read it here first, people.

That said, the TL;DR of this piece is that neither formalists nor Platonists have got it quite figured out. He has yet to draw his more radical conclusions at this point which defined him as a thinker, but nonetheless: amen to that.
Want to try again?

Planets are not able to move anything through space at all. Planets, like any objects under no forces except for gravity, including excrements and pieces of industrial waste, are just being mindlessly moved along geodesics.

Have a nice Friday.

A friend of mine was diagnosed with breast cancer two years ago. The few mammograms she did never showed any tumor. She never felt any pain in her breast. It was only by visual that her doctor decided that there was something wrong. I'm not even sure the further analysis she did ever confirmed the supposed tumor. Her doctor never sounded 100% sure. However she went through the whole chemotherapy, lost her hair, had her left breast removed, tough times... She is recovering now, but I do wonder if she ever had a malignant tumor at the end of the day.

Do you think I have nothing better to do than engage in never ending arguments with ignoramus like you? Arrogance is irritating even when there is a justification for it but in your case it is nothing but stupidity. You can ponder on this while trying to digest:

"From a mathematical point of view, indeed, the important opposition of doctrines here is precisely the opposition between un-willingness and willingness to posit, out of hand, an infinite universe. This is a clearer division than that between nominalists and others as ordinarily conceived, for the latter division depends on a none too clear distinction between what qualifies as particular and what counts as universal. In the opposition between conceptualists an.d platonists, in turn, we have an opposition between those who admit just one degree of infinity and those who admit a Cantorian hierarchy of infinities.

The nominalist, or he who preserves an agnosticism about the infinitude of entities, can still accommodate in a certain indirect way the mathematics of the infinitist-the conceptualist or platonist. Thought he cannot believe such mathematics, he can formulate the rules of its prosecution.” But he would like to show also that whatever service classical mathematics performs for science can in theory be performed equally, if less simply, by really nominalistic methods-unaided by a meaning- less mathematics whose mere syntax is nominalistically de- scribed. And here he has his work cut out for him."

The only relevant maths in the Universe is the maths I learned at school to get my points for my Baccalaureat and that has got me by in life so far. ;-)

"some spectrum of particles"

Could you elaborate on that sometime? Is it anything like the spectrum of light through a prism?

I think Tegmark's idea has genuine merit to some degree, but "show me the money": derive mathematical consequences out of it, make actual predictions.

One thing I do not agree with this post is placing non-commutative geometry in the crackpot bucket. Yes, the theory had its low points, like the incorrect prediction of Higgs mass, but all prior crises are now solved (I mean in the last 12 months). Non-commutative geometry is nothing but a mathematical duality at core (the Hilbert space formulation of QM vs. the phase space formulation of QM is a manifestation of this duality), and the standard model happens to be described in this formalism in a very compact way. The strange notion of distance in NCG using sup versus inf (like in Euclidean space) arise out of the operator norm on C* algebras. Is it a ToE? Not at all. Solves quantum gravity? Nope. It is an equivalent mathematical description of the SM Lagrangian weekly coupled with gravity.

Hi Lubos, what do you think about paraconsistent mathematics? It has some applications in quantum mechanics and could deal with things like Gödel's incompleteness theorem or the halting problem.
Greets

The design of the world can be 'mathematical' without having to admit that 'incompressible fluids' actually exist. I suspect that the hallmark of whatever that design is entails that one can no longer draw a nice boundary between that math and the physics - it would not be merely a tool

Popper (and no doubt many others) makes the distinction between the world of apriori truths (which he calls world 1), empirical truths based on the evidence (ie, science) which he calls world 2, and the truths of human experience (feelings of beauty, patterns of history, etc.) which he calls world 3.

To me this seems like a pretty good way to divide up the world of truths. Apriori truths are true by definition. Every mathematical true statement turns out to be a (sometimes deeply hidden) tautology.

About the nature of empirical truth I would not dare breathe a word on this blog. Why else do I come here except to learn.

Now, about that world no. 3: it may (no doubt is) a subset of world 2, yet trying to appreciate it in terms of abstract mathematical propositions seems (to me at least) inappropriate because unfruitful. I sometimes think of it as a kind of supra-natural realm: completely within the laws of nature but best appreciated by other means, namely, our own experience of ourselves and other people.

Anyway, I'm just an old man babbling and having fun. Cheers everyone! I love Lubot Motl!

This nice article neatly underlines why I always get annoyed when on Physics SE questions involving mathematical concepts / ideas get way too aggressively migrated away to Math SE ...

http://meta.physics.stackexchange.com/q/5473/2751

And it is a nice introduction to some set theory issues ... :-)

Hi Lubos,

Thanks for this spirited critique, which I think actually wins the prize as the most explective-filled one I've seen to date! You're obviously free to call me a "kook" etc., but if you in addition have some sober scientific critique of something I've claimed in the book, please let me know. You raise the important question of whether parallel universes are science or mere speculation. I'm not sure whether you had a chance to read the book before writing this post, but I discuss this question extensively in chapter 6 before starting to explore parallel universes.

First of all, please note that my book does *not* claim that parallel universes exist. Instead, all my arguments involve what logicians know as “modus ponens”: that if X implies Y and X is true, then Y must also be true. Specifically, I argue that if some scientific theory X has enough experimental support for us to take it seriously, then we must take seriously also all its predictions Y, even if these predictions are themselves untestable (involving parallel universes, for example). In other words, I argue that parallel universes are not a scientific theory, but prediction of certain scientific theories. Specifically, I claim that there are four implications:

1) Cosmological inflation generically implies Level I multiverse

2) Inflation + string landscape generically implies Level II multiverse

3) Unitary quantum mechanics implies Level III multiverse

4) The Mathematical Universe Hypothesis implies Level IV multiverse

I'd be interested to hear if you have objections to any specific claims that I make in the book. Would you object to the claims 1), 2), 3) or 4)? Or are you arguing that one of the theories (inflation, say) makes no testable predictions and is therefore unscientific?

Early detection increases the years between detection and death. Good luck explaining to people that this statement, while true, does not necessarily mean there is a benefit to early detection. This study will be dismissed as anti-woman and pinned on greedy insurance companies who don't want to pay for mammograms.

Well, you almost had me convinced of your position by the sheer volume of your humorless name-calling; but im sorry to say, your claim that you don't have anything better to do is at odds with the observable facts.

What these rather neutral observations you are quoting are supposed to prove eludes and ignoramus such as myself; but ill give you the benefit of the doubt, and will assume you have more important things to do than making a coherent argument.

One nice aspect of Tegmark's line of thinking is that it provides a possible solution to the age-old conundrum of why there is something rather than nothing. If the mathematical Platonists are correct, there is always something.

Ralph K

As a math prof, I really despise the use of 'maths' in place of math or mathematics etc... Your title would be more eloquent with two less 's''es.

Lukelea,

Nicely put discretization of truth. But why stop at 3? If you think of all human activities disciplined enough to be seen as methodologically seeking truth, one can discern equivalence relations leading to classes having as kernel certain models - physics, sculpture, music, theology, cinema, economics, … . It becomes unclear just how many axes are needed to describe all truths’ subtleties. And, jee, is empiricism orthogonal to fideism? Hmm, before you know it you are in Hilbert space and need to throw back another single malt. Have a good one.

This is somewhat misleading, mesocyclone. High efficiency (high bps/Hz) transmissions look like noise unless the receiver knows something in advance about the character of the transmitter. It is true that low bps/Hz are very inefficient but they are easy to understand.
Given the problems of interpretation that would exist even if the alien sender had a direct, noise-free, fiber-optic link to our planet, the sender is not likely to use high bps/Hz methods if he is trying to initiate contact.
Of course if we accidentally pick up alien communications not intended for initial contact what you say is correct but, then, not much has really changed since SETI’s early days.

There was some pretty good science done at the beginning of SETI by ex-Hewlett Packard engineers. Of course it was understood that a very large transmitting antenna would be needed to overcome diffraction limitations along with immense transmitted power unless the sender happened to be in our immediate cosmic neighborhood. Most thoughtful observers considered success to be very unlikely and they still do.

If we could accurately identify the senders direction and if the sender were to beam a powerful signal exactly in our direction it would be fairly easy but those are two huge “ifs”. We have no idea where to look and they likely would not know where to send even if they wanted to and why, exactly, should they?

The idea that mathematics consists essentially of “tautologies” is, I think, a common misconception. It occurs to people who think of mathematics as consisting of proofs and of proofs as being “tautologies”. But firstly, mathematics does not consists only of proofs, it also consists of “definitions” and even before one makes a formal definition there are mathematical objects that are at first understood intuitively. Secondly, the only proofs that can be considered “tautologies” are purely formalised ones, but “real life” proof are rarely completely formalised and are almost never discovered in this form.

Take for example the idea of a knot: this is a mathematical idea which formalizes a concept that is quite familiar from our experience. In real life we meet “knots” in various manifestations: they can be made of strings, rope or of DNA. We soon notice that these have something in common and can ask the same questions about them (like can they unknotted). From these considerations we move to an informal mathematical definition: a knot is a closed non-intersecting curve in three space. This definition is sufficient for certain “informal proofs”, but since these rely on geometric intuition it’s hard to justify calling them “tautologies”. One can (and does) go further and give a precise mathematical definition: an unoriented knot is the image of an embedding of the unit circle into the 3 dimensional euclidean space. One can now define certain computable invariants (Alexander-Conway polynomials, Jones polynomial, Vassiliev invariants) which enable one to answer various questions about unknoting of knots etc.

Even if the proofs of the properties of these invariants are, in some sense “tautologies” (and they can only be considered as such when they have been completely formalised since no argument that relies on geometric intuition, however seemingly obvious, can be called a “tautology”), surely the invariants themselves are not “tautologies”, and their properties are every bit as “real” as the properties of physical objects.

And this sort of stuff is what, I think, Popper’s “World 3” consists of.

I'm sorry if I didn't clarify. I was talking in the context of "intercepting their WiFi" - the article headline - i.e. capturing signals not intended for us.

Modern signals, very unlike those when SETI was created, are noise-like - effectively noise if one doesn't have the information to cohere it.

Lubos,

" Humans are actually discovering (pre-existing) mathematics rather than inventing it.'

This isn't exactly the platonic ideal forms, existing independent of their physical manifestation. Because physical reality expresses order, doesn't mean that order exists independent of its expression. There isn't much order in the void.

Women in general are confused about the value of mammography because they've been told disinformation about the medical procedure instead of the real truth (read "The Mammogram Myth" by Rolf Hefti).

The mammogram industry and their adherents, do what they've always done: either ignore or downplay the significance of the data of this new study or partly concede to, in a face-saving manner, the inconvenient facts by claiming now that the choice to have a mammogram is a "an individual patient decision," as if these tactics of damage-control would change an iota on the true facts about the exceedingly harmful procedure.

Dear Max, thanks for your visit. The word is written as "expletive", not "explective". I sometimes use them but it wasn't the case of this blog post. In particular, "kook" isn't an expletive. I think it's dishonest for you to pretend that you might get offended by this label. You know that all good theoretical physicists consider your papers on levels of multiverses to be crackpottery,don't you?

First of all, I find it very likely that *none* of the multiverses exists in the physical sense - so none of the claims 1,2,3,4 is "implied" by physics as we know it with the meaning of the verb "imply" as physicists are used to.

MWI i.e. what you rebrand as Level III Universe is a misunderstanding of quantum mechanics. If you study this blog really carefully, you may be able to learn these basics of QM and why "Level III Universe" is completely missing what QM is actually about. It is no accident that Niels Bohr recommended Hugh Everett to get out of physics. Everett's musings were crackpottery, at least a bit more originally than yours at that time. So your item 3) is fundamentally flawed.

The item 4) is containing no argument whatsoever, it is just a circular reasoning without any scientific backing. The Level IV multiverse and your MHU are two words for the very same thing, so saying that one implies another only shows that you're not capable of thinking logically.

Concerning 1), Level 1 multiverse - just regions behind the cosmic horizon - may look innocent and harmless classically, and some people wouldn't even call them a multiverse. However, it seems likely that quantum gravity implies that the regions behind the cosmic horizon don't have a separate existence due to the horizon complementarity - in analogy with the black hole complementarity. So the physics of the "better physicists" today will surely favor the answer that even the Level 1 multiverse doesn't exist in any physical sense.

So the only multiverse that is motivated enough according to modern science is the Level II multiverse envisioned by 2) - meaning the set of bubbles in the eternal inflation. However, a survey of all attempts to incorporate this meme into physics implies that there exists no credible, convincing, or motivated argument that would suggest that this Level II multiverse may be used to deduce anything about physics in any particular bubble. Like Level I universe, the other bubbles may very well be unphysical from a given observer's viewpoint.

Even if Level I and/or II multiverses exist, you didn't discover them. You just tried to give them new, stupid names - names that fallaciously encourage people to "accept" the other "multiverses" as well although they have nothing do with the evidence for a particular multiverse. And everything "new" you are actually saying about these "multiverses" is either vacuous or downright wrong.

SETI search to science is like lottery to hard work. It makes sense to not confuse them and that is the point.

You say no one knows for sure if we can detect them or not. Well guess what you never know anything for sure in modern science, that does not justify looking for anything you can come up with.

Hi Lucretius!
I am mostly impressed by your contributions. In this instance I am mainly impressed by that you don't seem to be humbled and scared by the fact that both your (mathematicians') and physicists' concepts are built from (!!approximately!!) 1st to 2nd to 3rd level pattern-detecting neurons' activity that forms an aha type 'intuitive insight'-type pattern in 'stringy extra-dimensional brainspacetime' -- and that then this specific pattern of 'pseudo platonic' output is and must be passed to and between Wernicke's and Broca's brain-areas before written representations can finally be put onto electronic paper to be largely and usually correctly critiqued by our humble but hard-nosed correspondent (Lumo). :-)

I like your comment and I refuse to think that age has anything to do with it! ;-)

If need be, I'll help you to defend it best I (someone as young as I) can! ;-)

@uncle al: beautiful argument by orthogonal reasoning. How many degrees of freedom do you posit - 11 maybe? I like your black swan analogy BTW.

This is not a topic that it takes many sentences to effectively philosophically terminate or finalize!

What gave rise to this our universe (definitely no thing, or not suitably characterized as 'thingy' and as surely a timelessly eternal potential or "pseudo process") did so only as a once off event (which both intuitively and by string/M-theoretical indications seem utterly unlikely) or it is a cosmological big bang producing process that does its 'mathematically kaleidoscopic energy producing and patterning thing' consecutively or in parallel or both sequentially and in parallel.

Next time I make a comment here (or directly to Lubos) I aim it to be on a topic most relevant to us humans, and in respect of which I think I just might have something 'atheistic enlightenment' promoting (or of complementary significance) to say about mainly (but not only) from a vantage point of evolutionary psycho[physio]logy type'.

This has been argued before in the skeptical community.

A Skeptical Look at Screening Tests

http://www.sciencebasedmedicine.org/a-skeptical-look-at-screening-tests/

What tests can explicitly prove/disprove multi-verse interpretation? It really seems MWI is an interpretation of QM/cosmology rather than a physical theory; it seems to provide a philosophical explanation, trying to make personal sense of nature rather than providing general rules about nature that can be tested and make realizable predictions.

Scrupulous avoidance of the substance of a fundamental critique of the premises of a scholastic theory is an essential feature of any scholastic theory. You insist in effect that what can be discussed here is the genealogy and fine anatomical structure of centaurs, but that asking whether centaurs can exist in nature is naive and evidence of the doubter's ignorance. What you call questions, or what should be formulated as questions in your view, are in fact legitimate criticisms of the fundamentals of the black hole hypothesis. I made two points:

1. There is no experimental evidence that warrants the assumption that is fundamental to the black hole hypothesis, namely that large masses of ordinary matter are compressible to arbitrarily small volumes. In fact such an assumption is patently absurd, invalidating the entire black hole hypothesis.

2. The notion that stars can avoid gravitational collapse by means of thermonuclear reactions violates Newton’s Third Law. In fact, if matter is ejected from the star during its active phase, this means that the pressure on the core due to gravitation is augmented by the inward directed counter-pressure generated by the ejection, and is thus episodically stronger than in the subsequent phase when the thermonuclear reactions are dying down. If the star did not collapse due to such extra pressures, why should it collapse after those pressures have ceased?

You remain true to the scholastic tradition by dismissing fundamental objections to the theory’s premises as evidence of ignorance, or as being somehow inappropriate. Contrary to what you state, I did not present a theory of my own, I only presented two fundamental objections to the strange hypothesis that you choose to believe. In the space you took to argue (twice) that I ought to ask someone else at another forum to answer my naive questions, you could have addressed the two fundamental objections I stated in my first comment. But as said, the fundamental assumptions of a scholastic hypothesis are not subject to scrutiny.

Instead of another patronizing reply, perhaps you could divulge to the patient readers of this blog the experimental or observational evidence that has led you to believe the patently absurd notion that the entire mass of a star substantially larger than the sun can be compressed to an arbitrarily small volume, i.e., a volume with a radius approaching zero.

According to Libet, a famous neuroscientist : Regarding the unity of conscious experience, it was increasingly evident that many functions of the cortex are localized, even to a microscopic level in a region of the brain, and yet the conscious experiences related to these areas are integrated and unified. We do not experience an infinite array of individual events but rather a unitary integrated consciousness, for example, with no gaps in spatial and colored images. Some unifying process or phenomenon likely mediates the transformation of localized, particularized neuronal representations into our unified conscious experience.
.
It should appear obvious that any particular brain representation and doing mathematics is just a particular case of generating brain representations, is a property of the material device, e.g the brain, generating them.
This is even a general property of all brains, so not only human, and that is certainly the reason why evolution has selected and developped this particular device as the most efficient way to adapt and control the environment.
.
So a cat jumping on a fly will aim at a point in space where the fly is NOT. This is only possible because its brain has extrapolated the fly's movement and considering the relative velocities has estimated the point of intersection.
Even if a cat has arguably no consciousness of itself, its brain has abilities which can be interpreted as generating mathematical representations of the reality and these representations guide actions (here signals to muscles orienting the jump).
Even more obvious is observing a cheetah attacking an antelope.
In the first phase the cheetah approaches slowly and low to stay hidden.
Then at a particular distance it decides to start the attack.
It knows that if it starts the attack earlier, the distance will be too large for the velocity differential and if it starts too late the antelope will see/smell/hear it and initiate evasive manoeuvers before the cheetah started accelerating.
Clearly the cheetah brain is able to estimate distances and this metrical representation of space can also be interpreted as a mathematical activity.
There are millions of similar examples and experiments (some concerning even more "sophisticated" activities like adition and order relations) that show that different "mathematical" brain representations of the reality are an universal property of brains.
I would agree with Lubos that the Platonic or non Platonic philosophy of mathematics is probably irrelevant to the real process which is neural activity generating brain states.
However as this specific kind of neural activity is extremely efficient in dealing with/predicting the real world, I am convinced that what the Nature wanted to do was to realise a duality between the real world governed by her "laws" and the brain representations of this world.
What is called mathematics would then be just the brain side of this duality.
Even if we are still very far from it, understanding the detailed brain functions that generate the mathematical representations and understanding what we (e.g science) can say about the real world would then be equivalent.
How the former is studied can be for example seen here : http://sulcus.berkeley.edu

Sorry, but you mistake me for someone else. I am very far from being an expert, as you would have realized had you read my own question further upthread (which, btw, has not been answered to date but you don't see me complaining).

I merely offered you some friendly advice on maximizing your chances of getting a useful reply, nothing more.

I am slowly getting the impression that the purpose of your "questions" is not to improve your knowledge by learning from what experts could tell you in answers, but to push your personal opinion about certain topics through and start unscientific not constructive discussions.

However, there seem to be rather interesting (astro)physics questions hidden in your comments. So if you are able to reformulate them in a more neutral less subjective opinion based way, you may indeed be able to get some good answers on the websites Eugene suggested to you ...

Cheers

Ahoy Lubos!
I'm not offended by your aggressive tone, merely amused. You make many strong claims about the views of the physics community that are at odds with my impressions from recent physics conferences, but you're obviously entitled to your sociological interpretations. If you have any concrete critique of my publications ("equation 115 in my consciousness paper http://arxiv.org/pdf/1401.1219v1.pdf is incorrect", say), just let me know.

Wow, now I remember why I like reading your stuff. If anything is beyond the empirical veil it is this multiverse BS, right up there with Russell’s teacup.

Mammography machines feel like instruments of torture. :-) They have a pair of glass plates between which the tissue is pressed quite firmly to get the image, and the plates are rotated 90 degrees for a second set of images and one's tissue pressed firmly in that orientation. Ouch! One really big improvement some years ago was to design automatic release of the plates once image was taken. First time I had one, the technician had to come over and manually release the plates - those additional seconds of discomfort were huge. Thank you to the engineer who tweaked this design! I dislike the nagging from the medical community to get these images so regularly. There is a sense of anxiety and fear in these mammography locales, overlaid with a veneer of childish cheer; pink teddy bears and pink hearts and pink ribbons. As others here have pointed out, let's face our mortality with some style and courage.

It's the other way around. Many well defined questions that are formally decidable (there is an algorithm), can *not* be solved by any physical process. They have resource requirements much bigger than the universe (in Plank units). You might call those problems "unphysical", and you would be right; they are not about the result of any physical experiment.

The "bureaucratic trick" is mostly physically irrelevant not because it labels too *many* problems "undecidable", but too *few*.

It is possible in principle that the reverse (mathematically undecidable problems with physical solutions) could happen, but all evidence so far is against that. So far as I know, no physical theories (including string theory) permit it.

Yep, that noncommutative geometry should belong to the no good things surprised me a bit too, maybe because I know not enough about it ...

So maybe somebody could explain to me what its problematic features are (just curious now)?

Are you joking ...?

Wow thanks Peter F. & Lubos for the video of the crow. These birds are really clever. It is said that most animals can become clever when they want food.

Common sense is neither common nor sense. So patently absurd is the well established theory fitting the observational evidence.
If you want an interesting read get "The Perfect Theory" by Pedro Ferreira. It answers your questions in nontechnical way and tells you where you will turn if you wish to learn. See chapter on collapsing stars especially.

Here I am, Anna.
"I chose homeopathy instead..."---in other words you chose a totally crackpot delusional system of belief in placebo and anecdotal-based drops of water. Gad. And you are proud to trumpet that here, on a science blog! If homeopathy worked, you would be cured of virtually everything by drinking tap water (geez, it must have one or two molecules of nearly everything in it, "succussed" by earth tremors.
This reminds me of the anti-vaccination stuff where people don't get say, polio shots, because they never get polio---that is, until they do. Do you have any other bat-shit crazy beliefs, like Lemurians in Mount Shasta?

BTW, I also think that, particularly in the USA, tests are grossly overordered.
The controversy (?) over mammograms saving lives is similar to that over ordering PSAs for men. For individual cases, of course they can save lives. The papers saying that they don't are churned out by bean counters and epidemiologists. In any case, ultrasounds should be used more.
Finding an isolated reasonably well differentiated breast CA earlier before it metastasizes is life saving. If it is anaplastic, probably not.
All those high tech tests in the US are often driven by profit motives of HPOs and hospitals, and by the lawsuit-crazy situation there.

Stop speculating about what my purpose might be, Dilaton, and try to deal with the substance of my arguments, which are not in any way hidden in my comments, as you claim, but on the contrary are quite clear and explicit. I am also entirely on topic, so your trying to shoo me off to another forum won't work either. It is your dodging and refusal to address the points I have made that is unscientific. Equally unscientific is the notion of infinite density, to which you seem to subscribe. I have also pointed to a fallacy in the notion that gravitational collapse can be triggered by the cessation of thermonuclear activity in the core of a star, since thermonuclear activity at the core of a star cannot alleviate the gravitational pressure of the outer layers without violating Newton's Third Law. The core experiences the entire pressure of the outer layers regardless of any nuclear activity taking place at the core and may occasionally experience additional pressure as a result of mass ejections. Hence if the core did not collapse when it was experiencing such extra pressures, why should it collapse upon the cessation of the activity giving rise to such pressures, simply due to gravitational pressure that was active all along?

Thank you for your suggestion, Rehbock, I will try to find the book. However the fact that a theory fits the observational evidence is not sufficient to establish its veracity. The notion that earthquakes are caused by movements of the turtle on whose back the world rests also fits the observational evidence, but it is patently absurd, though perhaps less so than the notion that stars can collapse to a singularity. Stars can obviously collapse, as they have been observed to do, but the notion that there is no countervailing force and that the collapse continues indefinitely, reducing the volume of an entire star to a size smaller than an atomic nucleus makes the turtle theory of earthquakes sound reasonable by comparison.

@ Florin Moldoveanu What is really non commutative geometry? What are its successes ? Can you give a simple minded description or point to a web reference?

It is really hard to have a simple description. But here are some references: http://arxiv.org/pdf/math/0408416v1.pdf and http://www.alainconnes.org/en/ For a popular introduction (if you manage to suffer through the very frequent commercials) http://www.dailymotion.com/video/xuiyfo_the-music-of-shapes_tech#from=embediframe

A nice explanation by Connes can be found here: http://www.alainconnes.org/docs/maths.pdf

The major application for the Standard Model is here: http://fr.arxiv.org/abs/0706.3690v3 and here: http://fr.arxiv.org/pdf/1304.8050v3

Connes is an expert in QM and von Neumann algebras, won the Fields medal and started a very important and active mathematical branch of non-commutative geometry. At core, NCG is about mathematical dualities (see the table on page 6 on http://arxiv.org/pdf/math/0408416v1.pdf) For a deeper dive in the subject I recommend the 2 books listed under: http://www.alainconnes.org/en/downloads.php

@Timo: You must be in U.S. When I was in India, under British educational system we used to call Mathematics as maths. This must be true for Europe also. They learnt English from Britishers! But you are absolutely right . In U.S. it is called math without the last s!!

Another flawed study. Once again, early diagnosis may not make a noticeable difference if the tumor is undifferentiated and highly anaplastic because metastasis may have already occurred with small tumors. Also, with highly differentiated tumors, it may take 15-20 years or so to kill someone...Really, if you find a solitary tumor in your prostate, and have screening to see if it has metastasized and biopsy to get the cell type and aggressiveness of the tumor, would you really not want to get treatment?

Rehbock, I just read a few reviews of the book you suggested and see no point in acquiring it or reading it. I have read dozens of such hagiographies of Albert the Stoned, basically fawning glorifications of his failed attempt at formulating a general theory of gravitation. Normally a theory fails because of some error in its fundamental premises. However the spectacular failure of general relativity is an exception to this general rule, as it started out with a correct fundamental premise (the equivalence of mass and acceleration) and still managed to screw up physics for at least a century. As I see it, it was Al's uncritical adoption of the fatally flawed Riemannian geometry that led him astray. In reality, Euclidean geometry is basically sound since the fifth postulate is rigorously provable on the basis of prior postulates, though Euclid, having failed to demonstrate the proof, treated what should have been a theorem as an additional postulate. This gave Riemann what he thought was a license to build geometries based on a rejection of the fifth postulate. Given that the fifth postulate is actually a provable theorem, Al's attempt at building his general relativity theory on the Riemannian rejection of the fifth postulate was doomed from the start. Al grasped at this straw since he needed added degrees of freedom to account for gravitation. Yet he proceeded to try to fit his entire structure within the constraints of the Cartesian reference system, an impossible task. Rather than rejecting Euclid and embracing Riemann, Al should have adhered to Euclid, or an updated version of Euclid, while recognizing and surpassing the constraints of the Cartesian reference system. As a bonus, such an approach would have given him a handle on quantum phenomena, which he was never able to properly account for.

In any event, I base my critique of the current astrophysics on standard texts such as Stars and Stellar Evolution by de Boer and Seggweis, or Evolution of Stars and Stellar Populations by Salaris and Cassini, not on The Complete Idiot's Guide to Stellar Evolution.

I had to look up hagiography. I did not mean to insult you. But you make no sense to ask a question for which you insist you have all the answers.

Given that treatment is continuing to improve (for example taxol) a 25 year study may not be appropriate. Also remember the shit storm when the US Preventative Services Task Force recommended screening start at 50 and not 40.

Needless to say, I do not claim to have all the answers; all I did was to venture an educated guess as to where Al took the wrong turn with GR. Had he accepted that the principle of equivalence is in fact the principle of identity, i.e., that acceleration is not just equivalent to gravitation, but is the same as gravitation and indistinguishable from it, i.e., gravitation is acceleration,though not in a single dimension as in his elevator thought experiment, but in three dimensions simultaneously, as experienced on the surface of any spherical body with mass, he might not have been so tempted to reach for Riemannian geometry, his fatal error in my opinion. He would have had to question the general validity of the Cartesian reference system, which cannot represent the true three-dimensional acceleration of a body such as the earth, Einstein did not succeed in generalizing his elevator thought experiment in that he failed to extend it to three dimensions, and tried to fudge the issue by bending space in the spirit of Riemann. Space cannot be bent, but acceleration can act in three dimensions simultaneously,not just in one dimension, as in his elevator example. What we perceive as gravitation is actually three-dimensional acceleration, which the Cartesian reference system cannot represent correctly, In the Cartesian reference system, only one-dimensional acceleration can be fully represented and all of its three axes, x, y and z are employed for the purpose. Acceleration in the other two dimensions is perceived as a force, the gravitational force in this case.

Just to clarify,I am engaging in a critique and not begging to be brought up to speed on current astrophysics, which is in a dismal state in my view and almost entirely absorbed in what amounts to scholastic debates about the precise temperature of the fires of hell.

Agree with you in this instance lucretius.
Unfortunately many Americans have adopted the unfortunate habit of believing the rhetoric of their own cultural ' exceptionalism' and 'selfieism' consistently downplaying or exploiting the intellectual and social achievements of other nations.
In the process they have ' dumbed down' trashed or distorted their educational system, language, metric system, environmental heritage, political system and ethical values in general to the point where they may be classified as a dysfunctional society.
Timos 'maths' rhetoric as a supposed intellectal member of the US respected academic community only confirms this worrying trend

Dear Gordon, how did you get the interval 15-20 years? Is there any science behind it or are we supposed to trust you just because your MD degree gave you extraordinary powers to determine such numbers without any science? It may also give you 80 years, right? This is really the point and meaning of the term "overdiagnosis".

I would surely not okay the treatment mindlessly. It would depend on what the treatment means and what is the prognosis with and without the treatment.

No smiley? you really take yourself seriously :).

The following is not for you, you have made up your mind and will not be bothered with the facts. It is for people, if they exist, wondering about my choices and in order to set strait the "theory" behind homeopathy, which will not give medicinal properties to the tap water.

First of all I am an experimentalist by training and an experiential sponge by construction of my DNA.

Homeopathy has worked for me, my sister, my deceased mother and father , my children and a wider variety of people. . This is the fact, and I consider it an experimental fact. It works.

The "theory" behind it depends on the old etheric model . I will state it though, I am as skeptical/dismissive as the next physicist about it, the theory I mean.

In this model, the physical body is the end product of materializing in these three dimensions. There exists the etheric body, whose total attributes can be called "soul" as the western culture defines it.

This etheric body is composed of seven consecutive layers and is the matrix/mold ( master plan) on which the physical body fits. Diseases appear first on the etheric body and it is the etheric body that has to be healed for the body to heal.

There are people who claim to see the etheric body of people. ( see Barbara Brennan physicist turned healer !) .

All atoms, molecules, etc have an etheric body too. That is what homeopathy is based on. Supposedly the appropriate medicine, usually a poison which would kill a person , has an etheric body. If these molecules are shaken and diluted many times , the water's etheric is imprinted with the etheric properties of the poison but will be absolutely not dangerous because of the great dilution in the three dimensions. It is the shaking that does the imprinting.

The idea is that the etheric medicine will resonate with the etheric problem and neutralize it ( that is why it is good if the symptoms increase the first day, the resonance shows that it is the correct medicine). Once the etheric is cured the body is cured.

Again, this is a model not based in physics as we know it and there have been no physics experiments to verify it. A colleague of mine, during the time of polywater fuss( extra properties in water that finally were not found) tried to make up a theory at the time.

And again, homeopathy works. I am sure that a physical theory will be found as physics advances towards a theory of everything. (think of all those extra dimensions in strings ;) ). History of physics shows that what was metaphysics before became physics for the future generations of physicists.

@dhtow01: Although some of your criticisms of American systems are worth considering, in this particular case of 'maths' I do not agree. May be I have lived in U.S. for too long! But if you want to have 4 lettered short names for the subjects, math is more reasonable, just as Physics is called phys rather than physs , Chemistry is called chem rather than chemy, Economics is called econ etc!! Of course this is just a little remark. Such differences in languages should not be taken seriously. Actually much more serious may be the way Britishers distorted names of Indian cities so much (because they could not pronounce them) that the old names are stuck in my head for 76 years!!!

Is any of this even worth discussing, especially on this post, which has nothing to do with whether "commonwealth conventions" or "U.S. conventions" are better?, but instead to do with Tegmark's papers, etc. ? You further deviate the conversation by going into things like criticising anglicisation of city names, etc. ?! I What about calling the British as "Britishers" , as you do above, then? ... And by the way I really doubt that the names are changed because they "Can't pronounce" anything. I am an Indian and I can pronounce most Indian city names, but I choose to use the anglicised names when speaking in English.
You state yourself, that "Such differences in languages should not be taken seriously", and defy it in the very next sentence!

Interesting post, and I agree with you. Tegmark's Level N multiverses are surely not physics, and the paper on consciousness in indeed laughable. But the Level N universes are fine as philosophy, and should keep them selfves in the pop-sci section of the ArXiV. The paper on consciousness, unfortunately, has gotten into the quant-ph section : (

When I first heard someone refer to mathematics as "math" it sounded to me like they had a cleft palate or some other sneech imfedinen — that kind of thing.

There's a lot of it about. Another fave is "sixth". Loads of people can't do that one. They say "sikth". Obviously the sibilant in the middle is too difficult for them. Jeremy Paxman has this diforder. But then he's an al beeboid so there's bound to be something wrong with him.

Murcans have no excuse. :)

Come on now, Luboš, don't hold back — tell us what you really think. :)

Tom, me too. Ace stuff!

@CentralCharge15: Yes. I agree we should not clutter up Lubos' blog with trivial things. The only reason I responded was that a math professor did not like the usage 'maths' although I had noticed it long time back.If you prefer anglicized names, that is your prerogative. As for me I firmly believe Britishers were using their colonial power in a completely unjustifiable manner to distort officially the city names : Vadodara became Baroda, Kolkata became Calcutta etc. I do not know how Chennai became Madras! This is not just a question of different nationalities pronouncing the names in a different manner. Anyway let me stop before other readers get irritated!!

There's a lo' of i' abou'.

Wow John, your glottal stops could halt the eurotrain in its tracks... 'Estuary English', I believe it's called?

Yes, I agree. Repulsive aren't they. I fucking hate them.

It's true: an Englishman only has to open his mouth to have another Englishman immediately detest him. But that's fine — it's healthy to maintain a certain level of native aggression in the population. After all, the world full of aliens, and you never know when you might need draw on the resource in earnest.

It's one reason I admire the efforts of our football hooligans. They keep the spirit alive.

P.S. Well done your hockey team! No mention of any crippling though. Well, never mind. Maybe next time. :)

Lubos--next time read my post more carefully.
1. 15-20 years was the time for the well-differentiated tumors to cause significant problems or to kill and those numbers were approx and plucked from the ether of experience.
That is why (gasp) MDs often DO NOT TREAT those and just suggest periodic psa blood tests to see if the growth is linear or exponential in the psa-exponential means the tumor has turned aggressive or metastasized.
The "anaplastic" tumors kill quickly. That is why they are operated on or treated.
Note: there are many ways of treating prostate tumors including focused infrared.
2. Yes, my MD does give me special insight and knowledge, just like your Phd gives you insight into string theory. Not all doctors are procedure crazy (just most US ones).
3. To my mind, chemotherapy and radiation should be used as a last resort, not a first---new treatments involve monoclonal antibodies, and stimulating the immune system.
Also, when a small sample (biopsy) of the tumor is available, it can be used to produce personal targeted therapy.
3. Tumors ARE omnipresent in the body...mutant cells crop up continuously but are mopped up by our immune systems, intrinsic and adaptive. It is when they escape the surveillance and reach a critical mass, that our evolutionary systems are overwhelmed.
The intrinsic system was fairly recently discovered (ie how it works) and there are innovative ways of bootstrapping it to kill tumors without nuking normal cells.
4. Just like physicists, there are smart doctors and dumb ones. Also, there are those who are tied to mainstream protocols and those who are not. Some of us have other advanced degrees and read books.
I do agree that often by the time treatments etc have reached the populace, that, for many reasons, the options have tunnel vision (legal reasons, regulatory reasons, in the US, financial reasons, etc) and that there are many routes abandoned in the past that may be resurrected (Coley's toxins, phage therapy for infections) as, say, antibiotic resistance accelerates.

As Leslie Orgel said "Evolution is smarter than we are"---
No one in Canada is treating every patient as a cancer patient. It is interesting how many people are conspiracy theorists when it comes to MDs, but flock to homeopaths, naturopaths and other ridiculous Smoits and Elmer Gantrys of biological sciences.

Dear Gordon, could you please at least show me a paper where this 15-20-year timescale is defended by some evidence?

My PhD isn't giving me any supernatural skills to determine the right values of things in the Universe without either measurements or arguments. But that's probably a difference between physics and medicine. Physics is a science rooted in the evidence, medicine is a form of shamanism that sometimes uses science but sometimes uses the old shaman authority-based methods - whatever is more convenient for a physician.

Homeopathy works because credulous people do not know what the placebo effect is. Their "experiments" are anecdotal in the extreme (my auntie had this xxxx, stood on her head and said drat three times and it went away, so do this :) (there is a smiley).
As interesting as your etheric theory sounds, it is really high on the crackpot scale....way, way to the right of the Gaussian, but I am sure if you wrote a book about it, it would be a best seller. Try "Extraordinary Popular Delusions and the Madness of Crowds"--a wonderful book that "cures" crackpottery...the cure is miraculous (sort of like homeopathic cures).

Good for you, and for it. ;-)

The literature is somewhat inconsistent but there are lots of powerful papers, like this paper with 200+ cits,

http://jnci.oxfordjournals.org/content/96/14/1094.long

that concluded that the reduction of the risk is huge, indeed.

Just google survival times for well-differentiated prostate tumors yourself Lubos. Stop fixating on the numbers I pulled out of the air--they are approx right. You don't understand that some tumors are indolent and others rapidly evolving and aggressive----prostate tumors is a set with many subsets and treatment depends on that. I absolutely makes a difference to survival in certain individual cases, the same as breast tumors. It absolutely makes a difference http://www.cancer.org/cancer/breastcancer/detailedguide/breast-cancer-breast-cancer-types
There is little point in arguing with you about this stuff. It is sort of like me arguing with you about papers on heterotic string theory.

Sorry, Gordon, prostate cancer and breast cancer just don't necessarily follow the same laws, timing, classification.

The paper that shows that regular mammography is useless in practice is a paper about breast cancer only and I won't immediately deduce any direct conclusions about prostate cancer because such a reasoning would be totally sloppy.

The only timing mentioned on the page you linked to is one that says that a form of cancer appears because of a previous treatment 5-10 years later. This isn't even remotely the evidence I was asking you about.

If we had a disagreement about heterotic string theory, I would lead you to the very focus of the disagreement and analyzed the finest detail you would ask for. You don't do anything like that - you are just referring to some supernatural skills to guess the right answer and "debunk" papers without anhy counter-evidence, skillls that you must have because of your occupation or degree. I was joking but it seems to me that this is really how you're thinking. Sorry, I don't respect any authority based on a similarly extremely shaky ground.

Lubos, there is loads of evidence. Things are not so simple or black and white as you seem to think. Einstein's warning not to make things simpler than they are is certainly true. Because i don't want to waste my time scouring for good papers amongst the thousands does not mean there is no evidence.Obviously I am feeling very frustrated by this blog post and by what I see as simplistic thinking prompted by media reports in people with no expertise in immunology and oncology.
In short, as you like saying when you are frustrated, "pearls before swine", even stubborn genius swine :)
I am much too busy to waste more time on this.

You are putting way too much faith in one (large) study. Things are not so simple as you think. You also seem to look on this as an intellectual exercise. I have operated on and treated people with these tumors for over 30 years, and have seen some live and some die. The sort of studies that "show" that mammograms and PSAs make no difference to population survival figures are imo always flawed because individual patients are saved in the right cases.
Tumors are not homogeneous. I think if you were immersed in the medical culture, you would understand and also understand the motivations of various authors of studies. Often a medical study that makes some Delphic pronouncement definitively, a year later is definitively negated. I don't really care if you don't respect my opinion on this--you should, but wtf. I never set out in these posts to make a case based on a paper fight, but, to put it mildly, the study's conclusions are controversial in the medical community. But you wouldn't know about that.
Some years ago, studies "showed" that hormone replacement therapy with estrogen increased risks of breast cancer. Then it was shown that more cancers were being diagnosed (estrogen receptor positive ones); now it seems that the culprit is progesterone, not estrogen. It is a prudent idea to place a mind holding pattern on medical studies for at least 6 months.

too narrow column

Wow!, Lubos. You said, “-medicine is a form of modernized shamanism-“.

Perhaps your doctors in Czechia are total crackpots but you would be very, very foolish, indeed, to so dismiss the doctors that my wife and I rely on in California. Our doctors are professionals in every sense of the word and, believe it or not, many of them are your intellectual equals. They save lives and prevent human suffering every day, including ours. I have enormous respect for the medical profession and I think you should too.
Gordon is not my doctor but I have every reason to believe that he is a credit to his profession and I would be very fortunate to have him as my primary care provider.
I would humbly suggest that you take him seriously just as he should take you seriously as a physicist.

Thanks, Gordon, for the reference but i have just made my position clear in my above response to our host.

I love you, Anna, but I have not read such bullshit in a very long time. Holy cow!

Universe has a tendency towards Development,
not Death by Entropy.

Well said, Ann. Facing our mortality is a necessary key to successful living, isn’t it?

Dear Gordon, I am no swine and I am working hard to learn about cancer from all sources that have something meaningful to say - which unfortunately didn't include you in this case, sorry.

This is about the quantification of benefits of a particular procedure and public health policy based on it and you have shown vastly more reasons to think that you are simply biased and financially vested than evidence. Check what you have shown and you will surely agree.

Dear Gene, there was no fear in the original paper I promoted.

The radiation from Fukushima is small and the radiation from X-rays methods in medicine is arguably "small", too. But it's clearly not negligible and in many cases, it may exceed any benefits.

It's not a fantasy that women have been killed by the treatment by getting a kind of cancer that only arises due to the radiation treatment. See in particular the paper about the cases ironically mentioned by Gordon:

http://www.ncbi.nlm.nih.gov/pubmed/12963926

55 women got cutaneous angiosarcoma which is only acquired as a result of radiation treatment. The survival rate for this condition is just 20%. I think that to remain silent about similar negatives of similar treatments is fraudulent - in fact, it is mass manslaughter.

I am just saying what I was always saying. Medicine as a practical occupation isn't science according to the normal hard scientific definitions of the word. It's reflected at all places, starting from the ludicrous low-confidence-level standards "sufficient" in medical papers to the actual practice that is only loosely connected to the research findings.

And I know that Gordon was eager to "cure" conditions he had absolutely no clue about, without ever seeing the potential patient, so I just don't trust this kind of doing things. It's shamanism and group think.

It is or should be a science-inspired profession but the work in it isn't really doing science itself, and the people aren't really validating their opinions. they're mostly parroting what they've heard from others who were also not validating it, with some extra bias for the doctors to help themselves financially. And indeed, papers that could imply negative changes to the funding are immediately - and without evidence - being attacked.

This applies to Czech medicine as well as Canadian or U.S. medicine. I have some experience with both Czech and U.S. medicine. It is silly for you to try to lower my credibility by the nationality-based attack: in the overall, our healthcare system is as good as the U.S. one.

Dear Gene, I think I have put enough disclaimers to show that it is not "my theory". It is a "theory" with ancient roots, proposed by people who do not know physics and have just a terminology of "energy and "vibrations". Humans need explanations and causes and that is the way they explain it to themselves.

On the other hand I have my experience with the method and it is positive in its effects. Thus I expect that at some point a physical theory will be found , of which the above will be a distorted myth.

Dear Anna, excuse me for butting in. I don't have a dog in this fight, but I can't help wondering why you do not even consider the possibility that no present or future physical theory explaining the efficacy of homeopathy exists and that instead a "double placebo" effect explains everything.

The first part of this effect is that physicians offering homeopathy (and probably even so-called naturopaths without a medical degree) are a self-selected group marked by idealism and a people-centric approach. They spend more time on patient interviews and they listen more intently to what the patients tell them. Most of them also genuinely, sincerely believe in the efficacy of homeopathic treatments. They exude a glow of positivity, which some see as fanaticism, to others it is inspiring and empowering.

The second part that completes the picture is patients' self-suggestion: encouraged by anecdotal "success stories" and by the belief of their doctors (or naturopaths), the body's considerable powers of self-healing are activated. More than once I have been told by a believer in homeopathy that they used to get frequent colds (sniffles, coughing, elevated temperature) but since taking homeopathic globuli they are free of recurrences. I have no reason to disbelieve them. The psyche is known to be intertwined with the body's immune system. Autosuggestion, coupled with an increase in "taking care of oneself" spurred by the attention received from a physician, is sufficient to bring about such a change.

Sadly, I cannot say the same for the cancer patient I knew who placed all her hopes in homeopathy. There is, after all, a limit to what autosuggestion can accomplish.

But in addition to the psychological devastation that comes from disappointed expectations for a cure from a terminal disease, there is also the "nocebo" effect to consider. The mirror image of the placebo effect, this denotes an adverse effect in the absence of a physical mechanism that could explain it. Since I am not in the medical field, I won't presume to write more about the nocebo effect, but you can easily find more information on the Web.

In previous exchanges with Gordon I had accepted the possibility that what I have seen in myself and my near and dear ones comes from the placebo effect, and stated that in that case it is good that we have collectively as a family found something that triggers the placebo effect. After all it has maybe 30% cure rate and is very much cheaper and no side effects .. If we manage to get that to 90% ( since there are a number of us) great.

The MD we go to always asks for diagnosis by specialists if something serious is happening before prescribing the homeopathy and would never dream of treating anybody with cancer just by pills. Rather he prescribes homeopathy that alleviates the side effects of surgery . After all a broken arm is a broken arm :).

The reason I expect a physical explanation of this "dilution and shakings" is because physics has explained a lot of things unexplainable in the 19th century when this therapy started. After all the placebo effect is still unexplainable except with handwaving like "psyche" ( soul) etc, not too far away from the etheric mold after all.

As for one molecule in a zillion, theY have found that butterflies can detect 1 molecule in a cubic meter of air of the pheromone and find a mate kilometers away. The physics explanation I have read is that that single molecule during its brownian motion at temperature T, radiates specific electromagnetic photons that fit the antennae in the insect's reception center for pheromones.

This is not too different from the model my colleague was trying to set up in water, that the shakings would generate "holes" with the signature of the seed chemical, which could have a similar effect on the field of the cells which balance the immune system, i.e. alert them to react. Unfortunately polywater was shown to be due to contaminations.

I am NOT CLAIMING this is the mechanism, I am just offering a potential model within the existing physics framework that might be tested experimentally sometime.

If a system is decidable it must be complete.
For instance, full arithmetic is not decidable, neither complete.
Stephen Wolfram, mentioned by Luboš below, speculates that
"undecidability is common in all but the most trivial physical theories".
I'm not sure why Luboš is so confident in accurate enough numerical simulation,
but I think that his point is that physical world only makes use of the decidable part of mathematics.
In fact, many mathematical systems used in physics, like lattice theory,
projective geometry, and Abelian group theory are decidable, while others, notably non-
Abelian group theory are not (A. Tarski, Undecidable theories)

"And I know that Gordon was eager to "cure" conditions he had absolutely
no clue about, without ever seeing the potential patient"

That is so wrong in in so many ways, as was your comment about my being biased by financial concerns. We are not paid to do tests here in Canada. We have no need to see more patients---we are totally swamped.
You are also confusing medicine at the patient level with the sciences of oncological research, immunology,etc...but there is no telling you this because you are making yourself an expert at these things through self study....read some Alexander Pope ("a little knowledge...).
Trying to pigeon-hole me as a biased non-scientific doctor tied to med-biz is simply stupid. You sort of know me. I have a broad scientific background including a stint at a cancer research institute that was treating melanoma patients with adjuvant-enhanced inactivated tumor cells to stimulate their intrinsic immune system.
I will not add to anything on this particular blog post because your mind is slammed shut... ( you are not a swine--I was pointing out my frustration and quoting you when you were irritated that people were commenting without reading your blog post.

As a second further reply, it has been found a strong connection between the halting problem and quantum physics, leading to undecidable measurement, according to http://phys.org/news/2012-07-classical-problem-undecidable-quantum.html (pdf: http://arxiv.org/abs/1111.3965 )

I welcome studies like this one, Lubos, if it can de-emphasize the importance of preventive medicine, and especially so-called "wellness programs." I can't think of a more wasteful use of our healthcare dollars than for employers to use their earnings to pay for wellness programs for their employees. Wellness programs are based on good ol’ common sense, so these programs should cost hardly anything to run. But the truth of the matter is that those in the wellness industry will find a way to overcharge you for giving out common-sense information. I already see this happening at the hospital where I work. The hospital has recently hired a gold medal winner at the 1999 Pan American games with a PhD in “Human Studies” ( I suppose that’s the opposite of “non-Human Studies”) and is paying her six figures to tell employees to do such common sense things like eat right, don’t smoke, look both ways before crossing the street, and always wear a seat belt when your behind the wheel of a car. Sorry, but this is something that a minimum-wage daycare worker is more than qualified to do. What an absolute waste of healthcare dollars!

Don't get me wrong, but I believe that preventative medicine is a bit overrated. Think about it, obesity has reached epidemic proportions, despite there being a whole slew of diet and exercise programs made available free of charge to the general public. (Michelle Obama and her "let's move and eat healthy" campaign deserves some of the most recent credit for this wasteful use of taxpayers' money.) This is why I believe ObamaCare will failed to achieve its primary goal, which is prevent many types of illnesses, chief among them is breast cancer. Keep in mind, ObamaCare mandates that patients pay nothing out of pocket for mammograms and other preventive screening tests. This will result in higher healthcare costs with very little to show for it terms of preventing illnesses.

Even though preventive medicine, aka primary care, has been short changed for years and deserves more funded, this shouldn’t be done by underfunding emergency and rehab medicine, aka acute and long-term care, respectively. Needless to say, most preventative medicine requires self-motivation. This means that if patients aren’t motivated to get a flu shot every year, eat right and exercise regularly, or stop smoking and wear a seat belt every time they get behind the wheel, no amount of prevention can change that fact.

Tegmark is correct on reality being nothing but a mathematical structure (literally), however, he is most likely wrong about the multiverse.

.http://www.qsa.netne.net/a.htm

If you look at the population density of stars (and by logical relationship, planets) in areas of the galaxy, then the central "bulge" the Milky Way galaxy is where all the action is, by several orders of magnitude. Therefore any intelligent life is by the same margin more likely to exist in this very high star/planet density part of the galaxy. Now where in this galaxy would such a species look for other intelligent life? The same high density area of the galaxy. There may be many intelligent species interacting with each other as we speak and we will never be a part of it because no one would bother to look out at the "boonies" part of the galaxy that we inhabit.

Those of us who step into the realm of physics from outside are at once met by an atmosphere of acrimony and insults -- crackpot being a favorite term of abuse. I was once tempted to take Jack Sarfatti seriously until I discovered that he at one time took Uri Gelller's spoon-bending seriously, having studied it and being fooled by it. The insults are somewhat amusing and make this most beautiful subject even more entertaining.

Dear Lupos. As a Platonist, you say that we discover pre-existing patterns by doing mathematics. What if the discrete disconnectedness of objects we perceive is merely an illusion? Then exact isomorphisms are impossible and the things we perceive can only be approximated by mathematics. Structures like objects, biochemistry, minds and computers are only seemingly discrete because they emerge in a metastable way from a possibly non-mathematical structure, a structure that cannot be described by our mathematical means. Where do mathematical patterns preexist then?

Or do you mean that discrete structures such as our brains yield the potential to produce all mathematical theorems (to a certain finite length) and therefore, when doing mathematics, we explore and therefore discover the theorems that are producible within this system?

Have not had time to respond until 'now. Your reference specifically points out the difference between US/Canada and almost the rest of the worlds written and spoken English. Well, dear Lucretius, Mr. Motl has an interesting diction to say the least, but his use of color, center, theater etc... lends one to infer his use of American/Canadian english is dominant. The world 'maths' is crossing over, albeit slowly into the US/Canadian system and to our ear it sound 'low' and uneducated. Your aligning Luboš' writing style to British/Australian I find surprising, I feel it is pronounced Americanized. That said, amazed how quickly and fun you choose to covert my "I despise the use" to "I despise the people". You are welcome to assume some American and Canadian are like that, but "I despise the use of" maths and feel math or mathematics is far more eloquent. I guess I should rush to judgement and determine that from whereever you come, are largely impudent, arrogant, miscreant's who choose to label people by their passport rather than their believe. But i will just keep judging England and Australia on their failed political analysis of climate change and cheerfully leave them with their own problems and keep mine any day.

Wow, my recommendation to Lubos was not rhetorical while your acerbic attack against a nation based on a twitter sized comment clearly shows some animosity. I will put my children, my students and most of my country up against most of Australia, England or any "fill-in your choice of English dialect" school system any day. My students, on average, are well prepared and reasonably versed. I will put our 'dysfunctional' education system up against any European 'tracking' system as well. Bash Americans all you like, continue to show us the depth of you modern cultural anthropology and how accurately it reflects who I am. Lastly, trashing Americans is just so much fun between you and yours, but I smile as I flip you off and am glad you represent the pinnacle of whatever education system wrought you. They deserve you.

Sounding "Low and uneducated" ? Sure people like Penrose, Dirac, Turing all must sound pretty dumb to an American math prof. I for one think maths is more accurate given that there are so many branches and parts.

I am an American and have seen five children, mine and others through our schools.
Fortunately none of their professors was you. Unfortunately none was the professor you think you are. Given your attitude it is you who need teaching.

Thank you. I just read an account of the "perceptonium" paper, realized that whenever contemporary cosmology (or whatever the "perceptonium" paper is) sounds like BS, it's likely to have Tegmark's name attached to it, felt compelled to Google "Max Tegmark is full of shit," and the first interesting-looking search result was this article. Thanks again.

@Rehbock, I comment that I feel math for Lubos to use is more eloquent. Get "mis place patriotism or ignorace" crack. I comment that the animosity towards american bubbles up quickly from only my opinion on Lubos' diction. They then continue to state we are dumbing down and are being classified as dysfunctional.

I then state our educated are well educated and could stand up to anyothers. And semi-tactfully them to bugger off.

Your response is: You don't like, me and my attitude. I will listen and kindly respond if you like. Curious what indiscretion I passed over?

Well, I have not spoke with Penrose, but I have heard Dirac and Turning and in their writings they don't use Maths but math or mathematics So these great men sound just fine to most american ears. As to low sounding,among many intercity youth and extreme rural young expression that are conjugated poorly or out right miss used, they sound 'uneducated'. Lastly, you may like the variation on math to maths as better, few if any educators use it in American Schools. And having searched the Turning archive I have not found one reference to maths, but many to the mathematics only. So perhaps you can just enlighten me as to how my comments enlighted you as to how I must surely do a disservice to my students?

Hi, just a few words so that you know where I am on this issue. I don't really care much.

Normally, I am conservative, including the usage of words such as "mathematics" (good) or "maths" (bad). Still, I find the efficiency of formulations important and "maths" is shorter. And because "maths" is used by some native speakers whose English still looks vastly superior over mine, I think that "maths" must be OK enough for me, too.

It is incorrect to consider others are inferior and ignorant by whether math is it's own plural.
The America is better than anyone attitude is also not agreeable with me. I think Lucretius and dhtow1 said it well.

That the Universe is completely described by mathematics is indeed an old idea, however Pythagoras and Galileo did not provide enough arguments why it is so! It is more like a postulate in their philosophy. It is easy to say that the Universe is mathematical but we need epistemological and ontological basis for such claims. I saw in your website the link to ontic structural realism (OSR) so I guess you are familiar with it. OSR indeed provides good arguments about the underlying invariant structure of all our theories.

I think Immanuel Kant is the first philosopher to provide the strong arguments why the Universe is described by mathematics. If you are familiar with history of philosophy, Kant reacted to the famous debate between Rationalists (Leibniz, Descartes, Spinoza) and Empiricists (Locke and especially David Hume). Rationalists claim that the source of knowledge is reason and innate ideas, while empiricist claim that the source of knowledge is experience through the senses. Both are right from their perspective. Kant said that to speak about innate ideas in our mind which ground mathematics, metaphysics (a priori knowledge) as rationalists did is lazy business. David Hume has shown that everything comes from experience but he had problems with establishing mathematics on firm ground because maths speak of experience a priori. He could not explain how mathematics is possible! Kant tried to defend this a priori knowledge (mathematics, theoretical physics) and so-called synthetic a priori judgments. That's why I have used Kant to model our cognitive framework (and the Universe as it appears to us) as a quantum computer defined on a grid of cells. I claim that this grid is invariant structure within which all our thoughts, knowledge and theories originate. The structure OSR seeks.

Kant had influenced such mathematicians as Henri Poincaré and David Hilbert. In philosophy of mathematics Kant belongs to intuitionist school. It is also interesting to study the logicist school, that is Frege, Russell. I know that you are involved with FQXi. I claim that we will not understand ultimate reality unless we view everything as a system of mathematics, theoretical physics, philosophy of science and cognitive science. Cognitive science is of absolute importance in understanding ultimate reality because all our thoughts about the world originate in our brain. I know that you come from strictly scientific background but philosophy of science, philosophy of mind cannot be left out if you want to understand the ultimate reality.

It seems that you have buried the philosophy of corporeal nature. This is the true purpose of proper metaphysics of corporeal nature - to assist mathematics and physics. They should go together. It does not matter that people did not know about the Higgs boson or the mathematical description of general relativity 200 years ago. What Kant and Hegel knew is fundamentals - how our knowledge about the world in general is possible. If you know the roots of your knowledge, the epistemological basis of mathematics and physics, everything else is just details. To understand ultimate reality we must understand how we understand things in the first place! That is, we must have the picture of our cognitive faculties in general. This yields the big picture of the Universe how it appears to us.

That's why I took Kant who asked and provided answers in his work to the questions: ''how is mathematics possible?''. ''How is physics possible?''. ''How is metaphysics as science possible?''.

Max, RE modus ponendo ponens , ("P implies Q; P is asserted to be true, so therefore Q must be true." )

I think it's a mistake to place such confidence in modus ponendo ponens. E.g. B. Russell remarks in an essay (Chap. 16, Non-demonstrative inference) in My Philosophical Development (Routledge, London)

"I came to the conclusion that inductive arguments, unless they are confined within the limits of common sense, will lead to false conclusions much more often than to true ones."
I think that this is too little appreciated by all kinds of scientists today. Perhaps you should consider Russell's arguments in that chapter.

Max, RE modus ponendo ponens , ("P implies Q; P is asserted to be true, so therefore Q must be true." )

I think it's a mistake to place such confidence in modus ponendo ponens. E.g. B. Russell remarks in an essay (Chap. 16, Non-demonstrative inference) in My Philosophical Development (Routledge, London)

"I came to the conclusion that inductive arguments, unless they are confined within the limits of common sense, will lead to false conclusions much more often than to true ones."
I think that this is too little appreciated by all kinds of scientists today. Perhaps you should consider Russell's arguments in that chapter.
I'm at a slight disadvantage here in that I can't lay my hands on a copy of the book right now but on the basis simply of what you have written above it sounds to me as if you have completely misunderstood Russell.

First of all, judging from your quotation, by "non-demonstrative inference" it seems that Russell here simply means what others might call inductive reasoning i.e. "induction". (Maybe he talks of other things too, such as heuristics, but I think most of us would assume he's primarily talking about induction when he uses such a description as "non-demonstrative inference". At least that would be default assumption in the absence of a specific classification.)

That being so, I have to say that modus ponens is NOT "non-demonstrative inference". Quite the opposite — modus ponens forms part of deductive reasoning, and only deductive reasoning. Indeed, it's the ONLY part. Deductive reasoning could equally be called "demonstrative inference", which is what I presume Russell is doing here.

As I said, I don't have access to the book, so perhaps my guess that Russell simply means induction (inductive reasoning) when he talks of "non-demonstrative inference" is wrong. But I very much doubt it. And if it is wrong then, again, my guess is that it is wrong only in so far as it doesn't also include possibly other types of reasoning (e.g. heuristic, which types I wouldn't expect Russell would spend any time on) since the expression "non-demonstrative inference" has a rather general ring to it.

Most of the relevant parts of chapter may be read via googlebooks.com (Key-terms: Chapter 16, Russell, My Philosophical Development). His arugument applies equally to "induction" and "deduction" since the point is that the quality of each turns on the validity of the logical inferences employed, not whether they are operate via a deductive or inductive use of empirical data.
Heuristics are merely more or less useful 'reasoning techniques'--aids to logical thought--and they also apply to both inductive and deductive processes. An analogy is a type of heuristic device--it may, according to the particular instance, be valid or invalid, just as both poor deduction and poor induction can produce erroneous conclusions. The essence is not in one or the other but in the virtue of the lack of it in the soundness of the logical relations of the premises and the conclusions on which the inferences rely.

John - You are,of course, correct regarding the quintesentially deductive nature of modus ponens.
While I have absolutely no idea what *anonymous* was attempting to convey I think that Russell was writing about the inclusion of uncertain or probabilistic premises within valid deductive arguments.
Many philosophers of that time thought that only axiomatic certainty was scientific.
If such things interest you, the Australian philosopher David Stove wrote in defense of induction (which is really just Bayesian inference). Much of his writing is available online, including some cogent criticism of Karl Popper and a wonderful essay titled 'What is wrong with our thoughts?'.

RE: "While I have absolutely no idea what *anonymous* was attempting to convey I think that Russell was writing about the inclusion of uncertain or probabilistic premises within valid deductive arguments."
To find out what I meant--and, more importantly, what Russell meant--read the relevant chapter I cited. Few writers are as clear as Russell and you are clearly confused about (or simply ignorant of) what are Russell's points concerning these matters.
Another cite from the article:
" I realised that all the inferences used in both common sense and in science are of a different sort than deductive logic, [ here, Russell is referring to formal logic as a branch of mathematics ] and are such that, when the premises are true and the reasoning correct, the conclusion is only probable."
This passage, by the way, is the one I'd intended to cite in the first post of mine, above.

I have just read the relevant chapter (again), and have just replaced the book in it's spot on the two shelves devoted to Russell. John's reply to you was correct and so was my reply to John.
Yes, Russell was always clear, but he was often wrong. His writings on these matters are no longer taken seriously, and with good reason. His Human Knowledge is also, in hindsight, almost risible.
You, it seems, are always wrong and often unclear (admittedly a non demonstrative inference; a phrase which goes back to Hume) - e.g. -
1) The passage you intended to cite makes a clear distinction between deductive logic and what he thought of as scientific inference, and yet you would cite it to cast doubt on modus ponens - wrong
2) your reply to John (just below) is almost entirely gibberish - unclear.
I don't think you understand Russell or any of the issues he was addressing.

RAF III,

Thank you very much. :) You saved me a lot of hassle.

Two whole shelves, eh? Now that's what I call keen! :)

I like Russell too and have read a few of his, but much as (some) philosophers are fun to read, one always finds 'flies in their ointment', somewhat like discovering a turd with a hideous brown miasmic aura at the bottom of a nice swimming pool after you've spent an afternoon diving in and splashing around, but just not quite as unsettling. The discovery doesn't stop me from doing it again though — reading philosophers, that is. The turd on the other hand ... well, it's a turd! And you don't want one of those on your hand, or anywhere else. Ever. :)

And thanks for the heads-up on Stove. I had heard about him around 20 years ago but never followed it up as I was philosophied out at the time. I'll put him back on my to-do list.

If you're a woman ... mwha! XXX. If not, I'll leave it with a thumbs-up.

However, I strongly suspect it'll have to be a thumbs-up, with probability approaching 1. :)
___

Anon,

I skimmed that chapter with its missing pages. I read nothing to change my mind. My comment stands.

Just a thought, but have you heard the one about the two builders and the professor of probability logic? If not, I'd like to ask you a few questions. :)

On second thoughts, I'll cut to the chase. I can't tell if you have a goldfish or not but I'd put my shirt on you not being overly familiar with the statement/propositional calculus.

If so, I'd recommend any book on it (usually covering the predicate calculus too) that's ordinarily recommended to undergraduate mathematicians, as opposed to books for philosophers — I never liked those books; there was always something odd about them; but maybe they've gotten better; dunno.

John - Thanks for the thumbs-up.
I've been a voracious reader since childhood and have kept every book (bought, inherited, or 'other') I've ever had. It makes moving house a nightmare. What you call keen others might call a psychological disorder.
I wouldn't go so far as your swimming pool example, however.
In many cases the conversation has simply moved on and the arguments have been rendered moot. Does anyone today,concerned with probability theory, care that Russell found Keyne's theory of probability defective because Keynes viewed probability as a relation between propositions rather than between propositional functions?
I also think it's important to understand the intellectual and cultural context in which such things were written in order to understand and appreciate what was meant - something that young and callow people seem unable to do.
Speaking of which, I expect anon to come back at me with some damn fool nonsense, and while I'm happy to have saved you some hassle, I hope you realize that someday you may have to take a bullet for me.
Cheers

RAF III,

Haha!

I found the essay you mentioned by Stove (What is Wrong with Our Thoughts?).

What a fun read. Great stuff.

Yes, that's much more to my liking. And it's funny too. I think Stove would make an excellent hooligan — he does seem to enjoy ripping each of those fakers and windbags a new arsehole. Some nice doses of ridicule there.

I'll find some more of his stuff and read that too.

But one thing about him puzzles me. Given his views and his experience (for example, he alludes to the hell of marking a myriad of bozo undergraduate essays) I wonder why he persisted with philosophy at all. I don't understand that. Once he worked out that it was a load of crap why didn't he jack it all in and turn his mind to something more rewarding? That was a rhetorical question by the way. I don't expect an answer.

Another thing I don't understand. The French are nothing if not proud of their nation. So why then do they appear put up with the likes of Foucault and the rest, let alone pander to them? Can't they see they're a national disgrace? Jean Bricmont (with Alan Sokal) had a go at them but I understand he's a Belgian, not French. How come we don't hear home grown criticism? Maybe there is such and it's just that it doesn't travel much? That was also largely rhetorical, but if Shannon is reading this then maybe she will shed some some light for us? :)