Sunday, November 19, 2006

Even creationists may be right on the money

Do you think it is possible that I could ever subscribe to every word in an article written by a creationist in an inexpensive tuxedo? You bet. His name is William Dembski.

In the first paragraph, he quotes and endorses a characteristically incoherent and absurd pseudoargument of a critic of physics whose goal is essentially to "prove" that science can never make any progress without knowing the answer in advance and without the guiding hand of an intelligent creator. ;-)




Technically, Nature can't naturally lead to better forms of life in the landscape of possible DNA codes, and people can't learn anything from string theory because in both cases any attempt to do so is just like trying random places in a landscape, these Gentlemen argue.

The quotation of the pseudoargument is authentic which is why I could also subscribe to the first paragraph. More importantly, William Dembski's summary is:
  • There’s not much difference here between [the physics critic]’s argument against string theory and ID arguments against natural selection. I have yet to read the new books by [two critics of physics whose names are not important], but I’m told it is astonishing how closely the controversies over string theory reflect the controversies of neo-Darwinism. In this regard, Ed Witten’s role in physics parallels Richard Dawkins’s in biology.

Well, very true, Prof Dembski. This isomorphism is also one of the reasons why one of the good reviews of one of the books was named Teach the controversy.

Let us analyze the question more carefully. The question is:

Is there a free lunch?

It is a rather important question that the kids should understand before they decide to do anything remotely related to science because when they're 50, it can already be too late to correct a wrong opinion about this fundamental issue.

We will be talking about three basic types of free lunches: the free lunch of energy, the free lunch of self-organization, and the free lunch of knowledge. The answer will be that although the "no-free-lunch theorem" may be true and useful in various contexts and at various levels of approximation, the "no-free-lunch theorem" certainly breaks down if you apply it to all of history or the whole Universe or all of science. Once again: it doesn't matter how strongly you believe that the "law" can't break down: the "law" clearly does break down.

In politics, these questions would get completely new dimensions. For example, trade is said to be a free lunch because both sides benefit. On the other hand, many redistribution policies neglect the fact that there is no real free lunch arising from redistribution. But I will avoid politics in this article.

Situations that don't allow a free lunch

As these non-scientific examples indicate, there are important situations in which it is correct to say and realize that there can't be any free lunch. In the context of the conservation of energy, we know that the energy must be conserved whenever the background spacetime geometry resembles the Minkowski space or any other static non-compact geometry.

The conservation of energy in physics is equivalent, as Emmy Noether has proven, to the time-independence of the laws of physics i.e. to a symmetry. In the context of the Solar System or during any event we ever consider on the Earth, the energy conservation law holds. You can always compute the energy of the system as the sum of various components and this sum is never changed. Most of us should know why this fact is important.

Free lunch: energy

Does the conservation law hold in cosmology? The answer is a resounding "No". General relativity doesn't allow you to define any meaningful global conservation law in a compact or generic universe. The general background geometry in general relativity is not static or time-independent. This is why Noether's argument breaks down.

The stress-energy tensor is locally conserved in the sense that the covariant divergence vanishes. But this local law can't be extended into a global law because the derivatives in the continuity equations are covariant. Alternatively, it is because the energy stored in the gravitational waves is locally ill-defined.

In the context of cosmology, the violation of the energy conservation law is very clear. The total energy stored in the latent energy of dust doesn't depend on time. But the energy stored in various forms of radiation such as photons decreases inversely proportionally to the size of the Universe. It's because the wavelength of every photon is expanding proportionally to the size of the Universe and the energy of a photon is inversely proportional to the wavelength.

If we know forms of energy that do not depend on time or that decrease as the Universe expands, are there also forms of energy that increase as the Universe expands? Of course, there are. All forms of energy whose equation of state is on the other side from the dust than the radiation - namely all forms of energy with negative pressure - increase with time.

The vacuum energy density is both the extreme example as well as the most important example of such a negative pressure. If the vacuum has a nonzero stress-energy tensor proportional to the metric tensor, the magnitude of this tensor will be time-independent. It means that the energy density won't change with time which is why the total energy of the expanding Universe will grow as the third power of the typical linear size of this Universe.

There are two basic examples of this vacuum energy density: the cosmological constant and the energy density driving inflation. The mathematical nature is analogous in both cases although the values of the vacuum energy differ by 100 orders of magnitude or so.

The cosmological constant as we have known it since 1998 is very tiny from a particle physicist's perspective but it has actually already become the dominant portion of the Universe's energy: it represents 70 percent. This increasing domination is exactly due to the maximal buoyancy of this form of energy: all other forms of energy grow slower or decrease as the Universe expands. Eventually all of the visible Universe will essentially be an empty de Sitter space, dominated by the vacuum energy.

The other important example of the role of the vacuum energy density is the cosmic inflation. Its co-father, Alan Guth, has once said that

  • the Universe is the ultimate free lunch.

The huge mass of the particles that we observe in the Universe used to be explained by the assertion that "God is great" and some people still use it as of 2006. Radical materialists such as Vladimir Lenin believed that this huge mass has always been around. It had to be so because dialectic materialism would otherwise be in trouble. Needless to say, both of these groups of zealots were wrong.

Alan Guth, Andrei Linde and a few others have figured out that the Universe has probably undergone an era of a dramatic, exponential expansion at the very beginning. During this era, its linear dimensions grew by more than 25 orders of magnitude which means that the volume has increased by more than 75 orders of magnitude. Because the energy density was constant throughout most of the inflation, the total mass (and henceforth energy) increased by more than 75 orders of magnitude, too.

This natural solution of general relativity with a scalar field with a potential not only shows that the free lunch is possible but, in fact, our entire existence is due to a free lunch at the beginning. The seemingly unnaturally large number "N" of the protons in the Universe is naturally explained because "N" is proportional to the exponential of a more reasonable number and a mechanism exists that explains why the exponent is more fundamental than "N".

Free lunch: self-organization

The critics of biology often argue that the Universe can't spontaneously develop more complex structures out of simpler ones. We see that they are wrong every day as new and better types of MP3 players are being designed by various companies. We see that they are wrong in millions of other situations. But the critics argue that these examples are driven by some "intelligence", whatever its definition exactly is, and these improvements consequently don't contradict the basic intellectual "pillars" of creationism because there was no intelligence (except for God) before the humans were created.

Of course that their reasoning is thoroughly unscientific. Intelligence is just one of many aspects of the structures in the real Universe that keeps on evolving. The life that existed billions of years ago already had some kind of intelligence in it and this intelligence, much like other attributes, kept on evolving along the lines discovered by Charles Darwin. The intelligence of the creationists can also be viewed as an ancestor of the intelligence of modern humans. ;-)

But we have the second law of thermodynamics, don't we? According to this law, everything should be driven towards an ever increasing chaos. Is there a contradiction?

There is no contradiction. If you look at your fridge, it is able to cool down the food. A cooler tomato has a lower entropy than a warmer tomato. How is this decrease possible? It is useful to learn how the processes actually work. At any rate, there exist processes during which the temperature and entropy of a physical system decreases. However, the total entropy of the Universe increases because the fridge can pump the heat to its environment. Refrigerators are interesting machines that can prove wrong thousands of philosophers who would think that you can't ever get cooler because of the second law of thermodynamics.

The living forms are doing something similar as the fridge. Life tries many new possibilities and produces a lot of extra entropy and waste, but it also has mechanisms to help localized low-entropy structures to become more organized, less chaotic, and more complex. Natural selection plays a key role here.

Free lunch - knowledge

OK, so can we find new correct answers to scientific questions without having them at the beginning? Surely, there are many local situations in which the answer seems to be "No". Some scientists are often confused and try to pursue a strategy that is guaranteed to lead to no new solid results except for those that were assumed since the very beginning.

Other scientists, and sometimes the very same scientists as those from the previous paragraph, believe that the goal of science is to fill in some details in a picture of reality as painted by a 17th century philosopher because science is inherently unable to find anything new and it is unable to show that a particular mind from the 17th century could be wrong because there is no free lunch. Science as we know it is deeply flawed, they argue, and that's the trouble.

Be sure that their argument can't hold and doesn't hold at the level of entire biology or entire physics or entire theoretical physics. How do I prove this conclusion? The fact that we have clearly made progress since the ancient Greeks should be enough.

But still, you might want to understand microscopically how it is possible that science is making progress and finding answers to questions that were not answered in the past. How is it possible that we can suddenly prove that Leibniz was wrong even though he may have been smart and despite thousands of believers who would like to see him as a prophet? The mechanism of this miracle - called the scientific method - is somewhat analogous to the processes in the fridge or to the dynamics of life.

Science is trying many new possible experimental and theoretical avenues and it is pursuing many new ideas and playing with many new devices. Science combines them and re-combines them in many ways. Many people, including some of the critics of science, usually understand this point although some of the critics fail to understand that other people may be able to answer certain questions even though they - the critics - are unable to do so themselves.

But there exists a second point that is at least as important as the first one and that the critics of science almost never understand: science must also work with a trash can. Ideas and theories that have been falsified must be abandoned. Whether or not a theory has been falsified is often subject to fuzzy logic, much like other things in the real world. If you throw away a rotten apple, there's always a chance you will take it from the trash can and eat it if you're really hungry. If you abandon an idea because of a contradiction, there is always a chance that you will revive it if there is some shocking new evidence. Nevertheless, you still need a trash can, at least a fuzzy one.

This trash can mechanism is fully analogous to the part of the Carnot cycle in which the fridge heats up the environment. It is also analogous to the death of the mutated animals who are not viable. This mechanism is paramount.

If you abandon the second mechanism, the fridge won't cool your Coke, evolution or industry won't produce any new better life forms or products, and science won't be getting any closer to better and more accurate answers to scientific questions.

Now, you know very well that I am convinced that various theories of hidden variables and discrete quantum gravity, among dozens of others, have been a part of this trash can for many decades. But I would also like to emphasize another point: the sociological questions how science should work must be separated from the scientific questions - from the questions which scientific hypotheses are actually correct.

I personally view any analysis that tries to blur the sharp differences between these two classes of questions - science on one side and sociology on the other side - and to pretend that the sociological ideas can have direct consequences for science to be a perverse, irrational, and pernicious way of thinking about both sociology and science.

Such a mixing has been tried many times in the history of science. The Catholic Church wanted to determine the rules of astrophysics and biology by their dogmas. The Nazis wanted to suppress most of the theoretical physics of their era - because most of theoretical physics was discovered by the Jews - so they defined the so-called Aryan physics. The Soviets fought against genetics by promoting Lysenkoism that was more compatible with their goals and ideology.

I always wanted to believe that these infamous events from the 2nd millenium were behind us and no person with a science degree would ever start to do something similar, for example a campaign against a scientific theory driven by purely sociological, political, and irrational pseudoarguments that sound good to various easily manipulable and uneducated zealots who are good enough to create the atmosphere that makes some kinds of scientific results "unwanted". Clearly, I was wrong as a certain recent blue book has proven. Even though the year is 2006, the attempts to distort and contaminate science by extreme ideologies and to use sociological justifications to revive dead theories from the trash can are unfortunately alive and well.

Although the previous sentence is highly discouraging, I must conclude: that's my memo.

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