The inherent non-problem with science

A curious phenomenon in the philosophy of science is anti-realism – the idea that despite the success of science, it still fails to deliver an accurate, or even a semi-accurate, description of the universe, and can’t do this even in principle. This is a serious philosophical view promoted even by scientists and science-enthusiasts, despite what appears to me an obvious flaw – they have explained science away, but science didn’t disappear – a reductio ad absurdum if I ever saw one. An exemplar of this view is a recent post in Think Gene, a science blog (!), on the inherent problem of science. (I found it via John Wilkins’ response to the above post, which may be constructive, but I’ll take a different approach. Think Gene replied, feebly in my opinion, but judge for yourselves.)

The author, Josh Hill, challenges Bayes’ theorem, the foundation of science and of rationality in general. The problem with it, he argues, is that it is probabilistic in nature. Since we are not omniscient, we can only assign probabilities to our theories, not absolute certainties (both pro and con). Furthermore, for every set of observations there exist an infinite number of theories, so the money spent on the LHC to find the Higgs boson is wasted – even if we find what we’re looking for, we can’t be sure we aren’t fooling ourselves by working with a wrong theory (out of an infinity available to us). Next up is Heisenberg’s Uncertainty Principle, which supposedly crushes all hopes of a finite number of theories by principle, followed by a defeatist admission of humanity’s limitations. The readers obligingly agree, and the author proceeds with his daily affairs, talking about the latest scientific findings and theories as if he has never written a post that refutes the efficacy of his subject matter.

An equivalent of this is shooting both your feet off, and then proceeding to win the Olympics in the running competitions. I can only conclude that the shells were blank, and here’s why.

First, regarding the number of theories that may explain a given set of observations. The author says it is an infinity, since we cannot even in principle have absolute information about the state of the world. (The “impossible in principle” part is inaccurate – there’s no real uncertainty in the quantum world – but that’s irrelevant.) But why? Suppose we are omniscient – are we then bound by only one theory, or a finite set? And suppose we subtract the knowledge of a single atom from our omniscience – do we then jump to an infinity of possible theories, or is our search space still finite? When exactly does infinity creep into this knowledge reduction process?

Second, what sort of theories should we be looking for? Let’s take Einstein’s theory of general relativity. Supposedly we should find an infinity of competing, equally-likely theories. One kind comes readily to mind – take general relativity, and add little green men that do the real work in the theory. Any sort of such superfluous information can be added, as long as it doesn’t change the math. Let’s say bare-bones general relativity takes N bits to encode, and our expanded theories take N+M bits. But where is the justification for M bits of apparent knowledge? By themselves they are unsupported – shouldn’t such theories be penalized under Bayes? Occam’s Razor appears to me to be a pretty good pruning algorithm for theories we should not even include in our search space, although unfortunately I don’t know its formalization (yet).

What about theories that contain no apparent superfluous information, are equivalent to the orthodox theory, but are not isomorphic to it? It would be very interesting if such theories popped up – but have they? As far as I know, all competing and equally-performing theories in the past have been shown to be mathematically equivalent. On reflection this is not so strange – you can think of theories as functions that take initial world states and output expected world states. Equivalent theories that predict the same results are functions that on every input give the same output – sounds pretty isomorphic.

The “theory landscape” we’re left with now consists not of an infinity of equally-probable theories (with the probability of each approaching zero, since there’s an infinity of them), but rather a countable number of theories, where one is the most probable (general relativity), one or two are probable to a small degree (string theory, although actually there are many string theories, but collectively we might assign to them a probability on the order of magnitude of 0.1), and the others are very improbable (Newtonian mechanics at high velocities). If you insist on including the theories we have pruned away, they get infinitesimally tiny probabilities. (Since Bayes penalizes superfluous information and since all the isomorphic theories are written under the same theory.)

(This obviously omits all the theories we haven’t thought about. But that’s OK – they represent the incompleteness of our knowledge. Every scientist would tell you that we don’t know everything, and ask for funding to fill the gaps. Scientific progress ensues.)

Enter the age-old question: how can a high probability be equated with certainty? Is it not possible in principle that some of our discarded theories are still correct? Maybe general relativity is a mass-hallucination? How do we prove general relativity, or any other theory?

The short answer is that we can’t. The longer answer begins with asking: what does a low probability mean? The chances of winning a lottery are low. Some still participate, since they feel their chances are high enough to justify the ticket’s cost. But if their chances will visibly drop – the lottery will involve a million random [1, 50] integers – they will not even bother looking at the ticket vendor.

The same approach applies to theories. A very low (say, one in googol) probability of X means that it is not worth to invest even one neuron into the consideration of X. Thus, it is irrational to even consider homeopathy, given the knowledge we have today. I’m sure the author will agree with me on this (otherwise – will he be willing to increase homeopathy-related posts to an appreciable level?), so why the despair regarding science in general?

The author gives the very old example of swans to illustrate the even older problem of induction. But swans and the laws of physics are different types of things. First, we observe the laws of physics much more often than we do swans. Second, we know enough about swans to say that the color of a swan is not something ontologically special – we would not be surprised to find a swan of a different color. But we know enough about physics to say with certainty approaching 1 that an atom of hydrogen is and forever will be indistinguishable from another atom of hydrogen. The probabilities are so different, they aren’t even comparable.

The final death throes of realism in the author’s mind is a variant of pessimistic induction (as pointed out by John Wilkins), which appears to me suspect. Wilkins gives the standard answer, which I think is good enough. Or, as Eliezer Yudkowsky likes to say – the ratchet of science turns, but it doesn’t turn backwards. If the author really thinks otherwise – I dare him to second-guess the modern synthesis or germ theory.

Even if you, dear reader, disagree, then please answer this – how does science alone work, if it is indistinguisable from competing religious, philosophical and other disciplines? And will you, failing to answer this, act out on this conclusion and flip a coin next time your teeth ache to see if you should visit a dentist or a faith healer? And if no – why? To borrow another saying from Yudkowsky, it is not enough to claim that the world is nothing – it is also necessary to show how the nothing works. Good luck.