Thursday, 24 December 2015

Laws of Nature as Patterns

An old definition of science could be that science is the study of cause and effect in nature. The idea that causality is the central idea in knowledge goes back at least to Aristotle's four cause analysis of the world and in many ways this is what people believe science does today. Instead of directly citing cause and effect, it seems to me that the intermediate notion of the "laws of nature" is interjected; science studies the laws of nature, which are about cause and effect in nature. Simple, right?

I want to propose an alternate idea based on how I view science and in particular, based on how I see modern science handling data. There's a caveat before I begin: as usual, I think much more about the canonical status of physics in science than I do of other equally legitimate branches of natural science. So what I say relates most to physics and (perhaps) the applicability slowly decreases as we move towards more qualitative sciences. Or it might not - my point is that I am making a stronger case for science as most exemplified in the hard, mathematical sciences.

Scientists do experiments and get data. This data is put often into tables or graphs and analysed, whereby models are produced which explain the correlations in the data by causal mechanisms. The model, if it is a good one, will make other predictions which can be tested to see if it is correct, and the more it passes those tests, the more credence it is given. That is the scientific method of observation, hypothesis, testing, conclusion. There are two very similar problems I see with this process: an error in data analysis and a deeper philosophical issue that Hume would have noted.

It is drilled into every data analysis/scientific statistics student that a correlation does not mean a causation and yet this explication of the scientific method clearly makes that jump. The justification is simple: eliminate as many variables as possible and the remaining correlations must be causation. That is simply mistaken and the history of science is rife with examples of deeper explanations being found of natural phenomena which destroyed the previously perceived causal mechanism.

Hume would have heartily agreed with this objection and would defiantly disagree with anyone who tried to maintain that, whilst correlation does not equal causation, a lot of correlation does, in fact, equal causation. His problem was two-fold: the assumption that the correlations of the past will hold in the future is only based on the observation that the correlations of the past have so far held true in the future. But that is circular, since in effect it says that the future is causally equivalent to the past because the past is causally equivalent to the past. But again, Hume had a deeper problem that simply the problem of induction. His biggest reason for scepticism is that causality was not a superficial relation between objects, in fact, we never really perceive causality at all, we perceive effects and infer causation. He called this "customary conjunction", or basically, correlation. For all this scepticism (and Hume unlike others branded with this title really was a sceptic), Hume did still believe in cause and effect, he simply thought it was beyond our knowledge.

I am not sure if I believe in cause and effect, but I propose right now the weaker claim that science does not study it. Science studies data to produce laws of nature which are expressed mathematically because, at bottom, the laws of nature are patterns in observable variables or parameters. In other words, the laws of nature are patterns of numbers that describe nature. Let me give an illustrating idea to stir the intuition of this proposal and consider how this relates to epistemology and the metaphysics of causality (if causality exists at all).

Think of the positive integers: 1, 2, 3, 4, ... They form a nice set whose properties can be analysed to yield fascinating mathematics. Relations can be defined on this set giving it order, taking a pair of numbers to another in the set by multiplication or addition, and so on. The tools of mathematics are about seeing mathematical structure in the integers, seeing what symmetries it might have, trying to see what patterns it has. A simple pattern in the integers is that the numbers are alternating odd, even, odd, even.

What if we tried to apply the tools of old fashioned science to the integers? It would yield fictitious language about causality to something which exists independent of causes: the fact that 2 is even is not caused by the fact that 1 is odd, even though we could conceivably speak of it that way. Many of the properties of the positive integers can be spoken of in terms of causality, but it is a fiction of our language, not a fact about the set itself.

So, I claim, it is in science. Equations like Newton's laws are mathematical statements which should not be thought of in terms of causality but in terms of patterns. It is still possible to make if-then statements: If a force is applied, then an acceleration will occur. That is a statement about what the second law predicts and codifies. It is also important to note that I am not simply saying "science produces equations that have no necessary connection to what really exists." This view is not scientific anti-realism, it is congruent with a critical realism about science.

It is important to dispel the objection that I am merely playing with words and the if-then statements are exactly equivalent to causality statements. But I refer back to the case of mathematics: it seems clear that "if you add one to an odd number you get and even number" is not equivalent to "adding one to an odd number causes an even number." The first is true, and the second uses perverted language to try and express, it seems, the first statement.

The pattern view has several advantages: for starters, it is epistemically conservative and codifies what the science actually shows rather than trying to make it jump over the correlation-causation barrier in the data. It is robust to quibbles over the meaning and nature of causality, in particular, it allows for a less stringent requirement on the necessary conjunction between a state of affairs and its antecedents; the pattern view may allow, once specified, the derivation of if-then statements, but it does not have to. Patterns can in principle be random or ordered.

It also avoids infinite causal regress problems. It seems intuitive to some (though not all) that causal chains must have a beginning (whether the causal series be per se or per accidens as Thomists would distinguish). But it does not seem to be obvious that patterns need to have a beginning: sure, the pattern of odd, even, odd, even in the positive integers has a beginning because it has a first member. But the integers have no first member because they stretch from negative infinity to infinity - and yet they still have the pattern of odd, even, odd, even. What is not definable is whether the first element was odd or even, because there is no first element.

But even if we take the positive integers, it still does not need for there to be something before the first member for the pattern to continue ad infinitum. To ask "what caused the first member of the positive integers" is a senseless question. Similarly, it may very well be the case that nature had a beginning and it is self-contained. The objection that "but it had to have had a cause, science demonstrates that!" is simply not true. The universe could be just like a set which starts at time zero and continues to infinity without  quibbling over whether there was anything at t = -1.

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