3 min and 10 sec to read, 793 words

Here a few notes on a question that I think would be worthwhile to explore more in detail in an essay — these are just my first notes.

In Narayanamurti’s and Tsao’s excellent book on how to nurture research – The genesis of technoscientific revolutions: rethinking the nature and nurture of research – the author suggest that science is composed of three elements – facts, explanations and generalizations. This model – admittedly simple – is helpful when we need to think about how science as a practice might change over time, especially with the introduction of artificial intelligence methods.

Facts, they suggest, are observed patterns and regularities in nature, and explanations provide causal understanding of the facts and how they are connected in different ways. If this is the case we can ask an interesting question: can there be facts without explanations?

It seems possible: we can observe a pattern or regularity without knowing why this regularity holds, but on the other hand the observation of a patterns seems to entail at least the possibility of finding an explanation for it — what if we used a new kind of scientific instrument that could detect patterns, but not provide us with any explanations for them, would those patterns then be facts?

The opposite view – that patterns that cannot even in theory be explained can never be facts – suggests something interesting about the notion of facts. Facts are patterns, then, in this view, that can at least in theory be explained. (Something like this Let F be a fact, P be a pattern, and E be an explanation. ∀P(∃E(E explains P) → P is F))

Some connection exists between this set of problems and the question of correlation and causation, and the challenge is made more complicated by the observation that as the number of variables in an observed set increases, the number of spurious correlations also increase. But what if some of those spurious correlations are stable enough to behave like facts? Is stability of a pattern a part of its “factiness”?

And is there a way to explore if a pattern can, in theory, be explained? What if a pattern is n-dimensional, and n is so large that it is not possible for us to grasp an explanation with that many dimensions? Will a simplification be enough? And if it is not – are we then comfortable with connecting the notion of fact with our ability to understand an explanation?

To some degree this is a question about the world we live in and the kind of knowledge we expect to find. Do we think there is scientific theories that are true, but inaccessible to us because of the complexity of those theories? If so, what is the size of the graspable set of scientific theories, and how does that relate to the whole?

We may, of course, reject the entire idea that facts are patterns, and suggest that patterns are not enough to establish facts (I do like the notion of patterns as facts, if for no other reason that it allows us to factor in time into the notion of facts, and it allows for facts to change and even deteriorate (see Sam Arbesman!)).

Much more to do here. A few thought experiments to consider:

• The mysteriously stable correlation. Tyler Vigen has shown that per capita margarine consumption and divorce rate in Maine correlate, and provided some great notes on this here. Now, let’s assume we consciously increase the per capita consumption of margarine, and we see the divorce rate go up — and we then restrict the consumption and it goes back down, ever more precisely correlated. There seems to be no causal relationship – is this now a fact just because the correlation is stable AND allows for predictions based on it, or is it something else?
• The black box predictor. A machine you can ask any question about a physical system and it answers it in ways you could not answer with today’s physics – but always correctly. Are the machine’s predictions facts?
• The machine theory of everything. An AI assures us that there is a connection that allows for the famed theory of everything, but that it can’t explain it to use because the number of dimensions of the theory are too many and we lack concepts and language for it — but it finds 5 predictions that bear the assertion out in the sense that it predicts things we cannot predict today, and asserts this is because it bases those predictions of this n-dimensional theory. Is this theory scientific?

And so on. Some of these thought experiments can be expanded and sharpened further — and I think this is not just idle speculation.