bigideas

blog main page

---

The Simple Truth

21 November 2007 – 4:22 pm by  

---

There’s a general preference for theories to be neat, clean and simple. The problem is, fundamentally, that the world isn’t any of those things. Cliffshill outlines a claim that simplicity makes a physical theory less, not more, likely to be true. (Hat tip to the current Philosophers’ Carnival).

Cliffshill’s example is of a theory that predicts a linear relationship between, say, the input and output of some experiment. If you actually do the experiment, you won’t find a linear relationship — not exactly. Instead you’ll see evidence of a complex relationship that’s roughly linear. Fitting a straight line to your data-points might look satisfying, but the straight line didn’t truly predict any of them.

I think the problem here is a straightforward one of asking scientific theories to do too much. They give precise predictions, but the accuracy of those predictions is within some margin of error. The “errors” in this case come from things like our finite ability to measure accurately (input or output).

They also reflect the limited size of our theories. We really just have to stop taking factors into consideration at some point; reality doesn’t, and factors that usually have little effect on their own often enough gang up on you to produce a small but noticeable one.

So the linear relationship is really a linear-within-some-margin-of-error relationship. The margin of error can’t be stated with infinite precision because if it could we’d have enough information to eliminate it. But if the theory is good then it’ll be fairly small compared the things we care about.

Making your theory fit experimental results more exactly can be worthwhile, or it can be a waste of time. We certainly can’t say, “the simpler a theory, the truer” or, “the simpler, the more plausible”. But was can say, in general, “the simpler, the easier to use”.

Ease of use is important, even when accuracy is important too. When building bridges, engineers use classical mechanics (as far as I know), which give a good enough approximation within a safe margin of error. They can’t decide to use quantum theory because it gives a more precise picture of what’s going on. Not only is it prohibitively hard but they couldn’t possibly assemble all the input data they’d need.

So simplicity can be a virtue in a scientific theory, but it doesn’t make the theory “more true” because a simple theory will commonly need a wider margin of error than a more complex one. Scientific theories are generally not aimed at a philosopher’s or mathematician’s idea of truth, but at something more empirical.

[Update 22 November 2007:

David Price at Language Games has a post about Occam’s Razor and feminist epistemology which many readers will find interesting in connection with this.

]

[Update 26 Nov: Corrected an attribution error, per Martin Cooke’s comment below]