## I thought the truth was apt to be simple

but Cosma says I’ve got another think coming!  He’s blogging the Ockham’s razor conference I mentioned in the previous post, and starts out today’s entry with the following bombshell:

The theme of the morning was that Ockham’s razor is not a useful principle because the truth is inherently simple, or because the truth is apt to be simple, or because simplicity is more plausible, or even because simple models predict better. Rather, the Razor helps us get to the truth faster than if we multiplied complexities without necessity, even when the truth is actually rather complex.

I have always thought of the utility of parsimony as derving from a tendency of true things to be simple.  But am I fooling myself?  I tend to think that mathematical truths are apt to be simple — for instance, that when I have truly understood a difficult mathematical argument I see that the main idea is simple and elegant, while the visible complications are somehow inessential.  But you could argue that this is just prejudice on my part, and I denigrate the complicated part as inessential just because it is complicated.

And certainly I don’t think the truth about big biological or social systems is apt to be simple.  In fact, because I know people are prejudiced to believe in simple explanations, I find myself leaning against them;  the fact that a simple explanation is widely believed by people I trust is less compelling as evidence than it would be, if the explanation in question were prickly or technical or otherwise unpleasant to believe.

## 4 thoughts on “I thought the truth was apt to be simple”

1. Sam Alexander says:

Sometimes when mathematics looks complicated to me, it’s because I’m looking at it from the wrong angle. I’ll make a conjecture based on parsimony principles; it will turn out to be badly wrong, and the truth will seem to be much more bewildering; then, a year or two later, I’ll realize that from some more general standpoint, the truth was simpler all along.

2. Alexander Woo says:

My general philosophical stance is that “science is Ramsey theory”.

What I mean by this is that the universe is actually extremely complicated and disordered. However, Ramsey theory (misused quite badly in this case – but it’s only a metaphor here) guarantees that in any system there are some nice ordered subsets, and what science has actually done is to find and use these nicely ordered (but actually quite rare) bits.

From this point of view, the point of Ockham’s Razor is not that truth is likely to be simple, but that useful truths are the simple ones, and complicated truths are not useful.

My experience in mathematics is that there are indeed some theorems that are extremely complicated. However, the mathematical community regards such theorems as not beautiful or not important (barring some extraordinary reasons to the contrary) and hence discourages mathematicians from working on such topics. (I have indeed gotten a review on a grant that said a particular line of research was not worth funding because the answer was likely to be very complicated and hence not interesting.)

3. David Speyer says:

Alex: If you believe that, then why do physically discovered laws so often describe situations which were not accessible to the original scientists?

For example, Hales-Jewett says that, if we bicolor $[n]^N$ for $n$ fixed and $N$ sufficiently large, there will be a “combinatorial line”. Suppose that the original generation of experimentalists can only look at $[n-1]^N$, and they find a bunch of monochromatic lines. When their instruments become stronger and they can see into $[n]^N$, they check to see whether their lines are still monochromatic. If all that was happening was Ramsey theory, then only $1/2$ of the lines would remain monochromatic. The fascinating property of science is that it does much better than this.

My own take is that “science is the study of those aspects of the world where simple patterns continue to remain true with high probability”. Superstition is Ramsey theory. I am open to the possibility that certain things funded by the NSF are actually superstition…

4. GilYoung Cheong says:

“But you could argue that this is just prejudice on my part, and I denigrate the complicated part as inessential just because it is complicated.”

Just a religious belief: I personally believe that “the complicated part” has its own simple meaning in the universe, but the language that we use is not always the best way to see the nice structure/meaning behind it. Moreover, to me, it sounds more plausible that there are notions that we cannot fully see and understand but we also do not know if they are able to be described in a simple manner or not unless we investigate enough. So, I agree that truths (not just mathematical) are likely to be simple, but the simplicity existant is independent to how we see them.