A Framework for Thinking about Knowability by John S Schultz

Ernesto Vaca

Hi John,

I enjoyed reading your essay. It was very clear, and your characterization of different pattern types was quite insightful. I had never thought of patterns like that before. I have a hard time imagining what a non-algorithmic patterns would be, especially in a pure sense. It almost seems that without an algorithm, it is not fair to call them patterns, but that is solely based on intuition, and is not highly thought out. Your example of mutation seems true, but chaotic, and chaos strikes me as a lack of a pattern, or at least one too complex for humans to understand, right now at least. Perhaps I need to think more on what you mean by non-algorithmic pattern.

I think I disagree that there is no adequate way to cut down on the infinitely many mathematical patterns that fit data, because some mathematical structures fit more data than others, and that is one way to cut-down on the possibilities. But based on intuition I do have a sense that science might very well go on forever regardless. We may never be fully right, but we can strive to be less wrong.

All the best,

Ernesto

John Schultz

Hi Ernesto,

I hope I clearly suggested two different plausible meanings for the word "pattern," and explained which one I was using. But I'm not too hung up on what string of letters goes with what meaning. If you'd like to suggest alternative terminology, I'm all ears.

Mutation is not due to chaos (in the normal technical sense.) If you mean that it can create bedlam (in an informal sense) I guess perhaps it can, but normally I'd say it was the other way around. More importantly, the question doesn't seem relevant to my essay. Perhaps we are misunderstanding each other.

And..., well, I guess you are saying that as we get more data we can eliminate some of that infinite number of patterns that fit (ALL) the data points. This is true, of course, but the number that are left wills still be infinite. And that, it seems to me, is one place judgement comes in. Obviously a polynomial equation with a few terms is something useful. A polynomial equation with thousands of terms..., rather less so! So we start with something simple and hope that new data doesn't eliminate it..., at least not too quickly.

Luca Valeri

Hi John,

I like your symmetric distinction of science and pure mathematics. Also it seems natural attach the question about knowability to the study of pattern as our main mental capability seems to be the recognition of pattern. Also very interesting is the distinction of algorithmic and non-algorithmic pattern. The non-algorithmic one you seem connect with random processes. I'm not sure if that is a to strong limitation. Although I couldn't come up with an other idea, what else non-algorithmic could mean.

My main critic in your approach is one that became clear to me in the course of a few discussions I had in this contest and that is a bit the topic of my essay. It is a critic on your conjuncture 1a: You postulate (at least implicitly) the existence of real world-patterns. And that they are isomorphic to the mathematical pattern. For me conjencture 1a is a pattern theoretic version of what I call naive or simplistic realism in my essay.

But the pattern version is much easier to criticize because it is used as a conjecture in all science and not only in fundamental physics, ,where it is much, much harder to criticize and even to think, the world could be otherwise. (This is what I try to show in my essay).

But what I mean by that? Let us take as example the classification of species. Certainly one can say, that there exist pattern, that favour some classification (although the pattern is never fully precise and without ambiguities). On the other hand, one could say that the classification (and the matching pattern) are somehow arbitrary, man made and serve different purposes depending on the field of inquiry: evolution, ethology, ecology, etc. You may say: but as far as these pattern can be found, they are objectively in nature. And have a corresponding mathematical pattern, that describes it. But the pattern to have a meaning and to be recognized as such, needs a context under which it becomes meaning full.

Somehow, I. have the feeling the pattern is imposed by us, as something functional and lies not in nature itself.

Does this make any sense to you?

Luca

John Schultz

Hello Luca,

My apologies if I was less clear than I thought. I tried quite hard to make a distinction between patterns that are partially random, and some other type that you and I are both unable to come up with an example for. Please reread that section and tell me if it now makes more sense.

1a, and ALL the conjectures are merely that. (More or less predictions.) If your intuition thinks otherwise, than our intuitions disagree with each other, which of course is okay. As I said in the closing, this may have sounded anti-realist, but it is not.

For your example, I would feel that the pattern exists, and the subjectivity comes from two places. One the one hand, we don't have complete knowledge of the pattern. And on the other hand, we do know an intractably bulky portion of the pattern, and we all have different ways to slice-and-dice it to make it more useful.

Luca Valeri

Hi John,

no need to apologize. I have read the essay really quick. So it is on me, not to have read the careful enough.

By the way, my essay is exactly about non algorithmic change of pattern that is not random. This comes like this (I might I misuse your terminology a bit - sorry for that). I impose the following limitation: The input and output must also be describable by the algorithmic pattern. I call this property semantical closed theory. If now a pattern P2 is richer, more complex and contains more pattern than P1. If now P2 follows in time P1. Then P2 cannot be predicted nor described by P1, because of a lack of language. That would be a non algorithmic change of patterns.

What do you think?

And yes, our intuition disagree and that is fine. And no, you do not sound anti-realist. It is good to know the limits of any realist theory.

Good luck in the contest!

Luca

James Hoover

John,

Hope you have time to check mine out before the deadline: https://fqxi.org/community/forum/topic/3396

Jim Hoover.

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