Born to do Math 43 – Metaprimes (Part 9)
Author(s): Scott Douglas Jacobsen and Rick Rosner
Publication (Outlet/Website): Born To Do Math
Publication Date (yyyy/mm/dd): 2017/04/19
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Scott Douglas Jacobsen: Also, off-tape, we were talking. What you were describing in things, it brought Gödel to mind. His two incompleteness theorems, where you’re dealing with partiality of information. A universe with incomplete information, but built on simple principles, would come up with, likely, just by natural development or an organic development, an associative form of information processing, which is both incomplete but probably the most efficient given its conditions.
Rick Rosner: I think one reason people are fascinated with Gödel incompleteness theorem is that it generates all sorts of objects in the mathematical sphere like propositions that are either true or false, but can never be proven true or false. I think there’s the idea that any axiomatic system that is sufficiently complex will generate weirdly undecidable propositions. So that’s one thing that’s interesting.
It’s scary in that one of the efforts of 100 years ago by Whitehead and some other people was to put mathematics and logic on an unassailable foundation of pure—it was to have an infinitely defendable and concrete system of math with a completely unassailable foundation. That Gödel says, “No, there are always going to be pitfalls and exploding principles and that it introduces the fear that there may some aspect of math that makes math blow up.
That it is fundamentally inconsistent and you can’t prove anything, which is apparently not the case. You may not be able to prove anything to an infinite degree of certainty, but we live in a world that’s highly existent. At the same time, at the smallest scales, it is completely nebulous and fuzzy and only on the borderline of existent. It is only when you get macro objects that you get definite existence.
So even in a Gödelized world where there is not an infinite certainty or precision in anything, you can still build a solid world.
SDJ: Our language reflects that too. When we describe things, they are not complete, but given certain conceptual mappings. They describe something incompletely, but you string a bunch of sentences together that are appropriate to context and that provides a sufficient mapping in the other person’s head based on their interpretation, if similar culture, similar conceptual mappings, similar language to relate to those. But it is incomplete. It is rough.
RR: When you’re trying write, one thing that frustrates me is that when you’re trying to write as precise as possible you’re trying to reach into lexical space for the right word. Sometimes, you can get nearly the right word. Other times, there’s just a missing word.
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