I agree, and one could think of this in terms of markets: a market cannot capture all information about the world, because it is part of the world.
But I disagree that this is fundamentally unrelated—here too the issue is that it would need to represent states of the world corresponding to what belief it expresses. Ultimately mathematics is supposed to represent the real world.
Ultimately mathematics is supposed to represent the real world.
Well, I think a better way to put it is that mathematics is sometimes a part of some models of the world. The relationship is world → inputs → models <-> math. Whether the part of mathematics that deals with self-reference and soundness and completeness of formal systems corresponds to an accurate and useful model of the world is not at all obvious. So, yeah, some parts of mathematics lossily represent some parts of the world. But it is a pretty weak statement.
Half-joking: Find me a mathematical statement that purports to not describe the real world and I’ll show you a mathematical statement that describes patterns in constructions of symbols made of the real world. Territory comes first; math can show us perfect patterns in the territory, but by the same token, it can only ever be map. The map, being part of the territory, can then make insightful statements about itself, through many layers of patterns of patterns of patterns of patterns, but you’ve never seen a mathematical statement that wasn’t in the territory.
Of course math is in the territory, everything is. Embedded agency and all. But it does not mean that the particular part of the territory that is a specific part of math is also a lossy compression of a larger part of the territory.
You overstate your case. The universe contains a finite amount of incompressible information, which is strictly less than the information contained in ZF+ωCK. That self-reference applies to the universe is obvious, because the universe contains computer programs.
The point is the universe is certainly a computer program, and that incompleteness applies to all computer programs (to all things with only finite incompressible information). In any case, I explained Godel with an explicitly empirical example, so I’m not sure what your point is.
That’s about as much of an argument as saying that the universe is contained in the decimal expansion of Pi, therefore Pi has all the information one needs.
I agree, and one could think of this in terms of markets: a market cannot capture all information about the world, because it is part of the world.
But I disagree that this is fundamentally unrelated—here too the issue is that it would need to represent states of the world corresponding to what belief it expresses. Ultimately mathematics is supposed to represent the real world.
Well, I think a better way to put it is that mathematics is sometimes a part of some models of the world. The relationship is world → inputs → models <-> math. Whether the part of mathematics that deals with self-reference and soundness and completeness of formal systems corresponds to an accurate and useful model of the world is not at all obvious. So, yeah, some parts of mathematics lossily represent some parts of the world. But it is a pretty weak statement.
Half-joking: Find me a mathematical statement that purports to not describe the real world and I’ll show you a mathematical statement that describes patterns in constructions of symbols made of the real world. Territory comes first; math can show us perfect patterns in the territory, but by the same token, it can only ever be map. The map, being part of the territory, can then make insightful statements about itself, through many layers of patterns of patterns of patterns of patterns, but you’ve never seen a mathematical statement that wasn’t in the territory.
Of course math is in the territory, everything is. Embedded agency and all. But it does not mean that the particular part of the territory that is a specific part of math is also a lossy compression of a larger part of the territory.
That’s syntax, not semantics.
HUH. iiiiinteresting...
You overstate your case. The universe contains a finite amount of incompressible information, which is strictly less than the information contained inZF+ωCK. That self-reference applies to the universe is obvious, because the universe contains computer programs.The point is the universe is certainly a computer program, and that incompleteness applies to all computer programs (to all things with only finite incompressible information). In any case, I explained Godel with an explicitly empirical example, so I’m not sure what your point is.
That’s about as much of an argument as saying that the universe is contained in the decimal expansion of Pi, therefore Pi has all the information one needs.
It’s really not, that’s the point I made about semantics.Eh that’s kind-of right, my original comment there was dumb.