I don't think Gödel is necessarily what is meant here, there are very good information theoretical(and other) reasons you can never describe a system with truly perfect accuracy. The map has to be become the territory for genuinely perfect accuracy.
Makes sense, but is it relevant to the upthread claim that "All provable models (theories, explanations) that we have, or could have, are by definition wrong or incomplete"? (Not being rhetorical and snide here, I'm curious and aware I may be missing something.)
If reality has irreducible randomness (an open question afaik), and we're talking about theories and explanations (so we're not necessarily trying to describe the actual state of every particle in the universe, but only the rules governing their interactions), couldn't we have a complete, correct theory that was much smaller than the universe and contained terms for the random elements?
There would always be the possibility that it would turn out to be wrong, but it could be complete and correct, so it seems like the original claim must depend heavily on the word 'provable' and not on the impossibility of describing a system via a map smaller than the territory.
edit: but also, surely 'the territory is randomized' is a contingent physical fact, and not a necessary truth of information theory. Until we know for sure that there is irreducible randomness, we can't know that the information content of the universe (including the actual state of all particles at all times) isn't losslessly compressible, right?
The “elements for randomness” are carve-outs for the parts of territory the map can’t contain. The more granular the map, the larger relative proportion that falls into that set. Nobody can predict the layout of my basement from a globe of the world.
We know with a high degree of certainty the universe contains things we can’t predict or observe, see Bell’s Theorem.
“Truth” doesn’t exist outside reality. There’s no substrate to hang it in. Information theory is likewise a subset of the territory, part of the universe, not apart from it. For these things to exist independently, you need something other than or bigger than the universe to put them in. If such a thing existed, sure, from that perspective maybe a lossless compression could exist. But that’s a metaphysical argument.
That, and the very idea of direct access to the territory (needed for any sort of “lossless compression”, among other things) is moot since we only perceive it indirectly through the lens of our consciousness, which is anything but objective.
>My job is uniquely creative and human, other jobs can be automated away but mine is just so special.
If you love mathematics so much, and it's not the prestige and accolades that drive you, then what stops you from just solving problems on your free time even if they are already solved by AI?
Why does your field have to remain economically viable for you, why does this not apply to textile manufacturing or something? Someone's positions in society is owed to textile manufacturing too, and it has a culture that some people would lament the loss of and so on.(See guild system, craftsmanship in Europe).
I can't predict whether this will be a good thing in the long run, but this is literally the same complaint that every industry affected by automation ever had, and many who are now complaining would dismiss it if it were about something they personally do not care about or isn't sufficiently "noble" or intellectual.
I know it hurts, but the core complaint is just economic displacement, many have had to deal with that before. Most people who have something they love have to do that on their free time because it's not economically viable as a job, tough luck.
What are these complaints really other than "I had a nice position in the previous system and I'm afraid of losing it"? Many felt disposable and not valued already, maybe it was a good system for you but not for many. You have a valued skill and you enjoy working in a field using that skill, well for 90+% of people that isn't what work is, you're lamenting the loss of something that the vast majority never had access to in the first place. What exactly is so great about our current predicament that it needs to be protected from new technology?
