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eli_sennesh comments on Is Scott Alexander bad at math? - Less Wrong
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Since much of this sequence has focused on case studies (Grothendiek, Scott Alexander), I'd be curious as to what you think of Douglas Hofstadter. How does he fit into this whole picture? He's obviously a man of incredible talent in something - I don't know whether to call it math or philosophy (or both). Either way it's clear that he has the aesthetic sense you're talking about here in spades. But I distinctly remember him writing something along the lines of how, upon reaching graduate mathematics he hit a "wall of abstraction" and couldn't progress any further. Does your picture of mathematical ability leave room for something like that to happen? I mean, this is Douglas freakin' Hofstadter we're talking about - it's hard to picture someone being more of a mathematical aesthete than he is. And even he ran into a wall!
Excuse me, I have to don a flame-proof suit now.
Just a question: what useful results for predicting and modelling a preexisting reality has Douglas Hofstadter produced? I mean, yes, GEB is... well, it's GEB. I find it quite dated and think that it skates by on having fun with patterns rather than explaining observed phenomena. I'm also a little aggravated that GEB includes no discussions of model theory, ordinal logic, and w-incompleteness, nor of algorithmic randomness and halting problems, nor of the Curry-Howard Isomorphism and how it matches computational systems to logical systems. It goes on and on about recursion and formal systems for a very long time without actually addressing the formal sciences that handle the various phenomena arising from talking recursively in logic!
Whereas something more recent like Universal Artificial Intelligence by Hutter succeeds on mathematical rigor and Probabilistic Models of Cognition on beauty of compression and presentation.
I'm sure GEB says at least a little bit about omega-incompleteness. Is my memory defective?
I think it does, and I know it at least alludes to ordinal logic and model theory.
Yes, though I think it's fair to say it says little enough about those that Eli's complaint could be reasonable.
Maybe I just didn't reach that part yet.
It's not a modeling handbook. It just fucks with your mind. Most people's minds are much too unfucked-with.
Perhaps, but that doesn't mean randomly fucking with them will improve them.
That's OK: GEB fucks with minds nonrandomly.
So am I fucked-up enough yet if I find it kinda boring and wish it would skip to the part where we model real phenomena, especially since, if I just want to make stuff up, I can make up rather crazier things than this?
Mirror, mirror on the wall...
X-D
GEB makes a very strong case for the idea that intelligent systems might not be formal systems. That idea is then developed in his subsequent writings, and has lead to a quiet branch of AI that still flourishes.
Depending on how you define "preexisting reality", most professional mathematics can be said not to achieve this. In any case, the terms under which people usually praise Douglas Hofstadter do not include this sort of achievement. And if you really want to know what Hofstadter has done, there's this.