Yeah, real analysis sucks. But you have to go through it to get to delightful stuff— I particularly love harmonic and functional analysis. Real analysis is just a bunch of pathological cases and technical persnicketiness that you need to have to keep you from steering over a cliff when you get to the more advanced stuff. I’ve encountered some other subjects that have the same feeling to them. For example, measure-theoretic probability is a dry technical subject that you need to get through before you get the fun of stochastic differential equations. Same with commutative algebra and algebraic geometry, or point-set topology and differential geometry.
Constructivism, in my experience, makes real analysis more mind blowing, but also harder to reason about. My brain uses non-constructive methods subconsciously, so it’s hard for me to notice when I’ve transgressed the rules of constructivism.
There’s also positive selection for itchiness. Mosquito spit contains dozens of carefully evolved proteins. We don’t know what they all are, but some of them are anticoagulants and anesthetics. Presumably they wouldn’t be there if they didn’t have a purpose. And your body, when it detects these foreign proteins, mounts a protective reaction, causing redness, swelling, and itching. IIRC, that reaction does a good job of killing any viruses that came in with the mosquito saliva. We’ve evolved to have that reaction. The itchiness is probably good for killing any bloodsuckers that don’t flee quickly. It certainly works against ticks.
Evolution is not our friend. It doesn’t give us what we want, just what we need.
Because they have no reproductive advantage to being less itchy. You can kill them while they’re feeding, which is why they put lots of evolutionary effort into not being noticed. (They have an anesthetic in their saliva so you are unlikely to notice the bite.) By the time you develop the itchy bump, they’ve flown away and you can’t kill them.
There’s two kinds of “work” here. One is to induce rain that would not have otherwise occurred, and the other is to induce rain that would have naturally occurred a few minutes or a few kilometers away. Call it “making” versus “moving” rain. A cursory examination of Wikipedia suggests the recent claimed successes have been at moving rather than making rain. And the failures at finding any effects have been at making rather than moving. And of course it would be far more useful to make rain than to move it.
Semiconductor chips don’t carry the secrets of their manufacture. Let’s say a modern chip fell into 1958. They had electron microscopes, so they could see there were tiny structures there. And they had analytical chemistry for macroscopic samples, so they’d be able to tell the chip was almost pure silicon, with small admixtures of the sort of impurities that form transistors. But they didn’t have ion milling and scanning microprobes, so they wouldn’t be able to tell how the impurities were arranged into devices. And they certainly wouldn’t know how to reproduce the highly developed engineering that manufactures these chips nowadays.
So the best they could do would be to start the development of ever-smaller semiconductors, knowing that someday they would be very impressive. And until then, they would do good stuff along the way. Which is pretty much what happened in real life.
Epistemic status: I designed chips from 1982 to 1994. I never saw an alien spaceship.
You write "This residual stream fraction data seems like evidence of something. We just don't know how to put together the clues yet." I am happy to say that there is a simple explanation-- simple, at least, to those of us experienced in high-dimensional geometry. Weirdly, in spaces of high dimension, almost all vectors are almost at right angles. Your activation space has 1600 dimensions. Two randomly selected vectors in this space have an angle of between 82 and 98 degrees, 99% of the time. It's perfectly feasible for this space to represent zillions of concepts almost at right angles to each other. This permits mixtures of those concepts to be represented as linear combinations of the vectors, without the base concepts becoming too confused.
Now, consider a random vector, w (for 'wedding'). Set 800 of the coordinates of w to 0, producing w'. The angle between w and w' will be 60 degrees. This is much closer than any randomly chosen non-wedding concept. This is why a substantial truncation of the wedding vector is still closer to wedding than it is to anything else.
Epistemic status: Medium strong. High-dimensional geometry is one of the things I do for my career. But I did all the calculations in my head, so there's a 20% of my being quantitatively wrong. You can check my claims with a little algebra.
You say “reversible computation can implement PSPACE algorithms while conventional computers can only implement algorithms in the complexity class P.” This is not true in any interesting sense. What class a problem is in is a statement about how fast the space and time increase as the size of the problem increases. Whether a problem is feasible is a statement about how much time and space we’re willing to spend solving it. A sufficiently large problem in P is infeasible, while a sufficiently small problem in PSPACE is feasible. For example, playing chess on an n by n board is in PSPACE. But 8 is small enough that computer chess is perfectly feasible.
There’s no point to my remaining secretive as to my guess at the obstacle between us and superhuman AI. What I was referring to is what Jeffery Ladish called the “Agency Overhang” in his post of the same name. Now that there’s a long and well-written post on the topic, there’s no point in me being secretive about it ☹️.
Because they’re under different selection pressures. Take a look at this paper by Robin Hanson: https://mason.gmu.edu/~rhanson/filluniv.pdf . When colonizing unowned space, victory goes to the swiftest, not to the cleverest, most beautiful, or most strategically lazy.
IIRC, this grew out of discussions in which I raised the problem of optimal interstellar colonization strategies. Robin thought about the problem and, with the methods of an economist, settled it decisively. Now this strategy is just part of the background knowledge that the author of this story assumed.