The worry “how will people find meaning with super-abundance?” has also me as tone deaf ennui of the already super-privileged. That we should be so lucky to have this worry.
Given that the abundance will be predictably hoarded by those in power — leaving everyone else even fewer table scraps than we already get — should however remain a concern.
After all, its not like some benevolent super-AGI will be deciding who the spoils get divided amongst, they will remain tools to perpetuate and intensify every incumbent power imbalance.
Much of the value of proof is in the development of math definitions and intermediate theorems needed to get you there, Grothendiek-style. This ability seems still to be beyond AI (at least, I haven’t heard of any fundamentally new and useful definitions such as “scheme” or “modular form” emerging from the latest blizzard of AI proofs). BUT, I wonder if AI could develop this skill too through a process of efficiently refactoring a big Lean proof into Lean pieces, then interpreting the pieces back into new, human-grokable definitions with evocative names?
1. An NYT commenter clarifies that the “Second Grade Teacher” of the article’s title is from a family worth $30+ billion. If true, this would seem to be egregious omission of context from the article.
I don’t understand the claim that Kolmogorov lower bounds are uncomputable. Three digit strings are unlikely to run as a program so surely 3 is a lower bound on Kolmogorov of the first million digits of pi, no? To tighten bound, one would need to try out every 4-digit program, every 5-digit program, and so on. Either these produce the first million digits of pi or they don’t when the program is run, so each possibility is checkable in finite time, no? There must be something I’m missing here.
I agree, producing a lower bound is possible. It's practically very hard to give a good lower bound though. Many programs do not terminate, so we don't know if they do produce the right output eventually. In practice the best that has been done on Turing machines is that we have now proved which 5-state machines halt and which don't. So proving any lower bounds larger than that is practically impossible.
But isn’t it conceivable, because the original quantum state contains probabilities of different outcomes, that one imprint might correspond to “up” and another to “down,” [...] [Zurek’s theory] predicts that all the imprints must be identical.
Does this not imply that there is an asymmetry, one half of the state gets imprinted, the other half neglected? This however also raises the question about the basis, what is a superposition and what is not depends on the choice of basis. Is there a special basis just as pointer states are somehow special?
Indeed, as you say, Decoherence explains why certain bases are special: when a system is in a pointer basis state, it does not continue entangling with environment (or, at least, does so minimally). When a spinning particle enters a Stern-Gerlach apparatus oriented in z-direction, spin-z is the pointer basis of the system during its time in the apparatus. A spin-up or spin-down particle does not entangle with the environment, but spin +x state would quickly entangle with environment, placing environment in a superposition and "branching" the total state vector of all the stuff in the universe.
Quantum Darwinism is just a refinement of this picture in which the "environment" interacting with the system is itself modeled a series of fragments (i.e. all the different photons that bounce off object). It turns out that the information about which pointer basis state the system is in (spin up or spin down) is redundantly encoded in each of these fragments. Hence, intercepting one photon that interacted with system and reveals "spin-up" (because the particle is in upper path) agrees with other photons that also bounce off object.
BUT, of course, due to linearity of unitary time evolution, there is another "branch" in which spin-down was the outcome of the measurement and everyone agrees on spin-down. This is exactly the Everett picture.
These debates over the interpretation of Quantum Mechanics (i.e. what ultimately happens when a “measurement” takes place) are important but don’t bear on the effectiveness of quantum computing. Regardless of your favorite interpretation (almost) everyone agrees that quantum computers should work and be able to do things classical computers cannot.
Yes, the MWI is falsifiable. It asserts that objective collapse does not occur, therefore any observation of objective collapse (such as predicted by GRW or Penrose-Diosi) would falsify it.
That's not true falsifiability; its asserting a negative.
I think people resort to MWI because they think it explains everything neatly; it does not!
For example, from my perspective, it does not explain what world I end up in, and if you are saying it's random, you need to come with a fundamental theory of randomness, unless the response is: it just exists, deal with it.
A negative, that can be falsified by a single black swan.
You are mixing up another kind of argument. Claiming there are elephants in the room we cannot see or touch is an example of an unfalsifiable claim.
In fact, claiming there is a quantum collapse, which always looks just like the field equations without a quantum collapse, would make collapse an unfalsifiable theory.
(I don’t believe most proponents of collapse are making that claim.)
It doesn’t. Decoherence is the technical step in the Everett picture defining what a “classical branch” even is and explaining how the state vector branches. Every claim that “Decoherence” somehow offers a distinct interpretation to Everett is pure confusion.
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