Wikitag Contributions
The option to buy SPY at $855 in January 2027 is going for $1.80 today, because most people don’t expect the price to get that high. But if in fact SPY increases in the intervening time by 50% from its present value ($582), as stipulated by kairos, then the option will ultimately be worth 1.5*582 - 855 ~ $18. I think this is where the 12x figure is coming from.
1Has anyone thought about Kremer/Jones-like economic growth models (where larger populations generate more ideas, leading to superexponential growth) but where some ideas are bad? I think there’s an interesting, loose analogy between these growth models and a model of the "tug of war" between passengers and drivers in cancer. In the absence of deleterious mutations the tumor in this model grows superexponentially. The fact that fixation of a driver makes the whole population grow better is a bit like the non-rival nature of ideas. But the growth models seem to have no analog to the deleterious passengers—bad ideas that might still fix, stochastically, and reduce the technology prefactor "A".
Such a model might then exhibit a "critical population size" (as for lesion size) below which there is techno-cultural decline (ancient Tasmania?). And is there a social analog of "mutational meltdown"—in population genetics, if mutations arrive too quickly, beneficial and deleterious mutations get trapped in the same lineages (clonal interference) and cannot be independently selected. Perhaps cultural/technological change that comes too rapidly leads to memeplexes with mixtures of good and bad ideas, which are linked and so cannot be independently selected for / against…
Note that addition to any achiral antibiotics, we could also use the mirror image versions of any chiral antibiotic. Even more powerful, we could use mirror image versions of toxins to all life (e.g. nucleoside analogs) that are normally hard to use because we share chirality with regular bacteria
Is that TinyStories model a super-wide attention-only transformer (the topic of the mechanistic interp work and Buck’s post you cite). I tried to figure it out briefly and couldn’t tell, but I bet it isn’t, and instead has extra stuff like an MLP block.
Regardless, in my view it would be a big advance to really understand how the TinyStories models work. Maybe they are “a bunch of heuristics” but maybe that’s all GPT-4, and our own minds, are as well…
I think in your first paragraph, you may be referring to: https://mason.gmu.edu/~gjonesb/IQandNationalProductivity.pdf
I believe the key issue here is with (i). Standard theories where the universe is infinitely large also suppose it was infinitely large at the moment of the big bang.
The discussion here may be helpful.
I think the basic answer is that your question “why does statistical mechanics actually work?”, actually remains unresolved. There are a number of distinct approaches to the foundations of the subject, and none is completely satisfactory.
This review (Uffink 2006), might be of interest, especially the introduction.
Personally, I have never found maximum entropy approaches very satisfying.
An alternative approach, pursued in a lot of the literature on this topic, is to seek a mathematical reason (e.g. in the Hamiltonian dynamics of typical systems statistical mechanics is applied to) why measured quantities at equilibrium take values as though they were averages over the whole phase space with respect to the microcanonical measure (even though they clearly aren't, because typical measurements are too fast---this can be seen from the fact that in systems that are approaching equilibrium, measurements are able reveal their nonequilibrium nature). This program can pursued without any issues of observer-dependence arising.
If the spike looks a lot like one that was experimentally generated to evade antibody responses, what are the odds that Omicron was created through such experiments?
The research in question seems to be described in this Nature paper, where the authors say (emphasis mine):
To more precisely map the targets of polyclonal neutralizing antibodies in individuals who are convalescent, we passaged a recombinant vesicular stomatitis virus (rVSV)/SARS-CoV-2 chimeric virus1,5 in the presence of each of the RU27 plasmas for up to six passages. rVSV/SARS-CoV-2 mimics the neutralization properties of SARS-CoV-2 (refs. 1,5) but obviates the safety concerns that would accompany such studies with authentic SARS-CoV-2.
So, regarding safety, it seems the place to start would be understanding the properties of this rVSV/SARS-CoV-2 construct. Further details are here.
You may be interested in inteins, which are protein domains that spontaneously excise themselves from the host protein (the N and C terminal pieces of the host are left stitched together).
I think minimal inteins are usually 100-200 amino acids, and require quite specific residues positioned appropriately, so will not meaningfully affect the 20^100 number here. Nevertheless, it is an existence proof of the kind of activity you have in mind.