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You might want to rethink the definition of "hardest problem" because I wouldn't expect the IMO committee to care particularly much that their problems are hard for machines as well as humans.

For example, if you look at the 2005 IMO, but suppose that problem 6 was geometry, so that the problem 3 was the "hardest", then you're in trouble. Problem 3 has a one-line proof "by sum_of_squares", assuming that someone has written a sum-of-squares tactic in time and that the sum-of-squares certificate is small enough to find within the time limit.

Alternatively, the IMO committee might set a problem without realizing that it's close to a special case of something already in mathlib.

As defined, I would put higher probability on solving the "hardest problem" than getting a gold medal and would bet on that.

Data from NSW, Australia. Delta was stable at 150-300 cases/day, so recent spike is likely omicron. 93% of people aged 16 or over are double-vaccinated.

Re. the NBA study, say I go get my antibody levels tested (which is easy here in Australia), do we know what counts as a high result?

Reusable respirator guide

  • In scope: information about half-facepiece reusable respirators. Out of scope: whether you should wear a mask, etc.
  • Reasons to prefer a reusable respirator over a disposable one: they're (i) more comfortable and (ii) prosocial, preserving disposable masks for medical personnel.
  • You need to buy two components: the mask and filters.
  • The mask. The wirecutter recommends 3M's 6500 series. I have the next model up, from the 7500 series. The 7500 comes in three sizes, small (7501), medium (7502) and large (7503). I think the idea of the sizing is: medium fits most, but there are also small and large (evidence: some stores only stock mediums). If you are familiar with the size of my head, I'm a medium. If outside the US, say in Australia, 3M masks might be hard to find, so you might try other brands like Sundstrom.
  • To disenfect the mask periodically, you can soak it in disenfectant.
  • The filters. These come in a vast number of options and it's all quite confusing. A good source of information is this 3M guide. For viruses, we're interested in particulate filtration. Summarizing page 3 of the 3M guide, a filter is described by a minimum efficiency (95%; 99%; or 99.97% \approx 100%) and a letter that describes whether the filter efficiency degrades in the presence of oil-based aerosols (N, R, P), which is not relevant for non-industrial use. You combine a letter with the minimum efficiency, e.g., N95 = minimum efficiency 95%, not suitable for use in the presence of oil-based aerosols, or P100 = minimum efficiency 99.97%, will not degrade in the presence of oil-based aerosols. Some brands will use European nomenclature: P2 = P95, P3 = P100.
  • A filter with higher minimum efficiency will be harder to breathe through. That said, I personally find it quite comfortable to breathe through a P100 filter (e.g., I find it easier to breathe through a respirator with a P100 filter than breathing through an N95 disposable mask), so I would recommend using a 99.97% efficiency filter. Maybe the trade-off between filter quality and how easy it is to breathe will be different for others.
  • Filters are sold in pairs. In terms of specific 3M P100 filter recommendations, the 2291 is the best (it's more expensive but designed to be easier to breathe through), then the 2091 is next best, and the 2296, 2297, 2096, and 2097 are fine too -- they have an extra layer of carbon filter for relief against nuisance levels of certain gases, which you don't need for virus filtration (but if you're walking around a busy city with lots of traffic, the 2297 or 2097 might be preferable). All these are fine though so get whatever is available. All of them are compatible with 3M 6500 or 7500 series masks.
  • I'm unsure how long a particulate filter lasts. I think the answer might be be months if you're not working in dusty environments. They become more efficient over time but harder to breath through. This 3M guide doesn't give a timeframe to expiry, it just says to replace them when they become dirty or difficult to breathe through.
  • Does the surface of a filter become contaminated? I don't know. Presumably? Maybe don't touch it. If you get a Sundstrom respirator, the filter is entirely encased in plastic, so you could regularly disenfect the parts of the mask that you can touch.
  • In the case of a shortage, there are a number of combination cartridges that filter against various gases as well as particles. For example, all those on page 18 of the first 3M guide. These will work for particulate filtration, you're just also paying for the gas filtration (in money, heaviness, and possibly in that it is more difficult to breathe through them).
  • Be wary of counterfeit filters. These are considerably cheaper.

Thank you very much for producing these. As someone who's rather time poor but trying to become more informed, they are very helpful.

It's also one night before full moon (which is at 4:50am on June 15), which should make the sky quite bright.

On a related note, consider what the moon looks like one night before it's full. Would you describe this as "over three-quarters full"? While that's technically correct, I wouldn't. I'd maybe describe a June 11-12 moon as "over three-quarters full" but I'd say a June 13-14 moon is "almost full". So we should up the probability that we're in a story/simulation/mirror.

Observation: If the purpose of this exercise is to run an AI box experiment, with EY as gatekeeper and the internet hivemind as the AI, then the ability to speak in parseltongue is problematic: It appears to make the game easier for the AI, thereby preventing the results from being generalized to a standard AI box experiment.

So why did Eliezer include the parseltongue constraint?

Maybe parseltongue is meant to introduce the concept of provability in a way that everyone can understand. To speak in parseltongue in real life, you just speak in logic statements and supply a proof with any statement you make. It seems reasonable (modulo computational complexity and provability concerns) for an AI to be able and/or required to supply proofs in an AI box experiment and parseltongue enables that in version of the game in the story.

I don't understand the constraint to speak only in parseltongue. Is that there to force us to focus on a solution set that is somehow of interest for friendly AI research?

Here's a flawed solution, but maybe someone can fix it.

Harry performs partial transfiguration on his brain, to transform it into a state where he thinks that he's booby-trapped the universe (for example, by transfiguring some strangelets along with a confinement field that will expire before the strangelets do). Then he just explains honestly to Voldemort why the universe will end if he dies.

The mirror and efficient simulation

Until the mirror appeared, the HPMOR universe could be simulated efficiently, at least as far as we knew. Time travel is limited to a six-hour cache; you can't transfigure arbitrary things, and Harry's attempts to use time travel to solve computational problems failed. This is likely to be deliberate.

So, how does the mirror exist? According to the inscription on the back, the mirror shows the actor's coherent extrapolated volition (CEV). Is this possible to compute efficiently from an actor's source code? I would guess not. (Is this right? Is there a hardness proof?)

Here are some possibilities to preserve efficient simulation:

  • The mirror is a trick and doesn't do what it says it does
  • Perhaps the NPCs are programmed to have known CEVs
  • Causality goes in the other direction. Computing the CEV from the source is hard, but constraining an actor to act in a way consistent with their CEV might not be. Perhaps everyone's CEV is set when they first look in the mirror, and then they are constrained to act in accordance with this. (This is somewhat akin to the way of avoiding paradoxes in a quantum universe with time travel, whereby if you go back in time and shoot your grandmother, the bullet diffracts around her.)
  • Maybe the previous item is only true of the NPCs. Is the mirror blank at the end of 110 because Harry is a PC (alternatively: simulating him is the purpose of simulation) and computing his CEV is too hard?
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