All of DavidS's Comments + Replies

As a minor addendum, I asked microcovid what it thought about spending 4 hours a day indoors unmasked with 20 people, but with a community incidence of 0.5%, attempting to simulate 2019 living with broad acquired immunity. It thinks this is 19,000 microcovids, suggesting it would still lead to infection in 50 days. This is depressing, I had hoped for a lot more gain than that.

Trevor Bedford took a crack at estimating the steady state back in October (so pre-Omicron). He came up with estimates of 20-30% of the population infected annually and deaths of 40K-100K per year in the US. https://twitter.com/trvrb/status/1448297978419101696 . Unfortunately, he didn't show enough of his work for me to understand where the 20-30% number comes from. Deaths is just multiplying number of infections by IFR. The big question mark here is whether high risk people will continue to get boosters; Bedford is guessing yes.

Here is my own attempt to e... (read more)

I am curious what kind of analysis you plan to run on the calibration questions. Obvious things to do:

For each user, compute the correlation between their probabilities and the 0-1 vector of right and wrong answers. Then display the correlations in some way (a histogram?).

For each question, compute the mean (or median) of the probability for the correct answers and for the wrong answers, and see how separated they are.

But neither of those feels like a really satisfactory measure of calibration.

"Naively in the actual Newcombe's problem if omega is only correct 1/999,000+epsilon percent of the time…"

I'd like to argue with this by way of a parable. The eccentric billionaire, Mr. Psi, invites you to his mansion for an evening of decision theory challenges. Upon arrival, Mr. Psi's assistant brings you a brandy and interviews you for hours about your life experiences, religious views, favorite philosophers, ethnic and racial background … You are then brought into a room. In front of you is a transparent box with a $1 bill in it, and an opaq... (read more)

A few years ago, I tried to write a friendly introduction to this technical part.

The grammar of the sentence is a bit hard to follow. When I am presenting this paradox to friends (I have interesting friends), I hand them a piece of paper with the following words on it:

Take another piece of paper and copy these words:

"Take another piece of paper and copy these words: "QQQ" Then replace the three consecutive capital letters with another copy of those words. The resulting paragraph will make a false claim."

Then replace the three consecutive capital letters with another copy of those words. The resulting paragraph wi

Well, I was trying to make the simplest possible example. We can of course add the monkey to our pool of experts. But part of the problem of machine learning is figuring out how long we need to watch an expert fail before we go to the monkey.

Suppose there are two experts, and two horses. Expert 1 always predicts horse A, expert 2 always predicts horse B, the truth is that the winning horse cycles ABABABABABA... The frequentist randomizes choice of expert according to weights; the Bayesian always chooses the expert who currently has more successes, and flips a coin when the experts are tied. (Disclaimer: I am not saying that this is the only possible strategies consistent with these philosophies, I am just saying that that these seem like the simplest possible instantiations of "when I act... (read more)

I thought it was interesting too. As far as I can tell, your result is special to the situation of two bettors and two events. The description I gave describes a betting method when there are more than two alternatives, and that method is strategy proof, but it is not fair, and I can't find a fair version of it.

I am really stumped about what to do when there are three people and a binary question. Naive approaches give no money to the person with the median opinion.

Here is another attempt to present the same algorithm, with the goal of making it easier to memorize:

"Each puts in the square of their surprise, then swap."

To spell this out, I predict that some event will happen with probability 0.1, you say it is 0.25. When it happens, I am 0.9 surprised and you are only 0.75 surprised. So I put down (0.9)^2 D, you put down (0.75)^2 D, and we swap our piles of money. Since I was more surprised, I come out the loser on the deal.

"Square of the surprise" is a quantity commonly used to measure the failu... (read more)

The operations on a Rubix cube aren't abelian. Is that just a typo on your part, or am I missing some subtle point you are making?

I'm not sure what you are getting at when you say you don't want to found math on sets. I definitely intended to use the word "set" in a naive sense, so that it is perfectly fine for sets to contain numbers, or rotations of a Rubix cube, or for that matter rocks and flowers. I wasn't trying to imply that the elements of a model had to be recursively constructed from the nullset by the axioms of ZFC. If you prefer "... (read more)

The reals can be studied as models of many theories. They (with the operation +, relation = and element 0) are a model of the axioms of an abelian group. They are also a model of the axioms of a group. The reals with (+, , 0, 1, =) are a model of the axioms of a field. The reals with (+, , 0, 1, =, <) are a model of the axioms of an ordered field. Etcetera...

Models are things. Theories are collections of statements about things. A model can satisfy many theories; a theory can have many models. I agree completely with So8res statement that it is importa... (read more)

"A model is an interpretation of the sentences generated by a language. A model is a structure which assigns a truth value to each sentence generated by some language under some logic."

I think this phrasing will be very misleading to anyone who tries to learn model theory from these posts. This is one thing a model DOES, but it isn't what a model IS. As far as I can tell, you nowhere say what a model is, even approximately. Writing out precisely what a model is takes a lot of space (like in the book you're reading!) so let me give an example.

Ou... (read more)

Let me suggest a world view which is much less negative than the other replies: I view panhandlers as vendors of warm fuzzies and therefore treat them as I would any other street vendor whose product I am most likely not interested in. In particular, I have no reason to be hostile to them, or to be disrespectful of their trade.

If they engage me politely, I smile and say "No thanks." I think the second word there is helpful to my mindset and also makes their day a little better. If they become hostile or unpleasant, I feel no guilt about ignoring ... (read more)

Here is an attempt to create a roadmap to the amplituhedron work. My relevant background and disclaimers: I am a mathematician with interests in particle physics who has been trying to learn about Arkani-Hamed and collaborators' ideas for the last two years. The specific result which is getting press now is one that has not been public for most of that time; my goal had been to understand the story of scattering amplitudes as described in his prior 154 page paper. I have been meeting regularly with a group of mathematicians and physicists here at the Unive... (read more)

"What hidden obstacle could be causing my failures?"

My mental shorthand for this is the following experience: I try to pull open the silverware drawer. It jams at an inch open. I push it shut and try again, same result. I pull harder, it opens a tiny bit more before stopping.

Reflection: Some physical object is getting in the way of the motion. Something could be on the drawer track, but more likely it is inside the drawer. It is a rigid object, because I always stop at the same place, although slightly squashable because I was able to yank and p... (read more)

So, what do you all think is Voldemort's goal here? In canon, he was a power hungry sadist, so conquering the world while torturing his minions made sense. But MOR!Voldemort seems to find people tiresome and is happiest as an immortal in lifeless space. In that case, why not Horcrux Pioneer 11, kill his earthly body and be done with it?

At the moment, he has a plausible motivation -- provoke Harry into discovering a better form of immortality than Horcruxes, and use it for himself. But it seems implausible that this was his goal until Harry came to Hogwart... (read more)

I remember hearing the story of a mathematical paper published in English but written by a Frenchmen, containing the footnotes:

1 I am grateful to professor Littlewood for helping me translate this paper into English.2

2 I am grateful to professor Littlewood for helping me translate this footnote into English.3

3 I am grateful to professor Littlewood for helping me translate this footnote into English.

Why was no fourth footnote necessary?

Other nitpicks (which I don't think are real problems):

If the Wikipedia article on Kakatuni's fixed point theorem is to be believed, then Kakatuni's result is only for finite dimensional vector spaces. You probably want to be citing either Glicksberg or Fan for the infinite dimensional version. These each have some additional hypotheses, so you should check the additional hypotheses.

At the end of the proof of Theorem 2, you want to check that the graph of is closed. Let be the graph of . What you check is that, if ) is a sequence of points in which app... (read more)

In the proof of Theorem 2, you write "Clearly is convex." This isn't clear to me; could you explain what I am missing?

More specifically, let ) be the subset of obeying %20%3C%20b%20\%20\implies%20\%20\mathbb{P}\left(%20a%20%3C%20\mathbb{P}(\lceil%20\phi%20\rceil)%20%3C%20b%20\right)%20=1%20). So }%20X(\phi,a,b)). If ) were convex, then would be as well.

But ) is not convex. Project ) onto in the coordinates corresponding to the sentences and %20%3C%20b). The image is %20\cup%20\left(%20%20[0,1]%20\times%20\{%201%20\}%20\right)%20\cup%20\left(... (read more)

This is pretty close to how I remember the discussion in GEB. He has a good discussion of non-Euclidean geometry. He emphasizes that originally the negation of Parallel Postulate was viewed as absurd, but that now we can understand that the non-Euclidean axioms are perfectly reasonable statements which describe something other than plane geometry we are used to. Later he has a bit of a discussion of what a model of PA + NOT(CON(PA)) would look like. I remember finding it pretty confusing, and I didn't really know what he was getting at until I red some act... (read more)