woopwoop

I've met a handful of people who have won at least one of the top prizes in mathematics, i.e. a Fields medal, Abel prize, or Wolf Prize. I would describe none of them as "weird nerds", and I don't think any of them are autistic. I chafe pretty hard at the suggestion here that one has to be socially ill-adjusted to advance scientific knowledge at the highest level.

I guess it's all in the way you look at things. I would say that the addition formulae for sine and cosine are more weird and technical than the Banach fixed point theorem, which I would say is much more fundamental.

I think mathematics is in a good place with regards to tolerance of self-promotion. I do not think that we should put up with excessive hype in the name of "humanizing" papers. I do think that a lot of mathematicians do not provide enough detail or motivation for their arguments. Not necessarily motivation in the sense of "why is this important", but motivation in the sense of "we are beginning a three page proof. Let me give you a paragraph to give you the outline so that you can fill in the details yourself, rather than having to read all of the details just to reconstruct the outline."

I do have a pet peeve about mathematical exposition. At some point, phrases like "obviously" and "it is easy to see" became verboten, or at the very least frowned upon. The problem is that it didn't become verboten to skip details (this would be impossible in general), and those phrases actually do contain information. Namely they contain the information that there actually is some detail remaining to fill in here. Often in papers there will be some missing detail which is not so hard to verify, but whose presence is so ghostly in the exposition that I think I've missed somewhere where it was stated explicitly, and have to go back. I feel like this is the case of someone excising an instance of "it is easy to see that" and replacing it with... nothing.

This is not the greatest essay in the world. No, This is just a tribute.

I know you're being facetious, but there's something to this. Both reading and listening are passive. They're indistinguishable from each other, but both are quite distinguishable from writing, or reading the way you would "read" a math or physics textbook (which involves very little of the activity of scanning words on the page and very much of the activity of scribbling stuff in a notebook and then staring at it for awhile).

Imagine you learn about some new conjecture in mathematics, and you try to predict when it will be resolved. Your prediction says that there is a 50% chance that the conjecture is resolved in the next 25 years, and a 90% chance it is resolved in the next 50 years. So, conditional on the conjecture not being resolved in the next 25 years, there is an 80% chance the conjecture is resolved in the subsequent 25 years. Wouldn't that be a little strange?

The article was about consumer goods in general, so data about cars overall is more relevant than a single brand. Nonetheless, the Toyota Prius is, by reputation, a very reliable car. Here a used car website used it's data to estimate car model's lifespan, finding that a Toyota Prius has a potential lifespan of 250000 miles, much greater than anything from the 1980s.

https://www.thestreet.com/personal-finance/cars-that-will-la...

They were simpler and easier to repair, but they absolutely did not last longer.

So this article implies that a number of things that we buy previously were built to last longer, and indeed did last longer. The first few examples are kitchen appliances. In this case I don't really know, but I'm at least willing to listen. Ultimately the evidence is people responding to a thread on Twitter where he solicited complaints. Not so compelling.

But then he mentions a "hybrid sedan". Here I'm aware of the data. It's not close. Modern cars are much, much more reliable and durable than ones built at any time in the past.

[0] https://www.nytimes.com/2012/03/18/automobiles/as-cars-are-k...

[1] https://www.jdpower.com/business/press-releases/2021-us-vehi...

The guy wants her to buy or found a music company. That's the point, I'd you were wondering.

I don't think that is true? As far as I know the grokking phenomenon was first observed (and the name coined) in this paper, not in any blog post:

https://arxiv.org/abs/2201.02177

The average American spends about an hour a day driving. You are awake for about 16 hours a day. So truly self-driving cars, where you can fall asleep or pull out your laptop and work on something else, give you 1/16th of your life back. If you live to the age of 80, it's like an extra five years.

That's worth a lot. Some kind of hybrid state where you need to always have your eyes on the road but maybe can take your hands off the wheel? Yeah I agree, I don't really see the point in that case. Or at least it's not something I get excited over.

Is he short microsoft?

This is from the GMU economics department. I actually agree with a lot of the worldview of the people there, but it is clearly a political project, not an academic one. Noteworthy wealthy political activists have donated enough to the department to pay the majority of the faculty's salaries for many years. For better or for worse (I think mostly for better), most academic departments are not like this one; it's nearly unique.

Yes

The model is open source

https://github.com/facebookresearch/segment-anything/

In this context does the word "system" have a different meaning than "thing"?

They've flagrantly violated her right to infect strangers with a deadly respiratory disease.

The point is the update method they use is the same one you'd get from using Newton's method to find the roots of the function f(x) = x^2 - 2.

A copy of the classic "Mathematics Made Difficult" (which by the way is perhaps the pinnical of human literature) is saved to my desktop as mathhard.pdf

Is it even a new evaluation? The article is really unclear.

Badly. It can't do math, to an extent which is honestly surprising given how well it produces code. I suspect that this will improve significantly in the next couple of years, but I kind of hope I am wrong. I am a mathematician by training, and I have my own romanticism.

For example, I tried a bunch of times to get it to give a proof of the infinitude of the primes. This should be repeated many times in its training data, and it clearly is given it's responses, but it always goes off the rails around the third sentence. Here's an example:

> One way to prove that there are infinitely many prime numbers is to use the contradiction method. Assume for the sake of contradiction that there are only finitely many prime numbers, say, p₁, p₂, ..., pₙ. Then we can form a new number N by multiplying all of these prime numbers together and adding 1: N = p₁ * p₂ * ... * pₙ + 1. Because N is greater than any of the prime numbers p₁, p₂, ..., pₙ, it cannot be divisible by any of them. Furthermore, N is not 1, so it cannot be a composite number (i.e., a number that can be written as the product of two smaller numbers). Therefore, N must be a prime number, contradicting the assumption that there are only finitely many prime numbers. This contradiction shows that our assumption must be false, and therefore, there must be infinitely many prime numbers.

No, this statement is true for every graph that doesn't have constant degree. It's not really to do with random graphs. Rather it's the fact that a random neighbor of a random node draws from a different distribution than a random node, and the former distribution puts more mass on nodes of higher degree.

The first thing I tried was "Lipschitz selection", a somewhat overloaded phrase that I encountered a lot in graduate school. I guess I had in mind a summary of this paper:

https://arxiv.org/abs/1801.00325

but would have been happy with a description of work related to this paper:

https://arxiv.org/abs/1905.11968

or any number of other things.

The page I got stated the following, obviously false, "theorem": let M be a metric space, and let S be a subset of M such that inf_{y in S} d(x, y) < infinity for all x in M. Then there exists a map f: M to S such that f(x) = x for all x in S. As far as I can tell, this isn't a garbling of something which is true, it's just nonsense.

It suggested that I look up "Whitney extension" which is indeed related to the first paper I posted, so I did that. The opening summary, if you squint hard enough, could arguably be interpreted as true:

> The theorems state that any sufficiently smooth function on a closed subset of Rn can be extended to a function on all of Rn with the same level of smoothness.

This is really vague though. Like if someone didn't know the actual statement of Whitney's theorem, they would not be able to intuit it from this sentence. You have to be really, really charitable to describe it as true. I'm not being nitpicky here, Whitney produced a pretty non-trivial definition of the notion of a C^m function on an arbitrary closed set (basically you have to specify the entire mth order Taylor polynomial at each point, or a section of the jet bundle if you're fancy). You can check out the actual wikipedia if you're interested:

https://en.wikipedia.org/wiki/Whitney_extension_theorem

The body of the generated article goes into more detail, and again produces something which is completely false, and not particularly close to anything that is true:

> Whitney's extension theorem states that any continuous function on a closed subset of Rn can be extended to a C∞ function on Rn.

Finally, I should just say that this is all still really impressive. The sentences are grammatical, and use words somewhat related to the subject at hand. I could imagine a student who hadn't studied the material and was totally in over his head in the class writing things like this on an exam! But I would never use this as a research tool.

Do any of those applications use neural nets in any non-trivial way? I'm pretty sure that kind of stuff is all classical statistical modeling.

> They literally designed this entire thing for dads that couldn't get the hang of T9

I had a phone like this, although not that model. It was great, T9 sucked. In fact, it was much more pleasant to type on than a touch screen.

That seems fine to me. What's so sinister about that?

I feel like the phenomenon of people in their twenties living with their parents should only be attributed to deep cultural currents after we're 100% sure that it's not the exploding cost of housing in the most productive, well-paying metropolitan areas (which also happen to be the most fun places for a young adult to live).

One example I can think of is the use of the phrase "current thing" to pejoratively describe when a certain political issue that no two reasonable people could disagree about, such as a dictatorship waging a brutal war of imperial conquest on a burgeoning democracy, develops high salience.

What is the point of reading? Most people would say "learning". So, to be provocative, I will make the following, slightly exaggerated, point. I have never, not once in my life, learned something important by reading about it. Everything meaningful I've learned, I've learned by doing. When you read a textbook, you can almost skip to the exercises immediately. That's where the learning is done anyway.