meiji163

A better description is "simple", not "easy".

"If you do not believe that mathematics is simple, it is only because you do not realize how complicated life is." -von Neumann

Some favorite math books

Intro to Smooth Manifolds, Lee -- sweeping intro to geometry with minimal prereqs, great at balancing the nitty gritty details with conveying intuition

A Course In Arithmetic, Serre -- classically terse and elegant intro to algebraic and analytic number theory. Goes from quadratic forms to Dirichlet's theorem to modular forms in a mere 100 pgs!

Princeton Lectures in Analysis, Stein & Shakarchi -- 4 books covering much of classical/modern analysis, they really shine in their discussion of applications

The large scale structure of space-time, Hawking & Ellis -- The most mathematically satisfying treatment of general relativity I've found. High points include proof of singularity theorems!

Spin Geometry, Lawson & Michelson -- Deep dive into the enigmatic "spin groups" and their applications in geometry. Also the only good (book) reference I could find on the index theorem

Milnor is a wonderful writer, in his books as well as his papers.

> I'm not sure how useful category theory actually is in the example cases.

It's hard to say that category theory is "applied" to this or that problem. you'll hear many mathematicians call it "abstract nonsense" half-jokingly. More than anything it's a unified way of talking about mathematical structures that gives you a certain point of view (which is where it might be useful).

The best book I've found for a non-math audience is Fong & Spivak, 7 Sketches in Compositionality.

In Theorem 1.1, f is a function of random variables, which might be where you're confused.

> doesn't that mean y is a predictable function of x

Sort of: as function of real numbers, sha256 is just some deterministic function. But point is its output "looks like" a uniform random variable for any reasonable input distribution i.e. as a function of random variables the input and output variables should have 0 correlation

Not only is the diagnostic framework a joke, it's the basis of immense amounts of iatrogenic harm [0]

[0] "Anatomy of An Epidemic", Robert Whittaker

+1 I recently read a The Idiot as well, another incredible work of his.

I'd be interested to see if these models are robust against algorithms like TextFooler [0]. I'm skeptical this trend of 10x'ing the parameters will solve the "clever hans" problem.

[0]: https://github.com/jind11/TextFooler

This article is a great example of what I'd call "mindless problematization" From what I've seen, this is you're trained to do in modern humanities departments. Take any seemingly obvious claim and "problematize" it.

It's telling that they do not say "nuance" it, rather it has to be made a _problem_. e.g. if you think "wilderness" is a thing you subscribe to a racist idea for "white male elites", if you think social media is affecting childhood development you're just caught up in the religious fervor of "scientized version of the biblical story of the Fall".

A whole lot of BS gets written this way, because these arguments have the superficial air of being subversive and contrarian.

I'm a fan of deepmind and all, but this story has been way overblown based on what I saw in the actual code. There's nothing particularly new about mathematicians using computers to investigate and make conjectures, even if you add ML into it.

What is the bottom line on masks and COVID-19? I am really out of the loop, since the toxicity of the debate was exhausting. The last I heard was that transmission is mostly via aerosolized viral particles, so most masks are essentially useless except N95 or higher grade.

Anyone have resources I can check out? thanks

Language models have the same defect - they are quite brittle and susceptible to black-box adversarial attacks ( eg arxiv.org/abs/1907.11932 )

I wonder if LZ would still be standard, if not for the inertia of gzip/zip? There are surely better and comparably fast algorithms (paq, ppm, etc.)

Tim Hecker!!

"I'm something of a scientist myself" -- Data Scientist

They'll put anything on hep-th nowadays

You can get a very good intuition with 3B1B's video ( https://www.youtube.com/watch?v=zjMuIxRvygQ )

The strongest open source engine right now is KataGo (https://github.com/lightvector/KataGo)

Throwing money at a corrupt bureaucracy didn't solve a complex problem? Shocker. Proposition HHH allocated $1.2 billion towards the problem and essentially nothing was accomplished.

Using a pretrained model is a little bit cheating, you would have to include the size of the weights in the ratio

I was just working on a similar project and didn't think you could do decode without sending weights, amazing!

It's just the fact that 1, 10, 100, 1000, ... = 1, 3, 2, -1, -3, -2, ... (repeating) mod 7

Here's a way I do it in my head: For every block of six digits "fedcba" calculate (a-d)+3(b-e)+2(c-f). The number is divisible by 7 if the sum is divisible by 7. Fun thing is you know any number with digits "abcabc" is divisible by 7.

What's amusing is that multiplying integers with periodic digits is much faster using this method

> What is the explanation for the flexibility in the weights? How much flexibility is there?

most of the terms are on the order of 1/N so on these would be negligible

Can someone liberate the article from behind the paywall for me?

I have to disagree on Einstein, without the field equations it's doubtful psuedo-Riemannian geometry or so-called "Einstein manifolds" would be so big in math. There is also his work on Brownian motion and diffusion. Even if you deny he did "mathematical research" his importance for mathematics justifies him being on a timeline of mathematics .. imho

My favorite is Context Tree Weighting (CTW) (https://ieeexplore.ieee.org/document/382012). Mathematically it's much nicer than PPM. Modern implementations of CTW achieve ratios close to or better than PPM in most domains (see e.g. P. Volf's Thesis "Weighting techniques in data compression")

>Cryptocurrency is a pseudo-asset built around the dubious notion of “speculation for speculation’s sake”

No, some people think scarcity and trustlessness make it a good store of value. This is not even addressed in the article.

> Cryptocurrencies disproportionately victimize vulnerable people and those in marginalized communities without access to traditional investments or financial advisory.

I don't see any good evidence for this, the goal of many DeFi projects is to increase access.

Overall an unfair and needlessly inflammatory evaluation. The idea that all cryptocurrency is a scam that "masses of dumb money investors" buy into is overbearingly pretentious, and a non-starter for legitimate criticism IMO.