mathgenius

What kind of mathematics have you been trying to learn?

Have you seen this: https://twitter.com/jonathanmccabeX ?

How does this work? Is it a C++ lib with python interface? Does it use llvm for the JIT? ...

John Baez was tweeting about this recently:

https://twitter.com/johncarlosbaez/status/146720413326244659...

He mentions Amir Alexander's book "Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World". It's a gripping read, I would highly recommend it. Here is a quote:

    On August 10, 1632, five men in flowing black robes convened
    in a somber Roman palazzo to pass judgment on a deceptively
    simple proposition: that a continuous line is composed
    of distinct and infinitely tiny parts. With the stroke
    of a pen the Jesuit fathers banned the doctrine of infinitesimals,
    announcing that it could never be taught or even mentioned.
    The concept was deemed dangerous and subversive, a threat
    to the belief that the world was an orderly place, governed
    by a strict and unchanging set of rules. If infinitesimals
    were ever accepted, the Jesuits feared, the entire world
    would be plunged into chaos.

I agree. It's good writing! So many artists complain about their lack of talent, this person is in good company.

Yeah I agree. There's so many details to work out about controlling these things that this is still significant progress. It's like we need an Elon Musk of quantum to tell us what's going on. We are making these just to blow them up, they aren't going to the moon.

It's over here: [1]. James Wootton makes some comments about it here [2]. Looks like 1% error rate which I think is too high to do much with, but it is still exciting progress for those of us working in the field!

[1] https://quantum-computing.ibm.com/services?services=systems&...

[2] https://twitter.com/decodoku/status/1460616092959883265

Modern ML algorithms are so powerful they will soak up any entropy that leaks into the data whatsoever. Much of the time spent developing these models is checking that this isn't happening. I compare it to high voltage electricity: a 100kV line needs some serious insulation around it.

If you are not excited by what you are building then there's something missing. I'm not sure that "build things for others" means anything. But maybe you're just a really great person and want to help others, I don't know. There's nothing wrong with "yet another Genshin impact wishes simulator" (wtf is that?) if you are excited about it! But you don't sound excited about it.

Yes, this is exterior algebra. It's also interesting to figure out how this works in ambient dimensions other than three. The author has a table of grades: 0 for scalars, 1 for vectors, 2 for "bivectors", 3 for "trivectors", and they count the number of bases for each of these grades as 1 3 3 1. These basis counts are the dimensions of the (vector space of) scalars, vectors, "bivectors", "trivectors". If you go to two ambient dimensions you get 1 2 1, and if you go to four ambient dimensions you get 1 4 6 4 1. It's Pascal's triangle.

What's the website?

I find traffic in LA is extremely chilled. For example, on the smaller roads turning cars yield to pedestrians always (at least in the more affluent areas). This is pretty unique. I've lived in big cities in four different countries and LA traffic is the most relaxed i've found anywhere.

Thanks for the feedback. Do you want your time refunded, or do you want answers to your questions? The two seem to be in contradiction. If it's the former then what is your hourly rate for watching well-intentioned youtube videos made by experts in the field ?

That sounds reasonable. On the other hand, if a quantum computer dropped out of the sky tomorrow, virtually no one would know what to do with it. So there is plenty of infrastructure, tooling and know-how that needs to be produced in that 10+ year timeframe. And there will likely be huge demand for all of these things as big co's scramble to get on the bandwagon.

> whose power cannot be really removed

Yes. It may not be too worrisome right now, but what if the cryptocurrency phenomena became several orders of magnitude bigger? Couple that with climate wars, failed states, and malignant corporations. I can imagine some very grim outcomes indeed.

And here is linear algebra as path counting [1]. This is closely related to path integrals in quantum physics. The rules for combining quantum amplitudes are the rules for combining path counts [2]. This is also how graphical linear algebra works [3]. And since we are all hackers here, if you replace the underlying number system with the min-sum semiring you get things like Dijkstra's algorithm. I really like how all these ideas are related.

[1] https://www.youtube.com/watch?v=ei6RfbplYZM

[2] https://www.feynmanlectures.caltech.edu/III_03.html

[3] https://graphicallinearalgebra.net/

Bart Jacobs is working on a book that uses the language of category theory to develop probability theory:

https://www.cs.ru.nl/B.Jacobs/PAPERS/ProbabilisticReasoning....

Yeah, I don't see how the colours are helping. It does make it look friendly and inviting, but switching back and forth between coloured balls and the usual symbolic mathematics (algebra notation) is jarring and confusing to me. Using colours instead of letters is a superficial trick and basically a step backwards. It's like those algebra memes where they use fruit instead of x, y, z etc. What's the point? But anyway I don't want to sound too dismissive because the mathematics literature definitely needs more of this kind of creativity!

One of the creators is on twitter:

https://twitter.com/neozhaoliang

It would be nice to understand (explicitly see) how these Coxeter diagrams give rise to these honeycomb pictures exactly.

The fourth dimension is enough to untangle a knot made out of a one dimensional space (a loop of string). But you can make two dimensional knots in four dimensional space: this is a surface that is knotted with itself in four dimensions. And probably the pattern extends to higher dimensions.

Yes. But also, it was pretty obvious to me at the time what was going to happen, modulo some details.

What I did not predict was that I would end up living in many different cities in many different countries, including Los Angeles and New York City. And by far, Americans are the most kind-hearted, generous and polite people I've found anywhere. Even the beggars in Manhatten would be more interested in how I am going and cheering me up than in actually getting any money out of me.

It's not just about memorizing stuff.. I think you need to find a different teacher, if you really are keen to keep going.

The python numba people learnt this lesson also: forget about the C++ api, just emit the (text) IR directly and feed that into LLVM.

Agree. The guy pretty much invented field theory. Yes, Maxwell wrote the equations, but Faraday had the great conceptual insights. For more on how this evolved into modern gauge theory:

https://www.physics.umd.edu/grt/taj/675e/OriginsofMaxwelland...

Yes, this is the interesting part of the story. I was just wondering how it works exactly. Is there a black market lebanese pound / USD? There is no mention of this in the article. Or do they use some kind of offical lebanese pound / USD exchange? If so how does that work, can you just show up at some office somewhere with local currency and get USD?

I'm an Australian in Krakow & I'd recommend it. Plenty of people understand English, and it's a small enough city that the vibe is fairly relaxed.

Places like this will help with a visa for a more extended stay so you can run your "startup":

https://twojstartup.pl/

> being graduated isn't worth anything these days

I'm gen-X and it's been like this for as long as i've been around too.

Degree says "this one is reliable / knows how to finish stuff". That's it.

I guess that a similar story could have happened to Greece. Nice to hear that crypto is helping people in such dire need of economic stability, although it was not clear from the article what happens to the lebanese cash that was used to purchase USDT. Someone must be left holding the bag, there must be some FX liquidity that they tap into?

"Negative spaces", I like this terminology for what the author is describing. This effect seems particularly prevalent on twitter, where it is just impossible to not leave stuff out. Then someone else comes along and inserts their own mindforms into the negative space, and hey presto, suddenly the original tweet means something entirely different to what was intended.

I think this is just a misunderstanding of the nature of language. It's closely tied to the "AI" fallacy; that we can encode meaning in mechanism. Somehow we need to keep re-learning this lesson, and many people refuse to give up on finding meaning in mechanism. I agree it does seem tantalizing, so I can empathize with this search for AI. But there are alternatives.