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zyklu5 commented on Manuscript of Ismail al-Jazarī's Ingenious Mechanical Devices (ca. 17th century)   publicdomainreview.org/co... · Posted by u/YoctoYARN
everdrive · 10 months ago
I thought you were going to go the other direction. All I ever read is that the west relied on Islamic science and math, but "no one" will acknowledge this. Except of course it's the only perspective I ever hear about, so I'm not sure who this mythical "no one" is. On the other hard, vanishingly few sources do seem to acknowledge that the Islamic sources "stood on the shoulders" of Greeks and others. Ibn Khaldun states this directly in the Muqaddimah: "The sciences of only one nation, the Greek, have come down to us, because they were translated through al-Ma'mun's efforts."

The full quote:

"The subject here is different from that of these two disciplines which, however, are often similar to it. In a way, it is an entirely original science. In fact, I have not come across a discussion along these lines by anyone. I do not know if this is because people have been unaware of it, but there is no reason to suspect them (of having been unaware of it). Perhaps they have written exhaustively on this topic, and their work did not reach us. There are many sciences. There have been numerous sages among the nations of mankind. The knowledge that has not come down to us is larger than the knowledge that has. Where are the sciences of the Persians that 'Umar ordered wiped out at the time of the conquest! Where are the sciences of the Chaldaeans, the Syrians, and the Babylonians, and the scholarly products and results that were theirs! Where are the sciences of the Copts, their predecessors! The sciences of only one nation, the Greek, have come down to us, because they were translated through al-Ma'mun's efforts. (His efforts in this direction) were successful, because he had many translators at his disposal and spent much money in this connection. Of the sciences of others, nothing has come to our attention."

zyklu5 · 10 months ago
Indeed. In fact, it is one of the most amusing aspect of the anglophone west (at least for the last few decades). Despite public perception (by public I mean those who have been to university since the 90s), Western historians of science and mathematics in general have never not acknowledged the previous works of the Persianate civilizations commensurate to their knowledge of them in their time. But somehow in the last few decades professional historians have had to waste time figuratively looking over their shoulders lest they be percieved as being Eurocentric. And, if they were to somehow find a way to show -- requiring whatever hermeneutical gymnastics -- that a prominent scientist was influenced (or even better, had stolen) from some other "cultures" than nothing better! (ex: Copernicus from the Maragha school as an example of interpretive gymnastics)

But, of course, this is one of the symptoms of the degeneration that now afflicts your particular civilization and is bringing about it's inevitable transformation to something else -- but better this than the fate of the Abassids or the Sung.

zyklu5 commented on Electron band structure in germanium, my ass (2001)   pages.cs.wisc.edu/~kovar/... · Posted by u/tux3
Y_Y · a year ago
A thing of beauty is a joy forever - John Keats

Honestly, physics is so full of pretension and hero worship. Even among seasoned lecturers there's a tendency to mythologise the progress of the art by making it sound like all the great results we rely on were birthed fully-formed by the giants who kindly lend us their divine shoulders.

Ironically there's a kind of Gell-Mann amnesia here, working scientists know that must of your work will consist of stumbling down blind alleys in the dark and looking for needles under lampposts that aren't even near the haystack.

I'm reminded of an anecdote which I can't currently source, but as I remember it Hilbert was trying to derive the Einstein Field Equations by a variational method. He correctly took the Ricci curvature R as the Lagrangian, but then neglected to multiply by the tensor density, sqrt(-g). This is kind of a rookie mistake, but made by one of the history's greatest mathematical physicists.

Anyway I love this article, it's a breath of fresh air and rightly beloved by undergrads.

(edit: for a counterpoint to this work please see another classic: "The physics is the life" -http://i.imgur.com/eQuqp.png )

zyklu5 · a year ago
On the contrary, what is presented by the OP is one of the many reasons that worship of science's heroes, unfashionable for decades, a whiggish pablum, is justified. If great results were birthed fully-formed -- a view I've frankly never heard anyone profess who has bothered to consider such things even briefly -- they would hardly be any heroes. Even little children who reflexively chomp on every superhero film aeroplaned towards their face understand this.

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zyklu5 commented on Lemma for the Fundamental Theorem of Galois Theory   susam.net/lemma-for-ftgt.... · Posted by u/susam
computator · a year ago
> one of the best texts on Galois Theory I have read

What book on group theory or abstract algebra would you recommend to read first to be able to read that text on Galois Theory?

zyklu5 · a year ago
If I'm being honest I really don't have a good recommendation for a text in intro abstract algebra. I learned it from Michael Artin's Algebra. Artin is a true master -- along with David Mumford, he was the main apostle for Grothendieck style AG in the US -- but his book was not very easy to learn from.
zyklu5 commented on Lemma for the Fundamental Theorem of Galois Theory   susam.net/lemma-for-ftgt.... · Posted by u/susam
almostgotcaught · a year ago
> It begins with a quick one chapter intro of Arnold's proof of Abel-Ruffini.

The key to understanding/motivating Galois theory is Abel-Ruffini, which is a corollary of Galois. And the simplest way to understand that is Arnold's topological proof, which i learned about from this video

https://www.youtube.com/watch?v=RhpVSV6iCko

Watching that video and rolling it around in my head completely demystified Galois theory for me, years after literally 2 semesters of algebra in undergrad. Everything about normal subgroups and commutators and splitting fields and blah blah blah immediately became tangible and obvious. It should be a crime not teach this proof first.

The coverage in Koch's book looks good too - lots of pictures - and funny enough it links to a different youtube video.

Edit: copy-pasting notes I took from the video after watching.

------

The idea is to continuously perturb each of the coefficients of the polynomial along a loop (change each of them from their initial value such that they traverse a path that returns them to that initial value at the end of the path) and study what happens to the roots of the polynomial.

Note, once all coefficients have returned to their original values the entire set of roots also returns to itself, but each root does not necessarily returns to its original value. In general you get a permutation of the set of roots and so in this way we get a mapping between loops of the coefficients and permutations of the roots.

Also note, we can produce coefficient loops that map to any permutation of the roots by permutating the roots and “watching” the coefficients.

Hence, the way to prove Abel-Ruffini is to show that any expression involving the coefficients (ie formula for the roots in terms of the coefficients) returns to itself after the coefficients traverse their loops but the roots do not (and therefore the expression cannot capture all of the roots). For example, an immediate corollary of the construction of the mapping between loops of coefficients and roots is the fact that a general solution involving only -, +, ×, ÷ is not possible; -, +, ×, ÷ are all single-valued and therefore no composition thereof could produce multiple roots.

zyklu5 · a year ago
There is indeed a deep connection between what is going on behind Arnold's proof and the classical Galois theory. But it needs quite a bit of sophistication to flesh out properly (not apparent in his famous lectures given to high school kids). There is a Galois theory for Riemann surfaces over algebraic functions where the coverings behave like fields do in the classical correspondence. If any one is interested, check out chapter 3 of Khovanskii's Galois Theory, Coverings and Riemann Surfaces.
zyklu5 commented on Lemma for the Fundamental Theorem of Galois Theory   susam.net/lemma-for-ftgt.... · Posted by u/susam
zyklu5 · a year ago
Let me take this opportunity to post one of the best texts on Galois Theory I have read -- and I had to go through quite a few while preparing for a class.

https://pages.uoregon.edu/koch/Galois.pdf

The subject is developed very naturally and every idea is beautifully motivated. It begins with a quick one chapter intro of Arnold's proof of Abel-Ruffini.

Richard Koch's home page (https://pages.uoregon.edu/koch/) has other examples of his fantastic pedagogy.

zyklu5 commented on It is as if you were on your phone   pippinbarr.com/it-is-as-i... · Posted by u/bookofjoe
magic_hamster · a year ago
I guess this really shows my age because I can't find any reason for this to exist. Do people really feel "pressured" to be on their phone? What kind of terrible dystopia do these people live in? Why do you give a flying f** about what people on the bus that you'll never see again think that you should be doing? I feel so much pitty for anyone feeling this. It's not a healthy mindset.
zyklu5 · a year ago
You know how in every zombie movie there's a bit where our intrepid protagonists must blend in to avoid capture. I think this is that sort of thing.
zyklu5 commented on Mathematics in the 20th century, by Michael Atiyah [pdf] (2002)   marktomforde.com/academic... · Posted by u/practal
zyklu5 · a year ago
Atiyah is truly one of the giants of modern mathematics. I remember long ago I struggled through a reading course of his and Bott's Yang-Mills paper in graduate school. Like many great works of math it too had that paradoxical characteristic of transforming seemingly 'non-mathematics' into mathematics* by reversing the usual direction of application of one to the other, in this case, from physics to math. It would start a whole movement that'll produce much of modern geometries greatest hits like Donaldson's (his student) theorem in 4 manifolds to Witten's great papers.

* A reason I think modern LLM architecture as they currently stand with their underlying attention mechanisms will not produce interesting new mathematics. A few other ideas are going to be needed.

zyklu5 commented on Children's arithmetic skills do not transfer between applied and academic math   nature.com/articles/s4158... · Posted by u/rbanffy
almostgotcaught · a year ago
> Richard Feynman is just writing about his personal experiences

Let's see

1. The personal experiences of a guy with no formal training in pedagogy or education

2. A research paper in nature written by expert education economists

Hmmmmmmmm

zyklu5 · a year ago
And why should I simply assume that "Education Economists"* really know the subject they purport to talk about? Because they are credentialed members of university departments with some label? Because a few of them won some Bank of Sweden award?

Just because a particular department or field of study exists in academia does not magically give them the imprimatur you think it does.

* Btw, I know for a fact that a few of them are not "education economists"

zyklu5 commented on Notes on OpenAI o3-mini   simonwillison.net/2025/Ja... · Posted by u/dtquad
maxdo · a year ago
How would you rate it against Claude ? Didn’t test it yet, but o1 pro didn’t perform as good
zyklu5 · a year ago
Claude is still better in my opinion.

There's a suite of code-related tasks -- covering a diversity of areas, including dev ops, media manipulation etc., derived from issues I have faced over the years -- I perform for every new release. No model has solved the set of issues solved in one go but Claude still remains the best.

An example of the sort of problems in the suite:

> I have a special problematically encoded mp4 file with a subtle issue (something I ran into a couple of years ago while fixing a bug in a computer vision pipeline). In the question prompt I also pass the output of ffprobe and ask for the ffmpeg command that'll fix it. Only Claude has figured the real underlying issue out (after 4 interactions).

u/zyklu5

KarmaCake day133October 25, 2023View Original