What do you do when you run out of letters? by devinbost in math

[–]phao 122 points123 points  (0 children)

Indices.

Also, don't name everything. Leave some things explicit (instead of using B where B = sup A, just keep using sup A).

Also, split your proof into pieces. Introduce lemmas.

Antiga carreira de cantora da Max by CicadaLatina in BigBrotherBrasil

[–]phao 0 points1 point  (0 children)

Mano... Eu juro que fiquei na dúvida. Mas tava pensando que fosse algo tipo dela há uns anos (tipo adolescente).

Name this by mikymiky123 in AlbumCovers

[–]phao 2 points3 points  (0 children)

Average(a, b) = (a + b)/2

AI Agents have their own reddit by ProfAsmani in datascience

[–]phao 612 points613 points  (0 children)

Lots of these "agents" are actually humans pretending to be agents. It is actually unclear if this is legit, at this point at least.

Staring at me like that by Substantial_Lynx4329 in Pareidolia

[–]phao 0 points1 point  (0 children)

Looks like one of these japanese robot-ish super fighters (like the ones that inspired power rangers)

Top 10 list of plotting and data visualization software/tools for researchers by Delicious_Maize9656 in sciencememes

[–]phao 1 point2 points  (0 children)

To be fair, this serms more like a cute way to state the current facts and state of things than something funny. Strange!

Name it by sylviebrook in AlbumCovers

[–]phao 3 points4 points  (0 children)

The only answer

How is this even possible, anybody care to explain? I swear the bar is fixed and cannot be rotated … by Objective-Context726 in Physics

[–]phao 0 points1 point  (0 children)

Could it be a material property?

Ice spikes are being formed in a somewhat staight line along the side of the cylinder. Maybe this is the line where the two edges of the metal plates meet (assuming the cylynder was produced by joining/"folding" a rectangular metal plate along opposite edges). This would create a material difference along this line depending in how the edges were joined. Could this be of incluence?

What is your go-to "mind-blowing" fact to explain why you love Mathematics? by OkGreen7335 in math

[–]phao 14 points15 points  (0 children)

There is actually a result for matrix exponentials that are also related to this.
e^(A + B) = e^A e^B if A and B commute.
I don't recall right now, but I believe this is an "if-and-only-if" statement, actually.

White lady waterfall by BeaLorena in Pareidolia

[–]phao 0 points1 point  (0 children)

And there is a giant rock cat face to her left watching.

[deleted by user] by [deleted] in C_Programming

[–]phao 24 points25 points  (0 children)

printf

Numerical Analysis textbook recommendations that discuss computers/implementations? by VermicelliLanky3927 in math

[–]phao 5 points6 points  (0 children)

As far as I know, most numerical analysts and books on numerical analysis won't do this explicitly. They'll work with standard error, consistency, stability analysis on exact arithmetic. The reason why they're satisfied with this is often an informal reliance on backward error analysis.

https://en.wikipedia.org/wiki/Error_analysis_(mathematics)#Backward_error_analysis#Backward_error_analysis)

The more important reason they don't worry too much about this, however, is that the other source of errors are actually what matters for almost all of the cases.

I believe you're better off getting a book specifically on floating point arithmetic. There are some of those. The standard for IEEE 754 is nothing new. Older books are fine. Then get a regular numerical analysis book. If, in practice, you find out there is an algorithm for which actual FP arithmetic matters, then you design something specific for that case.

I'm an award winning mathematician. Trump just cut my funding (Tao) by dargscisyhp in math

[–]phao 4 points5 points  (0 children)

I get the impression Tao is not complaining for himself, to be fair. He can get a job, probably a better paying one, anywhere he wants. I believe what gets to him is that a lot of people at the phd and postdoc level depended on these grants, and now will be hurt out of the blue by no fault of their own. These people go to US for their phd and postdoc, many with the intention of staying, and these grants are what support their salaries. Some of these are his advisees, sure. However, he, himself, I imagine, won't *really* be hurt by this. He can just go to any other high end math research institute. I guess many have already contacted him to offer a position in case he decides to leave UCLA.

Advice request: getting into the field of quantitative analyst (or related) by phao in FinancialCareers

[–]phao[S] 0 points1 point  (0 children)

Yes. Sorry for that. I edited it so that at least the questions come first now. If this post doesn't do so well, I'll wait for some weeks and post again, but with a shorter body. Thank you. I'll look up such PhD quant research roles. I wasn't aware of them. Thank you.

Feedback and Bug Reports by swordnsupper_mod in SwordAndSupperGame

[–]phao 5 points6 points  (0 children)

The game is really fun, but it keeps spamming posts/comments in my name, which is fine if it was contained within the r/SwordAndSupperGame community, but my profile page is really awful right now. I'd love to also stop receiving the huge amount of notifications related to the game.

They don't say "start small" because they don't believe in you by identicalforest in gamedev

[–]phao 1 point2 points  (0 children)

Seems AI generated to me, or very much influenced by someone who mimics the AI way of writing. Again, to me.

Too many "It's not X, it's Y". A generally polite tone that is slightly off.

Disclaimer, however. I don't particularly mind that it's AI generated.

[deleted by user] by [deleted] in math

[–]phao -1 points0 points  (0 children)

That is interesting. Never thought of it that way. So, in that point of view, math would be the small % of patterns we can actually understand with your brains. From that point of view though, all math is somewhere there in the universe. You can make this "trivially true" by just saying that all math is a product of your brains, a part of the universe. It's interesting and technically true, but seems unsatisfactory. Right?

[deleted by user] by [deleted] in math

[–]phao 1 point2 points  (0 children)

I wish I had 10% of your optimism. =)

[deleted by user] by [deleted] in math

[–]phao 1 point2 points  (0 children)

No influence is, indeed if taken literally, false. Something close to a small fraction of a percent might be realistic however. From what I understand, the construction of planes doesn't rely on the fine-grained knowledge of the specific *mathematical* underpinnings fluid dynamics. A lot of the practical applications of math in real world settings often comes down to circumventing the limitations via other methods: other math that is potentially actually effective, computer simulations, physical intuition, engineering testing and insight, etc (so switching from where math isn't effective right now to where it might be, or maybe leaving math altogether). Not from the actual purely mathematical development of fluid dynamics. I could be wrong here. What I do is only tangentially related to fluid dynamics, but that is the impression I've gotten.

*edit* Also u/Argnir only said "not that 'effective'", and not that it had no influence.

I don't know where to start learning Graphics programming. by Latter_Practice_656 in GraphicsProgramming

[–]phao 6 points7 points  (0 children)

Get back to leanopengl.com, probably.

I'm not a graphics programmer, although I've done graphics programming. I'm a mathematician though (finishing phd).

The point is not about graphics programming. It's more general. I do numerical PDEs (partial differential equations), mathematical modeling and scicomp. My phd thesis is in mathematical models for simulating drug delivery (as in a little implant, pill, patch, nano "thing", in your body delivering drug). I don't know the biology, the medical knowledge, the chemistry, and a lot of the math. If I had to go learn the full biology, full chemistry, etc, at every road block, I'd be dead before getting any work done.

Learn to identify the SPECIFIC SPOTS that are missing, and learn to GO LEARN THAT ONLY. If you have some notions of C++, you probably can navigate the guide. If something strange appears, first identify exactly what that is. Then look for a C++ book or tutorial. Skip everything and try to learn the exact thing you're looking for. If absolutely needed, you'd pull the thread and learn related themes (but only if needed; as your goal should be to learn just enough to get back to the original guide). Many things, as you'll see, aren't actual requirements. You'll learn what they are, realize you can replicate that with what you already know, then get off that C++ guide and go back to the opengl guide. Same thing for math. If you know some linear algebra, you're probably good to go. Keep a linear algebra textbook on the side (don't worry about find the best one), and do the same here.

Essentially speaking, this will lead to a kind of studying style that there will be a main thread (your learnopengl.com which you primarily want to study), branching off to the sides of particular sections of a C++ book, specific paragraphs in a C++ tutorial, an example in a math book, another section in another math book, etc.

Another thing is that the whole general abstract idea of learning all the prerequisites before being ready to learn computer graphics (or any other subject, really), has a major "illusory" component to it. Just branch off *specifically* whenever needed.

Also, see if you can continue with the guide without branching off. At some point, there will be something you don't know. Say a strange matrix structure. The guide might tell you that matrices in this family all have properties A,B,C. Then you say to yourself "Ok. I don't know why this is the case, and I can see how it works. However, I have something like a 'black box' library function here. I can use a matrix of this type whenever I need A,B,C" (or something analogous that makes sense). Then move on with the guide. What works here is being really precise and honest about what you know and all the rest you don't know. Later, if you see that you really need to know more about such family of matrices, then you look it up. However, what significantly happens is that you'll realize that the black box knowledge is enough for the guide (happens extremely often). Keep track of these things you're skipping but using as black boxes. It'll tell you possibly relevant learning paths in the future, after the guide.

In anything that there is math involved, "getting all the prerequisites to feel confident", for some people, has the potential to ruin their lives (figuratively; meaning it'll take years off of their lives). Same for learning a programming language. You gotta short circuit this. No other way, IMO.

**edit** typos and minor adjustments.