bollu

11 ms·

61.
by bollu 5y ago
Since you answered: do you have a good way to visualize the curvature of spacetime? I really don't understand how to think about light-cones being distorted, because it's the curvature of a lorentzian manifold that stiches togethe
62.
by bollu 5y ago
As best as I understand: light travels in space. Thus, if space is scrunched up, light can't escape. Gravity IS space. The scrunching up IS gravity. There is no "escaping", because gravity is literally the substrate.
63.
by bollu 5y ago
That's untrue. There are type-systems and type-checkers which can check for correctness , as specified by a mathematical formula. This is proof assistants such as Coq[1] work. For example, take a look at fiat-crypto [2], a project tha
64.
by bollu 5y ago
Nice explanation, I hadn't t heard this perspective, and it makes it a lot more intuitive! What's your favourite way to learn queueing theory? I feel like I'll get cool insights from this :D
65.
by bollu 5y ago
Can you point me to a paper from the 70s that explains how to flatten such calls? The best that I know is "stream fusion, to completeness" which was published in something like 2019!
66.
by bollu 5y ago
Could you name some pointers that I should look up to learn more about both sides of this debate?
67.
by bollu 5y ago
I'd like a reference for this explanation :)
68.
by bollu 5y ago
Do you have any recommendations to learn about how tropical geometry is used for control theory?
69.
by bollu 5y ago
I don't believe that my individual choice actually matters; What do I read to change my opinion?
70.
by bollu 5y ago
Where can I read more about how 72pt ~ 1 inch? Where does one g to for a "course on typography"?
71.
by bollu 6y ago
What is the tool that builds this literate source view from source code?
72.
by bollu 6y ago
I began to write an acerbic comment at "everything is a spring". I then thought about it, and realised you're so right. Linear algebra is crazy. Thank you for the insight. (It struck me that all of quantum mechanics I'
73.
by bollu 6y ago
I LOVED reading the culture. I'm still working my way through the books. They're eminently quotable. Here are some of my favourites: > “Empathize with stupidity and you’re halfway to thinking like an idiot,” > It would have
74.
by bollu 6y ago
I only learnt the (arguably) "real meaning" of the Jacobian once I studied differential geometry. I haven't seen this explained anywhere. I took a stab at an elementary exposition (with animations) of this view of the Jacobia
75.
The Jacobian, Geometrically(bollu.github.io)
2 points by bollu 6y ago|1 comments
76.
by bollu 6y ago
> No it won't We don't know either way. relationship between BPP, BQP, P, NP are all open.
77.
by bollu 6y ago
I am sorry. I shall reference Singular in the future whenever I discuss SAGE. Thank you for your fantastic work on Singular :)
78.
by bollu 6y ago
Good question. I mostly use it for algebra. It has varying levels of support for analysis. There is a SageManifolds project that allows for computations over differentiable and Riemannian manifolds, for example.
79.
by bollu 6y ago
Thanks! I'm studying this right now, after I got a taste of algebraic geometry (schemes) from Ravi Vakil's fantastic "algebraic geometry during the time of COVID" last year!
80.
by bollu 6y ago
Also, use computers! I use SAGE extensively to get a feeling for lots of mathematical objects! 1. Grobner bases: http://bollu.github.io/computing-equivalent-gate-sets-using-... 2. Localization: https://github.com
81.
by bollu 6y ago
Thank you for the reference!
82.
Hacker's Guide to Numerical Analysis(bollu.github.io)
356 points by bollu 6y ago|64 comments
83.
by bollu 6y ago
What's interesting textbooks andectures one can read on plasma fluid dynamics?
84.
by bollu 6y ago
Fascinating! Could you tell me more about who these optimal users are? Are they optimal because they are the most valued users in their firms? (Make the best trades or some such?) are they optimal as their opinion on the software matters a
85.
by bollu 6y ago
That's a very cool connection I'd never thought of before, that IID random variables correspond to "maximamal local instability". What's this perspective called so I can read more about it for my interest?
86.
by bollu 6y ago
What is free expression and where can I read more about it?
87.
by bollu 6y ago
Do you have more on how to get better at writing?
88.
by bollu 6y ago
Interesting, I'd love a book recommendation :)
89.
by bollu 6y ago
What do you mean by "derive" the Schrödinger equation? As best as I know, there is no "derivation" beyond some analogy with the classical wave equation. It's an equation penned down by Schrödinger, motivated by the
90.
by bollu 6y ago
That's not how it works, though. We can study any set of axioms we want. Mathematics often study "multiple incompatible worlds". For example, euclidean space where parallel lines never meet, and projective space, where parall

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