bollu

28 ms·

181.
by bollu 6y ago
Thank you, It does appear I am hopefully confused between hyperbolic and Lorentzian :) Thanks for patiently showing me where I am going wrong. For my selfish benefit, could you please collect the definitions of (i) Hyperbolic space (ii) Min
182.
by bollu 6y ago
So I think I understand the confusion here. - In Riemannian manifolds, we take R^n as the building block - Every hyperbolic space can be locally represented by R^n. If you do this, the hyperbolic manifold will have negative curvature. Hence
183.
by bollu 6y ago
If you understand fourier transform well, then perhaps this viewpoint will help. The fourier transform is 'just' a change of basis, with the basis being the sinusoidal functions. Why these? Well, because if we take a look at the d
184.
by bollu 6y ago
> If the space is flat (Riemann curvature tensor = 0) how can it have constant negative curvature? You are wrong. Locally our space is _hyperbolic_. So "flat" means "flat space-time" means "constant negative curv
185.
by bollu 6y ago
In the above setting, we don't have computers _finding theorems_. We're using computers to _machine check_ our proofs; The process of verifying whether a proof is correct or not is mechanical when a proof is broken down to its sma
186.
by bollu 6y ago
> A Lorentzian manifold is not necessarily locally hyperbolic and certainly the existence of light-cones do not follow from its hyperbolic nature. A Lorentzian manifold may be flat or curved, if it's flat we usually call it also a M
187.
by bollu 6y ago
I put in the work to study GR from Susskind' theoretical minimum (fantastic lecture series: https://theoreticalminimum.com/courses/general-relativity/20... ). I still don't understand GR. Yes I can now s
188.
by bollu 6y ago
I'm a huge fan of SAGE! I keep using it to discover new math. I generally play with the associate Sage module of any algebraic structure to get a real feel for what is going on. Some examples of: 1. Grobner basis: http://bol
189.
Ask HN: easist way to build digital logic on civilization collapse?
2 points by bollu 6y ago|2 comments
190.
by bollu 6y ago
For trace: there is a perspective that a trace is a generalized dimension counting operator. If we have a projection matrix (a matrix such that A A = A), then the trace of this matrix gives us the number of dimensions it projects onto. Inde
191.
by bollu 6y ago
It's more that in linear algebra, we have "the nicest theorems we can hope for", so there's no "nasty surprises" lurking around. This is qualitatively different from pretty much all other algebraic structures o
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by bollu 6y ago
There seems to be somewhat of a myth that it's hard to get GraphViz diagrams to "look nice". I (obviously biased) feel that the diagrams I generated for my reference implementation of RETE look quite clean: https:/&#x2F
193.
by bollu 6y ago
There is a thesis by Kondor: "Group theoretical methods for machine learning" - https://people.cs.uchicago.edu/~risi/papers/KondorThesis.pdf which provides links to the associated literature. The documen
194.
by bollu 6y ago
Intriguing; Is this actually serious? Like, is it possible that the unaccounted for matter (what, ~98%) is simply locked within dyson galaxies?
195.
by bollu 6y ago
Maybe it's just me, but I found matrix calculus atrocious. The rules aren't even useful for most situations, since they're essentially "hardcoded" for certain types of matrix situations that crop up often. I _much_
196.
by bollu 6y ago
I wrote this to show off how to write a compact and powerful animation library. It turned out to be a nice case study in declarative programming as I wrote it! I'd love feedback on the API design, website design, and content as I'
197.
The unreasonable effectiveness of declarative programming(bollu.github.io)
417 points by bollu 6y ago|122 comments
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Best Practices for Array Indexing(bollu.github.io)
9 points by bollu 6y ago|2 comments
199.
by bollu 6y ago
This is really funny; Back in the warcraft 3 days, we used to do the same thing inside its scripting language --- to attach some data to a timer, we would exploit the fact that a timer is in fact just a 'void *' underneath: so the
200.
by bollu 6y ago
Interesting; I have never heard the word "decephalized" before --- in what literature in this used?
201.
by bollu 6y ago
Can you please formally define what a spinor is? Like, mathematically, what are they?
202.
by bollu 6y ago
> it should reduce in the Newtonian limit to something that looks like a tidal effect, i.e. a gradient of the Newtonian gravitational field. Can you please explain to me how you went from"looks like a tidal effect in the Newtonia
203.
by bollu 6y ago
I honestly recommend the following: 1. Pick up the standard textbook by Nielsen and Chuang, Quantum computation and quantum information. read the first two to three chapters. 2. Solve the exercises for the Q# programming language.
204.
by bollu 7y ago
Can you please recommend software for this? which screen reader should I use? how should I configure it? how do you code with it?
205.
by bollu 7y ago
Yep, I'm waiting for MathML to be here so I can switch the whole thing over. Unfortunately, it's not here (yet)!
206.
by bollu 7y ago
I explained why I don't want to do this, right? > Far more importantly, it provides spatio-temporal locality. I add things in chronological order to tbe blog, as I learn thing. If I need to recall something I had studied, go to that
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Fast Math Rendering on the Web(bollu.github.io)
46 points by bollu 7y ago|20 comments
208.
by bollu 7y ago
precisely, you can't _because_ you'll have a "time leak" if you attempted such a thing.
209.
by bollu 7y ago
Let me provide you a different perspective: A lazy language is one that "leaks space". A strict language, however, can "leak time". Imagine building an infinite list and pulling only ten elements from it. This is a situa
210.
by bollu 7y ago
Depends on the university. Mine teaches all three, for example.

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