ogogmad

13 ms·

301.
by ogogmad 2y ago
How does this compare to a modern GPU?
302.
by ogogmad 2y ago
Base-factorial is a representation for real numbers between 0 and 1. The representation has the form A/2! + B/3! + C/4! +..., where A is in {0,1}, B is in {0,1,2}, C is in {0,1,2,3}, etc. Every irrational number in [0,1) has
303.
by ogogmad 2y ago
No, using complex numbers alone DOES NOT work. To really allow complex numbers, you also need Riemann surfaces. The function "ln" has type ln: R -> CC where "R" denotes the Riemann surface corresponding to the natural
304.
by ogogmad 2y ago
Looking at it in terms of compound interest seems random. That said, I think the expression lim((1+x/n)^n) is better motivated within Lie theory, since every Lie group admits a faithful linear representation in which the expression lim
305.
by ogogmad 2y ago
Did you eventually realise that the expression a^b should be understood to "really" mean exp(b * ln(a)), at least in the case that b might not be an integer? I think even in complex analysis, the above definition a^b := exp(b ln(a
306.
by ogogmad 2y ago
Tangential fact (har har): The Taylor series for e^x, combined with the uniqueness of representing a real number in base-factorial, immediately shows that e is irrational.
307.
by ogogmad 2y ago
I think this approach is the most logically "efficient". You can phrase it as defining ln(x) to be the integral of 1/t from 1 to x. Maybe not the most intuitive, though. Interestingly, a similar approach gives the shortest pr
308.
by ogogmad 2y ago
> for large n, (1+x/n)^n expands out to approximately 1 + x + x^2/2 + x^3/6 + ... The rigorous version of this argument uses the Dominated Convergence Theorem in the special case of infinite series.
309.
by ogogmad 2y ago
Is the problem mentioned in the article equivalent to deciding whether there exists a solution to a system of linear equations in the positive integers? I think no, because the vector additions are considered in sequence, and at no point ar
310.
by ogogmad 2y ago
> The comment above is probably from a bot. Wtf Is this happening?
311.
by ogogmad 2y ago
I think this needs the use of a CAS (Computer Algebra System, like Mathematica) to calculate the runtime of some code relative to different choices of computer architecture. Then it looks practical. Could even be added to IDEs. But without
312.
by ogogmad 2y ago
How do people feel about array languages (like J, APL, K, BQN, Uiua) versus spreadsheets?
313.
by ogogmad 2y ago
The only way for this to cause tens of thousands of death by self-driving alone is for people to suddenly need to drive the cars themselves, and not being able to do it well. Unless I'm missing something.
314.
by ogogmad 2y ago
Your use of the word "tribe" suggests you mean Jewish people, whether or not you realise that. [EDIT] Understood, thanks. It's more like some people could mistake the intention.
315.
by ogogmad 2y ago
> In safe driving failures are uncorrelated and safety procedures generalise. We do not yet know if, say, using self-driving very widely will lead to conditions in which "in a few incidents" more people are killed in those inci
316.
by ogogmad 2y ago
Isn't correlation a wrong way of measuring statistical dependence anyway? I thought that entropy-based method like Relative Entropy did this better.
317.
by ogogmad 2y ago
Could this lead us to being able to upload our brains onto computers? To kill death. Very cool.
318.
by ogogmad 2y ago
That's cool, but where does it say it's decidable?
319.
by ogogmad 2y ago
Some decidable extensions of Skolem and Presburger, searched for and found by ChatGPT: https://chatgpt.com/share/67e1d302-c930-800f-bc2a-85bdc60563...
320.
by ogogmad 2y ago
Skolem arithmetic is decidable too: https://en.wikipedia.org/wiki/Skolem_arithmetic I'm wondering whether there are decidable first-order theories about the natural numbers that are stronger than either Skolem or
321.
by ogogmad 2y ago
I wish tech people would stop using the term "FUD". "Fear, Uncertainty and Doubt", or "FUD", is how you don't ruin your life in one shot: https://news.ycombinator.com/user?id=shipscode &gt
322.
by ogogmad 2y ago
I'm not sure about other cryptocoins, but Bitcoin does not use encryption, it only uses authentication, which requires a DSA (Digital Signature Algorithms). Bitcoin's current DSA would in fact be broken by a cryptographically-re
323.
by ogogmad 2y ago
As I've mentioned to another commenter, Bitcoin relies only on the existence of an arbitrary DSA. Quantum computing-resistant DSAs have been known since the 1970s. I reckon that swapping out Bitcoin's current DSA with a quantum-re
324.
by ogogmad 2y ago
No. Crypto will be safe against quantum computers.
325.
by ogogmad 2y ago
Cryptocoins like Bitcoin only need DSA. Quantum-proof DSAs have been widely known since the 1970s*. Bitcoin only needs to change its DSA - and then everything will be fine. * see Lamport signatures
326.
by ogogmad 2y ago
> The rust produces safe code claim is also marketing garbage. The rust standard library has over 7.5k (of 35k) unsafe functions in it. The core library has 7K (of 21k) unsafe functions. So any Rust program that claims not to have “unsaf
327.
by ogogmad 2y ago
I don't work as a PM or for Microsoft. Perhaps the problem is a deeper one, which is constant and likely unnecessary UI makeovers. But among the endless blizzard of these, this is an odd one to make your last stand for. More to the poi
328.
by ogogmad 2y ago
But can you explain why this feature is/was so important? The fact that there are 3rd party tools that can restore it makes it even more marginal. There are gazillions of UI changes in every app we use, it seems strange that this very
329.
by ogogmad 2y ago
This seems extremely niche. Maybe even petty? Why do you care where the taskbar is? Remember that every change breaks someone's workflow : https://xkcd.com/1172/
330.
by ogogmad 2y ago
Whenever the Russian government denies something like you're suggesting, I take it to be an admission. I'm usually right. You're naive and wrong.

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