xkcd

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yes, automatically converting representations is definitely a bad idea, especially since the conversion process is often not "lossless" as you gave an example of. (also it's usually impossible to do automatically, as you can't convert a camera frame coordinate to a world frame coordinate w...

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a class of programming bugs i often commit involve mistaking the "representation" of a variable -- such as adding degrees and radians, treating a coordinate in the camera-frame as a coordinate in the world-frame, or forgetting to swap the channels of an image from BGR to RGB. this can be a...

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ffmpeg is a nice piece of software for reencoding video
imagemagick handles batch image operations (such as compression) pretty well

try something among the lines of
https://unix.stackexchange.com/a/38380/269525
https://stackoverflow.com/a/7262050/1858363

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Given a seed, the java code for setSeed is: seed = (seed ^ 0x5DEECE66DL) & ((1L << 48) - 1) The code to get the next n bits is seed = (seed * 0x5DEECE66DL + 0xBL) & ((1L << 48) - 1) result = (int)(seed >>> (48 - n)) And finally the code to get the nextLong (which is 64 bits) is result = ((lo...

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There are two equivalent formulations of NP -- the verifier and the machine definition (2.1 and 2.2 on the wikipedia page). I prefer the machine definition because I think it's pretty quick to intuit: the N in NP stands for non-deterministic, so imagine being able to write computer programs with a s...

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If you take all the ordinals with at most ℵ 0 predecessors, you have ℵ 1 of them (the next larger cardinal). This was the unintuitive part for me. Here's a proof I tried to put together, although I've never worked with ordinal numbers before. Suppose the cardinality of the set X of all ordinals wit...

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In the second to last section of this page -- with the puzzle, a claim is made that assuming the axiom of choice and the continuum hypothesis, you can order the real numbers in [0, 1] so that each number only has a countable number of predecessors. https://www.scottaaronson.com/democritus/lec2.html ...

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Here is a first attempt: Name the words of the book as X_i for the ith word in the first book (which contains underlined words), and Y_j for the jth word in the second book. Let U(i) denote whether X_i is underlined. Define A(i,j) to be a boolean function such that A(i,j) is true when X[i:] can be a...

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have some sort of planner (can be hard-coded OR learned) It's the ones that learn that are the powerful (scary) ones. If I want to open a box, I quickly come up with a plan (grab the scissors, cut the tape... How did you come up with this plan? Would you have come up with this plan the first time y...

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So it does seem that GIMPS's prime finding software using AVX can easily send processor temperatures to 98 C in a few seconds. The only other code i've run which does the same thing is some rendering software written in pure java (but which I suspect makes use of AVX under the hood of the JVM). Norm...

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From my very limited knowledge of the field, neuroscience research has a very long way to go before we can anything in the way of usable intelligence out of it. A hilarious paper about this is Could a Neuroscientist Understand a Microprocessor? (answer: probably not). A purely statistical approach i...

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So it looks like if you map vertices onto products and sets onto processes, (you need to have at least one parent process per product, and you need at least one set to cover each vertex), you can reduce the problem of minimizing non-leaf nodes into set cover, which is NP-hard and can't be approximat...

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I agree with the examples you gave.

I've figured out where I was confused now. I had the wrong definition of limit in my head. So e^k * cos k is an example of a function with no limit as k -> inf, but the lim sup would be infinity.

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I'm a bit confused by that. I'm under the impression if lim n -> inf of f(n) = infinity, then it means for every w, there exists n such that f(n) > w. according to wikipedia, lim sup is defined: https://wikimedia.org/api/rest_v1/media/math/render/svg/62cb7e298ae5b1647e0b64b9012c6012a2545b30 so this ...

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I recently had the same question, and after a lot of searching, dug up these two links: https://mathoverflow.net/questions/6444/how-long-for-a-simple-random-walk-to-exceed-sqrtt https://math.stackexchange.com/questions/210131/how-should-i-understand-the-sigma-algebra-in-kolmogorovs-zero-one-law/2101...

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Yes, i see now. It's almost like you can break the equation up as

X_{t+1} = aX_hi + aX_lo + c
where X_lo consists of the k' lowest bits and X_hi consists of the rest. Then X_{t+1} mod 2^k' is just aX_lo + c. So it's as if you had a smaller LCG inside the bigger one.

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An LCG is a random generator in the form: X_{x+1} = (aX_t + c) mod m where X_t was the last number to be output. All variables in this expression are integers. For performance reasons, m is frequently a power of 2, say 2^k. Wikipedia claims that this LCG (with power of 2 m) causes low-order bits to ...

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Has anyone else experienced a trend of moving the actual learning outside the classroom at different "levels"? I'm not criticizing the teaching, but I noticed that the amount I learn inside the classroom versus outside has decreased. In high school, classes usually consisted of 1. Introduc...

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What sort of code could I write in a low level language like C in order to induce maximum energy consumption (and hence melt my computer)? I remember being shown graphs in my computer architecture class that showed most of the energy expended during computation was from moving bits around, and that ...

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https://www.slideshare.net/DavidCollings/multi-span-suspension-bridges there is a journal paper behind this presentation, which is behind a paywall, but nonetheless, this seems to pinpoint exactly the issue behind multi-span suspension bridges, which is the fact that apparently, multiple spans resul...

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some more research: first, there seems to be multiple two-span suspension bridges (meaning 3 towers) in china: https://en.wikipedia.org/wiki/Taizhou_Yangtze_River_Bridge https://en.wikipedia.org/wiki/Ma%27anshan_Yangtze_River_Bridge but i was unable to find any three-span bridges, which did not make...

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i think we're all in agreement it is reasonable to have a 4 tower double suspension bridge over a 2 tower single suspension bridge the question is, what purpose does the middle pier serve in this 4 tower suspension bridge? we know it serves as an anchorage for the cables, but that reason doesn't mak...

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just to make it explicit, i believe that the force on the cables should be the same as long as the distance between two adjacent towers remains constant, no matter how many towers there are. it is for this reason that it's possible to hang electrical cables across many many pylons and the tension do...

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yes, i'm away of the reasons they couldn't build a single span, as well as the fact that the central pier happened to rest nicely on shallow water. but as soupspoon pointed out, this doesn't actually explain the presence of the central tower. in the image below, i have drawn out the forces on the ca...

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the west span of the bay bridge in san francisco looks like this https://en.wikipedia.org/wiki/San_Francisco%E2%80%93Oakland_Bay_Bridge#/media/File:San_Francisco_Oakland_Bay_Bridge_Western_Span.jpg as the image shows, it is a double suspension bridge, with a central pier in the middle of the two sus...

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i don't know enough about thermodynamics to be sure -- is the energy produced by the temperature difference between the black hole and the CMB equivalent to the amount of energy that would've been produced by fusing all that hydrogen? even with a "quickly" cooling CMB? (quickly relative to...

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speising wrote:You can use the hawking radiation.

wouldn't the vast majority of the hawking radiation be emitted at a temperature much lower than the CMB, making it useless for power production?

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Well both putting it into a star and putting it into a black hole rather defeats the point of the exercise, which is to store hydrogen for later use.

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Not so sure about the bigger plan but at least in the short term, it would be a very good idea to stop the wasteful "burning" of hydrogen on a cosmic scale. After that, power production can proceed in a careful, efficient manner, whether that is controlled fusion or dyson sphere

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as part of a project to delay heat death, suppose we've dissasembled every single star in the observable universe. by the way, i did the math and it would take a star like the sun 10^8 years to output enough energy to pay for it's dissasembly. what is the most energy and material efficient way of st...

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If we have a real symmetric matrix M which is diagonalized into QLQ^T where Q is orthogonal and L is diagonal (this is possible by spectral theorem), then is Q and L necessarily unique? Is there another orthogonal diagonalization using some Q' != Q or L' != L? I ask this because it seems many explan...

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Yes, i'm trying to say that i'm not too concerned with the technical details and logistics of the game I wrote up in the op since the goal is to not solve that one particular game but to solve a larger class of games, all of which have the same core "issue" which makes them difficult to so...

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i admit that the scenario in the op was a bit contrived, but that was part of my attempt to distill the original problem about a more complex game into a simpler one while retaining the challenging aspects. in case it helps, here's the original game: https://en.wikipedia.org/wiki/Hanabi_(card_game) ...

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So I took the easy way out and went googling. I was actually pretty skeptical there would be a solution to this, mainly because I have seen derivations for the expectation and covariance of the expression many times, but I have never seen an attempt to figure out what the distribution actually is. S...

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english has less than 1.5 bits of entropy per character, so with 30 moves you could send something like 20 characters, although it's possible that an address or something may have more entropy than your average sentence. but i'm not interested in a specific scheme for a scenario where you want to se...

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suppose you've been kidnapped and your captors want to play televised game of chess. if you lose, they'll double the ransom, so you don't want to lose. however, since you are a very forward-thinking individual, you have prepared for this scenario, and have set up a system for communicating to your f...

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if x is drawn from a multivariate normal with mean mu and covariance sigma, what's the distribution of z = x.T P x (.T denotes transpose and P is an arbitrary square matrix) i suspect that f(z) = ∫ p(x) dx where the integral is over all x such that x.T P x = z but i'm not sure how to carry out this ...

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thanks for the observations. i actually played a few test games against a friend yesterday and did notice the things you mention (though that may just be confirmation bias). hastily written code attached. in a spoiler tag, because the forum wouldn't let me attach any files for some reason #!/usr...

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i don't see any reason why, here's the wikipedia page on it
https://en.wikipedia.org/wiki/Superconducting_computing

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one way to get it down to about O(nk) where n is the number of points and k is the number of close-to-B points is by doing a dijkstra like algorithm. first treat the points as a graph with n vertices and n^2 edges. then run dijkstra, but start with the set B instead of the singleton set containing t...

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