polylog
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And this year's Turing Award goes to...
Support us on Patreon: www.patreon.com/Polylog
We explain why Avi Wigderson got this year’s Turing award: We show how you can make any randomized algorithm deterministic.
0:00 Intro
2:41 P = BPP
5:38 Statistical tests
7:52 Pi as a PRNG
9:44 Nisan-Wigderson PRNG
13:47 Finishing the proof
14:45 Zero-knowledge proofs
Blog post: coming soon
Code for the animations: github.com/polylog-cs/derandomization/
Richard Hladík: Script editor, animator
Václav Rozhoň: Writer, animator
Václav Volhejn: Narrator, animator, script editor
Thank you to our beta testers: Matěj, Honza, Filip
Animations: manim, a Python library docs.manim.community/en/stable/
Color palette: Solarized ethanschoonover.com/solarized/
Music: Thannoid by Blue Dot Sessions
Pictures: Wikipedia, Internet
Video clips used:
Avi Wigderson: czcams.com/video/YOrBVEwDqAg/video.html and czcams.com/video/ZzsFb-6wvoE/video.html
Seismograph: czcams.com/video/mbKEarx9CCs/video.html
zhlédnutí: 96 730

Video

Why arguing generals matter for the Internet
zhlédnutí 14KPřed 3 měsíci
0:00 Intro 0:31 The byzantine generals problem 3:51 First solution 10:13 Importance 12:00 Blockchain-based solution 15:57 Wrap-up Support us on Patreon: www.patreon.com/Polylog We solve the Byzantine Generals problem, a fundamental problem of distributed computing. Then, in classic Polylog fashion, we spend the latter half of the video discussing why it matters in the broader context, specifica...
The flaw in every voting system
zhlédnutí 415KPřed 9 měsíci
#some3 0:00 Intro 3:11 Definitions 6:44 Proof 11:39 Arrow's theorem 13:25 Approval voting 17:03 Outro Blog post: vasekrozhon.wordpress.com/2023/09/10/voting-systems/ Github: github.com/polylog-cs/voting-systems Patreon: www.patreon.com/Polylog Credits: Thumbnail by Alžběta Volhejnová To make this video, we used manim, a Python library: docs.manim.community/en/stable/ The color palette we use is...
The most powerful (and useless) algorithm
zhlédnutí 128KPřed rokem
0:00 Intro 2:44 The Algorithm 6:38 Why it works 9:28 Code 10:41 Final Thoughts Our implementation of Universal Search: github.com/polylog-cs/universal-search/blob/main/code/universal_search.py Our Patreon: www.patreon.com/Polylog Impromptu: impromptu.fun/ More about universal search: To prove that the universal search is asymptotically optimal, we implicitly used the fact that there exists a li...
The OPTIMAL algorithm for factoring!
zhlédnutí 41KPřed rokem
Our program: github.com/polylog-cs/universal-search/blob/main/code/universal_search.py RSA factoring challenge: en.wikipedia.org/wiki/RSA_Factoring_Challenge Big thanks to: Tomáš Gavenčiak, Matěj Konečný, Jan Petr, Hanka Rozhoňová, Tom Sláma Our Patreon: www.patreon.com/Polylog Credits: To make this video, we used manim, a Python library: docs.manim.community/en/stable/ The color palette we use...
The hidden beauty of the A* algorithm
zhlédnutí 826KPřed rokem
00:00 Intro 01:38 Change the lengths! 06:34 What is a good potential? 12:31 Implementation 16:20 Bonus Tom Sláma's video: czcams.com/video/umszOeerdsU/video.html Our Patreon: www.patreon.com/Polylog Some related stuff: One thing I did not mention is that Dijkstra's algorithm is designed to solve the problem of finding the shortest path from the start node to all other nodes of the graph. It doe...
AI cracked this Codeforces problem. Can you?
zhlédnutí 54KPřed rokem
Our Patreon: www.patreon.com/Polylog AlphaCode is a model by DeepMind. alphacode.deepmind.com/ The problem we discussed is from CodeForces. codeforces.com/problemset/problem/1566/E 0:00 Intro 3:29 Problem Statement 5:55 Problem Solution 11:20 Final Thoughts Music New World Symphony by Dvorak. musopen.org/music/4942-symphony-no-9-in-e-minor-from-the-new-world-op-95/#recordings Images The picture...
We designed special dice using math, but there’s a catch
zhlédnutí 527KPřed rokem
How would you order the players randomly? Tell us in the comments. :) Our Patreon: www.patreon.com/Polylog Some proposals that already appeared in the comments section: - Put cards with player names in a sack, shuffle, then take them out one by one to get the order. - Simulate the above process using dice (see the comments by Jordan Weitz and samuraiwarm for how to do it). - Just reroll the dic...
The Simplest Sorting Algorithm (You’ve Never Heard Of)
zhlédnutí 127KPřed 2 lety
Our Patreon: www.patreon.com/Polylog We know this beautiful algorithm from the recent preprint by Stanley P. Y. Fung: arxiv.org/pdf/2110.01111.pdf However, it turns out that other people stumbled across it multiple times, see e.g. the discussion here: news.ycombinator.com/item?id=28758106 Attributions: To make this video, we used manim, a Python library: docs.manim.community/en/stable/ The colo...
The trick that solves Rubik’s Cubes and breaks ciphers
zhlédnutí 2,7MPřed 2 lety
What do the Rubik's cube and a cipher from the 70s have in common? Let's find out. Our Patreon: www.patreon.com/Polylog 0:00 Rubik's cube 9:40 DES Links: Feliks setting the 4.73 record czcams.com/video/R07JiT0PlcE/video.html&ab_channel=FeliksZemdegs webpage "God's number is 20" www.cube20.org/ The fact it was verified computationally that every cube can be solved in at most 20 moves is super im...
How to Use Beads and Strings to Find the Diameter of a Tree
zhlédnutí 30KPřed 2 lety
This video was made for the Summer of Math Exposition 1. Check out other cool videos there! www.3blue1brown.com/blog/some1 #some1 Our Patreon: www.patreon.com/Polylog To make this video, we used manim: docs.manim.community/en/stable/ Our video is based on the following great book: Explaining Algorithms Using Metaphors by Michal Forišek and Monika Steinová you can buy it here: www.springerprofes...

Komentáře

  • @henryzhang3961
    @henryzhang3961 Před 8 hodinami

    fantastic video, and of course someone made a manim rubiks cube library lol

  • @judyyfong
    @judyyfong Před 9 hodinami

    Btw twin primes conjecture is provable if you relax some mental constraints/parameters or just have chatgpt prove it to you. Since chatgpt is that stupid

  • @judyyfong
    @judyyfong Před 9 hodinami

    Also widen your shot. The elbows being cut off really annoy me. Crash course channel layouts can teach you a thing or two

  • @judyyfong
    @judyyfong Před 9 hodinami

    Stupidity and ignorance

  • @philipoakley5498
    @philipoakley5498 Před 2 dny

    It's worth noting that many of the historic pseudo random generators had a repetition cycle that wasn't large enough to fully explore the possible options in many games of chance such as card games. If worst case, there was never a chance that four aces were not even dealable, so you'd have a lousy game, and it would be easier to fiddle the game. There's a lot of interest in the on-line gambling field about ensuring that overall the house wins, yet it's still 'random' enough. 52 cards, go through all the shuffle orders, once per second, every billion years take a 1cm step along the equator, when you reach the pacific ocean remove a 5mL spoon of water, every time the pacific empties, and a A4 sheet o paper to a pile, when it reaches the moon start actual counting, when you get to a million, realise you are still less than 90% of the way to completing the task. [you need 4 x 64bit words to represent the 52 card deck shuffle number]. And that's not even a 'large' number, never mind an 'arbitrarily large' one.

  • @ferverrel5519
    @ferverrel5519 Před 4 dny

    Where’s the other video

  • @Vannishn
    @Vannishn Před 5 dny

    2:14 Zwo Franken spotted !! hahah 🇨🇭 Gruezi von Genf :) 🇨🇭 Danke fürs Video, esch wirklich toll !

  • @shykj8892
    @shykj8892 Před 5 dny

    It just confuses me more. I won't question why people pursue the perfect "randomness" because I'm not a scholar, but things happen and while 111111 happens once in 1/2^6 occasions, when it happens it happens. True random number machine might just drop 11111111111111 and casually go on. Like how monkeys playing with typewriters might write a whole hamlet. I'm happy with my hardware noises processed through linear equstions.

  • @danypell2517
    @danypell2517 Před 8 dny

    and cache

  • @zeroTorsion
    @zeroTorsion Před 8 dny

    amazing

  • @lolol.y7935
    @lolol.y7935 Před 9 dny

    Can I use the paused image at 8:05 in a presentation ?

  • @theK594
    @theK594 Před 9 dny

    Can you explain to me how it is possible I have not yet learned about this wonderful channel? Dobrá práce kluci❤🇨🇿

  • @EnricoRodolico
    @EnricoRodolico Před 9 dny

    I was not prepared for the bowl cut... bro you could be handsome just buzz your hair and let it grow out jesus. great video otherwise.

  • @peteschaefer
    @peteschaefer Před 10 dny

    Alright guys, here's the secret behind Google Maps' algorithm: it's **not** A*. It's Contraction Hierarchies. Nice animations, though 👍

  • @morglod
    @morglod Před 10 dny

    just lol that you can get award for thing that programmers use for 20 years

  • @PolylogCS
    @PolylogCS Před 11 dny

    More details here: vasekrozhon.wordpress.com/2024/05/18/avi-wigderson-has-won-the-turing-award/

  • @nguyentientrungkien4661

    🤯

  • @simski394
    @simski394 Před 11 dny

    Bro really got the 13th century monk cut

  • @sret919
    @sret919 Před 11 dny

    Thanks for the video <3 These topics are so interesting

  • @jay31415
    @jay31415 Před 12 dny

    So...PRNGs can be used for random algorithms. This is a huge , groundbreaking, "no shit".

  • @willd4686
    @willd4686 Před 12 dny

    God dammit is everything relative to the observer!?

  • @bencrossley647
    @bencrossley647 Před 14 dny

    Does that mean if the 3-SAT problem can be reduced to a BPP polynomial equivalence problem then P = NP?

    • @PolylogCS
      @PolylogCS Před 11 dny

      As far as I know, this is not known. But if somebody proved that, I think most complexity theorists would start believing that P=NP at the very least!

    • @bencrossley647
      @bencrossley647 Před 9 dny

      ​​@@PolylogCSDo you know if this theorem applies to multivariable polynomials or is it limited to the case of 1 variable? If multiple variable polynomials are allowed then I may have something along the lines of 3-SAT -> polynomial -> apply BPP = P. So 3-SAT would be in P. I have 0 excitement over this btw. I'm a mathematician and haven't really studied complexity that much so I highly doubt I'll be the one to stumble across such an important proof.

  • @MT_Cuber
    @MT_Cuber Před 14 dny

    uzasne video!

  • @Egotrippade
    @Egotrippade Před 14 dny

    Thank you I know have a full understanding of randomness. Not sure what to decide about this nowledge though. Guess the pseudo part is part of this paradoxically parallell uni... Never mind. It seems to actually be hard to reapeth the zero knowledge proof in practice.

    • @Egotrippade
      @Egotrippade Před 14 dny

      At least it might have sown some seeds. Looking forward to the growth. Know I decidedly now I put that tree somewhere in this forest.

  • @sidharthghoshal
    @sidharthghoshal Před 15 dny

    what IS the assumption MOST researchers believe to be true.

    • @PolylogCS
      @PolylogCS Před 11 dny

      You can look here: vasekrozhon.wordpress.com/2024/05/18/avi-wigderson-has-won-the-turing-award/

  • @_hydrogelic
    @_hydrogelic Před 15 dny

    Noam Nisan from Nand to Tetris!!!!!!

  • @SuperLucasGuns
    @SuperLucasGuns Před 15 dny

    Very nice!

  • @vlc-cosplayer
    @vlc-cosplayer Před 15 dny

    9:35 - sorry for dragging semantics and philosophy into the discussion, but is there truly such a thing as "random"? You said that Pi only "looks" random, which is perfectly fair, since we have formulas to calculate it. However, if we had a way to perfectly predict any "random" physical process (such as radioactive decay, fluctuations in temperature, etc.) then all of those phenomena would become PRNGs. The state is the state of the universe, the function is physical formulas, and the outcome is perfectly predictable. I think you already touched on that when you mentioned flipping a coin as an example: randomness-as-unpredictability disappears if you can predict the outcome. Besides, once you get a "random" value, doesn't it stop being "random" because you just generated it? Like you said, if you take some digits from pi, they look random, but they're not actually random, because you obtained them through a computation. In more general terms, does that mean that "computable" and "random" are mutually exclusive, and that it's impossible to have a truly random value, because any value we can think of will be "computed" somehow?

    • @PolylogCS
      @PolylogCS Před 11 dny

      One implication of Wigderson's (and Kolmogorov's) work is that I find it philosophically very appealing to think about randomness as being ultimately about unpredictability. Even in the fully deterministic worlds where no "truly random bits" exist, whatever "truly random" means, you can still have construct pseudorandom bits that are for all practical purposes unpredictable and thus random.

  • @San93939
    @San93939 Před 16 dny

    My pb was 2.37 i swear

  • @deliyomgam7382
    @deliyomgam7382 Před 16 dny

    Is formula for circle (c1) x formula for cylinder (c2)= donuts (d) as in topology?? Admin plz do answer.

  • @Kargoneth
    @Kargoneth Před 16 dny

    My nondeterministic computatortron always solves problems in the least possible finite number of steps, or it runs forever. It runs all possible programs against all possible inputs in parallel. Each cycle of the computatortrob runs one cycle of each program/input. As soon as one of them spits out the solution, the computatortron halts.

  • @3141minecraft
    @3141minecraft Před 17 dny

    7:44 or more likely, it would terminate because of an algorithm that says something like this: return 2,2

  • @deliyomgam7382
    @deliyomgam7382 Před 17 dny

    Y not use quantum error in lottery😅😂😂 using three body problem i.e. input chaos.

  • @mattshu
    @mattshu Před 17 dny

    Idk why but I’m in love w you

  • @random_number_sequence

    is there anybody in there

  • @SSoup64
    @SSoup64 Před 17 dny

    Does this advance us in finding the elusive solution to the P vs NP problem?

  • @a.t10
    @a.t10 Před 17 dny

    thanks a lot. very simple and clear explanation.

  • @jameslew7269
    @jameslew7269 Před 18 dny

    wow, you should call it "bubble sort"

  • @LukePalmer
    @LukePalmer Před 18 dny

    Fantastic video, thank you. I understood not everything but enough to put it in my little brain folder of clever math tricks and algorithms in case I never need inspiration. Thanks for presenting this recent work so clearly and concretely, I really liked how you used concrete things like 99% and the polynomial detection algorithm instead of variables and generalities, it helps me think.

  • @user-vm1hi7bo5s
    @user-vm1hi7bo5s Před 18 dny

    Avi on the preview looks a lot like an old Maxim Katz, a russian politician and youtuber I actually confused with him. He's also an all-russian poker champion, the game you mentioned in the video. Now answer, is that random? 0_0 Nice video though, wasn't disappointed

  • @Erotemic
    @Erotemic Před 18 dny

    Surprise Mario

  • @JochemKuijpers
    @JochemKuijpers Před 18 dny

    14:20 - "Since A is correct for at least some seeds" -- where did this guarantee come from? A is correct for some pseudo-random inputs, but since the seed is shorter than the sequence of inputs, it doesn't seem that there's a guarantee that you will hit a random input for A is correct simply by iterating over all seeds. The space of potential inputs (of which >1% produce correct results) is exponentially bigger than the spaec of seeds; it could very well be that by the way the PRNG works, you'd miss all those sequences. Or is this guarantee coming from the assumption that the PRNG cannot be distinguised from 'real' random sequences?

  • @keyboard_toucher
    @keyboard_toucher Před 18 dny

    8:40 finding the k+1 ... k+nth digits of pi doesn't require finding the first 1...k digits.

  • @googleyoutubechannel8554

    What if this isn't even a good question... what if the idea of 'randomness' in the way that mathematicians 'want' it to be... what if this is just a nonsensical idea....

  • @francomarchesoni9004
    @francomarchesoni9004 Před 18 dny

    Nice

  • @VincentKun
    @VincentKun Před 19 dny

    Do the video where you do the zero knowledge proof with who is watching to prove you got right sudoku now

  • @EzBz982
    @EzBz982 Před 19 dny

    Hans Reichenbach: The Concept of Probability. Read it for a philosophical discussion of one of humanity’s most useful concepts that has no real philosophical basis and no empirical basis in reality.

  • @garretmh
    @garretmh Před 19 dny

    I have learned and subsequently forgotten how zero knowledge proofs work far too many times

  • @riteshbhartiya6155
    @riteshbhartiya6155 Před 19 dny

    For that polynomial matching problem, for a polynomial of degree d, we can just match values of polynomials for d+1 values. As different polynomials can have atmax d intersections, we can deterministically find if it's the same or different polynomial in polynomial time. Thus, it's a P problem.

    • @me_hanics
      @me_hanics Před 17 dny

      I was also thinking about this. Maybe it is because these are not only for polynomials, but other expressions, such as x*sin(x) which has infinitely many roots? Or another idea I had, is that maybe in some cases it's not easy to determine (an upper bound) for the degree automatically (by that I mean that a well trained mathematician may look at the expression and give an upper bound, but the computer isn't this smart). Or for high degrees such as 10000, testing 10001 points would be too time consuming, even if it is polynomial. @polylog could you clarify?

  • @andrewsomerville5772
    @andrewsomerville5772 Před 19 dny

    The hair.