Berry's Paradox - An Algorithm For Truth

แชร์
ฝัง
  • เผยแพร่เมื่อ 27 ก.ค. 2021
  • Go to expressvpn.com/upandatom and find out how you can get 3 months free.
    Hi! I'm Jade. If you'd like to consider supporting Up and Atom, head over to my Patreon page :)
    / upandatom
    Visit the Up and Atom store
    store.nebula.app/collections/...
    Lose at rock paper scissors www.cs.stir.ac.uk/~kms/schools...
    Subscribe to Up and Atom for physics, math and computer science videos
    / upandatom
    Follow me @upndatom
    Up and Atom on Twitter: upndatom?lang=en
    Up and Atom on Instagram: / upndatom
    For a one time donation, head over to my PayPal :) www.paypal.me/upandatomshows
    A big thank you to my AMAZING PATRONS!
    Lucas Alexander,
    Michael Seydel,
    Brian Wilkins
    , Cy 'kkm' K'Nelson
    , Thorsten Auth
    , Purple Penguin
    , bpatb
    , Chris Flynn
    , Scott Ready,
    Izzy Ca
    , Sofia Fredriksson
    , John H. Austin, Jr.
    , David Johnston
    , Rick DeWitt,
    Thomas Krause
    , Yana Chernobilsky,
    Lynn Shackelford, Adam Thornton,
    Andrew Pann,
    Anne Tan
    , Jan Gallo,
    Drew Hart
    , Tony T Flores,
    Russell Barlow
    , Jeffrey Smith
    , Brian Kent
    , Robert Hillier
    , Aaron Moffatt
    , Alex Hackman
    , Thomas V Lohmeier
    , Joel Becane,
    eris esoteric
    , Artem G.
    , Michael Hunter
    , Paul Barclay, 12tone,
    Zhong Cheng Wang,
    Damien Holloway,
    Mikely Whiplash
    , John Lakeman
    , Jana Christine Saout
    , Jeff Schwarz
    , George Fletcher,
    Louis Mashado,
    Michael Dean
    , Chris Amaris,
    Matt G
    , KhAnubis,
    Broos Nemanic
    , Dag-Erling Smørgrav
    , John Shioli
    , Joe Court
    , Todd Loreman
    , Susan Jones, Rudy Nyhoff, Colin Byrne, Nick H, Dr Andy Hill, Michael Miller, Jesper de Jong, Michael Lavin, Loren Hart, Ari Prasetyo, Duncan Adamson, Phat Hoang, Spuddy, Josh Bauer, Sascha Bohemia, tesseract, Stephen Britt, Will Miller, Dagmawi Elehu, Hansjuerg Widmer, John Sigwald, Carlos Gonzalez, Jonathan Ansell, Arsalan Noorafkan, Thomas Kägi, Courtney Rosenthal, James Palermo, Dominic Riverso, Jeroen Melchiors, Gary Leo Welz, Andrej Zon, Chris Teubert, Dylan Kolstad, Fran, Joe, John Sokolowski, Robert J Frey, The Doom Merchant, Wolfgang Ripken, Jeremy Bowkett, Vincent Karpinski, Nicolas Frias, Christopher Phipps, Louis M, kadhonn, Moose Thompson, Hal Roseman, Austin Rose, Andrew, John Klinkner, S, Rob Napier, Sam Ross, Peter Walsh, Garrett Chomka, Bobby Butler, Rebecca Lashua, Pat Gunn, Luc Ritchie, Elze Kool, RobF, Aditya Anantharaman, Frédéric Junod, Vincent Seguin, Bernard Wei, Help I'm trapped in a driver's license factory Roberts, Shawn, Israel Shirk, Ken Takahashi, Jesse Clark, Steven Wheeler, Philip Freeman, Jareth Arnold, Simon Barker, Dennis Haupt, Lou, amcnea, Renato Pereira, Simon Dargaville,and Magesh
    Creator
    Jade Tan-Holmes
    Animations
    Tom Groenestyn
    Sound Design and Music
    Junior Arruda
    / iamaduo
    www.epidemicsound.com/
    open.spotify.com/artist/1D30m...
    Sources and Further Reading
    An introduction to Kolmogorov complexity and its applications - Ming Li
    Infinity and The Mind - Rudy Rucker
    www.lesswrong.com/posts/Kyc5d...
    en.wikipedia.org/wiki/Kolmogo...
  • วิทยาศาสตร์และเทคโนโลยี

ความคิดเห็น • 1.9K

  • @ryanmccampbell7
    @ryanmccampbell7 2 ปีที่แล้ว +77

    You came *this close* to making a link between the halting problem and berry's paradox, which I've never thought of before. Would be cool to link this to Godel's Incompleteness theorem too. Great video!

  • @frenstcht
    @frenstcht 2 ปีที่แล้ว +172

    "Describe yourself"
    "Too complex for five words."

    • @General12th
      @General12th 2 ปีที่แล้ว +5

      I really like this.

    • @frenstcht
      @frenstcht 2 ปีที่แล้ว +1

      @@General12th:-)

    • @ashwinirao8133
      @ashwinirao8133 2 ปีที่แล้ว +2

      Too good👏

    • @vigilantcosmicpenguin8721
      @vigilantcosmicpenguin8721 2 ปีที่แล้ว +10

      I think the most information-efficient way to describe myself is:
      "I"

    • @frenstcht
      @frenstcht 2 ปีที่แล้ว +1

      @@vigilantcosmicpenguin8721 LOL!

  • @EternalDensity
    @EternalDensity 2 ปีที่แล้ว +20

    "So it runs the program and returns the result..."
    Ooohhh it's time for the Halting Problem!

    • @ShaLun42
      @ShaLun42 2 ปีที่แล้ว +3

      It's time for Zeno Machine!

  • @annannz9047
    @annannz9047 2 ปีที่แล้ว +16

    This is my first time watching your videos, and this might be my favorite educational video among thousands of amazing ones I watched on TH-cam. I've recently been trying to produce these kind of videos in my leisure time, but there are so much technical difficulties it frustrated me a bit. I just hope one day I can make something good like this. Thanks for the inspiration.

  • @RobertMilesAI
    @RobertMilesAI 2 ปีที่แล้ว +134

    Well. Time to throw away my solomonoff induction script...

    • @upandatom
      @upandatom  2 ปีที่แล้ว +53

      nah it's a cool topic and i'm sure you can cover it differently

    • @qqii
      @qqii 2 ปีที่แล้ว +22

      Please don't! The world definitely deserves move videos presenting this facinating topic in a digestible way!

    • @RobertMilesAI
      @RobertMilesAI 2 ปีที่แล้ว +46

      ​@@upandatom Thanks!
      But yeah I have so many topics to cover, and it takes me so long to make a video, that if I don't expect my video to be the best one about that topic, I'm better off covering something else.
      The plus side is I can now skip ahead and make videos that rely on these ideas, using this one as a prerequisite :D

    • @dylancope
      @dylancope 2 ปีที่แล้ว +1

      @@RobertMilesAI AIXI is the obvious follow up ;)

    • @michaelfrankel8082
      @michaelfrankel8082 2 ปีที่แล้ว +1

      @@RobertMilesAI How can it be the best if you cannot prove it’s the best?

  • @kyransoriano3527
    @kyransoriano3527 2 ปีที่แล้ว +50

    I have class in 4 hours and I haven't slept yet but I will watch this video because Jade teaches physics like no other.

    • @upandatom
      @upandatom  2 ปีที่แล้ว +18

      haha thanks! i hope you enjoy math and computer science too :)

    • @darshandev1754
      @darshandev1754 2 ปีที่แล้ว +2

      Dude it's math and computer science

  • @JPEaglesandKatz
    @JPEaglesandKatz ปีที่แล้ว +8

    You have a positive vibe gift of explaining things that I have no clue about.. I don't understand half of it but a lot of it sticks too!! Your way of presenting in your videos is so natural.!

  • @TIO540S1
    @TIO540S1 2 ปีที่แล้ว +7

    It’s amazing that Kolmogorov is mentioned only rarely, if at all, in online discussions of the greatest mathematicians. His name appears so often at such a high level in so many fields that he’s nearly unique. Among these are probability, logic, topology, fluid mechanics, and others.

  • @Agrajag819
    @Agrajag819 2 ปีที่แล้ว +201

    As a mathematician working in algorithmic information theory, I will definitely be saving this video for the next time I teach an intro course!

    • @hughcaldwell1034
      @hughcaldwell1034 2 ปีที่แล้ว +4

      Just got my BS and planning to go on to do graph theory - but information theory is definitely one of the areas that calls to me pretty hard. Hopefully I'll have time to study it as well. Plus, who knows, algebraic topology or something. There's too much maths I want to do and I'm only mortal.

    • @lonestarr1490
      @lonestarr1490 2 ปีที่แล้ว +1

      @@hughcaldwell1034 A good approach to information theory might be via ergodic theory and dynamical systems.

    • @aaaab384
      @aaaab384 2 ปีที่แล้ว

      What kind of "work" are you doing, if you need to be inspired by a video made by an amateur?

    • @hughcaldwell1034
      @hughcaldwell1034 2 ปีที่แล้ว +14

      @@aaaab384 "Amateur" content gets used a fair bit in teaching courses, because some people have a gift for educating, for explaining clearly and making things click for students, even if their interest in a particular topic is purely a passion for learning thing. These are not always the same people who necessarily specialise in researching a given topic. In fact, it is usually people who specialise in teaching, not in research, that make the best teachers. Go figure. So my question to you is: what kind of work are you doing that you think that showing a video to your class that clearly introduces a topic reflects at all on the quality of someone's research?

    • @vitocorleone6040
      @vitocorleone6040 2 ปีที่แล้ว

      @@aaaab384 to be fair I think this when ever I see someone start their Conment saying their in some crazy post at their job Not this person necessarily but so many people just happen to be in the best position possible with all this insight and “humbleness” when they just wanna state their position and that they can relate. I can’t believe I just wrote all this……I feel you lol.

  • @Adraria8
    @Adraria8 2 ปีที่แล้ว +57

    Seems like that FindShortestString program wouldn’t work because of the halting problem. It would eventually come across a program string that it couldn’t tell if it halts or not

    • @dwightk.schrute8696
      @dwightk.schrute8696 2 ปีที่แล้ว +13

      The FindShortestString program may never terminate itself. The main problem of the function is that it's making an assumption that it somewhat knows about all possible forms of computation. Let's assume for a moment that I create a new programming language where the number Pi can be generated by feeding it only one 1 bit of information. This way I can basically guarantee that FindShortestString will always return 1 for any input I throw at it because it completely sidesteps any complexity inherent to the process of decomposing that 1 bit of information into the original value.

    • @magneticflux-
      @magneticflux- 2 ปีที่แล้ว +6

      @@dwightk.schrute8696 Ahh, the Codegolf paradox lmao

    • @chriswarburton4296
      @chriswarburton4296 2 ปีที่แล้ว +16

      @@dwightk.schrute8696 Indeed, the choice of language determines the 'simplicity' of each string. However, regardless of which language we choose, we'll eventually reach programs which are so complex that they *implement other programming languages*, at which point we can use the shortest program in *that* language (plus the size of the implementation). For example, let's imagine we're looking for the Kolmogorov complexity of a string S by searching through machine code programs, but it just-so-happens that the string S only has a short description in Python; we'll call that description P. If we keep trying more and more machine code programs, we will *eventually* start to see programs which just-so-happen to contain Python interpreters; and programs which contain Python interpreters applied to Python programs; and eventually we'll find a machine code program which contains a Python interpreter applied to the program P. This program will be longer than P, but only by a constant amount (the size of the Python interpreter): the complexity of *any* string, measured using machine code, cannot be more than its complexity measured using Python, plus the size of a Python interpreter.
      Hence Kolmogorov complexitites can only change by at most a constant amount when switching from one language to another.
      By the way, you might like the 'minimalist languages' that John Tromp uses to calculate Kolmogorov complexities, like Binary Lambda Calculus tromp.github.io/cl/Binary_lambda_calculus.html

    • @gJonii
      @gJonii 2 ปีที่แล้ว +6

      @@dwightk.schrute8696 This is wrong. Kolmogorov Complexity is defined per programming language. Usually it's left ambiguous with the assumption "for most programs most results are similar, so no need to worry about details", but any concrete number depends on the language or encoding

    • @peterSobieraj
      @peterSobieraj 2 ปีที่แล้ว +3

      If it runs all programs, then at some point it will run it self.
      So it will be infinite loop.

  • @naderchmait5543
    @naderchmait5543 ปีที่แล้ว +12

    This is a fantastic video. Finally someone giving credit to Solomonoff's original work! Worth mentioning Levin's Kt complexity (Levin Search) which is a time-bounded version of Algorithmic/Kolmogorov complexity to go around un-computability. Please continue making such great videos :)

  • @allanlees299
    @allanlees299 8 หลายเดือนก่อน +1

    Occam's Razor is best expressed in words as "an explanation must be as complex as is necessary to explain a given phenomenon, but not any more complex than that." In other words, it's not "the simplest idea is the best" but rather "the idea that has no unnecessary elaborations or assumptions is most likely to be the best description of how the phenomenon is generated."

  • @IndurOutdoor
    @IndurOutdoor 2 ปีที่แล้ว +83

    I only discovered this amazing lady this year & she is amazing. Absolutly love all her videos. I Thank You

    • @upandatom
      @upandatom  2 ปีที่แล้ว +19

      Thank you!!

    • @johnbonnett5746
      @johnbonnett5746 2 ปีที่แล้ว +1

      I have followed her a bit longer but I always enjoy what she presents, especially a little min-bending like this one. The argument seems a little like some from Turing or Russell's Paradox.

    • @matthewwriter9539
      @matthewwriter9539 2 ปีที่แล้ว +2

      I only found her this hour.
      This is only her second video that I have seen.
      Though I am not sure which of the two she posted first.
      If a TH-cam creater posts 100 videos and I watch all of then in the opposite order that they were posted, which one can be said to be their first video that I watched? Video 1, or video 100? Couldn't both videos be said to be able to be described that way?

    • @Bassotronics
      @Bassotronics 2 ปีที่แล้ว +2

      Yea she’s smart and cool.

    • @Anuchan
      @Anuchan ปีที่แล้ว

      I bet the other students in her math classes are jealous of her deep understanding of the material.

  • @MarcSpctr
    @MarcSpctr 2 ปีที่แล้ว +112

    She really has so positive and happy vibes, it makes learning fun.

  • @rmt3589
    @rmt3589 2 ปีที่แล้ว

    These videos are insanely valuable! This is only the second one I've seen, and I've already subscribed. Please never stop!!!

  • @FromTheNard
    @FromTheNard 2 ปีที่แล้ว +3

    Had to write that down, ‘information is the resolution of uncertainty’. Great video, really nice studio / background. I couldn’t follow on a few points (my limited comprehension, not Jade’s presentation) but a lot was covered here.

  • @RealHypeFox
    @RealHypeFox 2 ปีที่แล้ว +143

    A minute in and I guess existential dread is what I’m doing this morning, lol!
    Always a pleasure to see your videos.

    • @upandatom
      @upandatom  2 ปีที่แล้ว +24

      hehe good morning :)

  • @RequiosWoW
    @RequiosWoW 2 ปีที่แล้ว +10

    I really love these computer science videos, it's surprising as a computer science student just how much of computer science I'm not exposed to. This video has made me very interested in learning Algorithmic information theory! thank you!!

  • @aBrokenShard
    @aBrokenShard 2 ปีที่แล้ว +2

    Simply Amazing!
    Really what else is there to say except you presented it very well; logically linking quite complex ideas ! Wishing you all the success.

  • @metametodo
    @metametodo 2 ปีที่แล้ว

    I hit like at the start of your videos in case I forget to do it later, and I've never came close to regret it. In my eyes you're unique in regards to content presented, I love how you're able to fit philosophy beautifully in your math, physics videos.

  • @MegaNancyLover
    @MegaNancyLover 2 ปีที่แล้ว +32

    Yay! You’ve been working on this one for a while!

    • @upandatom
      @upandatom  2 ปีที่แล้ว +31

      yes it took me a while to wrap my head around!

    • @rollomaughfling380
      @rollomaughfling380 2 ปีที่แล้ว +5

      @@upandatom You did a tremendous job. Thank you!

  • @domainofscience
    @domainofscience 2 ปีที่แล้ว +331

    This was so good! I learned loads and yeah, really fascinating journey, darned uncomputableness. Also, I love your animations, the characters are brilliant.

    • @vasudevraghav2109
      @vasudevraghav2109 2 ปีที่แล้ว +5

      Hello there

    • @shreddedtwopack6625
      @shreddedtwopack6625 2 ปีที่แล้ว +5

      Hello there

    • @upandatom
      @upandatom  2 ปีที่แล้ว +17

      Thanks Dom :)

    • @cedricvillani8502
      @cedricvillani8502 2 ปีที่แล้ว +1

      Lol just crap for other shills to copy and make VPN commercials, SHE LITERALLY SHOWED YOU NOTHING
      JUST CLICKBAIT.

    • @leif1075
      @leif1075 2 ปีที่แล้ว +1

      @@upandatom JADE! I really hope you can please respond to my last message when you can finally.

  • @josiah42
    @josiah42 2 ปีที่แล้ว +2

    Wow, what a journey! You've earned my subscription. Kolomogorov Complexity runs into the Halting Problem because it treats data compression like a recusive program. I'm not sure that would happen in a limited non-Turing Complete DSL though. That approach would get you a workable gauge theory if not the TRUE compression. I'm impresssed you managed to turn a math proof that we'll never know absolute truth into a positive and uplifting video. Informtation theory is very transforming and applicable everywhere. Great work!

  • @metamorphiczeolite
    @metamorphiczeolite 2 ปีที่แล้ว

    The realization you express at 11:05 is really amazing. Thanks!

  • @rentristandelacruz
    @rentristandelacruz 2 ปีที่แล้ว +133

    You: **looking for some universal algorithm or some complete axiom system**
    Paradox: "Oh hello there!"
    You: "Oh no!"

    • @timhaldane7588
      @timhaldane7588 2 ปีที่แล้ว +25

      Kurt Godel: told you so

    • @KitagumaIgen
      @KitagumaIgen 2 ปีที่แล้ว +20

      Turing: you'll never know when to stop looking...

  • @BubaMeyer
    @BubaMeyer 2 ปีที่แล้ว +200

    I bet that one of the dislikes is from David Hilbert

    • @vigilantcosmicpenguin8721
      @vigilantcosmicpenguin8721 2 ปีที่แล้ว +37

      At least Godel and Turing liked it.

    • @crhu319
      @crhu319 2 ปีที่แล้ว +4

      Nunez and Lakoff can't decide whether to dislike or like it.

    • @filiplaubert5001
      @filiplaubert5001 2 ปีที่แล้ว +8

      Its from people trying to find pattern in pi for 20 mins.

    • @jacobpeters5458
      @jacobpeters5458 2 ปีที่แล้ว +1

      @@vigilantcosmicpenguin8721 also Tarski !

    • @ernestestrada2461
      @ernestestrada2461 2 ปีที่แล้ว

      I do not know who David Hilbert is but I dislike this post because it assumes that everything is ones and zeros which is digital thinking. About 20 years ago I was discussing this with electrical engineers and ask them why we didn't go to trigital, positive one, zero and negative one.
      Turns out they've actually started making some devices experimental e that use trigital.
      Plus the claim that this includes philosophy is the biggest bunch of crap! Philosophy also includes human behavior and emotions. These items cannot be summed up with one's, zeroes and negative one's.
      You need to stop acting like everybody else is a jerk when you are the real jerk!

  • @tdtrecordsmusic
    @tdtrecordsmusic 2 ปีที่แล้ว +2

    I feel like the paradox / contradictions are only present when we narrow our focus to partial descriptions.
    Synchronicities seem special when we choose to become inspired by individual facets :)
    Choosing to become amazed when observations are more/less like a maze.
    Ur vids are more inspiring than morning coffee

  • @mahlas69
    @mahlas69 2 ปีที่แล้ว

    Just found your channel. You are a brilliant performer. Keep these videos coming. They are fascinating.

  • @anujarora0
    @anujarora0 2 ปีที่แล้ว +240

    My psychiatrist: Jade with a shaving cream on her face doesn't exist and can't hurt you
    Jade with a shaving cream on her face: 6:52

    • @force10guy26
      @force10guy26 2 ปีที่แล้ว +7

      I didn't catch that day first, was looking away. WTAF?! 😂

    • @thedeemon
      @thedeemon 2 ปีที่แล้ว

      still can't hurt you

  • @denkenunddanken5961
    @denkenunddanken5961 2 ปีที่แล้ว +6

    Just I thought of watching your videos on Paradox. And here came a New one. Thank God. Thank you. ☺

  • @szboid
    @szboid 2 ปีที่แล้ว +2

    Such interesting topics, and so clear and concise. We all benefit so much from your videos. Thank you.

  • @peterparker6377
    @peterparker6377 6 หลายเดือนก่อน +1

    You are my favourite amongst youtube educators and your way of explanations and your energy always amaze me

  • @huzaifaimran9468
    @huzaifaimran9468 2 ปีที่แล้ว +4

    Why can't my profs be as simple as you and as interesting as your goofy animations
    Great video!
    Really appreciate it clearing so many of concepts!

  • @Cerzus
    @Cerzus 2 ปีที่แล้ว +3

    4:55 The string of 9's gave it away for me

    • @T3sl4
      @T3sl4 2 ปีที่แล้ว +1

      Shame on me, I should've recognized the Feynman point!

    • @Cerzus
      @Cerzus 2 ปีที่แล้ว

      @@T3sl4 Shame on me for not knowing it has a name!

  • @brandonspad6661
    @brandonspad6661 ปีที่แล้ว

    I love how technical yet newbie friendly this channel is

  • @ayo94563
    @ayo94563 2 ปีที่แล้ว

    It's been a year and a half since I last watched any video of yours. Glad to be back

  • @keithbarron81
    @keithbarron81 2 ปีที่แล้ว +5

    It's always a better day when there's a new Up and Atom video.

  • @BallotBoxer
    @BallotBoxer 2 ปีที่แล้ว +3

    I didn't like math in high school but you make the subject so entertaining and understandable!

  • @kevparkin4846
    @kevparkin4846 2 ปีที่แล้ว

    This channel is amazing, well presented, simple explanations, very entertaining.

  • @geoffsecombe
    @geoffsecombe 2 ปีที่แล้ว +9

    4:40 obviously I suck at lip-reading. Surely you didn't say what I thought you said.

    • @upandatom
      @upandatom  2 ปีที่แล้ว +5

      never ;)

    • @TarEcthelion
      @TarEcthelion 2 ปีที่แล้ว +1

      "Only I didn't say 'Fudge'..."
      -Ralphie

  • @peNdantry
    @peNdantry 2 ปีที่แล้ว +20

    A fascinating presentation, Jade! As I was watching it, I was reminded of a poem I wrote. I think I should dedicate it to Ray Solomonoff! :)
    *Majestic sunrise*
    It’s sad but true that one can be
    adept at counting numbers,
    yet at the same time fail to see
    which ones make up the wonders.
    All things in life may be defined
    as strings of ones and zeroes.
    Discernment of a finer kind
    transforms someones to heroes.

    • @djpete2009
      @djpete2009 2 ปีที่แล้ว +1

      I love it!

    • @peNdantry
      @peNdantry 2 ปีที่แล้ว

      @@djpete2009 Thanks :)

    • @momom6197
      @momom6197 ปีที่แล้ว +1

      This is great. ^-^

    • @peNdantry
      @peNdantry ปีที่แล้ว

      @@momom6197 Thank you for that :)

  • @Navek2286
    @Navek2286 2 ปีที่แล้ว +1

    Wonderful and informative, as always! Love your enthusiasm and excitement for the field that you are in! And, I would probably lose to you at rock, paper, scissors 🤣

  • @ikartik90
    @ikartik90 2 ปีที่แล้ว

    Great video! This is quite similar to-and in my understanding what Alan Turing postulated through-the halting problem paradox.

  • @arkapravamanna
    @arkapravamanna 2 ปีที่แล้ว +4

    Amazingly written, explained. Really great video to explain a mind blowing stuff 🔥

    • @upandatom
      @upandatom  2 ปีที่แล้ว +1

      Thank you, glad you liked it!

  • @dogpadogpa
    @dogpadogpa 2 ปีที่แล้ว +47

    An AI that asks itself AI Paradox?
    Earth: It'll call themselves human.

  • @_Xeto
    @_Xeto ปีที่แล้ว

    Brilliant video! It's truly grand seeing how philosophy, math and everything comes together!!

  • @ElPsyKongroo
    @ElPsyKongroo 2 ปีที่แล้ว

    Wow you really blew up now. I remember watching you at only a couple thousand subs I'm really happy to see your channel grow :)

  • @adityaanantharaman7963
    @adityaanantharaman7963 2 ปีที่แล้ว +10

    It’s the truth there’s no algorithm for truth!
    As always a great video; your presentation was elegant and clean👍🏽😊

    • @upandatom
      @upandatom  2 ปีที่แล้ว +5

      thank you I appreciate that :)

    • @john-or9cf
      @john-or9cf 2 ปีที่แล้ว

      Hmmm, Fakebook and Twitter seem to think they have truth algorithms, no?

  • @wlritchi
    @wlritchi 2 ปีที่แล้ว +4

    4:56 I can't believe I actually knew this. That's knowledge that's been waiting 15 years for an application!

  • @additionaddict5524
    @additionaddict5524 2 ปีที่แล้ว +7

    Jade: What' the biggest number you can think of?
    Me: 6

  • @parth4819
    @parth4819 2 ปีที่แล้ว

    I love the way you talk, gestures and all! It's incredible!

  • @m00t
    @m00t 2 ปีที่แล้ว +58

    Occam's Razor is not merely "simpler is more likely" it is specifically, "plurality should not be posited without necessity". Or in less obtuse language: "all other things being equal, the simpler answer is preferred".

    • @CraftyF0X
      @CraftyF0X 2 ปีที่แล้ว +16

      Or, the explanation which requires the least assumption is the prefered.

    • @Daniel-ih4zh
      @Daniel-ih4zh 2 ปีที่แล้ว +1

      Yes, m00t, but she's explaining why this is the case.

    • @Nnm26
      @Nnm26 2 ปีที่แล้ว +3

      Duh, she's literally explaining why it is preferred instead of just saying that it's preferred. I love how you reduced the substance of a statement while simultaneously saying that there's more to it. Oh the irony.

    • @timhaldane7588
      @timhaldane7588 2 ปีที่แล้ว +3

      I usually translate it as, "all other things being equal, the fewer assumptions, the less likelihood for error."

    • @vigilantcosmicpenguin8721
      @vigilantcosmicpenguin8721 2 ปีที่แล้ว +1

      Yes, but Jade chose the simplest way to explain it.

  • @MedlifeCrisis
    @MedlifeCrisis 2 ปีที่แล้ว +506

    You know Jade, it's unkind to make jokes about shaving. Some of us have to do it four times a day.

    • @MedlifeCrisis
      @MedlifeCrisis 2 ปีที่แล้ว +113

      Joke's aside, this video *looked* gorgeous, loved the little text effects, colours and all the graphics. Worth the wait!

    • @christopherellis2663
      @christopherellis2663 2 ปีที่แล้ว +20

      For surgery, I suppose.

    • @upandatom
      @upandatom  2 ปีที่แล้ว +54

      Thanks Rohin :)

    • @peterpandaluki6663
      @peterpandaluki6663 2 ปีที่แล้ว +21

      Maybe try a new blade?

    • @based8223
      @based8223 2 ปีที่แล้ว +5

      Cringe

  • @edgeeffect
    @edgeeffect 2 ปีที่แล้ว

    Fabulous job Jade.... I love a nice paradox for Sunday lunch.

  • @trevorgwelch7412
    @trevorgwelch7412 2 ปีที่แล้ว +1

    This discussion makes me think of the Mandelbrot set and fractal equations . Great Video .

    • @loturzelrestaurant
      @loturzelrestaurant 2 ปีที่แล้ว +1

      Science is important to spread and i often offer Recommendations,
      but today i wanna do it a bit differently and try to bring-in People to watch 'some More News',
      a Satire-Version of corrupt and biased News-Channel.
      Just like Scientists bring Attention to Climate-Change and such Issues,
      that TH-camr bringts Attention to Homelessness and various other Issues.
      Unbiased and informed, his Talks about 'Obvious Solutions to Obvious Problems' are a Masterpiece.

  • @swayamprakashkar9664
    @swayamprakashkar9664 2 ปีที่แล้ว +3

    Hey Jade, good to see you after so long!

  • @olivierdeme3886
    @olivierdeme3886 2 ปีที่แล้ว +9

    Your channel is pure gold. Your teaching skills are unique and you don't hesitate to introduce viewers to topics that are seldom approached by other channels.
    Many thanks to you and your team. A TH-cam gem.

    • @upandatom
      @upandatom  2 ปีที่แล้ว +2

      Thank you so much :)

  • @papaowl13803
    @papaowl13803 2 ปีที่แล้ว

    Ahhh, my favorite YT math teacher. Always ready to learn. Thanks Jade. And thank you

  • @harrybarrow6222
    @harrybarrow6222 2 ปีที่แล้ว

    Excellent video. Very clear on a tricky topic.

  • @johngoshy4706
    @johngoshy4706 2 ปีที่แล้ว +3

    Awesome video! I love your work, Jade. Question: around minute 8-9 are we risking undercounting complexity when we convert complex objects to strings since each programming language or 'context' contains information that we overlook or undercount in that conversion?

    • @anywallsocket
      @anywallsocket 2 ปีที่แล้ว

      Practically yes, but mathematically these proofs are done with Turing machines which are defined by their ability to mimic any other program, which in this case requires the simplest way possible.

  • @SachinChauhan-ch6el
    @SachinChauhan-ch6el 2 ปีที่แล้ว +5

    Something disproved is equal to something proved! So I am pretty sure that the old version would not tell his young version to stop. He would have appreciated him, just like we did!
    Thanks for the great content.

  • @dbug2213
    @dbug2213 2 ปีที่แล้ว

    Very well done. Thank you for the great information and great laughs. :)

  • @amaurydecizancourt4741
    @amaurydecizancourt4741 ปีที่แล้ว

    Thank you for making me love maths even more. Your videos are fun, charming, and extremely clear. I am not a mathematician of any sort, but I adore its beauties. Did you make a video on Wolfram's rule 30? I cannot find it if it exists. If it does not, the wonderful universe of maths is missing something.

  • @EpicHobbyist
    @EpicHobbyist 2 ปีที่แล้ว +5

    I think you don’t even need to go as deep as you did to find it impossible. Wouldn’t the halting problem make FindShortestString impossible before even getting to Berry’s Paradox? Once FindShortestString reaches code that loops infinitely, it could never proceed, since it would be impossible to tell if the code would be looping forever (so neither a right or wrong output string, just no output) or if it would just be running for a really really long time.

  • @thetungwakou
    @thetungwakou 2 ปีที่แล้ว +9

    POV: you’re a computer, but they won’t stop asking you philosophy questions.

  • @Rekalus
    @Rekalus 2 ปีที่แล้ว

    Deeply interesting and wonderfully presented!

  • @adolfobahamonde2358
    @adolfobahamonde2358 2 ปีที่แล้ว

    This video was incredible!
    The study of complexity is such a vast field nowadays, from a physical point of view the Kolmogorov-Chaitin-Solomonoff complexity is not really a good complexity measure because it assigns large values to random strings while you wouldn't say a random string is complex, there are some other beautiful definitions of complexity such as 'logical depth' introduced by Charles Bennett or the 'Effective Measure Complexity' introduced by Peter Grassberger.
    I'm currently studying this so I'm quite excited with all the things I'm learning right now and the implications that they have in fields as diverse as biology (concerning the origin of life, as an example) and physics (particularly in the study of chaotic systems, are they more complex transition from order to disorder?) :D

  • @lunarpassion
    @lunarpassion 2 ปีที่แล้ว +6

    "I took out the first 99, so it wouldn't be obvious for the mathematicians out there"
    That was a sucker punch!

    • @Jivvi
      @Jivvi 2 ปีที่แล้ว +3

      She actually took out the first 100 decimal places (101 digits), and I recognised it almost immediately because I memorised it to 100 decimal places a while back, and then decided to keep going about a year later, but stopped at about 120. If she'd cut off a few more digits, I would have had no idea.
      I'm not a mathematician.

  • @FactTalkOfficial
    @FactTalkOfficial 2 ปีที่แล้ว +3

    Great Vid as Always!!!

  • @chandan_nitk0.5k
    @chandan_nitk0.5k 2 ปีที่แล้ว +1

    Love the way you explain everything ❤️

  • @sergiohl
    @sergiohl ปีที่แล้ว +2

    I've always been quite fascinated with kolmogorov complexity and one thing that intrigues me is the fact that I cannot entirely state the difference between this and the halting problem. Is it a different form of the same thing?
    Thanks for your videos

  • @user-li9xc9ur1m
    @user-li9xc9ur1m 2 ปีที่แล้ว +18

    Wait, wasn't the same thing proven earlier in Gödel's incompleteness theorem, and Turing's halting problem?

    • @swagatochatterjee7104
      @swagatochatterjee7104 2 ปีที่แล้ว +6

      Yes it is. A shorter proof. If I have an algorithm for truth, that algorithm can definitely say whether a program can halt or not. So an algorithm for truth should be able to solve the halting problem. But Church-Turing thesis implies that halting problem can't be solved. Yaah and Church Turing Thesis I guess was solved in 1930s

    • @chriswarburton4296
      @chriswarburton4296 2 ปีที่แล้ว +11

      They're definitely related. The reason FindShortestProgram doesn't work is that it will have to look at some programs which loop forever, but (due to the Halting Problem) it has no way tell those apart from very-long-running programs, and hence it can't choose which programs to 'skip'. Levin Complexity is a computable alternative to Kolmogorov Complexity, which takes (the logarithm of) the running time into account; hence it's able to 'skip' programs which take an exponentially long time (whether or not they happen to loop forever or not)

    • @chriswarburton4296
      @chriswarburton4296 2 ปีที่แล้ว +11

      Algorithmic Information Theory actually takes things a bit deeper than Gödel and Turing. For example, Chaitin's incompleteness theorem proves that (a) the amount of 'algorithmic information' in a system of mathematics limits the theorems it is able to prove, (b) the algorithmic information of a system of mathematics comes entirely from its axioms, (c) the information in those axioms are essentially random bits, which we're free to choose either way. In other words, theorems are just re-statements of the axioms; and are hence assumptions.

    • @NimhLabs
      @NimhLabs 2 ปีที่แล้ว +3

      There isn't too much for differences between The History of Maths and the works of HP Lovecraft
      To the point where comparing famous mathematicians to Lovecraftian protagonists is typically considered not funny for the reason of "that is an old joke--heard it too often--now it is lame"

    • @saeidakbari4788
      @saeidakbari4788 2 ปีที่แล้ว +1

      @@chriswarburton4296 Church-Turing thesis relies on the idea of "computable" functions. Sure, in the classical model of computation, which either humans, mechanical machines and digital systems can do, that is the case. Although a bit recently, there was a breakthrough in theory of math and physics: th-cam.com/video/HL7DEkXV_60/w-d-xo.html
      So maybe if (in the near future) we define "computation" as quantum computation, this thesis no longer holds.
      This is just my own understanding of the topic. Would love to hear your opinion on it too!

  • @marcoponts8942
    @marcoponts8942 2 ปีที่แล้ว +9

    What are the paintings/pictures you have in the background? And where can you get them? :)

    • @upandatom
      @upandatom  2 ปีที่แล้ว +8

      displate.com

  • @TheJuwailes
    @TheJuwailes 2 ปีที่แล้ว

    This is a really well made video. Thank you it!

  • @tyapca7
    @tyapca7 2 ปีที่แล้ว

    One of the most brilliant videos I've seen. Tears in my eyes, literally. Big thanks! Keep on...

    • @loturzelrestaurant
      @loturzelrestaurant 2 ปีที่แล้ว

      Science is important to spread and i often offer Recommendations,
      but today i wanna do it a bit differently and try to bring-in People to watch 'some More News',
      a Satire-Version of corrupt and biased News-Channel.
      Just like Scientists bring Attention to Climate-Change and such Issues,
      that TH-camr bringts Attention to Homelessness and various other Issues.
      Unbiased and informed, his Talks about 'Obvious Solutions to Obvious Problems' are a Masterpiece.

  • @PaulPaulPaulson
    @PaulPaulPaulson 2 ปีที่แล้ว +8

    6:14 That's protein folding and the riemann zeta function, both known to be involved in hard to solve problems. But can anyone figure out what chemical that is on the right or explain which problem it represents?

    • @michaelsommers2356
      @michaelsommers2356 2 ปีที่แล้ว +2

      All I know is that it's an acid.

    • @Fists91
      @Fists91 2 ปีที่แล้ว +2

      Chucking the structure into a Google image search narrowed it down to something in the fluroquinolone family of antibiotics, that may have been cheating though

    • @turun_ambartanen
      @turun_ambartanen 2 ปีที่แล้ว +1

      What are the equations on the pictures in the background?
      I can only identify Entropy, the cool equation, and Schrödinger Equation. The third pictures I can't place. Maybe something with gravity because of the big G?
      edit: nevermind, it's general relativity en.wikipedia.org/wiki/General_relativity

    • @kibrika
      @kibrika 2 ปีที่แล้ว

      Now I'm curious too!

  • @robmcdiarmid285
    @robmcdiarmid285 2 ปีที่แล้ว +3

    I feel like the context (compiler) used to interpret information needs to be taken into account. For a specific compiler the kolmogorov complexity can be computed using the technique in the video. But if you can pick the ideal compiler for an input string then the complexity of any string is 0 as the compiler could just hard code that string when the input is empty.

    • @b43xoit
      @b43xoit 2 ปีที่แล้ว

      "For a specific compiler the kolmogorov complexity can be computed using the technique in the video." Not for a language that is Turing complete, because the program could run forever and so the algorithm wouldn't go on to the next string.

    • @robmcdiarmid285
      @robmcdiarmid285 2 ปีที่แล้ว

      @@b43xoit ah, right

    • @anywallsocket
      @anywallsocket 2 ปีที่แล้ว

      Actually I think it’s taken into account mathematically, because yeah the shortest program to print string x is ./printx. So you can either shove the complexity into the compiler / language or into the algorithm, either way it’s a constant complexity.

  • @Snowflake_tv
    @Snowflake_tv 2 ปีที่แล้ว

    Wow... How delicate the concept is! Interesting!

  • @Cau_No
    @Cau_No 2 ปีที่แล้ว +1

    As a programmer, I denote series of 0|1 rather as *streams* (in this case, a bitstream) to avoid confusion with strings.
    Because "String" in almost every program language is used for an array of characters (usually one or two bytes) representing some kind of text containing all letters of the alphabet (and some more).

  • @cyto3338
    @cyto3338 2 ปีที่แล้ว +50

    You know the video is good if it has an undefined Like-Dislike Ratio

  • @ruferd
    @ruferd 2 ปีที่แล้ว +9

    8:28
    Me, an intellectual: ah yes, string theory.

    • @benurm2390
      @benurm2390 2 ปีที่แล้ว +1

      Don't think these are the same kind of strings, though.

    • @ruferd
      @ruferd 2 ปีที่แล้ว +4

      @@benurm2390 yes, that was the joke.

    • @vigilantcosmicpenguin8721
      @vigilantcosmicpenguin8721 2 ปีที่แล้ว +1

      I'm sure I can find a shorter string if I just cut a spool of thread.

  • @RAZREXE
    @RAZREXE 2 ปีที่แล้ว

    So cool, yet so simply explained. Thanks!

  • @bassett_green
    @bassett_green 2 ปีที่แล้ว +1

    I'm not sure if this video just had a different editing style, but I really like it - the whole thing seems a lot more conversational and peer-to-peer than others, if that makes sense?
    And I obviously informative as always, of course :)

  • @anshjain3617
    @anshjain3617 2 ปีที่แล้ว +3

    Outro music slaps tho!

  • @austinpowers7670
    @austinpowers7670 2 ปีที่แล้ว +4

    2:58 "As you can't describe all numbers, it logically follows that there must be a biggest number that you can describe"
    That's incorrect. Just suppose I can only describe every other number. In that case I cannot describe all numbers but there still is no biggest number I can describe since I can always jump to the next one I can describe by adding 2 to the last one I could describe.

    • @nickdsp8089
      @nickdsp8089 2 ปีที่แล้ว +1

      Unless your life ends the moment you just added 2 to the last one and the description ends abnormally. Which definitely will happen at some point on your quest by ALWAYS jumping to the next one.

    • @austinpowers7670
      @austinpowers7670 2 ปีที่แล้ว +1

      @@nickdsp8089 That only works if we are talking about the numbers I actually count. What I took Jade to mean when she said "The highest number you can describe" is not the highest number I have or will ever describe in my lifetime, but rather the highest number I could in theory describe (without having to count up to it or whatever). Even if there is a highest number I will have described at the end of my life, it is not necessarily the highest number I could in theory have describe.

    • @chriswarburton4296
      @chriswarburton4296 2 ปีที่แล้ว +1

      @@austinpowers7670 You don't have to count up to it, but you do have to describe it; and that takes time (and symbols, if writing it down).
      > it is not necessarily the highest number I could in theory have describe.
      Yes it is! You say "in theory", but don't say *which* theory. The relevant theory in this case is Algorithmic Information Theory, which says there *is* a highest number you can describe. In fact, Algorithmic Information Theory says there is a highest number that *mathematics* can describe! For example, see risingentropy.com/are-the-busy-beaver-numbers-independent-of-mathematics for a number which is easy to describe (the 7918th BusyBeaver number), but whose actual value is impossible to calculate in ZFC (i.e. the "usual" axioms of mathematics). The same BusyBeaver trick can be used to defeat any system of mathematics :)

    • @esquilax5563
      @esquilax5563 2 ปีที่แล้ว

      Nice catch!
      @Chris, algorithmic information theory isn't invoked in the syllogism Austin is criticising, so it's outside the scope of the conversation. Chris isn't claiming that there is no largest describable number, only that the given statement doesn't prove that there is

  • @roger_isaksson
    @roger_isaksson ปีที่แล้ว

    There is a beauty in describing complex phenomena with few words.

  • @thuongthuong4457
    @thuongthuong4457 ปีที่แล้ว

    Love those stories. Keep it up : D

  • @doctortroels
    @doctortroels 2 ปีที่แล้ว +4

    3:21 Liberryan... I see what you did there.

  • @christosvoskresye
    @christosvoskresye 2 ปีที่แล้ว +22

    Yeah. All of science comes down to running 7zip.
    Or maybe not.

    • @monad_tcp
      @monad_tcp 2 ปีที่แล้ว +4

      Oh, 7zip doesn't do compression that way, it is statistical compression with a rolling window applied on parts of the total stream (and the output, yes, it mixes input and output, that's the cleverness of data-compression in the real world), think of it as a clever Morse code generator, it just does a bit of ordering (Huffman trees) so it takes less bits than before.
      Its basically "cheating", because, of course you want 7zip to finish running before the heat death of the Universe.

  • @ayo94563
    @ayo94563 2 ปีที่แล้ว

    Came back to watch this again. Your videos look so much better by the way

  • @mireazma
    @mireazma ปีที่แล้ว

    I first stumbled on "Why the number 0 was banned for 1500 years" and now I can't stop hopping from one to another through your videos.
    Subscribed.

  • @NoNTr1v1aL
    @NoNTr1v1aL 2 ปีที่แล้ว +4

    I like that her soul is still attached to the chair.

  • @mjlambert210
    @mjlambert210 7 หลายเดือนก่อน

    13:46 . so, the way you helped me to truly comprehend this...thank you for your videos. you and your entire team

  • @RealHypeFox
    @RealHypeFox 2 ปีที่แล้ว +18

    Didn’t expect to see Devin (Legal Eagle) to make an appearance 🤯

    • @fajrulramdhan2005
      @fajrulramdhan2005 2 ปีที่แล้ว +1

      Where tho?

    • @MCLooyverse
      @MCLooyverse 2 ปีที่แล้ว +1

      @@fajrulramdhan2005 In the bit with everyone on a call
      Edit: 8:14

  • @IamKudos
    @IamKudos 2 ปีที่แล้ว

    God i love how Jade makes the banters and hooks, i just love jade in general.

  • @JohnLee-dp8ey
    @JohnLee-dp8ey 2 ปีที่แล้ว

    Another problem I have with the Find Shortest String algorithm (even if ignoring Barry's paradox), is that given a large enough number of bits, it'll eventually run into programs that do not halt, and since in general it's impossible to compute if a program halts (as proven by Alan Turing), it's possible for Find Shortest String to run a program that doesn't halt, and runs forever on that particular number of bits.

  • @estranhokonsta
    @estranhokonsta 2 ปีที่แล้ว +70

    You forgot to mention how this is related to the Russell's paradox and co.
    And here is question. Is the Occam's razor a "truth" that shaves all those truths, and those only, who do not shave themselves?
    And by the way,. all of this comment is a pure lie.

    • @williamtoner8674
      @williamtoner8674 2 ปีที่แล้ว +1

      this is actually a work of genius

    • @ccgamedes33
      @ccgamedes33 2 ปีที่แล้ว +1

      Ah you barber you :)

    • @salev5293
      @salev5293 2 ปีที่แล้ว

      I left two comment for her, check those out, involves Russel too.

    • @trueriver1950
      @trueriver1950 2 ปีที่แล้ว

      There is actually no paradox in the folliwing
      I mention that a certain town has a barber who shaves every man who does not shave himself.
      ...
      Clue: think woke
      ...
      Clearly the town has a lady barber.
      Next attempted paradox please...

    • @salev5293
      @salev5293 2 ปีที่แล้ว

      @@trueriver1950 Actually yes there is no paradox even when the barber is a man. This issue is more serious than you imagine and there is no place making jokes about it. It cost 3 times world war and we are in third one. Principles, value of information, certainty of human difference are replaced with practicality.
      First we see this approach in history with Greek philosopher Parmenides; then the Roman empire followed the same rule with power and cruelty. Russell applied it to knowledge and science by using modern mathematics.
      We are in the same cruelty but the specialty of human difference and solving problems with certainty do not exist anymore.
      Roman Empire was demolished Istanbul with another type of culture difference; now Russell’s modern politics will be demolished from the same type of culture with certainty.

  • @notgad3130
    @notgad3130 2 ปีที่แล้ว +38

    When ya first posted the picture of you shaving, I thought it was a [INSERRT RAZOR BRAND HERE] sponsorship.

    • @upandatom
      @upandatom  2 ปีที่แล้ว +14

      haha how would that sponsorship have come to be?

    • @TarEcthelion
      @TarEcthelion 2 ปีที่แล้ว +4

      I loved the discordance... Explaining simplifying things while a quick unexpected clip raises a bunch questions. O_o

    • @bamgm14
      @bamgm14 2 ปีที่แล้ว +4

      @@upandatom Dollar Shave Club?

  • @wizardoffrobozz
    @wizardoffrobozz ปีที่แล้ว

    Most of it is over my head. But your presentation is so ordered, that i glean something interesting from every video!!

  • @robertsullivan4773
    @robertsullivan4773 ปีที่แล้ว

    I just learned or perhaps been made aware of my biggest numbe 52 factorial. That one will keep me busy for awhile thanks 😊