Berry's Paradox - An Algorithm For Truth

[@EternalDensity]

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

[@ShaLun42]

It's time for Zeno Machine!

[@ryanmccampbell7]

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!

[@fss1704]

Lets not forget von neumann

[@user-yc3fw6vq5n]

Oh

[@charliesmith7169]

Or Church and Turing

[@RobertMilesAI]

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

[@upandatom]

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

[@qqii]

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

[@RobertMilesAI]

​@@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]

@@RobertMilesAI AIXI is the obvious follow up ;)

[@michaelfrankel8082]

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

[@allanlees299]

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."

[@theunintelligentlydesigned4931]

People really need to understand this. We cannot simplify an explanation by throwing out data or variables.

[@higztv1166]

Occam's Razor is uncomputable though?????

[@theunintelligentlydesigned4931]

@@higztv1166 A lot of logic is uncomputable though. Logic is similar to math but it isn't the exact same thing as math.

[@jdwebb42]

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]

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]

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

[@aaaab384]

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

[@hughcaldwell1034]

@@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]

@@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.

[@TIO540S1]

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.

[@user-yc3fw6vq5n]

Wow

[@user-yc3fw6vq5n]

He even gets fashion respect

[@Adraria8]

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]

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-]

@@dwightk.schrute8696 Ahh, the Codegolf paradox lmao

[@chriswarburton4296]

@@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]

@@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]

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

[@peterparker6377]

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

[@MarcSpctr]

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

[@orthocoinbitzantium1002]

Well so do some sociopaths...

[@user-yc3fw6vq5n]

@@orthocoinbitzantium1002 Like politicians . . .

[@JPEaglesandKatz]

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.!

[@kyransoriano3527]

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]

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

[@darshandev1754]

Dude it's math and computer science

[@EpicHobbyist]

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.

[@IndurOutdoor]

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

[@upandatom]

Thank you!!

[@johnbonnett5746]

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]

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 KZbin 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]

Yea she’s smart and cool.

[@Anuchan]

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

[@tdtrecordsmusic]

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

[@frenstcht]

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

[@General12th]

I really like this.

[@frenstcht]

@@General12th:-)

[@ashwinirao8133]

Too good👏

[@vigilantcosmicpenguin8721]

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

[@frenstcht]

@@vigilantcosmicpenguin8721 LOL!

[@annannz9047]

This is my first time watching your videos, and this might be my favorite educational video among thousands of amazing ones I watched on KZbin. 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.

[@BubaMeyer]

I bet that one of the dislikes is from David Hilbert

[@vigilantcosmicpenguin8721]

At least Godel and Turing liked it.

[@crhu319]

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

[@filiplaubert5001]

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

[@jacobpeters5458]

@@vigilantcosmicpenguin8721 also Tarski !

[@ernestestrada2461]

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!

[@Cat-gameur]

the shortest value that contain infinite information is 0 . eg. 0=mc^2-E can be created back to E=mc^2 , it will contain both true and false statement

[@m00t]

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]

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

[@Daniel-ih4zh]

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

[@Nnm26]

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.

[@blackshard641]

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

[@vigilantcosmicpenguin8721]

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

[@naderchmait5543]

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 :)

[@user-yc3fw6vq5n]

Yay^^

[@user-yc3fw6vq5n]

She even gives him fashion respect!

[@rentristandelacruz]

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

[@blackshard641]

Kurt Godel: told you so

[@KitagumaIgen]

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

[@DJ_Force]

The first problem with Find Shortest String is the Halting Problem. No way to compute if the program bring tested will ever stop and give an answer.

[@anujarora0]

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]

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

[@thedeemon]

still can't hurt you

[@FromTheNard]

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.

[@domainofscience]

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

[@vasudevraghav2109]

Hello there

[@shreddedtwopack6625]

Hello there

[@upandatom]

Thanks Dom :)

[@cedricvillani8502]

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

[@leif1075]

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

[@Cau_No]

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).

[@RequiosWoW]

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!!

[@thomaskist9503]

Efficiency and realistic computability can always be problems with very abstract math. Machine learning has an efficient algorithm for computing something like this it’s called and encoder decoder. The encoder, in a sense, creates the program and the decoder runs it. The real problem to make this general is the have a language that describes every possible encoder decoder architecture.

[@RealHypeFox]

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

[@upandatom]

hehe good morning :)

[@lunarpassion]

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

[@Jivvi]

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.

[@denkenunddanken5961]

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

[@eproulx]

Another way to get out of this hypothetical all-knowing computer system is you could imagine a short computer program that produces truly random output. If you run this program enough times it will produce every conceivable output. Thus randomness can be an algorithm for truth.

[@MegaNancyLover]

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

[@upandatom]

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

[@rollomaughfling380]

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

[@MedlifeCrisis]

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

[@MedlifeCrisis]

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

[@christopherellis2663]

For surgery, I suppose.

[@upandatom]

Thanks Rohin :)

[@peterpandaluki6663]

Maybe try a new blade?

[@based8223]

Cringe

[@olivierdeme3886]

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 KZbin gem.

[@upandatom]

Thank you so much :)

[@wlritchi]

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

[@SachinChauhan-ch6el]

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.

[@dogpadogpa]

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

[@johnnydubya8071]

Her enthusiasm for math is infectious and with such beauty and chram

[@geoffsecombe]

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

[@upandatom]

never ;)

[@TarEcthelion]

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

[@Rudxain]

This is the main reason why compression algorithms must do tradeoffs, because they can only approximate the output of find_shortest_string. This is also similar to the reason why compilers can only partially solve the halting problem, usually by doing Control-Flow-Graph analysis

[@cyto3338]

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

[@whythosenames]

infinite

[@metamorphiczeolite]

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

[@estranhokonsta]

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]

this is actually a work of genius

[@ccgamedes33]

Ah you barber you :)

[@salev5293]

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

[@trueriver1950]

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]

@@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.

[@thattimestampguy]

0:31 Biggest Number 1:07 1:23 Biggest Number you can describe? 2:27 Google Digits Long 3:11 Word Play 3:50 Ray Solomonoff seeks an Algorithim for Truth 4:41 Patterns 5:51 1 Algorithm 6:07 How? Scientific Method Ockham’s Razor Inductive Reasoning 7:10 How do I compare the complexity of different things? 7:45 Information- The Resolution of Uncertainty 8:52 Which is easier to describe? 10:04 Less Uncertainty = More Simple 10:44 Linking So Many Subjects into A Kogmotorov Complexity 11:48 FindShortestString 12:52 Give Us The Formula, The Rule which generates the data ‘13:36 14:06 150 -> A Contradiction 15:48 It’s Proven To Be Impossible 16:52 Internet Security ExpressVPN

[@christosvoskresye]

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

[@monad_tcp]

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.

[@mireazma]

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.

[@dangerkeith3000]

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

[@rollomaughfling380]

That statement is universally true.

[@Bluedragon2513]

I think it's like a a formation of words. While you can make a sentence out of words like "Everything I say and do makes sense," you can also make a nonsensical sentence with the same words "Do say I everything sense makes." In this way, trying to restrict a problem to be under a certain amount of characters is nonsensical. I also realize that I'm still having a hard time formulating this thought

[@austinpowers7670]

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]

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]

@@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]

@@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]

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

[@codenamelambda]

I was (in my head) essentially *screaming* "halting problem" shortly after 12:00. But that led me to another thing: The halting problem *is* solvable under some constraints: Specifically, you can simulate a finite state machine without inputs until it loops or halts; and a Turing machine with a finite tape is just a finite state machine with no inputs while running again. So in the worlds of computers, "all you need" is enough memory to detect loops, which funnily enough only requires double the amount of memory (plus some constant offset for the cost of simulation itself), not counting the description of the simulated machine - if all we need is the algorithm to terminate, we only have to run the FSM for as many steps as it has states; since if it's still running after, it has to have visited a state more than once, which, since it doesn't get any input besides the initial state, would mean it got into an infinite loop. So now I'm wondering: *Could* you define such a complexity not just by program size, but also memory and/or computation time size? That seems as though it ought to be computable, though still not computationally feasible. Or did I make a mistake somewhere in my logic?

[@АлександрКубанцев-я6л]

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

[@swagatochatterjee7104]

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]

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]

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]

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]

@@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: kzbin.info/www/bejne/fn2adXihjbuSbJI 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!

[@josiah42]

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!

[@TomVargheseKonikkara]

If you are doing this alone, then I'm so excited about you. Because, the hard work you have done to present each second of the video should be much appreciated. I know the pain, since you write a script to frame and to record and edit and publish... Everything alone. Appreciated

[@JohnLee-dp8ey]

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.

[@peNdantry]

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]

I love it!

[@peNdantry]

@@djpete2009 Thanks :)

[@momom6197]

This is great. ^-^

[@peNdantry]

@@momom6197 Thank you for that :)

[@additionaddict5524]

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

[@visheshl]

Me: 1

[@burkhardstackelberg1203]

Berry's paradox looks very much like the halting problem - indeed it might happen that one of the tested programs to describe the number you look for has an indefinite time to run, i.e. you can neither prove it run forever nor will you ever see it stop.

[@thetungwakou]

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

[@robbedemey]

The Kolmogorov complexity is not a feature of the string, it is a feature of the string and a set of given operators. It's the complexity of an object in the context of a set of given operators.

[@huzaifaimran9468]

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!

[@denielalain5701]

Hi! - Can you take a picture of anything in an infinite resolution? Like every single atom in one go, and more? - It would produce countless contradictions. (15:29) - You must find a suitable resolution first.

[@arkapravamanna]

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

[@upandatom]

Thank you, glad you liked it!

[@ayo94563]

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

[@RealHypeFox]

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

[@fajrulramdhan2005]

Where tho?

[@MCLooyverse]

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

[@KeltorRochridge]

I don’t think the use of concise language necessarily denotes greater certainty. For every huge complex concept we can envision, we can always make up a single word to encapsulate it. Each word is an encapsulation of an idea that is built on other encapsulations of ideas. It’s possible that it’s actually the most simple and common words that hold the most information.

[@adityaanantharaman7963]

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

[@upandatom]

thank you I appreciate that :)

[@john-or9cf]

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

[@codenamelambda]

This also reminds me of a very weird fact about real numbers: There's an uncountably infinite number of real numbers. But *descriptions* of numbers *are* countable (since text is, mathematical notation is, etc) - which means that there's an uncountably infinite number of real numbers that *cannot* be described.

[@whythosenames]

true I never thought about that, underrated comment

[@whythosenames]

but also somewhat plausible if you think about that, because nearly all real numbers you cannot write down in decimal form. But on the other hand, the ones you can write down are just a subset of the describable ones, for example pi. So mind blowing nevertheless

[@KingoftheJuice18]

It's impossible for any algorithm to calculate how much of this channel's success is due to Jade's scientific understanding and how much is due to Jade's personal charm.

[@patientlydormantinpassion]

Nerdy hot girl. It's probably not couth to let her know that the inverse of neckline equals a greater responsiveness of watched videos.

[@Mspad91939]

I love how technical yet newbie friendly this channel is

[@whythosenames]

The halting problem might be related to that, because at some point the programs will lead to endless loops, and since you can express an endless loop in

[@sneakyfred]

"you can't describe all numbers" "there exists at least one number you can't describe" =/=> "there is a maximal number you can describe" The numbers I can describe could easily form a growing sequence. The paradox doesn't arise because there's a maximal number you can describe. It arises from the second statement above combined with the fact that a non-empty subset of the natural numbers has a least element. (This is also called the well-ordering principle.)

[@PaulPaulPaulson]

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]

All I know is that it's an acid.

[@Fists91]

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]

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]

Now I'm curious too!

[@kellwillsen]

Logical break at 2:59. "As you can't describe all numbers, it logically follows that there must be a biggest number you can describe." No. These "indescribable numbers" are not a problem because of their size, but because of their irregularity. They will therefore be scattered throughout the numberline, not all grouped together past the "biggest describable number" barrier.

[@totallynotgad]

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

[@upandatom]

haha how would that sponsorship have come to be?

[@TarEcthelion]

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

[@bamgm14]

@@upandatom Dollar Shave Club?

[@bunnybro5977]

The rock paper scissors site is interesting in its simplicity. According to the people behind it, it just sees what you're most likely to pick based on your favourite play. Basically like rolling a weighted three sided die with the weight decided by your frequency

[@NoNTr1v1aL]

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

[@havenbastion]

Quantity is recursive boundary conditions. There is no largest number because there is no specific place where that happens. When you run out of energy to keep counting, that's when you've reached the largest number for you. Quantification is the process of recognizing delineated things as distinct from each other in the same relevant way which does not alter within the scope of it's use case.

[@marcoponts8942]

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

[@upandatom]

displate.com

[@mjlambert210]

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

[@HuntingCatIsBack]

Dissapointed that she made the "Decision" not to mention Gödel and "Halted" before invoking Turing. Then did a "number" on Chaitin, with a mention but no explanation. Otherwise a tantalizing introduction.

[@ruferd]

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

[@benurm2390]

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

[@ruferd]

@@benurm2390 yes, that was the joke.

[@vigilantcosmicpenguin8721]

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

[@neilgrundy]

I struggled to understand Steven Wolfram's explanation of this. Your explanation is very easy to follow.

[@grfn3135]

That run of 6 nines gave pi away!

[@matthiasmair8799]

This was also the moment, when I realised it: wait, you know only one "random" number with this sequence.😀 As I testet then to spell the digits as I Iearned them, I knew I was right. It's for a long time that I could use more than 5 digits of Pi.👍

[@szboid]

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

[@reubenstewart7995]

This is really interesting, but I can't seem to find any rational explanation for why the simplest solution is the best one. There could be infinite solutions to a problem why does the simplest one have to be true. I've come across Occam's Razor in my philosophy class and I'm just curious what the justification for it is.

[@hughcaldwell1034]

It's not a hard and fast rule, more of a guideline, but to suggest something of an answer, it basically boils down to not making unnecessary assumptions. For example, we ditched the Earth-centric model of the universe because we had to start making all sorts of weird assumptions and edge-cases for other planets, their moons, asteroids, etc. with no explanation of why they behaved the way they did beyond "because they do" or "because god said so". Seeing as how we already need a theory of gravity to explain things falling to the ground, it is more likely that gravity exists plus zero other assumptions than that gravity exists plus a bunch of assumptions.

[@darrylcloud7111]

Occam's Razor was only formulated to stop intellectuals from going insane. Apart from that, it makes no sense, like you suspected. Let's prove your conjecture: Since chaos is only an illusion, created by our lack of understanding, the more apparently chaotic a system, the more humiliating it is. So, unless we limit our quest to understand complex system, we will eventually reach the limit of our ability to comprehend them. And, because finding meaning, to apparently chaotic systems, is only motivated by our egos, after we reach the limit of our ability to comprehend complex system, we will injure our egos, to destroy the motivation for our quest. Then, once our brains collapse into hopelessness, they begin rebuilding our egos, on a new foundation, starting with the simplest problems, before ascending Jacob's ladder once more. Then, once this ego-driven spark blows off the top, it must start at the bottom again. If you reach this state, then you have gone insane, unless you apply Occam's Razor, to retain your sanity.

[@copernicus99]

Bayesian model selection is one way to give it some mathematical teeth. en.wikipedia.org/wiki/Occam%27s_razor

[@HeyHeyHarmonicaLuke]

2:58 "As you can't describe all numbers, it logically follows that there must be a biggest number you can describe." - I disagree, imagine that it were impossible for us to describe every hundredth number. We could still describe an infinity of numbers, going up forever.

[@doctortroels]

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

[@upandatom]

:D

[@stevengeorges9046]

The largest number without any pattern is, "Steve's number" π, without a decimal point.

[@landspide]

Good to see there are limits to human capability, now prove that there aren't ;)

[@ILsupereroe67]

3:04 "as you can't describe all numbers it logically follow that there must be a biggest number that you can describe" - no it doesn't logically follow. Unless you assume that any number bigger than a number that cannot be described, cannot be described either.

[@scientious]

"Where philosophy can ask the questions -- mathematics can answer." The reality falls so vastly short of the claim. Philosophers ask nonsense questions all the time. This isn't a real paradox.

[@DumblyDorr]

Personally, I like to go with what has been the understanding of "philosophy" since the ancient greeks at least - as all rational, methodological attempts to achieve verisimiltude in one's hypotheses about the world, as opposed to primarily narrative accounts of the world which fulfill socio-political functions. It is in this sense that Aristotle, Newton, Leibniz, Frege, Whitehead, Russell et al understood themselves as philosophers... and in that sense (also seeing how formal logic is a philosophical discipline), this kind of applied mathematics *is* philosophy. In fact - when you look towards the bleeding edge of mathematics: Homotopy Type Theory, infinity-Groupoid theory, Topos Theory ... there's lots of engagement between philosophers/logicians, computer scientists and mathematicians all developing theories about/with these notions. It's pretty awesome stuff - and certainly shows that it is false to think of science and philosophy as clearly separate things. They are neither for the general term (where philosophy encompasses all rational endeavours to understand and model the world) - nor for the specific academic field, since there is so much overlap and interrdisciplinary research with basically all natural sciences and with mathematics.

[@scientious]

@@DumblyDorr > shows that it is false to think of science and philosophy as clearly separate things. That is the common claim from philosophers, based I assume on feelings of insecurity. However, it false. To the extent that philosophy creeps into science (and I see it a lot in my field), it is clearly to the detriment of science. Philosophy has its place; it is very good at finding flaws in logical reasoning.

[@DumblyDorr]

​@@scientious Nah - not based on feelings - on logical analysis, historical genesis and actual experience. ...If you want to do more than guess - I'd recommend reading some Timothy Williamson on knowlegde and evidence - the methods of analytic philosophy are not disjoint from those of science. But... of course, such things cannot be judged ... you know... without studying epistemology. And - you can't do science without epistemology and metaphysics... you can just do it badly, naively - simply using epistemic and metaphysical assumptions and taking them for granted, or based on non-methodological reflection without the required rigor. Of course, there's lots of valuable "normal science" to do where there's really no need to reflect too much on fundamentals because the research is not at the boundaries where it matters that much - though you still need good understanding of epistemic boundaries of your results, which is really not easy - and often goes wrong. It's also good to note that scientists like Einstein, Planck, Heisenberg etc also were well aware of the importance of taking epistemology and metaphysics seriously - it pays to look into the history of both positivism and the vienna circle - and the cross-influence with the natural sciences as they were practiced in those times, e.g. through both personal and subject-related connections - e.g. - Carnap - Schlick - Whitehead - Russell - Einstein - Popper - Feyerabendt - Weyl - Reichenbach - Noether - von Neumann - Martin-Löf - Hilary Putnam - Patrick Suppes etc (bridging the gap from physics to mathematics and computer science in the end there). Today - every undergrad physicist will (usually confidently) speak of falsification... clearly useful stuff... and showing that Popper's thinking has made its way into a lot of science... of course, before that, it was Carnap's positivism that was en vogue in the physical sciences... but there's also been 80 years of philosophy of science since then, which is just as relevant as the stuff Popper, Kuhn and Feyerabend debated - and builds upon that. At least in one sense, It also doesn't "creep in" - it never left - there is a lot of extremely fruitful interdisciplinary research e.g. in cognitive science, evolutionary anthropology, evolutionary cognitive ethology, theoretical evolutionary biology, computer sicence (since... you know... logic is a philosophical discipline), fundamental physics, and mathematics (HoTT/UV etc). see e.g. UCSD, UCLA, NYU, Rutgers, Oxford, Cambridge, Munich etc. As you said - philosophy is good at logical analysis... and the higher theoretical issues in most sciences (which no longer belong to the object level) require that - so why should it be detrimental? All that interdisciplinary research (which has happened since forever, and has - e.g. vastly developed the theoretical account of ecological fitness, extended phenotypes and multi-level inheritance in theoretical evolutionary biology, or the epistemics and ontology of various theories of quantum mechanics - including MWI, QBism, Consistent Histories etc - a good deal of the bayesian analysis of MWI was done by philosophers of physics for example)... shows that it's clearly not in general to the detrminent of science There's no reason for analytical philosophy to feel insecure - it was essential in the linguistic turn (Frege, Wittgenstein) - and the cognitive turn in the 60s... also it developed e.g. logic, set theory and model theory to the point where they served and serve as the foundation for computer science and all of mathematics - and now is again instrumental in developing logics and formal semantics based e.g. on Topos-theory and HoTT in the growing structuralist trend in mathematics/computer science. The reason you can trace back the sciences to philosophy is that they become academically distinct when the philosophizing has become fruitful enough to develop a whole own toolset of reasoning, methodology, notation, formalism. That's how modern physics emerged from the natural philosophy of Descartes, Newton, Leibniz et al. That's how computer science emerged by way of formal logic - how the cognitive sciences emerged by way of the logical and linguistic turn. There is no field of science where - as mentioned - top-tier unis don't do revelant interdisplinary research with analytical philosophy... (of course, there's *bad philospohy* just as there is *bad science* - but that's just something that is bound to occur when many different people do something). Overall - good time to do philosohy of science - both as for scientists and philosophers.

[@scientious]

@@DumblyDorr Let's see: > the methods of analytic philosophy are not disjoint from those of science That claim is contradicted by the relationship between analytic philosophy and dualism. You can't be a dualist and claim to also follow science or rational thought. > without studying epistemology. I guess I could study palm reading while I'm at it. I did disproofs of epistemology some time ago. That hasn't changed. > you can't do science without epistemology and metaphysics I think what you meant to say was that you personally can't comprehend a way that someone could do it and therefore you assume that no one else could. Argument from ignorance fallacy. > simply using epistemic and metaphysical assumptions and taking them for granted, or based on non-methodological reflection without the required rigor. No. I needed something foundational back in 2016, but philosophy didn't have it. The philosophical definition of knowledge was particularly laughable. I had to start from scratch. > because the research is not at the boundaries where it matters that much I've been doing that since 2015. > there is a lot of extremely fruitful interdisciplinary research e.g. in cognitive science, evolutionary anthropology, evolutionary cognitive ethology, theoretical evolutionary biology, computer science You are describing a lot of what I work on. There's computer science, cognitive theory, cognitive evolutionary theory, animal behavior, information theory, abstract information theory, consciousness theory, and artificial general intelligence theory. > logic is a philosophical discipline True, but logical philosophy is a subset of science. I don't think the whole of philosophy is a subset but the useful parts tend to be. > As you said - philosophy is good at logical analysis... and the higher theoretical issues in most sciences require that - so why should it be detrimental? It isn't. Intuitive arguments are since they are almost always wrong and never useful. And as you should be aware, philosophers love intuitive arguments. > There's no reason for analytical philosophy to feel insecure Not yet, but it won't be too long.

[@DumblyDorr]

@@scientious I'm sorry... but your very first argument just shows you really don't know how this works... you're making metaphysical and epistemological "arguments" ... or rather, you claim epistemic and metaphysical points you're just taking for granted... That's not how any of this works. Also- that very first argument is not just a) a mere claim and b) betraying a very shallow to nonexistent understanding of the subject ... it's also a complete non-sequitur. It just doesn't follow. A specific family of accounts of something being incompatible with current understanding says just nothing about general methodology - or else chemistry is incompatible with science and its methods incongruent because there was a time when it advocated for a phlogiston theory - or physics and the luminiferous aether. (Also - it's much more complicated for various flavors of what is usually called dualism. Substance dualism- what you're thinking about- has, like the phlogiston theory, been dead since pretty much the late 1800s ... property dualism/pluralism e.g. has no such issues) Again - to judge the methodological issue requires a deep look and logical analysis of concepts like evidence and knowledge - which e.g. Timothy Williamson does provide... and is well worth studying.... but it's hard work and takes a lot of effort. But I'm glad you can just confidently make broad claims without even engaging with what you're making claims about... What you're doing, ironically, is like people claiming to be able to tell that QM/GR must be bullshit because it contradicts their preconceived notions without actually doing physics or looking at the maths. It's what I was saying - you can't *not* do philosophy. Judging such issues, you can just either do it badly/naively - or do it right by applying the necessary rigor. And you could do that - maybe you can even find actual arguments making a really strong case for your position ... in which case I'd be excited and open to being convinced...but it first requires actually doing the legwork... which starts by admitting that you don't yet know what you're talking about... and by wanting to learn instead of just dismissing. I know that when I want to make judgements on issues of physics... it would be ludicrous to think I'm competent without studying physics... same thing for epistemology and metaphysics... just that people are much more aware of their lack of understanding of physics... while hardly anyone considers their (lack of) competence in epistemology and metaphysics. People are just intuitively convinced their informal conclusions must be right. Sorry, this isn't worth anyone's time anymore

[@trevorgwelch7412]

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

[@loturzelrestaurant]

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 KZbinr bringts Attention to Homelessness and various other Issues. Unbiased and informed, his Talks about 'Obvious Solutions to Obvious Problems' are a Masterpiece.

[@St0RM33]

omg get to the fucking point already

[@magicmulder]

3:05 "As you can't describe all numbers, it follows logically there must be a highest number you can describe" Not necessarily as taking away even an infinite subset of an infinite set may still leave an infinite rest. To me the largest number I can still somehow comprehend is 3 "3 up arrows" 3 in the construction of Graham's number. It has about 150 billion digits so its written representation would extend from Earth to the sun.

[@jonathanreal8018]

The halting problem might be the easiest issue with the 'find shortest string' program to explain. The fact that the find shortest string program might be shorter than its output isn't a good contradiction. Because the shorter 'find shortest string' program would have been in the search space... which might be a nice place to introduce the smn theorem.

[@thedagit]

It's also worth noting that there are only countably many of these strings. Each string is a finite length generated from a finite alphabet, and therefore the set of all such strings is countable. However, some mathematical sets have uncountably many elements. Even if FindShortestString worked as intended, it wouldn't work for all real numbers. There's simply too many of them.

[@alanbunyan5007]

It seems to me that there are two fundamental flaws with Solmonoff's quest (despite its "accidental" techniological benefits), only one of which was identified in the video. The other is that Occam's razor is simply an assumption. Since it is impossible to prove that the simplest explanation is always the correct one (we may find it usually to be so, but that, needless to say, does not constitute a sound, scientific proof), the notion that calculating the inherent complexity of a theory is a way to prove/disprove its truth value is groundless to begin with!

[@marcelinogalicia7612]

The biggest number is (O) because that's where it begins, and that's where it ends.

[@Meckmester]

I must be misunderstanding, if a googol is 1 followed by 100 zeros, wouldn't a number with a googol digits long just be say 7 followed by 100 random numbers between 0 and 9? Which can fit easily on a post-it note, not reach the most distant visible star, right?