Numbers and Free Will - Numberphile

Artificial Intelligence gets Professor Edward Frenkel thinking about vectors and numbers --- and the nature of human existence!?
More links & stuff in full description below ↓↓↓
Extra interview footage: • Numbers and Free Will ...
More Numberphile videos with Prof Frenkel: bit.ly/Frenkel_Playlist
Prof Frenkel is the author of Love & Math... amzn.to/1g6XP6j
Prof Frenkel's website: bit.ly/EdwardFrenkel
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[@jacobj7608]

Whenever I see a video about free will, I have no choice but to watch it

[@madhuragrawal6897]

clever.

[@NomadUrpagi]

Underrated

[@DisfigurmentOfUs]

Nice one :)

[@yeet3673]

Lol.. another numberphile vid with this dude has a most-popular-comment that refers to "Russian Jamie Lannister" .. lol

[@lucky_lol]

Nice one

[@GravyBrainz]

this dude is a beast with analogies

[@y__h]

He reminds me a lot to Feynman

[@Raiment57]

Really!? Feynman would never have been so foolish as to lecture people about subjects he didn't understand. Even the maths in this was a bit sloppy and the rest was gibberish.

[@ractheworld]

USSR mathematicians were known for their intuitive approach to mathematics as opposed to say the French mathematicians whose approach is a lot more rigid and involves building on rigorous bases

[@FandangoJepZ]

GravyBrainz dis how we du in Russia

[@alvinlepik5265]

@@ractheworld Viva la Bourbaki :D

[@jakeandorbake9842]

"so look at this brown paper" yeah we've all been looking at it since the dawn of numberphile

[@CarterColeisInfamous]

You need to do a video on what's on the board behind him

[@naydennaydev7071]

This is for the Physicsphile channel :)

[@philippepoulin7842]

The board is about matrix (yes, really).

[@EugeneKhutoryansky]

The issue is not whether a vector is just a series of numbers, but whether everything about the vector can be represented by just a series of numbers. Therefore, the analogous question is whether everything about a human being, including our own consciousness, can be represented by a series of numbers.

[@XianStannard]

Agreed. If the representation of an entity is sufficiently complete using only numbers then a computer can model the entity in such a way that the model is indistinguishable from that entity. This seems to be the case with vectors. If we cannot distinguish between an entity that has free will and a complete model of that entity, does that mean that the model has free will?

[@IcepickL]

+Xian Stannard No. A flawless forgery of the Mona Lisa is not the Mona Lisa. It appears to be, and presents the same experience, but it is not fundamentally the same.

[@NoahTopper]

+Eugene Khutoryansky Pretty much exactly what I was going to say, although you might have been more eloquent.

[@NNOTM]

+Icepick L If every atom is the same, is it the same then?

[@dfghj241]

+Eugene Khutoryansky i don't understand how consciousness (with all the glorification this word usually gets from people that know nothing about biology whatsoever) would not be able to be represented by numbers.

[@mattlm64]

So are you telling me I can dodge bullets?

[@inigop.d.1270]

No. I'm telling you you won't need to.

[@darksider63]

+Matthew Mitchell No. When you're ready... you won't have to.

[@xevira]

+Iñigo P.D. Whoa

[@Menaceblue3]

you think that's air you're breathing?

[@darksider63]

+Menaceblue3 I just farted so I know it's not

[@SillyIdea]

Fifteen minutes and he's given me an entirely new way to think about mathematics....incredible. I hope you get more of him.

[@Smogshaik]

Languages are like coordinate systems for meaning

[@Smogshaik]

Thanks! I simply realized that the attributes Edward was giving to coordinate systems are very much what I learned about languages when studying Linguistics. I think that a comparison between coordinate systems etc and natural languages could be a really interesting topic.

[@nashton9964]

I suppose infinity in that regard would be the max possible number of differentiable mouth sounds in an infinite series of combinations. though, I suppose at some point the biological tissue required to compress the symbolic abstractions that language provides into the real substance of reality.

[@samvargas2868]

@showerthoughts

[@Gew219]

Thecrashthrash Yes. And the object you name ecist before that name itself, just like vectors exist before the asigned coordinates.

[@davecrupel2817]

This must go on a plaq!

[@boumbh]

This is not a comment, this is a string representation.

[@JBinero]

An string representation is what represents a string. For example "Test" is the C string representation for Test. What you posted isn't a string representation, it doesn't represent a string. It *is* a string.

[@D12golden]

+boumbh //This is a comment

[@piticea]

+Jeroen Bollen yes, but what he saw and what we see is the string representation (i think thats what he wanted to say ^^)

[@mv2112mv]

+Jeroen Bollen Technically it isn't a string either. It just looks like one because you're viewing it in reference to your computer screen. It's actually just a complex arrangement of electrons in our computers. From the point of view of your computer screen, it looks like "This is not a comment, this is a string representation.". From the point of view of your CPU, it probably looks like a sequence of electric pulses arranged in this order: 010101000110100001101001011100110010000001101001011100110010000001101110011011110111010000100000011000010010000001100011011011110110110101101101011001010110111001110100001011000010000001110100011010000110100101110011001000000110100101110011001000000110000100100000011100110111010001110010011010010110111001100111001000000111001001100101011100000111001001100101011100110110010101101110011101000110000101110100011010010110111101101110.

[@TheBluMeeny]

+D12golden I C what you did there. (underscore c)

[@VJsubstanceJ]

What I took away from this is that the expression "the human mind is just a series of numbers" is incorrect. What we should say is "the human mind can be represented by a series of numbers". But the same thing applies to computer programming. A software is not a string of bits, it is represented by a string of bits, describing the tasks we want to execute.

[@justanormalyoutubeuser3868]

If the mind could be represented by an array of numbers than it would be isomorphic to it and therefore mathematically equivalent. Whether there are many possible isomorphisms doesn't change anything.

[@witzar]

Is light a particle or a wave? Could this question have as much sense as asking whether the mug is a disk or a rectangle? Perhaps particles and waves are merely those specific projections that are available to our limited perception while the true nature (of light) stays beyond our sight? This analogy can be easily stretched onto other physical entities.

[@sadatnafis2032]

This is exactly what I think about the wave particle duality, maybe they are a third thing that can have properties of both a particle and wave.

[@jamesfullwood7788]

@@sadatnafis2032 Professor Frenkel actually used this same analogy when discussing particle wave duality on the Lex Friedman podcast...

[@sadatnafis2032]

@@jamesfullwood7788 Its always delightful to hear that an expert had the same idea that I, a layman thought of as well.

[@jamesfullwood7788]

@@sadatnafis2032 indeed!

[@ProFoxMike]

YES, YES, YES ! Finally Prof. Frenkel, I've been waiting for this. I hope you've made more than just one video with him. Love this guy.

[@jaredgarbo3679]

I'm a 18 year old straight guy and I find this guy super attractive.

[@MarshmallowRadiation]

+Jonathan Duffield There's a term for that. It's called "bisexual"

[@chairwood]

+Jonathan Duffield same

[@MEATLOAF2able]

+Noah Fence Attractive does not mean the same thing as sexually attractive. I find non human things, such as images, sounds, actual places etc. to be attractive. In the same sense, someone can find a human attractive without implying sexual intent or desire.

[@MarshmallowRadiation]

MEATLOAF2 I know that. But you have to admit sexual attraction was definitely implied in this context.

[@Ryan-lx8gi]

+Ryan Carlisle the point was I, just as jonathan had implied to have., had the passing thought of this person is attractive. I believe also the phrase "all things considered" would apply here for myself. Although, I could have been more clear at first; I only find the superficial attractiveness of males in 'the recognizing way.' To be fair, I think you were the first to bring up anything remotely sexual. Anything could be argued about what dude meant however, I suppose.

[@Ridabu]

The vector is just sitting there, enjoying its life!! Obviously. Haha, pure gold. I like this guy.

[@renecabrera3515]

Edward has a vast intuition and is a monster in coming up with vivid analogies!

[@stumbling]

I was thinking to myself, "this is exactly how I feel about the whole 'wave/particle duality' thing", and then I noticed the whiteboard… xD

[@Dagrond]

Love how great scientists and such can move from detailed abstracts to macro abstractions to put it in perspective. In the same sentence most of the time.

[@SlingerDomb]

Prof. Edward is just so amazing at discussing stuff like this I can’t explain it exactly but I’m so happy right now.

[@MarshmallowRadiation]

But the human brain itself works through abstraction and imposing its own logic onto the world in the first place. For example, colors. Color does not exist in real life, in real life there is only different combinations of different frequencies of light, and everything you see is simply your brain's interpretation of that. Saying that a computer cannot function like a human brain because it works through abstract numbers is like saying that a human brain can't enjoy a book because the book isn't actually happening in front of you, or that watching a movie isn't satisfying because all it is is patterns of light flickering at dozens of times a second. Numbers are simply a computer's way of understanding the world, just like how neuron pulses and chemical releases are ours. We are already abstract, just in a different way than computers. It's the goal of AI research to cross that gap.

[@MarshmallowRadiation]

Daniel Sparer​​​​​​​ I see what you're saying, but what you're describing--machine learning, self-correction, and adjustment to new information--is already being done in AI fields. Emergent behavior in AI machine learning algorithms is well documented, and I have no doubt that a fast enough computer could bring a rocket plane to orbit if given a learning algorithm and the conditions for success. [And to be fair, if you stuck a human pilot only trained for atmospheric flight in the cockpit of a rocket plane and told them to go to orbit they'd probably panic and crash anyway, so I'm not sure why you chose that example out of the myriad others that would have made more sense.] And the example of a machine being unable to make a coordinate system without preset rules is a misleading one, too, because the truth is you can't either. Everything you do is spacially oriented according to your body (left-right, up-down, forward-backward), and all imagined coordinate systems in real space are mere translations, rotations, mirrors, and skews of the one you instinctively make in your mind. You're not computing the distance in digital numbers down to the nearest decimal place, but you do think of things in terms of direction and distance to yourself. There's just no other way to do it. I don't believe that there really is any obstacle to humanlike self-awareness, "free will," or "sentience" in AI because I don't think that "free will" it truly exists in humans, either; at least not the romanticized notion that we are somehow the Great Deciders of the universe. Many, MANY studied have come up with strong evidence suggesting that our own actions arise unconsciously, and our conscious minds merely filter out the possibilities based on our experiences, imagined outcomes, instinctive aversions or preferences, and societal upbringing. Our decisions all come from somewhere quantifiable, and while it is currently too complex to model perfectly [it is, mathematically, a chaotic state], it is not impossible to replicate. Will AI ever function exactly like a human? No, of course not. But that's because humans are functional messes of instincts and associations kluged together over millions of years of evolution. We're way too complex for our own good, and our own sapience is just a recent layer on top of a giant pile of atavisms that we've only just begun to scratch the surface of. But of course, not all of that is good. We do things like judge on appearance, think in illogical and often dangerous associations, and fly into mass hysteria over things we only realize in retrospect are extremely stupid. I'm not saying AI is inherently superior because it doesn't do that, if course, but the study of AI can, does, and will continue to teach us more about ourselves as thinking beings as we discover more about just what it takes to build what we call "sentience," even if the only way we can is by abstracting it into number.

[@alfredrodenboog6693]

+Daniel Sparer I don't think Dr. Frenkel is discrediting AI, or implying that AI will never achieve the levels of complexity and plasticity of the human brain. I believe his argument was that even if we could create an AI that would be comparable to the functions of the human brain, that does not prove that our brain is merely an algorithm (which the AI clearly is). Just because an algorithm can do all the things our brain does (from a functional perspective) does not mean that our brain works like an algorithm. That is the vector analogy he uses, just because we can measure a vector, express it in numbers, calculate with it, does not mean that our numerical 'simulation' of this vector is the vector. The vector is a different thing all together. So is an AI that can simulate all the functionalities of the human brain merely a simulation, the brain itself is described by it, but it is a different entity all together. Also, AI might be a lot more intelligent than you think, self learning algorithms are perfected so that AI can teach itself to walk for instance. It does this on a trial and error basis (falling is bad, moving forward is good) and it can teach itself in a simulation for millions of iterations to fix its own walking algorithm so that it can eventually walk in real life, with nothing really programmed by humans except for the learning algorithm.

[@___________2204]

+Noah Fence But you see, you said it yourself. Colors do not exist but these _frequencies of light_ exist and according to our eyes we see them as colors, but these waves and frequencies do exist. They just translate into something simpler, or different.

[@MarshmallowRadiation]

The Vidlets Yes, I did, but I don't really understand what you're trying to say here.

[@dannygjk]

+Noah Fence Exactly.

[@speed488]

Philosophy and math... Even though they seem far apart, this man bridges the gap very well. From an engineering stand point, maths are VERY philosophical. It took me a lot of time to disjoint "application/usefulness" from the numbers/equations your play with (the representation). Results do not need to have an application in pure maths; they are simply a result. Frenkel pushes this a step further goes into the essence of these numbers. Great video!

[@martinskanal]

I love the fact that he drinks coffee from promo cup for the night club Amnesia on Ibiza. I think this alone somehow is a strong argument that machines will never take over this world.

[@PerihelionPhase]

What a legend

[@ProjSHiNKiROU]

In high school, I learned how to write computer simulations from "The Nature of Code", and that made learning calculus and linear algebra harder because I couldn't think in terms of abstractions: I needed to think everything in terms of coordinates (because that's what computer programs process), until I unlearned these computer representation stuff. I wish this video existed at that time.

[@TheSusej54]

I love this professor, always so interesting and enjoyable :)

[@MumboJ]

The map is not the territory. The recipe is not the meal. The rules are not the game. - Matt Colville

[@lukaskrause6022]

MumboJ the map has replaced the territory: everywhere there exists merely fragments of the real

[@caster-]

Did not expect a Colville quote here

[@MrTheNaboo]

I recently bought "Love and Math" and it is truly amazing to learn something about different fields of "pure" mathematics. It also improved my English due to all the proper math terminology. Thanks Prof. Frenkel!

[@MoronicChunk1]

this is a very interesting video but it isn't necessarily an argument for the existence of free will as it doesn't really serve to disprove cause and effect. for instance the two vectors will add together to form the same vector regardless of the coordinate system you choose to apply to it. even if they are abstract entities that exist independent of the realm of numbers they still appear to be governed by cause and effect. even if i cant figure out some sort of mathematical algorithm to determine the actions of an individual that still doesn't necessarily disprove cause and effect governing your life. regardless this was still a great video.

[@TheIceboundthrath]

Well he has the free will of where to start and possibly connect the vectors, I can see free will in that.

[@MoronicChunk1]

Thrath Jacobs are you familiar with philosophy at all because thats not any kind of argument. that is circular thinking where you think its a representation of free will because you already believe free will exists. you cant disprove that the environment around him and his brain patterns and everything at that exact moment causally determined where he chose to make that origin point. its the difference between the illusion of free will and actual free will.

[@catStone92]

+MoronicChunk1 why would you disprove cause and effect in order to prove free will? that makes no sense

[@zemitoqdemige]

+Tiavor Kuroma No, because you have increased the number of dimensions in your vector space. Two vector spaces are isomorphic if and only if they have the same dimension.

[@MoronicChunk1]

Pedro Gusmão how in the world does that make no sense? if everything is casually determined then there is no free will. that should go without saying.

[@sypim]

I want to thanks Numberphile because I uses to think poorly of my high school math classes and I though that math "definitely wasn't for me", but thanks to this channel I got to see how interesting and fun math can be, and I am now truly interested by mathematics !

[@maggot00yay]

He started to describe the "mug example" and I inmediatly thought about quantum physics. Then I saw the blackboard. Woah. "It's a particle!, it's a wave"... No, we are just seeing the shadows of the mug! This guy is a genious.

[@MobiusCoin]

I find his voice extremely soothing...

[@IceMetalPunk]

I see where he's coming from, but here's where I disagree: no one thinks a brain *is* numbers. When people say that, what they mean is that a brain can be deterministically represented by numbers. Obviously, a vector is not equivalent to its coordinate representation, and a synapse is not equivalent to a mathematical model of it, but that doesn't change whether the vector exists and is accurately represented, or whether a brain exists and can be accurately predicted. In physics, nothing exists in a vacuum (metaphorically; in a literal vacuum, lots of things exist). You can't pick one particle out of the universe and claim it exists; everything must interact with other objects. In this way, it's not important what something *is*, but how it *interacts* with other things. This comes full circle to the example in this video: yes, you can choose any arbitrary coordinate system you want, with an infinite number of possible translations and rotations and scales...but once you do, the *relationship* between vectors and other objects will always be the same. If we have two vectors, U and V, then the relationship between U and V will always be the same, no matter what numbers are dictated for them by the chosen coordinate system. Likewise, the relationship between molecules at a synapse will always be the same, no matter what model you use to describe them, even though the numbers themselves may change. It's because of this that, if we simulate those relationships well enough, then it doesn't matter what specific numbers we use, the simulation will be functionally equivalent to (or superior than) the brain.

[@john_titor1]

+IceMetalPunk I think you are missing the point. I think the idea is, no matter how well math can represent a brain, it is still not a brain. Regardless of whether we will one day be able to flawlessly imitate a brain, such imitations will remain just that; an imitation, not the real thing.

[@IceMetalPunk]

Epithom That depends: first define consciousness.

[@IceMetalPunk]

John Titor Have you heard about the Ship of Theseus? It's a thought experiment that questions the very nature of identity. When you say that something is or is not something else, what does that mean? For example, my brain is not your brain, but it is *a* brain. If I replace every neuron in my brain with an artificial one, but it acts identically (giving me the same memories, thought patterns, perceptions, etc.), is it still my brain? Or did my brain die when the neurons were replaced? What is "me"? What is "my brain"? If it's the form, then no brain can ever be reproduced, but similarly, no *thing* can ever be reproduced. If it's the function, then a perfect imitation *is* the brain.

[@john_titor1]

***** That may be your view, but that doesn't seem to be his. I can't really argue in his place however.

[@secularmonk5176]

+John Titor What is YOUR view?

[@juana.d.5446]

For those interested, the quote "the menu is not the meal" is from Alan Watts. But the concept appeared much earlier in Korzybski's "A map is not the territory" (1931). Korzybski acknowledges his debt to mathematician Eric Temple Bell, whose epigram "the map is not the thing mapped" was published in Numerology. I love the reference to the movie Matrix and the mug from the dance club Amnesia in Ibiza.

[@krishna9438]

These things reminds me to Bruce Lee's "It's like a finger pointing a way to the moon...don't concentrate the finger, or you'll miss all the heavenly glories" Oh meta-quotes! These many quotes are the representation of one idea that Lee, Korzybski's and Watts referred to,

[@oliverutriainen2837]

I love listening to this guy talk. Please more.

[@HamzaSayedAli]

This explained so many things that were bothering me. Loved it.

[@pa.l.2499]

This is increadably descriptive and enjoyable, makes me want to study more linear algebra.

[@locksh]

Absolute pleasure watching the man talk, one of those professors you remember for the rest of your life.

[@karlmadsen3179]

I love his presentations. I also get a kick out of him looking like he is having a great time when he does it.

[@Stormsson]

this was mindblowing. We need more video of him :D

[@wil3]

If we can simulate neurons and their connections what is to stop you from simulating a complete brain?

[@grahamrich9956]

Probably size and changing variables.

[@MrJohnsala]

+Wilplatypus number of variables and connections

[@QwertyuiopThePie]

+Graham Rich You can change variables freely, that's what most of programming is spent doing in fact.

[@AnstonMusic]

+Wilplatypus Yep, but how accurate is that simulation? Does it produce the same outcome every time? Every 999/1000 times? Even a small difference between the simulation and the real thing on the level of a neuron will bring a *huge* difference on the scale of a whole brain by the principal of chaos theory.

[@Vedvart1]

+Graham Rich and computing power

[@Debbie52S]

I want to sign up for his class. He seems very understanding and he can make the class interesting.

[@rocketsurgeon5758]

By far my favorite video so far, many many thanks!

[@videotrash]

"I even exist before I have an address" mind BLOWN

[@contenau22]

not according to the dmv

[@avrenna]

Not having a home address where you sleep at night is not the same thing as existing as a locationless entity. From the moment you began to exist there have always been coordinates which correspond with your location. Latitude, longitude, and elevation have arbitrary origins, but existing at a set of arbitrary coordinates isn't the same as existing in an unmappable, locationless way.

[@ez_is_bloo]

@@avrenna almost everything is defined by perception so it could also go either way.

[@avrenna]

@@ez_is_bloo Have you ever perceived yourself to exist outside of spacetime?

[@ez_is_bloo]

@@avrenna yes.

[@phampton6781]

I am not a number, I am a free man! - Number 6, "The Prisoner"

[@davecrupel2817]

Ahahahahahahahaha

[@prussian7]

Who is Number 1 ?

[@becamicusack3598]

Be seeing you...

[@richelliott9320]

@@prussian7 you are number 6

[@cgtoche]

Now I'm a fan of Edward! :) Good video again Brady, thanks!

[@chumamtabiso2548]

I'd love to attend one of this guy's lectures...he just makes mathematics interesting, something a lot of lecturers or teachers can't do

[@nO_d3N1AL]

Great video. Well-explained, nice analogy. A very enthusiastic and engaging point!

[@electromika]

I looked at the title and thought of this for some reason. "Jonny! Where is your homework?" "The numbers gained sentience and escaped to the internet."

[@redpepper74]

I love that in the background you can see written on the whiteboard “It is our choice of basis that makes us perceive reality as this or that.”

[@7neoxis1337]

Just finished my Linear Algebra class a few weeks back and all of this stuff makes perfect sense :>

[@NGEternal]

Yes but what can you do with vectors that you can't do with the numerical representation of them?

[@lc7269]

I like ur photo

[@NGEternal]

+Lucky Abat thx m8

[@UnashamedlyHentai]

+NGEternal Contemplate its Form (of Plato's Forms).

[@NNOTM]

+Keith Buckson He wrote the numbers on brown paper, so that you can see it. That's a visual as well as numerical representation of the vector.

[@adamlatosinski5475]

+NGEternal Any question about vectors that can be formulated without refering to a specific basis can be answered without using any basis or coordianates.

[@jony7779]

why does every single video have to start off with an introduction to vectors.

[@TwistedLemniscate]

hahaha. it's same with textbooks.

[@Sam-oz8pn]

To point you in the right direction

[@jony7779]

I see what you did there.

[@thanasisgiannakopoulos2315]

because they want you to follow the direction of their thought

[@steliostoulis1875]

Jon Deaton everyone did

[@bruinflight1]

The processes of the universe can be explained using numbers and processes in the way that a meal on your table can be explained by the list of ingredients and techniques of cooking. BRILLIANT.

[@raminmoheb6504]

Awesome discussion. Deep insight. I want to take this guy's class.

[@lpfan2457]

This video is awesome. It helped me to wrap my head around vectors! In school we only learned about them as numbers but now it makes sense

[@yoyoyogames9527]

just watched this again for the first time in ages, i am currently doing linear algebra and now i understand lots of what hes saying more precisely, absolute masterpiece of a video, really is

[@veramentegina]

what an interesting way to look at vectors. will never feel the same again.. thanks for letting us see how we have this need to frame and define what we don't comprehend or comprehend in a limited way.

[@hermest99]

Love the menu/meal analogy. Great video!

[@WayWeary]

He's acting like the coordinate grids come into existence when you choose them. No, they are all equally extant before you choose one. There already exists a set of all possible coordinate grids. Also, the full statement about a vector is not the numbers themselves but the numbers and the coordinate grid chosen which the numbers relate the vector to. I don't think any of this has much to do with AI or free will. He goes on to say that the representation of something is not the same as that thing itself. Of course not, but you could say the same about our experiences, thoughts, memories, etc. They are equally just representations of the world around us. The same would be true of a program.

[@SlackBruce]

+WayWeary Except that the programmers are choosing the programs - algorithms - to represent thoughts, or mental processes, which are not the same as the thoughts themselves.

[@WayWeary]

***** No, they are choosing, or, rather, discovering algorithms that represent things that exist in the outside world the way our thoughts represent things in the outside world. The question of whether or not you can easily download your own consciousness into a machine is a different one than whether you can create an algorithm or system of algorithms to create an equivalent level of intelligence to humans, artificially. The former is a taller order as it would require a perfect understanding of an individual's brain/mind but the latter is certainly possible. If we agree on the possibility of creating a true AI, the theoretical possibility of replicating or at least closely approximating an existing human's consciousness is at least theoretically possible.

[@catStone92]

+WayWeary the matter of wether they come to existence when you so choose or if you simply choose one is just a matter of wording. What he's saying is that you're not bound to one coordinate system and you can choose to change the coordinate system you use

[@WayWeary]

Pedro Gusmão There is no significance to being able to choose a different coordinate system. That's like saying that a thought in Spanish is somehow essentially different than the same thought in English. They are just in different languages or using different words. It's arbitrary which is used as it is with the choice of coordinate systems. Nothing he is saying has any real bearing on the viability of AI or neural mapping of humans. Its just a bunch of faulty reasoning by analogy.

[@BattousaiHBr]

+WayWeary expanding on that topic, AI experts overwhelmingly agree that at some time in this century computers will become smarter than us.

[@mykhailomykytyn]

cool, please make more videos about Linear Algebra

[@r0kus]

Excellent and thought-provoking. Prof. Frenkel's point boils down to this: a representation of a thing is not, and should not be confused with, the thing itself.

[@charlieng3347]

So grateful for youtube, a place where knowledge is put into consumable forms and sparks fires of curiosity for many people.

[@ibrahimalmetwale3282]

notice that: this could be a destructive argument for materialists, shortly , the argument could be phrased like this : "the scientific law is a representation to a universal law ( that is laid out there in the universe), and not that universal law itself, thus, the scientific law doesn't govern the universe , it just describes it "

[@takatalvi05]

Mind Blown.

[@tigerwas8309]

An astonishing mind brought to bear on the delicate subject of man and machine (or, dare I say, Man v. Machine)? From the profundity of the humble vector, this engaging Professor reminds us that the value inherent in life is only referred to by measure (numbers); the true measure is not found in a number; rather, the meaning, the feeling of meaning and value is beautifully hinted at through this elegant tool we've devised called numbers; let us not forget our essence is the living, not the abstraction! I feel privileged to have watched and listened to these many distinguished notables who grace the Numberphile pantheon of contributors. Every blessing to you all!

[@bm0204]

Woah! I have just started reading J Krishnamurti's first and last freedom and I am stunned by the similarity. He has been quoted saying that we forget that symbols are a mere representations, our projection to things and we tend to confuse them for things themselves. Just like you said vectors or positionality of something in a space exists before we put a coordinate grid on it to understand its position.

[@matthewbrauer5977]

This is kind of like saying: "the height of a peak depends on what you set as the zero datum, therefore free will." Not persuasive.

[@joshuarosen6242]

Spot on. It's clearly true that the representation of the thing and the thing itself are different but it is then a huge unjustified leap to suggest that choosing a frame of reference proves we have free will. He doesn't dispute the ability of numbers accurately to represent things so why cannot a numerical representation of a person create a work of art like a person can?

[@eagle3676]

Entropy is information and new information means new determinations and entropy increases constantly so new information comes all the time so yes free will is still possible. We cause entropy so we cause new info to come into the universe thus changing the formula if you will of the universe. Like it or not pure info is random which is entropy physically. Also things happen at the quantum level which are difficult to even grasp so for all we know we do have free will or we don't. We just don't know is the right answer here since it is above and beyond even the understanding of physicists and physicists we are not so we are more ignorant. Just accept that we both are grossly underqualified and extremely ignorant and move on

[@eagle3676]

Entropy is information and new information means new determinations and entropy increases constantly so new information comes all the time so yes free will is still possible. We cause entropy so we cause new info to come into the universe thus changing the formula if you will of the universe. Like it or not pure info is random which is entropy physically. Also things happen at the quantum level which are difficult to even grasp so for all we know we do have free will or we don't. We just don't know is the right answer here since it is above and beyond even the understanding of physicists and physicists we are not so we are more ignorant. Just accept that we both are grossly underqualified and extremely ignorant and move on

[@poutineausyropderable7108]

Well, first, planck instant, there is a munimum of time that can happen so there for, no random, erveything interact with each other on a way, of course, knowing something change it because the way of knowing it need to change it. When you want to look at something, you need to throw a photon at it, a machine that test electromagnetic field also makes elctromagnetic field. When you test something, you see how it was before you tested it (kinda too hard to explain with quantum superposition)... Or even(the next bit is pure theory) maybe, the machine that test the up or down spin of the electron quantum entangle with the electron. So that machine that will test the electron will change the electron making it the opposite of the machine result. (because of how quantum entanglement work, the particule are the opposite)

[@SirTranquilizator]

That's not what he was talking about at all. The free will here appears only at the point of choosing a coordinate system. All he is saying is just: "try to look at things from different perspectives, do not be stuck with only one interpretation"

[@Kram1032]

This is an important idea to get if you want to understand general relativity.

[@freetownJoe]

+Kram1032 I feel the same way. Can't agree more.

[@Kram1032]

***** ***** basically, all the stuff about bendable spacetime is mathematically described by constantly changing your basis vectors. And furthermore, the whole _idea_ of the theory was, that any basis you put over the system can only ever be a construct. It doesn't have anything to do with physical reality. Thus, all fundamental laws of nature (and specifically gravity) must be independent of your chosen basis. They must take the same form regardless. (Since your basis is arbitrarily chosen by you. The forces, however, are real.) If you want to know more, check out the last six or so videos of PBS Space Time - they actually tried to cover General Relativity 101 in basic terms and I think they did a great job with it!

[@MyFrenchfries]

+Kram1032 Always when I speak to people that understand general relativity I feel like I'm speaking to my 4D self... So how is it going with me on that side?

[@Kram1032]

Marcel Hattingh I would say me understanding GR is an overstatement. Not quite sure what you are asking there. Can you clarify?

[@MyFrenchfries]

General relativity implies that we live in 4D space-time world, where you and I are only 3D projections of this 4D world. Seperated by space and time, but linked directly in the spacetime fabric. I am you, and you are me, we are one.

[@JimBeezie]

Fascinating video. A bit difficult to get your head around the idea Frenkel is speaking on, but rather exciting when you do.

[@lavaande]

this is one of the best talks ive ever listened to!!!!!!!!

[@Epoch11]

Hello!

[@andrew_cunningham]

I see a lot of comments down below disputing this video in various ways, mostly quite successfully, but one thing I haven't seen brought up is the fact that, even if every argument made in the video is completely accurate, a computer is no more made of numbers than a human brain (this did start with some debate about AI, right?). Computers, and programs, and the algorithms they run on, are made of electrons, which are self-contained entities of largely unknown nature that can only be conceptualized through mathematics. Once they are thusly represented as binary numbers, they can be translated by various code compilers into a programming language that can be understood by humans, but the fact remains that your CPU is powered by the interactions of quantum particles that have existed long before the invention of the number.

[@ThomasVachuska]

For some reason this reminded me of Alan Watts. "A noun isn't a part of nature, it's a part of speech. There are no nouns in the physical world. There are no separate things in the physical world, either. The physical world is wiggly. Clouds, mountains, trees, people, are all wiggly. And only when human beings get to working on things--they build buildings in straight lines, and try to make out that the world isn't really wiggly." and "So the world doesn't come thinged; it doesn't come evented. You and I are all as much continuous with the physical universe as a wave is continuous with the ocean."

[@jdgrahamo]

+Thomas Vachuska I can see why this video reminded you of Alan Watts, who has a ... unique... approach to reality. He also said, "You don't have to know how to shine the sun -- you just do it."

[@ericsbuds]

+Thomas Vachuska Alan Watts was amazing

[@sully42682]

Ha! I literally just started reading Edward Frenkel's book, Love and Math, yesterday.

[@dude157]

This guy is awesome. I want him to explain wave particle duality

[@ashleyb7335]

did Numberphile just marry Vsauce?

[@richelliott9320]

Or is it?

[@0vesty]

Great video. I like these philosophical questions :)

[@jesscarter6504]

That comment over Edward's left shoulder is paraphrasing the entire idea he is explaining in this video...our choice of basis allows us to perceive reality as this or that...I like to say that when we change the way we look at things {our basis}, the things we look at will change {our perception}. Love you, Prof Frenkel!!!

[@hoarfyt]

This is not a really good argument sorry. Nobody is making the ontological argument that humans are numbers when they say our brain works like a computer, but simply that the same categorical structures (such as the existence of an origin, a > b and b > c => a >c, etc) that are present in some number system are also maybe present in human brains. Such properties are present in any particular base you pick. It really doesn't matter to say that the input of a neurons are 1 and 3 or Dopamine and Serotonin, so long they form a base, any base will be good enough. This is a really weird argument and I have never seen any philosopher or neuroscientist or computer scientist put it forward. If there are someone out there who fleshed this idea out I would like to know.

[@lukasdon0007]

+hoarf In a larger sense, however, people have argued that the universe is just pure mathematics. That, in fact, mathematical structures (numbers, vectors, etc.) are real and that they are the building blocks of the universe.

[@hoarfyt]

+Lukas don The very sentence 'universe is mathematics' is so ambiguous and packed that is hard to think about it since: 1. We don't have a clear definition of what mathematics and number really are. Some people think they really exist others that they are a product of human brain. 2. The very notion of equality is in dispute. According to Lavoisier, we can say that A e B are equal if everything that is true of A is also true of B. Is that what's meant when people say humans are numbers? I don't know.

[@OmegaCraftable]

+Lukas don Ugh mathematical platonism is the worst.

[@Em-gj2sg]

+hoarf I think his basic point is that numbers just represent reality but aren't actual reality. Just like the menu is not the meal. And also that these systems of representation can go too far and prevent us from seeing things in different ways or in an objective way

[@NickCybert]

+hoarf I think the professor is just trying to explain that computer algorithms are abstractions of thinking in the same way that a coordinate system is an abstraction of a vector. And then I guess there's a bit of naturalism thrown in at the end implying that because of this abstraction computers won't be able to adequately simulate a human brain. Regardless of what you make of that conclusion, the basic idea seems sound enough. Thinking does appear to be different from computing. Maybe computers will be able to be able to simulate thoughts in the future, maybe they wont. But we did figure out how to but vectors in a coordinate plane to a satisfactory degree.

[@jeffirwin7862]

I would be interested to hear what Professor Frenkel thinks about Gödel's Incompleteness Theorem. Does assigning a Gödel number to everything omit essential information, much like assigning coordinates to a vector in some arbitrary space omits information? I was once taught that an orthogonal basis is somehow "more efficient" than other bases. Now that I think about it, the choice of an inner product is just as arbitrary is the choice of a basis. So an efficient orthogonal basis in one inner product space may be less efficient in another inner product space.

[@amodgawade4323]

this video was angelic, enlightened me beyond. i love his analogies!!!!! want him as my prof

[@kiffe22]

It doesn't matter which numbers I assign to the vector(s). 2 or more vectors will always interact in the same way independent of the numbers that represent them. That means they will always have the same cause and effect regardless of the names you call them.

[@JonSebastianF]

The overall point is beautiful: A representation never does full justice to the thing represented; like an arbitrarily chosen numerical representation of a vector never fully represents the vector itself. BUT once he named the abstraction of the line on the brown paper 'a vector', he already CALLED it 'a vector'. So, strictly speaking, by initially calling it 'a vector', he already imposed a representation of a clear-cut mathematical definition on it. This made it rather confusing, as he then attempted to separate 'the vector' from its number coordinates that were defining the word in the first place. He could instead have used a separate word unspoiled by the definition accompanying that mathematical word 'vector', e.g. used the word 'the thing we haven't named yet' or simply 'it'. Right?

[@JonSebastianF]

Okay, well put. However, let me ask you philosophically then: Does this mean that the pure and abstract name 'vector' could exist meaningfully without any of its possible representations? In other words, if removing the total sum of possible mathematical definitions describing the object, would the word 'vector' still carry any meaning then? If "no", I would say that the word 'vector' is analytically inseparable from its mutually constituting grid of representations/mathematical definitions.

[@LtLollo]

+Jon Sebastian they are called free vectors also that's not the point, the point is that in geometry all their numerical representations are equally valid; that follows from the 'linear' part of 'linear algebra'

[@shhac]

+Jon Sebastian If something is impossible to represent then it is impossible to perceive, which means you cannot prove it's existence. The argument here isn't that you can't represent vectors with numbers, it's that the numbers are an abstraction of vectors. It's that his vector IS but it's also and and and (3/8 Pi radians, 44) and it's purple, and it's thicker than the line from the blue sharpie, and it's 6,371 km from the centre of the Earth, etc and etc and etc. Basically, that the two number representation is useful for loads of things and for communicating meaning, but it's not the entire existence of his specific vector. That said, I didn't follow how he got to "this proves no AI" or "this proves you can't think of brains as computers", so I don't agree with where he was ultimately applying his argument.

[@akiritescu]

amnesia ibiza + math => Love and Math: The Heart of Hidden Reality

[@handulldtd]

This video couples very well with a recent Hello Internet discussion about analogies. It made me think, and I see what you were getting at, but I wasn't convinced.

[@gudmythman]

This guy is truly one of my favorite Numberphile speakers

[@edliragega9519]

Awesome video, honestly Brady your videos should be shown in classes. Get people excited about Maths.

[@yttis3257]

I will upload my brain one day, but not with zeroes and ones, but with 2's and 3's.

[@davecrupel2817]

I'll go with ABCs

[@senselocke]

"The menu is not the meal" is a simply fantastic metaphor. Seems it has been credited to Alan Watts, and has been around at a minimum longer than I have, as he died before I was born. But I've never heard it until today.

[@BenderAlied]

Thank you. I wish i had algebra teacher like you. I understand about box idea. perfect!

[@emiel1414]

Thats one round ass dot

[@JoelBonasera]

Fantastic video. The professor seems like one of the most affable and approachable teachers ever.

[@tedk-42]

More this guy! He's great at explaining these things.

[@sharkdavid]

Wow that was enlightening, and I think I agree with Dr. Frenkel.

[@julsius]

"The map is not the territory".

[@stigekalder]

Robert de Niro in "Ronin"

[@random19911004]

Damn, I thought it said "numbers and free wifi"

[@centralprocessingunit2564]

lol

[@Nono-de3zi]

This reminds me of such painful memories. 1990. Competition to get into the best French school (after my "classes prépas"). Physics exam. I chose the wrong referential to project the movements onto. After 2 hours and 20 pages of dense calculations, I turn a few pages of the exam book (it was literally a book. The exam was to last 5 hours). I then see I completely messed up the referential. The initial calculation should have been trivial should have chosen the right one (a moving referential, travelling a circular trajectory). I gave up, left the room. The sun was shining, I enjoyed the day. I eventually joined this school, but I never forgot this lesson.

[@christianxfb]

I learnt more here than in a whole semester at uni XD......THANK YOU so MUCH!!!!! that was interesting, amazing and very helpful!

[@peterpodgorski]

I can see that he's very excited about this idea, but I can't help but to feel that he's barking at the wrong tree. Nobody's saying that humans are collections of numbers. Humans are chemical reactions - this is a fact that you can't argue against without bringing supernatural BS into the conversation (which, by my taste, he's on the edge of doing). On the lower level, we are information moving around, energy changing forms. Numbers don't really come into this unless you use them to describe the process, so I don't really understand what he disagrees with.

[@davecrupel2817]

Piotr Podgórski all those complex chemical bondings and mixtures that produce life can be represented by _numbers..._ All of those complex inner systems and multi-systems going on in a multicellular organism, all of it.... Can be represented by equations...and thus, by numbers...

[@peterjohnson4854]

In US you coordinate zvector. In Soviet Russia *Commrade ZVECTOR* coordinates you.

[@DisfigurmentOfUs]

He is very nice guy, i like his language and explanation

[@CalLadyQED]

I recognized that textbook very early on in the video, long before he picked it up. We used Friedberg, Insel, Spence for Linear Algebra when I was at CSUF years ago.