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.
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?
+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.
+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.
+Charles Miller Yay, civil disagreeing comments on TH-cam :) At least 95 % of what he's saying in this video is perfectly true, because it's maths (and it is indeed important to remember that any bases you choose are simply constructs you use to better understand/manipulate a given vector, but that the vector [in whatever sense] exists without those bases, too - students often have problems with that level of abstraction at start) ....but I can absolutely understand how the conclusions he draws from that and applies to the real world are not something one would easily take on board. Frankly I haven't fully made up my mind re. what he's saying yet, because it's not something I often think about (though I have, coincidentally, just watched several videos on robotics and AI)
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.
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
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.
+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.
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.
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.
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.
+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.
+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.
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.
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.
+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.
+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.
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.
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,
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.
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.
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.
+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.
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.
+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.
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.
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.
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.
"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.
+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.
+NGEternal Any question about vectors that can be formulated without refering to a specific basis can be answered without using any basis or coordianates.
Confusing a entity (even an abstract mathematical one) with a description of it (even a complete one) is the same kind of magical thinking that lead people to believe that something's "True Name" would grant you power over it.
his coordinate system argument is a variation of the 'map-territory relation' described by philosopher Alfred Korzybski famously quoted as "The map is not the territory".
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.
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!
His concept opened my mind, everything is (is perceived) based on reference to something else, if you change reference, it changes perceptions, without changing the real thing
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.
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.
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!
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 !
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.
+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.
***** 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.
+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
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.
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."
Love it. My favorite quote along these lines is "The map is not the territory." Maps are great and we can use them to plan trips and so on, but the map is NOT the mapped territory. It's just a model, and like all models it will NEVER capture the full reality of the world its mapping.
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.
If you're going to take a position on the nature of free will and how the human brain works and state it as if it's a known fact, you're going to need a much better argument than "computers are numbers and we aren't. Therefor intelligent machines are impossible." He's annoying in his arrogance and lack of understanding of brains, computers, or AI. He, like Stephen Hawking, is not an expert in machine learning and it shows in his complete lack of anything intelligent or interesting to say about the matter.
Both you and him are pointing out the same issue, but you missed something and he didn't. Your hostility only says you are a fool. He doesn't make the claim it's impossible, just improbable from the issues in algorithms we know of now that are required for things like neural networks. Computers are algorithmic because they were invented for a specific task. People are not like this, so it is foolish to assume a computer can do free will.
***** ***** 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!
+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?
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.
Complex numbers can be represented by vectors, but they hold different properties. So it makes sense to consider a vector different than an array of numbers.
An arbitrary vector cannot, in general, be represented by a pair of numbers that can be represented finitely. For any basis, there are vectors with real-valued , and most real values are beyond exact representation in a finite-space system. We can approximate to some value, like the number of Planck lengths, but that brings up a second point. In order to represent a physical object completely, one must know its quantum state (thank you, white board). Here we run into non-commuting operators, so it is not possible to know the exact state without a projection onto a linear combination of the operators. That is, you can project the coffee cup as a circle with a doohickey, or a rectangle, or some other shape from a different angle, but the two-dimensional projection doesn't capture the full cup (and you only get one projection). Could one capture a complete representation on a quantum information processor? Do we know all of the non-commuting operators that make up a real physical object? Is a person different from the quantum states that represent the person?
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.
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...
In reference to the example with the mug: You're projecting a three dimensional object and trying to represent it on a two dimensional plane. Why not use a computer simulated three dimensional plane? We can create that entirely with numbers, which I would argue DOES create the essence of the cup, as all of it's sides and features can be represented perfectly. Much respect for Professor Frenkel, this is just something that I didn't understand.
We should all aspire to the joy and equanimity of a vector just sitting there and enjoying its life, oblivious to those who wish to impose coordinate systems upon it.
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?
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
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
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)
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"
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 "
I would agree with Roger Penrose that argues that the argument Gerg Cantor used to show that some infinities are larger than other infinities is showing that human understanding is different from any artificial inteligence. Human understanding is not computable, because we are doing something which involve consciousness which i think impossible to be represented by numbers
This video was great, but I for one don't think the title is fitting. He is not arguing for free will, he's only arguing (the conclusion, at least) that an AI could never be the same type of intelligent being as a human. Free will may or may not be involved with that conclusion, it is not a given. An AI could have free will by the same definition as humans do.
The presenter's comment about a cup and it's projection causing people to interpret it as a disk or rectangle makes me think of photons "projection" (physicist's measurements) being interpreted as a particle or wave.
Interesting but I don't think you made the point at all. Yes, representations are different to the things they represent. Does this necessarily mean that a numerical representation of a thing cannot produce the same result such as a work of art? No, it does not and you did not address that point.
Joshua Rosen a numerical interpretation really can't; if you digitize the Mona Lisa, you'll lose resolution eventually. If you were able to quantify all the subatomic particles of the Mona Lisa, somehow obtained all of their positions and momentum, created a physical clone of the Mona Lisa, and rendered that in real life, you will experience a Mona Lisa Clone. The thing you've made is a representation of the Mona Lisa but ISN'T the Mona Lisa.
Em See I wasn't referring to a reproduction of the piece of art, I was referring to a reproduction of the artist. If a creature is intelligent, I don't see any reason why a representation of a creature shouldn't be. He completely failed to make that case. Saying they are both intelligent is not the same as saying they are identical.
The prof successfully made the point that a numerical representation cannot wholly capture the thing it represents. However, I agree, in terms of intelligence, a numerical representation need only be accurate enough to emulate the original's intelligence for it to display equal levels of intelligence, yet not be the same intelligence.
What he was trying to say is that humans are not 1s and 0s. We can use those to represent a flawed version of us but that is flawed so no humans are not numbers and machines is what he was saying and i think he made that point quite clear
+104356138790410752358 What he said was that the representation isn't the thing. No-one disputes that. What then claimed without supporting it in any way, was that that means a representation cannot be intelligent. I believe he is wrong about this but whether he is or not, he did not provide an argument to back that up.
In brief : Objects are described in a frame of reference and their could be multiple such frames. Thus, the objects look different based on the frame of reference that is chosen. And the philosophy in short : if an algorithm and few numbers can describe a human being then it is merely within the frame of reference that the algorithm is using i.e. another algorithm that is using another frame of reference would have a different description of that same person.
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
Bravo. Five Stars! Thank you! A a trained human scientist and a novice physical scientist, there are a great many science and mathematics videos on TH-cam that mistake the representation for the object. Thank you for this video.
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Whenever I see a video about free will, I have no choice but to watch it
clever.
Underrated
Nice one :)
Lol.. another numberphile vid with this dude has a most-popular-comment that refers to "Russian Jamie Lannister" .. lol
Nice one
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.
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?
+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.
+Eugene Khutoryansky Pretty much exactly what I was going to say, although you might have been more eloquent.
+Icepick L If every atom is the same, is it the same then?
+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.
I completely understand your point. But I respectfully disagree with your position.
+Charles Miller Yay, civil disagreeing comments on TH-cam :)
At least 95 % of what he's saying in this video is perfectly true, because it's maths (and it is indeed important to remember that any bases you choose are simply constructs you use to better understand/manipulate a given vector, but that the vector [in whatever sense] exists without those bases, too - students often have problems with that level of abstraction at start)
....but I can absolutely understand how the conclusions he draws from that and applies to the real world are not something one would easily take on board. Frankly I haven't fully made up my mind re. what he's saying yet, because it's not something I often think about (though I have, coincidentally, just watched several videos on robotics and AI)
+Charles Miller You agree with his point in vector space, but disagree with the way it's position is represented? Got you.
And because you failed to elaborate, your opinion holds no value here.
EcceJack I think you may have missed the point of Charles' post!
+Andreas Nergaard i think what he meant is he agrees with his proposition, but disagrees with his conclusion.
this dude is a beast with analogies
He reminds me a lot to Feynman
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.
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
GravyBrainz dis how we du in Russia
@@ractheworld Viva la Bourbaki :D
You need to do a video on what's on the board behind him
This is for the Physicsphile channel :)
The board is about matrix (yes, really).
This is not a comment, this is a string representation.
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.
+boumbh //This is a comment
+Jeroen Bollen yes, but what he saw and what we see is the string representation (i think thats what he wanted to say ^^)
+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.
+D12golden I C what you did there. (underscore c)
So are you telling me I can dodge bullets?
No. I'm telling you you won't need to.
+Matthew Mitchell No. When you're ready... you won't have to.
+Iñigo P.D. Whoa
you think that's air you're breathing?
+Menaceblue3 I just farted so I know it's not
"so look at this brown paper" yeah we've all been looking at it since the dawn of numberphile
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.
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.
@@sadatnafis2032 Professor Frenkel actually used this same analogy when discussing particle wave duality on the Lex Friedman podcast...
@@jamesfullwood7788 Its always delightful to hear that an expert had the same idea that I, a layman thought of as well.
@@sadatnafis2032 indeed!
Languages are like coordinate systems for meaning
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.
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.
@showerthoughts
Thecrashthrash Yes. And the object you name ecist before that name itself, just like vectors exist before the asigned coordinates.
This must go on a plaq!
I find his voice extremely soothing...
I love listening to this guy talk. Please more.
I'm a 18 year old straight guy and I find this guy super attractive.
+Jonathan Duffield There's a term for that. It's called "bisexual"
+Jonathan Duffield same
+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.
MEATLOAF2 I know that. But you have to admit sexual attraction was definitely implied in this context.
+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.
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.
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.
+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.
+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.
The Vidlets Yes, I did, but I don't really understand what you're trying to say here.
+Noah Fence Exactly.
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.
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,
I am not a number, I am a free man! - Number 6, "The Prisoner"
Ahahahahahahahaha
Who is Number 1 ?
Be seeing you...
@@prussian7 you are number 6
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.
What a legend
The vector is just sitting there, enjoying its life!! Obviously. Haha, pure gold. I like this guy.
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
The map is not the territory.
The recipe is not the meal.
The rules are not the game.
- Matt Colville
MumboJ the map has replaced the territory: everywhere there exists merely fragments of the real
Did not expect a Colville quote here
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.
Well he has the free will of where to start and possibly connect the vectors, I can see free will in that.
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.
+MoronicChunk1 why would you disprove cause and effect in order to prove free will? that makes no sense
+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.
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.
I love this professor, always so interesting and enjoyable :)
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.
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
Fascinating video. A bit difficult to get your head around the idea Frenkel is speaking on, but rather exciting when you do.
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.
+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.
Epithom
That depends: first define consciousness.
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.
***** That may be your view, but that doesn't seem to be his. I can't really argue in his place however.
+John Titor What is YOUR view?
this was mindblowing. We need more video of him :D
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.
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.
"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.
This guy is truly one of my favorite Numberphile speakers
Hello!
If we can simulate neurons and their connections what is to stop you from simulating a complete brain?
Probably size and changing variables.
+Wilplatypus number of variables and connections
+Graham Rich You can change variables freely, that's what most of programming is spent doing in fact.
+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.
+Graham Rich and computing power
Yes but what can you do with vectors that you can't do with the numerical representation of them?
I like ur photo
+Lucky Abat thx m8
+NGEternal Contemplate its Form (of Plato's Forms).
+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.
+NGEternal Any question about vectors that can be formulated without refering to a specific basis can be answered without using any basis or coordianates.
Confusing a entity (even an abstract mathematical one) with a description of it (even a complete one) is the same kind of magical thinking that lead people to believe that something's "True Name" would grant you power over it.
his coordinate system argument is a variation of the 'map-territory relation' described by philosopher Alfred Korzybski famously quoted as "The map is not the territory".
why does every single video have to start off with an introduction to vectors.
hahaha. it's same with textbooks.
To point you in the right direction
I see what you did there.
because they want you to follow the direction of their thought
Jon Deaton everyone did
Fifteen minutes and he's given me an entirely new way to think about mathematics....incredible. I hope you get more of him.
I like his philosophies and attitude
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.
The fundamental difference between metaphysics and epistemology, 'what is' versus 'how we understand it'.
Brilliantly demonstrated.
An excellent exposition that demonstrates how Immanuel Kant nailed it down with Transcendental Idealism.
Edward has a vast intuition and is a monster in coming up with vivid analogies!
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!
did Numberphile just marry Vsauce?
Or is it?
Thank you. I wish i had algebra teacher like you. I understand about box idea. perfect!
His concept opened my mind, everything is (is perceived) based on reference to something else, if you change reference, it changes perceptions, without changing the real thing
Prof. Edward is just so amazing at discussing stuff like this I can’t explain it exactly but I’m so happy right now.
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.
"I even exist before I have an address"
mind BLOWN
not according to the dmv
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.
@@avrenna almost everything is defined by perception so it could also go either way.
@@ez_is_bloo Have you ever perceived yourself to exist outside of spacetime?
@@avrenna yes.
For me, that's the best video in Numberphile.
Change of basses is the only thing i found hard in linear algebra, but i loved that course it made difequ so much easyer.
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!
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 !
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.
+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.
***** 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.
+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
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.
+WayWeary expanding on that topic, AI experts overwhelmingly agree that at some time in this century computers will become smarter than us.
Can we have more of him? He's genius.
+ignilc
Do you have evidence to suggest his logic is flawed? Opinion is irrelevant.
Absolutely brilliant.
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."
amnesia ibiza + math => Love and Math: The Heart of Hidden Reality
I must admit that this video was a bit boring, and rather pointless.
+WarpRulez watch it again.
Marcel Hattingh
It didn't help.
WarpRulez watch it again.
WarpRulez This video will remain pointless only as long as you want. Watch it again.
Love it. My favorite quote along these lines is "The map is not the territory." Maps are great and we can use them to plan trips and so on, but the map is NOT the mapped territory. It's just a model, and like all models it will NEVER capture the full reality of the world its mapping.
"It's our choice of basis that makes us perceive reality as this or that" (written on the whiteboard behind him)
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.
If you're going to take a position on the nature of free will and how the human brain works and state it as if it's a known fact, you're going to need a much better argument than "computers are numbers and we aren't. Therefor intelligent machines are impossible." He's annoying in his arrogance and lack of understanding of brains, computers, or AI. He, like Stephen Hawking, is not an expert in machine learning and it shows in his complete lack of anything intelligent or interesting to say about the matter.
Both you and him are pointing out the same issue, but you missed something and he didn't. Your hostility only says you are a fool.
He doesn't make the claim it's impossible, just improbable from the issues in algorithms we know of now that are required for things like neural networks.
Computers are algorithmic because they were invented for a specific task. People are not like this, so it is foolish to assume a computer can do free will.
AverageJoe8686 but why can't a computer be given the task to emulate a human brain?
This is increadably descriptive and enjoyable, makes me want to study more linear algebra.
I love how passionate the professor is on this topic P.S. Cool mug (amnesia is the best club in Ibiza)
King Jeoffry would be very proud.
This is an important idea to get if you want to understand general relativity.
+Kram1032 I feel the same way. Can't agree more.
***** ***** 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!
+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?
Marcel Hattingh I would say me understanding GR is an overstatement.
Not quite sure what you are asking there. Can you clarify?
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.
This explained so many things that were bothering me. Loved it.
Complex numbers can be represented by vectors, but they hold different properties. So it makes sense to consider a vector different than an array of numbers.
Now I'm a fan of Edward! :) Good video again Brady, thanks!
Damn, I thought it said "numbers and free wifi"
lol
I'm not buying it.
You don't understand it.
Nobody selling it.
"The map is not the territory".
Robert de Niro in "Ronin"
An arbitrary vector cannot, in general, be represented by a pair of numbers that can be represented finitely. For any basis, there are vectors with real-valued , and most real values are beyond exact representation in a finite-space system. We can approximate to some value, like the number of Planck lengths, but that brings up a second point. In order to represent a physical object completely, one must know its quantum state (thank you, white board). Here we run into non-commuting operators, so it is not possible to know the exact state without a projection onto a linear combination of the operators. That is, you can project the coffee cup as a circle with a doohickey, or a rectangle, or some other shape from a different angle, but the two-dimensional projection doesn't capture the full cup (and you only get one projection).
Could one capture a complete representation on a quantum information processor? Do we know all of the non-commuting operators that make up a real physical object? Is a person different from the quantum states that represent the person?
This is more to the discussion of "are numbers real" which can also be put as "is math invented or discovered
I will upload my brain one day, but not with zeroes and ones, but with 2's and 3's.
I'll go with ABCs
If you upload your brain without consciousness then where does it go. The point is you make a plan Stan
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.
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...
He or She.. oh yeah.. thank you .. Vector might have been offended if you didnt say he or she.. haha
In reference to the example with the mug: You're projecting a three dimensional object and trying to represent it on a two dimensional plane. Why not use a computer simulated three dimensional plane? We can create that entirely with numbers, which I would argue DOES create the essence of the cup, as all of it's sides and features can be represented perfectly. Much respect for Professor Frenkel, this is just something that I didn't understand.
We should all aspire to the joy and equanimity of a vector just sitting there and enjoying its life, oblivious to those who wish to impose coordinate systems upon it.
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.
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?
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
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
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)
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"
I don't really get his point unless he thinks computers literally run on abstract numbers rather than the same physical mechanisms as everything else.
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 "
I would agree with Roger Penrose that argues that the argument Gerg Cantor used to show that some infinities are larger than other infinities is showing that human understanding is different from any artificial inteligence. Human understanding is not computable, because we are doing something which involve consciousness which i think impossible to be represented by numbers
This video was great, but I for one don't think the title is fitting.
He is not arguing for free will, he's only arguing (the conclusion, at least) that an AI could never be the same type of intelligent being as a human.
Free will may or may not be involved with that conclusion, it is not a given. An AI could have free will by the same definition as humans do.
cool, please make more videos about Linear Algebra
yes indeed.. we must not forget that the map is not the territory..haha
Pretty much that, but without a need for a confusing 15-minute-long click bait video full of irrelevant blabber and shameless self-plugs ;J
This dude would make a perfect movie villain. Great video though :)
This is deeply philosophical. Many mathematicians won't get it.
The presenter's comment about a cup and it's projection causing people to interpret it as a disk or rectangle makes me think of photons "projection" (physicist's measurements) being interpreted as a particle or wave.
Interesting but I don't think you made the point at all.
Yes, representations are different to the things they represent. Does this necessarily mean that a numerical representation of a thing cannot produce the same result such as a work of art? No, it does not and you did not address that point.
Joshua Rosen a numerical interpretation really can't; if you digitize the Mona Lisa, you'll lose resolution eventually. If you were able to quantify all the subatomic particles of the Mona Lisa, somehow obtained all of their positions and momentum, created a physical clone of the Mona Lisa, and rendered that in real life, you will experience a Mona Lisa Clone. The thing you've made is a representation of the Mona Lisa but ISN'T the Mona Lisa.
Em See I wasn't referring to a reproduction of the piece of art, I was referring to a reproduction of the artist.
If a creature is intelligent, I don't see any reason why a representation of a creature shouldn't be. He completely failed to make that case. Saying they are both intelligent is not the same as saying they are identical.
The prof successfully made the point that a numerical representation cannot wholly capture the thing it represents. However, I agree, in terms of intelligence, a numerical representation need only be accurate enough to emulate the original's intelligence for it to display equal levels of intelligence, yet not be the same intelligence.
What he was trying to say is that humans are not 1s and 0s. We can use those to represent a flawed version of us but that is flawed so no humans are not numbers and machines is what he was saying and i think he made that point quite clear
+104356138790410752358 What he said was that the representation isn't the thing. No-one disputes that. What then claimed without supporting it in any way, was that that means a representation cannot be intelligent.
I believe he is wrong about this but whether he is or not, he did not provide an argument to back that up.
In US you coordinate zvector.
In Soviet Russia *Commrade ZVECTOR* coordinates you.
Great video. Well-explained, nice analogy. A very enthusiastic and engaging point!
In brief : Objects are described in a frame of reference and their could be multiple such frames. Thus, the objects look different based on the frame of reference that is chosen. And the philosophy in short : if an algorithm and few numbers can describe a human being then it is merely within the frame of reference that the algorithm is using i.e. another algorithm that is using another frame of reference would have a different description of that same person.
The title should be something like misconceptions between real (objects) and representative (numbers).
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
Mind Blown.
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
Bravo. Five Stars! Thank you! A a trained human scientist and a novice physical scientist, there are a great many science and mathematics videos on TH-cam that mistake the representation for the object. Thank you for this video.
what an enthusiastic man!
Fantastic video. The professor seems like one of the most affable and approachable teachers ever.