Leonard Susskind has a special gift beyond his obvious scientific genius. He's a teacher and he knows how to teach. I remember one of his first lectures in the Theoretical Minimum. The topic involved complex numbers. He turned to the class and asked "Does everyone understand complex numbers?". A few responded, but not many. He asked again - and then with a giggle said "Okay, let's go over complex numbers". Leonard shares his knowledge with anyone who's willing to listen. Simply put - he's a great man.
Mathematics work because of evolution ? Well, that is not quite an exact answer ! Wouldn't it be a Physical way, to say it works, because it is based on observation ?
struggling to explain things to a novice is a good way to keep check of your knowledge - he's also extremely efficient at neglecting unnecessary parts of the equation -- the way he talks skips over all unnecessary detail, it's just a joy to watch, because he demonstrates (maybe inadvertently) the processes that helps you quickly identify a winning answer as opposed to a dead end.
@Enter the Braggn' Its not a dumb question. We can't make math work, math works with or without or input. We discover proofs that just happen to be correct, 1 +1 = 2 because it does, not because WE made it so.
5:20... Mathematical intuition. That's the prize you receive at the bottom of the box after years of studying mathematics. When kids ask "why do I have to learn this nonsense and when am I ever going to use it" this is always my go-to answer. My own mathematical intuition had served me better than everything else I've ever learned, combined.
@@forbescallum It's helped tremendously in STEM (made understanding machine learning much later in life a total breeze) but it's also made me a more clear thinker and even a better writer (as odd as that sounds). Fact of the matter is that studying math fundamentally changes how you approach life.
Awesome. My comfort zone is verbal logic, or something like that. I'm decent at programming and philosophising. Well, guess that's up for others to decide but I've been told that's the case. I'm starting to think maths is a key thing I'm missing. We solve problems in maths but I get the impression that the process we engage in to do so is more important, regardless of whether the problem gets solved. The reorientation of perspective and drawing together of apparently disparate areas of knowledge is key. It's about looking at problem spaces differently, not just individual problems. And we do that in philosophy too but there's something about the unambiguous truth values of maths that could make teach me 'rigorous creativity'. Have I got that right?
Without math we predict by visualisation. But using symbols for quantities balanced in equations, and manipulating these equations, we can predict beyond our ability to visualise.
Math works because we are (1) lucky that patterns in math match patterns in the "physical" universe, or (2) because the universe is nothing but math (virtual).
well no - there are many geometric solutions to General Relativity - just like advanced geometries can be visualizable sometimes and others times not - we have a choice we can do either or we can do both - just like euclidean geometry and non-euclidean geometry can both be perfectly valid and yet so different
I studied chemistry and once sat through a lecture showing the development from integers to the simplest axioms of math and then continuing all the way to series and differential calculus. So it went all from first principles and "quantum" integers to the continuous math of integrals and differentials. It all hangs together quite neatly and coherently. After that I thought: "Well, if you consider the conservation laws governing physics, or in other words that 1 plus 1 always makes 2, then a universe which has any conservation laws must necessarily be one that is ruled by mathematics. A universe where 1 plus1 does not make 2 in all cases necessarily is unpredictable in the sense of being not strictly mathematical, and life can probably not exist there, because life needs reliable rules for input and output to work on. So, ultimately, this universe we live in may just be a mathematical one because 1 plus 1 makes 2 and everything else in math results from this starting point. Therefore there are, for instance, Legendre polynoms which together with their linear combinations form the basis of how atomic and then molecular orbitals look and behave. Because 1 plus 1 makes 2, the proper constraints together with the right dimensions and introduction of the Kronecker delta give you exactly these polynoms which are the underlying reason why atoms react with each other exactly the way they do."
the reason behind 1+1=2 itself came from abstract mathematical proofs and because of our working with decimal number system... abstract mathematics gives reasoning for all the crazy stuffs and their results are been used by scientists to represent their theory and discover beautiful structure in them
The way I look at it - Mathematics is a language of infinite variability, thus there will be one answer that maps most accurately to reality in an infinite sea of less accurate answers.
Mathematics is simply a way of bringing precision to our descriptions of the world and the way we perceive the world. An we have a tendency to want to get more and more precise in our descriptions... That's why we need a language of precision where we are all on the same page.
Dear Udacity, Thank you for posting this video. Watching it (while taking a break from school work revision) is therapeutic for the mind. (Paraphrasing): Mr Susskind talked about using mathematics to explain physics. Multidimensional stuff... As humans who evolved the ages, the way we visualize things are limited. To explain a physics concept, etc it would be hard to tell someone to visualize it. Hence we use mathematical equations to describe and explain. Someone who has developed a mathematical intuition over time, will be able to "visualize" such complex phenomenon. Appreciate the stretching of the mind.
Leonard Susskind is one of only a very few I hold a great deal of respect for, his buddy Dick Feynman, even moreso. Both of these men have opened my thinking into area's I never was aware I had, in more than 60 years of life. Not in the details of the advanced physics, that both stand head and shoulders, above their peers, in my opinion, but in their way of 'seeing", 'understanding"...how IT all works, and fits together, yet, humble enough to admit the vastness of what they don't know. Both men have admitted the critical importance of 'mathematics", while also admitting 'math" is a man made construct, and that math MAY not be ONLY solution to achieve answers. But, it is the best we have, for now. I think it is the the blending of theoretical physics and philosophy, that both of these men mastered in a unique way, that has made me gain such respect for both. If these 2 men can teach a dummy like me, the basics of the incredibly complex world of 'quantum physics", in a manner that helps me "get it"...they are truly great teachers. Freeman Dyson, is another that stands out, in my book. A genius that understood, and hated, the entire "Phd." farce, and proud to never having to be subject to it. Sadly, the world is lacking great teachers and minds like these.
xXxA- I never said, ..." math was completely and utterly useless ...", I think it is a wonderful invention of mankind, maybe the best invention, but it is a "tool", after all. Perhaps, as a tool, math is not being used correctly, or "math" itself, has reached it's limit in terms of written calculations or equations we humans express. I simply don't "worship" math as anything more than an a extremely useful tool...math is great, but some solutions to questions can not be written in equations, there are too many unknown factors to achieve concrete answers.
2:10 This reminds me about what I read recently regarding the Monty Hall problem. We're hard wired to wrongly perceive the true odds of the problem. The same could be said about many problems in probability and statistics. The same could be said about the nature of quantum physics and inherent uncertainty of the universe, it defies our built in reasoning so we have a hard time coming to grips with it. Trust the mathematics instead.
I think mathematics is so useful as a tool to describe our world because that's kind of what it was initially made for. Some merchants needed to inventory their warehouse, some architect needed it to determine the number of stones for a wall, a navigator for plotting a course, and the mathematicians managed to abstract from this and make multipurpose tools.
Great perspectives, have been watching Susskind's lectures re Qm with keen interest, thanks Any chance they can amend/update the subtitles, they aren't quite correct :-( Would only take a few mins surely...
Mathematics, all it encompasses and that it implies seems essential to me, a complex and comprehensive matter of necessity; that which can not, not be.
It's remarkable, that you can hear that he was befriended by Richard Feynman, just by how he speaks. I wish i was older and had the opportunity to speak to Feynman too.
Professor Susskind is a man of faith. "The world has some coherence to it. Things don't just randomly happen. " One needs faith to believe that things just randomly happen.
Not faith. Empricism. Sun keeps rising in the east all the time. Most humans have two eyes, two ears, one nose and one mouth. If you boil water, it evaporates.
The problem really is no problem and has a straightforward answer which was essentially given at the beginning of the interview. Mathematics is the science of possible structures. No matter what structure the universe had, there would be a mathematical structure that the universe exemplifies. In other words, so long as he universe has laws, some mathematical structure will be useful in describing it. As Susskind put it, how could mathematics not be useful?
i always thought of math as more of a limit. not the answer. thats where the question really shines. what if we were able to see and know all of these things via another form of perception? we cant ever really know what other scientific method is possible because we might not ever be able to see it. what i understood was "its what we saw so we just built upon it and we will build upon it until we cant" like what i beleive is , kind of what he said, we see building block patterns and we took from them and built past our brain capabilities to sort of see beyond what we perceive but what if we were able to see more or what if there was something we couldnt see and we've been skipping over this whole time? how much more would we know? idk im babbling at this point, repeating shit. my point becomes redundant after this.
Here is Design: Hello Martin Godwyn Here is Chaos: a;klsdfhnlnrklf;kfna;kjflkmnewl;mkn;f Design works and you can understand it. Chaos doesnt work, and you cannot understand it. That is why mathematics works, because the universe was designed. Godwins
@@portaadonai Hi. There really is no significant difference between the two strings, independent, that is, of some predefined translation scheme (or language). The only reason why the first *looks* like it is designed and the second doesn't (to you), is because you forget that you already know and can recognize the patterns common in English. But the second string could just as easily look designed and the former look like "chaos" - if you spoke and recognized the orthography of a different language. And, there *are* orthographies that look not dissimilar. Take, for example, certain First Nations orthographies: Hul’q’umi’num’ or T̕łat̕łasiḵ̕wala or Kisipakakamak or Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch... okay, that last one is Welsh, but you get the point.
@@AmorLucisPhotography Yes it takes Design to make a sentence that makes sense. And it takes intelligence to understand a sentence. If design and intelligence is not involved in a sentence, you get randomness: asdlkaslhaslkhafsjlafhlfsklslhk ~If you use the language of math to decipher the universe and you get randomness, the universe was not designed. ~If you translate the language of the universe into math and find that its an understandable equation [sentence] then it was Designed, by Intelligence
For years I've been turning this over in my mind and this is the first time I've ever heard someone address the question of why we struggle to understand something. Most books, etc for lay person science-lite people like me are designed to explain sciencey stuff in a non-sciencey way. Cool. I've read a bunch of that, most I still do not understand. All good. But I've been struggling with trying to figure out why we do not understand the universe better. I've come to think it's because we evolved to think in a certain way and that the universe is simply not comprehendible to the way we think. That is, out brains work the way they do because, had they not, we'd not be here. I always looked at it as a we have evolved and survived in large part due to a grasp of cause and effect. Not run from that bear and be injured, eat that berry and feel awful, watch Baywatch and learn about lifeguarding,. So, when trying to understand the universe, our brain is using the cause and effect tool - which for keeping the species alive worked great - but simply is not sufficient to grasp a universe where that tool applies. Like using a hammer to turn a screw. Susskind raising the 3 dimensionality of our evolution is really another facet of that, which is, once you get beyond 3D or beyond where cause and effect can be applied, the universe may simply not be something which our brains are equipped to understand. That mathematics allows us to express that which our brain cannot conceptualize is a cool meta-take on it. No idea, why I wrote this other than Susskind is the closest I've ever come to hearing anyone else talk about this.
Agreed, my dude. He's basically saying that mathematics is our way of cheating evolution. We are hacking into dimensions/conceptions that nature did not naturally give us access to. Pretty cool stuff.
Random thought: I can't imagine more than three physical dimensions but I might have an example of thinking in higher dimensional space; let's say a pastry is composed of 12 different ingredients. Would that particular type of pastry be sitting in a 12 dimensional space (cookie space) in which all the different possible combinations of those ingredients are represented by other points in the space? For some reason I feel like I can actually grasp what it might be like to move around in 12 dimensional cookie space. Was that interesting or relevant at all?
Yes! I've grappled with ideas of extra dimensions since I read Flatland as a kid many moons ago. IDK, but it made an impression. I won't quite say eureka, you've sorted it all out for me, but I am very grateful for this new terminology. My monkey brain is better at imagining cookie space than an abstract n-dimensional grid.
You got the point. You act in the abstract "Cookie space" when you make cookies, even if the cookies are physically contained in a three dimensional space. Our lives involve infinite dimensions, I think, even if the space in which our bodies exist has only three dimensions.
In a multiverse setting, an ensemble of universes that evolve randomly where information pops up or disappears randomly can be reshuffled into a set of universes where information is conserved.
Daaaaaamn this dude got me trying to come up with a lot of answers to a question my philosophy teacher asked about reality and science. When she did I kinda just repeated what was written in the text she gave
Now, I can only look at his ears, and miss what's being said. It's been said he uses them as a radio telescope for observing the universe.. that's where he gets much of his knowledge.
because we made it to work, it is literally what we see and define it as it is and just extrapolate the other math from this which holds the property of still working as the basis being defined is correct, math is a human construct based off of physical truths that builds upon itself
In addition to our neural architecture preparing us for three dimensions and time, it also prepared us for things that obey patterns and laws. This is the reason that we cannot imagine a world without laws that obey mathematical principles, just as it is the reason that we cannot imagine seven dimensions.
I love Lenny,he doesn't suffer Fools gladly but he is one of our greatest living Minds and a wonderful Teacher,you can understand why he and Feynman were close Pals
Well mathematical axioms were built to work with the natural world. Simply put, mathrmatics is the language for describing complex systems so thatbwe can understand them. It just happens that natural languages are too weak in detail so we developed mathematics. Its not only for physics mind you, for example graph theory is extremely useful in computer science, neural networks and how society works. But most importantly mathematics is build on the sheer curiosity of what abstract connections we can make using the axioms, or negating them.
I don't think it's fair to say that lots of mathematical axioms are built to work with the natural world. Admittedly we often get some intuition from the natural world e.g., in geometry to get going sometimes. But so much of pure mathematics is done in a setting which is so far removed from the natural world that it doesn't make sense to say that it is "built to work with the natural world".
The key here is that both math and physical reality are both constructs with inherent properties that exist REGARDLESS of whether or not the other thing exists. 1+1=2 independent of anything else. Systems possess all of their inherent properties (mass, energy, momentum, etc.) regardless of whether you attempt to describe them with math or not. A fitting analogy is a hand and a block of soft clay. Why does your hand leave a perfect imprint in the clay when you press on it? The imprint itself isn't the hand, but it is a representation of the hand, that exists in physical reality. Math is the clay, physical reality is the hand. Math doesn't work because of physical reality and physical reality doesn't conform to math. The two are independent entities. Equations that describe physical reality (physics) are basically a mapping of physical reality onto a logical system that makes sense to our brain.
lkjk lkjlkjkl You have described the dualism position in the philosophy of mathematics. You are closer to theism because of it. Evidence that information is not physical.
Mathematics is a language. It also has precision! Einstein's thought experiments may have been equal to mathematics but when he needed to explain his experiments with precision, you need mathematics or different language.
Reality is a complex geometry (or set of relations), and mathematics is language for describing geometries. Even the line of whole numbers is really just a set of relations that describe a geometry. The human brain doesn’t process geometries outside the basic three physical dimensions, but it does process language. Thus, we can use a language of geometries to describe what our brains can’t otherwise handle. When you want to describe the indescribable, you have to create a language of the indescribable.
I am doing research for a book on exactly this subject. My thesis for Maths and the use of Numbers, Quantities, is that humans have needed to communicate with symbols they can agree on their value. We need to know how much water to drink, how much food to eat, how much money to pay, how many inches to measure, how many stones to collect; how many items to trade. A large part of science as the Modern era's dominant logic mode, comes from foundations of arguments made from the mid 1550's to the end of the 1600's. Numbers and Maths is about people believing in the value of the symbol, in the meaning of what the symbols mean in regards to each other, a number scale. Then, once we agree on the number scale, we then need some Standard to depict the physical likeness of the number, a straight edge for example. Once we reach this level of agreement, we can communicate in ways that elucidate patterns and relationships. Because we already agreed on the value of the symbols via a number scale, and the patterns of the Maths operations, then we cannot deny or "fake" results from the symbols that we already agree upon. If we cannot agree on the symbols and their values; if we cannot agree on a standard to represent those symbols, then Maths doesn't work.
Imagine if evolution produces, someplace(s), sometime, a life-form capable of sensing higher dimensions, for instance... "So Mr. Lifeform, on this table I'm sitting at lies the algebraic description of a tesseract..." "oh but I perceive it in front of me, actually your table stands just on one of its faces!"
Define logical. And...see Godel’s incompleteness theorems, when you have a theory that includes arithmetic, mathematics doesn’t always have an answer. Invention or discovery? I’d say, both.
Suomen poika If only Frege could have done it too ! My point is to say that there is not one logic, and it always remains an axiomatic construction. « Purely logical », in that regard, seems meaningless to me. The more you study maths the more you realise that what seemed obvious often becomes not even a consensus amongst mathematician.
exactly - to understand a materialist universe we use logic that was developed by describing the world around us...and move beyond describing just what we can perceive ourselves, and begin to develop a more abstract understanding of the universe that has to be verified with the scientific method
Tensors seem difficult to grasp, but they are essential to making manageable many otherwise intractable problems. Mathematics may benefit by educators describing the problems different discoveries (and/or inventions) solve. Like Feynman said, most of mathematical advances are improvements in notation, so what has to be conveyed is what the notations represent. The glorious equations of Einstein, Maxwell, and Schrodinger look beautiful, if incomprehensible. But dissecting these symbols to understand what they mean, what they represent - that's the challenge in learning mathematics. Sometimes English can elegantly paraphrase: "Electric fields radiate, and never circulate; magnetic fields circulate, and never radiate"; "Mass tells space how to curve, curved space tells mass how to move." But these are bereft of precision - you can't design a three phase motor or a gravity wave detector without the quantitative aspect of these concepts.
You gotta admire Leonard Susskind, because he is a genius and at the same time he doesn't come off as a nerd. About the subject: Every equation can be reduced to 1=1, which is a true statement. Using mathematics is the "simplest" way to make a true statement that doesn't need to be supported by any other arguments. There is no room for misunderstanding.
James, When Susskind makes one of his acidhead flourishes about entropy, he'll sometimes give a footnote to Shannon. Follow it up and you find he's just waving a hand at Shannon, the whole opus, not any specific thing in information theory that you can hold up against his speculative yawp to look for parallels or support. At a crucial point in one of his wild and self-serving books he hangs his whole thesis on a footnote to 't Hooft. You follow the footnote and you find there was a paragraph there once upon a time, 't Hooft had withdrawn it and written nothing supporting the original old speculation. I am left with the feeling that Susskind and 'tHooft may have had the same wild idea years ago, Susskind liked the flash but the Dutchman decided upon further examination that it didn't hold up. I don't see Susskind as influential at all. His early, elementary mathematical lectures seem to me good solid undergraduate stuff. Everything he's written or said since he hit San Francisco and fell under the spell of John Paul Rosenberg, the phoney-baloney motivational speaker and "est" blowhard, has been hazy hippy hoo-ha, barely physics at all.
I think underneath what he is saying and especially beginning at 4:06 is the idea of symbolism. Symbolism among humans is a very powerful linguistic phenomenon. He points to abstraction. Think of the "men" and "women" symbols on public bathrooms. For most humans today these symbols are self-explanatory abstractions. You don't need to share a specific language (Chinese, English, Spanish, etc) to understand that these symbols denote gender. This can be directly translated to the use of x, y, & z for 3-dimensions. He says he can imagine these dimensions in his head (like most humans) but the x,y, z is a shortcut, a symbol for quick notation, recall, understanding, and communication. And the addition of further letters is the addition of further symbols that denote something we don't have experiential knowledge of - but the mere fact that these additional letters are brought into the context of symbolic language we do understand means that they become somehow intelligible even if abstract. We don't need to have a reference for this symbol because the laws of this language create an "intuitive" framework for understanding. Disclaimer: I am horrible at math, and I'm not a linguist so forgive my less than articulate little statement but I am an artist and the use of symbols and intuition is something that I think most artists work with on a regular basis.
Proof of Design Hi juanlambda27! How are you [You can understand the text] Proof of Chaos aljksdfaksjdflmnaljkdnsfoaflkn [You cannot understand the text it is random] Proof of Design 1+1=2 [You can understand the math] Proof of Chaos 1+1=66 [You cannot understand the math] _We live in a Universe that is Designed by a Designer_
I think in the end, it's still just a model - albeit a good one. That's not quite right though. Because in this case, we need the model to work within itself, not just as a model. Can I say that the model works within itself because it is what it is modelling?
Eugine Wigner is a Genius. Thinker of mathematics and its unique nature to unravel the laws of physical reality. When Sir Isaac Newton wrote Principia Mathematica, obviously in Latin, he combined physics with Pure Math but he never questioned the philosophy of mathematical equations specially when he explained laws of Gravity. But Eugine has opened another window of human Wisdom through 'Unreasonable Effectiveness of Math'
Math works because we don't use them where they don't. If planar geometry does not work on a sphere, then we don't use planar geometry, but spherical geometry. If commutativity does not work, use a multiplication (such with matrix) that it does. Math works because if it doesn't, we change the model so that it works, or we don't use math if none we have imagined yet works. We can draw a circle with algebra... since Descartes, before, we couldn't unless using a compass. It is not that x^2 + y^2 = 1 is a circle, it is because of the relation that we build between the cartesian plane and the circle. And I insist on the word RELATION. The circle itself has no, or more exactly, does not need x and y to exist. And a cartesian plane can exist without circle in it. It is the RELATION between the circle, and the plane, and the algebra, … that makes the whole thing works... and if it doesn't, modify it until it does. The world was existing before Descartes, you know?
If you follow the "grammar" of math to manipulate a true Math statement you will generate another true Math statement. Assuming you follow the rules of math no matter if the manipulation of the statement is otherwise random, you may or may not understand the new statement but you know it is true. On the other hand if you only follow the grammar of some human language you will probably generate modified statements you understand as well as the original, but you have zero certainty that the new statement is as true as the original. Say, you have a high school word problem. You can't immediately solve it perhaps by inspection. You restate the problem as a mathematical equation. You guess Math manipulations to get to the answer. At first you may manipulate the original equation to get new equations or statements that you don't necessarily understand, but you know they are true. Finally you stumble upon a statement using experience, learning and training that answers the question. Is it correct?. Well since you used the "grammar" of Math to perform each manipulation, you know the answer has to be correct - because math manipulations always preserve truth. You cannot do this with ordinary human language that you learn naturally from birth. It's easy in human language to start with a true statement , follow the rules of the language's grammar and end up with a worthless false statement. Math manipulation of statements creates new statements and sometimes new insights and all of those statements and eventual insights are presumed true. Whether your math is geometry, trig, calc, set theory , topology, tensor algebra or formal logic, truth is preserved in this way. The symbols don't matter, it's the "grammatical " rules of Math that make the difference. This is one reason why math is the language of physics. imo. You can replace all the equal signs, pi's phi's, psi's, +'s with human words, it doesn't matter. It's the "grammar." You can use the "grammar" of Math to generate new insightful statements that you know are true, and you can form the insights without necessarily being able to form the ordinary intelligent thoughts otherwise needed to manipulate ideas. All the mind has to do is passively recognize when a new insight has been achieved. In addition, once an idea has been preserved in Math, it is preserved the way a musical score preserves melody and harmony and cadences. Human thoughts are the best , but they have a way of evaporating and are easily lost in translation from one person to the next.
Harry Kirk How do you manipulate words according to grammatical rules? There aren't rules for that, unless you mean logic, which is as reliable as math. And in fact logical manipulation of words is exactly what underpins math.
There are rules for generating infinitely many new statements that are valid language statements in a very obvious way. What you're referring to is something else entirely. There are no complete set of rules for generating every linguistically valid statement in language. Therefore every academic or contrived proposed grammar is therefore invalid due to a lack of completeness and accuracy. However, it would be very easy to generate rules that would I think always generate linguistically valid statements. So complete grammars do not exist but partial grammars do exist. They (certain rules) can be used to transform or alter any given statement to another different, linguistically valid language statement. If you don't have that, you cant make an iterative rule to (as Chomsky says) generate an infinite variety of valid language statements. For example: The sum mass of One B type rock weighs 5 pound. The sum weight of Two B type rocks weigh 5 pounds . The sum weight Three B rocks weigh 5 pounds. ..and so on for ever. This increasing the number by one rule always generates a new perfectly grammatically correct new sentence, albeit in a trivial way. Language doesn't care, or say ten to the twenty fifth power plus one is just too big to make a new valid statement in the language of humans. Every single generated statement is fine. Some might be more beautiful than others to some or harder to pronounce for some, but they're all fine. However, in Math(s) only one of the statements is correct. Which is also the way Physics seems to work. What you are also referring to is the fact that you can use words as symbols to do a great deal of mathematics or logic as you say, although I would doubt all of topology and geometry could be done with only words for symbols. I don't think so. Maybe.
Mathematics is a symbolic toolset we have created through the course of centuries. We invented these axioms, rules, methods during production and with the aim of improving the productive capacity of society. It was useful for agriculture, trade, construction etc. With improved productive capacity there is more surplus value (i.e. more free time since less people have physically labor to produce for society). More and more people had more and more time to delve deeper into this symbolic toolset in the abstract. An exercise us humans are attracted to like the way we are attracted to choreographed dancing and making art or music. It has became extremely popular and widespread now due to the aid it provides in discovering laws of nature and controlling certain aspects of nature. Math works because it started out with the aim of it working. It has been built by us to work for us.
I think the reason why math works for physics is something like this: The universe is comprised of, or at least defined and measurable in terms of, differences...many differences...and incidentally more instances of differences than there are kinds of differences. Mathematics, if abstracted sufficiently, can be looked at as a representation of all the ways in which multiplicities of differences can arrange themselves, including all the (interesting) ordered ways. Some of these ways are physically possible, with the constraints given by some of the fundamental ways that the physical differences do measurably group, combine, emerge at different organizational levels, and transform, and some of these ways (in which differences could theoretically combine and organize) are contingently not physically possible. But the mathematics, being of a kind to the actual difference-structures, but more abstract, i.e. containing nothing but the essential skeletal description of (isomorphism to) possible structures, with no necessity for carrying particular additional incidental properties that attach to extant physical structures, is more general and can also describe counterfactual hypothetical (other possible worlds) topologically possible arrangements of differences. All mathematics must itself be instantiated as physical embodied symbols in some finite? physical medium; as information embodied in particular representing clumps of matter/energy (that as usual features (useful in this case) differences.) But mathematical information is fungible... the information essence can remain the same while the representation changes, by processes of information-preserving transformations. Not only is the (externality-representing) mathematics humans use always embodied in some matter and energy, but also the REPRESENTED matter, energy, organizations and constraints and interactions thereof, and the fields / metric spaces (the subject of the physics) that the mathematics describes also literally contain (perhaps some information-transformed version of) the mathematics (the symbol organizations.) If the purported representing mathematics was CORRECTLY representing, then the math (its information - its informational entities and relations - i.e. its difference-organizations) are literally IN the physical subject matter (an aspect of it), (alongside other incidental properties of the physical subject matter) as well as being on the blackboard, in the computer, or in neural structures and processes in the minds of the mathematicians and physicists. That's probably why it works.
Evolution did not do it to us. Mathematics works because it is a form of logic (e.g. Principia Mathematica). If evolution wired us to use only intuition and visualization as our guides for reality, making it hard for us to envision the efficacy of math, where did our ability to to conceive of multi-dimensions come from?
+Unknown Texan Your post is a non-sequitur fallacy. Evolution did not equip us to visualize more than 3 dimensions because we've never had any kind of evolutionary reason to interact with them. Your logic is equivalent to an adult scolding a small child for not knowing how to drive a car. You further assert that these higher dimensions suddenly came into existence when YOU were made aware of them.
He's saying evolution didn't give us the ability to perceive more than three dimensions. However with the human language/construct of math it can be perceived.
Unknown Texan: except evolution almost certainly _did_ wire us for mathematics - at least for the basics, which we expanded upon culturally. Do we have to be taught that if we see two bears go into a cave, and one go out, that it's probably not a good idea to go into the cave? Crows can count to six or seven, so it seems very likely we too have some mathematical ability built in.
Juke, Nothing is being "perceived" in all this "dimensions" claptrap. Sloppy thinkers are just using a single word to cover directions in space (e.g. up and down, right-and-left, front and back, which are said to be three dimensions, not six, for some reason), degrees of freedom in mathematical or other theoretical constructs, and other loosey-goosey aspects of large notions. Kyzercube, above, is spot on.
@@solbanan It captures it because we're obviously designed, more intricately and PURPOSEFULLY than anything we ourselves have designed. Hello Forest! Meet the trees...
Leonard Susskind is right! In fact, mathematics is the language of physics, chemistry, and biology since the natural sciences depends on physics described in the form of mathematics to give coherent quantitative measurements and qualitative sense geared to explaining of all natural phenomena.
Math is just a mental tool that humans created to understand, organize, and predict the world around them. If I have 2 marbles in one hand and 3 in the other, then I put them all into an empty bag I can know there will be 5 marbles in the bag. Even before I do it. Higher level math is the same basic understanding applied in a much more complicated form. I'm only in Calc 2, but I still have to apply addition, subtraction, multiplication, division, and understand fractions. A friend of mine who is about to graduate from college can use calculus in his field of electronic engineering. This allows him to create complicated machinery even before the pieces are made for the machine.
I can't believe one wouldn't pitch a simpler answer. (a) Math is quantitative so allows to have a tight grasp on the extent or degree something is one way or another (unlike "English language") and (b) Math is first and foremost a system of strict reasoning and logic. So it really works "by design". The question really is why the world admits simple enough models to make predictive/testable conclusions.
It's the finite human brain who doesn't like it, not the math. Math is just a language for thinking about stuff. ;-) But yeah, IMO from an existentialist perspective there's no reason to think that dimensionality ends with our 4D spacetime. Everything that can exist exists (including all stuff describable by our maths) but only a finite/limited part of it can be observed because the rest is beyond various horizons. So.. this is more about figuring out which part of the infinite we are observing.
Mathematics is a system created by extra ordinary humans in this planet. It works in our human point of perspective. In other words, Mathematics works for us humans because it is base on what we assume to be true and therefore, the numbers add up. If we go to another planet with a different system of numbers, we will not understand it from our point of view. I think I will go to bed now.
That's not true at all; the truths of mathematics are independent of the means by which math is symbolized. There are 5 platonic solids anywhere in the universe.
Thank you Lenny, Len I think the inanimate Universe communicates 24/7 in an inanimate language and mathematics` is the language of the Universe, we being animate are evolving the dimensional perception to understand the Universe speaking to its self and to all animate choice applicators, when we fully evolve our maximum capacity we will in equivalence converse and understand our Universe speaking to us and follow the direction the language tells us we should go, peace and love, your Metaphysical Bro., Doug.
Maths are the blueprints for all things... They are the consequential parallels to all of reality. They are a kind of abstract thinking to help us describe things which are in existence as well as that which is not so, it even describes things which are manifested in the mind to produce 'real world' results.
Leonard Susskind has a special gift beyond his obvious scientific genius. He's a teacher and he knows how to teach. I remember one of his first lectures in the Theoretical Minimum. The topic involved complex numbers. He turned to the class and asked "Does everyone understand complex numbers?". A few responded, but not many. He asked again - and then with a giggle said "Okay, let's go over complex numbers". Leonard shares his knowledge with anyone who's willing to listen. Simply put - he's a great man.
F Adler he says he loves to teach because this helps him get a deeper grasp on things. Hell of a win-win
Mathematics work because of evolution ? Well, that is not quite an exact answer !
Wouldn't it be a Physical way, to say it works, because it is based on observation ?
In another lecture he asked "Is anybody not familiar with complex numbers? If so, stand up and be humiliated."
struggling to explain things to a novice is a good way to keep check of your knowledge - he's also extremely efficient at neglecting unnecessary parts of the equation -- the way he talks skips over all unnecessary detail, it's just a joy to watch, because he demonstrates (maybe inadvertently) the processes that helps you quickly identify a winning answer as opposed to a dead end.
@Enter the Braggn' Its not a dumb question. We can't make math work, math works with or without or input. We discover proofs that just happen to be correct, 1 +1 = 2 because it does, not because WE made it so.
5:20... Mathematical intuition. That's the prize you receive at the bottom of the box after years of studying mathematics.
When kids ask "why do I have to learn this nonsense and when am I ever going to use it" this is always my go-to answer.
My own mathematical intuition had served me better than everything else I've ever learned, combined.
Are the benefits confined to STEM for you or do you feel it's contributed to how your engage with the world/concepts in general?
@@forbescallum It's helped tremendously in STEM (made understanding machine learning much later in life a total breeze) but it's also made me a more clear thinker and even a better writer (as odd as that sounds).
Fact of the matter is that studying math fundamentally changes how you approach life.
Awesome. My comfort zone is verbal logic, or something like that. I'm decent at programming and philosophising. Well, guess that's up for others to decide but I've been told that's the case. I'm starting to think maths is a key thing I'm missing. We solve problems in maths but I get the impression that the process we engage in to do so is more important, regardless of whether the problem gets solved. The reorientation of perspective and drawing together of apparently disparate areas of knowledge is key. It's about looking at problem spaces differently, not just individual problems. And we do that in philosophy too but there's something about the unambiguous truth values of maths that could make teach me 'rigorous creativity'. Have I got that right?
@@forbescallum Pretty much spot on. So you're at the beginning of your math journey?
@@thetedmang pretty much. I watch Numberphile and 3blue1brown but I need to get stuck in with the fundamentals, and start solving problems myself.
I love listening to Leonard Susskind. He is like a bridge between very complex things and my brain.
Without math we predict by visualisation. But using symbols for quantities balanced in equations, and manipulating these equations, we can predict beyond our ability to visualise.
Dude.... Yes!
Math works because we are (1) lucky that patterns in math match patterns in the "physical" universe, or (2) because the universe is nothing but math (virtual).
@@bobaldo2339 (3) God is a theoretical physicist.
Even so humans are really bad at basic physical intuition. The mathematics guides us to see past our often faulty instincts.
well no - there are many geometric solutions to General Relativity - just like advanced geometries can be visualizable sometimes and others times not - we have a choice we can do either or we can do both - just like euclidean geometry and non-euclidean geometry can both be perfectly valid and yet so different
Mike Ehrmentrout is a smart guy
Mike has lost some weight. Good for Mike.
@@steelsteez6118 swoosh
Olk
Yeah, don't cross him. He's not afraid to get extremely tough, even if it's not personal.
Bit of John Malkovich in there too.
Brilliant explanation of how mathematics works, and its power of understanding.
Here is this nervous young man asking questions of a superhero. The superhero is grace and kindness to the young man. What a great teacher.
I once asked this question to a young professor of math at Princeton. He said, "I don't think about these things, I just do the math."
AriBenDavid I asked this question in 9th grade and he said ,”it’s just the way it is.”
Yeah some profs are very dull, but creative scientists tend to think about everything.
@@againstsociety5308 Actually my first words were this question
@@roqsteady5290I must be a creative scientist then 🙂
@@Kraft_Funk I feel like mine were too 😅
I studied chemistry and once sat through a lecture showing the development from integers to the simplest axioms of math and then continuing all the way to series and differential calculus. So it went all from first principles and "quantum" integers to the continuous math of integrals and differentials. It all hangs together quite neatly and coherently.
After that I thought: "Well, if you consider the conservation laws governing physics, or in other words that 1 plus 1 always makes 2, then a universe which has any conservation laws must necessarily be one that is ruled by mathematics. A universe where 1 plus1 does not make 2 in all cases necessarily is unpredictable in the sense of being not strictly mathematical, and life can probably not exist there, because life needs reliable rules for input and output to work on. So, ultimately, this universe we live in may just be a mathematical one because 1 plus 1 makes 2 and everything else in math results from this starting point. Therefore there are, for instance, Legendre polynoms which together with their linear combinations form the basis of how atomic and then molecular orbitals look and behave. Because 1 plus 1 makes 2, the proper constraints together with the right dimensions and introduction of the Kronecker delta give you exactly these polynoms which are the underlying reason why atoms react with each other exactly the way they do."
the reason behind 1+1=2 itself came from abstract mathematical proofs and because of our working with decimal number system... abstract mathematics gives reasoning for all the crazy stuffs and their results are been used by scientists to represent their theory and discover beautiful structure in them
"Exploiting online games" Mcgraw, Garry. Was thinking about that book earlier today. Guess it's a good read if Susskind has it!
i don't believe that's his house/flat
Small correction for: 0:12 Gedankenexperiment, aka thought experiment. Not Duncan experiment, as the caption says. :)
the evolution of neural dimensional architecture is an amazing concept really.
The way I look at it - Mathematics is a language of infinite variability, thus there will be one answer that maps most accurately to reality in an infinite sea of less accurate answers.
This video could not have been recommended at a better time: I'm halfway through an essay on scientific realism.
Mathematics is simply a way of bringing precision to our descriptions of the world and the way we perceive the world. An we have a tendency to want to get more and more precise in our descriptions... That's why we need a language of precision where we are all on the same page.
This man never, ever, seize to amaze me!
I really love how articule he is
i know you probably didn't do it on purpose, but that is hilarious 😆
No need to ridiculate the guy.
Broccoli Highkicks classic
hahaha - the word is "articulate". I love how articule you are.
@@rippspeck ridiculate sounds like a harry potter spell
did not, Kant have this same issue basically in the 1750s? (specifically talks to the "architecture of mind" point I believe!)
Dear Udacity,
Thank you for posting this video.
Watching it (while taking a break from school work revision) is therapeutic for the mind.
(Paraphrasing): Mr Susskind talked about using mathematics to explain physics. Multidimensional stuff...
As humans who evolved the ages, the way we visualize things are limited. To explain a physics concept, etc it would be hard to tell someone to visualize it. Hence we use mathematical equations to describe and explain. Someone who has developed a mathematical intuition over time, will be able to "visualize" such complex phenomenon.
Appreciate the stretching of the mind.
Leonard Susskind is one of only a very few I hold a great deal of respect for, his buddy Dick Feynman, even moreso.
Both of these men have opened my thinking into area's I never was aware I had, in more than 60 years of life. Not in the details of the advanced physics, that both stand head and shoulders, above their peers, in my opinion, but in their way of 'seeing", 'understanding"...how IT all works, and fits together, yet, humble enough to admit the vastness of what they don't know.
Both men have admitted the critical importance of 'mathematics", while also admitting 'math" is a man made construct, and that math MAY not be ONLY solution to achieve answers. But, it is the best we have, for now.
I think it is the the blending of theoretical physics and philosophy, that both of these men mastered in a unique way, that has made me gain such respect for both.
If these 2 men can teach a dummy like me, the basics of the incredibly complex world of 'quantum physics", in a manner that helps me "get it"...they are truly great teachers.
Freeman Dyson, is another that stands out, in my book. A genius that understood, and hated, the entire "Phd." farce, and proud to never having to be subject to it.
Sadly, the world is lacking great teachers and minds like these.
xXxA- I never said, ..." math was completely and utterly useless ...", I think it is a wonderful invention of mankind, maybe the best invention, but it is a "tool", after all.
Perhaps, as a tool, math is not being used correctly, or "math" itself, has reached it's limit in terms of written calculations or equations we humans express.
I simply don't "worship" math as anything more than an a extremely useful tool...math is great, but some solutions to questions can not be written in equations, there are too many unknown factors to achieve concrete answers.
2:10 This reminds me about what I read recently regarding the Monty Hall problem. We're hard wired to wrongly perceive the true odds of the problem. The same could be said about many problems in probability and statistics. The same could be said about the nature of quantum physics and inherent uncertainty of the universe, it defies our built in reasoning so we have a hard time coming to grips with it. Trust the mathematics instead.
This man has wisdom 🧠🤝
Love this man. He holds your attention.
I think mathematics is so useful as a tool to describe our world because that's kind of what it was initially made for. Some merchants needed to inventory their warehouse, some architect needed it to determine the number of stones for a wall, a navigator for plotting a course, and the mathematicians managed to abstract from this and make multipurpose tools.
That GOF Design Patterns book is everywhere! :)
It is one of the few physical paper books I still open once in a while.
Nice to see _Refactoring_ on his bookshelf beside _Design Patterns_
I was surprised to see these books there as well. Also, hi Joe! :-)
A book on Refactoring?!
@@hmdz150 The original book by Martin Fowler.
@@jbrains He is probably in a CS department.
Leonard Susskind is one of the greatest scientist of our times, he is very honest also about the limits of knowledge and science in general.
Great perspectives, have been watching Susskind's lectures re Qm with keen interest, thanks
Any chance they can amend/update the subtitles, they aren't quite correct :-(
Would only take a few mins surely...
When I read his book I imagine his voice.
FANTASTIC EXPLANATION...THE BEST EXPLANATION ON MORE DIMENSIONS i HAVE HEARD!!! SERIOUS...
Very sensible and down to earth explanation.
Mathematics, all it encompasses and that it implies seems essential to me, a complex and comprehensive matter of necessity; that which can not, not be.
you know you are a CS graduate when you instantly notice Design Patterns chilling on the book shelf
That means it's not Susskind's office
@@t8m8r prove it.
As a souvenir from years ago maybe. Also has Javascript. Who still uses books, when by the time you finish one, it's practically outdated.
It's remarkable, that you can hear that he was befriended by Richard Feynman, just by how he speaks. I wish i was older and had the opportunity to speak to Feynman too.
interesting take and very well put. I always find his views insightful. Certainly very reminiscent of Feynman!
Professor Susskind is a man of faith. "The world has some coherence to it. Things don't just randomly happen. " One needs faith to believe that things just randomly happen.
Not faith. Empricism. Sun keeps rising in the east all the time. Most humans have two eyes, two ears, one nose and one mouth. If you boil water, it evaporates.
The problem really is no problem and has a straightforward answer which was essentially given at the beginning of the interview. Mathematics is the science of possible structures. No matter what structure the universe had, there would be a mathematical structure that the universe exemplifies. In other words, so long as he universe has laws, some mathematical structure will be useful in describing it. As Susskind put it, how could mathematics not be useful?
i always thought of math as more of a limit. not the answer. thats where the question really shines. what if we were able to see and know all of these things via another form of perception? we cant ever really know what other scientific method is possible because we might not ever be able to see it. what i understood was "its what we saw so we just built upon it and we will build upon it until we cant" like what i beleive is , kind of what he said, we see building block patterns and we took from them and built past our brain capabilities to sort of see beyond what we perceive but what if we were able to see more or what if there was something we couldnt see and we've been skipping over this whole time? how much more would we know? idk im babbling at this point, repeating shit. my point becomes redundant after this.
Here is Design:
Hello Martin Godwyn
Here is Chaos:
a;klsdfhnlnrklf;kfna;kjflkmnewl;mkn;f
Design works and you can understand it. Chaos doesnt work, and you cannot understand it. That is why mathematics works, because the universe was designed. Godwins
@@portaadonai huh interesting actually
@@portaadonai Hi. There really is no significant difference between the two strings, independent, that is, of some predefined translation scheme (or language). The only reason why the first *looks* like it is designed and the second doesn't (to you), is because you forget that you already know and can recognize the patterns common in English. But the second string could just as easily look designed and the former look like "chaos" - if you spoke and recognized the orthography of a different language. And, there *are* orthographies that look not dissimilar. Take, for example, certain First Nations orthographies: Hul’q’umi’num’ or T̕łat̕łasiḵ̕wala or Kisipakakamak or Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch... okay, that last one is Welsh, but you get the point.
@@AmorLucisPhotography Yes it takes Design to make a sentence that makes sense.
And it takes intelligence to understand a sentence.
If design and intelligence is not involved in a sentence, you get randomness: asdlkaslhaslkhafsjlafhlfsklslhk
~If you use the language of math to decipher the universe and you get randomness, the universe was not designed.
~If you translate the language of the universe into math and find that its an understandable equation [sentence] then it was Designed, by Intelligence
For years I've been turning this over in my mind and this is the first time I've ever heard someone address the question of why we struggle to understand something. Most books, etc for lay person science-lite people like me are designed to explain sciencey stuff in a non-sciencey way. Cool. I've read a bunch of that, most I still do not understand. All good. But I've been struggling with trying to figure out why we do not understand the universe better. I've come to think it's because we evolved to think in a certain way and that the universe is simply not comprehendible to the way we think. That is, out brains work the way they do because, had they not, we'd not be here. I always looked at it as a we have evolved and survived in large part due to a grasp of cause and effect. Not run from that bear and be injured, eat that berry and feel awful, watch Baywatch and learn about lifeguarding,. So, when trying to understand the universe, our brain is using the cause and effect tool - which for keeping the species alive worked great - but simply is not sufficient to grasp a universe where that tool applies. Like using a hammer to turn a screw. Susskind raising the 3 dimensionality of our evolution is really another facet of that, which is, once you get beyond 3D or beyond where cause and effect can be applied, the universe may simply not be something which our brains are equipped to understand. That mathematics allows us to express that which our brain cannot conceptualize is a cool meta-take on it. No idea, why I wrote this other than Susskind is the closest I've ever come to hearing anyone else talk about this.
Agreed, my dude. He's basically saying that mathematics is our way of cheating evolution. We are hacking into dimensions/conceptions that nature did not naturally give us access to. Pretty cool stuff.
A great explanation by a brilliant man.
Please turn up the volume. Thanks for the upload.
Subscription to a description makes it so, Leonard. That is why. We work out everything, from our perception.
Random thought: I can't imagine more than three physical dimensions but I might have an example of thinking in higher dimensional space; let's say a pastry is composed of 12 different ingredients. Would that particular type of pastry be sitting in a 12 dimensional space (cookie space) in which all the different possible combinations of those ingredients are represented by other points in the space? For some reason I feel like I can actually grasp what it might be like to move around in 12 dimensional cookie space.
Was that interesting or relevant at all?
Yes!
I've grappled with ideas of extra dimensions since I read Flatland as a kid many moons ago. IDK, but it made an impression. I won't quite say eureka, you've sorted it all out for me, but I am very grateful for this new terminology. My monkey brain is better at imagining cookie space than an abstract n-dimensional grid.
You got the point. You act in the abstract "Cookie space" when you make cookies, even if the cookies are physically contained in a three dimensional space.
Our lives involve infinite dimensions, I think, even if the space in which our bodies exist has only three dimensions.
Perhaps our imagination is a dimension of it's own. The "space" in which all possible things can exist.
In a multiverse setting, an ensemble of universes that evolve randomly where information pops up or disappears randomly can be reshuffled into a set of universes where information is conserved.
Daaaaaamn this dude got me trying to come up with a lot of answers to a question my philosophy teacher asked about reality and science. When she did I kinda just repeated what was written in the text she gave
This dude has magnificent ears.
@planet42 he was just talking in circles. Fuddling. Not much of a substance. Sorry.
Now, I can only look at his ears, and miss what's being said. It's been said he uses them as a radio telescope for observing the universe.. that's where he gets much of his knowledge.
because we made it to work, it is literally what we see and define it as it is and just extrapolate the other math from this which holds the property of still working as the basis being defined is correct, math is a human construct based off of physical truths that builds upon itself
In addition to our neural architecture preparing us for three dimensions and time, it also prepared us for things that obey patterns and laws. This is the reason that we cannot imagine a world without laws that obey mathematical principles, just as it is the reason that we cannot imagine seven dimensions.
I love Lenny,he doesn't suffer Fools gladly but he is one of our greatest living Minds and a wonderful Teacher,you can understand why he and Feynman were close Pals
Is that “Design Patterns” on the shelf? Respect.
as someone who hates OOP, disrespect :P
Well mathematical axioms were built to work with the natural world. Simply put, mathrmatics is the language for describing complex systems so thatbwe can understand them. It just happens that natural languages are too weak in detail so we developed mathematics. Its not only for physics mind you, for example graph theory is extremely useful in computer science, neural networks and how society works.
But most importantly mathematics is build on the sheer curiosity of what abstract connections we can make using the axioms, or negating them.
I don't think it's fair to say that lots of mathematical axioms are built to work with the natural world. Admittedly we often get some intuition from the natural world e.g., in geometry to get going sometimes. But so much of pure mathematics is done in a setting which is so far removed from the natural world that it doesn't make sense to say that it is "built to work with the natural world".
how multiplication comes from natural world, area of a square, negative times negative and so on.
Beautifully explained.
Very illuminatory! Thanks.
yep!...things don`t random happen... :)
some things do happen randomly, but randomness also adheres to rules described by mathematics.
Hi. The law of large numbers is the reason why many random events happening together end up being almost completely understandable.
@@bocckoka example of something completely random?
@@mitcHELLOworld nuclear decay?
@@bocckoka hidden variable? No it is a very good example though :)
The key here is that both math and physical reality are both constructs with inherent properties that exist REGARDLESS of whether or not the other thing exists. 1+1=2 independent of anything else. Systems possess all of their inherent properties (mass, energy, momentum, etc.) regardless of whether you attempt to describe them with math or not. A fitting analogy is a hand and a block of soft clay. Why does your hand leave a perfect imprint in the clay when you press on it? The imprint itself isn't the hand, but it is a representation of the hand, that exists in physical reality. Math is the clay, physical reality is the hand. Math doesn't work because of physical reality and physical reality doesn't conform to math. The two are independent entities. Equations that describe physical reality (physics) are basically a mapping of physical reality onto a logical system that makes sense to our brain.
lkjk lkjlkjkl You have described the dualism position in the philosophy of mathematics. You are closer to theism because of it. Evidence that information is not physical.
1+1 is defined as 2
@@santafucker1945 no it isn't.
@@william41017 please elaborate your disagreement.
@@santafucker1945 1+1=10.
What a beautiful walkthrough
What a genius explanation!
Nobody:
Evolution: You know i had to do it to 'em
shut up, andrew
shut up, andrew
Mathematics is a language. It also has precision! Einstein's thought experiments may
have been equal to mathematics but when he needed to explain his experiments
with precision, you need mathematics or different language.
God, I love listening to this man speak. I was too young to be around for Feynman, but I'll take Susskind instead any day.
Reality is a complex geometry (or set of relations), and mathematics is language for describing geometries. Even the line of whole numbers is really just a set of relations that describe a geometry. The human brain doesn’t process geometries outside the basic three physical dimensions, but it does process language. Thus, we can use a language of geometries to describe what our brains can’t otherwise handle. When you want to describe the indescribable, you have to create a language of the indescribable.
He reminds me of Mike from "breaking bad"
Aman Deep So so sooo much
Wow.
And I'm glad the kid shut up and let him continue to answer the question, unlike many adults.
I am doing research for a book on exactly this subject. My thesis for Maths and the use of Numbers, Quantities, is that humans have needed to communicate with symbols they can agree on their value.
We need to know how much water to drink, how much food to eat, how much money to pay, how many inches to measure, how many stones to collect; how many items to trade.
A large part of science as the Modern era's dominant logic mode, comes from foundations of arguments made from the mid 1550's to the end of the 1600's.
Numbers and Maths is about people believing in the value of the symbol, in the meaning of what the symbols mean in regards to each other, a number scale. Then, once we agree on the number scale, we then need some Standard to depict the physical likeness of the number, a straight edge for example.
Once we reach this level of agreement, we can communicate in ways that elucidate patterns and relationships. Because we already agreed on the value of the symbols via a number scale, and the patterns of the Maths operations, then we cannot deny or "fake" results from the symbols that we already agree upon.
If we cannot agree on the symbols and their values; if we cannot agree on a standard to represent those symbols, then Maths doesn't work.
We have come to a point that we need more than our brains to understand the complexity of the word around us, and that is when Math comes into play.
Imagine if evolution produces, someplace(s), sometime, a life-form capable of sensing higher dimensions, for instance...
"So Mr. Lifeform, on this table I'm sitting at lies the algebraic description of a tesseract..."
"oh but I perceive it in front of me, actually your table stands just on one of its faces!"
Mathematics works because it consists of purely logical developments upon a verifiable counting system?
Define logical.
And...see Godel’s incompleteness theorems, when you have a theory that includes arithmetic, mathematics doesn’t always have an answer.
Invention or discovery?
I’d say, both.
Yea but why should the universe, the natural world behave according to the rules of those logical developments.
Suomen poika If only Frege could have done it too !
My point is to say that there is not one logic, and it always remains an axiomatic construction.
« Purely logical », in that regard, seems meaningless to me.
The more you study maths the more you realise that what seemed obvious often becomes not even a consensus amongst mathematician.
This guy is such a logical, procedural thinker. If you guys haven't checked out his lectures on math and physics, I suggest you do
exactly - to understand a materialist universe we use logic that was developed by describing the world around us...and move beyond describing just what we can perceive ourselves, and begin to develop a more abstract understanding of the universe that has to be verified with the scientific method
he looks much like John Malkovich
Lmao
He looks exactly like him!
Great takeaway. Amazing.
Some DMT could help
Thanks Joe.
Thanks, Joe
Tensors seem difficult to grasp, but they are essential to making manageable many otherwise intractable problems. Mathematics may benefit by educators describing the problems different discoveries (and/or inventions) solve. Like Feynman said, most of mathematical advances are improvements in notation, so what has to be conveyed is what the notations represent. The glorious equations of Einstein, Maxwell, and Schrodinger look beautiful, if incomprehensible. But dissecting these symbols to understand what they mean, what they represent - that's the challenge in learning mathematics. Sometimes English can elegantly paraphrase: "Electric fields radiate, and never circulate; magnetic fields circulate, and never radiate"; "Mass tells space how to curve, curved space tells mass how to move." But these are bereft of precision - you can't design a three phase motor or a gravity wave detector without the quantitative aspect of these concepts.
You gotta admire Leonard Susskind, because he is a genius and at the same time he doesn't come off as a nerd.
About the subject: Every equation can be reduced to 1=1, which is a true statement. Using mathematics is the "simplest" way to make a true statement that doesn't need to be supported by any other arguments. There is no room for misunderstanding.
Professor Susskind is probably the most influential physicist of the 21st century.
Stephen Hawking's still alive.
James,
When Susskind makes one of his acidhead flourishes about entropy, he'll sometimes give a footnote to Shannon. Follow it up and you find he's just waving a hand at Shannon, the whole opus, not any specific thing in information theory that you can hold up against his speculative yawp to look for parallels or support.
At a crucial point in one of his wild and self-serving books he hangs his whole thesis on a footnote to 't Hooft. You follow the footnote and you find there was a paragraph there once upon a time, 't Hooft had withdrawn it and written nothing supporting the original old speculation. I am left with the feeling that Susskind and 'tHooft may have had the same wild idea years ago, Susskind liked the flash but the Dutchman decided upon further examination that it didn't hold up.
I don't see Susskind as influential at all. His early, elementary mathematical lectures seem to me good solid undergraduate stuff. Everything he's written or said since he hit San Francisco and fell under the spell of John Paul Rosenberg, the phoney-baloney motivational speaker and "est" blowhard, has been hazy hippy hoo-ha, barely physics at all.
more popular doesn't mean more relevant
sounds like someone has a hard on for susskind
Hawking is more popular. Ed Witten is likely to be the most influential. Susskind is also quite influential. Another one is Maldacena.
Casually 'Exploiting Online Games' sitting on the shelf.
There is the book "Design Patterns: Elements of Reusable Object-Oriented Software" by the Gang of four in the library! Cool!
I think underneath what he is saying and especially beginning at 4:06 is the idea of symbolism. Symbolism among humans is a very powerful linguistic phenomenon. He points to abstraction. Think of the "men" and "women" symbols on public bathrooms. For most humans today these symbols are self-explanatory abstractions. You don't need to share a specific language (Chinese, English, Spanish, etc) to understand that these symbols denote gender. This can be directly translated to the use of x, y, & z for 3-dimensions. He says he can imagine these dimensions in his head (like most humans) but the x,y, z is a shortcut, a symbol for quick notation, recall, understanding, and communication. And the addition of further letters is the addition of further symbols that denote something we don't have experiential knowledge of - but the mere fact that these additional letters are brought into the context of symbolic language we do understand means that they become somehow intelligible even if abstract. We don't need to have a reference for this symbol because the laws of this language create an "intuitive" framework for understanding.
Disclaimer: I am horrible at math, and I'm not a linguist so forgive my less than articulate little statement but I am an artist and the use of symbols and intuition is something that I think most artists work with on a regular basis.
Proof of Design
Hi juanlambda27! How are you
[You can understand the text]
Proof of Chaos
aljksdfaksjdflmnaljkdnsfoaflkn
[You cannot understand the text it is random]
Proof of Design
1+1=2
[You can understand the math]
Proof of Chaos
1+1=66
[You cannot understand the math]
_We live in a Universe that is Designed by a Designer_
Nothing is real except math
:P
It's effective in the sciences because of the range of it's applicability
You've gotta spend a wee bit of time with epistemology.
And you a wee bit of time with Godel
@@Onoma314 uh, i don't see how gödel and epistemology are mutually exclusive.
3:31 Admitting God created the Universe.
3:32 Regretting saying God created the Universe.
I think in the end, it's still just a model - albeit a good one.
That's not quite right though. Because in this case, we need the model to work within itself, not just as a model.
Can I say that the model works within itself because it is what it is modelling?
Did the math come before the physics, or came physics before math... did the universe create itself or is it just a process of multiverses ...
Eugine Wigner is a Genius. Thinker of mathematics and its unique nature to unravel the laws of physical reality.
When Sir Isaac Newton wrote Principia Mathematica, obviously in Latin, he combined physics with Pure Math but he never questioned the philosophy of mathematical equations specially when he explained laws of Gravity. But Eugine has opened another window of human Wisdom through 'Unreasonable Effectiveness of Math'
Who would have known that Breaking Bad was home to so many scientist?
Math works because we don't use them where they don't.
If planar geometry does not work on a sphere, then we don't use planar geometry, but spherical geometry.
If commutativity does not work, use a multiplication (such with matrix) that it does.
Math works because if it doesn't, we change the model so that it works, or we don't use math if none we have imagined yet works.
We can draw a circle with algebra... since Descartes, before, we couldn't unless using a compass. It is not that x^2 + y^2 = 1 is a circle, it is because of the relation that we build between the cartesian plane and the circle. And I insist on the word RELATION. The circle itself has no, or more exactly, does not need x and y to exist. And a cartesian plane can exist without circle in it. It is the RELATION between the circle, and the plane, and the algebra, … that makes the whole thing works... and if it doesn't, modify it until it does. The world was existing before Descartes, you know?
it is like discovering Creators logic.
I'm not sure if Descartes would agree with on the world not existing...
جَزَاكَ ٱللَّٰهُ خَيْرًا......وفقك الله الطريق الصحيح...شكراً
Why are so many programming books in Dr Susskinds’ room? I can see Gang of Four design patterns book to his left
If you follow the "grammar" of math to manipulate a true Math statement you will generate another true Math statement. Assuming you follow the rules of math no matter if the manipulation of the statement is otherwise random, you may or may not understand the new statement but you know it is true. On the other hand if you only follow the grammar of some human language you will probably generate modified statements you understand as well as the original, but you have zero certainty that the new statement is as true as the original. Say, you have a high school word problem. You can't immediately solve it perhaps by inspection. You restate the problem as a mathematical equation. You guess Math manipulations to get to the answer. At first you may manipulate the original equation to get new equations or statements that you don't necessarily understand, but you know they are true. Finally you stumble upon a statement using experience, learning and training that answers the question. Is it correct?. Well since you used the "grammar" of Math to perform each manipulation, you know the answer has to be correct - because math manipulations always preserve truth. You cannot do this with ordinary human language that you learn naturally from birth. It's easy in human language to start with a true statement , follow the rules of the language's grammar and end up with a worthless false statement. Math manipulation of statements creates new statements and sometimes new insights and all of those statements and eventual insights are presumed true. Whether your math is geometry, trig, calc, set theory , topology, tensor algebra or formal logic, truth is preserved in this way. The symbols don't matter, it's the "grammatical " rules of Math that make the difference. This is one reason why math is the language of physics. imo. You can replace all the equal signs, pi's phi's, psi's, +'s with human words, it doesn't matter. It's the "grammar." You can use the "grammar" of Math to generate new insightful statements that you know are true, and you can form the insights without necessarily being able to form the ordinary intelligent thoughts otherwise needed to manipulate ideas. All the mind has to do is passively recognize when a new insight has been achieved. In addition, once an idea has been preserved in Math, it is preserved the way a musical score preserves melody and harmony and cadences. Human thoughts are the best , but they have a way of evaporating and are easily lost in translation from one person to the next.
Harry Kirk How do you manipulate words according to grammatical rules? There aren't rules for that, unless you mean logic, which is as reliable as math. And in fact logical manipulation of words is exactly what underpins math.
There are rules for generating infinitely many new statements that are valid language statements in a very obvious way. What you're referring to is something else entirely. There are no complete set of rules for generating every linguistically valid statement in language. Therefore every academic or contrived proposed grammar is therefore invalid due to a lack of completeness and accuracy. However, it would be very easy to generate rules that would I think always generate linguistically valid statements. So complete grammars do not exist but partial grammars do exist. They (certain rules) can be used to transform or alter any given statement to another different, linguistically valid language statement. If you don't have that, you cant make an iterative rule to (as Chomsky says) generate an infinite variety of valid language statements. For example: The sum mass of One B type rock weighs 5 pound. The sum weight of Two B type rocks weigh 5 pounds . The sum weight Three B rocks weigh 5 pounds. ..and so on for ever. This increasing the number by one rule always generates a new perfectly grammatically correct new sentence, albeit in a trivial way. Language doesn't care, or say ten to the twenty fifth power plus one is just too big to make a new valid statement in the language of humans. Every single generated statement is fine. Some might be more beautiful than others to some or harder to pronounce for some, but they're all fine. However, in Math(s) only one of the statements is correct. Which is also the way Physics seems to work. What you are also referring to is the fact that you can use words as symbols to do a great deal of mathematics or logic as you say, although I would doubt all of topology and geometry could be done with only words for symbols. I don't think so. Maybe.
"I don't know the answer." Done.
Mathematics is a symbolic toolset we have created through the course of centuries. We invented these axioms, rules, methods during production and with the aim of improving the productive capacity of society. It was useful for agriculture, trade, construction etc. With improved productive capacity there is more surplus value (i.e. more free time since less people have physically labor to produce for society). More and more people had more and more time to delve deeper into this symbolic toolset in the abstract. An exercise us humans are attracted to like the way we are attracted to choreographed dancing and making art or music.
It has became extremely popular and widespread now due to the aid it provides in discovering laws of nature and controlling certain aspects of nature.
Math works because it started out with the aim of it working. It has been built by us to work for us.
I think the reason why math works for physics is something like this: The universe is comprised of, or at least defined and measurable in terms of, differences...many differences...and incidentally more instances of differences than there are kinds of differences. Mathematics, if abstracted sufficiently, can be looked at as a representation of all the ways in which multiplicities of differences can arrange themselves, including all the (interesting) ordered ways. Some of these ways are physically possible, with the constraints given by some of the fundamental ways that the physical differences do measurably group, combine, emerge at different organizational levels, and transform, and some of these ways (in which differences could theoretically combine and organize) are contingently not physically possible. But the mathematics, being of a kind to the actual difference-structures, but more abstract, i.e. containing nothing but the essential skeletal description of (isomorphism to) possible structures, with no necessity for carrying particular additional incidental properties that attach to extant physical structures, is more general and can also describe counterfactual hypothetical (other possible worlds) topologically possible arrangements of differences. All mathematics must itself be instantiated as physical embodied symbols in some finite? physical medium; as information embodied in particular representing clumps of matter/energy (that as usual features (useful in this case) differences.) But mathematical information is fungible... the information essence can remain the same while the representation changes, by processes of information-preserving transformations. Not only is the (externality-representing) mathematics humans use always embodied in some matter and energy, but also the REPRESENTED matter, energy, organizations and constraints and interactions thereof, and the fields / metric spaces (the subject of the physics) that the mathematics describes also literally contain (perhaps some information-transformed version of) the mathematics (the symbol organizations.) If the purported representing mathematics was CORRECTLY representing, then the math (its information - its informational entities and relations - i.e. its difference-organizations) are literally IN the physical subject matter (an aspect of it), (alongside other incidental properties of the physical subject matter) as well as being on the blackboard, in the computer, or in neural structures and processes in the minds of the mathematicians and physicists. That's probably why it works.
Evolution did not do it to us. Mathematics works because it is a form of logic (e.g. Principia Mathematica). If evolution wired us to use only intuition and visualization as our guides for reality, making it hard for us to envision the efficacy of math, where did our ability to to conceive of multi-dimensions come from?
By adding W and V...
+Unknown Texan Your post is a non-sequitur fallacy. Evolution did not equip us to visualize more than 3 dimensions because we've never had any kind of evolutionary reason to interact with them.
Your logic is equivalent to an adult scolding a small child for not knowing how to drive a car.
You further assert that these higher dimensions suddenly came into existence when YOU were made aware of them.
He's saying evolution didn't give us the ability to perceive more than three dimensions. However with the human language/construct of math it can be perceived.
Unknown Texan: except evolution almost certainly _did_ wire us for mathematics - at least for the basics, which we expanded upon culturally. Do we have to be taught that if we see two bears go into a cave, and one go out, that it's probably not a good idea to go into the cave? Crows can count to six or seven, so it seems very likely we too have some mathematical ability built in.
Juke,
Nothing is being "perceived" in all this "dimensions" claptrap. Sloppy thinkers are just using a single word to cover directions in space (e.g. up and down, right-and-left, front and back, which are said to be three dimensions, not six, for some reason), degrees of freedom in mathematical or other theoretical constructs, and other loosey-goosey aspects of large notions.
Kyzercube, above, is spot on.
He subconsciously knows the brain was "purposefully built" but his rebellious conscious nature caught & corrected his Theistic slip.
No, it's just that it makes sense to say "purposefully built" because it captures how the evolutionary forces constrain and mold us in distinct ways.
@@solbanan It captures it because we're obviously designed, more intricately and PURPOSEFULLY than anything we ourselves have designed. Hello Forest! Meet the trees...
Leonard Susskind is right! In fact, mathematics is the language of physics, chemistry, and biology since the natural sciences depends on physics described in the form of mathematics to give coherent quantitative measurements and qualitative sense geared to explaining of all natural phenomena.
Unless you read On the Origin of Species. No math
Very understandably...beautiful.
We really are just an advanced breed of monkeys... crazy.
leonard is sus
Math is just a mental tool that humans created to understand, organize, and predict the world around them. If I have 2 marbles in one hand and 3 in the other, then I put them all into an empty bag I can know there will be 5 marbles in the bag. Even before I do it. Higher level math is the same basic understanding applied in a much more complicated form. I'm only in Calc 2, but I still have to apply addition, subtraction, multiplication, division, and understand fractions. A friend of mine who is about to graduate from college can use calculus in his field of electronic engineering. This allows him to create complicated machinery even before the pieces are made for the machine.
I can't believe one wouldn't pitch a simpler answer. (a) Math is quantitative so allows to have a tight grasp on the extent or degree something is one way or another (unlike "English language") and (b) Math is first and foremost a system of strict reasoning and logic. So it really works "by design". The question really is why the world admits simple enough models to make predictive/testable conclusions.
Dimensions rise to infinity after the forth.math doesn't like infinity.
Does that make any sense to anyone besides myself?
It's the finite human brain who doesn't like it, not the math. Math is just a language for thinking about stuff. ;-)
But yeah, IMO from an existentialist perspective there's no reason to think that dimensionality ends with our 4D spacetime. Everything that can exist exists (including all stuff describable by our maths) but only a finite/limited part of it can be observed because the rest is beyond various horizons.
So.. this is more about figuring out which part of the infinite we are observing.
Mathematics is a system created by extra ordinary humans in this planet. It works in our human point of perspective. In other words, Mathematics works for us humans because it is base on what we assume to be true and therefore, the numbers add up. If we go to another planet with a different system of numbers, we will not understand it from our point of view. I think I will go to bed now.
That's not true at all; the truths of mathematics are independent of the means by which math is symbolized. There are 5 platonic solids anywhere in the universe.
Thank you Lenny, Len I think the inanimate Universe communicates 24/7 in an inanimate language and mathematics` is the language of the Universe, we being animate are evolving the dimensional perception to understand the Universe speaking to its self and to all animate choice applicators, when we fully evolve our maximum capacity we will in equivalence converse and understand our Universe speaking to us and follow the direction the language tells us we should go, peace and love, your Metaphysical Bro., Doug.
Maths are the blueprints for all things... They are the consequential parallels to all of reality. They are a kind of abstract thinking to help us describe things which are in existence as well as that which is not so, it even describes things which are manifested in the mind to produce 'real world' results.