34 comment  view:34   blogger:0 view

  1. Lex Fridman

    I really enjoyed this conversation with Grant. Here's the outline:
    0:00 – Introduction
    1:56 – What kind of math would aliens have?
    3:48 – Euler's identity and the least favorite piece of notation
    10:31 – Is math discovered or invented?
    14:30 – Difference between physics and math
    17:24 – Why is reality compressible into simple equations?
    21:44 – Are we living in a simulation?
    26:27 – Infinity and abstractions
    35:48 – Most beautiful idea in mathematics
    41:32 – Favorite video to create
    45:04 – Video creation process
    50:04 – Euler identity
    51:47 – Mortality and meaning
    55:16 – How do you know when a video is done?
    56:18 – What is the best way to learn math for beginners?
    59:17 – Happy moment

  2. Lara Erikson

    Grant and lex conversation about abstraction from visualisation to the concept of infinity and the very essence of science is the highlight of this video. So succinct and apt to use the abstraction as processed by an AI to human concepts. Love your work Lex and Grant. Keep up the good work.

  3. Nnish Anad

    Love you lex but sometimes I have know idea what your trying to say…. thanks for bringing Grant Sanderson on. Good episode.

  4. Parimal Paritosh

    Weird how 3B1B isn't a 45 year old balding guy. That was my first impression.

  5. Timo Möbes

    Very exciting character and thanks, Lex, for making this interview happen.

  6. Gourav Dangey

    You have created a great channel, Lex, and your interview with Grant was fascinating.

    However, while I agree that we should not expect alien intelligent species to have developed mathematics the same way as we have, Grant needs a better example than the real numbers. The real numbers comprise the unique complete ordered field. Furthermore, the reals are the completion of the natural numbers, through the intermediate steps of the integers and rational numbers. The natural numbers are the result of applying a successor function to the empty set.

    I cannot imagine a mathematical system without the empty set. it may well take thousands of years before aliens understand their mathematics, like it did for us from the time Euclid discovered axiomatic proofs. But any alien species must eventually understand how the unique complete ordered field is a natural consequence of accepting the empty set as real. They may use different axioms than Zermelo-Fraenken, but they must have a number system isomorphic to our reals.

    It is not our choice that measurements made in our universe produce real numbers. Every intelligent species in this universe must develop something isomorphic to the real numbers because that is dictated by quantum physics for measurements. Similarly for the complex numbers.

  7. Arkadeep

    Whenever you are puzzled about abstractions, consider what doctors are doing. They are giving some extremely realistic and practical service to the society and yet, in their minds they are thinking of the body to be composed of interacting organ systems. These organ systems are the abstractions. You can never think of a cardiovascular system completely separated from the musculoskeletal system. I mean, where would you draw the line? Every system has structures, molecules and properties, some of which are similar to other systems while some are unique.

    The reason thinking in these terms are essential because, in medical science you are given a complex system to work with and you want to reduce it down to basic principles. That’s why the infinity here is blown inwards. Since we are approaching the lower levels of organization from a higher one, the definitions that work at a higher level of organization, breaks down at lower levels. When we finally zero in on finer details of the human body, the definitions we made earlier dissociate into abstractions. A very well defined concept of organ systems at an organismic level disappears in the cytological level.

    Just like convolutional neural networks, human knowledge too is studying every subject at several resolutions. And definitions made at one level can become abstract or inconceivable, when we simply alter the resolution of our thought.

  8. Kurt Loban

    Favorite Quote from CGP Grey, regarding 51:47 – "Death gives life meaning? This is madness. Misery doesn't give happiness meaning. Happiness is meaning itself…No parent would ask the reaper to wrinkle their child's skin, weaken their bones, dim their vision and their minds, cripple them in a thousand ways over decades to ultimately kill them, 'to give their life meaning', and so your brain gives you sweet lies that the horrors that you can't avoid are good for you."

  9. Tom Ryan

    Hey Lex! Enjoying the podcasts. Maybe you'd be interested in having Isaac Arthur as a guest? He talks about sci fi things but also touches on AI in some videos. Just a suggestion

  10. liszt

    No, yea, yes

  11. Roos B

    Very interesting conversation!
    The part where you talk about living in a simulation got me thinking. Grant says that the computational power/resources needed to simulate our universe would be impossible to have. But that is an argument based on what is possible in our world.
    However, there should be another universe where we are simulated in. And simulations that we run are usually less complex than our own world. Therefore, there might be a more complex world that simulates our simple universe, one in which those resources would be readily available.

    Of course this is also an argument inferred from our experience. I guess we're not really getting anywhere, are we? 🙂

  12. liszt

    “we should be clear about terminology“

  13. liszt


  14. CreationTribe

    @31:50 "I'm just as uncomfortable with you are." … I'm stealing this. what a great way to shorten a bunch of words in a way that everybody thinks it was a mistake. I'm going to you did.

  15. Henri Krynauw

    Wow that was awesome ! Thanks a lot for these podcasts.

  16. Walter Alter

    Alien civilizations and their mathematics? The far more interesting question is – Why would it requires an infinite universe and an infinite amount of time to create a single planet containing sentient mammals?

  17. Jaap Versteegh

    Grant is great. I'm looking forward to the time when he's "no longer dating" the Riemann zeta function and just sees her for "who she truely is" 😀 !

  18. Александр Багмутов

    My favourite so far, thx!

  19. chematarraga

    This is so fruitful

  20. Soumya

    I donot know if anybody will agree with me on this…Grant has a weirdly beautiful voice !

  21. Justin Kellner

    SOLID content thanks from wisconsin

  22. Ryan Mahuron

    Was just thinking about how great it would be to have him on your podcast. You are two of the most impressive channels out there, thank you both for doing this interview!

  23. Thomas Carlsen

    Math is a model language….so of course math itself is invented – it is a silly question.
    To elaborate. The physical world is what we were interested in to begin with or patterns in system etc.. But to comprehend the physical world and express/simplify patterns we model it/them with math. So one can argue if the patterns were invented by us or not – that is a valid question if you ask me. The physical world was certainly there already so for us to simplify or understand it better we model it with math. So math was invented to explain the physical world which was there. I do not like this question at all. Math is just a mapping of "things" to numbers/symbols. Everything can represented as numbers. So the question should be about what the numbers represents. Math within itself have different fields and forms that are not comparable.
    Don't want to hate but I see this question being asked a lot and people forget why math came about and what math is.

  24. tariq elkhatit

    First time on this channel. I subscribed right away.
    Thanks for the interview

  25. Austin Fastidio

    34:50 This is why I have always thought it important to view math as a language.

  26. StoneChickenImagica

    Lex, you're a hero and so are all the people you interview!

  27. synchronium24

    This is not the crossover we deserve, but the crossover we need. Thanks for having Grant on the podcast!

  28. Johannes Terzis

    His Linear Algebra videos are nothing short of revolutionary. They make a topic of mathematics which often seems just algorithmic and abstract into something intuitive which you can draw up in your head.

  29. Tom Meyers

    Do one on low IQ races. Like the ones we are building a wall to keep out. Thanks.

  30. Yogesh Kulkarni

    Which mathematics Grant is talking about around 2:50…any references?

  31. B

    Grant is on a whole other level than Lex.

  32. Charles Van Noland

    Nope, not gonna cut it: you're going to need to have Grant as a recurring podcast guest a few times a year, at the very least, because this was some great stuff. Maybe not particularly AI-specific, but great stuff nonetheless.

  33. Charles Van Noland

    As far as the argument about the Pythagorean is concerned, I agree with what Grant is saying about how our representation of space is what makes the theorem hold true. For instance: if we represented 2D space/coordinates entirely using polar coordinates, with a 0-360 angle and then a radius or magnitude at that angle, is there any equivalent for the Pythagorean in that space? What if polar coordinates is the defacto widely-used coordinate system among alien beings, and they've discovered truths about that spatial representation that we've yet to come close to discovering?

  34. Adam Gaskill

    You gotta get Sal khan on here

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