The evolution of mathematics, from agriculture to quantum mechanics | Michelle Thaller


Oğuzhan, you asked, why is mathematics the
universal language? And this is something I’ve actually thought
a lot about. Mathematics is in some ways kind of scary
in how useful it is at really describing how the universe works around us. Now, to give you an idea, the origin of mathematics
seems very straightforward. We can count on our fingers up to 10, and
maybe it was useful to understand how many sheep you had? So you could start counting sheep and then
you either added or subtracted sheep as you got more or as you lost some. It was a simple thing. We learned how to count. We learned how to add and subtract. The idea of multiplying and dividing is a
little more abstract, but that also makes sense. That’s something that we can kind of visualize. But then what amazes me is that this led us
on a tremendously complicated journey that’s still going on to this day. And we had no idea where this would lead us. If you can do multiplication and subtraction,
it’s not too long before you begin to develop the basic building blocks of calculus. And calculus describes how moving objects
can change, how things can accelerate. If you want to describe an apple falling from
a tree to the ground or a ball rolling down a hill, that’s calculus. It’s the mathematics of how things can change
over time. That’s really interesting, and the amazing
thing is it works so well. If you use these equations to predict how
a ball will roll down a hill, reality matches that. It really does tell you how something is going
to behave. So now we’ve gone from counting on our fingers
how many sheep we have to being able to predict what the universe around us is going to do. That’s incredibly powerful. Now we look around us and we see things like
planets orbiting the stars or the galaxy turning around, and we realize those equations of
motion apply to everything else in the universe. It’s not just here. It’s not just on the surface of the Earth,
but we can look at things literally billions of light years out in space, and they’re following
those same rules of mathematics. But now things got strange. We started to play with calculus. We started to see where it would go. What happens if you put in more variables
and you solve for more things at once? And we end up with some very strange abstract
concepts that turned out to be surprisingly useful. One of the things that kind of worries me
is something called imaginary numbers. Imaginary numbers are numbers that don’t really
make sense in our proper definition of mathematics. Take, for example, the square root of negative
1. Now, in mathematics, if you multiply something
by itself it always turns out to be a positive number. That’s never a negative number. But somebody said, what happens if we start
to do the mathematics of how an imaginary number — this can’t be real. The square root of negative 1 doesn’t make
any sense. But it turns out to be able to describe how
things rotate, and that became the foundation of quantum mechanics. And here’s the thing, now when you use a number
that shouldn’t exist — that doesn’t make any sense — it predicts exactly how an atom
will vibrate, It will predict how quantum mechanics at a very small scale runs, and
it needs a type of math that doesn’t make any real sense to us but it works. It works perfectly. So we keep getting led farther and farther
down this rabbit hole. Where does math lead us? Now we realize that you can describe physics
incredibly well if you allow the universe to exist in many different dimensions– more
than three dimensions that we’re familiar with. In fact, specifically, if you want to do particle
physics, it requires 11 dimensions. That’s not something our minds comprehend,
but we can do the math. We can do the math of how things would behave
if they could move in 11 different directions. And it turns out to predict exactly the results
we get from particle physics. That’s kind of scary. Does that mean that’s real? Are there really 11 dimensions? The math works so well, and the predictions
are so strong that it can’t just be nonsense. But now we’ve gone to the limit of what I
can tell you; is it real or not? Our math has given us something incredibly
useful, but it’s taken us completely out of our realm of common sense, of human scale
of how our minds work and even our sense of space and time. I don’t think that journey’s over yet. Where is math going to lead us? It may lead us to understand things like the
universe is a type of a hologram? That was a mathematical solution to How things
work around a black hole, and it works really, really well. So I think it’s wonderful and a little bit
scary that you start counting on your fingers. You get to 11 dimensions of space and time. And where else?

Comments

  1. Michelle Thaller,she is a very good orator.She expresses so clearly her lecture that it becomes easier to understand what she is trying to say.

  2. math is not the universal language or the language of the universe. The logic is. And math is just a way of visualizing or explaining the logic. The logic is simply reasoning. What causes what. This is the language of the universe. Something causes something to happen and this leads to another thing. And that is what we call time. Which is entropy.

  3. Mathematics is good at "modeling" which is the description of certain types of phenomena under certain conditions. However, when you apply that to the real world, it only works for those phenomena that you are using it to describe, and the rest of reality is ignored. On the other hand, math is a lot of fun.

  4. This woman is a prime example of high IQ individual trying to put some sense into sheep. Now you can go back to watching Kim Kardashian videos. SHEEP !!!!!!!

  5. 1. I share the philosophical idea that Math is a human invention (and yeah, I don't deny the fact that its explanatory power is a big problem for that position)

    2. Scientist talk a lot of shit about philosophy… But hear them babbling about, for example, numbers, and you'll understand why philosophy is necessary.

  6. Very unterresting point of view. However, math is not always right like when the series 1+2+3+4+… = -1/12. I know this identyty have been used in the theory behind Casimir effect, but to me it's still a non sens.

    Also, the imaginary number, i or j depending of the convention, is well used in engineering. It is extensivly used in electricity, in noise ans vibration. It then is not as mysterious as you say here. It is a very practical way to write wave functions or transfer fonctions.

  7. Love this woman! Explains things in a manner in which even us ignorant folk can understand! 😁. I’ve learned from her about many things! Thanks for all you do! I can’t wait for the day a Scientist runs for for President! 👍

  8. Assume we were "spirits" first — multi-dimensional beings who wanted one thing: to make new experiences.
    So we created a sort of "sandbox", which is our spacetime. Only 3 dimensions, plus time, but with an arrow, a preferred direction of movement we cannot invert: the "arrow of time". And all the "imaginary" math is just dealing with all the rest, with all those higher dimensions, which are "above" the three dimensions we are able to grasp right now in this form of existence.
    The purpose? Only if there is such an arrow of time there will be change: a state "before" (now knowing something), and a later state "after", when we have learned it and did make this experience.
    To learn in this manner would not be possible from our original, multi-dimensional "spirit"-point of view; there we would overlook all (time) states at once; we could never experience a change due to having learned something new ourselves.
    So our "job" here sould be exactly that: to learn, to make experiences. And maybe the universe (the matrix?) keeps presenting us always the right task we need for our next ecperience.

  9. I like looking up at the clear night sky wondering if there is an intelligent life form out there on a distant planet looking up at their night sky wondering the same thing.

  10. This lady and Hakeem Oluseyi are so good and fun to listen too I am just glued to there speech…Thanks for your hard work so us mortals can understand some of whats going on around us.

  11. 11 dimensions? There is time and the original 3, but what are the others? We solve the Schrodinger equation in the quantum physics class, but we don't see those other 7 dimensions.

  12. Everything is quantitized and has a minimum. We need to use quantitized math. It solves the singularity conundrum.

  13. I love this video and I just want to clarify something:
    "Imaginary numbers" are as real as any number can be. We can think of real numbers as a straight line, you only go forward or backwards, meaning one dimension. But we think of "imaginary numbers" as an infinite plane, we can go forward, backwards, up and down and any combination of the above. With this, "imaginary numbers" live in two dimensions.
    So "imaginary numbers" allow us to to do mathematics in two dimensions in a more flexible way, more importantly calculus.
    We may ask, can we make three dimensional numbers? Hamilton found out that that's not possible but four dimensions work and later we found out that 8 works, and also 16 and so on. But each time we go higher and higher we lose nice properties that make mathematics less and less "useful".

  14. It doesn't matter whether math is "real" or not: the whole thing could be wrong. However that would mean that we would have found something that is even greater and more "real" than math, for example. We can never truly know what is ultimately real or not, and that's fine, because we'll always perceive reality imperfectly.

  15. I think music is the universal language. Not Math. All people can understand what music says to them. It is personal. Mathematics says nothing of value to me. String Theory would agree

  16. Dr. Michelle Thaller is such a nice lady, the type of individual I wish I had why struggling with simple algebra even. 5/2019

  17. Me/Not-Me – 1 and 2. Them/Me – 1 and 2. Us – More than 2. Projected into shape Geometry, they become Platonic Solids. Numbers and Abstractions.. I am There/ I am not There – 1 and -1.. Ain Soph /Ain Soph Aur – Zero and before Zero. Still an Abstraction and not the Thing though surely. It remains 'A' Language.

  18. [-1] sqrt is Euler BS and 11th dimension more BS for $$$ of university teachers. Physics, pfft, design a car.

  19. Math is always ahead of experimental science . It took one hundred yrs to detect gravitational waves from the time it was predictable. I am scared of String Theory because if proved in a lab the consequences are unimaginable .
    I believe eventually we will .

  20. Listening to a teacher repeatedly use adjectives such as 'scary' to describe the effectiveness of math when communicating the deeper subtleties of nature, the probability is high that the majority of what's being said is bluff and bluster. Unfortunately some may be bamboozled to think that 11 dimensional holographic space is actually science rather than fantasy. There are serious problems in many of the models used to describe the nature of space, so for those who have a genuine interest in the development of cosmology check out the YouTube channel SkyScholar. Peace!

  21. I just came to add to the many comments going on about how great Michelle Thaller is. Splendid speaker and educator

  22. I really wish I could understand mathematics, beyond the obvious basics. To me it’s a mysterious language that only a relatively small group of us can speak, or think in. I actually feel quite left out. Reminds me of the movie “A Beautiful Mind” where everything he perceives is a mathematical equation. Blessing? Or curse?

  23. Dr M Thaller and N deGrasse Tyson are my heros. Is there something wrong with me? Probably but I don't care. All scientists are my heros

  24. Here is a theory. You mentioned 11 dimensions. And what if the universe is a hologram. What if each of our senses are the frequencies of each dimension? And when each dimensions collide this dimension is created? There is theory that we have more than 5 senses, so what if???

  25. There is only 1 logical conclusion to where mathematics will lead us.
    Our inevitable creation of a sentient self improving AI.
    Followed by the collapse of human civillization either by annihilation or a merge with AI on some level.

  26. I have become a big fan! I'm a math teacher and I have to make a few comments. I think it could be misleading to some to say, for example, that i (square root of -1) "doesn't make sense." It doesn't (or didn't) make intuitive sense but it did become intuitively sensible when it was attached to a coordinate model and interpreted via rotations. Please avoid the suggestion that i=sqrt (-1) is somehow not "real" (in the common sense of the word.)

  27. We are a pattern seeking species. The fact we believe our modest understanding of mathematics is our downfall in discovering a unified theory. All our so called understanding is from a third party outside point of view. In short, does the act of observation change the outcome?

  28. I WOULD LIKE TO GET A MANATEE NEAR THE SURFACE AND BURN ITS EYES WITH A GIANT MAGNIFYING GLASS AND THEN BOIL IT ALIVE FOR SOME MANATEE SANDWICHES !

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