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  • Some people ask the question of what good is mathWhat is the relationship between

  • math and physicsWell, sometimes math leadsSometimes physics leadsSometimes they

  • come together because, of course, there’s a use for the mathematicsFor example,

  • in the 1600s Isaac Newton asked a simple question: if an apple falls then does the moon also

  • fallThat is perhaps one of the greatest questions ever asked by a member of Homo sapiens

  • since the six million years since we parted ways with the apesIf an apple falls, does

  • the moon also fallIsaac Newton said yes, the moon falls because

  • of the Inverse Square LawSo does an appleHe had a unified theory of the heavens, but

  • he didn't have the mathematics to solve the falling moon problemSo what did he do

  • He invented calculusSo calculus is a direct consequence of solving the falling moon problem

  • In fact, when you learn calculus for the first time, what is the first thing you doThe

  • first thing you do with calculus is you calculate the motion of falling bodies, which is exactly

  • how Newton calculated the falling moon, which opened up celestial mechanics.

  • So here is a situation where math and physics were almost conjoined like Siamese twins,

  • born together for a very practical question, how do you calculate the motion of celestial

  • bodiesThen here comes Einstein asking a different question and that is, what is

  • the nature and origin of gravityEinstein said that gravity is nothing but the byproduct

  • of curved spaceSo why am I sitting in this chair?  A normal person would say I'm

  • sitting in this chair because gravity pulls me to the ground, but Einstein said no, no,

  • no, there is no such thing as gravitational pull; the earth has curved the space over

  • my head and around my body, so space is pushing me into my chairSo to summarize Einstein's

  • theory, gravity does not pull; space pushesBut, you see, the pushing of the fabric of

  • space and time requires differential calculusThat is the language of curved surfaces, differential

  • calculus, which you learn in fourth year calculus. So again, here is a situation where math and

  • physics were very closely combined, but this time math came firstThe theory of curved

  • surfaces came firstEinstein took that theory of curved surfaces and then imported

  • it into physics. Now we have string theoryIt turns out

  • that 100 years ago math and physics parted waysIn fact, when Einstein proposed special

  • relativity in 1905, that was also around the time of the birth of topology, the topology

  • of hyper-dimensional objects, spheres in 10, 11, 12, 26, whatever dimension you want, so

  • physics and mathematics parted waysMath went into hyperspace and mathematicians said

  • to themselves, aha, finally we have found an area of mathematics that has no physical

  • application whatsoeverMathematicians pride themselves on being uselessThey love being

  • uselessIt's a badge of courage being useless, and they said the most useless thing of all

  • is a theory of differential topology and higher dimensions.

  • Well, physics plotted along for many decadesWe worked out atomic bombsWe worked out

  • starsWe worked out laser beams, but recently we discovered string theory, and string theory

  • exists in 10 and 11 dimensional hyperspaceNot only that, but these dimensions are super

  • They're super symmetric.  A new kind of numbers that mathematicians never talked about evolved

  • within string theoryThat's how we call itsuper string theory.”  Well, the

  • mathematicians were flooredThey were shocked because all of a sudden out of physics came

  • new mathematics, super numbers, super topology, super differential geometry

  • All of a sudden we had super symmetric theories coming out of physics that then revolutionized

  • mathematics, and so the goal of physics we believe is to find an equation perhaps no

  • more than one inch long which will allow us to unify all the forces of nature and allow

  • us to read the mind of GodAnd what is the key to that one inch equationSuper

  • symmetry, a symmetry that comes out of physics, not mathematics, and has shocked the world

  • of mathematicsBut you see, all this is pure mathematics and so the final resolution

  • could be that God is a mathematicianAnd when you read the mind of God, we actually

  • have a candidate for the mind of GodThe mind of God we believe is cosmic music, the

  • music of strings resonating through 11 dimensional hyperspaceThat is the mind of God.

Some people ask the question of what good is mathWhat is the relationship between

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B1 中級

郭道夫:神は数学者なのか? (Michio Kaku: Is God a Mathematician?)

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    ykk に公開 2021 年 01 月 14 日
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