Edward Frenkel
speaker
2,304 appearances
1 recordings
1 series
first heard Apr 2023
last heard Apr 2023
Edward Frenkel’s voice in public audio — every appearance, attributed to the second.
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So any field of mathematics can be presented as what is called the formal system.
And at the core of the formal system is a system of axioms or postulates.
These are the statements which are taken for granted.
Without proof.
An example would be, so one of the very first formal systems was the system, was Euclidean geometry, developed by Euclid in his famous book, Elements, about 2200 years ago.
And it's about, well, it's a subject familiar from school, because we studied.
But what it's really about is about the geometry of the plane.
And plane by plane, I mean just this tabletop extended to infinity in all directions, kind of a perfect plane, a perfectly even table.
And so Euclidean geometry is about various geometric figures on the plane, specifically lines, triangles, circles, things like that.
So what's an example of an axiom?
An example of an axiom is that if you have two points which are distinct, two points on the plane, then there is a unique line which passes through them.
Now, it kind of sounds reasonable, but this is an example of an axiom.
In mathematics, you have to have a seed, so to speak.
You have to start with something.
And you have to choose certain postulates or statements which you simply take for granted, which do not require proof.
Usually, they are ones which are kind of intuitively clear to you.
But in any case, you cannot have any mathematics without choosing those sections.
The observer comes in the process of choosing the axioms.
Who chooses the axioms?
As Alan Watts liked to say, who is watching the watchers?
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