Explore the fundamental question of whether the universe is geometric or algebraic in this thought-provoking Einstein Lecture by Minhyong Kim. Delve into the historical context of this inquiry, from Platonic solids and Pythagorean philosophy to modern concepts in computer vision and cognitive science. Examine the interplay between numbers and shapes in nature, including complex numbers and Clifford algebras. Investigate the role of geometry and algebra in quantum mechanics, particle physics, and arithmetic geometry. Gain insights into how mathematicians and physicists approach this profound question about the nature of reality, concluding with perspectives from contemporary thinkers like Nima Arkani-Hamed.
Is the Universe Geometric or Algebraic? by Minhyong Kim
International Centre for Theoretical Sciences via YouTube
Overview
Syllabus
DATE: 21 December 2018, 15:00 to
Is the Universe Geometric or Algebraic?
Platonic solids
Pythagoras: All is number
1. Perception
A Puzzle
Shapes and Numbers
Computer Vision
'The Mind's New Science: a History of the Cognitive Revolution' by Howard Gardner
ll. Reality
Number or Shape?
lll. Some numbers in nature
Points on a line
Points in the plane
Complex numbers
Question
Geometric algebra or Grassmann algebra
V. Number and shape in the 19th century II: Clifford
Clifford algebra
Clifford on space and gravity
Clifford on number and shape
VI. Some elaboration on microscopic numbers
Addition of particles
Schroedinger's Cat
Inspiration + Perspiration
Multiplication of particles
So why is this operation multiplication?
VII. Arithmetic Geometry
From Numbers to Shapes
Numbers - Shapes
Is the universe number or shape?
Nima Arkani-Hamed
Taught by
International Centre for Theoretical Sciences
