There is a curious parallel between definitional difficulties in physics and in mathematics. The Austrian physicist and philosopher Ernst Mach (1838 1916) advocated a particularly empirical approach to how fundamental concepts in physics ought to be introduced: by linking definitions to explicit measurements.

In this video we discuss Mach's thinking, talk about the difficulties with several fundamental elementary concepts in physics, especially the problematic issue of "mass", which has seen considerable evolution over the centuries, up to modern quantum field theory.

And then we compare the situation with the corresponding difficulties in modern pure mathematics where definitions often float freely in a thought bubble ultimately pinned down by "prior understanding" and "intuition" rather than by explicit procedures for writing down expressions.

This discussion is particularly important when we try to understand Special Relativity.

Video Contents:
00:00 Ernst Mach
2:02 Key concepts of physics
5:10 Critical role of mass
12:16 Confusions in physics and in mathematics


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