Theories of Everything with Curt Jaimungal Norman Wildberger on the Problem with Infinity, The Foundations of Mathematics, Finitism, and the Real Numbers
Feb 9, 2022
Norman Wildberger, a professor of pure mathematics from the University of New South Wales and the mind behind Insights into Mathematics, dives deep into the concept of infinity. He challenges traditional views, arguing that infinity cannot be 'done' and critiques its role in physics and mathematical computations. The discussion also touches on the limitations of real numbers, the inherent complexities of circle computation, and the need for rethinking foundational mathematical concepts. Wildberger advocates for a more grounded approach, emphasizing clarity in understanding and teaching mathematics.
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Infinity's Core Problem
- Norman Wildberger's main issue with infinity is the assumption of completing infinite tasks.
- He believes in focusing on doable, computationally-representable mathematics.
Computational Limits
- Wildberger demonstrates computational limits with examples like factoring large numbers and calculating e^7.
- He highlights how these operations become impossible with increasingly large numbers, even before reaching infinity.
Invalid Definitions
- Wildberger argues that the definition of e^7 is invalid due to its reliance on infinite steps.
- He compares it to defining something based on an unreachable point, like the end of a rainbow.
