Finite versus infinite and number systems | Sociology and Pure Mathematics | N J Wildberger

Описание: A social scientist wanting to understand the culture of mathematics needs also to have at least some familiarity with the role of number systems throughout history. This is a rich and surprising topics, and in subsequence videos in the series we will be investigating quite different historical roles, starting with the fascinating Egyptian and Mesopotamian number systems and then move forward towards to modern European epochs and eventually the current difficulties that beset the so-called theory of "arithmetic with real numbers".

There are many important sociological questions that arise when looking at the almost deliberate attempt by the academy to ignore discussion of this crucial topic.

The rift between the realities of computational mathematics and the dreaming of pure mathematics in the direction of "real numbers", "infinite series" and "transcendental functions" (just to get started) is now so pronounced that it is become impossible to dismiss. One place to anchor the discussion in the difference between studying a finite discrete system, say a list or sequence , and the corresponding "infinite or unbounded" concepts --which are at their core quite different mathematical objects and need to be treating quite differently.

So let's start a wide ranging discussion about the role of numbers in mathematics, and how to explain the sociological forces that maintain the pretense that all is well despite obvious evidence to the contrary.

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Here are all the Insights into Mathematics Playlists:

Elementary Mathematics (K-6) Explained:    / playlist  
list=PL8403C2F0C89B1333
Year 9 Maths:    • Плейлист  
Ancient Mathematics:    • Плейлист  
Wild West Banking:    • Плейлист  
Sociology and Pure Mathematics:    • Плейлист  
Old Babylonian Mathematics (with Daniel Mansfield):    / playlist  
list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
Math History:    • Плейлист  
Wild Trig: Intro to Rational Trigonometry:    • Плейлист  
MathFoundations:    • Плейлист  
Wild Linear Algebra:    • Плейлист  
Famous Math Problems:    • Плейлист  
Probability and Statistics: An Introduction:    • Плейлист  
Boole's Logic and Circuit Analysis:    • Плейлист  
Universal Hyperbolic Geometry:    • Плейлист  
Differential Geometry:    • Плейлист  
Algebraic Topology:    • Плейлист  
Math Seminars:    • Плейлист  
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And here are some of the other Wild Egg Maths Playlists (some available only to Members!)

Solving Polynomial Equations:    • Плейлист  
Exceptional Structures in Maths and Physics via Dynamics on Graphs"    • Плейлист  
Triangle Centres:    • ENCYCLOPEDIA OF TRIANGLE CENTERS  
Six: An elementary course in pure mathematics:    • Плейлист  
Algebraic Calculus One:    • Плейлист  
Algebraic Calculus Two:    • Плейлист