[HN Gopher] Mathematics Without Numbers (1959)
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       Mathematics Without Numbers (1959)
        
       Author : measurablefunc
       Score  : 5 points
       Date   : 2025-12-02 01:08 UTC (4 days ago)
        
 (HTM) web link (www.jstor.org)
 (TXT) w3m dump (www.jstor.org)
        
       | dinkelberg wrote:
       | The article by mathematician John Kemeny, who amongst other
       | things was an assistant to Albert Einstein at the IAS, describes
       | four methods of applying mathematics to problems that are not
       | innately about numbers (algebraic) or space (geometric). He
       | divides the space of such methods firstly into a) not using
       | numbers, b) introducing artificial numbers, and secondly also
       | into using either 1) algebra or 2) geometry.
       | 
       | For geometry not using numbers, he shows how graph theory can be
       | applied to the problem of social balance as defined by
       | psychologist Fritz Heider. This example is based on work by
       | Dorwin Cartwright and Frank Harary.
       | 
       | For algebra not using numbers, he chooses the theory of group
       | actions, and applies it to a way of preventing incestuous
       | relationships that was used in some cultures, which works by
       | assigning each child a group that they are exclusively allowed to
       | marry in. This example is based on work by Andre Weil and Robert
       | R. Bush.
       | 
       | For geometry using numbers, he uses an adjancency matrix to show
       | how you can find out how many ways there are to send a message
       | from one person to another in a network.
       | 
       | For algebra using numbers, he defines axioms for a distance
       | function for rankings with ties, which can be shown to be unique
       | (probably up to some isomorphy), and which can be used to derive
       | a consensus ranking from a set of rankings. This appears to be
       | the central piece of the article, as that is an example that he
       | developed himself together with J.L. Snell and which was yet to
       | be published.
        
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