[HN Gopher] Esoteric Base Number Systems
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       Esoteric Base Number Systems
        
       Author : fildon
       Score  : 9 points
       Date   : 2023-06-25 21:39 UTC (1 hours ago)
        
 (HTM) web link (rupertmckay.com)
 (TXT) w3m dump (rupertmckay.com)
        
       | peter_d_sherman wrote:
       | >"The Quarter-Imaginary numeral system was first proposed by
       | Donald Knuth in 1960.
       | 
       |  _The trick with this base is recognising that powers of 2i
       | "rotate" through the Gaussian plane._"
       | 
       | Powers:
       | 
       | -1: -(1/2)i, 0: 1, 1: 2i, 2: -4, 3: -8i, 4: 16, 5: 32i, 6: -64
       | etc.
       | 
       | PDS: Now this is highly interesting to me! A system which
       | collapses a 2D number system, that is, non-imaginary + imaginary
       | numbers (AKA, the "Complex (2D) Plane") -- back into what is
       | basically a number line -- or a single-dimensional linear system
       | (choose whatever terminology or linguistics you prefer...)
       | 
       | But the point is -- it _reduces dimensionality_ from N to N-1
       | dimensions -- while still preserving imaginary numbers...
       | 
       | To accomplish this weird trick, Knuth spaces out imaginary
       | numbers (and negative numbers) at intervals of 4 -- basically you
       | _cycle through properties_ (positive real, positive imaginary,
       | negative real, negative imaginary) with every cycle of 4.
       | 
       | Could this be accomplished with other bases and other number
       | systems having more than one dimension? Based on Knuth's example,
       | it would seem to be very possible!
       | 
       | I can only wonder what interesting mathematical properties future
       | mathematicians might discover by using such structures...
       | 
       | They might turn out to be useful for a lot of things!
       | 
       | I'd also be highly curious if there is any Mathematician who has
       | applied such a structure to one or more specfic problems, and if
       | it helped them solve a specific problem in an elegant or novel
       | way!
       | 
       | What would be interesting is a list of mathematical problems
       | (like a wiki page) whose computation could be aided by using such
       | a structure, and how specifically to perform calculations using
       | the structure, etc., etc.
        
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       (page generated 2023-06-25 23:01 UTC)