A proposed number system
Numbers with
more to say
Myrions extend complex numbers into any finite number of dimensions - while letting the shape of a calculation become part of its meaning.
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Why the name?
Countless directions
one new name
myriad+ions
Myrions takes its name from myriad, meaning countless. It reflects a system with no fixed upper limit on its dimensions. The -ions ending places it alongside other multidimensional number systems.
The premise
Complex numbers gave us a second direction. Myrions ask what happens when there is no prescribed limit to the number of directions - and when the route through a multiplication matters as much as its inputs.
Any finite
dimension
Commutative
multiplication
Association
dependent
Read & explore
Begin at the
edge of familiar
A different kind of extension
Not just more
dimensions
In myrion arithmetic, multiplication is commutative - order does not matter. But beyond two dimensions it is no longer associative: changing the brackets can change the answer.
That makes each calculation a small tree, carrying a history of how its values came together.
The formal work
The Myrion
Number System
A mathematical treatment of the algebra, its singular division locus, square-root closure, and possible relevance to structured neural computation.
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