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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A myrion multiplication cycle linking i, j, and their negatives.

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.

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

Begin at the
edge of familiar

A branching myrion calculation tree showing i, j, k, and l.

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 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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