<bonda_000>
clever: you were so right about polynomials though
<bonda_000>
if infinitesimal change in our differential geometric system is described in atomic operations
<bonda_000>
then every function we will have to define in terms of these atomic operations
<bonda_000>
so we take a Taylor expansion of each standard math function and approximate it at the lowest terms
<bonda_000>
clever: and if you look at a binary adder, that also may be another independent vector in the system
<bonda_000>
along with flips and shifts
<bonda_000>
but having two works good with binary having only two states on or off so the third one is hard to fit
<bonda_000>
so geometrically speaking with two basis vectors being flips and shifts and third vector being add that we cannot express in binary number system, we are on a plane in a 3d space at least
<bonda_000>
that add may come helpful later on with noise though
<bonda_000>
however!
<bonda_000>
we can incorporate adds but instead of vectors we will have to go up a dimension and use matrices
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