Friends like octonions, sedenions aside,
Why bother whether x times 3 should be defined
as (xx)x or as x(xx), since these are equal? — it’s said.
Then again, is the property of certain operations in mathematics,
computer science, whereby they can be applied multiple times without changing the result beyond the initial application adequate rendition of true idempotence?
Then, for ‘any two such polynomials f and g, we have that (fg)(a) = f(a)g(a)’ ’tis true. Now, for the realm of automorphism wiki doth writ,
‘By definition every isomorphism has an inverse which is also an isomorphism, and since the inverse is also an endomorphism of the same object it is an automorphism,’ preserving hyperidentity kinetic
for stricture all across the board.
As in the case of all jargons without distinction
as interchangeable banalities inextricably mixed.
For the orbifold atlas has it thus, that ‘main example of
underlying space is a quotient space of a manifold under the properly discontinuous action of a possibly infinite group
of diffeomorphisms
with finite isotropy subgroups’.
Behold then, The Cyclic, the Ekpyrotic Cosmos where ἐκπύρωσις = “conflagration,”
as per Chrysippus, the bulk of whose cosmic models early and late for experiment consisted of ramps made for rolling grapes!

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