That is a logically valid observation with Kant observing the categorical imperative as formulating, through "moral necessity", the synthesis of mathematical symbols as an extension of one's rational faculties. Mathematics as an extension of reason in itself however curves space as we can see at the abstract level through "symbolism" or in the physical manner of creation (which manifests also as a symbolism). In these respects mathematics are not only and extension of Kant's Categorical Imperative, but a structural extension (possibly through inversion) of Neitzche's Will To Power.Arising_uk wrote: ↑Fri Nov 17, 2017 11:59 amI'd have thought this Kant not Hegel?Eodnhoj7 wrote:The are both quantitative and qualitative duals under what "could be" called, at least what I argue, Synthetic (or neutral) Space.

In simpler terms, respective of Kant, we are obligated to "synthesize" reason where necessary as observing disorder reflects the need for order.

We can see this at some level's of certain cultures which anthropomorphized certain degrees of the human condition. Take for instance in Norse Mythology, Odin the god of Wisdom, Fury and Madness, crucified/hung himself from the world tree (it is interesting in mathematics how necessary truth trees are in linear thinking and in observing both limits and possibilities) for 9 days and 9 nights and gained the "runes" for his endeavor.

We see in Abrahamic and Pagan religions the foundation of "the word" or "logos" forming reality as it synthesizes itself through creation.

How is the pursuit of mathematics any different considering that the human mind is geared towards circular rationality through the inevitable paradox?

To get back on point, although a valid argument can be presented for Kant, I would argue that Hegel's (technically Fichte's also) observation of a triadic structure of reality as thesis, antithesis, and synthesis corresponds qualitatively to the ψ⟨+|-⟩ with:

Thesis = +

Antithesis = -

Synthesis = ψ *****with ψ = possibility

Pythagoras also observed this universal nature of triadic structure and argued that: "If you can break a problem down into three parts then you are 2/3's done in solving it".

Synthesis is an inevitable foundation for mathematics' that provides not only it's means but justification through observing in inevitability of

1 and 3.

So to get back to the "cyclic numbers" argument, the title alone argues the qualitative nature of quantitative natures. Observing the cyclical nature of numbers, in function, corresponds in form to the numbers having a geometric nature by default. We can only describe numbers in their fullness through the application of geometry as the study of space. The same logic applies in reverse in that we can only understand geometry through number.

In these respects number and space, where often times describe as a necessary relation of description, in reality are inseparable as the nature of describing is the nature of apply definition. Definition is structure, structure is order, order is being.

In these respects number and space are inseperable, but the question is how are they "unified". Hence the 11 points I argued above and the necessity of "reflection" (or "mirroring") as the "means" of "means".

All structures are viewed as creating "centers"as points corresponding to zero dimensions or "zero".

However if we "turn"(pay attention to this word, as it is an extension of "cycle") this observation around and view structures as extensions of "centers" we get a whole new perspective all together.

The observation of these "center" as a 1 dimensional point folding into itself to manifest further points as structure extension, changes not only our understand of geometry and number, but allows a unity being geometry and number.

We can observe this necessity of reflection as corresponding to "meaning", as Philx questions in "Do number groups have more meaning than individual numbers". His question deals primarily with the nature of numbers and numbers, however it may be observe that the Mirroring process of "number as point" allows meaning to take place.