## Cyclic numbers

What is the basis for reason? And mathematics?

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Eodnhoj7
Posts: 5039
Joined: Mon Mar 13, 2017 3:18 am

### Re: Cyclic numbers

Arising_uk wrote:
Fri Nov 17, 2017 11:59 am
Eodnhoj7 wrote:The are both quantitative and qualitative duals under what "could be" called, at least what I argue, Synthetic (or neutral) Space.
I'd have thought this Kant not Hegel?
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.

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.

Eodnhoj7
Posts: 5039
Joined: Mon Mar 13, 2017 3:18 am

### Re: Cyclic numbers

One reflecting upon itself maintains itself while manifesting as approximates 2 and -1.
1 ≡ 1 → 1,2,-1
*****(1 = ⦁), (-1 = ─ ), (-1, 2 = ⧟)

One reflecting upon itself maintains itself as an act of stability and unity. This act of Self-Reflection or Mirroring is equivalent to One as Point directing itself into itself.
a) 1 ≡ 1 → 1 ∵ (1 ≡ 1) = (⦁ = 1)

Simultaneously it manifests "2" because 1 reflecting 1 is structurally congruent to 2. 2 exists perpetually as 1 reflecting upon 1 and in this respect, exists at the same time in a different respect to 1. As one is always mirroring itself, 2 is ever present.
b) 1 ≡ 1 → 2 ∵ 1 ≡ 1 ≅ 2

Simultaneously it manifests "-1" because 1 reflecting 1 is an approximate of 2 and this approximation is the deficiency between 1 and 2 which “separates” them. One mirroring itself takes a dual role of reflecting itself as both 1 and 2. In these respects 1 and 2 manifest as approximates of each other through (1 ≡ 1) and as approximates are separated through “1” (as 1 is approximated through 2, by 1) as -1.
c) 1 ≡ 1 → -1 ∵ 1 ≡ 1 → 1 ≈ 2

As all number is composed upon a self-reflecting one, all 1n follows the same form and function

(1,2,-1) ≡ (1,2,-1) → (-3,-2,-1,0,1,2,3,4)
****with (1 = ⦁ ), (2,-1 = ⧟), (3,-3 = △)

a) 1 ≡ 1 → 1 ∵ (1 ≡ 1) = (⦁ = 1)
b) 1 ≡ 1 → 2 ∵ 1 ≡ 1 ≅ 2
c) 1 ≡ 1 → -1 ∵ 1 ≡ 1 → 1 ≈ 2

d) 1 ≡ 2 → (1,2) ∵ 1 ≡ 2 = (⦁ = 1,2)
e) 1 ≡ 2 → 3 ∵ 1 ≡ (1 ≡ 1) ≅ 3
f) 1 ≡ 2 → -1 ,-2 ∵ 1 ≡ 2 → (1 ≈ 2, 1 ≈ 3, 2 ≈ 3)

g) 1 ≡ -1 → (1,-1) ∵ 1 ≡ -1 = (⦁ = 1, - = -1)
h) 1 ≡ -1 → (0) ∵ 1 ≡ -1 ≅ 0
i) 1 ≡ -1 → (0) ∵ 1 ≡ -1 → (1 ≈ -1, 1 ≈ 0, -1 ≈ 0)

h) 2 ≡ 2 → (1,2) ∵ 2 ≡ 2 = (⦁ = 1,2)
i) 2 ≡ 2 → 4 ∵ (1 ≡ 1) ≡ (1 ≡ 1) ≅ 4
j) 2 ≡ 2 → -1 ,-3, -2 ∵ 2 ≡ 2 → (1 ≈ 2, 1 ≈ 4, 2 ≈ 4)

k) 2 ≡ -1 → (2,-1) ∵ 2 ≡ -1 = (⦁ = 2, - = -1)
l) 2 ≡ -1 → 1 ∵ (1 ≡ 1) ≡ -1 ≅ 1
m) 2 ≡ -1 → 0,-1, 3 ∵ 2 ≡ -1 → (1 ≈ -1, 1 ≈ 2, 2 ≈ -1)

n) -1 ≡ -1 → (-1) ∵ -1 ≡ -1 = (- = -1)
o) -1 ≡ -1 → -2 ∵ -1 ≡ -1 ≅ -2
p) -1 ≡ -1 → 1 ∵ -1 ≡ -1 → (-1 ≈ -2)

Eodnhoj7
Posts: 5039
Joined: Mon Mar 13, 2017 3:18 am

### Re: Cyclic numbers

The function of arithmetic simultaneously manifests through "one as point" mirroring itself when we look into the nature of 1 as a "positive" or "+".

One reflecting upon itself maintains itself while manifesting as approximates 2 and -1.
+1 ≡ +1 → +1,*2,-1

One reflecting upon itself maintains itself as an act of stability and unity. This act of Self-Reflection or Mirroring is equivalent to One as Point directing itself into itself. In these respects, addition manifests itself as the foundation of arithmetic through a mirroring process.
a) +1 ≡ +1 → +1 ∵ (+1 ≡ +1) = (⦁ = +1)

We can observe this further within multiplication as the "addition of addition" or addition reflecting itself. Take for example 2 x 3 is equivalent to saying 2 adds itself as three additions. Considering all multiplication exists as a second degree version of addition, multiplication of whole numbers begins truly with "2".
b) +1 ≡ +1 → *2 ∵ +1 ≡ +1 ≅ *2

Simultaneously it manifests "-1" because 1 reflecting 1 is an approximate of 2 and this approximation is the deficiency between 1 and 2 which “separates” them. One mirroring itself takes a dual role of reflecting itself as both 1 and 2. In these respects 1 and 2 manifest as approximates of each other through (1 ≡ 1) and as approximates are separated through “1” (as 1 is approximated through 2, by 1) as -1.

We can observe subtraction as a deficiency in structure itself, which manifests if and only if their is "approximation". This "deficiency as approximation" results with the structure extension 2 being an approximation of its original source of "1" while still being composed of "1". Subtraction exists if and only if their is addition, and this addition begins with one's reflection as two.

Subtraction can be viewed as the median form and function of number between addition and multiplication as a result of the inherent approximation of "positive" functions also.

c) +1 ≡ +1 → -1 ∵ +1 ≡ +1 → +1 ≈ +2

Simultaneously, division exists as the subtraction of subtraction (ex: 8/2 is how many subtractions of 2 from 8 ) as the inevitable result of -1 reflecting -1 as -2.

Eodnhoj7
Posts: 5039
Joined: Mon Mar 13, 2017 3:18 am

### Re: Cyclic numbers

Eodnhoj7 wrote:
Sat Nov 18, 2017 7:31 pm
The function of arithmetic simultaneously manifests through "one as point" mirroring itself when we look into the nature of 1 as a "positive" or "+".

One reflecting upon itself maintains itself while manifesting as approximates 2 and -1.
+1 ≡ +1 → +1,*2,-1

One reflecting upon itself maintains itself as an act of stability and unity. This act of Self-Reflection or Mirroring is equivalent to One as Point directing itself into itself. In these respects, addition manifests itself as the foundation of arithmetic through a mirroring process.
a) +1 ≡ +1 → +1 ∵ (+1 ≡ +1) = (⦁ = +1)

We can observe this further within multiplication as the "addition of addition" or addition reflecting itself. Take for example 2 x 3 is equivalent to saying 2 adds itself as three additions. Considering all multiplication exists as a second degree version of addition, multiplication of whole numbers begins truly with "2".
b) +1 ≡ +1 → *2 ∵ +1 ≡ +1 ≅ *2

ex: (2) ≡ 3 → (-5,-4,-3,-2,-1,1,2,3,6)

(2) ≡ 3 → (1,2,3) ∵ (2) ≡ 3 = (⦁ = 1,2,3)
(2) ≡ 3 → 6 ∵ (1 ≡ 1 ≡ 1) ≡ (1 ≡ 1 ≡ 1) ≅ 6
(2) ≡ 3 → -1 ,-2,-5,-4,-3 ∵ (2) ≡ 3 → (1 ≈ 2, 1 ≈ 3, 2 ≈ 3, 1 ≈ 6, 2 ≈ 6, 3 ≈ 6)

Simultaneously it manifests "-1" because 1 reflecting 1 is an approximate of 2 and this approximation is the deficiency between 1 and 2 which “separates” them. One mirroring itself takes a dual role of reflecting itself as both 1 and 2. In these respects 1 and 2 manifest as approximates of each other through (1 ≡ 1) and as approximates are separated through “1” (as 1 is approximated through 2, by 1) as -1.

We can observe subtraction as a deficiency in structure itself, which manifests if and only if their is "approximation". This "deficiency as approximation" results with the structure extension 2 being an approximation of its original source of "1" while still being composed of "1". Subtraction exists if and only if their is addition, and this addition begins with one's reflection as two.

Subtraction can be viewed as the median form and function of number between addition and multiplication as a result of the inherent approximation of "positive" functions also.

c) +1 ≡ +1 → -1 ∵ +1 ≡ +1 → +1 ≈ +2

Simultaneously, division exists as the subtraction of subtraction (ex: 8/2 is how many subtractions of 2 from 8 ) as the inevitable result of -1 reflecting -1 as -2.

Following the same form and function, exponentiation would result as "the multiplication of multiplication" and in these respects begins as "4" (we can observed this as the first act of expontientation, 2^2, begins as four.)

a) *2 ≡ *2 → ^4

In these respects what we understand of arithmetic breaks down to a mirror effect with:

1) The first degree as addition and subtraction through 1
2) The second degree as multiplication and division through 2
3) The third degree as exponentiation and roots through 4

Eodnhoj7
Posts: 5039
Joined: Mon Mar 13, 2017 3:18 am

### Re: Cyclic numbers

1)If we look at the nature of number as stemming strictly from 1 as a positive value.

2) and all number stemming from 1, in itself being composed of 1

3) and all number being composed of 1 manifesting ad infinitum

4) Ad infinitum is 1 revolving into itself to produce all possible numbers.

5) All possible number exist through all mathematical functions, as all mathematical functions theoretically are strictly extensions of positive (addition) and negative (subtraction) values.

6) As all mathematical functions are extensions of positive and negative values (founded in basic arithmetic), these mathematical functions provide foundations for further mathematical functions (multiplication, division) ad infinitum in correspondence to the ad infinitum nature of number (considering form and function are interjoined as +1 and -1).

7) In theory there are infinite mathematics stemming from a core base synonymous to "1", and these infinite numbers/functions are a result of 1 revolving through itself.

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