power body cornerstone construction
order: absolute dead center hypercube: the
three unique TRANSDECIMAL number identities
1) The absolute dead center cube is unique among all cubes. For the proof, see, on this web, Theorem & Proof: The Uniqueness of the Absolute Dead Center Cube. The Plot of the equation unique to this cube among all cubes is
2) Real trinary logic is perfectly indifferent to the mathematical operations of addition, multiplication, subtraction, and division (a perfect indifference found neither in Boole nor Peirce, cf. D.G. Leahy, Foundation: Matter the Body Itself (Albany 1996), III.1, passim), and, as been demonstrated elsewhere (see, on this web, Real Trinary Logic Geometric Series Matrix of the Numeric Geometric Series & the Series of Perfect Numbers) the infinite sequential summing (= operationally relating) of the elements of real trinary logic according to the universal operation of this logic () immediately i.e., prenumerically, produces the geometric series of ordinary mathematics where x = 2 (the mathematics of mitosis and sexual reproduction) and shows itself at once the manifest foundation of the series of perfect numbers, and, finally, at the very inception of this logic the foundationally demonstrated form of the absolute positive alio-relative identity (cf. Leahy, Foundation, III.1) is i2 / j2 = 1, whose Plot,
manifests mathematically the perfect indifference of the logic to plus and minus: i2 / j2 = -i2 / j2 = i2 / -j2 = -i2 / -j2 = 1.
3) Part and parcel of the uniqueness of this cube is the fact that unlike all other cubes the face of this cube may be divided into 36 equal squares each of whose areas = √82944 and each of which may be inscribed in a circle whose area 144π equals the circumference 144π of the circle in which the whole face (= 36√82944 = 10368) may be inscribed (cf. Leahy, Foundation, pp. 524f., n. 98).
Let there be the face of the absolute dead center cube divided into 36 equal subsquares arranged as quadrants each occupied by a successive counterclockwise turning of the real trinary logic Cornerstone (cf. ibid., III. 1) and positioned in the 1st and 3rd quadrants of the coordinate system on the analogy to the above Plot of the equation unique to the absolute dead center cube, as here illustrated:
When in the above equation x is negative the position of the analogized 36-fold squares is reversed and occupies the second and fourth quadrants of the coordinate system with its elements turned accordingly. Taking into account the ultimate indifference of real trinary logic to plus and minus the coordinate system may be filled in analogously in the following way:
4) The transcendental deduction of the order of construction of the cornerstone is accomplished by starting with the ultimate equation of the power body analogue of the power set and placing the digits on the left side of the equation, each in order, successively in the leftmost topmost appropriate and unoccupied cornerstone subsquare (see, on this web, The Real Beyond the Void: the Beginning/the Power Body, Note 4; see, also, on this web, The Deep Epidermal Surface: The Cornerstone Construction Order, Minimum Order Tetrahedron Hypercube, & Absolute Dead Center Hypercube). Thus, following the Beginning/Power Body sequence, 1, 1, 1, 1, (1), 1, (1), (1), 1, the cornerstone is constructed in the order here illustrated:
The Thread of Dr. Hoath’s Analysis
On June 1, 2012 SB Hoath communicated to the writer (and to his fellow students in The New York Philosophy Corporation Spring 2012 course on “Philosophy of the Body”) the results of his study relating to certain of the logical patterns set out, above, in paragraphs 3 and 4.1 He first substituted in the four foursquares of rotating logical cornerstones occupying the four quadrants of the coordinate system, as illustrated, above, in paragraph 3, the numbers corresponding to the construction order of the real trinary logic cornerstone, as illustrated, above, in paragraph 4, conceiving that the rotation of the cornerstone in each quadrant takes place by quarter turns:
Sometime earlier Dr. Hoath had started to apply a two-sided approach to following the thread of the cornerstone construction order:
In this case he decided to employ the singularly one-sided approach to the construction order here illustrated:
The reader will note that this drawing combines as one the previous front and back sewing patterns—effectively rendering the cornerstone perfectly transparent. This perfectly one-sided pattern is then applied to the four foursquares of the logical cornerstone (numbered according to the construction order) occupying the quadrants of the coordinate system, with the 4 cornerstones in each quadrant made of one thread running out from the 9-subsquare of each cornerstone to the 1-subsquare of the cornerstone preceding it in the counterclockwise rotation:
Dr. Hoath then focused his attention on the four central spaces created by the unification of each of the foursquares of cornerstones occupying one each of the coordinate system quadrants — with these beautiful visual patterns appearing:
He then calculated the area of the black central surface of each of the four foursquares of cornerstones unified by the thread joining together 9-square to preceding 1-square as previously described. Starting at the top right foursquare and running counterclockwise to the bottom right foursquare, the areas are 288, 672, 4032, and 1209.6.
The Absolute Balance Point
Then drawing upon the conjunction of the transdecimal identities (see, on this web, Transdecimal Calculation of Number Identity: A Note on Integral Product & Related Terms) of the mathematics of the Hebrew terms נקדת האפס של תנופה (‘dead center’/’point zero of energy’), מדות שטח (‘area measure’), and נקדת העיון (‘point of balance’),2 he multiplied each of the aforesaid areas in turn by the rational product of נקדת העיון (‘point of balance’) (288 × .0297̅6̅1̅9̅0̅4, 672 × .0297̅6̅1̅9̅0̅4, 4032 × .0297̅6̅1̅9̅0̅4, and 1209.6 × .0297̅6̅1̅9̅0̅4) to produce this parallel balance point sequence: 60/7, 20, 120, and 36.
Knotting the Thread — Cutting the Knot
In order for the 4th (the last) cornerstone in the rotation order of cornerstones to be the 4th (the last) cornerstone in the rotation order of the cornerstones in the 4th (the last) quadrant there is nothing for it but that it be qua 4th (qua last) the 1st cornerstone in the rotation order of cornerstones in the 1st quadrant:
Thus the minimum order 4−1-2-3 (cf. Leahy, Foundation III.1, et passim). The writer notes that when the central area numbers calculated by Dr. Hoath are placed in their respective quadrants of the coordinate system, and the corresponding absolute balance point reductions are likewise so placed in a separate configuration, then, multiplying the 2 sets of 4 numbers together chiasmically in accord with the minimum order 4−1-2-3
yields the following products of the resulting irreducibly chiasmically related sets of chiasmically structured square roots:
(IV’ × I) × (IV × I’) = (36 × 288) × (1209.6 × 60/7) = 1.0368e4 × 1.0368e4 = 1.07495424e8
= the absolute dead center hypercube volume whose ratio to its integral product = 82944/784/1 (see, on this web, Measure Beyond Beyond Reach), and
(II × III’) × (II’ × III) = (672 × 120) × (20 × 4032) = 8.064e4 × 8.064e4 = 6.5028096e9
= the hundredfold product of the three unique natural numbers identically their integral products (1 × 784 × 82944) (cf. ibid.; also, Leahy, Foundation III.6). Cf. the integral product of Euclid’s term for the golden section ὁ άκρος καὶ μέσος λόγος (‘the extreme and mean ratio’) 6.5028096e37 (see, also, on this web, Theorem & Proof: The Uniqueness of the Absolute Dead Center Cube).
1 The writer thanks Dr. Hoath for sharing the results of his study including his original images the greater number of which have been adapted and combined in what follows for the sake of economy of presentation.
2 Cf. Leahy, Foundation, p. 521: “Let, then, ‘absolute’ נקדת האפס של תנופה (‘dead center’/’point zero of energy’ [integral product, 8.2944E22]) be denominated ‘absolute’ מדות שטח (‘area measure’, qua proportion, 40 : 4 :: 6 : 400 (::) 300 : 9 :: 8 : , whose integral product is 3.31776E11) 8.2944E22/ 3.31776E11 = 2.5E11. ‘Absolute’ נקדת האפס של תנופה (‘dead center’/’point zero of energy’) divided by ‘absolute’ מדות שטח (‘area measure’) equals ‘absolute’ נקדת העיון (‘point of balance’, qua proportion, 50 : 100 :: 4 : 400 (::) 5 : 70 :: 10 : 6 :: 50 : , whose integral product is 2.5E11). Identified as ‘absolute area measure’ ‘absolute dead center’ is ‘absolute balance point’. The rational product or ‘identity’ of נקדת העיון (‘point of balance’) is .0297̅6̅1̅9̅0̅4.”