THE RABBIT TREE &
THE LOGIC OF LIFE'S BEGINNING

 

 

To illustrate the first of the "Six Theorems,"1 and show how the logic governs the family structure of the Rabbit Tree.

Let there be the Rabbit Tree where 0 is a "pair in utero" and 1n is an "immature pair". Let 1n correspond to Kepler's 'lesser' 1. Let (1n 0) be a "mature or 'pregnant' pair." Let (1n 0) correspond to Kepler's 'greater' 1. Let [(1n 0) 1n] be a "mature or 'pregnant' pair with offspring." Let 0 = the logical value "0" where "0" -- a "pair in utero" -- is unborn but clearly not "nothing." Let 1n = the logical value "U12.bmp (174 bytes)" where "" -- an "immature pair" -- is something more than not nothing, born, but not yet reproducing itself. Finally, let (1n 0) = the logical value "1" where "1" -- a "'pregnant' pair" -- is something more than not nothing, born and reproducing itself. Now, since the logical calculus says that 1 = 0,2 let [(1n 0) 1n] = "0", where "0" -- a "'pregnant' pair with offspring" -- is a fully reproduced pair continuing to reproduce itself, the real identity of a "pair in utero." The Rabbit Tree is then seen to be an instance of the "logic identical with growth" 01: 0 = 1, 10 = , 1 = 0, in which the order of the elements of the 3rd equation (, l, 0) is the order of elements in the left-right middle row, the bottom-up middle column, and the top-down right-left forward-diagonal middle of the "cornerstone."3

When the numbers of the Fibonacci sequence4 are seen as the sums of the elements of the ratio of 'pregnant' to non-'pregnant' pairs of rabbits in each successive generation of the Rabbit Tree,5 then it is easily seen that this triple middle order is precisely the infinitely repeating order of the elements occupying the dead middle position in each generation of Fibonacci rabbits, led by the 0 that is not "nothing," followed by Kepler's 'lesser 1', here, initially, 11, followed in turn by 1, here, initially, (11 0):
 


                                                                                                                                                                                                                                        et cetera, ad infinitum.

 

The perfect symmetry of this arrangement is most easily seen when the elements of the Rabbit Tree are converted into their logical equivalents:

 

 

                                                                                                                                                                                                                                        et cetera, ad infinitum.


Where the underlying 1
n 0 structure of the 1's beside the simplified central digit of each level remains visible as 0 this is alternatively rendered:

 

                                                                                                                                                                                                                                        et cetera, ad infinitum.

 

Beginning with the first iteration of the levels 0, , and 1, where x = the total number of digits beside the central digit 0, and = the total number of digits beside  in the  level last previous to x, and the total number beside 1 in the 1 level last previous, x = + + 2.  Where y = the total number of digits beside the central digit , y = x + + 2.  Where z = the total number of digits beside the central digit 1, z = x + y.

The essential middleness of the logical sequence which is the perfect balance point of the infinite Fibonacci sequence is evident in the fact that the logical product of the left side of any generation times the logical value of the dead middle position times the logical product of the right side -- in that order or the reverse, but with the middle in the middle -- always equals the logical value of the dead middle position.6 When attention is directed, as in the first rendition of the Rabbit Tree above, to the qualitative differences within the elements of the ratio whose sum equals the Fibonacci number in each generation, that is, to the "live" differences in the rabbits which are the constituents of the elements of the discrete ratio which each number is in reality, it is further evident that the dead middle position is occupied successively by the 1st, 3rd, 5th, 7th, 9th, . . . nth pairs of rabbits in a direct line of descent from the first pair, 11, 13, 13-2, 13-2-2, 13-2-2-2, etc., that is, by pairs whose ordinal values in the direct line of descent are the series of odd numbers or successive differences of the squares of the natural numbers, and further that each odd-numbered pair in this central line of descent occupies in its turn in order the logical positions, , 1, 0, so that the central "trunk" of the Rabbit Tree is the substitution, in the infinite repetition of the set { 1 0}, of the odd-number for the natural-number ordination, i.e., the substitution of the ordination 1, 3, 5, . . . for the ordination 1, 2, 3, . . .. This substitution is dictated by the very structure of the "foundation-stone," where the differences between the three successive subsquare expansions constituting the ninefold square, viz., 1, 3, and 5, are successively the sets of subsquares which are the positions of the three sets of logical digits, {1}, { 1 0}, and {0 1 0 } (note the left-right bottom-up middle set is again 1 0). But since 00 = 1, = 1, and 0 = 1, the arithmetic sums of the three sets of logical digits which occupy the three sets of subsquares expanding between, respectively, 0 and 12, 12 and 22, and 22 and 32, are, respectively, 1, 2, and 3 (note the arithmetic value of the { 1 0} middle set, 2, corresponds to the fact that the rabbit pair 13 is actually 11-2, so that the odd-number direct line of descent which is the spine of the Rabbit Tree might as well be written, 11, 11-2, 11-2-2, 11-2-2-2, 11-2-2-2-2, etc.).

What is demonstrated in terms of the logical foundation of the "nothingless" Fibonacci sequence is not the non-dynamic identity of "nothingness" and "something," but rather the perfect asymmetry of "nothing" and "something," the very identity of the "nothingness" of the beginning in which beginning nothingness is not something and not something is not. The real trinary logic values, 0, , 1, "not nothing," "not not nothing," and "universe," replace the binary values of the logics of Boole and Peirce, 0, l, "nothing" and "universe." If, with its either-or structure, and the consequent inconsequence of its beginning, the binary logic approximates the system of life, the trinary system of the beginning, with its perfect middleness, is the very logic of life.7

 


 

Notes


1 D.G. Leahy, Foundation: Matter the Body Itself (Albany, 1996), Section III.2.
2 Cf. Leahy, Foundation, Section III.1, and Section III.2, Theorem 5.
3 Ibid., and Section III.2, Theorem 4.
4 The Fibonacci sequence is built into the geometric series where x = φ.  Beginning at the top of the unique φ pyramid and descending row by row by either φ's or 1's: φ, φ, φφ, φφφ, φφφφφ, φφφφφφφφ, . . . = 1, 1, 11, 111, 11111, 11111111, . . . = 1, 1, 2, 3, 5, 8, . . ..

                                                                    φ1 =   φ =                                                                              φ
                                                                    φ2 =   φ φ =                                                                    φ + 1
                                                                    φ3 =   φ
φ φ =                                                          φ + 1 + φ
                                                                    φ4 =   φ φ φ φ =                                             φ + 1 + φ + φ + 1
                                                                    φ5 =   φ φ φ φ φ =                             φ + 1 + φ + φ + 1 + φ + 1 + φ
                                                                    φ6 =   φ
φ φ φ φ φ =       φ + 1 + φ + φ + 1 + φ + 1 + φ + φ + 1 + φ + φ + 1

et cetera, ad infinitum.

5 Cf. Leahy, Foundation, Section III.2, Theorem 1.
6 Where the underlying 1n 0 structure of 1 beside the simplified central digit remains visible as 0, as in the last rendering, such will not always be the case if a binary based trinary logic (where the digit third to 0 and 1 functions as an “intermediate”) is substituted for the  of real trinary logic.  In that event, the perfect logical multiplicative symmetry will fail in the case of both the 0 and 1 levels in the second iteration of the three levels.  For the contrast of binary based and real trinary logic, cf., on this web, Quantum Gravitational vs. Quantum Logic: Virtually Left-handed Real Trinary Logic.
7 Cf., on this web, Real Trinary Logic Geometric Series Infinite Iterative Sequential Summing and Banach-Tarski Paradox & the Real Trinary Logic Matrix of the Fibonacci, Geometric, and Perfect Number Series.

 


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