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 "
"
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 1n 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 ẏ = the total number of digits beside in
the level
last previous to x, and ż the total number beside 1 in the 1
level last previous, x = ẏ + ż + 2. Where y = the
total number of digits beside the central digit ,
y = x + ż + 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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