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. . . . standing up against gravity, weeds, junkmail, pollution, & noise. . . Evolution = Anti-entropy :
<^> " Every extreme is exceeded eventually " <^>
. . (the known 1/f noise law )
Generation = Anti-closure
. . . Re : Fermat's n^p under (+) :
they are the best possible additive generators mod p^k
. . . . . . XLT (extra large theorem, Waring for residues, Number repres'n by powersum):
. . . . . Each residue mod p^k is the sum of at most four p-th power residues
homepg ref[6].pdf
Digits (fingers) are more or less significant (Msd & Lsd).
. . . Says Msd to Lsd: "Hey, I'm much bigger than you",
. . . . . . . answers Lsd: "Big deal, you copy my structure"
So what's more important : Size or Structure ?
- - - On balance : use both, linear Size ('groot is mooi en veel is lekker') and quadratic Structure
. . . . (= coupling between parts : quality, 'small is beautiful' ). . the first & second dimension.
<^> Beyond closure modulus m, its successor m+1 (code 11, base m) can be seen as:
. . . Holy/All (3) . . . . . . . . . Mystery (5 : 3^2 + 4^2 = 5^2)
. . . Special/extra/sunday (7). . . Good-luck/ideal/Budda (8)
. . . Strange/funny/carnaval (11) . . Bad-luck/dangerous (13)
. . . Spirit/beyond (50: 101 b7) . . . Magic (1001= 7.11.13)
<^> For good measure & balance, don't forget predecessor m -1,
like C2 = {+/- 1} mod p^k (prime p),
. . . or : m_k -1 versus m_k +1 in Euclid's proof of the infinitude of primes (m_k = \prod first k primes)
. . . or : 60-1= 3.4.5-1= 59 : . . . Triplet solutions to FLT mod p^k for some p >= 59. . . [1]
<^> I-Ching (the book of changes, among 8x8=2^6 states): . . the oldest binary coded State Machine.
. . . state 59 : 'Hwan' (wind-over-water) = ' the Solution ' of a stuck-at situation. . . . Coincidence ?
I-Ching (symbol 59 & text).
<^> In many branches of science the mode of communication seems to be pointing out the other's mistakes
. . . So the ultimate reward is utter silence : . . . and the rest is silence. . . (Shakespeare, Hamlet).
" Non-Western philosophies orient more toward letting things happen (vs. forcing),
. . . . acknowledging the interplay of the worldly and the divine, and respecting things unseen ".
. . . . . . (P.Goldberg, The Intuitive Edge).
<^> . . If Stuck@Closure (mod ...) use the Carry . . . ;-)
. . . . In other words: if you feel there's something missing : expand/explore (Euler's trick)
From "Chinese Remainder theorem" to (Chinese) "Carry theorem": x^p + y^p == z^p (mod p^k)
. . . . The carry makes the difference in the FLT inequality
. . . . . . EDS: Exponent p Distributes over a Sum: z == x+y mod p^k
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-- N.F.Benschop ( n.benschop -at- chello.nl ) Sep'97 --
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