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Infinite tetration and superroot of infinitesimal
I was not able to wait too long:

So finally we have first ill defined definitions-they has to be ill defined as they include infinities so that we can build logical structures out of them defying Godel.

1) i is undiferrentiated structureless infinitesimal(s) (or -i, or both- they are NOT equal.)
2) the phase state of undifferenntiated, structureless infinitesimal is perfect chaos: no structures, just motion
3) the entropy of primordial see of such infinitesimal(s) is -i*lnI=-pi/2
4) It is maximal negative entropy there can be
5) The direction of development is such that infinitesimals organize in structures reducing negative entropy ( increasing share of entropy of structures moving in infinitesimal sea.
6) When there is no structures, just motion, any temperature is absolute 0, as is any kinetic energy .
7) What are the first structures remains to be seen, but surely interaction of i with itself as there is nothing else in a way that increases entropy from -pi/2
Cool When there are structures, they move in infinitesimal sea, and there is temperature corresponding to kinetic energy of such structures.
9) between each level of structures of infintisemals, SCALES are increasing infinitely, speed is decreasing infinitely compared to previous scale.
10) Imaginary continuos time which works in these scales appears as first structures appear. Before that, when there is only motion, there is no TIME.
11) The time scales of imaginary time get infinitely longer with each scale, still being infintiely small
12) Infinitesimal behaviour in SQ EQUALS continuous mathematics- which may be missing at least tetration operation to give full picture, but probably all hyperoperations
13) As structures are created, entropy gets less negative, temperature and kinetic energy grows-
14) There is a threshold point where 1/2 of initial negative entropy is reduced by thermal motion of created structures of ALL scales so far that infinitely bigger structure witn infinitely larger scale can not be created anymore. So the next scale is finitely larger, time gets real and discrete, speed - finite.
The limiting entropis are -pi/2, -pi/4(leading to sqrt(2) - long live Pythagoras! - 0, +pi/4, pi/2

4 phase regions, 1 still missing.

15) Quantum mechanics works in 2scales on BOTH sides of this phase transition- from here the ambiquity it has. K-vortex operates below this when it is just oscillating, slipping differential, above when it gets a grip and spin aligns with the axis that caused that grip to appear.
16) From this point onwards, thermal motion increases faster than creation of structures- so increased complexity of structures is possible only in limited space, not all SQ domain- so we start to see aggregation of structures in particles, etc etc.

That is how far i have gotten. All this is connected to the prime number theorem, so that:

in SQ, lni/i > entropy , entropy being -pi/2, -pi/3 etc, - probably, i representing a structure in each scale in such formula , so here the internal complexity of infinitesimal structures is not obvious- math lacks this dimension. On attempt to register it was backtetrating hyperdimensional volume -i and writing each dimension as dI , so that step to next dimension is -I+di, and it is possible to think about integration.differentiation along this dimension of infinitesimals. dI is basically a change in infinitesimal structure expressed as change in hypervolume.

In SQ, lni/i is bigger than number of "primes", primes representing structures built.

in limit case, phase transition between continuous/discrete, number of primes counted from both sides has a property lnx/x=pi(x)

above SQ, pi(x) < lnx/x

above SQ, the entropy of structures is pi(x) while the entropy of chaos left is lnx/x . x = infinity at phase transition point, so the bigger local structures are built in qbove quantum space, the bigger the difference between lnx/x and pi(x) , until, at last discrete scale, ln2/2 < 1 or ln1/1<1 .

if the state of perfect order is possible to reach, it would have only structure and no motion, so entropy would be pi/2.

As we know/ there should be 4 phases of Aether - one of which is perfect chaos, another structured chaos, another chaotic structures, another perfect order.

Each has a well defined number , entropy. 5th is missing- i think that is the one living inside that phase transition between SQ and quantum, may be wrongly.

That is as far as I have got.

Messages In This Thread
RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/30/2008, 08:21 PM

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