spacetime inverses and 1-to-1 mapping

[labelwench]

I thank you for new directions to explore, not to be interpreted as total comprehension or even the ability to continue the dialogue at the present moment.

Several challenges to deal with in the slow motion world of 3-D tomorrow, albeit considerable mental and physical dexterity shall be expected from this biological unit.

I bid you gentlemen good evening and look forward to catching you somewhere on the flip side.

Until then........

Push the limits, gentlemen.

We have nothing to lose as anything that can't hold it's own will shake down in the process of examination from a multitude of perspectives.

[SteveA]

Thank you very much for the pleasant company, Lorrina I think you're one of those bright spots on the horizon and it's nice having the inspiration.

Enjoy your evening and sweet dreams.

Until later ...
Steve

[SteveA]

As a more detailed mathematical extension of this, imagine a fundamental unit of time filling space at the equivalent of an infinite (though a precise, singular and maximal form of infinity) velocity.

I'll call this quantity, Time, and it's basically the largest natural number that constructs existence at any moment and there is no other natural number greater than it, so by this definition, all problems exist on a single ("existencial" ) natural number line and all unknown quantities or variable arise from the influence of a single unknown quantity, Time.

Using this form of mathematical system we can derive many forms of mathematics that can be applied on fundamental/quantum scales. For example, two representations of Pi that are constructed via different forms would not be identical, except to whatever extent there existed specific moments/quantities of Time that allowed these two forms to be constructed identically.

For example, perfect binary hypercubes would only be capable of being constructed with fundamental units having volumes as powers of 2, such as 1, 2, 4, 8, ... and the density of these ideal volumes with increasing quantities of "Time" would decay logarithmically and as an example, we could say that recurring physical phenomenon that required such to exist would either become "infinitesimally" rare (though this is not a vague "infinitesimal", by this definition, but a precise relationship relative to Time, which would happen to be unknown, but we could assume effectively infinite) or alternately that systems version of Time (which would just be a lowercase time as it would not be fundamental) would have to also logarithmically decay relative to Time and retain some constant relative quantity of intersections with those powers of 2.

We could apply approximate methods to this by defining all mathematical forms as arising from a single natural numbered quantity and derive the equivalent of a real number line as an ordered set of mathematical forms that in the limit grow with some constant ordering in their relationship between them and we can assume that the only valid functions result in quantities less than t and any set of quantities that exist in a relationship cannot sum to a value equal to t (unless it was known to be some complete set of operations).

For example (for n>1)

1<n<log(t)<t^(1/n)<t/n

1 and n would not be dynamic quantities and infinite, but represent objects within a space.

A multiplication by 0 can be defined as a division by t and this allows us to retain a logical connection/form in the construction of a multiplication by 0 as a scaling toward an infinitesimal. Additive zeroes can be removed from an equation as they're uninfluencial.

Notice that we can construct definitions like this, due to the fact that t is similar in calculus to a reference of some variable approaching infinity:

1/t=0
t*0=1
(1+1/t)^t=e (base of natural log, though there's actually a more precise way of defining e as this form is not really the ideal definition of e)

We could construct a nested space, using these "dimensions above", by recursively applying these structures (though there are more forms of growth that could exist, such as an inverse factorial growth would be between constant, n and log(t)):

For example if we recursively applied the set of operations to logarithm, we'd have:

log(1)<log(n)<log(log(t))<log(t^(1/n))<log(t/n)

And we could embed this within our initial "infinitely ordered number line":

1<n<log(1)<log(n)<log(log(t))<log(t^(1/n))<log(t/n)<log(t)<t^(1/n)<t/n

We could proceed to continue to do this and create a fractal tree of structures interleaved over a common space with boundaries similar to phase transitions between areas of space (for example, moving from log(t^(1/n)) to log(t/n) creates a specific form of "dithering" between these two spaces).

We could also see each of these as shells of expansion over Time that cross and interact between each other with various densities as Time progresses.

Slower growths require greater quantities of interconnections or "higher dimensional" forms of motion/growth and so higher dimensional structures are witnessed toward the interior of this expansion, whereas the leading edge of time is nowhere specific within any of these spaces and is interleaved throughout all of them.

For a rough or course approximation to the magnitudes of infinite growth, similar to calculus, we could just construct a representation similar to a ternary (3 symbol) code to describe which of those 3 possible operations had been applied to construct a space. And if we assigned 1 to represent a logarithm, 2 to be a fractional polynomial and 3 to represent a fractional scaling, then we could list (n>1):

0.0=n

0.1=log(t)
0.2=t^(1/n)
0.3=t/n

0.11=log(log(t))
0.12=log(t)^(1/n)
0.13=log(t)/n

0.21=log(t^(1/n))
0.22=(t^(1/n)^(1/n)
0.23=(t^(1/n))/n

0.31=log(t/n)
0.32=(t/n)^(1/n)
0.33=(t/n)/n

and we could construct these to arbitrary lengths, though they possess specific orderings and it's convenient if we append a 4 to the last digit:

0.0=n -> 0.04

0.1=log(t) -> 0.14
0.2=t^(1/n) -> 0.24
0.3=t/n -> 0.34

0.11=log(log(t)) -> 0.114
0.12=log(t)^(1/n) -> 0.124
...

Then we can place all these forms of growth as ordered shells of expansion with different spacial properties:

0.04 (fixed objects of n way symmetry) < 0.114 ( motions arising from 2nd order or two orthogonal layers of exponential/logarithm structures) < 0.124 (motions of logarithmic/exponential forms nested within polynomial or Euclidean multidimensional spaces) < 0.134 (etc.) < 0.14 (etc.) < 0.214 (etc.) < 0.224 < 0.234 < 0.24 < 0.314 < 0.324 < 0.334 < 0.34

These can exist similar to adjacent spaces with independent properties that are near enough to each other to potentially be seen to be continually accelerating into each other (like overlapping branches of a tree, but this is a tree of infinitely diverse forms of unique and infinite forms of motion - basically the equivalent of the space of interaction between otherwise independent infinite lives).

We could extend upon these with other forms of growth, but the can grow quite complex. The areas in which much of the diverse dynamics occur are between layers of these expansions as they split over Time (similar to areas where two branches begin to spread away from each other but some interactions between them remain) and there could exist some spaces of intersection that contain properties of all forms of conceivable motions (however large the list is, as long as it's finite there can be specific areas/locations within this "tree" that dynamically extend over time with intersections of all these forms of motions present in different densities, and even potentially dynamically alterable)

Yes, I recognize these concepts are quite difficult to follow, but still a few keywords might click for people ... anyway, it seems like at least one quite interesting pathway to explore

If we interpreted those operations similar to a DNA sequence, threading the needle between those two (or more) infinite pathways might vaguely resemble traveling through this structure? Though there could be a few extra forms of "orthogonal motion" that could be added ... might want to put together a wish list

[AntonioLao]

Who can honestly testify that they achieved complete one on one reciprocity with themselves, with someone, with a thing or two, with God, or with their own demons? Reciprocity in this case would mean a positively constructive (not destructive) continuous feedback loop.

[SteveA]

Who can honestly testify that they achieved complete one on one reciprocity with themselves, with someone, with a thing or two, with God, or with their own demons?

A new position in this space would not be identical in all aspects to a previous position, though this space does have highly fractal and recurring features. Some structural forms recur rather predictably.

The information required to select even a single unique quanta out of an infinite spacetime is also infinite (of a lower order, but all infinite things are effectively identical over time in this respect - the limit of the square root of an infinite quantity is also infinite and so is the square root of a square root etc. and in fact these have a contextual gain of information present in the spaces of each of these as they become embedded within higher dimensional (perceptual) spaces, yet retain that infinite quality as well).

I don't even think we're experiencing time in its fundamental form, which also provides a lot more freedom of motion in time. Does time have a direction? Well you can search around and try to find it ... my suggestion is that time does it wants or is driven to do. There's fundamentally no form or structure that appears capable of constraining time, except potentially desire. What determines what that is? Well I can only assume that whatever experiences time would have the best guess at what that direction is.

Reciprocity in this case would mean a positively constructive (not destructive) continuous feedback loop.

In a sense, that's an inevitable state in time. There's no manner to make a decision in time, related to events in time and not have it be such a positive construction from the perspective of making that decision and experiencing the results of it.

The presence of the ability to interact with/in time is itself such a continually creative influence.

The most basic form of choice appears to simply be the binary decision of self-determination or not - whether to simply allow additional unknowns accumulate or to apply a selective reconfiguration of things (relative to ones values, which would be appear to be the equivalent of a second dimension of possible time arsing from the existence of self embedded within this - it's extent would be a function of available resources and effectively finite relative to self, but that same self, though of a lower order form of growth, can exist within a higher dimensional context and because that self is also a function of an infinite, grows or is infinite in time and those finite resources, as recursively nested components of self similarly grow).

The possible directions in which such motions of self can occur are also potentially infinite and we can convert a linear represenation of an infinite quantity into a contextual infinite number of degrees of freedom and that can arise within the context of the second dimension of time as derived by a vector orthogonal to the perceived direction of time in (perceptual) space by self.

This would require a mechanism to learn all motions (such as a computation of Eigenvectors, these are commonly used in artificial intelligence) existing in the perceived direction of time and an ability to construct an orthogonal motion to it (which would require a locally growing spacetime/memory of events).

We could extend upon this in greater detail including ways to optimize things with parallel searches for value functions etc., but the real question I guess is simply, could we restrain reality to not have such things? I'd have to say that likely we could never describe the capabilities and our wildest dreams hardly begin to touch the potential.

If there was some God that created the place, do you believe such would beyond his/her/its capabilities?

If you could explain how time operates, that might help place limits on its capabilities, but I haven't been able to find much of anything to constrain it to being of a specific form.

My comments were regarding how to transform information accumulated over time into a representation that provides a space of greater, though more local freedom. (We convert a more linear space of events into a higher dimensional, less distant and more relevant version by applying personal values and a little time Sounds much like a prototype of real life? Once again, likely not a coincidence as most mathematical functions tend to have persistent or recurring features of one form or another).

What can I say Antonio, I've given up trying to explain how time is possible. It's something that appears to be beyond description. There is no specific form that constrains it to being one thing or another, so I give up assuming it must be constrainable to a potential limited by comprehension . Time won and I'm going to flow with it for a while ... kicking and screaming and making a lot of growing vortexes to add to the stream and learning along the way (I'm still trying to line up a nice shot to see how far it can go! ). Feel free to make yours as large as you want too - they end up overlapping perfectly - and at least there's one thing that logic is good for.

[AntonioLao]

I will be back with a longer reply...

[AntonioLao]

Since the year 1905, the concept of time was mathematically joined with 3D space by Einstein and others. The new concept of spacetime became physically successful in the hands of many physicists. Dirac as the founder of quantum field theories (QFT) was able to combine the old quantum mechanics with special relativity of spacetime thus creating a relativistic quantum mechanics which described a theory of electron spin that agreed with experimental observations and calculations of spectral emissions and absorption of quantized energies of atomic orbitals. Consequently, the theory of atomic orbitals became the foundation of all chemical elements and heralded the success of other sciences and much of modern technologies. However, the most surprising prediction from Dirac’s theory of the electron is the possible existence of antimatter.

The concept of time became a useful physical construct as a mathematical object that indicates certain uniformity of physical quantities. This uniformity strongly suggests that time as a physical quantity can never be slowed down or speeded up. Its rate of change is a true constant of nature. On the other hand, the rates of change of all other physical quantities with respect to time can vary from constants to exponential growth and decay while accelerated changes are rates of change with respect to time with respect to time. This twice time respecting implies that true absolute physical quantities must always change with respect to the square of time. The change of length (linear displacement) with square of time is defined as linear acceleration while the change of angular displacement with square of time is defined as angular acceleration. The latter becomes a very important component for all successful quantum theories from Bohr’s quantized angular momentum to the spins of fermions and bosons. Nevertheless, unless superstring theories incorporate the square of time in addition to its 10 spatial dimensions instead of 10-space plus 1-time of 11D, no convincing demonstration for the existence or non-existence of graviton can be given. The truth of the matter is that the best theory of gravity such as Einstein’s general theory of relativity is really based on the principle of equivalence between linear and angular acceleration with respect to the square of time. Subsequently, square of time is conjugated to the square of energy to give a more predictable form of the uncertainty principle.

[Lloyd Gillespie]

Dirac was correct, until the pop-physics culture talked him out of his initial visions of a total and absolute photon sea__His first quantum field idea...

Time = Absolute linear c in vacuum, and group c-motions, in all other substances__The only foundation possible, to measure time against...

The last 100 years pop-physics culture, has just over-complicated the simple and absolute c, and group c-motions...

Antonio, define square of energy, without circular logic...???

[AntonioLao]

Square of energy is defined as the product of 2 primary forces with their 2 infinitesimal local gauges: FxFxGxG.

[Lloyd Gillespie]

I still see no physical entity answer, in your answer Antonio__just guage fields of more ungrounded math...