continuity

[AntonioLao]

In one desktop dictionary, it is defined as the state of being continuous, an unbroken succession, or a logical sequence [perhaps of thoughts]. The word ‘continuous’ is defined as unbroken, uninterrupted, connected throughout in space or [and] time. However, in this context, continuity would be defined as the single point connection between two quanta of space-time charges. On the other hand, since the topological surface of a space-time quantum holds a one to one correspondence with the double infinity of points of two linked circles (or any two closed loops will suffice, more so if these loops are equivalent to the Möbius topology), a single quantum of space-time is always everywhere and everywhen connected equally but not totally to twice infinities of infinitely countable space-time points with the caveat that if a single quantum is completely connected to singular infinity it cannot be connected to twice infinities. The inability to connect prevented it from performing contact transformation to go beyond singular infinity. This is equivalent to a guiding enveloping umbrella principle of directional invariance asserting that absolute motion and hence absolute rest is forever localized to the infinitesimal domain of the space-time continuum while the principle of relativity remains valid only between two infinities.

For the purpose of clarification, the double infinity of the real number line can be used to illustrate the idea. The infinity of the irrationals can only exist between two given rational numbers, says, between zero and unity or between 1 and 2 or between 2 and 3. Likewise, the set of integers (both negative and positive) can exist only between negative and positive infinity of the real number line. Historically, efforts of mathematicians to go beyond singular infinity made the discoveries of imaginary numbers and the complex numbers. Efforts to extend them out of the one-dimensional real number line or the two-dimensional complex plane created the mathematics of quaternions, vectors, and tensors. However, none of these mathematical formulations can break the barrier of double infinity.

[labelwench]

Antonio,
Are you able to explain, as for a child, what you mean by this statement....

However, none of these mathematical formulations can break the barrier of double infinity.

Thank you for your consideration of my request.

Labelwench

[PoPpAScience]

Hi Antonio;

I enjoying reading your posts, even though I only have grade ten math in my head. I was always the top student in math at school and should have made a life of it. But leaving home at 16 stopped that endeavor.
This year I have been contemplating on my theory of "Infinity for Eternity" and hope to write it up and post it this winter when I have time. I wish I had your level of math skills to add to it.

In "Infinity for Eternity" I say that Space/Substance is infinite in nature. It can be attenuated, but not individualized.

I woke this morning thinking that Substance/Infinity seeks rest, that's why it is centre seeking when it is in motion. Infinity/Space continued at rest far longer then in Motion, so is inherently restful. It is the child of "Infinity for Eternity", Motion, that disturbs the resting nature of Infinity/Space/Substance.

Eternity/Continuity/Time has the opposite nature of Infinity/Substance/Space, it seeks to be in Motion. It is this interaction of seeking Rest and seeking Motion, that gives rise to the force of Centripetal. Centripetal force being the engine that builds all form.

Centripetal force attenuates "Infinity for Eternity", creating form.

I love the name of this thread. It is what I have been contemplating about all this year. I have been contemplating about the most under discussed topic of reality, and that is the 'continuity of substance'. The fact that the core substance of this universe exists continually. I like to call this continuity: Eternity.

The Continuity of Substance, is "Infinity for Eternity".

I hope to be able to express more clearly my thoughts about "Infinity for Eternity" someday. But, as you know, Infinity and Eternity are not easy things to talk about, let alone express.

[AntonioLao]

mean by this statement

The lack of visual inputs derived from experience. However, in mathematics, no one can see a number without its physical correspondence, for example 2 and 2 apples. The former is an abstract input the latter is a physical and real inputs.

[AntonioLao]

The Continuity of Substance, is "Infinity for Eternity".

Unfortunately, modern science and technology are based on the quantum nature of physical reality.

[PoPpAScience]

Unfortunately, modern science and technology are based on the quantum nature of physical reality.

Yes, modern science is based on the quantum nature of "Infinity for Eternity" in Motion. Physical reality is the product of "Infinity for Eternity" in Motion.

[SteveA]

In one desktop dictionary, it is defined as the state of being continuous, an unbroken succession, or a logical sequence [perhaps of thoughts]. The word ‘continuous’ is defined as unbroken, uninterrupted, connected throughout in space or [and] time. However, in this context, continuity would be defined as the single point connection between two quanta of space-time charges. On the other hand, since the topological surface of a space-time quantum holds a one to one correspondence with the double infinity of points of two linked circles (or any two closed loops will suffice, more so if these loops are equivalent to the Möbius topology), a single quantum of space-time is always everywhere and everywhen connected equally but not totally to twice infinities of infinitely countable space-time points with the caveat that if a single quantum is completely connected to singular infinity it cannot be connected to twice infinities. The inability to connect prevented it from performing contact transformation to go beyond singular infinity. This is equivalent to a guiding enveloping umbrella principle of directional invariance asserting that absolute motion and hence absolute rest is forever localized to the infinitesimal domain of the space-time continuum while the principle of relativity remains valid only between two infinities.

For the purpose of clarification, the double infinity of the real number line can be used to illustrate the idea. The infinity of the irrationals can only exist between two given rational numbers, says, between zero and unity or between 1 and 2 or between 2 and 3. Likewise, the set of integers (both negative and positive) can exist only between negative and positive infinity of the real number line. Historically, efforts of mathematicians to go beyond singular infinity made the discoveries of imaginary numbers and the complex numbers. Efforts to extend them out of the one-dimensional real number line or the two-dimensional complex plane created the mathematics of quaternions, vectors, and tensors. However, none of these mathematical formulations can break the barrier of double infinity.

Basically it sounds like you're saying much the same problems I've seen.

A deterministic system describes cause and effect relationships that are linear. (They also happen to be required to retain all information as 1 to 1 mappings along the way if they're to be provably correct, otherwise any number of initial states could lead to the observed results - this is often overlooked)

If anything non-deterministic exists, then it can't be described in terms of this predictable mapping along a line and we have to add a second dimension - now there are choices about which linear sequence is selected, but the selection process itself is not deterministic and so these separate 1 dimensional "threads" are not logically/deterministically connectable. If the selection process was determined by such a linear sequence, then these 1-D sequences would be limited in length and all lie in a single dimension.

The can exist multiple unbounded quantities and variables or unknowns in a single dimension if the length of that dimension is not known, though the length can be seen as the single controlling factor by which all these other infinite/unknown/variables are dependent.

As soon as we add a single additional unknown/variable/infinite quantity and we do not attach it in relationship to the length of the first dimension, then it's a free parameter that exists in another dimension and it becomes unrelated to the first dimension (it not longer exists within the same space as the first).

So if we were to say that some truly indeterminant form of selection can choose a position in a second dimension, then this effectively disconnects all the lines in the first dimension as they're no longer related.

Whereas if we instead construct relationships across this 2-dimensional space, then knowing the value in 1 dimension will limit us to some deterministic subset of the second dimension and so these two dimensions can be seen as nested.

Though much has been learned by people pursuing 10-11 dimensional string theory, these ultimately need to be compressed down to a single dimension and "Universal Computation" is a generalization of string theory. There's nothing that a string theory could predict that we couldn't describe using transistors or 2 input NAND gates or a Rule 110 automaton etc.

In the end, any form of provably correct, deterministic logic appears to be constrained to describing 1 to 1 mappings over time between states - if this, then that (which implicitly becomes this) and that again and again ...

Because we can't work with an infinite quantity of symbols in science (it might be assumed we could continue to construct ever larger and larger numbers, but it isn't possible to predetermine where these will be placed over infinite spaces and how to locate them - communication and the representation of numbers in science occurs via. physical means and this is a real limit to science - it's possible that individuals can go further, but science isn't going to be able to provably follow), these relationships must ultimately repeat and so everything deterministic forms a loop in time and that's where strings are derived.

It may be that reality is not something entirely provable nor something entirely deterministic - if there exists even a single unknown at any point in time, then there can exist an unlimited number of unknowns over any quantity of time, because a single unknown is capable of transitioning between two timelines that are indistinguishable for any length of time, yet ultimately become divergent in any number of ways.

Notice that in science, the attempt has been to place all the unknowns into a single unknown at the "beginning", which is simply any unobservable point and this can be seen as correct in that having multiple unknowns is logically redundant - one unknown is enough, but notice as well that this unknown never disappeared and remains existant and is measured constantly in the present as well. So we have the continual influence of a potential, if not required, infinity over time.

A good question would be whether or not time is separate from this infinite source. It could be that the first dimension - time itself was always indeterminant and that all deterministic states collapse into points in this sequence (actually that's probably what happens. I haven't been able to figure out how a deterministic system could perceive time - in fact the idea of a deterministic system evolving over time, in itself appears to possess a possible paradox - how can something that is entirely determined with absolute certainty change? Only the entire "table" or mapping remains constant, not the current state within it, so the system itself is what is constant and unchanging and deterministic, but not the transitions because we need to know where we're at within the system, but the system cannot also tell what specific state is being observed within it without collapsing the system to only describing a single point, those "wave collapses" can't be deterministic relative to the system describing the wave but could only be deterministic relative to something outside it, if that)

[Meem]

Microwave background filtering and analysis? I heard some of the theories about time and time travel have the idea that it could be possible to send a message through time or possibly dimension with microwaves. And if it were possible, that there should be some sort of message in the "big-bang." It was a little more specific and sounded pretty interesting.

[SteveA]

I think I'm getting a better picture of the problem.

Consider that a logical system, in which everything is interrelated and changes by rules needs to be filled with information. Logic itself needs to exist (as well as the data it works with).

Now even if logic and data can be compressed to a single thing, there's still that initial thing from which it all unfolds.

Now what defines that first thing? Nothing can define it. Everything that defines something is already inside it, it has to be the first seed and nothing can constrain what it contains and this single seed can unfold into anything without limit - everything else that's logically determined by that seed must ultimately be connected to it though and similarly anything that can be described in a predictable way in science must be attached to it, but there is no limit beyond this as to what it can ultimately become.

[SteveA]

Microwave background filtering and analysis? I heard some of the theories about time and time travel have the idea that it could be possible to send a message through time or possibly dimension with microwaves. And if it were possible, that there should be some sort of message in the "big-bang." It was a little more specific and sounded pretty interesting.

In some ways this is entirely normal - the mind is already able to predict physical events before they occur and know future properties - we don't have to wait around for a falling apple to hit the ground to know that it will eventually hit something (if nothing else decides to alter it) and when the Sun rises in the east, we know it will later set if the west (unless, once again, something else decides to alter that).

Physically there is no setting in the west or apple hitting the ground yet, but the mind is capable of making predictions of the future (unless some will decides to change its mind).

Of course these are just mundane and mostly instinctual examples, but consider that knowledge of the future isn't particularly beneficial unless it's alterable, in which case this foresight would appear unreliable and uncertain.

For example, let's say that you knew that you knew you'd get in a car accident tomorrow and so you decided to not drive, and lo and behold, you did not get in a car accident. Now did you actually predict the future correctly? No, though you may have correctly predicted a consequence to one possible action.

This is also an ability that we already possess - I know that if I don't take a shower for a week, some coworkers will likely complain - I have foreknowledge of the future and a result that will occur if I choose a certain path of (in)action. I don't particularly want to prove my intuition correct though and my coworkers wouldn't want me to test this theory out either. So I will instead predict that I will take a shower this week and that my coworkers will not complain in that regard ... and lo and behold, my predictions will almost certainty prove true (unless something else decides to change something).

So anyway, all these components that many people consider to be impossible already exist. The only difference is that it's such a familiar experience that people overlook it and if we consider that someone perceptive and able to make intelligent (and wise?) predictions of consequences is already doing this, then it may be more of a matter of degree instead of possibility. Of course there's no utility to any of this knowledge without actions (will) made dependent upon them, so these elements can be seen to already exist in daily experiences, but I think the better able one is to see the "butterfly effect" the more efficient (which can also appear as subtle) ones actions can be in determining the results. There's probably a way that by moving a single pebble somewhere on the Earth you can change who becomes the leader of some country a year from now ... of course the interactions are far too complex to be realistically analyzed, but the possibility appears to be there and how knows if there might be something quite instinctive to these relationships. It may be that we already do things instinctively like this that are not yet understood until the consequences are physically observed later - it generally takes much more processing power on a computer to learn to do something than it actually takes to simply do it, once programmed specifically to do so. Or similarly, a computer can simulate another computer, but at a much slower speed and from a real-time perspective the "density" of the simulated component is much smaller than the unsimulated component over a time (though that's somewhat paradoxical in that it can't be simulating itself without simulating simulations ad infinitum, so there would always be something "above" the simulation that was not simulated).