Cosmology

[desiresjab]

There is Euler's formula which relates e and sines and cosines. If you put pi in for x, you get Euler's identity. This relates e, pi and i together.

Fourier analysis can approximate general functions with sums (superpositions) of trig functions. My positivist leanings make me doubt that reality actually contains these superpositions, for example the view that one might be able to use them to split reality into "many worlds", although they make a mathematical model of reality easier to work with.

Lie algebra is applied to infinitesimal transformations. This sounds like it could be relevant to the quantum jumps you spoke of earlier. I know that a particular brand of it is being used by at least one research group to investigate relations between consciousness and quantum theory, which automatically makes it of interest. In various algebraic structures some normal properties of arithmetic hold and others do not. The kind of object it is depends on which particular properties hold and which do not. Monoids, groupoids, sub groups, magmas, lattices et al, all merely pervert one or more of these properties or eliminate operators. Good old Abelian groups have all the properties of normal arithmetic, I believe, right up to commutivity. Everything else seems like a brand of perversion of Abelian groups to explore deeper and deeper complexity and explain more relations easily. But the non-Abelian structures work, too, and have plenty of applications in advanced research.

Maybe models from one of these structures will eventually be able to capture some laws of consciousness in quantum mechanical math, or even vice versa! Wouldn't that be something? One cannot help but think of the words of Yeats, since this is a literature forum: Whatever flames upon the night/Man's own resinous heart has fed.

Are the laws of consciousness to be found in quantum mechanics, or the laws of quantum mechanics in consciousness?

[desiresjab]

The continuity of important transcendentals might be the most natural smoothing functions across quantum jumps, similar to Euler's Gamma function and the factorial function. The action all takes place in the complex system, not the lowly reals, these days. The great graphs like the Mandlebrot set, all come from complex number manipulations. Attempts to solve the Reimann hypothesis, for instance, the most important unsolved problem in prime number theory, take place in the complex domain. If it falls, other important problems will fall right behind it, yielding many conjectured and unproven results.

[YesNo]

I don't know what you mean by the "continuity of important transcendentals".

[HCabret]

I like when non-scientists talk about quantum mechanics like they have anything approaching an understanding of it.

"I think I can safely say that nobody understands quantum mechanics" -Richard Feynman

[YesNo]

Yeah, it is not easy to understand. Nor is it easy to understand why it is so hard to understand, but if Feynman could not understand it either, I feel in good company.

[HCabret]

Yeah, it is not easy to understand. Nor is it easy to understand why it is so hard to understand, but if Feynman could not understand it either, I feel in good company.

I am completely uncomfortable with my inability to understand quantum mechanics. I am, however, confident enough to admit that I have literally no understanding whatsoever of quantum mechanics.

I've read Elegant Universe, and I barely understand the big picture basics of general relativity. At least enough to watch Interstellar.

[desiresjab]

I don't know what you mean by the "continuity of important transcendentals".

I was clumsy with that. What I intended was that the continuing values in each decimal place of pi or another constant might turn out to provide best-fit bridges of continuity across quantum jump states. Speculation. Dreaming. I wouldn't put it past them, though. Something for a science fiction story.

[desiresjab]

I am completely uncomfortable with my inability to understand quantum mechanics. I am, however, confident enough to admit that I have literally no understanding whatsoever of quantum mechanics.

I've read Elegant Universe, and I barely understand the big picture basics of general relativity. At least enough to watch Interstellar.

I think one of the things that now makes physics so appealing to artistic types is its mystery. The quantum world is not the same old Isaac Newton block party. It is not even the Einstein block party. It is a wilder party than both.

[desiresjab]

If no universe is possible where two is not the successor of one, that would act as a constraint upon a creator of universes, would it not? Or would act as a constraint upon the random creation of universes through any process, if you prefer.

But does this even qualify as a constraint, since it does not, in fact, eliminate even one possible universe? It is as tautalogical as saying: You may not create any universe which may not exist.

Now the big question? How much of basic arithmetic must be true in any universe we can conceive of--a universe of actual particles and physics, not just abstractions? Not enough is known about how particles come to exist in the first place to answer this authoritatively.

But even in our everyday world various algebraic structures have numerous and sometimes profound applications and implications, though they are not of our natural "home algebra." Each one of them defies axioms of our home arithmetic by tweaking just one or more deep properties, such as distribution across multiplication or association across addition, and letting the system run, so to speak. My belief is that the job is going to require all the tools of mathematics and likely some strains that are not invented yet.

Could a type of universe whose existence is impossible from our perspective ever make the leap from abstraction to reality? Does our inablity to imagine a universe make its existence impossible?

[YesNo]

I am completely uncomfortable with my inability to understand quantum mechanics. I am, however, confident enough to admit that I have literally no understanding whatsoever of quantum mechanics.

I've read Elegant Universe, and I barely understand the big picture basics of general relativity. At least enough to watch Interstellar.

I don't know much about it either. Someone posts something. I check it out further. Jim Baggott's "The Meaning of Quantum Theory" is a good summary of the issues.

Quantum physics is not only for physicists as desiresjab mentioned earlier. It is not Newton's or Einstein's block party. The standard Copenhagen interpretation ties the hands of physicists with its positivism and leaves the interesting interpretations for those willing to speculate on what reality might actually be. It is now a philosopher's playground.

[YesNo]

If no universe is possible where two is not the successor of one, that would act as a constraint upon a creator of universes, would it not? Or would act as a constraint upon the random creation of universes through any process, if you prefer.

Since our universe had a beginning and is finite, I assume there are other universes. However, I don't think the various universes were created randomly. That is the sort of speculation one can expect to hear from those pushed up against the wall with our universe having a beginning who do not want to admit that something or someone made a choice to start it. I am not interested in looking for constraints on whatever consciousness created ours.

But does this even qualify as a constraint, since it does not, in fact, eliminate even one possible universe? It is as tautalogical as saying: You may not create any universe which may not exist.

The more interesting question is does one need consciousness for our universe to exist at all.

Now the big question? How much of basic arithmetic must be true in any universe we can conceive of--a universe of actual particles and physics, not just abstractions? Not enough is known about how particles come to exist in the first place to answer this authoritatively.

But even in our everyday world various algebraic structures have numerous and sometimes profound applications and implications, though they are not of our natural "home algebra." Each one of them defies axioms of our home arithmetic by tweaking just one or more deep properties, such as distribution across multiplication or association across addition, and letting the system run, so to speak. My belief is that the job is going to require all the tools of mathematics and likely some strains that are not invented yet.

Could a type of universe whose existence is impossible from our perspective ever make the leap from abstraction to reality? Does our inablity to imagine a universe make its existence impossible?

I think we already discussed this and I granted that mathematics is true in itself. It does not depend on the existence of a universe for it to be true. So the question of how much of basic arithmetic must be true in any universe is trivial. If the mathematics is logically consistent, it is true in any universe.

This sounds to me like you are confusing models with reality. Our universe is not reducible to mathematics. Some theories within mathematics may find use-value as approximations of reality. They allow us to make predictions through them more simply, but those models are only approximations. They are not reality. They did not create reality.

This is one of the reasons I brought up the Tarot earlier as well as economics or psychology or Elliott Wave technical analysis of the markets. These are all models which offer some predictive power, but they have little mathematics backing them up. My point: a useful model of reality does not even have to be mathematical.

[YesNo]

If no universe is possible where two is not the successor of one...

It occurred to me this morning that two being the successor of one is a binary order relation on the set of integers. One could also define an opposite binary relation where two is less than one. Both of these relations would be possible in all universes, both real and imaginary, since they are based on definitions which are independent of those universes.

[desiresjab]

It occurred to me this morning that two being the successor of one is a binary order relation on the set of integers. One could also define an opposite binary relation where two is less than one. Both of these relations would be possible in all universes, both real and imaginary, since they are based on definitions which are independent of those universes.

That would not interfere with duality. Duality is independent of the spelling of the numbers one uses to define it.

[desiresjab]

It occurred to me this morning that two being the successor of one is a binary order relation on the set of integers. One could also define an opposite binary relation where two is less than one. Both of these relations would be possible in all universes, both real and imaginary, since they are based on definitions which are independent of those universes.

I don't think that would interfere with duality. Duality is independent of the spelling of the numbers one uses to define it.

It seems much more simple after all to ask: How much is it possible for home arithmetics to differ in other universes from our own? No doubt mathematics could be approached in different ways. Requiring rigorous proofs (our way) would be only one way to proceed. Does mathematics always end up in the same palce, no matter where it starts? It is not the same even among human cultures. Yet mere counting is at the heart of all mathematical beginnings that I know of. Must that itself be so? I find it difficult to imagine how a civilization might come upon the arithemetic of matrices first and then develop our normal arithemetic as a strange alternative. Could our fundamental arithemetic seem strange to them but operations on matrices seem completely normal and natural? Not sure how that could happen, or if it could. How would such a universe support that view?

[desiresjab]

In the end I go back to Shakespeare. There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy..

How so? I have even dreamed of universes I cannot imagine. Therefore all of these and more must exist, if Shakespeare is right.