# Stuff and Things > HISTORY, veterans & science >  the vocabulary of AI and quantum reality

## nonsqtr

I keep telling y'all the Copenhagen weenies were having a bad day. ("Decisions by committee", nyuk nyuk). The cat is NEVER both alive and dead. There is no condition or set of conditions under which the cat is both alive and dead. Such a construction is simply LUDICROUS. So let's talk about what's really going on.

But let's not use the vocabulary of the clueless group of physicists at Copenhagen (  :Yo2:  ) - instead, let's make use of some concepts from neuroscience and AI.

The central concept of the quantum state is that "all possibilities exist" until something is measured. (Some people say "observed", but that's not accurate - it's a measurement that involves an interaction with the environment).

In AI, we call this a "possibility space". It is a space of possibilities, which technically speaking has a representation in memory - and usually it is a "restricted subset" of the total information space based on contextual constraints - so you can look at it like a "buffer memory" that gets loaded in the short term with "possibilities related to the current situation".

The possibility space in AI, has the same features as the quantum state in physics - the members are "probabilities", and the outcome is unknown until it's actually looked at. "All possibilities exist" until the moment of collapse, as it were.

Some people confuse the wave-like nature of photons in a double slit experiment, with the idea of probability waves in a quantum state. The two are not the same, they're distinct phenomena. Up and down spin is not the same as a quantized Hilbert space.

What is really happening at the moment of measurement? Well... in terms of information, at that point, many possibilities are being reduced to one. So, you actually have LESS information (in the system) after the collapse. Before there were many possibilities, now there's only one - that's a loss of information. The system is giving up information to the environment.

If we were to look at this in terms of information theory, the "before" state is lots of possibilities so the likelihood of any particular one is small - whereas "after", there is only one possibility and the likelihood of the actualized outcome is one. According to information theory this is equivalent to the proverbial "event that always occurs", in other words the information content is ZERO. "Before" you had a small amount of information, and "after" you have zero. The system has given up information to the environment.

And, the environment has picked it up - in the form of a measurement - which, as Smarty and I were discussing recently, really means "any interaction with the environment".

In AI, or in a neural network, what happens in these situations is the system goes to one of the corners of a hypercube - the one that represents the actualized outcome. This behavior corresponds to an "instantaneous phase transition" in a spin glass. It's highly dependent on the dimensionality, you get different behaviors in 2d and 3d because ultimately the topology matters. The Ising model of spin glasses is formally identical to the Hopfield model of neural networks. There is a pretty rich literature on phase transitions in spin glasses, it's worth a checkout.

So then, if this relationship is meaningful, it should also mean that the environment gives up information whenever it pushes a defined state into a quantum superposition.

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Foghorn (04-02-2021),Jen (04-07-2021),OldSchool (04-27-2021)

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## UKSmartypants

Exactly. The implication also being that matter, energy and information are equivalent and interchangeable. And its the lack of inclusion of information into the field equations that creates the holes in that Standard Model IMHO..... and thats cos theres no quantitative mathematical unit of information you can use in the equations. Eg whats the computational equivalent, the Informational SI unit of one gram of matter or one Joule of energy ?

so i reckon 

E²=(mc²)² + (pc)²   needs to be E²=(Imc²)² + (Ipc)²

where I is the information equivalence to M

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nonsqtr (03-31-2021)

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## nonsqtr

> Exactly. The implication also being that matter, energy and information are equivalent and interchangeable. And its the lack of inclusion of information into the field equations that creates the holes in that Standard Model IMHO..... and thats cos theres no quantitative mathematical unit of information you can use in the equations. Eg whats the computational equivalent, the Informational SI unit of one gram of matter or one Joule of energy ?
> 
> so i reckon 
> 
> E²=(mc²)² + (pc)²   needs to be E²=(Imc²)² + (Ipc)²
> 
> where I is the information equivalence to M


Well, so maybe we can reformulate the information piece into something more useful.

First let's consider some elementary features of the information landscape. 

The "bit" has two states - but you wouldn't know that unless you knew it in advance. So that's one axis, the dof in the unit.

And, what does a "0" mean? It does NOT mean "lack of a bit", it's actually one of two possible "states" of a bit. It COULD mean lack of a bit, if you were somehow "expecting" a bit...

So then, "how many bits" is interesting, because it matters whether they're labeled or not, and it's another dof. If they're not labeled then all you can do is count "how many" in the result set, but if they're labeled then you can tell "which ones" are in the set. A label could be a location in memory or a position within a byte.

And, if we consider a stream of bits we arrive at the distribution, which is where "number of possibilities" becomes important, because the sum of probabilities has to equal 1. So yet a third dof. And then the moments and the shapes thereof and so on.

So then, from the information theoretic standpoint, if you have one bit, and you increase the number of states from 2 to 3, then as long as the new state appears "sometimes" it means the probabilities of the other two states have to decrease and therefore their individual information contributions have decreased. (They've been "dissipated" by the new arrival).

If you add bits (say, double the number of bits from one to two), then if the bits are distinguishable (by position or label) you get n^2 the possibilities, and if they're not you get 2n+1. Either way the value of a single bit declines, relative to the total information space. (I hear a bell ringing at this point, do you?)

So then - the reason quantum mechanics works is because the structure of the distribution is known in advance, and the stationarity translates into the anterior probability being equal to the posterior probability in all cases. The Gibbs formalism guarantees this, the probabilities are calculated from combinatorics of available states.

But... when the information space grows, those combinatorics change. Central limit says they may only change "a little", but on scales of 10^2 to 10^4 they'd be well within the range to cause chaotic transitions and such. You can see this in action in a neural network - if you add one additional neuron into a network that's already learned, it'll adjust it's representations and you'll see new behaviors you never saw before.

Break time...

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## nonsqtr

K, so here's my proposal.

I propose, a "thing" has two kinds of information:

Self-information
Relative information

An example, is a bit within a byte. The bit itself has two states, that's self-information. And, it has a position within the byte, that's relative information.

The relationship between self and relative information can be visualized this way:

Consider a differential manifold M, where each point is defined to be a probability distribution over some other field X. Then, the metric tensor for this manifold is given by the Fisher information metric, and what it measures specifically is how much information about the distribution you get from a single observation of X.

Fisher information metric - Wikipedia

The Fisher Information Metric is the only Riemannian metric that maps statistical (probabilistic) manifolds. This means that such manifolds, simply by mapping to distributions, have an intrinsic non-trivial geometry.

Information geometry - Wikipedia.

That takes care of the first case. 

The second case is more interesting. It is basically "non-local structure", that is to say, you wouldn't know the position of a bit within a byte, unless you knew it in advance. And what it really is, is relationships (correlations), between said bit and every other bit. And such correlations may or may not be visible. If they are, they would represent coincident behavior in spacetime, either different places at the same time or the same place at different times. Non-local structure has deep ramifications for information - for example, if we remove a bit from a byte, does the whole byte become meaningless? Because if so, there is an instantaneous (not speed-of-light, because there is no transmission involved) change of information in the other bits just by virtue of having their external structures destroyed.

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## nonsqtr

Boy, that bell is ringing louder and louder.

So, non-local structure, and, instantaneous effect.

The idea of "superposition" is that all the slots in the distribution are being filled. And this indicates "more information", which is verified by the overloading of qubits and etc.

The thing is, the external structure must have meaning. In other words, let's say we were looking at the "4" bit in a byte. It's a 4-bit because that's the way the computer understands the structure - and if the 4-bit suddenly went away (like if someone yanked the wire or something) the computer would generate an error on the entire byte, because the structure has been destroyed.

So for example, in the Fourier domain there is built-in structure, in the form of harmonic relationships. In algebraic and geometric topology, there is built-in structure too.

Conceptually this seems easy enough, doesn't it?

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## nonsqtr

So then, back to the manifold. There are a number of ways of quantifying the effect of external structure.

First though - an observation on smoothness. We defined the manifold so each point corresponds to a probability distribution over some field X. And, we defined a tensorial metric on this manifold.

Consider now, a slightly different definition of "distance". Let's say we have (any) two distributions p and q, and we want to know how different they are. (Distance in terms of information, rather than distance along the manifold). For this purpose we use the Kullback-Leibler divergence D, which turns out to be a sum of piecewise differences:

Kullbackâ€“Leibler divergence - Wikipedia

In quantum-land these concepts are all based on "relative entropy".

Quantum relative entropy - Wikipedia

And in quantum-land, distributions are predictable in advance unless there are spooky things we don't know about...

However in neural networks the distributions are under the direct control of neural processes.

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## nonsqtr

So here's my proposed method:

I want to reconstruct the information "space". I don't know what that space is, don't know what it looks like. However I know some elementary things about it - like for instance, I have a Banach algebra of functions on the space (which follows from Hausdorff), and therefore I should be able to reconstruct the space from some category of sheaves on it, yes? (At least that should work in the commutative case)...

I'm not sure what do to with this non-commutative business yet. In stochastic-land very few things are symmetric (the "normal distribution" is quite the exception), for example the divergence D is in general not symmetric and not commutative (D(p||q) is in general != D(q||p))

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## nonsqtr

Well, fuck me royally.

There's a mathematician named Ulam who seems to have been after the same thing. An Ulam measure is a Banach measure that takes values in {0,1}. Here's one of his papers:

The conjecture of Ulam on the invariance of measure on Hilbert cube - ScienceDirect

https://www.jstor.org/stable/2303800?seq=1

Here's the "fuck me" part - the existence of the measure depends on the existence of a certain kind of transfinite cardinal number. I kid you not.  :Geez: 

Cardinal number - Wikipedia

Agh.

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Foghorn (04-02-2021)

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## nonsqtr

Help! Can anyone explain WTF they're talking about here?




> Equivalently, κ is measurable means that it is the critical point of a non-trivial elementary embedding of the universe V into a transitive class M. This equivalence uses the ultrapower construction from model theory. Since V is a proper class, a technical problem that is not usually present when considering ultrapowers needs to be addressed, by what is now called Scott's trick.


K is a "measurable cardinal".

Anyone?  :Thinking:

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## Oceander

> Help! Can anyone explain WTF they're talking about here?
> 
> 
> 
> K is a "measurable cardinal".
> 
> Anyone?


I thought K was one of the agents in MiB.

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Foghorn (04-02-2021)

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## nonsqtr

> I thought K was one of the agents in MiB.


So did I.  :Grin: 

This is actually pretty fascinating from the standpoint of pure math. The whole idea that points at infinity can determine the infinitesinal-scsle system behavior is pretty powerful.

But yeah, I'm looking for ways of quantifying non-local structure, and the only people who've done any useful work on this are the AI types. And most of what they use is based on pre-existing assumptions about the information.

Ultimately we have the same problem the physicists do: "renormalization". And it doesn't work so good in unmeasurable surfaces.  :Grin:

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## nonsqtr

K. So far so good. The manifold seems accessible and the topology seems accessible - the problem I'm having is constructing the space of distributions. I'd like it to be geometric, but that means I have to have smoothness and continuity between neighboring distributions, which is easy as long as we're only dealing with Gaussians, but becomes almost impossible in the general case. The only way I can think of is with piecewise construction and that's not even worth the effort, since we know in advance it'll be computationally intractable.

So, I'm looking for a combinatorial method. Which is not really my bailiwick. But here's what I'm thinking - you can use Dirac indicators to label and sequence the source set, and then you can generate all possible permutations if the source set "one bit at a time", so neighboring curves differ by at most (or even exactly) one bit. Which automatically defines a consistent metric, and if you can "represent" that geometrically you're home free.

Does that make sense? It's kind of the combinatorial equivalent of a space of functions, yes? I'm kinda flying blind on this, would appreciate any helpful suggestions.

I want to make a "space" from the possible distributions, and represent it geometrically. I want to order the distributions so the space is smooth and continuous, differing by at most one bit between neighbors. Is such a thing possible? I can't find that it's already been done...

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## UKSmartypants

> Well, fuck me royally.
> 
> There's a mathematician named Ulam who seems to have been after the same thing.


Hes the Ulam who came up with the Teller-Ulam design for a fission-fusion-fission device.  His concept, now called "staged implosion" was first proposed in a classified scientific paper,  _On Heterocatalytic Detonations I. Hydrodynamic Lenses and Radiation Mirrors

_
He once described himself as "a pure mathematician who had sunk so low his latest paper actually contained numbers with decimal points."

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nonsqtr (04-03-2021)

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## nonsqtr

K, so, I think I've discovered that the key is in the ordering. Trying to visualize a geometry that would make a set of permutations smooth. So let's say you have 8 qubits (for simplicity, and in keeping with the previous example). You can arrange them in order, and keep them all zero but allow the last one to vary. And, you can lay out the range of probabilities from 0 to 1 in the Y axis, in such a way that they're monotonically increasing. So great, so far so good, you have a smooth curve. The problem arises when you go to the second qubit, because there you have a discontinuous jump in probability from 1 to 0. So what you do instead is interleave all the qubits, so the "order" becomes a cycle 1-8, and you change one dP at a time until you get to the end, at which point you reverse direction and keep going. This way, all your changes everywhere are exactly one "bit" (or in the continuous case one dP which was the metric we wanted in the first place), and the endpoints are "special" only insofar as they specify where the direction should be reversed. So your final map ends up looking like this (representing qubits as 1-8 and states beginning with A which differ by definition by exactly one bit or one dP):

1A-2A-3A-4A-5A-6A-7A-8A
8B-7B-6B-5B-4B-3B-2B-1B
1C-2C... etc

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## nonsqtr

So, I think, it looks like I'm gluing together slices of dP but reversing all the even ones. Could it be that simple?

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## UKSmartypants

> So did I. 
> 
> 
> Ultimately we have the same problem the physicists do: "renormalization". And it doesn't work so good in unmeasurable surfaces.


Renormalisation is an abortion, its a way of fiddling the equations so they dont blow up into infinities.   They need to find a way to express field equations without reverting to renormalisation

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nonsqtr (04-04-2021)

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## nonsqtr

> Renormalisation is an abortion, its a way of fiddling the equations so they dont blow up into infinities.   They need to find a way to express field equations without reverting to renormalisation


Yeah. This is one of the reasons I'm studying singularity theory. It says, singularities can be handled by "expanding the dimension" at the point in question (algebraically). So why don't they do that? Is that verboten for some reason?

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## nonsqtr

K, here's a great graphic of the problem. This is an example from permutation theory, where you have 4 qubits instead of 8.



You can see that the transition from 4 to 5 is basically smooth, the graphs are "very, very close", but the transition from 5 to 6 is horribly discontinuous.

This has to do with the cycles in group theory, I'm sure.

Sigh.  :Frown:

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## nonsqtr

And I have another question.

Is there such a concept as "permutations of an infinite space"?

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## nonsqtr

Wow, this is deep stuff. The simple symmetric group doesn't work at all. There's something called a Lusztig group, here:

AMS :: Transactions of the American Mathematical Society

which looks somewhat like an affine Lie algebra.

Partitions and cycles. Jeez.  :Geez:

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## nonsqtr

Maybe I found a way to make this play.

Make the permutations a bijection, that way the "space" becomes a wedge product and the natural action is described by a torsor.

Which also lets me account for the non-commutative cases.

What do you think? Will it work?

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## nonsqtr

I'm going to start another thread called "the bizarre world of infinities".

I'm looking at permutations of infinite sets, and it turns out this has a lot to do with "series" and the construction thereof -

So y'know, here's the Riemann series which deals with convergence, but this thing is totally f'in WIERD, like, by a suitable rearrangement of terms (permutation) you can get the series to converge to ANY desired real number, or diverge.

And, where the weirdness is, is in the infinities. If you do the math on this you come up with totally nonsensical stuff, like the cardinality of K (an infinite set) is the same as the cardinality of K^K. Which totally contradicts Cantor's hierarchy of alephs and etc.

So like, I'm getting mad now 'cause it looks like I have to spend another year with the books just to answer a simple question. 

But I did have one interesting thought. (Shout-out to the string theorists). Would it be possible to "lift" the random space into a higher dimensional space that isn't random at all? So that, what "appears" as random in the lower dimensional space, is nothing more than a projection of things that happen in higher dimensions?

So then, translating - for a given random walk W(t), is it possible to find a set of *smooth, continuous* functions that describe the trajectory?

Conceptually it seems it should be do-able, since the walk is in fact continuous in both space and time.

If the walk can be described this way for one set of probabilities, then it should be describable this way for all sets of probabilities, meaning all distributions. Yes?

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## nonsqtr

Hironaka's Theorem says this should be possible.

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## UKSmartypants

> I'm going to start another thread called "the bizarre world of infinities".
> 
> I'm looking at permutations of infinite sets, and it turns out this has a lot to do with "series" and the construction thereof -



and BANG, he crashes into the Banach-Tarski Paradox........

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nonsqtr (04-04-2021)

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## nonsqtr

> and BANG, he crashes into the Banach-Tarski Paradox........


I hate that head banging stuff - ordinarily I'd smoke some weed to kill the pain but then I can't understand nothin no more...  :Dontknow: 

Well, on to the external part.

This part is kinda interesting, 'cause the concept of "correlation" misses the mark.

Consider the "bit within a byte" example. The relationship is "part of". It's not a correlated relationship because the bits change randomly according to whatever the byte says. But there is "external structure" that defines the byte, and the bit influences and becomes influenced by that structure when it becomes a "part of" it.

The structure assigned to the byte has a higher dimensionality than the structure of the bit. This is reflected in its information "distribution", which according to probability theory has to be normalized so the sum of probabilities adds up to 1. Therefore the more bits you add the less influence any particular bit has. This is not a property of the bit, it's a property of the byte. There are 256 combinations possible within these 8 bits, kinda thing.

This is definitely topology, no question about it. It looks like I have to play with the convergence of periodic series and things like that, and somehow map that onto group cycles. 

It seems that this whole area is sufficiently complicated that it makes sense to start with a simple example. For instance, it's easy to construct a continuous space of Gaussian distributions, which can be parametrized by two variables in the trivial case and a set of (decomposable) moments in the general case.

(btw, ain't it convenient how the physicists like to throw away all but the first order terms? lol  :Grin:  )

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## nonsqtr

K well, as expected the simple Gaussian case works out to the usual Cameron-Martin space.

I did find one interesting construction that might help. It's called *negative probability*. It's basically the probabilistic equivalent of an imaginary number. It was invented by Gabor Szekely. The idea goes like this: if we flip a coin we get heads or tails with probability 0.5 - but let's say we had two "half-coins", each of which has infinitely many sides labeled with 0,1,2,etc - if we invert all the EVEN indexes so they have negative probabilities (which basically corresponds with my earlier example of running every other distribution backwards), then when we flip two half-coins we discover the outcome is either 0 or 1 with probability .5, just as if we had flipped a single real coin.

Negative probabilities are not new, there is for example the Wigner distribution in physics. But this idea that inverting the order allows continuous mapping could be a very useful generalized tool.

With this setup, the Hilbert space starts looking a little funny. However it's still useful for generalized functions, with a small set of caveats.

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## Physics Hunter

I will speak in a colloquial vernacular.  Mostly since I consider of this all crap.

Let me explain.

If there is a space in a state of flux, with many possible decisions/results/outcomes... that significantly effect the outcome of the situation, this is called Chaos.

Decisions, actions, and real world results always result in a cascade of (for lack of a better word) consequences.  

In Chemistry these things are called precipitate.

The probabilistic state has less information, more randomness and probability, then after the decision in an information space or grain of salt is cast into a super-saturated liquid there is a result, and thus information.  

Don't over think things.

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Foghorn (04-06-2021),nonsqtr (04-06-2021)

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## nonsqtr

> I will speak in a colloquial vernacular.  Mostly since I consider of this all crap.
> 
> Let me explain.
> 
> If there is a space in a state of flux, with many possible decisions/results/outcomes... that significantly effect the outcome of the situation, this is called Chaos.
> 
> Decisions, actions, and real world results always result in a cascade of (for lack of a better word) consequences.  
> 
> In Chemistry these things are called precipitate.
> ...


Sorry, but you're missing the mark.

You're expressing a traditional mechanical viewpoint that's become outdated because it doesn't work. It's not general enough to explain "other-than-linear cases", which includes most of nature.

As a physicist you should know there is plenty of structure in chaos. Chaotic catastrophes describe "most" of the structural changes in nature.

I will describe the issue succinctly. You can't use a Riemann integral on certain kinds of functions (we'll call them generalized functions - distributions - including Dirac delta "functions" and do on). And you can't use Lebesgue integration on certain kinds of functions. Which one you can use what on, is important.

For example - consider a random walk in a Wiener space. The walk is continuous except at the bumps. So in theory you could use a Weierstrass transform if you could arrange the intervals so they were all somehow the same extent. But you can do the equivalent thing by changing the metric at each bump point. 

The bump points carry information, and the length of the intervals carry information. This is about the INFORMATION, nothing else. In the traditional (Gaussian) formulation the moments are symmetric, but we know in advance this can't possibly be true because the metric itself isn't symmetric.

There's something fundamental missing from the traditional concept of "information". I already clearly stated the result. Information theory says that events that always occur carry no information, and that is a FALSE statement, it's so false it's practically self evident.

Proving it is a different story.

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## nonsqtr

Let me explain further.

Whether a system is chaotic or not makes no difference whatsoever to the number of available states.

The Gibbs formulation says the distribution is based on the number of available states.

So, the intuitive idea that a regular system somehow carries more information than a chaotic system, is directly contradicted by thermodynamic theory.

Because, the concept of information is wrong. There's something missing. The Shannon/Gibbs formulation is "incomplete".

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## nonsqtr

Here is yet another restatement of the same issue.

Consider a "space filling curve", and it's underlying fractal process. There is information added at every branch point, would you agree? So let's say you take the process through 100 iterations and then stop, which gives you X extra information. Now you increase the size of the ambient space or its boundary. Obviously, the relative information has changed (which can be proven by recalculating the relative entropies), but information theory says it stays the same.

The problem is, that information theory only deals with channels, it doesn't deal with the structure of the ambient space.

Another way of saying it is, it only deals with the bits, not the bytes.

The model in information theory is, you're plucking a bit OUT of the ambient space and passing it through a channel.

What I'm saying is, by doing that, you have altered the information structure/content in the ambient space.

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## UKSmartypants

> There's something fundamental missing from the traditional concept of "information". I already clearly stated the result. Information theory says that events that always occur carry no information, and that is a FALSE statement, it's so false it's practically self evident.



If, as I propose, thers a mass/energy equivalence with information, but probably in higher dimensions, then it clear any mass greter thana neutrino, or any temperature higher than absolute zero, has information.

We havent spotted it cos no one AFAIK has ever explored the concept of information in 10 dimensions.

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nonsqtr (04-06-2021)

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## nonsqtr

> If, as I propose, thers a mass/energy equivalence with information, but probably in higher dimensions, then it clear any mass greter thana neutrino, or any temperature higher than absolute zero, has information.
> 
> We havent spotted it cos no one AFAIK has ever explored the concept of information in 10 dimensions.


We're exploring it right now!  :Smile: 

Lookie, getting closer:

Gowers norm - Wikipedia

Confirms what I said about the polynomials.

Let's look at another part of the "byte", we'll number the bits 0-7, so the byte looks like 76543210.

So, the 7-bit, has 128 times the influence on the outcome of the byte, only because, the byte is being interpreted in a certain way. The byte, is our "closed system" (because we don't care about other bytes or anything that happens outside of the byte), which specifically means that any given bit is NOT a closed system.

The nature of the byte is such that the state of the 7-bit affects the meaning of the 0-bit. This is a "non-local interaction".

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## Authentic

Think binary, act non-locally.

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## Authentic

Wouldn't the information be contained in a state of change? If an event is always occurring, where is the change? No change, no information.

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nonsqtr (04-07-2021)

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## Physics Hunter

> Let me explain further.
> 
> Whether a system is chaotic or not makes no difference whatsoever to the number of available states.
> 
> The Gibbs formulation says the distribution is based on the number of available states.
> 
> So, the intuitive idea that a regular system somehow carries more information than a chaotic system, is directly contradicted by thermodynamic theory.
> 
> Because, the concept of information is wrong. There's something missing. *The Shannon/Gibbs formulation is "incomplete"*.


No trouble selling that Shannon, while foundational and useful is rudimentary at best, and the traditional info folks lean too hard on it.

My point about the influence of Chaotic processes on unresolved complex information spaces is both the unpredictability of results from any particular decision, and the problem knowing what the range of the result space is...

Nor any problem if you can show me that the limits of derivation of any mathematical process as applied to some particular type of complex problem.  One of my pet peeves as an engineer was watching engineers apply equations or solutions on problems that were outside of the range of their derivation.
It was fun being the only Physics guy in teams of various information system programs, over the years.  The crazy things that vendors would claim their apps could do based on approaches that did not do those things...   :Geez:

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nonsqtr (04-07-2021)

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## UKSmartypants

> Wouldn't the information be contained in a state of change? If an event is always occurring, where is the change? No change, no information.


Surely if it exists, it has information per se. The activity it undergoes is just more information on top.  Even a 2D Spinor has information - spin.  My theory is that every entity has information in ten dimensions, and if my other idea is correct , that mass, energy, and information are equivalent and interchangeable, that means there's a massive amount of energy/mass/information we cant see from just D4. Maybe thats what Dark matter and Dark energy is, all the missing information, in the upper  6 dimensions .......

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Authentic (04-07-2021)

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## nonsqtr

> Wouldn't the information be contained in a state of change? If an event is always occurring, where is the change? No change, no information.


Well, that's a naive version of information theory. But...

Wrong. Completely wrong.

See... this is why we have to be very careful with this stuff, and use actual math.

What you (and the information theorists) are talking about is "the bit". But information is more than that.

Consider - that word "always" is loaded. It's a very imprecise word. A human being can not get to "always", the best we can do is called "sampling". We "measure" from time to time, we "sample" the measurement space. Which is not the same as the event space.

Here is what I contend: if the event has a label (that is, a representation "anywhere else"), then the observation of the event occurring "always" has meaning.

The apple "always" falls down, that has meaning, yes? It means it NEVER falls up, which is meaningful too.

The point being, that I, in my near-infinite wisdom as a human being, have a pre-existing representation of Newton's law in my brain somewhere, and I "expect" that it will "always" be true. Every time I sample, I expect a positive outcome, always. That's information. And it's meaningful "because" of the pre-existing label in my brain's memory, which is "external structure".

The external structure, is like the byte. It doesn't belong to the bit, the bit has no knowledge of it.

But the bit "belongs to" the byte, it's a "part of" the byte. And in a way, once that same kind of external structure exists in my brain, Newton's law becomes a "part of" my brain. That is to say, a relationship of conditional expectation develops between my brain and any future observation of gravity.

This is kinda where our mathematical understanding seems to be at this point - we're looking at the concept of "almost". As in, "almost" certain. "Almost" like a polynomial. "Almost" like a surface, but missing a few points. "Almost' like the manifold, just wiggle it a little bit.

If I have a bit within a byte, and that bit is "always" 1, that has meaning. Yes? That is meaningful information. Usually the software guy says "what the heck is wrong with this computer" and calls field service, right?  :Grin:

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Authentic (04-07-2021)

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## nonsqtr

> Surely if it exists, it has information per se. The activity it undergoes is just more information on top.  Even a 2D Spinor has information - spin.  My theory is that every entity has information in ten dimensions, and if my other idea is correct , that mass, energy, and information are equivalent and interchangeable, that means there's a massive amount of energy/mass/information we cant see from just D4. Maybe thats what Dark matter and Dark energy is, all the missing information, in the upper  6 dimensions .......


Hm. External structure - and what I've discovered in this last week is, it has a lot to do with boundaries and boundary conditions. They talk a lot about series converging and things like that, but intuitively these are boundary conditions. Such conditions would "look" different in a projective geometry, yes? Don't have much more time for this "right" now, but the infinities are worth another week of study.

This non-local business is still very confusing though. I'm trying to understand how a compactified dimension can have "extent" along another, and the only way I can visualize it is if it becomes cylndrical along the other. (So literally a "parallel" dimension).

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## nonsqtr

K so, continuing with gravity and byte analogies, ultimately the reason the relationship of conditional expectation continues to exist is because of MEMORY. If the memory in my brain were wiped I would no longer know about the byte, nor would I necessarily expect the apple to fall up or down.

And memory is the label, it's the "representation of the event" I was talking about.

So, if we're looking for interesting nonlinearities, it makes sense to look for representations that persist. Which is memory. Which can be studied by pumping noise through the system and going after the Volterra kernels.

I find myself wondering whether anyone has tried this at the quantum level?  :Thinking:

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## nonsqtr

Hm. Is there a type of "noisy observation" that an entanglement can withstand?

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## UKSmartypants

> Hm. External structure - and what I've discovered in this last week is, it has a lot to do with boundaries and boundary conditions. They talk a lot about series converging and things like that, but intuitively these are boundary conditions. Such conditions would "look" different in a projective geometry, yes? Don't have much more time for this "right" now, but the infinities are worth another week of study.
> 
> This non-local business is still very confusing though. I'm trying to understand how a compactified dimension can have "extent" along another, and the only way I can visualize it is if it becomes cylndrical along the other. (So literally a "parallel" dimension).



well thats how i visualise it

if this is dimensions 1 2 and 3



so dimension 4 5 and 6 look the same except they have a composite 1,2,3  world space on each axis, and then again dimensions 7 8 and 9  have a composite 4/5/6 world space  on each axis  (which themselves each have a composite 1,2,3 world space). D10 is the single overlying dimension that holds them all - maybe its the brane it all sits on, since its one dimensional, or its a single world line with one single overall Quantum Wave Function on it

Bit like how USSAF bomber formations used to fly

3 planes together, then 3 groups of 3 together, then 3 groups of 3 groups of 3 = 27 planes, one squadron.  

So thats why I insist there no such thing as time. Time is merely our perception of only being able to move in one of the next  group of 3 dimensions (4/5/6). Because we can only move in one of them, we can only do it one Planck frame at a time, ie one slice of D4 one Planck distance thick.  Moving back in 'time' is moving in the opposite direction on that world line.

So to get back to the subject in hand, we must have 6 dimensions packed solid with information from the bottom 3 dimensions, which would show up i propose as dark matter and/or dark energy if, i propose, mass, energy and information are interchangeable. Would information look like mass or energy at lower dimension, after all, i say spatial movement looks like time in the same situation

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## nonsqtr

:eyebrow:

Bifurcation memory - Wikipedia

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## UKSmartypants

Look at it like this:  all the mass/energy/information that falls into a black hole  undergoes reverse symmetry breaking because it all gets squished to nothing. If there really is a singularity at the centre, that must embrace all10 dimensions, So effectively all that stuff falls  into the remaining compactible higher dimensions, effectively reunifying them with the  four that unfolded. Where else can it be, other than sitting on compacted dimensions on the same bit of 2D brane we erupted from?  In which case we would feel the effects but be totally unable to physically  see it as a particle. Thats the problem - where is the gauge boson for dark energy? Maybe its a 10 dimensional particle, which is why we cant see it?  it would also solve another problem - the variance in the speed of light and the strength of gravity since the Big bang, cos were pretty sure both of them have changed

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## nonsqtr

Yeah. I'm just now looking at how to.look at this. Are you familiar with the Takens (and Whitney) embedding theorems?

The Takens theorem for instance, is what let's me do "convergent cross mapping" in my neural networks, so I can distinguish causality from mere correlation.

Convergent cross mapping - Wikipedia

Distinguishing time-delayed causal interactions using convergent cross mapping | Scientific Reports

What this method does specifically is measure the correlation between the reconstructed and recovered manifolds of observations.

CCM identifies the leading subsystem in all cases except when the average coupling coefficients are approximately equal. It correctly describes the dynamics of the Lorentz attractor "almost always".

Causality Analysis: Identifying the Leading Element in a Coupled Dynamical System

And, check this out (pretty pictures!):

HÃ©non map - Wikipedia

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## nonsqtr

The question is, why does this method work?

It's fundamentally a combinatorial method.

Malliavin only works on Gaussian spaces, that's it's biggest drawback. This method though, is mostly geometry-agnostic, as near as I can tell.

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## nonsqtr

Seems this is the answer, and it's kinda self-evident. Any measurement you can do is on the posterior probabilities "only". So, unless you have a map between the anterior and the posterior, you're screwed. You can only observe the outcome in the sample space, you cant directly observe the event space, so very literally "all possibilities exist" until t+dt.

See so, the missing part is this: the probability measure only gives you the posterior information. But the information has CHANGED between t and t+dt. That transition in the information, is exactly what we're interested in.

The "standard, orthodox" way of approaching the linkage is to calculate expectation. For instance you can update the conditional probabilities after an observation (this is the Bayesian way of inference). And, meaningful linkage is achieved by reconstructing what is essentially an ensemble - and this is basically equivalent to throwing gazillions of darts at a dartboard to recover its shape.

This process just mentioned, can absolutely result in a geometric manifold, or let's say, "almost" a manifold. You could look at it and see its shape in the same way you can look at an orbital and see its shape.

Seems to me, the salient observation is, that in these kinds of systems, "impossible geometries are allowed". For instance, there are stochastic systems with strange attractors shaped like Klein bottles.

The whole trick is defining the manifold "near enough to be a manifold", if you know what I mean.

The answer is, the missing information is precisely dt, it's the incremental change in the shape of the manifold.

Which could come from factors inside the manifold (shrinkage or expansion), or factors outside the manifold (deformation).

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## nonsqtr

All right. So maybe we could theorize this way:

You have to put work in, to get an entanglement. The energy goes into information, which somehow creates a new stable ("entangled") state. But it's a very sensitive state, any supraquantal perturbation is gonna destroy it, and when it's destroyed, you lose the information in the distribution but you get the work back out of it (like in the Casimir effect and the quantum refrigerator).

So is that a true statement? "You have to put work in, to get an entanglement"?

And if so, can we measure how much?

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UKSmartypants (04-08-2021)

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## nonsqtr

Ha - here's a great restatement of the problem.

The difference between "disjoint" subsets in the event space, and "independent" outcomes in the sample space. The two are not the same!

Two random variables can be dependent under one probability measure, and independent under another (as the bit-in-a-byte example shows).

Furthermore - furthermore - if you have any two disjoint events A and B, each with positive probability, then these events are by definition dependent and negatively correlated.

The measure is wrong. They're using the wrong f'in measure. Bingo.

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## nonsqtr

Yep. Check it out -

Information theory mixes up (confuses) two different kinds of probabilities: internal and external.

Well... it's not actually the theory itself that does this, it's the dumbass theorists.

If you have a bit in a byte, the bit settings are mutually dependent and correlated within themselves, but not with the rest of the bits. 

The exception to this general picture occurs when all the bits in the byte are updated "as a unit", so the changes are correlated in time even though the values themselves may not be.

Information theory, has no concept of the byte. It doesn't deal with anterior probabilities, at all. It can't handle the cases that depend on "potential energy" between the bits - and any attempt to apply it in this context is a misapplication.

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## UKSmartypants

> Yeah. I'm just now looking at how to.look at this. Are you familiar with the Takens (and Whitney) embedding theorems?
> 
> HÃ©non map - Wikipedia




Ahh no, thats called  Henon Attractor, it's one of a class of Chaos theory objects called Strange Attractors.  To be exact, its a recapitulate the geometry of the Lorenz attractor in two dimensions:



ive also seen this done in 5D, its pretty mind boggling. Also, the climate  can be modelled using this attractor

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## UKSmartypants

> All right. So maybe we could theorize this way:
> 
> You have to put work in, to get an entanglement. The energy goes into information, which somehow creates a new stable ("entangled") state. But it's a very sensitive state, any supraquantal perturbation is gonna destroy it, and when it's destroyed, you lose the information in the distribution but you get the work back out of it (like in the Casimir effect and the quantum refrigerator).
> 
> So is that a true statement? "You have to put work in, to get an entanglement"?
> 
> And if so, can we measure how much?



well thats it, thats essentially restates what I said, but in smarter terms :P  It just workign in 10D.  Cos that's where all the information goes.

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nonsqtr (04-08-2021)

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## nonsqtr

> Ahh no, thats called  Henon Attractor, it's one of a class of Chaos theory objects called Strange Attractors.  To be exact, its a recapitulate the geometry of the Lorenz attractor in two dimensions:


Exactly. So, play this out on a random surface.  :Grin: 

In other words, you're dealing with a system where the dominant attractor changes shape and position in real time. So, how do you tell whether a bit is being influenced by one or the other and by how much?

This is a good example because it's fundamentally non-Gaussian.

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## nonsqtr

> well thats it, thats essentially restates what I said, but in smarter terms :P  It just workign in 10D.  Cos that's where all the information goes.


Yeah. I think you've hit on something important here. The idea of "orthogonality". Which is intuitive in Euclid-land, but gets a little wierd in probability. As ever having to do with the inner products and angle preserving transformations.

Seems this is worthy of some study. I'm not sure anyone's really looked at selection from inhomogeneous spaces. The spaces are always assumed to be uniform in some way.

If you read about the Henon attractor, its solution set includes a Cantor dust. THAT is interesting. Yes?

A combinatorial solution that has no otherwise obvious reason for existing.

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## UKSmartypants

> Yeah. I think you've hit on something important here. The idea of "orthogonality". Which is intuitive in Euclid-land, but gets a little wierd in probability. As ever having to do with the inner products and angle preserving transformations.
> 
> Seems this is worthy of some study. I'm not sure anyone's really looked at selection from inhomogeneous spaces. The spaces are always assumed to be uniform in some way.
> 
> If you read about the Henon attractor, its solution set includes a Cantor dust. THAT is interesting. Yes?
> 
> A combinatorial solution that has no otherwise obvious reason for existing.



Oh yes  I fell in love with chaos theory, fractals and attractors many years ago.   My concentrated admiration is directed at Gaston Julia, the Frenchman who invented Julia Sets. What made him REALLY smart was he did all his work before the invention of the computer, so he couldnt show people the objects created, it was all in his head






Now this was really clever stuff.  But the person that came next was also smart - Benoit Mandelbrot

HE realised you could grade how open, closed or broken up a specific Julia set was - one piece, many islands thin, fat.  If you represent this by a single dot of a specific colour, and plot all the points  according to the x and y values what you get is THIS



Most people have seen this, they have no idea how clever it is.  Every dot in this image has a corresponding Julia Set based on the X and y coordinates. It is, in fact an Index of Julia Sets. And Benoit Mandelbrot was the first person to print out a Julia Set, and to print out  the Mandelbrot set.  Its been described as "the most complex mathematical object in the Universe"

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nonsqtr (04-08-2021)

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## nonsqtr

Wow, that's pretty impressive. All in his head? Ha ha - seems more space-filling than a Riemann sphere, as it were.

K, so the internal and external information metrics are different. What can we do with that?

Even though we can't directly measure the event space I'll bet we can derive information about its topology by studying the outcomes. I'd be surprised if this wasn't true somehow. Topology meaning and including, things like Betti number. 

I mean, reaching into a nice flat circular space and pulling out an outcome is easy to conceive, but what happens if you reach into an oddball topology with singularities or discontinuities?

The way that's worked so far, is to model the event space. That's what Gibbs tries to do. But because everything is in flat-land, the idea of modeling the event space is kinda taken for granted. It's easy when you're flipping a coin, and only "slightly" harder with molecules flying around in a gas, and only "slightly" harder with the gravitational behavior of celestial objects - but what about the "information" geometry?

We need another level of indirection. I mean, think about the idea of an "error" in a bit. That's an interesting concept, isn't it? Is it possible to have an "error" in a spin state? No, not really, it's just a probability in the first place. It's only really definable as a state "with some level of confidence". Hence quantum error correction and all that.

The topology of the distribution, as distinct from the topology of the event space.

I feel like we're making progress. Not sure how yet, but I sense a light bulb moment on the horizon.

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## nonsqtr

Okay. I think I found a framework that'll work. Here's how it goes:

The "information" in a distribution is encoded in the form of its sigma-algebra. (I'll use s-algebra for short). The s-algebra tells us the number of available states and how those states are defined.

The light bulb moment comes this way: from stochastic processes and the theory of *filtration*.

There is one scenario which has been especially well studied, which is the time series, which represents "ever increasing information", and therefore the filtration is related to the fact that the s-algebra always grows, with each new time step dt.

But, when we think outside of the box, we realize the s-algebra doesn't always have to grow. It can shrink too. However, interesting things happen when it grows.

Growth of the sigma-algebra is associated with a behavior called right-continuity, which basically means you get a smooth family of growing sigma-algebras that ultimately form a surface. It is this surface we're interested in.

This property of right-continuity does some fascinating stuff in the context of growing s-algebras. For instance, it allows an infinitesimal peek into the future at t+dt, which is fully one half of what I need to prove. If there is left-continuity I have the other half. Unfortunately it's not that easy. (It never is lol).

You can prove left-continuity in the case of a similarly shrinking s-algebra (which is somewhat analogous to running time backwards), but the mixed case is very complicated. If you can guarantee neither shrinkage not growth then the continuity assumptions fail and you have to consider the size of the s-algebra itself as a random variable. Which kinda means you can only see one direction at a time. (However if you had two such manifolds and they were alternating... it would be about the same thing as reversing every other sequence in the earlier bitwise example, yes?)

Now - *filtrations* have a "mesh size", almost like the one induced thermodynamically in an Ising spin glass model. The coarsest mesh size is when you have no information, and the finest mesh size is when you have all the information from the beginning of time. And, a sigma-algebra can be dual'd by complement. So if the mesh size goes from fine to coarse, you have what amounts to a stochastic optimization engine over the information space - that is to say the "space of information", which relates to the number of available states.

Topology? Hell yes! The optimization surface unquestionably has a topology, just like the energy surface in an Ising model or a Hopfield neural network model.

I think we're there, because the sigma-algebra is a very flexible device, it can be dimensionalized and orthogonalized pretty much as needed and it's topology can be constructed in such a way that it satisfies the essential symmetries.

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## nonsqtr

Yeah. Hell yes. This whole scenario maps directly to "memory that has a time course".

Memory that has an onset, lasts a while, and then decays. 

The decay is the shrinkage of the s-algebra.

Home run.  :Thumbsup:   :Smile: 

Now I can get back to music.  :Smiley ROFLMAO: 

It'll take me some years to prove this works, I'm not very good with math. But I'll betcha I could build a working simulation faster than I could prove the math. Conceptually it's not all that hard, you just have a Hilbert space of filters sweeping in opposite directions.

The sigma-algebra is quantifiable, it has a topology and a geometry, and it maps combinatorially directly into the information space. It has everything we need.

This idea of mesh size, though, is stellar. It lets you determine pairwise correlations practically in real time - AND, it immediately suggests a method for achieving the scale invariance needed for self-similarity. 

At this point I'd probably hire a subject matter expert to take the ball and run with it (if I could find one ha ha). This is great stuff, it's worth a career if anyone wants one.  :Grin:

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## UKSmartypants

> This is great stuff, it's worth a career if anyone wants one.


nah im retired,i dont do brainachy stuff anymore  :Stick Out Tongue:

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nonsqtr (04-09-2021),Oceander (04-09-2021)

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## nonsqtr

> nah im retired,i dont do brainachy stuff anymore


This is great though. Your nonlinearities measurable with Volterra kernels map to changes in the underlying s-set. You don't have to "control the distribution", it happens by itself! In the linear time series you have basically two distributions of interest, Gaussian for value and Poisson for time. Both are based on combinatoric assumptions about the s-set, mostly related to equivalence classes. 

The best part of it is, it works in discrete-land (quantized, where every s-subset is open with the discrete s-set topology) and in continuous-land (fields, where the open subsets are neighborhoods with measurable volume). 

People have studied this already in the linear case, Fisher-Rao is unique in any Markovian situation and etc - and - there is an interesting literature on "hierarchical clustering" that might be germane, having to do with matrix methods in the multivariate cases (proving for instance, that the Rao distance is just the geodesic of Fisher-Rao on the manifold). The nonlinear approach is badass stuff though. There's a pretty decent literature on the geometries induced by Fisher Rao on various distribution spaces, but I only found some very recent stuff from 2018 and 19 on deformations in the nonlinear case. Looks like people are thinking about it though. I'll betcha ten bucks there's a simple convolutional solution or something.

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## UKSmartypants

*Did time flow in two directions from the big bang, making two futures?*
*

Why time only flows forwards is one of the great mysteries of physics. 
A new idea suggests that it actually went in two ways from the big bang – and, even more radically, that time emerges not from entropy, but from the growth of structure*

PHYSICS 3 March 2021
By Julian Barbour

TIME moves forward. This is so obvious that we take it for granted, and the rule seems to apply everywhere we look. Observable phenomena only ever unfold in one temporal direction. We get older, not younger. We remember the past, not the future. Stars clump in galaxies rather than dispersing, and radioactive nuclei decay rather than assemble.

The big question is, where does this forward-facing arrow of time come from? The most popular explanation relates to entropy. In this picture, the flow of time is essentially a manifestation of the universe’s inescapable inclination towards disorder.

I have a different idea, or rather two. The first is that time goes both ways – that the big bang isn’t an origin for time, but a midpoint from which two parts of one universe play out, running in opposite directions. We can never see the one unfolding in the other temporal direction, yet it is there, I suggest, as a consequence of a fundamental law of nature.

My second idea is even more radical. It could transform our understanding of the very nature of time. The consequences might even reach beyond the realm of classical physics, the world we can easily see, and offer fresh clues to the quantum nature of gravity – the elusive theory that marries general relativity with quantum mechanics.

Physicists’ current ideas about time owe much to Albert Einstein. His general theory of relativity merged the three dimensions of space with one of time into space-time, the all-encompassing backdrop against which events play out. In principle, if not always in practice, we can move in space as we wish. Not so in time. Time insists on a direction of travel: we have no choice but to be swept along from past to future.

This flow of time isn’t dictated by the fundamental laws of nature. All but one of these are time-symmetric: they work equally well towards the past or future. Take the collision of two billiard balls, governed by one of these laws: a film of what happens doesn’t look odd when played backwards or forwards. The one time-asymmetric law we know of is one that dictates the decay of certain elementary particles, an oddity that prevented the complete mutual annihilation of matter and antimatter in the early universe and ensured that we, being made of matter, are here today. But there is no way it can explain the onward flow of time.

To explain this, physicists have instead turned to a law that isn’t considered fundamental, but which emerges from more basic laws. The second law of thermodynamics says that in a closed system, overall disorder, characterised by a statistically defined quantity called entropy, always increases. It does so because there are many more possible states of disorder than of order. Thus, a small ice cube in the corner of a large box will melt and become liquid water, spreading the molecules out and increasing disorder. Entropy has increased. Note the “statistically defined” bit: the laws of physics don’t rule out this process being reversed, but just say that event is statistically hugely unlikely.

In this picture, the direction of time is created by the increase in disorder. If snapshots showing the position of the molecules in that box were shuffled out of order, my 4-year-old granddaughter could put them back in order. For many scientists, this is enough: entropy puts direction into time.

For my part, I don’t doubt the robustness of thermodynamics. Einstein described it as “the only physical theory of universal content which I am convinced that, within the framework of applicability, its basic concepts will never be overthrown”. I wouldn’t be so bold as to disagree.

But Einstein’s caveat is important, and leads to a question: does the “framework of applicability” of thermodynamics include our universe? It doesn’t appear to be a closed system. It might be infinite in size and is certainly expanding, possibly without impediment. If so, it isn’t in a box. But a box, physical or conceptual, is crucial for the interpretation of entropy.

That alone is reason to question the application of thermodynamics more or less unchanged to cosmology. But there is another reason. With the entropic arrow of time, physicists assume that the universe began at the big bang with very low entropy, a special state of extraordinarily high order. That is arbitrarily imposed. One of the most profound aspects of existence is attributed to a special condition put in by hand. This has been called the past hypothesis and in my view it isn’t a resolution to the issue of time, but an admission of defeat.

In fact, an alternative to the past hypothesis may have been staring us in the face for more than two centuries. In 1772, mathematician Joseph-Louis Lagrange proved something about the behaviour of a system of three particles that interact according to Isaac Newton’s law of gravitation. This says that every particle attracts every other with a force proportional to their masses and inversely proportional to the square of the distances between them.

*Past forwards*
Lagrange’s result, which extends to any number of particles, showed that if a system’s total energy (potential plus kinetic) is either zero or positive then its size, essentially its diameter, passes through a unique minimum at just one point on the timeline of its evolution. This process runs just as well backwards as forwards, Newton’s gravity being time-symmetric. And with one fascinating exception to which I will return, the size of the system grows to infinity both to the past and future.

Interestingly, the uniformity with which the particles are distributed is greatest around the point of minimum size. It has long been known that a uniform distribution of particles is gravitationally unstable and breaks up into clusters. What nobody seems to have realised, however, is that when you run the evolution of the particles’ motion backwards from the clustered state to the minimum, most uniform state and then take it beyond this point, it goes on to become clustered again.

In a paper I published in 2014, together with Tim Koslowski at the National Autonomous University of Mexico and Flavio Mercati at the University of Naples, Italy, we showed that this is the case in a simple proxy of the universe. A computer simulation of a thousand particles interacting under Newtonian gravity showed that pretty much every configuration of particles would evolve into this minimum state and then expand outwards, becoming gradually more structured in both directions. I call the minimal state the Janus point, after the Roman god who looks simultaneously in opposite directions of time.

What would this mean for us? If we lived in the model universe I have just described, we must be on one side or the other of the Janus point. We find Newton’s time-symmetric law governs what happens around us, but also a pervasive arrow of time that defines our future. In our past direction, we can just make out fog – what we call the big bang – and nothing beyond it. Not realising the fog is a Janus point, we invoke a past hypothesis to explain the inexplicable. But Newton’s laws say the special point must be there, so there is no need to invoke the past hypothesis. Instead, we can mathematically define a quantity that reflects the evolution of our system of particles into something that looks like structure. Let’s call it “complexity”.

Complexity is calculated using all the masses of the particles and all the ratios of the distances between any two of them. It has nothing to do with the statistical likelihood of possible states and differs from entropy in that its growth reflects an increase in structure, or variety, rather than disorder. I argue that it should take the place of entropy as the basis of time’s arrow.

In my recent book The Janus Point, I take things further. I propose that, ultimately, our model suggests that the history of the universe isn’t a story of order steadily degrading into disorder, but rather one of the growth of structure or complexity, as we define it.

“Complexity doesn’t just give time its direction – it literally is time”
The suggestion for this comes in the first place from Newton’s theory of gravity. It isn’t yet clear it can be extended to a general relativistic description of gravity. But in many cases, Newtonian gravity predicts behaviour almost identical to relativity, so there is a hint to look for a similar effect in Einstein’s theory.

This brings me to the fascinating exception to Lagrange’s result I mentioned earlier. In everything discussed so far, the minimum size of the “universe”, at the Janus point, isn’t zero but finite. But general relativity at the big bang leads to a zero size of the universe, known as a singularity, where the equations break down.

It has been known since a remarkable paper by Frenchman Jean Chazy in 1918 that singular events called total collisions can also occur in Newton’s theory. In them, all the particles come together and collide simultaneously at their common centre of mass. At this point, Newton’s equations break down; they can’t be employed to continue any solution past a total collision. Instead of two-sided solutions, we have one-sided solutions.

If we take this exception seriously, we cannot say time has two opposite directions but, significantly, it doesn’t rule out complexity giving time a direction.

The equations for Newton’s gravity are still time symmetrical, so the solutions that terminate at a total collision can run the other way. They become Newtonian “big bangs” in which all the particles suddenly fly apart from each other. Right at the start, the particles are arranged in a remarkably uniform way, but they soon begin to look like the motions on either side of the Janus point we saw in our calculations.

As they emerge from zero size, their configuration, characterised by the complexity, satisfies a very special condition. There are plenty of configurations, or shapes, that satisfy the condition but just one has the absolutely smallest possible value of the complexity. It is more uniform than any other shape the universe could have.

This is where a radical twist in the tale was all but forced on me, during the final stages of writing my book. The fact that the universe had an extremely uniform shape immediately after the big bang set me thinking. Could the special shape I’ve identified, which I call Alpha, serve as a guide to a new theory of time – and also point the way to arguably the biggest prize in physics, a quantum theory of gravity?



Quantum theory describes the often counter-intuitive behaviour of subatomic particles. For all its successes, it has always relied on an essentially classical conception of a time that exists independently of and outside the system. But surely any attempt to create a quantum theory of the universe, and with it gravity, should start without the notion of a pre-existing external time. Time has to originate somewhere, and where else but the quantum realm.

My ideas about complexity can help. What I’m proposing might be called Newtonian quantum gravity because it unifies aspects of Newton’s theory of gravity, above all this value of complexity, and the two key novel features of quantum mechanics: probabilities for the state a system finds itself in, and an entity known as a wave function that determines how these probabilities evolve.

The idea is that a wave function of the universe determines the probabilities of all the possible shapes it can have. This is relatively conventional. What I’m suggesting, however, is how that happens: I put the birth of time at Alpha, this uniquely uniform configuration of particles, and make complexity time itself.

*Heaps of time*
I said my granddaughter could sort the shuffled snapshots into the correct order. Now suppose I give her snapshots of all possible shapes of the universe to sort into heaps, one for each value of their complexity. In the first heap there will be just that one most uniform shape: Alpha. After that, there will be infinitely many for each value of complexity. The wave function determines relative probabilities for each of the shapes within each heap.

This is what standard quantum mechanics does for the probabilities of a system’s possible states at different external times. My proposal includes something similar but with invisible, external time replaced by complexity, which is visible in the sense that it is directly determined by the shape of the universe. Hence, complexity doesn’t just give time its direction – it literally is time.

The picture I have sketched matches the known history of the universe, but is only a start. The good news for next steps is that there is, at least in principle, an observational test.

Scrutiny of the first light in the universe, known as the cosmic microwave background (CMB), indicates that very soon after the big bang the distribution of matter in the universe was extremely uniform, while also revealing tiny fluctuations of a very specific structure. Inflation, a theory that suggests the universe underwent a huge expansion in its first split second, can explain the form of those fluctuations rather well. But it doesn’t tell us how inflation began and key parameters must be fitted to match observations.

According to my idea, the universe must begin as uniform as it possibly can and then develop small nonuniformities. This might sound like an arbitrary assumption, but it is a direct consequence of the simplest quantum law one can propose for the universe, which forces the wave function to evolve from a necessarily unique condition at its most uniform shape. It is possible we could use first principles to directly predict the form of the fluctuations, which we could at some point verify or rule out by further scrutinising CMB.

This idea could go either way. I am hopeful, and not only because Newtonian complexity has a counterpart in Einstein’s theory. I also find encouragement in the thoughts of Niels Bohr, a founder of quantum mechanics, who said any new quantum idea needs to be crazy. The idea that complexity is time is certainly that – and it could be transformative. If time really is complexity, and it is a big if, it will kill two birds with one stone: provide a new starting point from which to formulate a quantum theory of gravity and show, on the basis of simple first principles, how time gets its direction.



Read more: Did time flow in two directions from the big bang, making two futures? | New Scientist

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nonsqtr (04-11-2021)

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## UKSmartypants

Fits in with my proposition. If time is a spatial dimension D4, it make sense that it flows in 2 directions, since D1 D2 and D3 all have two directions of freedom.

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## nonsqtr

K so, you're going to need math that can handle all this. So - filtering. Let me explain why this is so cool.

The word "filtering" is related to adaptive filtering, but it's not the same thing.

Normally, in probability theory, you have an event space, and you have a sample space - and what relates the two is a probability "density", which I'm going to conceptually call a "distribution" (the vocabulary here is loose and descriptive).

The sample space, that's what you can see, what you can measure. The sample space contains "outcomes", which are samples from the event space. Every time you sample from the event space you get an outcome, and the probability of getting one outcome or another is described by the probability distribution.

The event space is the "space of all possible outcomes", and it has to be a measurable space because the act of sampling is essentially a "function" that maps from the event space to the sample space. To make the event space measurable we create a Borel space which is basically the set of all possible subsets (of events, in this case).

In a time series, we have a "repeated" experiment, because we have one sample after another (kind of like a stock ticker), and if we insist that each sample has to be independent then we say that the probability distribution is "stationary" (doesn't change from one sample to the next). The stationary property is also called "Markovian".

So now, what I've been talking about in this thread, is the non-Markovian case, where the probability distribution changes over time. (The reason it might do this is because of the acquisition of new information or the loss of existing information).

Considering the general case of a distribution changing over time, "sometimes" we can describe distributions with well behaved mathematical functions (like the Gaussian distribution is that way), but other times the probability density looks quite random. If you get lucky you can parametrize changes in the distribution which means you get what amounts to a smooth family of curves - for instance a Gaussian is parametrized by mean and variance, and if you plot mean and variance on the x and y axes and move a dot around the resulting changes in the distribution are smooth and continuous.

However we saw in the bit-in-a-byte example, that changes in the probability distribution don't have to be smooth, and neither do they have to be continuous. If we change the 1-bit we get a different "shape" than if we change the 4-bit. As bits change the densities fluctuate wildly and they're not smooth or continuous. So how do we handle these cases?

The answer is, "filtration". What this means is, in the time series example, every time we take a sample we're going to grow the Borel space. Formally this means we're going to add the outcome to the event space, and then recalculate all the subsets so we still have a nice clean Borel measure. The small change in measure is essentially a "deformation" of the probability distribution. If we get enough of these it's like covering the dartboard with a series of darts instead of a series of smooth functions - but if we get enough of both, the dartboard should look exactly the same either way.

The advantage of the filtration method is it lets you handle nonlinear behavior at the combinatorial level and map it directly into a parametrized family of functions by considering each function as a stochastic process (like the throwing of a dart). This way all of the function mapping is beautifully retained and therefore you can map to any other covering (because the concept of a smoothly varying surface of distribution functions changes into a stochastic manifold).

So what this method is really doing is, it's giving you access to the ambient space. (Which information theory doesn't know about and is agnostic about). It gives you a topology - precisely what it gives you is the embedding of the ambient space into the distribution(s). You end up with the shape of the manifold just like you would if you were parameterizing it with a smooth family of curves, and if you were to do a combinatorial solution in the smooth case you'd be doing Taylor series expansions on exponential functions, whereas in the stochastic case the spectra map to moments (which is where the predictive power comes from). Either way you can integrate and differentiate, calculate lengths and angles and preserve them with transformations, and relate the bitwise combinatorial distributions to the shapes of the parametrized function spaces.

Ultimately we're interested in the cost of entanglement. This method doesn't answer that question, but it gives you a way of mapping work into rearrangements of information (including adding and subtracting information) under the influence of what is essentially a "Hamiltonian" (a "cost surface"). Powerful stuff.

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## nonsqtr

@UKSmartypants, a filtration in the original sense represents an ever-increasing amount of information. (Or complexity).

Although in the sense we're discussing it here, it doesn't have to be ever-increasing, it just has to change (because a dart landing in the same spot adds no information).

There are many examples of time related nonlinearities in physics. Not the least of which is "quantum memory" associated with entanglement.

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## UKSmartypants

So hers a thing.

If time is indeed moving in two directions in D4, is it a mirror image of this worldline? an opposite? or a copy? Does the net information content double or cancel ?  Would the other worldline look like dark matter/energy?  And how u gonna work it into your theory?

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## nonsqtr

K so, just to be clear - the event space is by definition the space of all possible outcomes - the key words being "all possible". It suggests you know ahead of time what "all" means. So that's one kind of combinatoric, I call it "internal".

Then there's the whole separate idea of shifting (perturbing) the distributions by small amounts to get a surface of parametrized distributions (which is a different kind of combinatoric, I call it "external").

Two DIFFERENT information metrics, one internal, one external.

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## nonsqtr

All right, well, I think this works, so now I'm interested in any and all cases where it DOESNT work. So if any of you physics type would like to clobber my ignorant butt, here's your chance.

This works easily and intuitively at the classical level, the idea is you take two closed systems and bring them together at which point they will "equilibrate", but what's really happening is the event space ("number of states") is growing and the combinatorics are being recalculated to achieve a new set of distributions.

At the level of a quantum entanglement the same thing happens, you take two pure states and you bring them together to get a mixed state, and what's really happening is the information space is growing but because of the geometry it doesn't "equilibrate" instantly (because the starting state turns out to be tentatively stable), it just kinda sits there in mixed-land until something else interacts with it.

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## nonsqtr

Far out.

This gets even better.

Filtrations map directly to spectral sequences which means we can compute homology groups.

They also map to directed graphs.

They also have deep applications in queuing theory.

Mathematics | Free Full-Text | A Time-Non-Homogeneous Double-Ended Queue with Failures and Repairs and Its Continuous Approximation

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## nonsqtr

K. I can give you a simple example now.

We're going to roll an ordinary 6-sided dice.

But before we roll it, we're going to look at it. From this observation we determine the dice has six sides. This our starting information, our "seed".

So now we construct our first event set from the seed, it looks like {1,2,3,4,5,6}, and the s-set is its power set.

What else can we find out about the system at this point? Nothing. We have no outcomes yet, so we can't say anything more.

And now we roll the dice, and let's say the outcome is a 4. Now we can ask questions. Which subsets of the event space contain "4"? By answering this we can obtain an initial guesstimate for the probability of obtaining a 4.

After enough trials we can verify that our outcomes are independent. You can easily see, that after each outcome the filtration contains the totality of the information that is known about the system.

So, here's the question: in this example, what is the internal information, and what is the external information?

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## UKSmartypants

hey  @nonsqrt look at this, just what we were  talkign about#


"The quantum theory of computation originated as a way to deepen our understanding of quantum theory,  our fundamental theory of physical reality. By applying the principles  we have learned more broadly, we think we are beginning to see the  outline of a radical new way to construct laws of nature. It means abandoning the idea of physics as the science of what’s  actually happening, and embracing it as the science of what might or  might not happen. This “science of can and can’t” could help us tackle  some of the big questions that conventional physics has tried and failed  to get to grips with, from* delivering an exact, unifying theory of  thermodynamics and information to* getting round conceptual barriers that stop us merging quantum theory with general relativity,  Einstein’s theory of gravity. It might go even further and help us to  understand how intelligent thought works, and kick-start a technological  revolution that would make quantum supremacy look modest by comparison."                  

If its paywalled dm me and ill copypasta the whole article to you

Quantum computers are revealing an unexpected new theory of reality | New Scientist

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nonsqtr (04-15-2021)

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## nonsqtr

> hey  @nonsqrt look at this, just what we were  talkign about#
> 
> 
> "The quantum theory of computation originated as a way to deepen our understanding of quantum theory,  our fundamental theory of physical reality. By applying the principles  we have learned more broadly, we think we are beginning to see the  outline of a radical new way to construct laws of nature. It means abandoning the idea of physics as the science of whats  actually happening, and embracing it as the science of what might or  might not happen. This science of can and cant could help us tackle  some of the big questions that conventional physics has tried and failed  to get to grips with, from* delivering an exact, unifying theory of  thermodynamics and information to* getting round conceptual barriers that stop us merging quantum theory with general relativity,  Einsteins theory of gravity. It might go even further and help us to  understand how intelligent thought works, and kick-start a technological  revolution that would make quantum supremacy look modest by comparison."                  
> 
> If its paywalled dm me and ill copypasta the whole article to you
> 
> Quantum computers are revealing an unexpected new theory of reality | New Scientist


'Kay, I read the link about information.

Can you answer my question?

Hint: there are three different types of information (at least) involved. Each is quantifiable, albeit differently. There should be a common metric somewhere.

The first one is a freebie. You're assigning algebraic structure to the set when you use a numeric sequence to label the points.

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## UKSmartypants

> '
> 
> Can you answer my question?


No

Your into all this esoteric stuff, im a quarks and black holes kinda  guy

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## nonsqtr

> No
> 
> Your into all this esoteric stuff, im a quarks and black holes kinda  guy


We're studying the same thing.

The key word here, is "scope".

Quite obviously, the definition of "degrees of freedom" depends on what you include in your system.

The theory demands a "closed system", but that's never the case in real life. The best approximation we get is a part of the universe that's somehow isolated and unperturbed.

Just as in thermodynamics (or "particle-in-a-box"), if you move the boundaries the range of possible states changes. What we have traditionally called "information" always depends on assumptions (or knowledge) about the whole. And what constitutes the "whole" system is usually treated by handwaving.

We only know the probability is 1/6 because we looked at it ahead of time and saw there were six regular faces. OR, we had to take the time to perform a thousand experiments so we could reconstruct the distribution to within three standard deviations.

The idea of looking at the dice and observing six faces is making a statement about the GENERATOR, the process itself. We could also make physical arguments in this bucket, like the strength of the throw, the angle of the wrist when thrown, the care with which the dice are picked up, etc etc. All these things are not empirical, they're theoretical. The effort is to align the theoretical view of the generator, with the actual outcomes observed from experimentation.

Think - in the Gibbs formulation, what happens if you add an extra molecule, or move the walls a tad? By doing such a thing you're not changing any of the existing components, you're only changing the definition of "the system". Which reflects directly in the observed outcomes.

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## nonsqtr

The idea of a filtration is very powerful.

The expanding universe is a filtration.

Think about it.

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## nonsqtr

> No
> 
> Your into all this esoteric stuff, im a quarks and black holes kinda  guy


First thing is, the information structure you gave the event space when you sequentially labeled its sets. The sample space inherits the algebraic structure of the event space. 

When an outcome happens, you can't ask the question "is it even" unless you know what 'even" means in the first place.

And, "even" is not a property of the outcome itself, it's a property of the ALGEBRA, or rather the number system you assigned to the event space.

So the first lesson is: attributes (information) assigned to an outcome may actually belong to something else.

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## nonsqtr

The second type of information is what you introduced when you looked at the dice. To arrive at a guesstimated probability of 1/6 for each outcome, you had to say "aha! It's a regular polyhedron and therefore the probabilities of each outcome must be equal". 

Furthermore, you had to exclude the concept of a die landing on an edge or a corner.

Your initial estimate of the raw probabilities came from your knowledge of geometry.

In this case, the probability of an outcome IS a property of the mapping function from the event space - and therefore we see that this time the geometric embedding has affected the event probabilities directly.

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## UKSmartypants

> The idea of a filtration is very powerful.
> 
> The expanding universe is a filtration.
> 
> Think about it.



Well exactly, thats why i say the second law is bollox, its definition of a closed system doesn't stand up to scrutiny when applied to the universe.

Hence if the second law doesnt work, then entropy isnt the arrow of time. Something else is. And if mass=energy=information  then it has to lie in that equivalence.  And thus D4 isnt a time dimension, all 10 must be spatial dimensions, and thats where all the spare information is.

See my loopy theory Ive had for about 20 years is slowly hanging together. You have a more esoteric view of it, but its the same thing.

Your filtration is changing but only one Planck frame at a time,

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## nonsqtr

> Well exactly, thats why i say the second law is bollox, its definition of a closed system doesn't stand up to scrutiny when applied to the universe.
> 
> Hence if the second law doesnt work, then entropy isnt the arrow of time. Something else is. And if mass=energy=information  then it has to lie in that equivalence.  And thus D4 isnt a time dimension, all 10 must be spatial dimensions, and thats where all the spare information is.
> 
> See my loopy theory Ive had for about 20 years is slowly hanging together. You have a more esoteric view of it, but its the same thing.
> 
> Your filtration is changing but only one Planck frame at a time,


Well, if it's discrete it seems to make the math easier. We're thinking along the same lines, there's 26 orders of magnitude between Planck scale and anything measurable. Plenty of time for the law of large numbers to add up to a nice consistent Gaussian distribution, and even plenty of time for optimization.

The universe expands "everywhere", right? Not just at the edges.

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## Authentic

> Well, if it's discrete it seems to make the math easier. We're thinking along the same lines, there's 26 orders of magnitude between Planck scale and anything measurable. Plenty of time for the law of large numbers to add up to a nice consistent Gaussian distribution, and even plenty of time for optimization.
> 
> The universe expands "everywhere", right? Not just at the edges.


That's racist.

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## UKSmartypants

> That's racist.


The Universe is largely black, how can it be......

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## nonsqtr

The third type of information is neither algebraic not geometric. I'll call it "external meaning". In the bit-in-a-byte example, bit 4 differs from the dice experiment because it's a separate outcome, and it's not related to the geometry of the die which in this case equates with the geometry of the bit itself. And it's not the same as rolling 8 die at once unless those die had further external organization. The point being that the "organization" of the bits into a byte, is not a property of the event space, and it's not a property of the ambient space. It's "external", in that way.

In each case there is some kind of violation of the concept of a "closed system".

What we really want consider is the "exchange" of information - the ways in which, for example, external structures affect internal processes.

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## nonsqtr

K so, after further research, "I was right". The Shannon entropy doesn't measure what we want.

In fact it's worse than that - the Shannon information is the unique measure satisfying three axioms, all three of which are "not what we want".

What the Shannon entropy actually describes, is the expected self-information of a random variable. Which is not what we want.

What we want, can be achieved by a small change in the definition of "entropy".

RÃ©nyi entropy - Wikipedia

The Renyi entropy is not just a measure, it's a whole family of measures. It's almost like a Hilbert space of measures.

For instance - this paper calculates an exact solution for thermalization in a quantum many-body system.

Phys. Rev. Lett. 102, 240603 (2009)  -  Matrix Product States for Dynamical Simulation of Infinite Chains

The interesting thing about the Renyi entropy is it can be negative in the continuous case. And the Renyi entropies are measurable:

Measuring entanglement entropy in a quantum many-body system | Nature

What this is exactly is the nonlinear dynamics of isolated quantum many-body systems.

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## UKSmartypants

yes but this is all still based on Gibbs entropy. It might work on dice, but im more interested in the loss when information is compressed into a black hole then decompressed when the black hole collapses and explodes, because that becomes a modelfor the entire universe. No compression/decompression is lossless, so where does the lost information go, it has to go somewhere, and it isnt all Hawking Radiation, since you cant destroy information , if it has matter/energy equivalence.....entropy in information still has the same issues as mass/energy entropy on a macro scale...

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## East of the Beast

I just read this whole thread.Can I get the last 15 minutes of my life back........if time flow both ways it is possible.....right?

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## UKSmartypants

> I just read this whole thread.


You're a sad git with no life then....





> Can I get  the last 15 minutes of my life back........


Unlikely. No refunds, no returns.






> if time flow both ways it is  possible.....right?


Nonsqrt might agree. I dont believe in time.

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## East of the Beast

[QUOTE=UKSmartypants;2741119]You're a sad git with no life then....Then what's that make you?




Unlikely. No refunds, no returns.........damn!





Nonsqrt might agree. I dont believe in time.......I guess if you don't believe in it, you never waste it.

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## UKSmartypants

> ...._Then what's that make you?_


even worse. we're the two sad gits that wrote it



 (btw this is  a perfect example of jocular banter, something you americans just never seem  get the hang of   :Smiley20: )






> Unlikely. No refunds, no returns.._.......damn!_
> 
> Nonsqrt might agree. I dont believe in time......._I guess if you don't believe in it, you never waste it_.



Absolutely.  :Smiley20:    What do you do for a hobby?

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## nonsqtr

K, after much wrangling here's what I need:

I need a formula for filtration in space.

I'm looking for a stochastic equivalent for "flux density", so I can measure the information flowing across a 2-manifold, or equivalently the surface of a 3-d volume.

Here's the idea. You have a bit. It's a closed system. Let's say it's "small", maybe infintedimslly so.

So now, without changing the bit itself, I want to progressively increase the size of the system, in the way of a filtration that equates with dV, where V is the volume.

For example - the particle density in empty space is about a million per cubic meter. So as I increase the V around my qubit, I should start running into the influences from these other sources of information.

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## Authentic

What's a git?

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## OldSchool

All I know is: The 'need' word sucks.

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## nonsqtr

> All I know is: The 'need' word sucks.


Focus. You want to define all informational interactions within the volume you call "the system".

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## OldSchool

> Focus. You want to define all informational interactions within the volume you call *"the system".*


Actually: no.

I'm just not focused on your thread. Haven't read it, don't know where you're coming from and what you're getting at. I shouldn't have said a word. But, to explain: It's simply best to have all our bases covered and to not be in need of anything. But then to not be in need of something(s) would be to not be alive.

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## nonsqtr

> Actually: no.
> 
> I'm just not focused on your thread. Haven't read it, don't know where you're coming from and what you're getting at. I shouldn't have said a word. But, to explain: It's simply best to have all our bases covered and to not be in need of anything. But then to not be in need of something(s) would be to not be alive.


 :Smile: 

It's real easy. A byte is 8 bits, they're in order high to low with the 1-bit on the right.

The "meaning" of the byte can only be determined by reading all 8 bits, "at once". Because, there is implicit information hidden in the ordering of the bits. You have to arrange them in the proper order to get the intended meaning.

But what happens if you "reduce the universe", by considering only 2 of the bits, let's say the two lowest order bits on the right. So now your "system" has 2 bits instead of 8. 

One relevant question is, is there any way you can infer the existence of the other six bits by just observing the two?

And, would it make any difference if they were the two bits on the left instead of the two bits on the right?

You see, @UKSmartypants and I are seeing the same thing from two totally different perspectives.

The vernacular has it that entropy relates to disorder, but that is WRONG, it's a stunningly incorrect viewpoint.

Physics tells us that the universe is expanding at all points equally. My example says that when you add more bits you get more information, therefore you increase the number of possible states in "the system" (however that's defined). 

So let's say you had the two bits (so the system has 4 possible states), and now a third bit grows between them, what happens? Now your system has 3 bits and 8 possible states - but, if you didn't know the third bit existed and you were only looking at the two original bits, your system now has twice as many ways of achieving the same states.

So, in the bit-in-a-byte example, you can progressively increase the size of the system under consideration, from 2 bits to 3 to 4 to 5, all the way up to 8, and that is a "filtration" according to the classical definition 

However you'll get a DIFFERENT outcome with a new bit, than you will with an existing one, and that is the point of this post and the reason for the need. Your universe doesn't grow till you add the new bit. Said another way, it is impossible to artificially increase the information in a closed system, if you try to do that the energy will adjust itself so the information stays the same.

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## UKSmartypants

> What's a git?



git

[ɡɪt]




NOUN
BRITISH
informal 
derogatory



an unpleasant or contemptible old person

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Authentic (04-27-2021)

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## OldSchool

> It's real easy. A byte is 8 bits, they're in order high to low with the 1-bit on the right.
> 
> The "meaning" of the byte can only be determined by reading all 8 bits, "at once". Because, there is implicit information hidden in the ordering of the bits. You have to arrange them in the proper order to get the intended meaning.
> 
> But what happens if you "reduce the universe", by considering only 2 of the bits, let's say the two lowest order bits on the right. So now your "system" has 2 bits instead of 8. 
> 
> One relevant question is, is there any way you can infer the existence of the other six bits by just observing the two?
> 
> And, would it make any difference if they were the two bits on the left instead of the two bits on the right?
> ...


If a tree falls in the woods, but you're not there to hear it, it does make a sound. It's a vibration that we perceive as sound, but has a very real effect on it's surroundings. i.e. a bit that's a part of a byte to be read and comprehended. If that bit is perceived to happen in a forest, but in fact happens in NY's central park..... well, you're interpretation and conclusion of events leading to how the world is.... will be skewed.

It's my firm belief that we, as humans, have a limited perspective. Meaning we will never have all the bits in the right places.... thus can not properly read the bytes. Good luck with your quest in need to attain full and proper understanding.

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## nonsqtr

The science of it - here's the problem - "information" is inherently non-local. Because, it really doesn't matter if the bits in your byte are right next to each other, or if they're light-years away in the next universe. (Same for entanglement, btw).

What I'm trying to understand is how the geometry plays into it. Because it does.

But the relationship between the geometry and the information is not at all obvious.

There are three major areas of science, and two of math, which currently study this relationship. In science we have theoretical physics, neuroscience, and quantum computing, all three of which study "information geometry" in some way. In math there is differential geometry and stochastic processes, and the latter is still in its infancy and is just now formulating the concepts around stochastic manifolds. (Also we should probably mention the financial analysts, some of whom are very smart and very clever with math).

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## OldSchool

"math" assumes that 'components' of the logical equation are not disputable. There-in lies fault with the equation, without proof that what should be variables are substantially assumed.

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## OldSchool

Here's a question: Is there any truly constant in the universe which all equations can rely upon?

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## OldSchool

I'm saying science and math will never provide all the correct answers with indisputable evidence.

Next level????

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## nonsqtr

> Here's a question: Is there any truly constant in the universe which all equations can rely upon?


Yes. Fundamentally the constancy has to do with numbers, that is to say, how things behave when you count them.

For instance, around the year 1400, long before Newton and Leibniz, the Indian mathematician Madhava of Sangamagrama discovered the series expansions for sine and cosine and the invariant mathematical definition of Pi, which is defined as follows:

Pi = 4 * (1 - 1/3 + 1/5 - 1/7...)

Madhava of Sangamagrama - Wikipedia

The actual numeric value might look different if you were, say, in base 8, but the ratio is a universal constant.

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## OldSchool

> Yes. Fundamentally the constancy has to do with numbers, that is to say, how things behave when you count them.
> 
> For instance, around the year 1400, long before Newton and Leibniz, the Indian mathematician Madhava of Sangamagrama discovered the series expansions for sine and cosine and the invariant mathematical definition of Pi, which is defined as follows:
> 
> Pi = 4 * (1 - 1/3 + 1/5 - 1/7...)
> 
> Madhava of Sangamagrama - Wikipedia
> 
> The actual numeric value might look different if you were, say, in base 8, but the ratio is a universal constant.


I passed advanced math class's easily in my school days.... that was many years ago, when I just had to make sense of equations as taught.

Math does make perfect sense of things that are before our eyes. But, fact is: there's way too much that's beyond our perception.....and unforeseen variables do come into play.

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## OldSchool

And by the way: I do not believe in the multi-universe  theory....  this is life as we know it..... there is only one universe.

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## nonsqtr

> I passed advanced math class's easily in my school days.... that was many years ago, when I just had to make sense of equations as taught.
> 
> Math does make perfect sense of things that are before our eyes. But, fact is: there's way too much that's beyond our perception.....and unforeseen variables do come into play.


Well, but there is structure in the actual numbers.

Independently of any realization in the real world.

Pi is pi, in all number systems, in all representations. There are other magic numbers like this, e is another one. All of them are "series", that is to say, patterns (structures) of numbers.

So let's continue with this train of thought.

If we were to ask, how much information is in a number? For instance Pi - you need an infinite number of digits to represent it, does that mean there's a lot of information in it?

Or, is it just a number? If I'm an electronic tech and I have a voltmeter and it reads 3.14159 volts, does that give me any more information than if the meter just said "2"?

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OldSchool (04-27-2021)

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## OldSchool

> Well, but there is structure in the actual numbers.
> 
> Independently of any realization in the real world.
> 
> Pi is pi, in all number systems, in all representations. There are other magic numbers like this, e is another one. All of them are "series", that is to say, patterns (structures) of numbers.
> 
> So let's continue with this train of thought.
> 
> If we were to ask, how much information is in a number? For instance Pi - you need an infinite number of digits to represent it, does that mean there's a lot of information in it?
> ...


Structure? When pie has no definition?

I like information, in fact I'm hungry for it at times. But, I'm content enough to know I'll never understand it all.  Sure, there's plenty of explanations... but math doesn't tell me why one plus one equals zero when the marriage goes to hell.  :Wink:

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## OldSchool

What should be the simplest of things is to use a math equation that relates to measuring the radius of a circle to determine it's circumference.....

Hmmmm,,..... guess that's one we'll pass on and figure all else is fine.  :Geez:

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## nonsqtr

Okay. So here is the beginning of a new framework, for "information".

We discussed internal vs external information. The states of a bit (0 and 1) belong to the bit, the internal information is "localized". However when you position the bit within a byte, the bit becomes part of a higher level information "network", which I'm going to call an information "*schema*", and this external information network is different, it's non-local, the information doesn't live in the bit or in any combination of the bits within the byte.

Yet the "whole" byte consists only of bits. So here is the concept I'd like to introduce. (You'll have to bear with me, because it's counterintuitive at first, but once I explain it you'll get it). My claim is: there is no actual information in the state of a bit. "Information" happens when you CHANGE the state. Let me explain.

I'll give three examples. Start with the usual classical situation of a bit in a computer. It's part of a byte, or a word, or a double floating point longword or whatever. There are three fundamental things you can do to the bit: flip it, store into it, and retrieve from it. Additionally there is a fourth operation called "test", which requires the external conditional "if". So for example, "store a 1" is equivalent to "if 0 flip". Information theory says, you don't even know the bit exists till the first time it flips, then you can "notice" it. This dovetails with the new model, information happens when the state changes.

Second, consider a qubit. The qubit is "constantly changing", therefore it can "carry" ("hold") information. A qubit can "hold" up to TWO bits with superdense coding, but one of them belongs to the qubit, you can't retrieve it. You can only read out one bit from a qubit. Why? Because of quantum collapse. When it stops changing, no more information. This also dovetails with the new model.

Third, consider placing the bit into a byte. Assigning meaning to the byte involves assigning a geometric position to the bit. As bytes are transferred across the computer bus, we never stop to think (or measure) that the probability of bit 2 being 0 should be 50%, because we take for granted that inclusion in the external schema means abandoning the internal distribution. The bit changes it's behavior when it is made part of a network of conditional expectations that may or may not relate to the individual behavior of the bits.

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## nonsqtr

To further understand the action of an information *schema*, consider the following example.

In a room, you have two bits and a person.

The bits are unrelated, let's say, they're on different wires in different computers in different rooms.

Without the person, the two bits are independent. If you were looking for conditional probabilities you wouldn't find any.

But now, along comes the scientist-person, and she introduces a schema. She construes that the bits are part of a system, and she arbitrarily says the bit on the left means 2 and the bit on the right means 1.

By doing this, she is layering a system of conditional probabilities over the independent bits.

In essence, this is an "entanglement". So how does it differ from a real physical entanglement?

The answer is: it doesn't.

Think about it.

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## UKSmartypants

> And by the way: I do not believe in the multi-universe  theory....  this is life as we know it..... there is only one universe.



If a quantum fluctuation on the D10 can cause one planck sized dimensionm to erupt out, because the energy density is enough the break the constraining heteroic string, theres absolutely no reason to think it cant happen multiple times.  The only real if/but is how many of the universes manage to be generated with similar physical constants as ours, and thus end up like ours, how many fail to expand , and simply collapse again, how many fail to create matter and remain empty and black...etc etc...the sensible view is that all possible universes constructed with all possible variants of physical constants will at some point emerge somewhere on the metaverse's D10 Brane, and most of them will terminate just as fast, having  parameters that are not viable.

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## UKSmartypants

> Structure? When pie has no definition?



ofc it has a definition, that existed the moment the universe existed.

Pi is the ratio of the circumference of a circle to its diameter. its an absolute pure number independent of observation. It just exists, and didnt need us to discover it. There are 19 different physical universal constants like that, absolute pure numbers,  another is the Fine Structure Constant - a dimensionless quantity related to the elementary charge e, which denotes the strength of the coupling of an elementary charged particle with the electromagnetic field, by the formula 4πε0ħcα = e .

Others critical numbers are
The Gravitational Constant G
The Speed of Light c
The Planck constant h
The 9 Yukawa couplings for the quarks and leptons
The 2 parameters of the Higgs field potential,
The 4 parameters for the quark mixing matrix,
The coupling constants for the gauge groups SU(3) × SU(2) × U(1) 
The mystery is what determined the value of them, why did they end  up at these values, were  they random, or is ther a deeper underlying theory that sets them at the point where 4D spacetime (sic) erupts. ?

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## OldSchool

I don't buy into all the assumptions/constants that make complex mathematical equations solvable, with perfect logic, in relation to how the universe is and/or is thought to be and even proven to be by math..... with our limited perspective.

That's simply my take and I don't care to argue about it.

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## OldSchool

But, for those who believe math has all the answers: 

Even Albert Einstein Had His Doubts About Black Holes - HISTORY




> The concept that explains black holes was so radical, in fact, that  Einstein, himself, had strong misgivings. He concluded in a 1939 paper in the _Annals of Mathematics_ that the idea was “not convincing” and the phenomena did not exist “in the real world.”


Testing Einsteinâs Theory of General Relativity From the Shadows and Collisions of Black Holes

April 30, 2021




> General relativity, Einstein’s theory of gravity, is best tested at its most extreme — close to the event horizon of a black hole. This regime is accessible through observations of shadows of supermassive black holes and gravitational waves  — ripples in the fabric of our Universe from colliding stellar-mass  black holes. For the first time, scientists from the ARC Centre of  Excellence for Gravitational Wave Discovery (OzGrav), the Event Horizon  Telescope (EHT) and the LIGO  Scientific Collaboration, have outlined a consistent approach to  exploring deviations from Einstein’s general theory of relativity in  these two different observations. This research, published in _Physical Review D_, confirms that Einstein’s theory accurately describes current observations of black holes, from the smallest to the largest.

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## Authentic

I need to find the article I read this morning. Some black professor of cosmology complains that too much stuff in physics and her field were named by white males. She has issues with the term dark matter not so much because of its meaning but because it wasn't named by a person of color.

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## Authentic

Here it is. Chandra Prescod-Weinstein.

Black physicist rethinks the 'dark' in dark matter | CTV News 

At the end she dreams about "every child having access to a dark night sky and the oppurtunity to sit and wonder beneath it."

She blames "racism, transphobia, and other forms of oppression for this disparate impact.

My first thought upon reading that was that there are a lot of dark night skies above Africa.

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Oceander (05-04-2021)

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## nonsqtr

Kay. Let's talk about entanglement.

Turns out, based on what we just learned, the answer is incredibly simple and elegant.

A quantum entanglement is a "mixed state". What that means is there are "pure states" somewhere, but their exact nature has to be discovered.

The answer is given by the Schmidt decomposition, here: 

Schmidt decomposition - Wikipedia

A state w is entangled if and only if its Schmidt rank is > 1, which also means w != u cross v.

So, here is a precise quantitative relationship between the state and the information.

Quantum entanglement of a harmonic oscillator with an electromagnetic field.

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## nonsqtr

Bingo.

If you study the research of MV Fedorov in Russia and KG Fedorov in Germany, you'll have the answer.

Read this:

https://arxiv.org/pdf/quant-ph/0605208

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## nonsqtr

@UKSmartypants, this view strongly suggests that gravity isn't quantum at all, it's something completely different. It's a "sponginess" in the mass that reflects an imperfect infinity.

And... how do you get an imperfect infinity? Easy! There's lots of those in nature. An incomplete distribution, is one way. Strings that can't oscillate fast enough, is another.

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## UKSmartypants

> @UKSmartypants, this view strongly suggests that gravity isn't quantum at all, it's something completely different.


Ive thought that for a long time if you draw a straight line graph with time along the bottom and the total energy of the universe going up, you can put a dot on the line where (supersymmetry) electromagnetism split off, another further up (higher temp, earlier time) where Strong Nuclear force broke, another where the Weak Nuclear force broke...and Gravity cant be slotted on the line, in fact  the obvious place to put it is before the t=0, ie gravity is from the Metaverse D10. and i suspect so is dark/ energy and dark matter
.

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## UKSmartypants

hey @nonsqrt  look at this  

RÃSONAANCES:  Why is it when something happens it is ALWAYS you, muons?

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nonsqtr (05-08-2021)

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## nonsqtr

Okay, I may have something useful.

Filtration. Filtration in space, rather than time.

The usual interpretation of filtration is from the reference frame of the event set, as it impacts the sample space. So, every time there's a new outcome, it adds to the information in the distribution.

However let's do a thought experiment, let's say we're in a quantum lattice and we have a circle of radius R centered at the object under study (centered "in space", geographically), and we begin growing the radius by dR... what happens?

Conceptually it's real easy - every time the increment dR comes to encompass a new object there is interaction. What used to be a pure state now becomes a mixed state, and it is possible that it just so happens we encounter the other half of a pair of entangled photons.

So our information space is growing in exactly the same way as if we had more outcomes - in other words the conditional expectations are being affected by the new information.

At the end of the day the primary dependency is what you consider as the "set". If you add a point into the event "set" it changes the distributions.

So, kinda, geometrically, we're looking for subspaces of compactness, irrespective of the actual geographic location.

The question is, are there compact subspace solutions to the Lindblad equations, based on geometry alone? Usually we depend on compactness when we grow dR. The question is whether we can formulate this experiment outside of 4-space, in such a way that we get compactness even if it isn't present in the 4-space?

Let me rephrase that - in 12 dimensions, can we get a compact subspace that doesn't involve ordinary 4-space?

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## UKSmartypants

@nonsqtr


this is from a long article on Superdeterminism
_
"That is because, according to Huw Price, a philosopher at the University of Cambridge, backwards-in-time causation  is the one thing that can make superdeterminism plausible. Price argues  that superdeterminism works if you take the “block universe”  perspective of Einstein’s special theory of relativity, where past,  present and future all co-exist in a big four-dimensional grid we call  space-time. In this scheme, time doesn’t run in any one direction. Time’s arrow  isn’t fundamental to relativity – or to quantum theory, for that matter."


_
Bingo, its what ive been saying for years .  Time is just one spatial axis of a higher dimension, and it all exists, in both directions to infinity.


If you want to whole article PM me and ill paste it too you, its too long to post here.

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