Phase transitions of space-time?

[Boris Leykin]

Don't you know what are http://motls.blogspot.com/2005/03/melting-crystals-and-quantum-foam.html" ? Horse-radish, you will understand that.

What I imagine.
At the beginning there was space-time and it was a solid, a crystal. Then there was the Big Bang, there came a Brane and knocked space-time, as a result space-time heated and started to melt. Now the space-time is a liquid or a gas, right?
Oh, idea! Just have thought up, that space-time when it is solid or liquid must evaporate too, and there must be space-time steam. This steam may come even from other brane.

 

[Boris Leykin]

http://cerncourier.com/main/article/44/4/17"
Does a melting crystal provide the key to developing a quantum description of gravity? Advances at the first Simons Workshop point to a connection.

Is it like I imagine or what I just can't get that.

This led Okounkov, Reshetikhin and Vafa to conclude that topological string theory and crystal theory are "dual" descriptions of a single underlying system valid for the whole range of weak and strong string coupling, or equivalently, high and low temperatures, respectively.

Why haven't they found "dual" liquid or gaseous theory, interesting?


What? Ooh? Ah? hoo? Who linked this topic back to motl's blog?

 

[Boris Leykin]

Listen. I was watching Lenny Susskind's http://www.geocities.com/borisleykin/susskind/susskind.htm"

What he said:

There is a complicated landscape of possible universes. Now, are we any better of where we've been before? We have a huge number of possibilities, who picked the right one? Well, physicists, what they often do when they don't understand a thing, they make a name for it, and once they make a name they start to feel comfortable, good. It's the vacuum selection principle or the geometry selection principle. [] Something selects out one of these. Once you've named it you are free, you don't need to explain it anymore. Unfortunately the vacuum selection principle is [] lot like a Lochness monster, a lot of people believe in it but nobody have ever seen it. And many of us just don't think it exists, that there is any particular selection procedure that will pick out one of 10^(500). What's the alternative? The alternative is that there's no vacuum selection principle, that they all play a role. And there's some fabrication mechanism for making all of vacuums, exactly the same way that Darwin had a mechanism for fabricating all of possible species types.
And I'll show you what a fabrication mechanism is that some of us believe in. It is called eternal inflation. Here is a picture.

This process of eternal inflation it looks obscure incomprehensible to me. How does it work exactly? So when I saw these Calabi-Yau crystals... This is it, right? Quantum foam melts and gives a needed Calabi-Yau manifold?

And suddenly after that another thought have come
Remember I was asking about "string" computers?
https://www.physicsforums.com/archive/index.php/t-125043.html"
What is the answer to a question Why there are no computers which are more powerful than quantum ones? http://scottaaronson.com/blog/?p=215", they said "But I did once query the best available wetware oracle: Ed Witten. Witten said that he didn’t see any new computational power in quantum gravity, then cited the holographic bound."
It seems like some mechanism exists which forbids their existence, what is this mechanism? Quantum foam is computationally infinitely powerfull, but when it goes phase transition to spacetime it becomes less powerfull.

Want to hear any comments on all this, what do you think?

 

[setAI]

to my thinking the Beckenstein bound limits quantum computation really in terms of 'bandwidth' of the interface- you can extract the answer as fast as polynomial time [with an ultimate limit of the B bound]- but the nature of a quantum computer says that it actually computed all the possible answers at once- which includes all possible states- and some of those must correspond to the n-qubit quantum computer in a state of an n-qubit quantum interface to an unlimitedly larger quantum computer or network lying in one of the infinite states of the multiverse- [and that to a larger- and so on ad infinitum]essentially there are paths of computation which ultimately harness the entire quantum multiverse if needed- so the upper limit of accessing the answer is the Beckenstein Bound- but the computation itself is virtually limitless in a sense- because fundamentally the quantum computer is like a logic structure which connects to an already existing infinite hilbert space of 'all possible answers to all possible problems'

as for classical computation- the power and speed of classical computation is determined by the physics of the spacetime in which the computation occurs- here are some nice papers which explore the possibility of infinite classical computation in different types of spacetimes- such as the Malament-Hogarth space near certain types of black holes:
http://arxiv.org/abs/gr-qc/0104023
http://arxiv.org/abs/gr-qc/0609035

ultimately what is being called 'omega point' computation in computer science circles these days [borrowed form Tipler's big cruch omega point http://www.idsia.ch/~juergen/computerhistory.html ] - that is virtually infinite limitless computation- is considerd quite solvable and inevitable- infinite computers have been anticipated since the 60s [ Marvin Minsky, “Computation: finite and infinite machines”- Englewood Cliffs, N.J., Prentice-Hall, 1967]

 

[Kea]

Does a melting crystal provide the key to developing a quantum description of gravity? Advances at the first Simons Workshop point to a connection.

This is really very intriguing! Thanks for the links. And yes, melting crystals are important for understanding quantum gravity. Think of a 3D Young diagram (like the 2D diagrams inside squares in the plane) - this is like the corner of a cube of crystal, melted away. Now cubic paths are essential to the combinatorics of the categorical non-commutative Fourier transform, which underlies the higher categorical structures needed to axiomatise QG. Hope that helps.

 

[Boris Leykin]

... 'all possible answers to all possible problems'...

Thanks for the links
In other words you said that it is me who is limited in computational power but not a quantum computer.
This statement confuses me, have you looked at Scott Aaronson's blog, he says that probably quantum computers will not be able to solve NP complete problems.
Oh, that all is so intricate, I can't understand.

This is really very intriguing! And yes, melting crystals are important for understanding quantum gravity. ... Hope that helps.

Thanks, Kea, but no, it doesn't help
There is some obscure thing http://cerncourier.com/main/article/44/4/17"
They say:

At high temperatures the idealized crystal melts into a smooth surface with a well-defined shape. This surface is a two-dimensional portrait of a CY space, called a "projection" of the space

Why this "projection"? Why they just don't say that crystall melts into 6 dimensional Calabi-Yau? And what is the dimension of a crystall itself? Oh.

 

[setAI]

Thanks for the links
In other words you said that it is me who is limited in computational power but not a quantum computer.
This statement confuses me, have you looked at Scott Aaronson's blog, he says that probably quantum computers will not be able to solve NP complete problems.
Oh, that all is so intricate, I can't understand.

in a nutshell- quantum computers ARE limited by the Beckenstein bound and can only produce answers in polynomial time- but the bottleneck is "bandwidth" and not "processing power"- which is fundamentally limitless because a quantum computer is a quantum system in perfect superposition of all possible states where the desired state is extracted- however this limit is also the limit of observable information of our universe anyway

also- here are several methods for using quantum computation to solve NP complete problems:

http://www.arxiv.org/abs/quant-ph/9912100
http://www.arxiv.org/abs/quant-ph/9801041
http://www.arxiv.org/abs/quant-ph/0508177

 

[Kea]

Why this "projection"? Why they just don't say that crystal melts into 6 dimensional Calabi-Yau?

Calabi-Yau spaces are complicated things. One also needs to know, for instance, about maps of surfaces sitting inside Calabi-Yau spaces. These 'projections' are an important part of the picture. Now physically, one doesn't want to take string compactification seriously, but the Calabi-Yau spaces will still arise as 3 dimensional analogues of elliptic curves (and quantum gravity needs some fancy number theory, by the way) in a heirarchy of quantizations.

 

[Fra]

Listen. I was watching Lenny Susskind's http://www.geocities.com/borisleykin/susskind/susskind.htm"

What he said:

There is a complicated landscape of possible universes. Now, are we any better of where we've been before? We have a huge number of possibilities, who picked the right one? Well, physicists, what they often do when they don't understand a thing, they make a name for it, and once they make a name they start to feel comfortable, good. It's the vacuum selection principle or the geometry selection principle. [] Something selects out one of these. Once you've named it you are free, you don't need to explain it anymore. Unfortunately the vacuum selection principle is [] lot like a Lochness monster, a lot of people believe in it but nobody have ever seen it. And many of us just don't think it exists, that there is any particular selection procedure that will pick out one of 10^(500). What's the alternative? The alternative is that there's no vacuum selection principle, that they all play a role. And there's some fabrication mechanism for making all of vacuums, exactly the same way that Darwin had a mechanism for fabricating all of possible species types.
And I'll show you what a fabrication mechanism is that some of us believe in. It is called eternal inflation. Here is a picture.
pic33.JPG

This process of eternal inflation it looks obscure incomprehensible to me. How does it work exactly? So when I saw these Calabi-Yau crystals... This is it, right? Quantum foam melts and gives a needed Calabi-Yau manifold?

Oddly enough, I am not a string fan, but ignoring this fact and just reading it, the "eternal-inflation" idea is plausible to me, and to me this can have meaning beyond string theory. I think if you can infere options, but no principle to choose one over the other something is wrong. I doesn't make sense that these options appeared in the first place? I suspect the introduction of options is made in a mathematical way, therefore no one understands what the options mean outside the mathematical formalism.

I've always had the feeling that the string theory, has a lot of mathematical fiddling that's done without knowing what it means in terms of reality. I guess the reliance is on some mathematical consistency and they hope to find out later what it all means. I personally have really hard to understand the driving motivation of the individual in such approach. At least it's not the way my head works.

Anyway, I strongly believe that we need generic evolutionary models, regardless of wether it's string theory or not.

A bold guess is that if they find the right evolutionary selection mechanism I'd expect that the "string" or brane starting point is not needed in the first place. Then, perhaps I could like it too.

/Fredrik

 

[Boris Leykin]

This process of eternal inflation it looks obscure incomprehensible to me. How does it work exactly? So when I saw these Calabi-Yau crystals... This is it, right? Quantum foam melts and gives a needed Calabi-Yau manifold?

Oddly enough, I am not a string fan, but ignoring this fact and just reading it, the "eternal-inflation" idea is plausible to me, and to me this can have meaning beyond string theory...

I just wanted to say, that all these bubbling nucleating universes, what is it that thing which is "boiling", is it quantum foam or what? And there is no explanation why it is "boiling", right?

also- here are several methods for using quantum computation to solve NP complete problems:

Mmm. Thanks, setAI. I am trying to understand Scott Aaronson's
http://scottaaronson.com/thesis.html"
http://scottaaronson.com/talks/anthropic.html"

But the idea that computational complexity classes are somehow connected to phase transitions, is it good what do you think?

Calabi-Yau spaces are complicated things...

Mmm.

I think I finally understood what all those things about n-categorical description of quantum gravity are about: There are two landscapes one is mathematical (I read Eugenia Cheng's http://math.unice.fr/~eugenia/misc/4000.pdf" ) and the other is a landscape of string theory (physical landscape), but really they are the same thing!


Also wanted to ask somebody about Susskind's lecture.
He says:

Here is the soviet version of the vacuum. Everything is homogenious, everything is the same everywhere. And from time to time a little flickering motion, a little place will occur which is slightly different, different in a different point on the landscape. The Calabi-Yau manifold is changed, the flux numbers change, something happens over here. But if it's small enough the result that its neighbours will pull it back, and a little nucleating bubble disappears. Really what happens is that this is going on all the time, back and forth, back and forth, all over space. But what happens if accidentally a slightly bigger bubble gets nucleated and eventually it will take over the whole space.

This statement about neighbours is strange, little fluctuation they can stop but not a bigger one. I wonder if there are any papers which explain this mathematically or is it just a speculation? Just curious

 

[Kea]

I think I finally understood what all those things about n-categorical description of quantum gravity are about: There are two landscapes one is mathematical ... and the other is a landscape of string theory (physical landscape), but really they are the same thing!

A bit of an oversimplification, but on the right track! The classical reality of many worlds is made of the very motives of mathematics. I don't think it helps, however, to think of the landscape as a collection of stringy vacua. QFT looks quite different when formulated in a categorical language. Strings are there more like the way they were in the early days of hadron physics, when dual resonance had contact with experiment. This categorical landscape does not imply an effectively arbitrary set of SM parameters. On the contrary, particle masses (for instance) are computable precisely because they are localisable in the numerical landscape.

It is often said that the physics of Geometric Langlands is just the geometric correspondence and not about the whole number theory thing, but this is no longer true in categorical QG. We are finding that generalised number theory underpins everything. This brings us to a close connection with the voluminous work of Matti Pitkanen, who has worked entirely on his own for many years trying to understand this generalised number physics from the TGD viewpoint. In particular, he identified the heirarchy of quantizations early on. Second quantization is only the first step of an infinite process which is required in order to represent physical numbers constructively. Mass cannot be investigated without going to the third level, where the 3D melting crystals come in, and non-associative as well as non-commutative algebras arise.

 

[Fra]

I just wanted to say, that all these bubbling nucleating universes, what is it that thing which is "boiling", is it quantum foam or what? And there is no explanation why it is "boiling", right?

Without going into specific models, what makes sense to me is there is always a certain "noise", that originates from constraints in information representation and processing in a changing environment. It seems hard enough to even come up with a single foolproof statement
without having an small opening to it.

I think there's always possibilities "cooking" around the corner, but for reasons I suspect again has to do with observer constrains, memory sizes etc possibilities below some confidence threshold are sort of auto repressed. Only significant possibilities grow. An intuitive picture is that due to memory and processing constrains, it is unfavourable to consider(process/explore) low quality options.

I think in the biology analogy, in physics we are considering organisms, systems, or observers that feed, and grow on information. And as any organisms, there is no need to fill your memory with noise, when there are more interesting data to process. So data, and any dimensions hiding there, is effectively marginalized.

Similarly I picture that in times of starvation, we are desperate enough to process noise.

I think physical systems are organisms feeding on order in evironment for their own growth. And since, order is relative, there seems to be no such thing as "ultimate disorder".

I'm currently working on some similar ideas, having nothing to do with string theory, but I can't help seeing strong analogies on the interpretational sides in many of the standard approaches. I am looking for a stronger, and clearner information theoretic approach.

I'm inspired by approaches simiar to that of Ariel Catichas ideas of bayesian inference, ME methods and information geometry and how that links to the physical world and dynamics. Ultimately there need only need to be a generic information representation, and a learning/evolution rule.

/Fredrik

 

[Boris Leykin]

We are finding that generalised number theory underpins everything.

Generalized number theory?! Mmm. (I am scratching my head)

I think physical systems are organisms feeding on order in evironment for their own growth

Sorry, Fra. I am completely confused by what you are saying.

 

[setAI]

Generalized number theory?! Mmm. (I am scratching my head)

basically: Pythagoras was right after all

 

[Kea]

Fra, I think you have an insightful way of expressing things. I look forward to hearing more about your work.

basically: Pythagoras was right after all

Yes, that's a simple way of putting it! Pythagoras did not know about octonion Jordan algebras or higher categories, but he sure understood the importance of symbolic reasoning and relationalism.

 

[Boris Leykin]

Generalized number theory?! Mmm. (I am scratching my head)

Oh! Indeed. I am recalling that http://arxiv.org/abs/hep-th/0401049" .


To setAI: Here's another thing about computers from http://arxiv.org/abs/hep-th/0602266"

But some problems are too difficult for the multiverse to solve in polynomial time. This is made precise by Aaronson’s definition of an “anthropic computer.” [1] Using these ideas, Denef and I [7] have argued that the vacuum selected by the measure factor exp(1/Lambda) cannot be found by a quantum computer, working in polynomial time, even with anthropic postselection. Thus, if a cosmological model realizes this measure factor (and many other preselection principles which can be expressed as optimizing a function), it is doing something more powerful than such a computer. Some cosmological models (e.g. eternal inflation) explicitly postulate exponentially long times, or other violations of our hypotheses. But for other possible theories, for example a field theory dual to eternal inflation, this might lead to a paradox.

He points to [1] http://arxiv.org/abs/quant-ph/0412187"

 

[Fra]

We are finding that generalised number theory underpins everything. This brings us to a close connection with the voluminous work of Matti Pitkanen, who has worked entirely on his own for many years trying to understand this generalised number physics from the TGD viewpoint. In particular, he identified the heirarchy of quantizations early on. Second quantization is only the first step of an infinite process which is required in order to represent physical numbers constructively. Mass cannot be investigated without going to the third level, where the 3D melting crystals come in, and non-associative as well as non-commutative algebras arise.

Kea, I am not too familiar with the original motivation of the formal category approaches, but your typing is strikingly similar to seemingly unrelated and more philosophical lines of reasoning. Indeed the quantization procedure is an induction step in an expansion model. This is completely in line with what I'm hoping to accomplish, however my motivation is intuitive and I am trying to find the formalism that matches intuition. I smell that this abstract things will nicely merge with a very natural philosophy. But I suspect that the hardcore guys working on the math have another motivation, but I suspect we will meet somewhere in the middle. It's too similar to be a coincidence.

I take you you more or less get what I mean, so I'll throw out this fuzzy question: It's clear that the model evolution at first seems to go on forever, increasing complexity indefinitely. That is a problem because at some point the model complexity alone with dominate the system in a certain sense.

I'm currently trying to understand howto find the balance here, I picture the model is somehow formualated by someone, an observer or a system in general. And the model needs some representation - memory. And limited memory will limit the evolution, because the _model itself_ i think must required representation and thus ultimately take on physical properties... but this can't go on forever or the system would get infinitely heavy.

If the question doesn't make sense, ignore it. But if it does, can you roughly note if and how this problem is solved in your approach?

/Fredrik

 

[Kea]

Indeed the quantization procedure is an induction step in an expansion model. This is completely in line with what I'm hoping to accomplish, however my motivation is intuitive and I am trying to find the formalism that matches intuition.

Hi Fredrik

This is good to hear. What I have been thinking is not really like 'traditional' formal higher category theoretic physics (if such a thing exists) but it does bear some relation with certain CompSci ideas. I agree that the more mathematical string philosophy seems to be heading towards the heirarchy too, albeit with an entirely different, and seemingly unclear, motivation.

It's clear that the model evolution at first seems to go on forever, increasing complexity indefinitely. That is a problem because at some point the model complexity alone will dominate the system in a certain sense. I'm currently trying to understand how to find the balance here.

Oh, I think I see. I am convinced that a second major QG principle, which I simply call Mach's principle, acts on the heirarchy to link the observer's internal view to the actual cosmic model. In Pitkanen's TGD this is an atman-brahman principle, wherein the whole constructed reality must reside in the model of self. String theory vaguely picks this up with its web of dualities, but misses the n-alities (triality, ternality etc.) entirely because it fails to consider the higher levels. This Machian balance is absolutely crucial to constraining physical amplitudes, which I see as 'pairings' in the universal cohomology between the atman and brahman manifestations of the observable. Sorry if this isn't clear.

You mention memory. Pitkanen has thought a lot more about this than I have. Basically, the fundamental duality can create the memory half of reality. A memory operation is just like how we see it inside our own heads: a reaching out to distant events along a path in a secondary (immaterial) space, which is intertwined with the material model in such a way that we cannot hope to describe it without the balance principle. Note the influence of Penrose's thinking here. I think that this secondary principle is inherently gravitational (hence the term Machian).

Cheers
Kea

 

[Fra]

Hi Fredrik

This is good to hear. What I have been thinking is not really like 'traditional' formal higher category theoretic physics (if such a thing exists) but it does bear some relation with certain CompSci ideas. I agree that the more mathematical string philosophy seems to be heading towards the heirarchy too, albeit with an entirely different, and seemingly unclear, motivation.



Oh, I think I see. I am convinced that a second major QG principle, which I simply call Mach's principle, acts on the heirarchy to link the observer's internal view to the actual cosmic model. In Pitkanen's TGD this is an atman-brahman principle, wherein the whole constructed reality must reside in the model of self. String theory vaguely picks this up with its web of dualities, but misses the n-alities (triality, ternality etc.) entirely because it fails to consider the higher levels. This Machian balance is absolutely crucial to constraining physical amplitudes, which I see as 'pairings' in the universal cohomology between the atman and brahman manifestations of the observable. Sorry if this isn't clear.

You mention memory. Pitkanen has thought a lot more about this than I have. Basically, the fundamental duality can create the memory half of reality. A memory operation is just like how we see it inside our own heads: a reaching out to distant events along a path in a secondary (immaterial) space, which is intertwined with the material model in such a way that we cannot hope to describe it without the balance principle. Note the influence of Penrose's thinking here. I think that this secondary principle is inherently gravitational (hence the term Machian).

Cheers
Kea

Hello Kea, thanks for your response. This sounds like it's potentially interesting, and I'm impressed that you seem to be able to decode the fuzzy question of mine considering that this is our first communication

If this atman/brahman/balance principle is some kind of standard element in this view, do you know of any good links to papers that explains the fundamental motivation for this principle? (And not just the implementation of the principle in the specific model) I have no prior familiarity with Pitkanens work.

It sounds from my interpretation of your writing, that this principle might have common denominators with my thinking. My idea of the balance principle involves what I like to describe as the "observer" (in my thinking, any subset of the universe can formally be treated as an observer - this should be required by some symmetry principle), constraining it's own understanding. A physically limited observer has at first a limit to what it can encode, then either it reaches a stable steady state, or it has to physically grow larger to encode more info. And "growing" involves dynamics. My idea is that all this need not be put in ad hoc, it can rather emerge as natural mechanisms from a generalized probability/learning theory, whose foundations I think will be natural enough for most to accept.

I'm curious to see if there's a connection between my thinking and the ideas you mention? I do not have any papers yet, and the papers I've found by others on this illustrates some of the ideas, but is far from complete.

But perhaps the different fields are sometimes doing the same things, but in different disguises I want to see if I can see through the view-specific representation, which is not the important thing anyway. I think the same story might be told from several views.

/Fredrik

 

[Fra]

Note: I also agree with your association with "gravity". Which I put in quotation marks, because I think it's not necessarily the standard gravity as we know it, but rather a generalistion of it. And it will involve news views on what is mass and what is energy in terms of information.

/Fredrik

 

[Fra]

then either it reaches a stable steady state, or it has to physically grow larger to encode more info.

Of course, the third option is that it, rather than growing, is shrinking, and "evaporates" away. I this should also be seen uniformly with the sea of possibilities. I definitely want to associate "gravity" with these things. I suspect ultimately stable systems can be given such an steady state or pseudo-steady state interpretation. Intuitively this clearly has a potential to major unification at the cost of a true minimum of ad hoc elements introduced, and while there are some serious problems on howto turn this into something well defined and computable, I can't see a better option atm.

/Fredrik

 

[Kea]

Hi Fredrik

Yes, there seem to be close connections with what our little group has been thinking. This balance principle is primary in my own view (since I started from a gravitational perspective) and is currently forcing an investigation into new kinds of higher categorical structures. As for references, I'm afraid the best I can do at present is direct you to

Pitkanen's homepage: http://www.helsinki.fi/~matpitka/
My blog: http://kea-monad.blogspot.com/ (which has some good links)

After years of attempting to publish actual papers, we've basically given up trying.

...in my thinking, any subset of the universe can formally be treated as an observer - this should be required by some symmetry principle.

I'd prefer to use a term like Neo-Copernican rather than symmetry. (Technically, this approach has a lot in common with Carl Brannen's - see http://www.brannenworks.com/about.html - very pragmatic operator version of the standard model, and we cringe every time somebody says that symmetry is the basis of SM physics. It isn't - Feynman diagrams are.)

My idea is that all this need not be put in ad hoc, it can rather emerge as natural mechanisms from a generalized probability/learning theory.

All the best

 

[Kea]

...the third option is that it, rather than growing, is shrinking, and "evaporates" away...I definitely want to associate "gravity" with these things.

OK, good. Personally I'm convinced that the only language that can achieve this is a higher categorical one, since the heirarchy already takes this form. Loosely speaking, the shrinking and growing are like categorification/decategorification processes between higher toposes (which haven't been defined properly yet).

Technically, we know a few things already. For instance, Michael Rios has figured out how to reconcile the string and LQG black hole entropy computations using his Jordan algebra approach. And there are connections to the very mathematical approach of Connes. Lots to learn!

 

[Fra]

Pitkanen's homepage: http://www.helsinki.fi/~matpitka/
My blog: http://kea-monad.blogspot.com/ (which has some good links)

After years of attempting to publish actual papers, we've basically given up trying.

Thanks! I'll try to look at those pages and see if I can extract the ideas.

But before I look, can you described say in a few scentences what the basic motivation for your approach is? Ie what are your first principles, and your starting points? How does the model interface to "reality"?

/Fredrik

 

[Fra]

OK, good. Personally I'm convinced that the only language that can achieve this is a higher categorical one, since the heirarchy already takes this form. Loosely speaking, the shrinking and growing are like categorification/decategorification processes between higher toposes (which haven't been defined properly yet).

This sounds plausible, but I somehow don't worry about the language, I think we will invent the language we need on the fly. It's not like I need to be a professor in linguistics to speak. I'll just start making sound, and if everything works as it should I'll converge into something that makes perfect sense :) This is all in line with the approach a I favour. I might as well put it to test in other ways than the intended, that's how I usually do things and it usually develops a good intuition :) In my experience this is efficient.

I really have no ideas how long this project will take me, I resumed physics modelling just 3 months ago, after a 10 years doing other stuff. The good part is I have a lot of new ideas and a flushed mind.

The thing I've been thinking about lately is to define the measure that determines the advantage/disadvantage in growing/shrinking. What I'm looking for is an estimated probability measure, that makes selections of possible expansions. Whether this exactly fits in your approach I don't know. Simple reasoning suggest that memory that isn't used - it's discarded (collapse of structure), and on the other hand memory capactiy will be created when needed. I think the balance here can be quantified. Then these things will be subject to dynamic evolution.

I'll check those papers on the link.

/Fredrik

 

[Fra]

Pitkanen's homepage: http://www.helsinki.fi/~matpitka/

Pitkanen says he's been working 23 years on TGD, that is an impressive amount of work. Clearly I can't expect to grasp all that quickly, but I think the basic motivation is paramount, so I try to understand that before I can decide to "invest" in the problems, whose construction then are conditional on that motivation/view.

Kea, perhaps you can comment on this?

From http://www.helsinki.fi/~matpitka/TGDsummary.html:

"TGD is an attempt to unify fundamental interactions by assuming that physical space-times can be regarded as submanifolds of certain 8-dimensional space, which is product of Minkowski space future light cone and 4-dimensional complex projective space CP_2."

Is there a motivation / line of reasoning somewhere leading him to make this assumption? Or, what is the proper starting point in a proper line of reasoning that will lead me to TGD?

I looked at http://www.helsinki.fi/~matpitka/gravit.html

TGD was born as an attempt to construct a Poincare invariant theory of gravitation, the difficulties related to the precise definition of energy concept serving as main motivation

What would the meaning of "Poincare invariance" be in a general scenario (ie before we've made sense out of space and time), and what is the TGD argument for taking that as some "first principle"?

From http://www.helsinki.fi/~matpitka/pdfpool/itgdview.pdf

TGD as a generalization of the hadronic string model

This seems to be the second motivation?

Am I correct in trying to understand the ideas by focusing on this?

the difficulties related to the precise definition of energy concept serving as main motivation

Has he come up with the precise definition?

/Fredrik

 

[Fra]

I'll read a bit more in http://www.helsinki.fi/~matpitka/pdfpool/itgdview.pdf - perhaps I'll find some answers there.

/Fredrik

 

[Fra]

I tried to scan some of Pitkanens pages, but I still haven't understood his fundamental motivation or starting points. I suspect it's some generalisations made, motivated by some magic mathematial principles, but I don't understand why. Anyway, some things he writes smells good to me.

In particularly I'm curious is what the motivation is behind the "p-Adic length scale hypothesis" saying that "physically interesting values of p correspond to primes near prime powers of two". Is is a matter of having faith in the magic of math or did I not find the motivation? I only scanned some papers because it's a lot to read

The reason why I'm interested in further motivation is that in my thinking which rather starts out by a basic notion of distinguishability as a logical 0 or 1, and then everything else evolves ontop of that. Usually in a continuum hypothesis things are smeared, but I can't ignore this jump, because I see indications (in my thinking that is) that significant things happen at the end wher the continuum hypothesis is clearly not valid. The fact that I seems to single out the binary system from scratch bothers me a bit. It seems anything less that two options is hard to picture, so therefore I've suspected that a proper development of the line of thinking I believe in, may turn out to give predicions that is related to number theory... but the exact thread is not something I currently investigated... it quickly seems to get very complex. My plan is that when I get to that stage, I'd have to rely on numerical modelling in software to see what kind of number series that appear, if they are related to Pitkanens thinking I have no idea.

Please forgive my ignorance, but is the p-adic principles somehow a way to make a selection between options? or?

/Fredrik

 

[Kea]

Hi Fredrik

First of all, I started looking at what Pitkanen has been doing only relatively recently, and I'm sure he can better discuss his perspective (talk to him on his blog). My own point of view began with a simple picture of Mach's principle which requires relating observables for black hole and cosmological horizons, and which requires correcting the lack of background independence in GR, to begin with through Penrose's twistor philosophy which had similar aims way back in the 1970s (and I don't think this is well enough appreciated).

Secondly, quantum observables should describe the logic of the experimental question, and this is why I think that higher topos theory is absolutely essential. Moreover, a topos framework is also geometric and can make contact with the gravitational requirements.

I'm curious is what the motivation is behind the "p-Adic length scale hypothesis" saying that "physically interesting values of p correspond to primes near prime powers of two".

The powers-of-2 business comes from the appearance of Fermat primes in the details of TGD and is not something fundamental. The p-adic length scale hypothesis is more important. You can roughly think of the p as indexing the heirarchy of quantisations. I am trying to make contact with this hypothesis from the higher category point of view, but there is a lot of difficult mathematics involved once one tries to invent 'constructive number theory'. But difficult as it may be, it appears to be essential. It is about 'locating' the numerical outcomes of experiments in the mathematical reality, so one has to be extremely careful about descriptions of numbers. Naturally one does not prefer the reals over p-adic fields.

The reason why I'm interested in further motivation is that in my thinking which rather starts out by a basic notion of distinguishability as a logical 0 or 1...

OK, great. At present we are thinking of ordinary toposes as the realm of 0 and 1. This corresponds to the prime 2 (in TGD) above. In our study of mass generation one encounters the number three, and ternary logic based on 0,1 and 2. But one can't just squeeze this ternary logic into a 1-topos: there are a thousand reasons why higher categories are needed. Probably you already have your own picture of how the heirarchy comes in here.

The fact that I seems to single out the binary system from scratch bothers me a bit. It seems anything less that two options is hard to picture...

This reminds me of my own problems trying to picture boson-fermion duality some years ago. I think the answer is that nothing interesting happens until one looks at the 0/1 case (p = 2), but we can certainly make sense of the ordinals p = 0,1 in what we're doing. Philosophically, this goes back to C. S. Peirce's work on signs and even much earlier to Leibniz's ideas on monads. To him these were the essence of 'unseparability' - and the term is rightly used in modern category theory.

 

[Fra]

Hi Fredrik
First of all, I started looking at what Pitkanen has been doing only relatively recently, and I'm sure he can better discuss his perspective (talk to him on his blog). My own point of view began with a simple picture of Mach's principle which requires relating observables for black hole and cosmological horizons, and which requires correcting the lack of background independence in GR, to begin with through Penrose's twistor philosophy which had similar aims way back in the 1970s (and I don't think this is well enough appreciated).

Secondly, quantum observables should describe the logic of the experimental question, and this is why I think that higher topos theory is absolutely essential. Moreover, a topos framework is also geometric and can make contact with the gravitational requirements.

The powers-of-2 business comes from the appearance of Fermat primes in the details of TGD and is not something fundamental. The p-adic length scale hypothesis is more important. You can roughly think of the p as indexing the heirarchy of quantisations. I am trying to make contact with this hypothesis from the higher category point of view, but there is a lot of difficult mathematics involved once one tries to invent 'constructive number theory'. But difficult as it may be, it appears to be essential. It is about 'locating' the numerical outcomes of experiments in the mathematical reality, so one has to be extremely careful about descriptions of numbers. Naturally one does not prefer the reals over p-adic fields.

Ok, thanks for your comments! I think while there may or may not be a direct connection between our thinking, I think we start from different starting points.

OK, great. At present we are thinking of ordinary toposes as the realm of 0 and 1. This corresponds to the prime 2 (in TGD) above. In our study of mass generation one encounters the number three, and ternary logic based on 0,1 and 2. But one can't just squeeze this ternary logic into a 1-topos: there are a thousand reasons why higher categories are needed. Probably you already have your own picture of how the heirarchy comes in here.

Yes, of course the 0/1 in my thinking isn't the end, it's only the the simplest, nontrivial case, the beginning - as it seems, which can serve as a starting point. But I do not like that I have to "choose" a starting point! But I think that in the end there will be a cure to this, since the entire description is scalabe in several ways, I should be able to pick an arbitrary starting point, the important point is the evolutionary rules. The reason I consider the minimalistic starting point is that, like is always the case in math problems, it's much easier to find intuition and identify the induction step when you consider the simplest case. Because my brain is limited. But exactly like you hint, I have also noticed that some phenomena doesn't enter the description until at higher levels of complexity. For this reason I am also in parallell considering the more general case of 0/1/.../m, where m is an arbitrary natural number instead of just 0/1. Then these two descriptions must evolve into a consistent common during special cases, as the former collapses and hte later expands. I consider it as a datastream where each sample is (0/1/.../m). A binary stream is the simplest case. But depending on the contents of the data stream, a binary stream may self-organise into, say a hex stream, if it's the most efficient representation. But this is just one possible mechanism out of many.

My best intuition for this is my own brain, which I a lot of empirical evidence supporting it's functionality :) Having studie physics I obviously have some math skills, but I do not consider myself a mathematician to mind, I'm more of a philosopher. This is why I have a different method I think. But suspect that the formal category modelling might be a good language for this. But so far I have not made a choice what language I want to speak, I just try to find the "words" I need to express what I need to express.

And even though it seems clear to me here that we do not use the same thinking, it may still be related. My thinking is that of learning logic, and bayesian thinking. The state 1 for example, my "split" into two. But two states may also collapse into one.

/Fredrik