Foundations of a theory of quantum gravity - Johan Noldus' book.

[tom.stoer]

Careful,

regarding

let me help a bit

In section 5 we learn that a new investigation to the relationship between spin and statistics has to be performed ...

Can you do me a favour and ask Noldus when talking to him next time ( ;-) if it's possible to write a short introduction with a summary in the spirit of your post #47 and update the paper on arxiv accordingly?

Tom

 

[Careful]

Careful,

regarding


Can you do me a favour and ask Noldus when talking to him next time ( ;-) if it's possible to write a short introduction with a summary in the spirit of your post #47 and update the paper on arxiv accordingly?

Tom

That might be helpful, the reason why I did not write it like this in the introduction is because many of these insights require further explanation and I was afraid they might confuse the reader at this point. Therefore, I opted for a more conservative approach in which I decided to follow the historical route. It is very difficult to find the right balance in such work because it is personal and I have received many contradictory advises.

But there will appear more of my thoughts on this in the FQXi submission I still have to hand in.

 

[Careful]

1) Is it ok to assume that you by conscious beeing = any physical observer. (ie. any physical system, that observers it's environment?)

Yes, here I go further than Penrose and ''dead matter'' can have a minimal form of consciousness too.

2) To agree about the outcome of experiments: Here I wonder, do you distinguish between, and if so how, between "having consistent" expectations of a future experiment, and encoding/holding consistent RECORDS of history (past experiments).

Both these things which you mention are a matter of dynamics and not of kinematics. For example if we both look at a frog, you may decide it is green while someone who is color blind may call it grey. What I mean with to agree on outcomes of experiments is that once an observer makes a record, this fact must be communicated to the other observers. They have no full free choice anymore, which they could have had if the first observer didn't measure in the first place.

What I mean is that any observer, has an expectation (ie a prediction if you like) of the future. This may be revised once the future has passed. so I wonder if you think that different observers, must have the same expectations, or agree on historic events.

No, not at all, every observer has a personal window on the entire universe and these windows certainly do not need to be consistent. Even more, the theory reveals that your personal expectation of the future (and experience of the past) is going to influence the probabilities of outcomes of your and other observers' future.

 

[Fra]

Yes, here I go further than Penrose and ''dead matter'' can have a minimal form of consciousness too.

Ok, I think I see what you mean, and I probably agree with this view.

Although I would not choose to use the word consciusness because a lot of people associate to the wrong things. Consciousness in the sense of how matter encodes and holds information and expectations of it's own environment is pretty much inline with how I view this.

I think a problem, is to make sure people don't misunderstand it. Even when you speak about physical systems as observers as I do too, a lot of people tend to associate observers with something that has a brain. This is why I think it may be dangerous to use the words you do.

But I suspect that I agree with your perspective.

What I mean with to agree on outcomes of experiments is that once an observer makes a record, this fact must be communicated to the other observers. They have no full free choice anymore, which they could have had if the first observer didn't measure in the first place.

This smells a little bit Rovelli RQM.

Who ensures that this "communication" is successful and results in an agreement? As far as I remember, Rovelli in his RQM paper says that the only way for two observers to compare their subjective observations, is to interact/communicate. But he assumes that this communication somehow follows QM, but he avoids intricate discussions of this. But then Rovellis ambition isn't to change or revise, just to find a reinterprettaion of existing formalism that he thinks is more suitable for his next step.

Anyway, thanks for your notes. Perhaps it will become clear as I look further in your paper.

your personal expectation of the future (and experience of the past) is going to influence the probabilities of outcomes of your and other observers' future.

Makes good sense to me, thanks for clarification.

Maybe more comments coming when I get around to go further in your paper.

/Fredrik

 

[Careful]

This smells a little bit Rovelli RQM.

But it is very different ! Rovelli lives in a one observer universe (Carlo's), in my case all observers live in the same one but the quantum theory nevertheless allows for different perceptions.

Who ensures that this "communication" is successful and results in an agreement?

By communication, I mean objective collaps of the wavefunction. It by no means implies agreement. Agreement has to be a dynamical effect; for example it might be that everybody sees the frog in a different color. For example, I am sure that my green is not the same as yours; agreement then arises because people are going to look for a more elementary way of understanding green. For example, by means of the wavelength.

But then Rovellis ambition isn't to change or revise, just to find a reinterprettaion of existing formalism that he thinks is more suitable for his next step.
/Fredrik

Yes, I have extended and revised QT in a substantial way; you have to, no choice !

 

[Fra]

By communication, I mean objective collaps of the wavefunction. It by no means implies agreement. Agreement has to be a dynamical effect; for example it might be that everybody sees the frog in a different color. For example, I am sure that my green is not the same as yours; agreement then arises because people are going to look for a more elementary way of understanding green. For example, by means of the wavelength.

What I meant is, if this "objectivity" inferred or emergent, or just present as some realist constraint on the theory?

I didn't go into all details on Penrose as although I think Penrose connection is interesting, I do not share his view. But I think Penrose idea is to implement the objective collapse as a form of constrain on the theory; so in his view I think it's NOT inferrred. It's just a conjecture (this is the sense in which he is a realist) that such an objectivity must exists somehow?

Penroses somehow tries to explain or get rid of the collapse by some objective thing (gravity in his case).

I OTOH, think gravity is rather emergent and that the collapsing wavefunctions is a key. So instead of finding some constraint that restores objectivity, I think objectivit and gravity is emergent and at say some level of equiblirium, this may be the flip side of the penrose coin.

Do you see it differently? If you don't have a simple answer to the fuzzy question we could get back to this when I had time to read more. I just see already now, that the details around this are strategic.

/Fredrik

 

[Careful]

What I meant is, if this "objectivity" inferred or emergent, or just present as some realist constraint on the theory?

Emergent.

I didn't go into all details on Penrose as although I think Penrose connection is interesting, I do not share his view. But I think Penrose idea is to implement the objective collapse as a form of constrain on the theory; so in his view I think it's NOT inferrred. It's just a conjecture (this is the sense in which he is a realist) that such an objectivity must exists somehow?

I always find it hard to say what someone else with brains thinks; but as far as I understand Roger, he simply says the collaps of the wave function is an objective process and not tied to one particular class of observers. I fully agree with him. This does not imply that objectivity of perception is not emergent.

Penroses somehow tries to explain or get rid of the collapse by some objective thing (gravity in his case).

I am afraid you misunderstood him here. The collapse is vital for his (and mine) interpretation of quantum mechanics; all he says is that there is a mechanism behind the collaps and that gravity is the origin of this mechanism. Here I disagree with him: for me, consciousness comes on the first place, not the second.

I OTOH, think gravity is rather emergent and that the collapsing wavefunctions is a key. So instead of finding some constraint that restores objectivity, I think objectivit and gravity is emergent and at say some level of equiblirium, this may be the flip side of the penrose coin.

Gravity is fundamental, you cannot get around that, and so is quantum mechanics. The standard model may be emergent.

 

[Fra]

(Just trying to tune it and see that I understand you correctly)

the collaps of the wave function is an objective process and not tied to one particular class of observers. I fully agree with him.

By class of observers, do you mean normal classification based upon references frame withing GR and SR context, or one based upon COMPLEXITY ie. human observer vs a subatomic observer?

/Fredrik

 

[Careful]

By class of observers, do you mean normal classification based upon references frame withing GR and SR context, or one based upon COMPLEXITY ie. human observer vs a subatomic observer?

/Fredrik

Aha, this is the interplay between classical and quantum! I mean dynamical reference frames (tetrads) determined by the expectation values of the matter currents in the state of the observer (as an identity within the ''state of the universe''). If you want to understand how this is possible: it are the local particle notions and local (infinite) windows on the entire universe which accomplish this.

 

[Fra]

the collaps of the wave function is an objective process and not tied to one particular class of observers. I fully agree with him.

By class of observers, do you mean normal classification based upon references frame withing GR and SR context, or one based upon COMPLEXITY ie. human observer vs a subatomic observer?

I mean dynamical reference frames (tetrads) determined by the expectation values of the matter currents in the state of the observer (as an identity within the ''state of the universe''). If you want to understand how this is possible: it are the local particle notions and local (infinite) windows on the entire universe which accomplish this.

I want to make sure I see it your way, and if it connects to how I would see it or not.

Do you somehow picture that one picture of the entire universe (or observable universe) encoded IN the state of the observer; and that IN this state, the first observer can identify let's call it "secondary observers" (maybe even so called elementary particles; as seen from the first observers "frame" or perspective) living coded on the system of complexions defined by the first observer, so that the collapse relative to these secondary observers, are "objective" relative to the first observer?

IE. almost a bit holographic view, where the dynamics of the state of the observer, in particular what it encodes, somehow mirrors or reflects the remainder of the universe?

But somehow the complexity of the mirror, or observer, bounds how much information that can be encoded. So it would correspond to a truncated holographic view. That the theory encoded IN the observer, doesn't necessarily describe the environment, but rather only the expectation of it - and in some cases these things will agree, and there would be a perfect holographic connection as a special case?

Usually I wouldn't expect this ot make sense to anyone else when phrased like this as as it's very fuzzy, but since your views may or may not be in this direction let's see if you connect and this is anything near what you attempt.

(I still haven't read more, just responded to the above, at best i'll read more later tonight)

/Fredrik

 

[Careful]

Do you somehow picture that one picture of the entire universe (or observable universe) encoded IN the state of the observer; and that IN this state, the first observer can identify let's call it "secondary observers" (maybe even so called elementary particles; as seen from the first observers "frame" or perspective) living coded on the system of complexions defined by the first observer, so that the collapse relative to these secondary observers, are "objective" relative to the first observer?

Yes, with one small proviso. There is something replacing the objective state of the universe but every local observer reads it in a different way. It is his particular lecture which makes him identify the ''rest'' of the universe. So if this local observer makes a measurement, then not only do the other observers change, but they partially change in the way he sees them. This is fully democratical and doesn't distinguish anybody or anything.

IE. almost a bit holographic view, where the dynamics of the state of the observer, in particular what it encodes, somehow mirrors or reflects the remainder of the universe?

Yes, the gravitational theory and quantum theory are fully holographic. But you have to distinguish the local information defining the observer itself and the nonlocal information on tangent space with respect to which he observes the rest of the universe. These are like Leibniz' monads: a personal mirror on the entire universe.

 

[Fra]

Unfortunately I feell asleep again last night (Except sometimes on weekends I read paper in two situations; when taking a bath or before going to sleep as it's the time when I usually have the time).

Since I am not a philosopher I'm not much educated in various in history of ideas. The only two areas where I just read a few books are on the philosophy of science and the scientific method and the philosophy and history of emergence of more formal probability theory as a form of rational reasoning from the first irrational degrees of belief used in a less rational reasoning. Although I am aware of that lebnitz philosophy is quite different than Newtons, I am not familiar with that in detail.

Yes, with one small proviso. There is something replacing the objective state of the universe but every local observer reads it in a different way. It is his particular lecture which makes him identify the ''rest'' of the universe. So if this local observer makes a measurement, then not only do the other observers change, but they partially change in the way he sees them. This is fully democratical and doesn't distinguish anybody or anything.

Does this "objective state" enter into calculation of expectations?

I am hoping that your "objective state" is something that is evolving in a generally undecidable way, from the point of view of any real observer, with some darwinian elements.

If the answer is yes two both question, then predictions of any observer, would formally be a subjective expectations that more or less guides (not fully determines) that observers actions.

This is how I think of things, so if this is what you do them our thinking may be quite similar. (Though I'm still looking for the poitn of disagreement as you declare yourself as a realist, I'm as far from it as you can be I think)

But you have to distinguish the local information defining the observer itself and the nonlocal information on tangent space with respect to which he observes the rest of the universe. These are like Leibniz' monads: a personal mirror on the entire universe.

You mean distinguish between the mirror and the real thing (except the best view of the real thing we ever has IS the mirror image)?

If so , yes I understand what you mean there. But for me which is not a realist, the "real thing" is indistinguishable from the mirror, by the observer. It's just that of course each observer has their own mirror image. Now in my view, the inconsistent mirror images encodes the physical interactions between the observers. So what in normal mainstream models RESTORE the consistenct and some level of invarance or covariance is the transformation laws that scale the mirrror from one observer to theother one.

If would expect of a realist to picture that such transformations in principle exists, and are objective.

In my view, they are merely emergent. And each local group of observers will then at equilibrium agree with each other on this transformation law, not in the sense that they fully infer it, but that they evolve into a state of harmony PROBABLY just like the leibniz idea of harmony (although I'm not expert on leibniz so I avoid details).

The difference between such a "harmony" and FULL agreement in the realist sense is that the harmony IMHO at least corresponds to a special case: an equilibrium. The full agreement corresponds to some more (to me irrational) form of structural realism.

So I wonder if this realtest to your thinking, and exactly why do you label yourself a realist?

/Fredrik

 

[Careful]

Does this "objective state" enter into calculation of expectations?

Partially, but not completely.

I am hoping that your "objective state" is something that is evolving in a generally undecidable way, from the point of view of any real observer, with some darwinian elements.

First of all, I work in a generalized ''Heisenberg'' picture. But even then, I agree although this evolution is very very slow on our timescales of observation so that we can safely ignore it for laboratory experiments.

predictions of any observer, would formally be a subjective expectations that more or less guides (not fully determines) that observers actions.

yes

This is how I think of things, so if this is what you do them our thinking may be quite similar. (Though I'm still looking for the poitn of disagreement as you declare yourself as a realist, I'm as far from it as you can be I think)

Everyone is a realist. You just have to ask yourself ''WHAT is real ?''.

The difference between such a "harmony" and FULL agreement in the realist sense is that the harmony IMHO at least corresponds to a special case: an equilibrium. The full agreement corresponds to some more (to me irrational) form of structural realism.

Naive realism is a better word.

So I wonder if this realtest to your thinking, and exactly why do you label yourself a realist?

/Fredrik

See the above.

 

[Fra]

But even then, I agree although this evolution is very very slow on our timescales of observation so that we can safely ignore it for laboratory experiments

Slow enough to not affect lab experiemtns yes absolutely, yet it's crucial to see that it IS slowly evolving and not static. So it seems we agree here. It all makes sense to me so far.

Thanks for your comments.

I can say that so far, your basic reasoning seems possible in line with my own views. But then I had the same feeling when starting to analyse rovellis view. It's further down the road that things may start to diverge. But I need ot try to find the time to look at your massive paper first (which will probably grow even more massive in the final version:).

/Fredrik

 

[Careful]

But then I had the same feeling when starting to analyse rovellis view. It's further down the road that things may start to diverge. But I need ot try to find the time to look at your massive paper first (which will probably grow even more massive in the final version:).

/Fredrik

I don't know why you had that feeling. Rovelli says something far more simple than what you suggested so far. I learned Carlo's view from his Quo Vadis paper, I was not very positive (to say it like that ) and my impression about his ''ideas'' certainly did not improve over time.

 

[Fra]

I don't know why you had that feeling. Rovelli says something far more simple than what you suggested so far. I learned Carlo's view from his Quo Vadis paper, I was not very positive (to say it like that ) and my impression about his ''ideas'' certainly did not improve over time.

This feeling was based on first I got his LQG book, and I had a vision, where a sort of action network may enter; but I soon found out that in order to get his point, I went back to his RQM paper, and it starts out nice, but later in the paper it was clear to me that I disagree. It was a wuick process though. So I do not adhere to rovellis view. Compared to me, rovelli is a structural realist. What I had in mind with the action netowrks, proved after all to be not anything like rovelli does. The similaritiy was more formal and coincidental than to spirit.

He also is too conservative. I think QM needs to be modified, that doesn't mean the modified QM doesn't agree with the predictions konwn from the QFT sector though. It merely has major consqeuences for how QM is extrapolated to the yet not tested domains, nd for the quest of unification.

However, even a modest bunch of papers may take some time for me. Daytime I do not have time to read anything. There a lot of other stuf I'm doing so there are not so many timeslots for me to work on my own ideas and to read other peoples papers. So although it may not take that long to read a paper, it takes considerably longer when you don't have the time to read it in one go.

This is why I commented early on that your paper is large. But my first assessment of your thinking is promising to me. So I'm motivated to look further into your ideas... but it will take some time.

/Fredrk

 

[Careful]

He also is too conservative. I think QM needs to be modified, that doesn't mean the modified QM doesn't agree with the predictions konwn from the QFT sector though.

I know so although interactions will look very different, they will approximately give the same result.

It merely has major consqeuences for how QM is extrapolated to the yet not tested domains, nd for the quest of unification.

Indeed

I will write in a few months a more accessible summary (where I will split the physics/mathematics/philosophy) although such thing always involves a loss of coherence and depth ; for me the main thing was to get the material out in the way I understand it.

 

[Fra]

I will write in a few months a more accessible summary (where I will split the physics/mathematics/philosophy) although such thing always involves a loss of coherence and depth

I agree with that, and I have no personal problem with the mix. A mix is good, the only problme is that it's a massive paper. But you can only simplify something to a certain point of course.

I'm not a philosopher, so I certainly seek a mathematical model and framework, yet the ideas are crucial, if not for anything else, at least for deeper understanding and motivation, which may prove important when it's generalized.

There is a nice quote from ET Jaynes (that I learned about from one of Kevin H Knuth's paper http://algomagic.com/knuth/1009.5161.pdf) that I like

"the essential content of both statistical mechanics and communication theory, of course, does not lie in the equations; it lies in the ideas that lead to those equations"

Sometimes just looking at a particular mathematical representation or equation, hides the real logic.

/Fredrik

 

[Careful]

I'm not a philosopher, so I certainly seek a mathematical model and framework, yet the ideas are crucial, if not for anything else, at least for deeper understanding and motivation, which may prove important when it's generalized.
/Fredrik

Let me tell you a story. My first love when I was 15 was in metaphyics, philosophy and psychology, but I soon realized a couple of things : (a) philosophy is not something you should study, it is something you do, it is an attitude in life (b) philosophy without mathematical representation is empty, therefore it is much too important to leave it only to ''professional'' babblers (as I call them). That is why I went on to study mathematics and physics when I was 18. Philosophy is something you shoud do when you are young and have a fresh mind, it trains the brain much better than physics and mathematics ever can. Because you learn to think on a meta-level (and symbols become merely a limited way of writing something far more complex), you get more and more able to make shortcuts a ''machinal thinker'' can never make.

 

[Fra]

Set aside the philosophical part; which I partly make sense of, I find it a bit unclear to understand what your starting point for your mathematcal reconstruction is. If I flip between your initial reasoning and then the parts where you start using computations it seems to be some leap.

Otoh, you have plenty of referencs that I haven't read. I'm not sure if you have to read all references to see the picture. In that case it gets it seems to be pretty dense and hard to read.

Or maybe I expect something you don't, since I personally want to start at a very basic level, without continuum defined yet. Also in my personal view, I do not in any way assume 4D space, or ANY classical physics. In particular I do not pull or use classical hamiltonians or actions.

So my first confusion, is to identify your starting point.

To take an example, somehow the almost differentiable homeomorphism of yourse, appeards out of nowhere. I mena, how did you infer or construct this just from your initial philosphy? What I mean is: Is this homeomorphism supposed to represent a structure encoded in the observers microscate? and the "points" of if, symbolized the "secondary observers" I mentioned earlier?

Are you somehow assuming classical realtivistic physics as some sort of starting point?

I hope you undersand my question. I am not asking what is a homeomorphism of course :) I am tryign to understand your thinking; how did you arrive at this abstraction? By some original construction hidden somewhere in the referencfe list, or by (like I think) somehow by pulling it from classical physics, or from some idea of an index of some configuration or event space?)

You also talk about hilbert spaces. Same here. This is clear in normal QM, but since you attempt here a new "foundation of QG", I expect an explanation or these objets when first used.

Or is this later in the paper? I've tried to both jump and read from start (though I have not gotten far) and I seem to not understand exactly what the set of baggage you assume to start with, is. Perhaps a short section of "initial assumptions" should be nice.

Edit: To just give a short insight of how I do my reconstruction, it may help you understand my question:

Even my reconstruction is relative to an hypotethical observer, and would this "scale".
The starting point is the notion if distinguishable events. and a notion of a history or such.
These histories some how are like partiall ordered sets, and are constrained by a complexity limit specific to the observer ( to be loosed associate to energy or mass). The total strucutre of the observer, thus are decomposed into a "surface" measured by the index, the internals are the encoded truncated histories. Further this "system" are subject to permutations and form this an entropic type flowis defined. So far there is no 4D space, not time - just order of events. And this order is of course not global it's specific to this observer (implicit in the entire constructiion) Further I elaborate how the history structure is re-encoded with non-commutative structures of which teh total strucutre is a kind of direct product. But there are transformation rules in between then (for example Fourier type). And here "quantum logic appears" merely as en evolutinary stage. Next is the question to explain how two such observing structure can communicate when t hey share part of their surface (communication channel). etc etc... so far only abstraction discrete ifnormation space, not 4D, not classical actions. All actions are reconstructed from entropicflows or spontaneous comptutations.

So this is my perspective. And when I read your paper, suddently there is a continuous homeomorpgism... I trying to give this a place in my world, where did it come from and why?

Perhaps I am asking for somthgin that may be far in the future in your line of reasoing (as you said ion the other tread you don't reconstruct the logic). But I'm just try to establish where your starting point is. Can you clarify briefly and maybe sav me som decoding time?

/Fredrik

 

[Careful]

Set aside the philosophical part; which I partly make sense of, I find it a bit unclear to understand what your starting point for your mathematcal reconstruction is. If I flip between your initial reasoning and then the parts where you start using computations it seems to be some leap.

Yes, there is a big leap! The initial reasoning is ''simple'' and conservative, the point of sections 4 and 5 - as I wrote explicitely in the text is mostly to show that this conventional approach breaks down (and I do almost everything to rescue it). I said that I opted for the historical approach, going for the logical presentation would cut it by 30 pages but it would not be worth the price to pay.

Otoh, you have plenty of referencs that I haven't read. I'm not sure if you have to read all references to see the picture. In that case it gets it seems to be pretty dense and hard to read.

In principle you have to read none of those. They are just there to conform to the usual requirements of academic publishing :-)

Or maybe I expect something you don't, since I personally want to start at a very basic level, without continuum defined yet. Also in my personal view, I do not in any way assume 4D space, or ANY classical physics. In particular I do not pull or use classical hamiltonians or actions.

Classical hamiltonians and actions are relegated to the trashbin from section 7 onwards (that is where the new theory is laid out) but the continuum is a crucial assumption. About the latter, I will publish soon a serious motivation.

So my first confusion, is to identify your starting point.

The starting point is the philosophical section three.

To take an example, somehow the almost differentiable homeomorphism of yourse, appeards out of nowhere. I mena, how did you infer or construct this just from your initial philosphy? What I mean is: Is this homeomorphism supposed to represent a structure encoded in the observers microscate? and the "points" of if, symbolized the "secondary observers" I mentioned earlier?

As I said, a deep motivation for differentiable bundles will appear within 10 days (at the FQXi contest - but I will put it on the arxiv too).

Are you somehow assuming classical realtivistic physics as some sort of starting point?

Initially, but not finally.

Hope this helps.

 

[MathAmateur]

On page 156

"Science will
always be a game of humans running behind their own tale as well as a vital
ingredient in changing our own future and the laws of the universe themselves;"

I would consider changing the word "tale" if you mean story. There is an idiom in English about chasing ones tail (pronounced the same) that makes the use of the word tale here a bit confusing and which actually kind of fits in a humorous way.

I would also take a look at what Douglas Hofstadter has said about Penrose's conclusions in your context (if you haven't already).

 

[Careful]

I would also take a look at what Douglas Hofstadter has said about Penrose's conclusions in your context (if you haven't already).

Don't know him; can you summarize his point of view in a few lines? Notice that my position is a lot more moderate than the one Penrose takes. But he looks like an interesting guy, thanks for the link. I will look a bit at his work when I have the time.

 

[MathAmateur]

Douglas Hofstadter a professor of Computer Science at Indiana University. He takes the opposite track as Penrose, claiming that the human brain is just a machine that can be (and eventually will be) duplicated and exceeded by computers. He argues that looking at computers as fixed and inflexible is the same as looking at the human brain at the neuron level. He argues that human thought needs to be modeled at the symbol level and there is no reason why machines can not also have a symbol level riding on top of the levels that occur in today's machines.

There is quite a bit of debate going on in this field right now and there are a lot of different opinions.

 

[Careful]

Douglas Hofstadter a professor of Computer Science at Indiana University. He takes the opposite track as Penrose, claiming that the human brain is just a machine that can be (and eventually will be) duplicated and exceeded by computers. He argues that looking at computers as fixed and inflexible is the same as looking at the human brain at the neuron level. He argues that human thought needs to be modeled at the symbol level and there is no reason why machines can not also have a symbol level riding on top of the levels that occur in today's machines.

There is quite a bit of debate going on in this field right now and there are a lot of different opinions.

I just glanced on his Wikipedia page and must have had then the wrong impression. I thought he was very cautious regarding developping computers as intelligent as humans. I feel this point of view is very unlikely because of some Godelian arguments regarding self reference. However, unlike Penrose, I do not attack strong AI; I do however conjecture that physics might put some constraints which forbid the realization of such machines in nature. But still then, you have not given any convincing argument why human brains would be supercomputers; for example, why do we compute the square root of three so slowely where a much more primitive machine does it far quicker ? Are you going to claim that a higher order machine gets more confused about the simple tasks ?

 

[qsa]

I just glanced on his Wikipedia page and must have had then the wrong impression. I thought he was very cautious regarding developping computers as intelligent as humans. I feel this point of view is very unlikely because of some Godelian arguments regarding self reference. However, unlike Penrose, I do not attack strong AI; I do however conjecture that physics might put some constraints which forbid the realization of such machines in nature. But still then, you have not given any convincing argument why human brains would be supercomputers; for example, why do we compute the square root of three so slowely where a much more primitive machine does it far quicker ? Are you going to claim that a higher order machine gets more confused about the simple tasks ?

http://webcache.googleusercontent.com/search?q=cache:SxGLCeA8tzQJ:citeseerx.ist.psu.edu/viewdoc/download;jsessionid%3D9E50FF3FF779DA57466200CF255F8489%3Fdoi%3D10.1.1.57.5645%26rep%3Drep1%26type%3Dps+neurons+path+integral&cd=1&hl=en&ct=clnk&gl=kw&source=www.google.com.kw




Path Integrals for StochasticNeurodynamics

Toru Ohira and Jack D. CowanTR-94-016June 30, 1994 Sony Computer Science Laboratory Inc. 3-14-13 Higashi-gotanda, Shinagawa-ku,Tokyo, 141 JAPAN Copyright c1995 Sony Computer Science Laboratory Inc.
Page 2
In Proceedings of the World Congress on Neural Networks, San Diego, June, 1994
Page 3
Path Integrals for Stochastic Neurodynamics

Toru OhiraSony Computer Science Laboratory3-14-13 Higashi-gotandaShinagawa, Tokyo 141, JapanJack D. CowanDepartment of Mathematics, The University of Chicago,Chicago, IL 60637June 30, 1994


Abstract We present here a method for the study of stochastic neurodynamics in the frameworkof the "Neural Network Master Equation" proposed by Cowan. We consider a model neuralnetwork composed of two{state neurons subject to simple stochastic kinetics. We introducea method based on a spin choerent state path integral to compute the moment generatingfunction of such a network. A formal construction of the path integral is presented andthe general expression for many neuron networks is obtained. We show explicitly that themethod enables us to obtain the exact moment generating function for a single neuron case.Possible directions for the analysis of many neuron networks as well as an alternative pathintegral formulation are discussed

 

[Careful]

Your point being ?

 

[MathAmateur]

What I wrote is my impression of Hofstadter. But then I (as my PF name implies), I am just an amateur in the world of physics and math.

 

[Fra]

The starting point is the philosophical section three.

Classical hamiltonians and actions are relegated to the trashbin from section 7 onwards (that is where the new theory is laid out) but the continuum is a crucial assumption. About the latter, I will publish soon a serious motivation.
...
As I said, a deep motivation for differentiable bundles will appear within 10 days (at the FQXi contest - but I will put it on the arxiv too).
...
Initially, but not finally.

Thanks, I'll try to look again in this light. In particular chapter 3. The choice of headline for chapter 3 made me think it was not the starting point, but I'll read again ands see if things get clear.

I look forward to your fqxi paper to motivate those structures. When it's published please let us know. I want to read it.

/Fredrik

 

[tom.stoer]

Classical hamiltonians and actions are relegated to the trashbin from section 7 onwards ... but the continuum is a crucial assumption.

@Careful: unfortunately I still didn't read you book carefully, but it seems that this is an important step. Classical actions or Hamiltonians may be a way to motivate the structures and symmetry principles of a quantum theory, but there are indications (which we discussed elsewhere) that it is impossible to derive the quantum theory rigorously from the classical one. The problem is that the quantum theory has much more structure which is "washed away" in the classical limit and can therefore not be reconstructed in doing a "quantization". The structure is not derived from classical physics but put in by hand via the quantization procedure. This must not necessarily be wrong, but one has to be aware of the fact that additional assumptions enter the scene.

Do you have any idea which principle could single out 4-dim. spacetime? I have one but it's still rather vague. It came to my mind as you mentioned the continuum as a crucial input.