h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

http://www.bbc.co.uk/science/horizon/2001/paralleluni.shtml is worth a look about reality and cosmology, especially the transcript on http://www.bbc.co.uk/science/horizon/2001/parallelunitrans.shtml

Just thought I would mention it.

Thanks for the links!

You know, if a person were into gambling, he or she might want to start an Internet pool on the length of time it will take the above-linked gentlemen, and other bigtime luminaries of mainstream physics and cosmology, to arrive at the following momentous conclusion:

If all of those parallel universes cartwheeling around and colliding with or otherwise belittling our poor universe are real, then the higher-dimensional meta-universe in which they are frolicking must be real. But then the basic task of cosmology consists not merely of explaining any insignificant little subuniverse in particular, but of explaining that more fundamental higher-dimensional meta-universe!

But one's career as a gambler would only be starting. For once somebody wins *that* pool, one can easily start another pool on the length of time it will take one of these celebrated geniuses to suggest, to the enthusiastic applause of his academic colleagues, that the so-called "fundamental" higher-dimensional meta-universe in question can be "explained" as one of many crummy, insignificant little higher-dimensional not-so-meta-universes cartwheeling around and colliding with each other in a yet-more-fundamental meta-*meta*-universe!

One's career as a gambler would then be assured. For once somebody wins the second pool, one can start the cycle over again for a whole new generation of suckers! And round and round the mulberry bush they go, the theoretical monkeys chasing the cosmological weasel, the weasel popping like a little cosmogonic gas grenade every time it loops the loop, a new meta-meta-(...)-meta-universe forming directly in its malodorous purple wake with each pass.

Isn't mainstream cosmology a gas?

Just ask the monkeys!

Yes...The book "Three Roads to Quantum Gravity" was published in 2001, and "Introduction to the CTMU" precedes this publication. I recall that Mr. Smolin was one of the first cosmologists to come up with the universe within a "Meta-Universe" idea. So why the change of ideas? I can only speculate... Mr Smolin also talks about his college years as a student, walking around with different colored socks, and uncombed hair ."Trying to be like Einstein". He also tells about how he would sit and stare at the walls for hours at a time, contemplating the universe.

The meta universe idea is highly speculative. And if a spacetime contains our own spacetime, what laws does the higher type of spacetime obey?

Hoprfully, the great ideas in the CTMU will remain intact, and not be lost for all time.

nice one Chris!

A question that comes automatically from my lips is, does God give a damn? - why are humans more important that the Dodo?

I found a link that serves as a basic introduction to the concepts of meta-mathematics, randomness, Godel, Turing, etc.

A Century of Controversy over the Foundations of Mathematics by Greg Chaitin.

http://www.umcs.maine.edu/~chaitin/lowell.html

O.K, I had been arguing that there could be laws of physics which cannot in principle be modelled by a computer, and these laws of physics could be harnessed to do things which evade the limitations of Godel's thereom. (i.e. I was arguing that there could exist non-computable laws of physics which can be harnessed to escape the limiatations of Godel's theorem and answer mathematical questions which are supposed to be unknowable).

Several people in this forum were ridiculing me I believe. (Playboy look sidreways at xyroth and coughs)

Guess what. A stunning article appeared in the April 6th edition of 'New Scientist' - the article is not on-line yet, but you can read it in the print edition of the mag. (The contents page for that edition is on-line. Click on the link and look at the summary for the article 'Smash and Grab')

http://www.newscientist.com/inprint/previous/20020406.jsp


It appears that a couple of mathematicians have proved that quantum mechanics can be used to construct a device which can perform supposedly 'non computable' operations! The device makes use of qautum superpositions to carry out operations which were thought be non computable. The device is not subject to Godel's theorem and escapes all of the Godel limitations.

Kurt Godel has been smashed!

hey Clay Toy, and anyone else interested.

That article sounds interesting. I'll have to check it out.

I just finished reading Penrose's _The Emperor's New Mind_. It was an interesting book. I wonder if anyone would like to chat about some bits in there that I didn't quite understand? Specifically, the EPR-paradox. I don't get what's paradoxical about it.

Hello Bacchus! Playboy is slipping a

So you read tENM! Good, good. It's heavy duty stuff but it's really damn good. Penrose talks about virtually everything in science in there. The guy's a genius, no doubt about it. He's got a lot of pretty unconventional ideas but he really knows how to put forward an argument - entertaining.

I've got a bit of a confession to make. Um... I don't fully understand some of it myself Every so often I go back and re-read it and I may be understand a little more each time. I grasped the general ideas, but there is just so much in there that you'd have to an expert in the various areas to understand it fully.

I think Lucinda has read the book. And I'm sure that there must be a number of other people at h2g2 who have read it as well.

Regarding EPR - my understanding is this: In quantum mechanics you can have systems which are 'entangled' , meaning that the whole system is represented by a single coherent quantum wave function. According to quantum mechanics the precise microscopic properties of particles are not actually determined until the moment they interact with a measuring device. The system is instead in a 'superposition' of states, in which all possible states exist simultaneously - in the case of spin for instance a particle does not possess a definite spin until measurement. But at the moment we measure the spin of a particle, its spin is immediately determined to be either 'Up' or 'Down' (for example). That is, the quantum wave function is deemed to have collapsed, and from then on the particle does assume a definite state.

The thing is that components of coherent system can be separated by huge distances. For instance you might have two particles which end up light years apart. But when the wave function of the system is collapsed, the collapse is supposed to occur instantaneously across the whole system.

The reason that this is deemed to be paradoxical is relatively theory. According to relativity nothing can travel faster than light, but quantum mechanics requires instantaneous correlation’s between particles, even though they may be separated by huge distances. The paradox is known as 'quantum non-locality' or 'EPR' for Einstein-Podolsky-Rosen, the three people who first pointed it out. To this day it has never been fully resolved.

Hopefully some one here can explain EPR a lot better than I can.

Any way... back to the central argument of Penrose's book. The way I saw it was that Penrose argued that the brain cannot be a computer - that is - the physical processes going on the brain cannot (even in principle) ever be simulated on a computer. This is very strange, because all known physical processes (at the time of publication of Penrose's book) COULD be simulated on a computer. The radical conclusion that Penrose drew was that the brain had to be making use of some as yet, unknown laws of physics, laws which would enable the brain to carry out 'non-computational' operations.

Now you might be interested to know that the publication of tENM made quite a big splash, but the establishment to this day has more or less rejected his claims. The idea that the brain makes use of unknown physical processes which can bypass Godels theorems and carry out 'non computational' operations was just too radical to be believed. Many people accused Penrose of 'mysticism'. If you look at xyroth's comments in this thread, they more or less represent the position of conventional science. The conventional view was (right up until this very week in fact!) that Penrose's theories were interesting, but unlikely to be correct.

Now the ‘New Scientist’ article. Two mathematicians from New Zealand of all places have just came up with a strong result. They were using quantum mechanics to try to see whether there might be some physical situations in which ordinary 'computability' fails. And they claim to have found it. They found that a device could in principle be constructed capable of performing operations which escape the Godel limitations! A device capable of carrying out operations which were supposed to be 'non computable' If this result is confirmed it will vindicate at least some of the ideas of Penrose. It demonstrates that non-computability does exist in nature, and Godel's theorems will no longer limit us.

If anyone is interested in reading it it’s the cover-story of the April 6th edition of 'New Scientist' (now on magazine stands everywhere ). The words are right there in giant lettering: 'THE GREAT ESCAPE' - and a giant hand is metaphorically smashing it's way through the mighty Godel's theorems. The article is called 'Smash and Grab'.

Hello Clay Toy.

I will try to find the magazine at the bookstore. It sounds very intriguing!

Russ

I have been unable to find a copy of the magazine, but I would guess that what they are actually talking about is using quantum computers to handle "intractable" computer problems (problems which are computable, but not in usefull amounts of time) which has been know about for a few years, rather than uncomputable problems which are a different ball game.

Even if they are talking about "uncomputable" problems, then this relates mainly to turing, not godel.

turing covers what is computable given the rules. godel covers what is knowable using the meta-rules. I have yet to see anything that effects this.

ps clay-toy. do you still think you have debunked Godel, Escher, Bach in half an hour?

Hello CT, hello all!

"So you read tENM! Good, good. It's heavy duty stuff but it's really damn good. Penrose talks about virtually everything in science in there. The guy's a genius, no doubt about it. He's got a lot of pretty unconventional ideas but he really knows how to put forward an argument - entertaining."

It is a well written book. Penrose is even pretty up-front about when he's being logical and when he's being emotional, and arguing from fear, which is nice. The really slanted language is confined to a few sections, which are easy to spot. His explanations of Godel's and Turing's proofs, and his account of the strange role of observation in quantum theory are the best I've read, by far. I especially thought it was fun playing with some of the simple Turing machines he provided in the text. Playing with Turing machines is a good way to kill time when you're travelling by train!

Regarding EPR, yes, everything you say sounds fine, but I still don't get it. Specifically, I'd like to look more carefully at his illustration of the paradox, in which he has two detectors that can detect spin at 120-degree angles... I'm not describing it well here, but it's right there in the text. I don't have the book with me now, but I will later. I feel that, if I could really understand that example, then I would have a much better grasp of EPR.

Would anyone be interested in going through the details with me? There may be experts around, and they're welcome to drop by and help out, but I'm inclined to think that we've got a collection of reasonably bright people on this thread now, and we should be able to muddle through it, and probably learn something along the way. I'll happily start the conversation, by summarizing my understanding of his example, next time I have the book handy.

I'd say, Clay Toy, that you summarized the main argument of the book fairly accurately. Where I found him less than convincing was when he argued that the brain does things that are necessarily non-algorithmic. I don't think he proved that, at least not to my satisfaction. Oh, and of course when he appealed to his anxiety about being surpassed by our creations. That got absolutely nowhere with me, but that's a personal issue.



I'll try to find that New Scientist article... "magazine stands everywhere," eh? You obviously haven't seen the typical magazine stand in Nairobi. Like I said, I'll keep an eye out for it. If a copy turns up online, I trust someone here will toss us a link?

GTB

Penrose has a number of highly dubious assumptions that seem to pervade his writting and generally make it (to me at least) completely unreadable drivel.

The first is the frankenstein assumption, which is a distinctly western belief that all technology will be abused by the scientists. this is decidably ropey anyway, but is often a position held due to technophobia, or to problems handling the speed of change.

Then their is the problem of the fear of the ultra intelligent machine (or UIM for short). This is also a position of fear, often due to applying the frankenstein assumption to the basic AI position that if we can make a machine almost as intelligent as a human, why should it stop learning when it reaches human intelligence. (the worst proponent of this fear is kevin warwick).

Then you take penrose's belief that there is some vital element to humans (and specifically human thought) which stops you from making a machine think like a human. This viewpoint is almost always presented by people who cannot cope with the idea that humans might be "nothing special", and is usually just a rehash of vitalism.

As to the EPR paradox, cosmology has since newton been built on localised action. Einstein extended this by demonstrating why the speed of light must be a constant. Then quantum mechanics points out that you can take coupled particles, seperate them, and they will remain coupled, even when you collapse the wave-form that describes the pair, thereby allowing for instantanious action at a distance, in breach of relativity.

As you can imagine, Einstein was not too chuffed at this perceived attack on relativity. It has become more of a problem in recent years, due to both relativity, and this coupling of particles when seperated having been demonstrated experimentally.

This leaves a contradiction right in the heart of physics, connected to the nature of time. In effect, current experiments and theory have shown that the speed of light is a onstant which nothing can go faster than, and that in this special case, the information travels instantaniously from point to point, thereby travelling faster than light.

Very uncumfortable for physicists to have to live with.

xyroth, I think your summary of Penrose's fear-based assumptions is pretty spot-on. There's a sentence from the Introduction that captures this attitude pretty well: "If machines can one day excell us in that one important quality in which we have believed ourselves to be superior, shall we not then have surrendered that unique superiority to our creations?" (Oxford Press, paperback edition, p.4) It is his desperate will that this not be true that drives the rest of the book, although he only really spells it out in the Introduction and in the final chapter.

From the final chapter: "Perhaps when computations become extraordinarily complicated they can begin to take on the more poetic or subjective qualities that we associate with the term 'mind'. Yet it is hard to avoid an uncomfortable feeling that there must always be something missing from such a picture." (ibid, p. 579) That "uncomforatble feeling" *could* be Penrose's keen philosophical intuition, whispering the truth of vitalism... or it could be something he ate.

In the rest of the book, he sticks to explaining math and physics concepts quite well, staying within the domains of those respective subjects. It is only his ventures into the philosophy of mind that are so completely undisciplined.

I would not suggest that it is proven or demonstrated that minds *are* merely computational. Penrose just hasn't proven that they aren't. He's clearly shown that he doesn't want them to be.



As for EPR, I'm reading through the quantum theory chapter (ch. 6) again, slowly and carefully. It's already beginning to make more sense, and I'm getting a lot out of the perspective that, to talk about the existence of a 'particle' when it's not being observed is just nonsense - that what *exists* is a wavefunction, propagating according to Shrodinger's equation. What we call a 'particle' is in fact an event which involves the collapse of a wave function and a 'detection' of a 'particle'. (presumably this collapse is a discontinuity in the evolution governed by Shrodinger's Eq?) Apparently the EPR paradox is that the collapse is deemed to be caused at a particular location - whereever a detector is placed - and yet the collapse occurs everywhere that the wavefunction is defined (all of space?) simultaneously, although simultaneously from the p.o.v. of what observer is not clear.

I'm not entirely certain how they know that the information about the collapse does not just spread at the speed of light like any other well-behaved information, but I'm still re-reading the chapter.

Hey again Bacchus,

I really enjoyed ENM, but like you, I was not entirely convinced that thinking requires non-algorithmic action.

That's way I also recommend Penroses second book - 'Shadows of The Mind' It's a sequel to the first one. tENM came out in 1990, but 'Shadows' came out 5 years later. Penrose has really improved his arguments, and his case is stronger. He also covers the EPR paradox in the second book, and he's got some cool examples which are much clearer than the ones in tENM.

Interesting what you and xyroth say regarding Penrose's motivations. I must admit there does seem to be a fear element - he doesn't like the ideas that humans aren't special and that machines may surpass us. Hmm...

The 6th April 'New Scientist' - no on can find it? Mag stands in Nairobi - right

xyroth - the article was definitely talking about genuine 'non algorithmic' processes, and not just speed improvements to deal with 'intractable' problems. In this article the claim was definitely being made that quantum mechanical processes could do 'un computable' things. I am trying to locate details of the claims and I'll put a link up if I find them.

When two particles interact (an event) the laws of physics state that momentum is conserved.

Then the two particles are separated a far distance.

When the 2nd particle is observed, the wavefunction collapses and it conforms according to the laws of physics apparently "instantaneously".

But remember, as the 2nd particle was traveling to a far distance, it never exceeded the speed of light.

When the observation is made and the wavefunction "collapses" it will still be within the lightcone of the first event.

In other words, memory of the event was carried along by successive layers of space-time. Space-time is quantized in units of hf.

The brains of most life forms on the earth are much more complex that our simple computers. But basically a neuron is a switch, it is either "on" or "off". Basically the same principle as a computer.

unfortunately, while I can agree that minds are just symbol processing machines, they do not work "just like a switch".

neurons work using a funny form of logic. When a neuron fires, it effectively empties a reservour of energy between ALL of the neurones it is connected to. having become discharged, it then takes in charge from all of the neurons that are connected to it, and when a critical level of charge is reached, it fires.

This means it uses some form of logic based on the number of pulses per second, which makes for some very strange mathematics to explain it.

Having said that, when you look at individual circuits in the brain, the functions are clearly defined, and can easily be modelled using standard sequential (mostly) logic to give a function that does the same job, but takes a different amount of time.

Given the computability of every function so far found in the brain, there is as yet no reason to believe that there is anything in the brain that will not be suseptable to this approach.

Thanks for the clarification xyroth. I will have to research this topic(neurons) in greater detail.

But you cannot refute... that a neuron, or neurons, is/ are basically part of an information processing system called "the brain".

Thanks for the information.

Indeed I can't. In fact I said so in the previous post.

I stated that minds were indeed geneeral symbol manipulation machines (also known as turing machines) and that so far, every function found in the brain (when decoded) had been found to be computable.

This points to the likelyhood (but does not prove) that brains, while capable of interacting at the quantum level, don't seem to use it and stick to electronic and chemical levels which don't bring quantum mechanics into the question at all.

This also means that minds are just as liable to suffer the problems of godel and turing as computers are.

It appears that neurons are information processing systems in their own right, and the brain is a type of "very advanced" biological computer. There is also the "holographic aspect" to the brain, in the way it stores information.

I will have to read Dr. Penrose's book.

Very interesting.

Heisenberg Uncertainty might also relate to Godel, so I will post my alternative to the CTMU.

First I would like to say that this is not a refutation of the CTMU, because the CTMU is logically irrefutable.

I propose that the Universe must be expanding.

There is a nagging doubt about the CTMU that just will not leave me alone. As it turns out, the "Heisenberg-devil" was on my shoulder.

According to general relativity and quantum theory, the Universe has no choice but to expand.

Basically the concepts of "inside the Universe" and "outside the Universe" are not precisely defined.

Concentrations of mass-energy... curve space-time Space becomes "compressed" and time becomes "dilated". Since the cosmos is a four dimensional hypersphere, there is a region of space-time in which the concept of "inside" and "outside" cannot be sharply distinguished. As the limit of *outside* is approached the rate of passage of time increases until time is approaching an infinite rate, or time is compressed to zero. Space would be approaching infinity.

A region between "inside" and "outside" the Universe, a gray area of uncertainty that can allow the cosmos to expand! Shades of gray! Everything cannot be black and white!

The Universe does not stretch like a rubber sheet, but space "grows" as units of Planck space multiply.

So...yes...there must be a region of heisenberg uncertainty with a type of duration and extension. It is not a sharp border. It cannot be BLACK|WHITE...it is BLACK(GRAY)WHITE.

Uncertainty is irrefutable...

The Universe MUST be expanding.

Russ