Okay, okay...I do know what an eigenstate is, but I don't claim to have a comprehensive knowledge of QM...
Scientific metaphors are frequently used way out of context, because the user of the metaphor sees some kind of parallel. This is not meant to be taken literally, necessarily, and the butchered scientific principle is not actually at work in their argument...they have merely spotted a parallel phenomenon. For example, if my mother says: "Your room is a mess, clean it,", I could responds "Hey! Whoa! 2nd law of thermodynamics, Mom. I'm not going to mess with entropy!" Of course, I'm dead wrong, since Boltzmann's equation coupled with the scond law holds only that the average entropy has a tendency to increase (S =k log W, dQ < T dS), so the net order in my room can be increased. However, I have used it as a fairly decent metaphor, and my mother would not know the difference.
Similarly, people are always talking about 'survival of the fittest', in reference to all kinds of phenomena. This is of course pretty meaningless, as the 'fittest' organism can only be determined as the one that survives, so that is a tautology. However, there is some meaning, that in some contexts makes sense as a way to illustrate a point (republican rhetoric...).
However, in this case, I will have to agree and say that StarValleyWy must more clearly define what he means by a 'quantum mind', because he is not making a metaphor here. He is attempting to put some object out for analysis, and this cannot be done without a clear definition.
Is it possible that he is talking about the mind as some kind of discrete-state machine that changes states randomly on a small level, but tends in one direction and so is capable of executing some algorithm? Maybe he is talking about something akin to a Turing machine...?
Bbarr-out of curiosity, where did you get your knowledge of QM?
Maybe chess is a good metaphor for the universe. Consider this. A chessboard is an 8x8 matrix C, and say for convenience that it is numbered from a1, so that a1 is the element (0,0), and the horizontal and vertical components take on integer values between 0 and 7 inclusive, so we have h8 eing (7,7). Now let f be a one-one correspondence between the chess pieces and the integers 1-32. For example, let 1-16 be the white pieces, and 17-32 the black pieces, numbered in some way among themselves. Finally, let f=0 when a square is empty. So at any given point in the game, let the state of the board be
F(C)={f(0,0), f(0,1),...f(7,7)}. A 'move' is really just a discrete change in the state of C, bounded by some fixed rules. (I'd estimate that in an average game-say 40 moves, there are 10^40-10^45 such states of C possible.) So ultimately, 'chess' is just a directed graph with a vertex corresponding to a state of C, such that at t=0, C is in its basic state, at t=1, there are 20 possible states for C at t=2, there are 400, at t=3, there are 5632, etc.
So if there is really, as StarValleyWy maintains, a set of discrete time intervals governing the universe, what we have is the universe (a set of discrete positions, each occupied by either nothing or an object), and some matrix of values indicating which object corresponds to a given position. This uber-matrix changes state in a fairly random way, with the caveat that at some level (the level we observe), there is a limit on the position change for a given value, as we observe macroscopic motion to be continuous. So we just have big chess, the only difference being that f in this case may take on a denumerably infinite set of values rather than just {0,1,2,...32}.
But that's just my opinion, I could be (and probably am) wrong....
Originally posted by royalchickenIf he is likening the mind to a Turing machine, then the state-changes couldn't be random, because Turing machines change states according to an algorithm that maps current state + syntactic imput to a resultant state. He could mean something like a probabilistic Turing machine...
Is it possible that he is talking about the mind as some kind of discrete-state machine that changes states randomly on a small level, but tends in one direction and so is capable of executing some algorithm? Maybe he is talking about something akin to a Turing machine...?
Bbarr-out of curiosity, where did you get your knowledge of QM?
I learned what I know of QM from various graduate seminars with the eminent Arthur Fine and the less-eminent Marc Lange, both professors here at the University of Washington specializing in the philosophy of science generally and the philosophy of physics in particular.
I just wonder if the order of complexity of a mammalian brain is such that it can be considered a chaotic system - and thus not readily amendable to understanding by simple (or even not so simple) mathematical or basic physical laws and their subsequent derivations. Here's what I mean: Assuming we have a complete and full understanding of the interactions between protons, neutrons and electrons, which comprise the vast, vast majority of subatomic particles found in the earth, and an exact (forget Heisenberg for the moment) knowledge of the state of all of those atoms at the moment the earth was created, would we be able to predict with 100% accuracy who will win the 2003 world series? Chaos theory says no, the degree of complexity of the system is such that even statistically insignificant variations from expected results are continually amplified in such a way that it becomes impossible to accurate predictions.
Given what I know about the brain, I believe it to be of a similar order of complexity (not to mention that there is still quite a bit that is not known about the brain) and therefore not capable of being wholly governed strictly by processes that exist solely a level where quantum phenomena occur.
-mike
Originally posted by bbarrThat I know...I was making two guesses as to what he is talking about.
If he is likening the mind to a Turing machine, then the state-changes couldn't be random, because Turing machines change states according to an algorithm that maps current state + syntactic imput to a resultant state. He could mean something like a probabilistic Turing machine...
Originally posted by bbarrFrom what angle was it discussed (I am curious here, because the little I know about QM I got from Eugen Merzbacher's "Quantum Mechanics" )?
I learned what I know of QM from various graduate seminars with the eminent Arthur Fine and the less-eminent Marc Lange, both professors here at the University of Washington specializing in the philosophy of science generally and the philosophy of physics in particular.
Originally posted by royalchickenProfessor Fine was facing South for the most part. This was a philosophy of physics class, so the 'angle' was trying to get clear on what the philosophical implications are if QM provides a complete account of the evolution of physical systems. We studied the evolution of the theory, the discovery that different formulations of the theory by Heisenberg and Schroedinger were just notational variants of one another, the experiments that supported the theory, the thought experiments that brought out its 'weirdness' in relation to our realist intuitions, hidden-variable theories like those of Bohm, the many-worlds hypothesis, the even stranger many-minds hypothesis, the Bell inequalities, etc. etc. Although we had to get clear on the formalism of the theory, and see how particular empirical results supported this or that interpretation, what we were primarily interested in was whether our realist metaphysics could be reconciled with QM and if not, what QM seemed to force upon us.
From what angle was it discussed (I am curious here, because the little I know about QM I got from Eugen Merzbacher's "Quantum Mechanics" )?
That's quite interesting, since I primarily faced North while reading Merzbacher. I read it really as another mathematical game, with some rules supposedly supplied by someone's observations. What were your basic conclusions? (I remember in a discussion on Cantor, you discussed how you had come upon certain concepts through philosophy, and that T1000 had come to them through mathematics. The same interface here could yield a few interesting ideas.)
being the object of "he" as used by bbar and RC ... Quantum Mind is only that which is capable of operating in a quantum universe. It only makes 1 assumption... that as the "very small" QM meets mr. Einsteins "very large" there must "some day"... be a recocilliation. "Some day" has not arrived yet, but a lot of very bright "minds" are working on it. (of these minds... some are quantum and some are continuous and some are evern asynchronous <this is what is known as a joke folks, so don't jump on it>😉 So... no unification yet. This has been variously refered to as GUT (Grand Unified Theory), TOE (Theory of Everything) , and "Einsteins Grand Unity" of quantum space-time. I happen to think that it will be done by arriving at some smallest (quanta) time, distance and mass.. that PUSHES THE MACRO WORLD inevitably forward. A Dust Storm is a good analogy. Unravelling. Unfolding. Whatever. There is nothing mysterious about quantum mind at that point. I have already stated (twice, in this thread) a very compact description of what i believe quantum mind "might" be. As i stated... i am not a god and i hardly think my point of view is worth arguing over. If i had anything beyond a "feeling"... i wouldn't be describing it on a chess site, but elsewhere... where it might be considered by people a whole hell of a lot smarter than i (obviously) am not... in my current quantum and/or continuous state. <snicker>🙄😵
I think that a 'mind' is, very roughly, the software operated by our brains (the hardware) to accomplish what really amounts to manipulating a vast array of data. This information, which StarValleyWy maintains is derived wholly from our senses (and we are not arguing about this necessarily), is the input data for the various algorithms executed by our brains. I think it quite likely that many of these mental algorithms function in an essentially statistical manner, by sacrificing certainty for a vast increase in speed and efficiency. (A good analogy might be many modern cryptographic algorithms which make use of tests of pseudoprimality-rather than determining a number to be prime, they determine, much faster, that it has properties making it almost certainly prime.)
So in a sense, certain aspects of QM might provide a metaphor for what I (and the Quantum Bump) suspect is the way in which our mental algorithms work.
Originally posted by royalchickenYou are advocating what is known as 'functionalism' in the philosophy of mind. Perhaps the majority of philosophers, cognitive scientists and cognitive psychologists agree as to the aptness of the computer metaphor in relation to mental states (at least in regards to the individuation of such states, nobody has a clue about why any such states are conscious). But I'm not sure how QM even plays a metaphorical role in this way of looking at the mind. What does it mean to say that a mental process occurs in a statistical manner? Do you mean that sometimes people come to believe a proposition for inconclusive reasons? Do you mean that mental processes are instantiated in a physical medium in a manner such that causal imput into the system doesn't quarantee the accuracy of the output? To speak of certainty (an intentional predicate) indicates the prior reading, to speak of speed and efficiency indicates the latter. In either case the relation with the brute randomness of QM processes seems obscure. The only relation with QM I can tease out of these comments is that perhaps the physical medium in which the mind is intantiated is itself a quantum system, but if QM is true then not only is this trivial, but uninteresting for another reason: the weirdness associated with quantum processes at the micro-level tend to cancel each other out at the macro-level, and the brain is a macro-object.
I think that a 'mind' is, very roughly, the software operated by our brains (the hardware) to accomplish what really amounts to manipulating a vast array of data. This information, which StarValleyWy maintains is derived wholly from our senses (and we are not arguing about this necessarily), is the input data for the various algorithms executed by ou ...[text shortened]... phor for what I (and the Quantum Bump) suspect is the way in which our mental algorithms work.
Originally posted by bbarrPass something round.
Just to bring this whole thread back 'round, how is the study of quantum phenomena supposed to illuminate consciousness? It has become fashionable for people to wave their hands saying 'QM this' and 'QM that', while talking about wholly unrelated topics like Eastern mysticism, the putative freedom of the will, consciousness, etc. ad nauseum. But nobody ...[text shortened]... creating the world around us, and dude, pass the bong..."😉.
What exactly is a Quantum Mind?
Did we?
Did we?
did we all want to bring it back to Bbarr's cocktail party?
Linda.
Originally posted by bbarrYou are advocating what is known as 'functionalism' in the philosophy of mind.
What does it mean to say that a mental process occurs in a statistical manner? To speak of certainty (an intentional predicate) indicates the prior reading, to speak of speed and efficiency indicates the latter. In either case the relation with the brute randomness of QM processes seems obscure. The only relation with QM I can tease out of these commen ...[text shortened]... e micro-level tend to cancel each other out at the macro-level, and the brain is a macro-object.
At least someone agrees with me 😉.
But I'm not sure how QM even plays a metaphorical role in this way of looking at the mind.
I'm not really defending any connection to some kind of quantum picture of the mind, rather I am attempting to interpret StarValleyWy's statement.
What does it mean to say that a mental process occurs in a statistical manner?
Take the 'functionalist' view and assume that our minds are constantly executing algorithms of various sorts. Now assume that arithmetical (set-theoretical) operations are all that are necessary for any of the manipulations of data done in our minds. (I have never seen a convincing refutation of this belief...people who disagree vastly underestimate the power of what can be done by computational algorithms-besides, no-one can provide a well-defined alternative.) Clearly, then, each of the myriad situations with which our minds can deal are presentable as computational problems. Our mind consists of algorithms for the solution of these problems. It is also fairly clear that our mind cannot functionally solve NP or NP-complete problems. However, I am willing to bet my feathers that many situations faced and dealt with by humans are only presentable as problems that are too computationally intensive for a complete solution in polynomial time. The human mind thus must deal with these problems in some other way....approximation! Statistical methods! Instead of using brute force, approach the problem randomly, and the running time of the resultant algorithm is usually reduced....(more to follow when I get home)...
Originally posted by royalchickenI'm not sure what you mean by "our mind cannot functionally solve NP or NP-complete problems". Could you (or anyone else) please explain NP and NP complete to a non-mathematician?
Take the 'functionalist' view and assume that our minds are constantly executing algorithms of various sorts. Now assume that arithmetical (set-theoretical) operations are all that are necessary for any of the manipulations of data done in our minds. (I have never seen a convincing refutation of this belief...people who disagree vastly underestimate the ...[text shortened]... unning time of the resultant algorithm is usually reduced....(more to follow when I get home)...[/b]
You have warned about the dangers of underestimating the power of computational algorithms, but then you yourself seem to be underestimating the power of a mind. What is the "computational" power of your mind? (I've used quotes because I'm not entirely comfortable with your assumptions. Certainly, a mind comprises algorithms, but is there not anything else that goes into it?) Unless you know the power of a mind, how can you conclude that any problem is too "computationally intensive" for it to solve?
Rich
I of course am just guessing. I have no justification for this belief, but it seems to make some sense and explain a few phenomena. I will talk more about this when I have articulated it better...just got back.
About NP...A computational algorithm requires some input of size n. Basically, if the number of operations required to perform the algorithm grows as a polynomial in n, then we say it is a polynomial-time algorithm and say it is in the class "P".
If it can't be done in polynomial time (for example, if the number of operations is exponential in n), then it is a computationally intensive problem and we say it is in the class "NP".
People have conjectured that P=NP, that is that there is a polynomial time algorithm for any problem, but this is unproven (and, FWIW, I don't think it's true).
Finally, if a problem can't be solved in polynomial time, and any solution candidate can't be verified in polynomial time, then the problem is NP-complete.
I think that for suitably large input, the human mind can't handle NP problems. The main reason for this is the following:
1. A slow computer can solve and NP problem for small n, but as n increases, the computational resources can't catch up.
2. The same goes for fiendishly fast things, even quantum computers.
3. My brain is not 'fiendishly fast', and niether is anyone else's when it comes to executing many massive algorithms simultaneously (hell...I have to concentrate to pat my head and rub my stomach simultaneously...).