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The Large, the Small and the Human Mind (Canto)

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Let me first say something about Roger Penrose. One notices how certain other mathematicians and mathematical physicists speak of him. He is not only admired and respected; it seems that he is positively enjoyed! This may be a bit surprising when one notices that Penrose is something of a thorn in the side of several popular ideas in contemporary physics (and psychology). Cosmic inflation theories and ideas regarding the fundamental nature of quantum uncertainty find a formidable and articulate critic in the Oxford mathematician. Of the somewhat less popular, but ever fanciful "many-worlds" interpretation of quantum superpositioning, Penrose says "[the 'many-worlds' view] is not a very economical description of the Universe but I think things are rather worse than that for the many-worlds description. It is not just its lack of economy that worries me. The main problem is that it does not really solve the problem." He brings the same mental rapier to what he has called "the missing science" of mind and to the idea of computational / artificial intelligence. It is the problem of superpositioning described by Schrodinger and the decoherence caused by quantum measurement that prompt Penrose's search for an 'objective reduction' (OR) of quantum state vectors, the key ingredient in a "revolutionary" physical theory that remains a mystery. He speculates that this physical mystery may be related to the mystery of consciousness. He is unconvincing in this regard, but his ideas and arguments are quite interesting.
Well, let me now take this a bit further. Penrose also seems to terribly irk certain others! In particular he really raises the hackles of proponents of strong AI and the Dawkins/Dennett camp of 'consciousness-is-merely-mechanism' dogmatists. His views are much closer to those of perhaps most mathematicians and philosophers and stand on a deeper logical footing than do the doctrines that the human mind is mere biology. Let me say that I agree with Penrose in that the 'simple biology' view is never going to win this argument for reasons that can be demonstrated by the application of mathematical logic. To say that Penrose "doesn't understand biology" is to miss the point. The author freely admits, "there is a good deal of speculation in many of these ideas". Of course there is; science is largely -- we might even say wholly -- speculation. A more perceptive analysis would suggest that those committed to a rigid materialistic aesthetic don't understand (don't want to understand) the mathematics. Those who summarily dismiss Penrose do so unwisely. Given his contributions to mathematics (e.g., Penrose tiling, computability, mathematical logic) and his stature within the mathematics community, and given that the history of mathematics is essentially written by mathematicians, Roger Penrose may come to be considered the greatest mathematician of his generation. Given his work on black holes and space-time geometry (he recognizes the apparent "flatness" of the universe but suggests a more elegant geometry to describe that flatness), he may be one of his day's greatest physicists as well. Should his hunch ("OR") one day prove "true", his stature would approach that of a Newton or Einstein. The point being that any scientist who avoids or ignores Penrose's views, or is inclined to dismiss them by erroneously characterizing them, does so, as I say, unwisely.
Chapters 4, 5, and 6 are challenges to Penrose from A. Shimony, N. Cartwright, and S. Hawking, respectively. Apart from Shimony's discussion of A. N. Whitehead's views, its not on a par with the author's discourses; Cartwright suggests that nature may be a mess of "patchwork" laws (her view itself seems a horrible mess), and Hawking is disappointingly flippant. Penrose certainly meets these challenges.
I must say that the "controversy" over Penrose's Platonism is nothing less than nonsensical. Hawking complains "basically, he's a Platonist," as though calling him an offensive name and thereby granting the reader cause to disregard Penrose's arguments. That's unfortunate. Most of history's great minds have been Platonists; even Aristotle*, so often cited as the philosophical godfather of reductionism, was arguably a Platonist. Augustine, Kepler, Descartes, Pascal, Newton, Leibniz, Kant, Linnaeus, Einstein*, Schrödinger, Gödel, Whitehead -- the list of Platonists is long and impressive. As Penrose has said, "... it is my direct personal impression that the considerable majority of working mathematicians are at least 'weak' Platonists." Yet it seems as if some who call themselves "positivists" feel a calling to be science's mind-police. I suggest that this should be the real controversy... So-called positivists would do well to honesty consider Gödel's observation that the idea that mind/mentality is simply material is nothing more than the "prejudice of our time."
There is a rather child-like glee in the way Penrose sees and uses mathematics. His investigations and speculations are those of an extremely astute mind having fun! In his aggressive curiosity, his boldness, his clear-eyed honesty about the frailties of human thought and the limits of science, it seems to me that Penrose is something of a treasure and an inspiration. As he candidly states, "... the world-view that present-day physicists tend to present may well be grossly overstated as to its closeness to completion, or even to its correctness!" This volume presents a concise look at the Penrose ideas/arguments and even if nothing much ever comes of these arguments, they present a shining example of the kind of creative thinking that moves science into new frontiers.
*(footnote: While recognizing that it can easily be argued that Aristotle and Einstein were not "strong" Platonists, it seems obvious to me that they were each Platonists in some fundamental ways. I consider them to have been "weak" Platonists.)

On the back of the book jacket it states that this book provides an "accessible" introduction to Roger Penrose's ideas. This is simply false, unless you are a physicist, a mathematician or a genius. For all others (in which category I fall), this book is close to incomprehensible. Roger Penrose is brilliant, has a wonderfully clear mind, and can write beautifully and clearly. I think that _The Emperor's New Mind_ and _Shadows of the Mind_ are wonderful books. Penrose can make extremely difficult ideas wonderfully clear, by breaking down complex arguments into clear simple steps. Some pages of Emperor's and Shadows take a long time to understand, (I must admit that I have read quite a bit less than all of either book), but the argument is spelled out so clearly that with effort and patience it can be fully understood. Penrose, I think, understands the questions he is wrestling with as well as any one alive, and his is a mind of great depth as well as clarity. Even if you don't find his arguments entirely convincing, you can't help but learn a great deal from these books, and develop insights of great value. What went wrong with _The Large, the Small and the Human Mind_? I think the key to answer lies in a comment Penrose makes on page 105, where he writes "The first 200 pages of _Shadows of the Mind_ were devoted to trying to show that there are no loop-holes in the argument that I am goind to give you." He then gives his argument in a few pages. The main part of the book (not including the replies of others and Penrose's replies to these replies) is just 139 rather small pages long. The book has many paragraphs like the following: "The first is the Geroch-Hartle scheme for quantum gravity, which turns out to have a non-computable element, because it invokes a result, due to Markov, which asserts that topological 4-manifolds are not computationally classifiable. I shall not go into this technical matter, but it does show that this feature of non-computability has already come up in a natural way in attempts to combine General Relativity and quantum mechanics." If, like me, you don't know what the Geroch-Hartle scheme is, and you don't know what topological4-manifolds are, you really won't know what to make of this paragraph. By "not going into this technical matter" Penrose is not omitting a minor technical detail of interest only to a select few, he is leaving readers like me completely baffled. Penrose tried to write a short book that would give a clear idea of his basic ideas, and I think he failed. I know that he can make complex ideas wonderfully clear when he takes the time. In this book he has shown that, at least on this occaision, he can not write a book that is both brief and clear. Here is another example, this time from Penrose's response to Abner Shimony's comments: (pages 176-7) "Abner mentions Mielnik's non-Hilbertian quantum mechanics....In ordinary quantum mechanics, the space of density matrices consitutes a convex set, and the 'pure states', which would have a single state vector description, occur on the boundary of this set. This picture arises from an ordinary Hilbert space, being a subset of the tensor product of the Hilbert space and its comples conjugate (i.e. dual)." Did you understand that? If so, you might learn a great deal from this book. There are a number of topics that I have read about previously in other books, for example, non locality, Schroedinger's cat, the EPR experiment. In almost every case, Penrose's presentation was the worst I have seen. Probably everything he says is quite correct, but the presentation is so compressed that it was usually almost impossible for me to follow. There are sections that I could follow, but even there he was so sketchy that I ended up with only a vague idea of _why_ he believes what he does, even when it was clear _what_ he believed. For instance, on pages 100-101 he is concerned with four approaches to awareness, which he labels A through D. "D" is as follows: Awareness cannot be explained by physical, computational, or any other scientific terms. Here is, in its entirety, what he has to say about "D": Finally, the is always viewpoint D, according to which it is a mistake to look at these issues in terms of science at all. Perhaps awareness cannot be explained in scientific terms. Penrose likes one of the other four positions, which is clearly stated, as is "D." But I would have liked to see Penrose develop in detail the reasons for his rejecting D. He does this only indirectly, by arguing for his preferred alternative, and this quite briefly. I think that I understood enough of the book to say that if Penrose turns out to be even roughly correct, he will be regarded as one of the great geniuses of the century. His proposals are bold, and deal with questions of the greatest interest. If only I could have followed his arguments! I hope that somebody who can follow his arguments posts a review.

A previous commentator claimed that this book was not readable enough for a mass audience--I have to disagree with this view wholeheartedly. I would say that his previous works, especially "Shadows of the Minds" were difficult to digest due to the amount of mathematics contained in almost all of the chapters (this doesn't negate the power of his ideas--he just makes them hard to understand). This latest work presents all of his major ideas on cosmology, quantum physics, and the nature of the mind in an extremely clear manner. His treatment of quantum physics is the best I've seen to date in a popular work. A short and rewarding read.

As my background is mainly in the brain sciences, I was most interested in what Penrose had to say about consciousness and the brain in this book, so I'll concentrate mostly on the chapter that had to do with that. This is not to say I didn't enjoy the other chapters, just that I'm not as qualified to critique those as I am the one on the brain. There has been a lot of speculation in recent years about such things as computability and the brain, quantum consciousness, and so on, and I was interested to find out what Penrose might have to say about that.

One of Penrose's major ideas in this chapter is his demonstration that consciousness, although perhaps mathematical, isn't computable, in the sense that you could program a computer to simulate it. Penrose uses the example of geometric tilings or polyominos that are deterministic in their coverage of the Euclidean plane, but that aren't computable, to show this. Since, as Penrose points out, there are plenty of mathematical concepts that aren't computable and that can't be done on a computer, but that the human mind can understand, Penrose concludes that there is something beyond computability in both pure mathematics and the human brain.

This is interesting, and Penrose might be right about that. However, I must point out that while consciousness itself may not be computable (and I'm not really prepared to conclude this for sure at this point, because of what I'm about to say), nevertheless, many aspects of the brain's functioning have been shown to be computable, so I'd like to discuss that briefly.

For example, sensory neurophysiology has been shown to be both quite mathematical and computational as a result of the work of a pioneering mathematician by the name of David Marr 25 years ago, whose ideas revolutionized neurobiology almost overnight, after which the field was never the same. Marr examined a number of different fundamental sensory mechanisms, and showed, for the first time, that the way in which the visual system was processing light information was consistent with the operation of certain sophisticated spatial-frequency filtering transforms that are well-known in many engineering applications. To mention just a few of his important ideas, Marr's demonstrations that retinal receptive-field geometry could be derived by Fourier transformation of spatial-frequency sensitivity data, that edges and contours could be detected by finding zero crossings in the light gradient by taking the Laplacian or second directional derivative, that excitatory and inhibitory receptive fields could be constructed from "DOG" functions (the difference of two Gaussians), and that the visual system used a two-dimensional convolution integral with a Gaussian prefilter as an operator for bandwidth optimization on the retinal light distribution, were more powerful than anything that had been seen up to that time.

It was as if vision research suddenly acquired its own Newtonian Principia Mathematica, or perhaps General Relativity Theory, in terms of the new explanatory power Marr's theories provided. Basically, in one fell swoop sensory neurobiology also became an area of theoretical physics rather than purely biology, giving the area a rigor and elegance never before seen--an amazing achievement for a young man who died so prematurely from leukemia at the age of 36.

The main point of all this is that all of these mechanisms are both mathematical and computable, although the way in which they're done in the brain is probably more like how a computer would use numerical analysis to solve a differential equation, rather than using the original equations in a purely analytical way themselves. Since Marr's time, there has been further progress in this area, such as the great Bela Julesz's demonstrations that the visual system can extract and compute binocular disparity cues point-by-point for depth information from abstract, non-representational pictures or textures such as random-dot stereograms, the extension of Marr's ideas about monochromatic edge detection into color edge detection, the mathematical bases of non-linear visual field distortions present in optical illusions, and many other areas.

Furthermore, in the last few years, the nature of consciousness itself has been shown to be composed of many different separate mechanisms in the brain that are being coordinated in time in order for consciousness to occur. It simply isn't one process or central program that runs in the brain, nor is there a "master" brain center that one can point to where it can be said that consciousness resides. I'm sure the progress of this research will also have implications for ideas about the nature and computability of consciousness.

So overall, a fascinating and enjoyable discussion about the brain and consciousness by Penrose, even if I don't completely accept one of his major ideas about it for the reasons that I discuss above.

Penrose concisely manages to give us an overview about 3 somehow interconnected fields, the mathematically described large-scale world, the deterministic quantum microcosm and the recently emergent mind science. His major aspiration is to see the new generation of scientists erecting a bridge between the quantum world and the always controversial substance of conscience.

Having in his mind (in a neo-platonic way) the idealistic nature of mathematics that apply to the physical world as a well-justified model, he firstly presents some themes from cosmology and abstract mathematics (e.g. hyperbolic, Riemann geometry), and why, in his opinion, Guth's inflationary universe theory, has weak points (see also Penrose's book- Difficulties with inflationary cosmology) In chapter 2 ,quantum physics related, he gives us interesting examples (the paradox& puzzles reference shows his great sense of humor) and explain us how wavefunction's reduction can assist us to deal with the probabilistic nature of events in this level.
In the most interesting third one, he is concerned to lay an in-depth foundation between quantum procedures through neurons, so as to explain his main belief - brain function (that creates conscience) can't be simulated through A.I. Even though I tend to prefer J.Searle opinion (presented in his book Mind,Brain & Science) Penrose's points are adequately justified, thus leaving an open window for Free Will.

In the next three chapters certain Penrose's point's are opposed from Shimony (physician, philosopher) Nancy Cartwright(logician, philosopher) and the renowned Steven Hawking.
Shimony in a formalistic language, but slightly excessive for the common reader, finally makes a conjecture about a hyperselection law, in order to avoid quantum dualism, while Mrs Cartwright sets a contronversy against the usefulness of a perception that sets Physics the only explanatory science for mind theory and not for example Biology.(which for Penrose is reduced to Physics)
Hawking denies an indispensable and direct correlation between quantum gravity and the yet inextricable conscience and in chapter 7 Penrose responds to all so as to end this dialectically fair and fruitful discussion.

Overall this was worth my time, not only for this subject's great interest but because Penrose explains his thesis, clearly and distinctly.The uprising need for 'popular' science is reflected and adequately satisfied through this lucid book which succinctly presents a contemporary overview in a 'hot' scientific field.

Even non-expert readers (no special background in maths or physics is needed) will be able to follow and admire the ongoing revolution of scientific thought.Given it was written in'97 I'm looking forward and will benevolently embrace another similar work of a splendid thinker such as Penrose

I see others have praised this book richly and a couple others poorly. One reviewer said one needed to be a mathematician and a physicist to understand the book. It would certainly help, but Penrose describes enough about the function of the math concepts he invokes so that I can follow him (and even in maths one has to have studied things like those density matrices to really understand in depth). I do understand about computability and problems which have been proven non-computable, and I think he is possibly right, that 'mind', because it shares/crosses the quantum/macro world boundaries, cannot be easily mathematically described without finding a 'bridge' between those worlds. I found his description/hypothesis about the microtubules fascinating (and again I am not a biologist but I am not disturbed that he didn't try to explain or prove his hunch regarding the possible functioning of these structures).
I appreciated the book for the wonderfully clear style as well as the content.

This book is a smattering of loose conjectures and comments on relativity, particle physics, and the intersection between physics and mental processes. This book, contrary to one reviewer, can be read without a deep background in math or physics. I have had some mathematical logic and a philosophy of physics course, but nothing extensive; this book was accessible for the most part. Multiple readings would definitely carry out the main points without much ambiguity.

The style is lecture-ly. That is, it glosses over some controversial points while delivering the author's main viewpoint. These books are useful if one wants to get some insight into the deeper implications of physics. Penrose is not a theorem prover only, but a problem solver and he is interested in "important" problems. Not every mathematician or physicist has a gift for identifying such significant problems. So if a reader wants some schooling in this art -- finding interesting areas among the many potential research directions -- they should give this book a look. It's very short so won't take long to get through.

This book sparked my interest because I am one who also wonders about the mind's relation to the physical world. Penrose believes that the physical mechanism behind consciousness underlies new physics relating to quantum mechanics. He also believes that this new theory is not computable or programmable. This book is meant for general audience, no physics background needed. In fact the conceptual physics are actually explained well by Penrose. So if your curious, or an actual mathematician/physicist attempting to understand consciousness this is a good book to get some interesting ideas from. Its not polished out, the writing is in lecture style, but I like this, it gives a better down to earth feeling. You basically get Penrose telling you his thoughts without much editing.

According to Stephen Hawking, Roger Penrose is a Platonist, who believes there is a unique world of ideas that describes physical reality. I think it is a good thing that someone actually believes Plato was right all the way and makes the case for it concerning Relativity, Quantum Gravity and Consciousness. So, as inspiration I found the book a good read - But I don't particular believe all of Penroses arguments. Especially the part about that our brains can't be modeled by computational systems and hence that strong artificial intelligence will remain in science fiction was to me unconvincing.

-Simon

Turned off by the strong AI type point of view of consciousness, yet looking for a scientific explanation, I have repeatedly turned to Penrose's work hoping he would have enlightening ideas. At first, he seems to be on the right track, but when he starts making conclusions, things go awry.
As a biology student, I can say that his understanding of biology seems mediocre at best. And physics may be even worse - in fact his skepticism about the "flatness" of the universe has recently been rendered bascially obsolete.
I feel that the unified brain quantum undulation camp, if you will (penrose, zohar) paint themselves into a frightful corner. For instance, penrose never explains why his microtubule ideas would apply to the brain in particular...we've got oodles of them in every cell in our body! Basically, these ideas try to strike out against the strong AI poing of view, but actually create a new version of it! It's not the neuron construction, they say, instead it's a mechanism even more arbitrarily linked to the brain!
Penrose seems to be a great mathematician...and should stick to that. Still searching for explanations...