Once again, Roger Penrose really sounds like he knows what he's talking about...

-----Original Message-----
From: Darien Large [] 
Sent: Monday, November 30, 1998 2:26 AM
To: 
Subject: Shadows of the Mind


OK, well, I looked and looked for a more-or-less comprehensive review of this 
book on the internet, and came up with almost nothing I could access.  Hence 
this message.

At the risk of sounding derivative of so many reviews of so many books, I'll 
say that Penrose's book is really three books.  

In the first "book" he re-examines what is essentially an old, discredited 
argument from John Lucas that uses Gödel's theorems to conclude that no 
computer can be programmed to derive all the mathematical results accessible 
to human understanding. In Penrose's scheme, the conclusion is that, since 
everything a computer can do (the term "computer" being taken in the sense of 
a "Turing Machine", that is, a computer of the same abstract design as we 
understand them today) is accomplished according to well-defined 
"computational rules", but since human consciousness can accomplish all this 
*and more* (this is what Penrose believes Gödel's theorem tells us), then 
human understanding must involve some sort of *noncomputational* activity.  
Penrose is not led hereby to assert a form of *dualism*, however. He does 
believe that there can exist an "exact" science of consciousness, but that 
its discovery and development will require some fundamental changes in our 
understanding of the physical world.  In other words, current scientific 
thought is wholly inadequate to encompass the phenomenon of consciousness, 
and science will require a revolution in some fundamental aspects that have 
to do with the relationship between quantum physics and the macroscopic, 
"classical" everyday world we live in.

[

I haven't devoted much time here to Penrose's treatment of the Gödelian case 
against AI because I've found some excellent references on the Web that do a 
much better job.  I really urge you to investigate them if you're interested 
in assessing the ultimate strength of Penrose's argument in his book. Here 
are four links that elaborate part one of Penrose's book, in which he asserts 
that Gödel's theorems demonstrate that human consciousness must be 
noncomputational in nature.  They're listed here in roughly increasing order 
of technical difficulty (the first one will take you to the website of the 
New York Times, which may require you to register before accessing their 
site; registration is free):

The Best of All Possible Brains? By Hilary Putnam

The others are journal reviews archived at Monash University in Australia:

Can Humans Escape Gödel?

Minds, Machines and Mathematics

Penrose's Gödelian Argument

]




In the second book Penrose explores the current state of quantum theory and 
focuses on what he believes is the great mystery of quantum physics: how does 
the "quantum wavefunction" collapse, so that we observe physical events in a 
more or less "classical" way, and are not confronted with the paradoxes of 
quantum theory at a macroscopic level?  And what sort of ontological status 
does this collapse have?  Is it "real"; that is, is it a physical event?  
This is where Penrose really shines; it's the most interesting part of the 
book and can more or less stand on its own, I believe, not as yet another 
popularization of quantum theory, but as a fairly rigorous exposition of the 
ways in which quantum theory seems to give us an incomplete view of the 
physical world, and a very interesting but often overlooked question about 
the relationship between the quantum world and larger-scale "everyday" 
experience.

The problem is neatly encapsulated by the famous thought experiment of 
Schrodinger's cat.  A live cat is sealed in a box along with a device that 
will release a poison gas to kill the cat if it detects the decay of a 
radioactive particle, and not otherwise.  The decay of the particle is a 
quantum even and is governed by the quantum wavefunction; the system of the 
cat, the detector, and the box constitutes a magnifier of the quantum event 
to a classical level.

If you follow these events using quantum theory, the "time-evolution" of the 
system encompasses both possibilities: after a certain amount of time has 
elapsed, the system is found to be in a "quantum superposition of states", 
one in which the particle has decayed and the cat is dead; and one in which 
the particle has not decayed and the cat is alive.  There is nothing at all 
in quantum theory to distinguish between the two alternatives.  So the 
question becomes, "After a given amount of time, will the cat be alive, or 
will it be dead?"

There's a common misconception about this kind of scenario, which goes like 
this: quantum events do not follow deterministic laws; they are essentially 
random events, and this is the sense in which quantum theory does not decide 
whether the cat dies, or lives.  One must assign a *probability* to either 
outcome, so that in repeated trials one will find that some percentage of the 
cats will be alive, some dead. This probability distribution can be predicted 
with great accuracy, whereas the outcome of a *single* experiment is wholly 
undetermined.

This is simply untrue.  The time-evolution of a quantum system is *completely 
deterministic*; randomness and probability does not enter into the picture at 
any point, in any form.  The results and predictions of quantum theory are 
complete, unambiguous, and precise.  What's more, the theory has been 
experimentally confirmed to an extremely high degree of accuracy--in fact, as 
I understand it, it's by far the best-confirmed theory by experiment of all 
physics.

So quantum theory seems to tell us that the two "alternatives"--cat alive, 
cat dead--both have equal claim to "reality".  They're both given equal 
treatment, and both are required to develop the further time-evolution of the 
system, or of any other system with which it interacts.  Quantum theory does 
not decide which outcome "actually happens", because, in a strong sense, 
*both are equally true*.

The paradox results when one reflects that we never actually see a large-
scale, macroscopic event in this strange "superposition" of states.  When we 
open the box, we *always* find that the cat is either alive, or dead, but we 
*never* see a cat that is half-alive and half-dead (or more appropriately, we 
never see a cat that is *both* alive and dead at the same time). (This result 
is often referred to as "the collapse of the wavefunction"--the quantum 
superposition of states seems to collapse and choose *one* alternative over 
the others.) We never register on our detector that the radioactive particle 
has *both* decayed and not decayed.  It's always either one or the other. Why 
is this? 

[To digress a bit, it is precisely *here* that probability enters into the 
picture in a more complete understanding of quantum theory and its 
relationship with large-scale events.  We can predict that a certain 
percentage of the time, the particle will decay to trigger a macroscopic 
event, and the remainder of the time it will not.  The proportion can be 
predicted to a high degree of accuracy, while at the same time the result of 
any *one* experiment is wholly uncertain. But this has to do with events on a 
*macroscopic* level, e.g. opening the box to examine the cat, or listening 
for the audible click of a Geiger counter.]

There is really nothing in the current understanding of quantum theory, or in 
any area of physics, that explains this fundamental fact of observation.  All 
attempts at explanation are speculative, and more or less philosophical or 
metaphysical. One school of thought asserts that it is *awareness* of the 
event that prompts the collapse of the wavefunction into one or the other 
alternative.  Until the experimenter opens the box to check on the cat, it is 
neither alive nor dead, but rather the system evolves happily in its quantum 
superposition of states waiting until the last moment to decide what to do.  
The details of how "consciousness" prompts the wavefunction to collapse, or 
even what counts in this scheme as awareness, are totally obscure.  

If followed to its logical conclusion, this argument leads to scenarios that 
are at least as distasteful as the original problem. Suppose *you* look in 
the box, while I'm in the other room.  Now you and your measurements can be 
considered to be a part of the quantum system that includes the box, the cat, 
the detector and the radioactive particle.  This system is, from *my* 
perspective, still evolving according to quantum laws.  Suppose you write 
down your results and publish them, archive them in a library, future 
generations of scientists study the historical record of the event; but until 
I become aware of or investigate the results myself, this entire system has 
not yet chosen "cat alive" or "cat dead", and so it is at the very moment I 
look up your paper in the library that the wavefunction collapses. Until that 
moment, your journal article reads *both* "the cat lived" *and* "the cat 
died", even though the actual experiment happened many years ago!  Now this 
scenario is *logically* acceptable, but what have we gained by such an 
explanation?

Another interpretation, known as the Copenhagen school of thought, asserts 
that the wavefunction *does not collapse* at all.  At each juncture, at each 
point in the time-evolution where a "choice" is to be made (in our example: 
does the cat die, or does it live?), there is a bifurcation, a split, and 
each alternative evolves on its own from that point forward with no further 
interference from the alternative possibility.  There is one path of 
development in which the cat lives and another in which the cat dies.  These 
two paths basically constitute a scheme in which the single universe in which 
the experiment is performed, *splits* into two alternative universes, one with 
a dead cat and one with the cat alive.  This branching-off happens *every 
time* a quantum event of this type would result in a superposition of states, 
and each universe from then on evolves in "parallel", with no interaction 
whatsoever between them.  This is popularly known as the "many worlds" 
interpretation of quantum theory.

Again, this interpretation doesn't really solve very much.  Since the entire 
universe is supposed to split whenever a "quantum decision" is made, you and 
I must also exist in these many universes simultaneously.  There is one 
universe in which you observe that the cat has died, and another in which you 
find the cat is alive.  Why, then, are we only aware of one of these 
alternatives, and not of all of them at once? Why is it that we all agree, 
and are all aware of the same universe? And why this particular universe, and 
not any (all) of the others?  There is another problem with this solution, 
which is why it's referred to as an *interpretation* and not a theory: there 
are no observable consequences whatsoever to this scheme; that is, it cannot 
be confirmed or disconfirmed by experiment, so it cannot properly be 
considered as a scientific explanation at all.

It is this mysterious "collapse of the wave function" that interests Penrose 
in his "second book": is it real? Is it a physical event?  Penrose concludes 
that it is, and examines the uneasy relationship between two more-or-less 
distinct physical theories of the material world-- Einstein's general theory 
of relativity on the one hand, and quantum physics on the other--to seek a 
general outline of a physical theory to explain the collapse of the quantum 
wavefunction.

These two theories govern very different classes of phenomena in the material 
world; they more or less sit side-by-side, untouched the one by the other, 
each providing its own *incomplete* picture of physical events.  Einstein's 
general theory of relativity describes the structure of spacetime and 
explains the phenomena of gravitation as essentially geometrical features of 
the world. Gravity, the structure of empty space, and the presence of mass 
are all subsumed into a purely *formal* description that more or less 
explains physical events and features of the universe in terms of geometrical 
properties and attributes.  Quantum theory, on the other hand, describes 
interactions between very small "particles" that exchange small amounts of 
energy, and uses the complex mathematics of wave mechanics to develop the 
laws according to which the state of the material world changes over time.  
General relativity has almost nothing to say about the "small-scale" features 
of the world where quantum effects are found; and quantum theory has no 
explanation for gravitational effects--at the quantum scale, the curvature of 
spacetime described by general relativity is virtually nonexistent, and the 
force of gravity is so weak that there is no chance for it to act on the 
quantum level. And yet both theories are required to understand the universe 
on all the scales that we can observe physical events to occur.

This situation makes physicists very uneasy; the march of scientific 
understanding demands some sort of "unification", so that a single, 
comprehensive theory can coherently explain, at least in general terms, *all* 
physical events at scales both large and small.  In fact, this problem of 
unification looms very large at the edges of research; one might even say 
that it is *the* question now confronting modern physics.  If both general 
relativity and quantum physics describe (each incompletely) the same physical 
universe, then how can they be unified conceptually; in other words, *how* 
can they each explain the same universe?

Again, there is really no very convincing answer to this question.  Penrose 
postulates one possible form an answer might take, and this is, for me, the 
most provocative and interesting portion of his book.  Basically, Penrose 
points out that a quantum superposition of states of a given physical system 
can very easily result in the superposition of two fundamentally incompatible 
*gravitational spacetimes*, that is, two mutually inconsistent *geometries* 
of the world demanded by Einstein's general theory of relativity.  Penrose 
describes this state of affairs as "unstable", and it must find some sort of 
resolution, some sort of "way out".  This is what prompts the wavefunction to 
collapse, and one or the other alternative is the result.

It should be emphasized that Penrose is really speculating here; and yet the 
question of unification of quantum theory with general relativity and 
gravitation is such a pressing and fundamental one, that I find this idea 
really fascinating.  Penrose freely admits the speculative nature of his 
explanation, but presents some interesting experimental evidence that he says 
is in basic agreement with his hypothesis.  This "gravitationally induced" 
collapse of the wavefunction depends on the *degree* to which each 
alternative is incompatible with the other; when the gravitational energy 
involved is very small, a system may be able to exist in a quantum 
superposition for some time, whereas large gravitational differences 
precipitate a very rapid collapse into one result or the other.  Penrose 
works out some of the math involved in quantifying the difference in 
gravitational energy, and the time scales involved, and finds that it agrees 
relatively well with the experimental fact that quantum effects of 
superposition can actually be observed on the level of subatomic particles, 
atoms, and small molecules, but never at levels of, say, cats or human 
beings, or of planetary systems.  

At the large scale, the incompatibility of the alternative spacetime 
geometries is too great to be maintained in superposition, so it is always 
found that either the one or the other configuration has "precipitated" out 
of the quantum wavefunction.  At the small end of the scale, such 
inconsistencies are "confined"; their contradictory natures are in little
danger of "infecting" the larger system, so the superposition can persist 
for a considerable duration (several seconds, or even longer in some 
circumstances).  Thus the collapse of the wavefunction, when it occurs, is 
*real*; it is an objective fact and a feature of the real world. It does 
not depend on the "awareness" of an observer to collapse the wavefunction, or 
on the other hand relegated to an unreal status, an illusion dependent on the 
"many worlds" interpretation where the wavefunction persists by virtue of the 
universe splitting into every possible alternative billions of times every 
second.

Thus Penrose's proposed unification of general relativity and the physics of 
gravitation with quantum theory capitalizes on the fact that quantum effects 
become important when small differences of energy are concerned; he 
translates this into small differences of *gravitational energy*, and it is 
in this sense that he believes the yet-to-be-discovered theory of *quantum 
gravity* to be an essential ingredient in future theories of the material 
world, and in particular, it will be required in order to bring the study of 
consciousness under the umbrella of science.  Why is this?

Penrose's proposed explanation of the collapse of the wavefunction relies on 
the unstability of simultaneously superposed but incompatible spacetime 
geometries. The exact circumstances of the collapse into one or the other 
viable alternative is not fully determined; rather, it is expressed as a 
statistical likelihood that the function will collapse, and result in only 
one classically describable alternative or the other.  The larger the energy 
difference, the more rapidly this collapse will occur, but the *exact moment* 
is not predictable in advance.  In other words, it cannot be modeled by 
purely computational means. This is where Penrose finds an entrance in a 
classical model of the physical world for "noncomputational action" where 
these events are susceptible of a purely *physical* description but not of a 
*computational* one.  The portion of the classical material world that 
interests Penrose most is, not surprisingly, the physical activities of the 
human brain; and specifically the activities that result in the "phenomenon 
of consciousness" or awareness. His third "book" is concerned with the ways 
in which the small-scale structures of the human brain exploit this 
noncomputational quantum activity to ultimately evoke conscious awareness and 
understanding.

Penrose quickly disavows any arguments that would rely on quantum effects at 
the level of neuronal activities; although he points to recent evidence that 
individual neuron firings cannot be simply modeled as yes/no firing decisions 
or primitive logic gates, this is not what really interests him.  For Penrose 
it is irrelevant that neuron-level brain activity could, perhaps, be 
accurately modeled by a computer program or "neural network", because the 
really significant operations in the brain occur somewhere else: in the 
cytoskeleton of neurons and other cells in the brain, and in their role in 
overall brain function.

Penrose investigates some recent discoveries in neurobiology that reveal 
exceedingly complex structures that form a significant part of individual 
cells in the brain.  The cytoskeleton of each neuron forms what is 
essentially its entire outer structure and is its primary interface with 
other cells in the brain and their surrounding environment. (Actually, *all* 
eukaryotic cells have a complex cytoskeleton that contributes more or less 
significantly to the overall functioning of the cell and the larger 
structures that cells form--tissues, organs, systems and so on. For single-
celled organisms, the cytoskeleton can in a sense act as a nervous system by 
means of which an amoeba, say, can interact with its environment.)  The 
structure and function of the cytoskeletons of neurons in the brain is only 
now becoming understood, but Penrose points out some intriguing features--the 
cytoskeleton of neurons is the primary means by which they "communicate" 
through electrochemical signals.  Long, thin, hollow "microtubules" extend 
from the neuron to some distance and seems to be highly organized between 
neurons.  Following Penrose's account, these microtubules are filled with 
extremely pure water that is coherently organized, and which forms an 
environment in which effects of quantum superposition of states can be 
preserved across a significant distance and for a considerable time.  The 
relative isolation of these networks of microtubules from the rest of the 
environment of the brain, which exists by virtue of their structure and their 
"insulation" by this coherently organized blanket of water (which extends to 
some distance outward from the microtubules themselves) allows 
"noncomputable" physical events to be preserved through the brain so they 
eventually contribute significantly to overall brain function.

Penrose very rightly points out, by means of his discussion of the 
cytoskeletal features of neurons, and the complex processes that occur in and 
between the microtubules of the cytoskeletons, how very complex the 
biological and cellular basis of neurological activities is.  If the 
computational complexity of the brain is in any significant way determined by 
the sub-cellular processes occurring at the level of the microtubules in the 
cytoskeletons of neurons, then Penrose estimates that the human brain 
performs on the order of 10^27 "computational events" per second; whereas if 
the firing of an entire neuron itself constituted a computational event, then 
only about 10^14 operations per second are possible. This constitutes an 
increase in the computational ability of the human brain by a factor of 
10^13; in other words, taking cytoskeletal activity into account, the human 
brain may be able to perform up to *ten trillion times* the number of 
primitive operations than prior research had indicated was likely, focusing 
on the neuronal level as the appropriate "level of description".

But this is not the point of Penrose's discussion.  For Penrose, the 
difference between 10^14 and 10^27 computations per second makes no 
difference to the plausibility of the claim that consciousness has a 
computational basis, and can thus be simulated on a computer of sufficient 
complexity. A purely computational model of consciousness is impossible *in 
principle* because purely *noncomputational* activity is an essential 
ingredient of consciousness. This noncomputational activity is physically 
located in the microtubules that interconnect neurons with one another 
through their cytoskeletons; the neuron-level activity acts as a sort of 
macroscopic magnifier of quantum effects up to the level of cellular 
activity, and further upwards to larger-scale cognitive processes.

As a single provocative example from the field of medicine, Penrose digresses 
briefly on the still somewhat mysterious efficacy of general anesthesia.  
Penrose points out that many different, chemically unrelated substances seem 
to have the effect of completely suppressing conscious activity; he 
postulates that these different substances all rely on their common ability 
to disrupt the signals passed along the microtubules throughout neurons in 
the brain.  Because it is in the organization and interactions of these 
signals that the essential ingredients of consciousness are to be found, when 
their actions are disabled consciousness disappears while leaving purely 
automatic or "unconscious" (though not in the psychological sense) brain 
functioning unimpaired.

Penrose does not dwell on this bit of speculative medical theorising, but I 
believe it is significant because it reveals the general bias of Penrose's 
position towards the idea that consciousness and awareness is something above 
and beyond, and in a sense separable from, other human activities that are 
generally believed to involve consciousness in some form or other. For 
example, in the first part of his book Penrose makes a considerable effort to 
distinguish between human mathematical research and discovery, on the one 
hand, and awareness and understanding of the *meaning* of mathematical ideas, 
on the other.  For Penrose, a great deal (although in an important way, not 
all) of human mathematical knowledge could in principle be "programmed" into 
a computer so that this computer program could then proceed to generate new 
mathematical theorems and make discoveries similar to those accessible to a 
human mathematician.  

What this computer could *not* ever do, no matter how complicated, is to 
*understand* what it is asserting about mathematics, and to be *aware* of its 
"discoveries".  For Penrose, true awareness and understanding is something 
undivided and whole; it is not an emergent property of purely computational 
processes, but rather is something different in principle (although it may 
exist in varying degrees in, say, other mammals than human beings, and 
perhaps in a rudimentary way in lower forms of life as well), and therefore 
requires some essentially enlarged idea of what science considers to be 
relevant.

In other words, if we were to take the neuron-level model of brain 
functioning as sufficiently encompassing everything that the brain does to 
exhibit awareness, and try to simulate it on a computer, we might end up with 
something that models important aspects of "conscious behavior", but it would 
never be conscious.  It is important to understand, however, that Penrose 
asserts something stronger than this: no purely computational model of, say, 
the human brain, could ever *fully* model this conscious behavior.  There 
would always be important areas of activity that a human could engage in that 
a computer could not.  Penrose believes he can assert this because of what he 
claims Gödel's theorem tells us about the inherent limitations of a formal 
system (here, "formal system" can justifiably be read as "computational 
system") as opposed to a conscious brain, whose activity is in certain 
important respects, not computational. 

This idea shields him from critiques that can be leveled against the "Chinese 
Room" argument.  (In a nutshell, this argument against artificial 
intelligence says that even if one could create a simulation of conscious 
activity in all its aspects, it would still not be conscious because its 
mechanisms are all revealed to be carried out by brute force application of 
seemingly meaningless rules; there's no *understanding* built into the 
process at all, so consciousness can never emerge out of a mindless mass of 
rules.) Penrose says that without a noncomputational ingredient in the mix, 
the question of whether a computer that *behaves* as if it were conscious, is 
*actually* conscious or not never arises, because in principle the 
construction of such a computer is impossible.

For Penrose, one vital aspect in which human brains can excel where computers 
fail is in comprehending the type of reasoning that results in Gödel's 
theorem.  I won't rehash his entire argument, except in broad outline.  It 
basically relies on the idea that if our reasoning could be represented by a 
consistent formal system, then we would 1) be capable in principle of knowing 
both that it is consistent, and 2) that it in fact fully represents our 
reasoning.  Accepting these premises, Penrose invokes Gödel's theorems to 
provide a "Gödel statement" that we must accept to be true, but which cannot 
be demonstrated by the formal system that represents our mathematical 
understanding.  Since we *do* accept the truth of our Gödel statement, but 
the formal system that was supposed to represent our mathematical 
understanding cannot itself demonstrate that statement, this formal system 
cannot actually represent the whole of our mathematical understanding.

Penrose goes to considerable lengths to convince us of both 1) and 2) above, 
but all his arguments leave me pretty much unconvinced.  I'll leave the 
details of this criticism to the reviews referred to below.

Finally, I'd like to discourse a bit on the general rhetorical shape of the 
book.  The most disappointing thing about the arc of Penrose's discussion is 
that, even if one were to accept the necessity of "noncomputational activity" 
in evoking consciousness, he makes no effort whatsoever to elucidate the 
manner in which this could happen. There is no real search for "The Missing 
Science of Consciousness" in this book.  Penrose's "proof" that 
noncomputational activity *must* be involved in consciousness could be 
forgiven, and treated instead as an interesting "What if?" sort of 
discussion, except that Penrose just sort of peters out after a vaguely 
plausible (but very provocative) idea of where in the brain this sort of 
thing might happen.  Really, the effect that this has on the question of 
consciousness is for the reader to conclude something like, "Well, if we need 
something this wacky to explain consciousness, then perhaps consciousness 
really *can't* be explained by science, after all."

One is left with the distinct impression that Penrose is, ultimately, much 
less interested in saving a science of consciousness, than he is in saving 
consciousness from cognitive scientists, and in refuting some of the basic 
premises of AI research. So the fact that he fails ultimately even in his 
refutation leaves one with some very intriguing ideas about a possible future 
for a science of quantum gravity, some glancing allusions to current research 
in neurobiology, and an author with a chip on his shoulder.

Penrose doesn't even try to hide the fact that he's anti-AI in the sense in 
which all trends in AI research are alike.  The entire first part of the 
book, where he claims to show that consciousness cannot be a formal system, 
begins with this assertion and then proceeds to search for methods to show 
that it is true.  Along the way he litters the path with allusions to "robots 
whose intelligence will at first be equal to, but which will soon far 
outstrip, human intelligence", which seem to have no purpose but to cloud the 
issue with emotional appeals.  In fact, one of the concluding sections of the 
book is solely concerned with the *social dangers of technology* and of 
computers in particular: it takes the form of a cautionary tale in which evil 
programmers use a computer virus to rig a national election!  There is no 
explanation of how this digression bears on his argument, but its rhetorical 
purpose is clear.  Penrose basically ends his book by saying in so many 
words, by means of this fable, "We should *hope* that computer programs can 
never be conscious, because if they could, the implications are too dreadful 
to be imagined."  His computer virus story has no other conceivable purpose 
in this book.  And this sort of thing is really unworthy of such a great mind 
as that of Penrose. While he surely is one of the few great scientific minds 
in physics today, I believe that he's amply demonstrated that he's not really 
interested in contributing to any sort of a scientific understanding of 
consciousness, his protests to the contrary notwithstanding.  Instead Penrose 
seems to have made it his personal crusade to destroy the "strong" claims of 
AI.  Penrose should stick to mathematical physics.  I wish he'd write a book 
about *that*; I'm sure then I could really learn something.