A publication of the Foresight Institute
Modeling an assembler on a computer before trying to build one
seems a sensible idea. It's faster and cheaper, and it lets us
look beyond current manufacturing limitations. Of course, an
assembler might have millions of atoms. If we want to model such
a structure on a computer, we'd have to enter the coordinates of
those atoms. Many molecular modeling software packages use a
"point and click" interface to add atoms to a
structure. If we want to specify the location of each atom, we'd
have to press the mouse button millions of times...
This horrible image inspired the obvious thought: automate the problem. Write programs that generate the coordinates of all the atoms in the structure. If the program accepts a few parameters, then any one of an entire class of structures can be generated quickly and easily.
We've already written the first such program: a little more than 800 lines of C generates any member of a class of tubular structures. Conceptually, the tube is made simply by taking a flat rectangular sheet of diamond and bending it until the edges meet and can be bonded together. (This is a description, not a recipe for making the structure.) The length, radius, tube wall thickness, and the crystal surface and orientation can all be specified by the user. Crystal surfaces are usually specified by a triplet of integers, such as: 111, 110, 010, 322, etc. By entering a triplet, the nature of the surface of the tube wall can be specified. Finally, the rotational orientation of the surface with respect to the axis of the tube must be specified. Appropriate changes in this parameter can make the "grain" of the surface point along the axis, at right angles to the axis, or spiral down the length of the tube.
With a fast and easy method of generating tubular structures, it's easy to investigate many of the questions that naturally arise. For example, as the tube wall becomes thicker and thicker and the radius becomes smaller and smaller, the strain becomes greater and greater. Finally, when the strain is too great, bonds in the wall will rupture. How small a radius and how thick a wall can we choose before the tube becomes unstable? Even if a tube does not spontaneously break, how much external force can it tolerate? It's quite straightforward to analyze these issues using the molecular mechanics techniques in PolyGraf, a molecular modeling software package produced by Molecular Simulations, Inc.. These methods include energy minimization using any one of several empirically derived forcefields (such as MM2), molecular dynamics, and analysis of strain by examination of bond length and bond angle data from the minimized structure, etc.
Given two tubes of differing radii, we can insert the tube of smaller radius into the tube of larger radius. This creates a simple bearing, for the outer tube can rotate with respect to the inner tube. What surface is best in such a bearing: the 001, the 110, the 111? Some other? With what orientation? How different should the radii be? If we grip the two tubes and try to pull them apart, how much force must we apply? Again, using molecular mechanics it is not too difficult to get reasonable answers to these questions.
Figure 1. A 2,808-atom steric-contact sleeve bearing, based on concentric cylinders of strained diamond with modified (100) surfaces (oxygen and sulfur termination). Energy barriers to rotation are small compared to thermal vibrational energies. Designed by E. Drexler at Xerox PARC using Polygraf software and a computer-aided design tool under development by R. Merkle.
Figure 2. Same as Fig. 1, in an exploded view. Interlocking ridges on the shaft and sleeve give large strength and stiffness in resisting axial displacements at the sliding interface.
If the tube is being used as a component in a positioning device (perhaps a nano-arm for an assembler), we would like to know its stiffness. How far will it bend under the influence of thermal noise? What changes can we make to improve the stiffness? If we push on something with our nano-arm, how much will it bend?
While tubular structures are quite interesting, they are only one of many components in an assembler, and this program is only the first of many other similar programs. Of course, at some point we'll want to design a language that can be used to describe the different kinds of nano-components, and a compiler to turn descriptions in that language into actual atomic coordinates, but that's a future project.
Lakshmikantan Balasubramaniam (usually known as Bala, it's much easier to pronounce!) has joined us at PARC for the summer to work on these and other problems that arise in molecular manufacturing. Bala is a graduate student in the mechanical engineering department at MIT specializing in computer aided mechanical design.
Dr. Merkle's interests range from neurophysiology to computer security; he heads the new Computational Nanotechnology Project at Xerox Palo Alto Research Center.
|Foresight Update 12 - Table of Contents|
One of the most talked about and reviewed books of recent
years is Roger Penrose's The Emperor's New Mind
(1989, Oxford Univ. Press). So why publish yet another review?
Because the popularity of a book whose jacket declares it
"dares to suggest that the emperors of strong AI have no
clothes" has apparently given some casual observers the
impression that Penrose has dealt a death-blow to artificial
intelligence (AI). This is not even close to being right.
Being read is not the same as being believed. Most reviewers have praised the book as original, well-written, thought-provoking, etc., and then gone on to take issue with one or more of Penrose's main theses.
Penrose seems unfamiliar with the existing literature in cognitive science, philosophy of mind, and AI. The handful of reviewers who agree with Penrose don't seem to have paid much attention to his specific arguments--they always thought AI was bogus. See, for example, the 37 reviews in Behavioral and Brain Sciences (BBS), Dec. 1990, V13, pp.643-705.
But aren't most of these reviewers fuzzy-headed philosophers of mind and computer science researchers, while Penrose is a good, solid, world-renowned mathematical physicist? Penrose himself repeatedly emphasizes the speculative nature of his musings, warning that "my point of view is an unconventional one among physicists and is consequently one which is unlikely to be adopted, at present, by computer scientists or physiologists."
But if appeals to consensus and authority won't persuade you, let's get down to details. First let me agree with most reviewers that this is a great book. It makes the reader think. Most of the middle of the book is a wonderful tutorial on various subjects, mostly in physics. If you understand Penrose's discussions of entropy, for example, you can easily see why cosmological theories of "inflation" cannot deliver what their proponents claim. Wrapped around these tutorials, however, and mostly confined to the introduction and conclusion, is a sloppier collection of arguments for what is clearly a deeply-felt opinion: "Yet beneath this technicality is the feeling that it is indeed 'obvious' that the conscious mind cannot work like a computer, even though much of what is actually involved in mental activity might do so. This is the kind of obviousness that a child can see..."
Penrose grants that we may be able to artificially construct conscious intelligences, and "such objects could succeed in actually superseding human beings." But he thinks "algorithmic computers are doomed to subservience."
Penrose's argument is two-fold. First he tries to show why human-type intelligence could not be implemented by any Turing-machine equivalent computer (ordinary, parallel, neural, or otherwise). Then he tries to show how it could be physically possible that the human mind is not algorithmic in this sense.
Penrose gives many reasons why he is uncomfortable with computer-based AI. He is concerned about "the 'paradox' of teleportation" whereby copies could be made of people, and thinks "that Searle's [Chinese-Room] argument has considerable force to it, even if it is not altogether conclusive." He also finds it "very difficult to believe ... some kind of natural selection process being effective for producing [even] approximately valid algorithms" since "the slightest 'mutation' of an algorithm ... would tend to render it totally useless."
These are familiar objections that have been answered quite adequately, in my opinion. But the anti-AI argument that stands out to Penrose as "as blatant a reductio ad absurdum as we can hope to achieve, short of an actual mathematical proof!" turns out be a variation on John Lucas's much-criticized "Gödel" argument, offered in 1961. A mathematician often makes judgments about what mathematical statements are true. If he or she is not more powerful than a computer, then in principle one could write a (very complex) computer program that exactly duplicated his or her behavior. But any program that infers mathematical statements can infer no more than can be proved within an equivalent formal system of mathematical axioms and rules of inference, and by a famous result of Gödel, there is at least one true statement that such an axiom system cannot prove to be true. "Nevertheless we can (in principle) see that P_k(k) is actually true! This would seem to provide him with a contradiction, since he ought to be able to see that also." This argument won't fly if the set of axioms to which the human mathematician is formally equivalent is too complex for the human to understand. So Penrose claims that can't be because "this flies in the face of what mathematics is all about! ... each step [in a math proof] can be reduced to something simple and obvious ... when we comprehend them [proofs], their truth is clear and agreed by all."
And to reviewers' criticisms that mathematicians are better described as approximate and heuristic algorithms, Penrose responds (in BBS) that this won't explain the fact that "the mathematical community as a whole makes extraordinarily few" mistakes.
These are amazing claims, which Penrose hardly bothers to defend. Reviewers knowledgeable about Gödel's work, however, have simply pointed out that an axiom system can infer that if its axioms are self-consistent, then its Gödel sentence is true. An axiom system just can't determine its own self-consistency. But then neither can human mathematicians know whether the axioms they explicitly favor (much less the axioms they are formally equivalent to) are self-consistent. Cantor and Frege's proposed axioms of set theory turned out to be inconsistent, and this sort of thing will undoubtedly happen again. Apparently, Penrose didn't do his homework on the Gödel issue.
Penrose raises one issue that I do think deserves closer scrutiny, namely exactly what sort of "motion" an algorithm would have to be put into before it could subjectively "feel" and be conscious. If we wrote down an algorithm equivalent to Einstein in a book, "would the book-Einstein remain completely self-aware even if it were never examined or disturbed by anyone?" This issue has been raised before, and is not particularly threatening to computer-based AI, but is interesting nonetheless.
The other half of Penrose's arguments is a speculative "germ of an idea" about how it could be that people are devices which can compute things that a Turing machine can't, even though all known physical laws do not allow the construction of such devices, and even though "Most physicists would claim that the fundamental laws operative at the scale of a human brain are indeed all perfectly well known." One usually describes the evolution of a quantum system by two processes, U and R, acting on quantum states. Usually the unitary process U is in control, but on occasion (when, exactly, is not very well understood) a reduction process R intervenes.
Penrose is (refreshingly) a firm realist about quantum mechanics, believing both these processes and the states they act on are quite real and independent of observers. Penrose speculates that this view will have to corrected somewhat when quantum mechanics is integrated with general relativity. Penrose hopes that a quantum gravity R will be exactly non-deterministic enough to counterbalance the merging of state trajectories due to the evaporation of black holes, and just time-asymmetric enough to satisfy his thermodynamics-explaining conjecture that the Weyl curvature approaches zero at past singularities. This R will happen when the difference between components of a quantum superposition approaches a one virtual graviton level, so as to avoid awkward superpositions of differently shaped space-times. We will need a radically new concept of space-time to deal with simultaneity problems of an objective reduction law. Oh, and one other thing: At the "borderline which interpolates between U and R" "some new procedure takes over." "This new procedure would contain an essentially non-algorithmic element" so that "the future would not be computable from the present, even though it might be determined by it."
Now, general relativity doesn't affect life on Earth much, and its effects are very hard to discern even in astrophysical contexts. Quantum gravity should be a small correction to general relativity, revealing itself in even more unusual circumstances, such as distance scales of 10-35 cm. Nevertheless, Penrose speculates that this new quantum gravity U/R interpolation procedure is how nature assembles the recently discovered quasi-crystals since "the general tiling problem ... is one without an algorithmic solution" because of non-local constraints.
Similarly "somewhere deep in the brain, [as yet unknown] cells are to be found of single quantum sensitivity" so that "synapses becoming activated or de-activated through the growth or contraction of dendritic spines ... could be governed by something like the processes involved in quasicrystal growth," simultaneously trying out "vast numbers [of possible alternative arrangements], all superposed in complex linear superposition." All this somehow affects only our conscious mind, leaving our unconscious to compute algorithmically, and quantum non-locality explains "the 'oneness' of consciousness." "True intelligence requires consciousness" and the conscious mind (of mathematicians) has "a direct route to truth, the consciousness of each being in a position to perceive mathematical truths directly."
Penrose believes "mathematical ideas have an existence of their own, and inhabit an ideal Platonic world, which is accessible via the intellect only." "The mind is always capable of this direct contact. But only a little may come through at a time." This contact is what explains "the deep underlying reason for the accord between mathematics and physics." I am not making this up. If you are not familiar with modern physics or physiology, I do not know how to convey to you just how unlikely Penrose's scenario is, except to offer 100 to 1 odds against it. Yes, it is logically possible, but only if everything goes just Penrose's way.
A more popular quantum realist position than Penrose's (though quantum realists are still a minority) is the "many-worlds" view, which says there is only the process U and that R is an illusion. (I'd bet this has at least a 1 in 20 chance of being the closest we have to right.) Penrose rejects this view because "a theory of consciousness would be needed before the many-worlds view can be squared with what one actually observes." That is, we don't know how to test it yet.
In BBS, Penrose expressed surprise at how many AI reviewers support the many-worlds theory, and makes a snide comment about trusting "that their reasons for believing in the validity of the AI programme are more soundly based." Yet the review in Science by a physicist also supported many-worlds. Moreover, many-worlds is especially popular among quantum gravity researchers, and one of Penrose's main plausibility arguments comes from a demonstration by Deutsch that with many-worlds a 'quantum computer,' though still algorithmic, could get a large speed-up relative to an ordinary computer.
Martin Gardner calls Penrose's book "the most powerful attack yet written on strong AI." If so, AI must be doing pretty well. If the book were condensed to a paper by deleting the excellent tutorials, and if Penrose's name weren't on it, I doubt if the paper would have been much noticed, or even published.
Regardless of your opinions about the appropriateness of current AI research strategies, or about the length of the road ahead, Penrose's book offers no substantial reasons to change your views about the long-term possibility of computer-based AI. The fact that many casual observers have been misled about this is yet another indication of the inadequacy of our current methods of forming and communicating scientific consensus.
Robin Hanson (firstname.lastname@example.org) does AI research at NASA Ames, has degrees in physics and philosophy of science, and on the side studies alternative methods for scientific consensus.
|Foresight Update 12 - Table of Contents|
The prospects for using molecular manufacturing techniques to
benefit the environment will be explored at the Ecotech
conference, a nonprofit project of the Tides Foundation to be
held November 14-17 in Monterey, California. Eric Drexler will
speak on how molecular technologies could both reduce
environmental damage from new production and clean up
already-existing wastes. Following the talk the Foresight
Institute will hold a workshop to explore participants' ideas on
what can and should be done. In addition, Foresight will be on
hand in the "marketplace of ideas" section of the
conference to discuss how nanotechnology-based tools and products
can aid environmental restoration. In addition to educating
attendees, we hope to build broader contacts with experienced
environmental activists sharing an interest in the potential of
Nanotechnology is just a part of this large meeting devoted to encouraging companies to make environmental issues an integral part of their overall business strategies. The meeting will help managers, strategists, planners, communicators, educators, lawyers, legislators, investors, scientists, and entrepreneurs understand how they can participate in solving the tough challenges that lie ahead.
An intriguing mix of speakers has been lined up, some of whom you may recognize as friends of Foresight. A few of the better-known speakers are entrepreneur/author Paul Hawken; Peter Schwartz, president of Global Business Network (which cosponsored the First Foresight Conference on Nanotechnology); Paul Saffo, research fellow at the Institute of the Future; Whole Earth Ecolog editor J. Baldwin; and scientist/author Amory Lovins.
Conference attendance is limited to 450 registrants. Registration fees are $500 per participant and $250 for representatives of nonprofit organizations. For more information, contact Mike Whitacre at 619-259-5110.
From Foresight Update 12, originally published 1 August 1991.
Foresight thanks Dave Kilbridge for converting Update 12 to html for this web page.