Metamagical Themas, page 62
It turns it into a problem of personal identity, no less perplexing than the problem it replaces.
One can fall even more deeply into the pit of paradox when one realizes that there are branches of this one gigantically branching universal wave function on which there is no Werner Heisenberg, no Max Planck, no Albert Einstein, branches on which there is no evidence for quantum mechanics whatsoever, branches on which there is no uncertainty principle or many-worlds interpretation of quantum mechanics. There are branches on which the Borges story did not get written, branches in which this column did not get written. There is even a branch in which this entire column got written just as you see it here, except for one noun which was replaced by its exact antonym, at the column's very beginning.
Post Scriptum.
Quantum particles: the dreams that stuff is made of.
David Moser
If this was your introduction to the weirdness of quantum mechanics (which I doubt), then may I say how delighted I am to have been your guide. But in that case, I also must say that you really deserve a more complete introduction. This article was aimed mostly at people who already have at least a nodding acquaintance with quantum phenomena. The Feynman books alluded to in the article are ideal introductions. There are other books that purport to explain quantum mechanics to novices, and in some cases they may do a fairly good job of it, but some of them have the serious drawback of trying to link quantum-mechanical reality with Eastern mysticism, a connection I find superficial and misleading. I cannot fault people who wish to make some observations about the worldview of ancient Buddhists and to point out that a few statements written thousands of years ago can, if very liberally interpreted, be taken to say things that are not inconsistent with discoveries of modern physics, but to claim that "Western science is only now catching up with the ancient wisdom of the East", as most of those authors do (and in roughly those words), is, in my view, both silly and anti-intellectual.
I call it "anti-intellectual" because most Western people infatuated with Eastern mysticism hold a grudge against the encroachment of science on territory they consider beyond science. This attitude may be a holdover from the bitterly anti-scientific, anti-intellectual mood that gripped the United States during much of the Viet Nam War era. Those people have some sort of axe to grind, perhaps subconsciously; they want to see science "put in its place". Curiously, many of them are scientists themselves and revel in a kind of self-deprecation, thinking that they are lifting themselves up to transcendent heights and seeing things from a "higher plane of enlightenment" than science affords. Usually, at that point, their prose abruptly changes mood, moving from precise terms to mushy, vague, poetic terms (such as "mushy", "vague", and "poetic"). Don't you just hate that sort of thing?
These are the sorts of people who propagate misinformation about the discoveries of modern physics (such as the pseudo-uncertainty principle). They encourage people to think that any wild theory explaining any mystery (or alleged mystery) might well be correct, as long as it uses voguish technical terms from physics-terms like "tachyon", "Bell's inequality", "EPR paradox", "gravitational waves", and so on. A typical abuser of physics in this way is Arthur Koestler; in his book The Roots of Coincidence, he purports to explain "psi phenomena" in terms of some five-dimensional theory of particle physics that includes a host of hypothetical particles called "psitrons".
To me, a very troubling aspect of an "explanation" such as this (which, actually, Koestler didn't invent himself but borrowed from a physicist named Adrian Dobbs) is that very similar explanations are used by physicists .themselves-not so often of "psi phenomena", but of currently unexplained real phenomena in particle physics. When I was a graduate student in particle physics, quite a number of years ago, I read paper after paper in which not only new particles were invoked to explain some observation, but new families of particles were routinely postulated. As a matter of fact, one of those papers was the straw that broke the camel's back, as far as I was concerned. In that three-author paper, the authors had the audacity to invent some totally off-the-wall superfamily of particles that consisted of a large number of families, each containing quite a few particles on its own. As I recall, there were something like 140 new particles introduced in one fell swoop-and, mind you, this was done merely to explain some rather small discrepancies between things measured and things predicted by previous theories. A far cry from the days when it was a highly daring step to introduce even one new particle! It was at that point that I decided I should bow out of that branch of theoretical physics.
* * *
I am not really trying to castigate the whole field of particle physics, because all I learned for sure from my long, gruelling, and ultimately broken engagement with that field was that I personally was not cut out to be a particle physicist. However, I did learn one disillusioning thing about science in general, and that is that large segments of it-including, very often, the most forbidding and technically prickly papers-are just as nonsensical and empty as the pseudo-scientific papers that try to shore up "psi phenomena", "remote viewing", "telekinesis", or the like. (Is it reasonable for me to continue using quotation marks around those words? I think so. I don't like using words in such a way that I help to lend them legitimacy when I think there is nothing behind them.) Bad science permeates good science the way that gristle runs through meat (a "meataphor" exploited in a different context in Chapter 21).
I am afraid that this is an example of an inevitable phenomenon: If you are throwing darts and want not only to hit the bull's-eye every time but also to cover the entire bull's-eye evenly, so that you are equally likely to hit any point inside the bull's-eye but totally unlikely to go outside of it, then you are dreaming a pipe dream! You have to pay in some way for the privilege of filling up that inner circle-and you pay either by sometimes overflowing the boundaries of the bull's-eye (being too loose, so to speak), or by covering it unevenly, having a high concentration in the middle of the bull's-eye and a low concentration near its edges (being too tight or controlled). In science, this translates to the trade-off between being too speculative and too cautious. It is impossible for all the papers in a field to be both right and significant. Either many will be wrong or many will be trivial. The former corresponds, obviously, to throwing outside the circle, and the latter, a little less obviously, to covering it fully but unevenly. This inevitable trade-off is very much like that spoken of in Chapter 13, where in trying to produce all -the truths expressible in a formal system or all the members of a semantic category, you wind up with either an incomplete system or an inconsistent system.
I guess this makes me sound somewhat cynical about science. But I would make similar noises about human endeavors of any sort that involve skill. For instance, not all the letters I receive from people who have read things I've written hit the bull's-eye; some of them are the cat's meow, but a larger number are either old hat, off base, full of hot air, or some combination thereof. So if I want to get some good letters, I have no choice but to be willing to wade through a bunch of bad ones, too. And, regretfully, I must say that this law applies just as much to my own output: not all of it can be of the same caliber. If it's all correct, then much of it will be mundane; and if I regularly dare to go far beyond the mundane, then some of it will wind up being wrong.
Some people choose to see trade-offs such as these as more examples of a kind of "uncertainty principle": you can't have both total correctness and total novelty. You must take your pick. This "either-or" quality, however, has very little to do with the quantum-mechanical substrate of our world. It just has to do with statistical phenomena in general.
* * *
I would like to say something about the alienness of quantum-mechanical reality. It is no accident, I would maintain, that quantum mechanics is so wildly counterintuitive. Part of the nature of explanation is that it must eventually hit some point where further probing only increases opacity rather than decreasing it. Consider the problem of understanding the nature of solids. You might wonder where solidity comes from. What if someone said to you, "The ultimate basis of this brick's solidity is that it is composed of a stupendous number of eensy-weensy bricklike objects that themselves are rock-solid"? You might be interested to learn that bricks are composed of micro-bricks, but the initial question-"What accounts for solidity?"-has been thoroughly begged. What we ultimately want is for solidity to vanish, to dissolve, to disintegrate into some totally different kind of phenomenon with which we have no experience. Only then, when we have reached some completely novel, alien level will we feel that we have really made progress in explaining the top-level phenomenon.
That's the way it is with quantum-mechanical reality. It is truly alien to our minds. Who can fathom the fact that light-that most familiar of daily phenomena-is composed of incredible numbers of indescribably minuscule "particles" with zero mass, particles that recede from you at the same speed no matter how fast you run after them, particles that produce interference patterns with each other, particles that carry angular momentum and that bend in a gravitational field? And I have barely scratched the surface of the nature of photons! I like to summarize this general phenomenon in the phrase "Greenness disintegrates." It's a way of saying that no explanation of macroscopic X-ness can get away with saying that it is a result of microscopic X-ness ("just the same, only smaller"); macroscopic greenness, solidity, elasticity-X-ness, in short-must, at some level, disintegrate into something very, very different.
I first saw this thought expressed in the stimulating book Patterns of Discovery by Norwood Russell Hanson. Hanson attributes it to a number of thinkers, such as Isaac Newton, who wrote, in his famous work Opticks: "The parts of all homogeneal hard Bodies which fully touch one another, stick together very strongly. And for explaining how this may be, some have invented hooked Atoms, which is begging the Question." Hanson also quotes James Clerk Maxwell (from an article entitled "Atom"): "We may indeed suppose the atom elastic, but this is to endow it with the very property for the explanation of which .... the atomic constitution was originally assumed." Finally, here is a quote Hanson provides from Werner Heisenberg himself: "If atoms are really to explain the origin of color and smell of visible material bodies, then they cannot possess properties like color and smell." So, although it is not an original thought, it is useful to bear in mind that greenness disintegrates.
* * *
One of the most beautiful features of the quantum-mechanical description of reality is how a bridge is erected between the microscopic and the macroscopic. The nature of that bridge is characterized by the correspondence principle, which states:
In the limit of large sizes, quantum-mechanical phenomena must look indistinguishable from their classical counterparts.
This can be converted into a more mathematical statement, as follows:
In the limit of large quantum numbers, quantum-mechanical equations must reproduce their classical counterparts.
A physicist does not have to work to make an equation describing quantum phenomena obey this principle; if the equation is correct, it will obey it automatically. However, a physicist cannot always be sure that a proposed equation is correct. Therefore, the correspondence principle provides a very useful check on any proposed equation-for if it fails to yield the familiar classical equation in the limit of large sizes (or more accurately, large quantum numbers), it is surely wrong. Of course, merely passing this test is no guarantee that an equation is right, but it is a confirming piece of evidence.
Quantum-mechanical phenomena are characterized by "quantum numbers", which are always integers. When those integers are small-less than 5 or so-you have quintessentially quantum phenomena. But when you plug fairly large values such as 20 into the equations, you get behavior that floats midway between the quantum style and the classical style. And when ou take the limit of infinitely large values, you should get back the familiar old equations from the pre-quantum era: such things as Newton's laws of motion, for instance.
A striking example of this idea is furnished by so-called "Rydberg atoms", highly excited atoms whose outermost electrons have very large quantum numbers, and which are consequently tethered so loosely to their central nucleus that their orbits begin to be somewhat less "cloud-like" (i.e., less quantum-mechanical), and more like the familiar planetary orbits that electrons used to follow, back in the short-lived "semiclassical" era of physics, after Ernest Rutherford's discovery of nuclei, but before Schrödinger and Heisenberg. These bridges between the alien world and the familiar world help provide the intuitions necessary for macroscopic people to imagine how jolly giant greenness could emerge from murky, unfathomable microdepths. .
Section V Spirit and Substrate
The world has traditionally been divided into the animate and the inanimate. Inanimate things do not have feelings or wills of their own, and can therefore be smashed, burned, or harnessed by animate ones without the animate ones having to feel guilty. This borderline, so long taken for granted by people, is gradually becoming blurrier with the advent of computers, especially as programs acquire more and more flexibility-and with that flexibility, a seeming mentality or personality. How and when could mind and emotions-surely the essence of the animate-emerge from complex inanimate substrates? What does it take to make spirit out of pure matter pattern? A number of recent artificial-intelligence programs have been touted as "thinking". Yet no one who looked closely could fail to see that there remains a huge gap between human self-aware fluidity and such programs. Even the best of them is still relatively rigid and unaware of anything, let alone itself. But where is the borderline between the highest inanimate flexibility and the lowest animate sentience? When does a system or organism have the right to call itself "I", and to be called "you" by us? Will we be able to recognize systems deserving of our respect when they come along, or will we abuse them? Will such systems have as much free will as we don't? These and other philosophically motivated questions about mind and mechanism, free will and determinism, randomness and rule-following, are examined in the following six chapters.
21 Review of Alan Turing: The Enigma
November, 1983
AN true intelligence be embodied in any sort of substrate-organic, electronic, or otherwise? Is mind more than pattern? How can we distinguish between a genuine mind and a clever facade? Is free will compatible with a materialist, mechanistic view of living beings? Is there a contradiction in the notion of rule-bound creativity? Do our emotions and intellects belong to separate compartments of our selves? Could machines have emotions? Could machines be enchanted by ideas, by le, by other machines? Could machines be attracted to each other, fall in love? What would be the social norms for machines in love? Would there and improper types of machine love affairs? Could a machine be frustrated and suffer? Could a frustrated machine release its pent-up feelings by going outdoors and self propelling ten miles? Could a machine learn to enjoy the sweet pain of marathon running? Could a machine with a seeming zest for life destroy itself purposefully one day, planning the episode so as to fool its mother machine into "thinking" (which of machines cannot do) that it had perished by accident?
These are the sorts of questions that burned in Alan Turing's brain, and, taken at another level, they reveal highlights of Turing's troubled life. It would require someone who shares much with Turing to plumb his story deeply enough to do it justice, and Andrew Hodges, a young British writer with a doctorate in mathematics, has wonderfully succeeded in doing so. His 500 page biography of Turing painstakingly put together from innumerable sources, including conversations with scores of people who knew Turing at various stages of his life, provides as vivid a picture as one hope of a most complex and intriguing individual. And it's about time,
for not only was Turing a very significant person in the science of this century, but his fascinating and difficult life illustrates serious problems that yet has not yet grappled with successfully.
Hedges' rich and engrossing portrait is not the first book about Turing, since his mother, Sara Turing, wrote a sketchy memoir a few years after her son's death, which presents an image of Turing as a lovable, eccentric boy of a man, filled with the joy of ideas and driven by an insatiable curiosity about questions concerning mind and life and mechanism. Hodges goes far more deeply into Turing's mind, body, and soul than Sara Turing ever dared, for she wore conventional blinders and did not want to see how poorly her son fit into the standard molds of British society. Alan Turing was homosexual, a fact that he took no particular pains to hide, especially as he grew older. And for a boy growing up in the 1920's and for a man in the next few decades, being homosexual-especially if one was British and belonged to the upper classes-was an unmentionable, terrible, and mysterious affliction.
Alan Turing, an atheist, homosexual, eccentric English mathematician, was in large part responsible not only for the concept of computers, incisive theorems about their powers, and a clear vision of computer minds, but also for the cracking of German ciphers during World War 11. It is fair to say that we owe much to Alan Turing for the fact that we are not under Nazi rule today. And yet this salient figure in world history has remained, as the book's subtitle says, an enigma.
Turing was born in London in 1912 of relatively well-to-do parents in the civil service in India. Not long after his birth, his father returned to India, followed by his mother, and they spent the next few years there, leaving young Alan in England. Then they decided to return closer to England, and for a time lived in France, which gave Alan the opportunity to take school vacations there and learn French. As a boy, he was inquisitive and humorously inventive but definitely not a child prodigy. At age thirteen, he was sent off to a boys' private boarding school called Sherborne, in the west of England. He made quite a hit his first day, for he arrived on bicycle, having pedaled the 60 miles from Southampton, where the ferry from France had left him on a day of general strikes and no trains. However, as the weeks passed, his hero status declined as he revealed himself to be a rather untidy pupil prone to getting ink all over himself, and one who did not distinguish himself in most of his classes. Alan was a solitary boy and his first venture into serious friendship came to an unexpected and tragic ending, when his friend and idol, Christopher Morcom, succumbed to bovine tuberculosis.
