ALAN MATHISON TURING: THE MAKER OF OUR AGE
By Justin Leiber (this paper was written for the Delphian
Society and conforms to their question/answer
In his short life, Alan Turing (1912-1954) made foundational contributions to philosophy, mathematics, biology, artificial intelligence, and computer science. He, as much as anyone, invented the digital electronic computer. From September, 1939 much of his work on computation was war-driven and brutally practical. He developed high speed computing devices needed to decipher German Enigma Machine messages to and from U-boats, countering the most serious threat by far to Britain's survival during World War Two. Yet few people have an image of him.
Because of official secrecy, his war time exploits were unknown until the
1980s. By that time some of his inventions were so well absorbed that they no
longer seemed connected to a real human being. Literature buffs read classics.
Scientists just cite them. For example, Turing's 1936 paper, "On
Computable Numbers," was almost instantly recognized to be the most
important theoretical paper ever written on computation. Soon it was absorbed
into every textbook. And soon many mathematicians, engineers, and computer
scientists came to write of "turing machines" and "universal
turing machines" almost or completely forgetting that there was
an Alan Turing. Almost the same thing happened with his breezy and very
readable 1950 paper, "Computing Machinery and Intelligence." From it
scientists and philosophers extracted the goal of writing
"intelligent" computer programs good enough to pass the "turing
test" for simulating human intelligence. While some computer scientists
boasted that they would program a "passer" within a decade, they have
not come close after five decades.
On the other hand, some of Turing's work was so far ahead of his time that
it earned credit only in retrospect. His last published paper (1952)
anticipated the most important new approach in developmental biology. But it
wasn't until the late 1970s that scientists began to refer to "turing
structures"! Similarly, Turing suggested several other ways, aside from
programming, that might be used to simulate human intelligence. When he did so,
he anticipated approaches that have been ballyhooed in the 1980s and 1990s.
Personally, Alan Turing was amiable, eccentric, and modest. He didn't put
his name on any of his discoveries. The world did that. At one point during the
war, he couldn't find his belt and went to work, as director of the Enigma
decrypting effort, with string holding his pants up. He didn't get around to
replacing the string for weeks. He was also a marathon runner and might well
have represented Britain in the 1948 Olympic Games if he had not damaged his
knee in the run ups.
OPEN DISCUSSION QUESTION NUMBER ONE
WHAT WAS THE "ENIGMA MACHINE"? HOW DID TURING AND HIS
COLLEAGUES MANAGE TO DECODE THE U-BOAT MESSAGES?
I made this a trick question. I should have written "DECIPHER."
What's the difference between a code and a cipher? A code book gives you
parallel lists of words (the second list can also be nonsense letter
sequences). Your secret message is written in words from the first list and
then encoded by taking the parallel letters from the second list. The
people who get the message reverse the process by using their identical code
book. So in encoding "torpedo" might become "ygnp" and in
decoding become "torpedo" again. In practice, this system is slow. It
is also easily breakable if there are a lot of messages. So its use is rare in
modern war or business.
A cipher is different. It works on individual letters. When Julius Caesar
sent messages from Gaul back to Rome, he used a simple cipher. He would take
the first letter of his message and substitute the third letter down the
alphabet. So A would become D, B become E, etc. When he got to the bottom of
the alphabet he would circle back to the beginning, so X would become A, Y
become B, and so on. Back in Rome, his people would reverse the process by
going three letters up the alphabet. Except when they got to C, which would
become (you guessed it!) Z, B become Y, and A become V. From now on, think of the
alphabet in this circular way. Any cipher starts with the first letter of a
message, moves some number of letters around the alphabet and substitutes that
letter; then it repeats this for the next message letter, and so on. The
recipient then reverses this process.
Caesar's cipher may have baffled some Gauls but anyone who knew Latin and
little about ciphering could have broken it. In English, for example,
"t" and "e" occur most frequently. So you could make a
start by taking the two most common letters in the ciphered message. Then see
if moving around the alphabet by a simple rule like "move three around the
alphabet" would get you to "t" and "e." Of all the
letter sequences that are possible, very few are English, so you would soon
have the cipher key.
The Enigma Machine had a typewriter key board. When you hit a key electricity would "count around the alphabet" through a series of rotors until it printed a letter. The rotors (arranged like the mileage meters in cars) would also move into a new position, so that if you typed the same letter again, there would be a different letter printed out. The machine had 264,316 different internal states. Worse yet, the German Enigma messages would start with a message indicating what rotor settings to use, so every individual message had a new cipher key. The Germans remained convinced throughout the war that their messages could not be deciphered, always blaming "spies" for inexplicable mishaps. Faith in machinery!
Turing had to figure out how to wire together an enormous quantity of
magnetic relay "flip-flops" so that they could simulate all of the
"internal states" of an Enigma machine. To run the system was to
rapidly review what varieties of initial rotor settings that could turn coherent
and relevant messages with German syntax and spelling into the endless stream
of enciphered short wave messages Britain picked up. In particular, to find the
particular settings that produced this message and so be able to
decipher out the original message in German. Eventually, the relay switches
were replaced by faster vacuum tubes. By 1944, Colossus had the
material architecture and speed of the first general computers. Turing's
machines often deciphered German Admiralty messages to U-boats before the
U-boats did. Werner Von Braun built rockets for Germany and later the United
States, but his war time V2s proved to have no real military value in
proportion to their cost. Alan Turing, however, saved his country and on his
way learned how one might try, as he put it, "to build a brain."
OPEN DISCUSSION QUESTION NUMBER TWO
WHAT EXACTLY IS THIS "TURING TEST"? WHY IS IT SO HARD
Turing asked you to imagine the following "imitation game." We
have some judges who communicate by a terminal to A and B's terminals (think of
it as a party game). One of these terminals is operated by a woman, one by a
man. Under the judge's questioning, the woman tries to convince them that she
is the woman, while the man tries to convince them that he is the woman. For
example, the judges might ask, "How do you do your hair?" and
continue with further probes. Turing comments that the best strategy for the
woman is to tell the truth. Interrogators look for inconsistencies and telling
the truth is the simplest way to avoid them. The man is going to have a lot
to keep track of. If the man manages to win, you might say he can think
like a woman.
Turing then proposes that we substitute a computer for the man. If the computer "passes," Turing suggests, that proves that the computer can think like a human being and that proves that the computer can think period. Turing remarked that the test draws a clear line between the physical and mental. He likened putting the contestants in separate rooms, so the judges can't see them, to musical contests where the players perform behind a screen, so the judges won't be biased by their physical appearance. This is what we now call the "turing test." Turing didn't think it was going to be easy to create a passer. He provided a vivid and testable goal for artificial intelligence research.
When Turing proposed this in 1950, many had what you could call a
"Germanic" reaction of faith in machinery. But the reaction
came in two rather different flavors. Many reacted by saying "It
would be simple task to make a computer do this" but that this
"clever trick" would not establish that the computer was really
thinking (having thoughts, being conscious, etc.). On the other hand, many
people leading the artificial intelligence effort after Turing's death simply
said, "Give us ten years and we will have programed a computer to be an
intelligent 'turing test' passer." Both groups were quite wrong!
In fact, as Turing himself expected, producing a turing test passer is perhaps the toughest task science has ever taken on. Fifty years of energetic failure (with many valuable spinoffs), which has also focused direct research into human cognition, have taught us more about human cognition than the previous three thousand. In the 1960s and 1970s researchers confidently tried to model "general human intelligence." This would be what could pass the turing test by exhibiting human intelligence in a variety of areas, by knowing the sorts of things that intelligent, well-educated and skilled humans know. By the late 1970s, this attempt began to look too ambitious. In good part because we tried programming, we uncovered a number of features of human cognition that are hard to simulate programmatically. In recent years, less ambitious "expert systems," which simulate human expertise in narrow areas, have been successful in parts of medicine and law, and of course chess (Turing sketched out the first chess playing program in 1946). A program restricted to answering questions about Shakespeare's comedies in a witty and human way recently "passed" as a human expert.
But in the 1980s many researchers switched to modeling cognition through
training "connectionist nets," which are idealized and simplified
models of the brain's neurological structures. Still others have proposed to
"embody" and "educate" artificial intelligence -- by
supplying the computational system with input from artificial "eyes"
and "ears," and giving it motor control over these and over
artificial "limbs" and "hands"! Turing, himself, suggested
these approaches as well. Surely thinking of Mary Shelly's Frankenstein,
the New Prometheus, he joked "In order that the machine should have a
chance of finding things out for itself it should be allowed to roam the
country side, and the danger to the ordinary citizen would be serious."
Alan Turing never directly addressed the question, should we build a turing test passer? Perhaps he assumed that an attempt was inevitable. He certainly seems to have wanted to try. Since we have not, as yet, succeeded the question is an open one for us. Could we stop? The Japanese medieval wars ended in the massive use of muskets and cannon (copied and improved Portuguese guns). In the 1610s, the victorious Tokugawa had all the guns melted down and firearms did not return to Japan until Britain and the U. S. forced the country open to trade in the mid nineteenth century. Japan did not stagnate during the this "closed" period; many non-military technological advances occurred.
OPEN DISCUSSION QUESTION NUMBER THREE
YOU DODGED THE REALLY TOUGH QUESTION. SUPPOSE WE REALLY DID
PRODUCE SOME KIND OF COMPUTATIONAL DEVICE THAT COULD PASS THE TURING TEST.
WOULD THAT DEVICE REALLY BE THINKING, REALLY BE
You got me. I just wanted to sketch how things have gone with Turing's project before raising this big question. What has happened is rather reassuring for ordinary human pride. And it is earned and honest pride, rather than the bluster and avoidance of saying, "This would be a simple thing to do but it wouldn't prove anything." It is elevating to realize that the ordinary intelligence and everyday skills we all share, and therefore think unremarkable, cannot now be programmed or otherwise packed into the fastest computer, and may never be, while some expertises can be. World (Human) chess champion Gary Kasparov may feel dejected, but humanity can feel amazement and generosity. Were Alan Turing still alive, I think he would have been delighted. He disliked the British class system. Part of the system's rationale was a University education largely restricted to the upper middle class (the white collar "brains" who were good at math and abstract reasoning -- computers would take them down a step or two!).
Much of Turing's 1950 paper is a reply to various objections including the
one you have just raised, which is still sometimes debated. I will give his
replies to some of the other objections first.
Turing considers the "theological objection" that thought or
consciousness requires a soul or divine spark. His saucy but sound response is,
"Who are we to set limits to God's power?" Maybe God intends us to
create intelligent machines that He will endow with souls.
Turing also considers the objection that the machine will just do what it is programmed to do. It won't be original. His reply is that programs often do things programmers don't expect; mostly this is a pain but occasionally the results are wonderful. Moreover, each of us is almost entirely, or perhaps entirely, a product of our nature and nurture (our "genetic and educational programs"). He also points out that if we make an intelligent creature by training a "child machine," we won't know what's going on inside it.
To "arguments" that a machine cannot "be kind, beautiful,
fall in love, enjoy strawberries, make someone fall in love with it,"
etc., Turing gives the dead-pan devastating reply
The inability to enjoy strawberries and cream may have struck the
reader as frivolous. Possibly a machine might be made to enjoy this delicious
dish, but any attempt to do so would be idiotic. What is important about this
disability is that it contributes to some of the other disabilities, e.g., to
the difficulty of the same kind of friendliness occurring between man and
machine as between white man and white man, or black man and black man.
Now let's get back, as promised, to what Turing called "the solipsist
objection." Some of you may ask, "What's a solipsist?" A
solipsist maintains that the only way to really know that you think is
through introspection, through consciously experiencing your own thinking. The
solipsist therefore reasons that since he can't introspective or experience
other people's thinking, he cannot really know whether anyone else thinks. This
position haunted philosophy since the middle of the seventeenth century.
Turing asks us to imagine, hypothetically, that we have built a successful
simulation of human intelligence, what we call a "turing test
passer." Someone raises the objection, "Yes, it is a clever trick,
but there is no real thinking going on inside, no consciousness, no 'inner
life' like I have." Turing momentarily accepts the solipsistic criterion.
He concludes that then the only one who could ever know that the machine thinks
is the machine itself, and we of course would not take its word for it. By the
same token, however, only I can really know that I think and I can't know
whether anyone else does. Everyone else is in a similar position. Turing
jokes that we have a "polite convention" of assuming that other
humans think. But his basic point is this. If we can't establish that a
computer thinks through its observable behavior, then we can't establish that
other humans think either, because all we see is their observable behavior (we
can see inside their brains but we don't see thoughts there, just brain
Long ago philosopher/scientist Rene Descartes (1596-1650) asked how we can tell whether something that looks like a human being really thinks and isn't an automaton. He suggested "a true and certain test," namely "whether it can reply appropriately to whatever might said in its presence." The Descartes/Turing way may not be the only way we can tell that someone is intelligent. But it does seem the most obvious, comprehensive, and decisive way.
People have suggested that Alan Turing was somehow so emotionally disturbed that he tried to "cool himself down" by trying to prove that he, and other humans, were biological machines. Others have even suggested that he was trying to betray the human race by creating our equals or successors. I myself don't agreed. Yes, Turing did believe we are complicated products of natural evolution, whose origins, growth, neurology, emotions, and cognition are in principle subject to scientific investigation and explanation. But he seems to have believed that all his life, long before he developed an interest in computation. And I agree with those who feel that Turing, quite rightly, opposed human chauvinism, opposed the assumption that we have some unquestionable perfection that no alien, no animal, no artifactual machine can remotely approach, opposed the assumption that only we can really think or feel, that only we can have moral status, rights, or companions. Myself, I think we need non-human companions and conversations, if only to acquire a sense of balance. One place to look is to fellow animals, especially apes. But given their limitations, we may need to build some as well. You will find a spread of views about such matters and more stuff about Turing, in my dialogue, Can Animals and Machines Be Persons?
Of course, as Turing was aware, the creation of intelligent machines is a momentous step. In San Francisco in the 1980s the local zoo demanded that Stanford scientist, Penny Patterson, return the young gorilla, KoKo, that she had been allowed to do signing experiments with. Patterson's lawyer said he would plea that KoKo, having absorbed and demonstrated "language abilities," was a person legally and could not be subjected to slavery. The zoo settled out of court, essentially giving the gorilla to Patterson without payment. Might there be a point where a computer would realize that its "owner" intended to dismantle it and then contact lawyers, via internet, to represent its "right to continued existence"? These are points worth considering. Even if we never reach Turing's goal, we are entering into a symbiotic relationship with our smart machines like the one between the fungus and alga in a lichen. We are smarter together than either separately.
OPEN DISCUSSION QUESTION NUMBER FOUR
I NOTICED THAT THE FULL TITLE OF TURING'S 1936 PAPER IS "ON
COMPUTABLE NUMBERS, WITH AN APPLICATION TO THE ENTSCHEIDENGSPROBLEM." WHAT
DOES THAT DREADFUL LAST WORD MEAN? WHAT ARE THE MACHINES HE WRITES ABOUT THERE?---THE
ONES SCIENTISTS NOW CALL "TURING MACHINES" AND "UNIVERSAL TURING
The dreadful word is German for the "decidability problem," one of a list of unsolved fundamental problems that a German mathematician, David Hilbert, gave in an address in 1900. The question was whether there is a finite mechanical procedure for deciding (computing) whether any given mathematical statement is true or false. Most mathematicians assumed decidability. Turing had his doubts. He realized that the key was to get clear about what a "mechanical procedure" (or computation) was. Mathematicians tended to assume that it meant "explicit, step-by-step, requiring-no-creativity, etc." and left it at that. Remember that before World War Two, "computer" meant a human being whose job was fast mathematical calculation. Turing saw that if a procedure were mechanical, it could be automated.
Turing's answer was to imagine a starkly minimal machine. He called it a
"theoretical computing engine," for he had no intention of building
one. This was a machine to think with. It was fed by an indefinitely long tape
divided into frames like those on a roll of film. The machine had a "read
head" which could tell whether the frame under it had a "/," a
"\," or was blank. The read head was also a "write head"
that could erase, write in a "/" or "\," or do nothing.
After the read and write head finish, the machine can move one frame forward or
backward or stay in place. Then the move is repeated. At the beginning of each
move, the machine is in one of a small number of "internal states"
and this may switch to another after the move. The machine is built to enact
instructions in its machine table of the form "if / is read and the
internal state is 1, then erase, move one frame forward and go into state
2." A turing machine for adding would get, say, the input sequence
"// //" and then automatically change it into "////"
through a long series of steps and then stop. For us this would be the
computation "2+2=4." Since Turing was thinking about a theoretical
device, he didn't mind that a million would be represented by a like number of
Turing went on to show that anything that mathematicians had called a
mechanical problem or computation could be represented by some turing machine.
Further, he showed that there was a universal turing machine. Depending on the
input tape sequence, this turing machine can turn itself into any particular
turing machine, do a computation, and then turn itself into another turing
machine and do a computation, and so on. In the process of trying to prove that
some mathematical statements were not decidable, Turing had thought up the
general purpose digital computer and given its definitive abstract description.
The tape could also store data and programs ("memory,"
"skills," "plans"), represent incoming data ("sensory
input"), and issue output instructions ("motor outputs"). So
Turing had also given the framework in which to describe any sort of individual
thinker, you and me included. As many scientists have said since the 1960s, we
are, more or less, universal turing machines and so are our digital electronic
computers; for the same reason, we now think of thinking as computing or
data-processing. When Alan Turing showed up for war in September, 1939, he already
knew what he had to do theoretically.
"Hold on," you may say, "why didn't he just build a literal
universal turing machine?" The answer is that Turing had ruthlessly
sacrificed speed, complexity, and all sorts of shortcuts, to make his machines
as simple as possible. Of course you could build a literal turing machine but
even with present day technology it would be much slower than human beings, let
alone our practical digital electronic computers, whose architecture contains
all sorts of speed-increasing complexities and shortcuts. When you compute
"2+2=4," your mind goes through some neurological steps, and your
computer, with a very different architecture, will go through some quite
different electronic steps. But what both have in common is the that they are functionally
equivalent to a turing machine adder that clunks laboriously through 30
odd moves to change "// //" to "////."
"And did Turing show that some mathematical statements are 'incomputable'?" Yes, indeed he showed there were an infinite number of such. For many of these, if you imagine the turing machine that would resolve them, it turns out we cannot know whether the machine will ever reach a decision or whether it will come out true or false. He also showed that if there were a mechanical decision procedure for all mathematical statements, this would mean a certain kind of turing machine would have to exist. Then he showed that this kind of turing machine would contradict itself. That is, it couldn't exist.
Hodges, Andrew (1984). Alan Turing: The Enigma. New York: Simon & Schuster.
Leiber, Justin (1985). Can Animals and Machines Be Persons? Cambridge, MA: Hackett Publishing Co. This is a short dialogue.
Leiber, Justin (1991). An Invitation to Cognitive Science. Oxford: Blackwell.
Turing, Alan (1936). "On Computable Numbers, with an Application to the Entscheidungsproblem." Proceedings of the London Mathematical Society.
______(1947/1970). "Intelligent Machinery." In Meltzer, B. and Michie, D., eds., Machine Intelligence. New York: American Elsevier Publishing Co.
______(1950). "Computing Machinery and Intelligence." Mind. Also available in many other places including Hofstadter, D. and Dennett, D. (1984). The Mind's I. New York: Basic Books. (This book also contains at excerpt from my first novel, Beyond Rejection. New York: Ballantine Books, 1980.)
_____ (1952). "The Chemical Basis of Morphogenesis." Philosophical
Transactions of the Royal Society.
Justin Leiber is Professor of Philosophy at the University of Houston. He received a BA and PhD from the University of Chicago and a B. Phil. from Oxford University. His other books include Noam Chomsky: A Philosophic Overview, Structuralism, and Paradoxes; his novels include Beyond Rejection, Beyond Humanity, and Beyond Gravity.