Turing again:
I have just read Jack Copeland, Turing, Oxford University Press, Oxford, 2012. It is a most fascinating life. I would encourage you to run off and read it before continuing this, lest I spoil some of it for you … you’re back. Good.
I had heard of some of Turing’s work, but I had no idea how extensive it was and how many different things involving computers he invented. But let me skip to the end; I had always thought that he committed suicide because he was a homosexual … ok, I’ll be correct … gay then … in a society that did not accept it. The book calls that into serious question. He was found dead in bed with a half eaten apple and smelling of cyanide. Sound’s pretty suspicious, but he had been playing with electrolysis in the next room, really just a cubby hole, and his tinkering there involved using cyanide. So he finished his playing around, went to his room, changed into pajamas, rather strangely put his shoes outside his room – maybe they smelled of cyanide – stretched out in bed and passed away. Copeland considers the death suicide, murder or accident with accent on accident. Suicide really doesn’t wash. He was never depressed, was busy making arrangements for the near and more distant future, was a sociable chat; I think Copeland makes the point.
Copeland doubts he was killed by the secret service. I doubt it, too. Certainly he knew many secrets, but he was evidently still useful to the government. The question of the day was maybe homosexuals were a security risk. His loyalty was never questioned, and even the most rabid homophobe would have trouble saying why a homosexual should be a security risk except if he lived in a society where that might render him subject to blackmail or make people think he could be subject to blackmail. But he’d already covered that one. Two years before his death he had been convicted of homosexual behavior. Going over how it happened, it smells like a setup. He deliberately got “caught.” Remember, this is a very intelligent man. By getting himself publicly convicted, it put the blackmail issue totally off the board. And then, get this, his punishment was to be required to take female hormones. Let’s see. He’s to be punished for being effeminate so they give him female hormones. Now I do smell the secret service at work. He talked the blackmail business over with people in the British secret service, they pointed out that it did constitute a hazard to him, Turing, since he might be kidnapped by someone undertaking to blackmail him and that would have unpredictable consequences. So they thought up the conviction business and the spook said, “And what would you like for your punishment?” “Well I’ve always wondered what female hormones would be like. Can we do that?” “I’ll see what I can do.”
So I put murder out of the question, too.
And I don’t really like the idea of an accident. Sure, the stuff’s dangerous, and indeed the coroner reported smelling it in his tissues, but by the time he’s put up his things, changed and climbed into bed I really would think the poison would have done its worst.
So my own guess would be natural causes. Yes, there was an autopsy. Did they open the pulmonary veins looking for emboli? Did they check the brain for a berry aneurism? I don’t know. If I can find out, I’ll tell you.
So back to the good stuff. Back in the 1930’s Turing made a number of remarkable contributions. For one thing, he described how a generic computer should work. It should be able to search a file, read from the file, write to the file, have a handy short term memory and obey a list of instructions, what we would now call a program. With that it could do some very interesting things.
He called this a universal computer.
Another thing he did was to prove that any universal computer could do anything any other personal computer could.
And, this is the good one, he proved that there are some things a universal computer can not do that a human can do. Iconic among those things is the “Print Problem.” That states that if you give a list of instructions to a computer, the computer can run them, but if it does not do so it cannot tell, for instance, whether the computer itself will print out a zero if it runs the program.
Here’s an example. I put a challenge to myself, which was to remember everything I thought in the process of solving the puzzle. If I could do so, I ought to be able to program a computer to do what I did. It’s a fool’s errand, but you’re welcome to try. So here goes: Take an odd number greater than vigintillion, which is a one followed by 63 zeros in America; it’s more than that in the UK, and you can go with either one. Good, you have your number. Next you print the number. Easy enough. Now subtract 2. Print the new number. Subtract 2 again and so forth. When you get below minus 7 stop. Now did you print a zero?
The answer is of course that you are coming down odd numbers till you get to, say, 3. Then it goes 1, minus one, minus three and on down. You didn’t print the zero. I’m sure you figured it out. If not, try it again but using 1 instead of 2 to subtract. I’ll assume you got that one. (If not, email me as the web site suggests.)
You have just done something no computer will ever be able to do. You have solved the print problem. The computer would have to run the program. And the program can never be run. At any realistic speed, it would take too long. The sun would explode, the galaxy burn out, stuff like that.
Given infinite time and memory, the program could be run. But even then the computer could not tell whether there was going to be a zero without running the program. Even if the whole universe were computer it couldn’t do it. So the universe cannot contain a computer that can solve the print problem. But you just did. (I don’t pretend to be an expert here; if it matters, consult the appropriate authority.) So since the universe cannot hold the computer that can draw the inference – that can understand and solve the problem - , you must have accessed something outside of the universe.
I’ve already pointed out that the simplest way to build a universe that contains consciousness is to have the same consciousness enter the universe many times. So your consciousness reaches outside the universe. Your reasoning ability certainly reaches outside, and I’d say your moral sense and your emotions do, too. And the same hold for animals.
Odd isn’t it. I can follow the design of the universal computer. I really wish I could prove that they all have the same abilities and that they cannot solve the print problem, or whether my example really is an example of the print problem.
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