Alan Turing, flawed heroes, and the nature of reality

You know, I look at the title I just wrote and it makes it seem as though this will be a monster post of amazing depth and insight. Don’t get your hopes up. 🙂 I am busy working on a couple of Tomorrow’s World scripts for taping next week (one on the biblical “Man of Sin” and one about the observance of Easter), but it helps to unknot the brain every few moments by doing something else. This post will be one of those “something elses” and a nice brain stretch — a standing up, stretching the legs, and walking around before sitting down to hammer away at the task at hand some more.

The Alan Turin biopic coming out — “The Imitation Game” — got my attention when I first saw the initial trailer. It comes across like a WWII intellectual thriller and character study, where viewers will watch Benedict Cumberbatch play the role of Alan Turning as he and others crack the Enigma code. Turing was an interesting figure, one which current movie tastes certainly makes attractive for cinema (more on that in a moment), and the idea of seeing a movie depicting the man who laid the foundation for modern computing and, truly, so much more (as I will also get to in a moment) is appealing.

And yet it isn’t. Alan Turing was also an unrepentant and publicly professed homosexual in a time when such activity was illegal. The talk I hear concerning the movie, which premiers November 28, is that it is an “important story for our times” (or something like that), and such language, given its subject matter, suggests to me that much will be made of Turing’s sexuality and how someone so crucial to victory in the war–someone so gifted, etc.–was persecuted for simply “loving differently.” Whatever. Hollywood is very good at crafting stories influencing us to admire the heroes it presents us with in such a manner that our actively cultivated admiration may cause us to overlook whatever chosen element of immorality they are trying to change our minds on. It would be as if the Bible were rewritten by an author hoping to use David’s virtues to get us to think less critically of adultery, as opposed to the Bible’s actual approach, which is to present its flawed heroes as just that: flawed heroes. And recognizing someone as a flawed hero requires one to recognize flaws for what they are: flaws.

Alan Turing’s immoral sexual behavior was a flaw of character. It does not diminish the greatness of his intellect or insight. However, neither does the greatness of his intellect or insight diminish the immorality of his sexual behavior. I suspect that Hollywood is hoping that we will ignore the second of these facts.

So, I’m not as interested in seeing the movie as I otherwise would be. And why would I be interested in seeing the movie? Because I think Turing’s work, like Kurt Gödel’s and, more recently, Gregory Chaitan’s, has played a significant role in changing not only how mathematics is seen, but how reality is seen.

I’ve mentioned Gödel before — actually, not on the blog, I think, but in a telecast: “What Is Truth?” Don’t have 28 minutes to watch? We also made a TW Short version of “What Is Truth?” that is only 3 minutes long and an article of the same title. Actually, Kurt Gödel is mentioned in all three incarnations of that work, and including a mention of his “logical nuclear bomb” is one of my all time “feel good moments” concerning my work in our media. (And kudos to our video editors, who also allowed me to get images of the Fundamental Theorem of Calculus in there.)

That “logical nuclear bomb” was his work on the incompleteness of mathematics, demonstrating mathematically that not all mathematical statements can be proven, nor can the consistency of mathematics be proven mathematically. (That’s my own summary–forgive me for washing over details for those who are nitpickers.) I’ve long thought it fascinating since I first saw the result mentioned in a PBS program as a child (probably a NOVA episode, but I am not sure). However, an old OMNI magazine article (anyone remember OMNI?) pressed me to consider what the result might be saying about reality, given the intimate connection between reality and mathematics — an intimacy deeper than that of the physical sciences, since it is the relationship on which the sciences depend.

I’m currently enjoying Chaitan’s popular book Meta Maths: The Quest for Omega, which talks about the author’s own fascination with Gödel’s work and his extension of Turing’s discoveries concerning the halting problem (i.e., the question of whether or not there would ever be a way to predict which programs, out of all possible programs, a computer could run that would come to a stopping point versus running forever without stopping; turns out there is no way to do this for all programs). The point of the book is to discuss the implications of the number omega, defined to be the probability of a randomly constructed program of halting. It is a well-defined number that surely exists, and yet no computer will ever be able to calculate it — not because of limits to memory, computing power, programming language, etc., but because it is actually, in its existence, impossible to compute. Its every digit, in a sense, represents a mathematical truth that mathematics cannot determine, though the existence of the number is well established.

Among the things I am enjoying about the book is that Chaitan discusses thoughts that have been rattling around in my noggin for a few years, now (though he does so with intelligence, experience, and insight, where as my thoughts have been characterized by more of a dull hum…). For instance, do what we call the “real numbers” exist in the world? I don’t mean that in the sense of Platonism (i.e., is there some sort of abstract “reality” where these things exist in a non-physical sense), but, rather, is there any real physical representation of them anywhere? We can take a square that is exactly 1 meter by 1 meter in dimension, and its diagonal would be the square root of 2 meters. And we can take a circle that is exactly 1 meter in diameter and its circumference would be π (pi) meters. So, surely, the square root of 2 and π are things that exist in reality… except that there is no square in existence where the sides are exactly 1 meter each, nor is there a circle in existence with a diameter of exactly 1 meter. Can such numbers still be said to exist?

OK, just imagine the points invisibly in space, without a physical object assigned. Can’t we define such numbers by these invisible distances between these infinitely small points, which, though conceptual, surely do exist as locations in real space? No, not necessarily. Evidence, by some accounts, continues to mount that our physical reality is not continuous like what we imagine the line of a perfect circle to be but discrete and made up of “bits” like a circle on a computer screen looks when you look close enough to notice the pixels making up the image. Life (and reality) would not be a continuous flow, but a passing from frame to frame, like a strip of film showing in a movie theater–an illusion of continuous movement but actually a series of stills shown in rapid succession.

If there is no true continuity to existence, if all is discrete, then there is no room for infinite strings of digits in reality. And without infinite strings of digits, the vast majority of real numbers on the number line disappear into nothingness — including our favorites, like π and e. They remain only as “useful fictions” that allow us to use an imaginary continuity to model a very discrete reality.

Leaving earth behind, might there be a perfect circle in heaven, or a perfect square? Since the word “perfect” here reflects not an actual perfection of morality or existence but, rather, conformity to an idea than man has defined, I’m not so sure there are.

My old Platonism is looking pretty tattered these days. 🙂 As much as I love Cantor’s work and believe there is real value to it, more and more I am beginning to think of Leopold Kronecker’s famous statement “God made the natural numbers; all else is the work of man” as being possibly true at more levels than I had ever given it credit for.

Anyway, that sort of stuff, among other things, is what comes to mind when I hear of Alan Turing. And I look forward to the general resurrection when, if I can be so indulged at that time, maybe I can see Gödel, Turing, Cantor, and Kronecker at tea together not only discussing such insights but comparing and contrasting their thoughts with a revealed view of reality, all while having the privilege of helping them to get to truly know the Author of all they had been studying.

Wow — I really wandered around in this one, huh? Probably fell into a few ditches, too. Looking back, I read some of what I wrote and think, “Just what was in this salted caramel mocha, anyway?” If you read this far without falling asleep or getting a headache, congratulations! This probably hasn’t been the best expression of my thoughts on these things, but it still feels good to get it into writing in some way. I might try and write about these things again in the future — I’ve been wanting to write about how I first began to lean toward the belief that zero might not actually be a number in a very real sense, and if some of you out there have been having a hard time falling asleep, let me know and I will go there for you. 🙂 And the break has been nice — now, back to the scripts!

7 thoughts on “Alan Turing, flawed heroes, and the nature of reality

  1. obeirne

    I won’t read this blog for the present, Mr. Smith, but will later. But I have been hoping that some one of you would write article and present telecasts on a few subjects in which I have an interest. One them concerns how people, because of their disenchantment with professing Christianity – in fact, specifically Catholicism on the case of a friend of mine and a second cousin, who quotes the Dalai Lama and other persons who spout comforting altruisms as if they had some kind of a deep and true understanding of matters spiritual and pertaining to the human spirit. It seems he may think that the type of meditation might be helpful in attaining peace of mind. I would love to see sermons, articles and telecasts dealing with these deceptive spiritual leaders and have the opportunity to share the articles in particular. I will get back to you on the other subject I’d like to see address. Thank you!

  2. Yes, I’ve heard of OMNI (used to subscribe to it). No, I’ve never heard of Omega (although that is perhaps the weirdest thing I’ve ever heard of in mathematics). Yes, I love Godel’s Theorem and your use of it. Yes, you’re probably right about Turing’s use by Hollywood as a social tool (we’ll see). But you’ll have to pry my belief in the objective existence of things like perfect circles on the spiritual plane out of my hands with a really big logical crowbar. 😀

    And what about the proportions of the monoliths of 2001 and 2010 (the films): 1 by 4 by 9 in three dimensions alone, down to the limits of measurement (e.g., six decimal places for the big one, in 2010)? And Clarke wrote that the progression of cubes didn’t stop there… 😀 Too bad none of the monoliths in the films, so far as I can see, actually fit those dimensions, even though 2010 at least raises them… but there you are, “proof” that real numbers exists in the “real world”. 😉

    Of course (leaving that lame joke aside), I tend to think that, say, the throne on which the Father sits, the outer wall of New Jerusalem, etc., really are precise in a way material things aren’t.

    I look forward to the results of your scripts. “Why Believe in God?” (TW) was for me one of the best programs we’ve ever produced.

  3. Mike

    Perhaps not entirely on your point, but concerning perfect circles and squares, I’ve often been out driving or walking and looked at the dichotomy between the natural world and man’s creation. The natural world tends to take on more repeated patterns like spirals and fractals in the way trees grow and flowers bloom, but there’s nothing “perfect” in those patterns like those expressed in our straight-angled houses and buildings, triangular roofs and rounded skyscrapers.

    That said, I wonder if God designed nature to grow around what we create, perhaps even continuing to work through the imperfection we were surely to introduce. I think how everything that Moses created in the tabernacle was a copy of the heavenly. So perhaps in heaven there is a laver that’s perfectly round, and the temple perfectly squared-off at the corners because there is no imperfection that has to be accounted for there. Or it’s possible that, like we show our small children, simple concepts like numbers, colors and shapes point to a much more complex and amazing reality beyond our current comprehension.

    (I just heard Mr. King say in one of his Feast sermons that it’s possible there are more spiritual senses than just the 5 we typically account for… Mind blowing.)

  4. obeirne

    I’ve read your blog, Mr. Smith and the first few paragraphs concerning Alan Turning I got. But once you got into mathematics, I was lost. I certainly agree with what you say concerning how Hollywood will use this man’s brilliance, in conjunction in working with others, in the breaking the Enigma Code and using that as a means of glossing over his sexual perversions. Oscar Wide, a brilliant Anglo-Saxon author – one who penned brilliant plays, a novel, short stories and poetry, was into the homosexual scene of the late 19th century. He hired ” rent boys ” – young, adolescent male prostitutes to gratify his perverted sexual urges. But his down was brought about because of his involvement with one Lord Alfred Douglas, whose father had called him a ” sodomite “, although Douglas’ father had misspelt that term. Wilde sued for libel and lost and his sexual depravity was exposed to the world and in one instance a ” love ” poem he had written to Alfred Douglas was read to the court. He spent five years in Reading jail for his crime. For many decades Wilde’s name was spoken of with derision, but in recent times he has been rehabilitated and his brilliant writing has been used to offset his disgusting sexual life. Having said all that, I would like to let you know that another subject I’d like to see dealt with in sermons, telecasts and articles is that concerning single parent families – the single parent families in charge of the mothers. In essence, I am talking about fatherless families and the damage the absence of fathers does to the children of such unions. We don’t get enough hard facts and figures on the physical, mental and spiritual damage from which children who are without fathers suffer. Please excuse my diverging from the blog topic by raising the two matters to which I’ve referred.

  5. As a mathematician, I really enjoyed this – very interesting thoughts, Mr. Smith! I’ve long thought that Gödel’s incompleteness theorem would make for an enlightening spiritual message but that it would probably lose the audience, and I appreciate you sharing your perspective on it for my own gratification. Do you have an educational background in math or science, or is your interest just casual curiosity?

    On the main topic of the article: I’m sure they’ll really play up Turing’s homosexuality in order to “dramatize” the story. Despite having studied Turing machines in school, I’ve never actually read about his personal life and so I don’t know the extent of what details are known, but I’m sure that they’ll sensationalize it until it’s barely recognizable and fits their agenda! If you remember the movie A Beautiful Mind about John Nash, they did a similar thing – although that had more to do with making the movie compelling than with progressivism, at least as far as I’m aware.

  6. Thanks, Mr. Britt, and it is good to hear from you. My degree is in theoretical mathematics from Texas A&M University. Admittedly, I don’t do as much mathematizin’ now that I am ministerin’, but I still have a passion for the subject and talk about it perhaps more than I should. I actually have referenced Gödel’s theorem in a message here and there when the gist of it would be accessible and the spirit of it was applicable, but you’re right — for most messages where referring to it or alluding to it would have any play or helpful impact at all, a little of it goes a long way but a lot of it goes nowhere. 🙂 That particular telecast seemed a pleasant exception, even if I was a little nervous pronouncing his “ö”-blessed name out loud. (When I hear it on the video, it sounds like I say it more like “girdle.” I will apologize to him in after the second resurrection.)

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