Turing vs. Church and the Great Mathematics Throw-Down

“A Great science fiction detective story”
- Ian Watson, author of The Universal Machine

Days to Centenary: 126

Mathematicians, math students, and secret math hobbyists who go to sleep at night fantasizing about having an Erdös number: I  want to hear from you.

And in particular I am calling out one Robert Irving Soare (playfully, mind you).

In a recent post entitled The Computable Artist — On Turing and Michelangelo, I featured (and linked to) a brief paper by Robert Irving Soare in which Soare asks the question: why Turing and not Church?

Given that Alonzo Church — who was after all Church’s teacher — worked out so many of the things that are now associated with Turing, why is Turing’s work considered definitive while poor Church is relegated to the background?

Maybe Turing simply overtook and surpassed his teacher, like Kwai Chang Caine in the old Kung Fu television series, who was able — after many attempts — to finally snatch the pebble from his master’s hand.

Or perhaps it had more to do with Turing’s dramatic life story and untimely end, while Church — heterosexual, married, not convicted of any significant crimes that I know of — lived a more sedate existence and survived until the ripe old age of 92.  In his most famous portrait, he looks positively cheerful.

Alonzo Church, looking unperturbed by the fame of his student, Alan Turing

So what’s the answer?

Soare argued in his paper that Turing’s work was more beautiful than Church’s comparing Church to the artist Donatello, who was great and all, but who was no Michelangelo, the artist to whom he compares Turing.

This argument didn’t sit well with one person on Reddit.  He originally wrote to respond to a different post of mine (Alan Turing is “the Key Figure of Our Century,” Marvin Minsky), asking the same question Soare had asked: why Turing and not Church.  He wrote:

Wha’bout Alonzo Church? This is accurate to the best of my knowledge:

• Lambda Calculus precedes the Turing Machine,
• Alonzo Church was Turing’s PhD Advisor
• Stephen Kleene (another of Church’s students) showed Universal Turing Machines and Lambda Calculus to be equivalent and used them to define computability

Now, I understand that John Von Neumann (the man for whom Von Neumann Machines are named) referred his colleagues to a Turing paper, specifically, during the building of the ENIAC (considered, via Wikipedia, “the first general-purpose electronic computer), but I’m still curious about elevating Turing about Church.

I’m sure someone else reading this thread knows more about the matter than I do, so it’d be very interesting to hear about why we emphasize Turing (say, a reason that isn’t related to him cracking encryption during wartime).

I directed him to my post on Soare’s paper, but he remained unconvinced:

I truly don’t find the aesthetic argument as the reason Turing gets remembered over Church to be very convincing.

For two reasons:

1. People don’t say, “hey, Alan Turing really made a conceptually-beautiful version of general computability. Sure, Alonzo Church was there first and stated results every bit as ‘powerful’ as Turing’s, but Church’s model is so much less appealing.” In actual fact, they frame the discussion in the terms your blog post does—the importance and power of the discovery, itself. I’m open to the possibility that somehow lambda calculus has a less obvious connection to computers and that (as a result) it had less ability to influence people, but I’ve never heard that argument made.
2. Turing machines are downright ugly compared to the elegance and conceptual clarity you find in the lambda calculus. This is admittedly a statement that I can’t make absolute, but since we’re talking about popular conception, it’s fair of me to reference popular taste (popular relative to a piece of math/theoretical computer science’s capacity to be so). A general criterion for mathematical beauty is elegance—i.e. getting a lot out of a little. Lambda calculus to me seems ridiculously more elegance, and I think if you polled the mathematically literate and asked them to compare the two, they’d overwhelmingly find the lambda calculus more appealing than the Universal Turing Machine.

Well, as I readily admitted to him, I don’t have enough math to really enter this fray, so I prooposed two things.  First, that I would post his comments here and invite everyone out there to comment, and second that I would specifically write Soare and see if we could persuade him, in the spirit of friendly debate, to respond.  

So the gauntlet has been thrown down.  It’s your play Dr. Soare, if you care to defend your thesis.  My email informing you of this challenge is on its way to you even now.

And as for the rest of you, have at it!

Is the “beauty” argument persuasive?

Or is there perhaps some other reason that seems more convincing to you as to why Turing’s star has partially eclipsed Church’s?

You can use the comment page or write me at nas@homoartificialis.com.

The Computable Artist — On Turing and Michelangelo

“A Great science fiction detective story”
- Ian Watson, author of The Universal Machine 

Days to Centenary:  162

Turing and the Art of Classical Computability [12pp., download PDF here] sounds like the name of yet another derivative paper, maybe a survey or a restatement of established mathematical principles.

No, Turing-ites!

Because its author, Robert Irving Soare, who has written several papers in honour of the Alan Turing Year, is using the word “art” in the way you and I would use it when visiting a gallery. He means art as in a skill, but also art as in an aesthetic endeavor.

Soare, who is  the Paul Snowden Russell Distinguished Service Professor of Mathematics and Computer Science at the University of Chicago, writes:

Mathematics is an art as well as a science. It is an art in the sense of a skill as in Donald Knuth’s series, The Art of Computer Programming, but it is also an art in the sense of an esthetic endeavor with inherent beauty which is recognized by all mathematicians.

In his essay, Soare asks why Turing receives so much credit with respect to the issue of computability when Alonzo Church, as he puts it “got it right and … got it first.”

Soare answers this question by reference to Turing’s mathematical artistry through a side-trip into classical art and a comparison of Donatello, to whom he likens Church, and Michelangelo, whom he compares to Turing.

Michelangelos '"David" (detail)

Soare’s argument is entertaining and enlightening, and will probably be so even for those who don’t end up convinced by his argument, so I recommend reading the paper yourself.  At twelve pages, it’s admirably economical and will more than reward the short time it takes to read it.

Michelangelo's Pietà, completed when he was twenty-four, the same age as Turing when he published his "On computable numbers with an application to the Entscheidungsproblem."

Soare insists — as many commentators have done in relation to scientific disciplines that can be practiced in a theoretical manner, such as mathematics and physics — that math is not simply a matter of getting the right result, but of doing so in a way that is elegant and that may therefore be judged aesthetically:

Mathematicians are not assigned projects like building bridges. Like artists, they choose which problems to work on according to taste and beauty. Like artists, what they produce is evaluated on the basis of beauty as well as mathematical results. The greatest results are those arising from a completely new vision and a profound intuition into the area.

I’m not a mathematician and therefore not in much of a position to judge the relative aesthetics of Turing’s work myself, but if it does constitute great art that bears comparison with Michelangelo I wouldn’t be much surprised.

Great art can be judged by many particulars, but one of its hallmarks is its capacity to be endlessly fecund, and with all of the things that have flowed from  Turing’s brief period of creation his work is certainly that.

Touring Turing — Awesome Artists for a Genial Genius

Do not miss this: the official Alan Turing Year 2012 is on IndieGoGo.com to raise funds for a Turing-centric art exhibition that will be staged at a number of different venues.  This will be a travelling exhibit entitled  ”Intuition and Ingenuity,” which will include workshops, talks and other events.  As the title says, Turing’s touring.

There are some truly awesome artists already confirmed, including: Roman Verostko, Boredom Research, Patrick Tresset, Greg Garvey, Anna Dumitriu and Alex May.  Click on the artists’ links — you will not be underwhelmed.

So do the right thing and lend a hand! Donate a dollar, or a Euro, or some latinum if that’s what’s in your pocket! The Turing-elves command you! And an apparition which just might be the ghost of Alan Turing lurks in the background, in case you don’t. Forget the Ghost of Christmas Past — you do not wanted to be haunted by a mathematician. Click here to avoid the ire of the Turing-verse.

Now as a reward you get to watch one of Patrick Tresset’s robots in action. Enjoy.

The Gentleman Vandal and the Turingator

Days to the Centenary: 239

Posterchild is the nom de guerre (or maybe nom d’art) of a Toronto street artist, a self-styled “gentleman vandal” who creates independent public art.  Sometimes his work is in a familiar style, like stencilling.  Other times his projects are participatory, as with Take a Picture, Leave a Picture, in which he mounted cameras in public places for anyone to use, then later replaced the cameras with framed prints of the photos people had taken. He maintains a blog on which he has documented his work for years, using text, still images, and video.

In 2006, Posterchild meditated upon the question “What if Alan Mathison Turing — the man often considered to be the father of modern computer science — was actually a highly specialized T-800 model, sent back in time to ensure the eventual creation of Skynet?”  The result of his musings was the Turingator, pictured below.

The Turingator, Toronto, September 2006

Posterchild then revisited the Turingator in February 2007, after it had been up for a few months.

The Turingator, Toronto, February 2007

Naturally the street had had it’s way with it. As the artist says:

The paper has gotten nice and yellowed, and has been torn at a great deal. But the key parts are left. It looks great. I think it has aged very well.

Then, in 2009, Posterchild recycled the Turingator as a sticker to celebrate the British government’s official apology to Turing for his prosecution for having engaged in gay sex and his subsequent chemical castration, both of which are widely thought to have contributed to his suicide.  Posterchild put up over 100 of the stickers.

Turingator sticker, New York, October 2009

Now, I would never encourage anyone to break the law, but neither would I want to exclude street artists from being Turing Elves and creating their own works for the Turing Year, so to the extent that there are already people going out and posting images or graffiti or other forms of independent public art, there are worse things they could do than to honour Alan Turing.  I’m just sayin’.

Here is a link to a video of Posterchild at work, in this case on one of his astronauts (they are a theme with him: sometimes doomed, sometimes dead, often faceless, and for his first gallery show, embodied in fabric dolls) .  Caution: the video opens with some rather loud construction noise, though it then quietens down and settles into some nice music.

Turing’s Legacy – Art: Turing Inspires the Godfather of Pop Art

Days to Centenary: 251

On a Sunday (like today) most of us who can do so like to take a break from the workaday world and, if we’re really lucky, from other mundane quotidian concerns like cleaning and shopping, to engage with life’s larger context. Some people like to get out into nature, while others like to engage in spiritual contemplation. For me there’s nothing like allowing myself to be absorbed in the arts.

Whether I watch a film, immerse myself in a book, or visit a gallery or museum, it removes me from the pettier issues of day to day life and reminds me that life can be awesome, both in the slang sense of that word (really cool, like, say the movie Inception) and in the more traditional sense (inspiring genuine awe, for instance reading William Blake and lingering over his art), sometimes at the same time (the movie Lawrence of Arabia or T.E. Lawrence’s book The Seven Pillars of Wisdom, take your pick).

All of which is a long way of bringing this blog back to the subject of Alan Turing and the arts. I’ve previously touched on the subject of sculpture, in a post on the Turing-inspired work in Guildford, and film, in the post that not only revealed (along with about a thousand tweets from everyone and their brother) that a script based on Turing’s life had been sold to Warner Brothers, but also reminded the world (on this point without any company that I’m aware of) that there was already a Turing-inspired movie with the title The Imitation Game, albeit one that is only eight minutes long (see the embedded video in the link above). And I’ll no doubt return to the arts given that there are more than 250 days left until the centenary and I still haven’t talked about the most prominent stage/screen adaptation of Turing’s life to date.

Today I want to direct your attention to the visual arts and the work of Sir Eduardo Paolozzi, who produced a series of eight images based upon or relating to the life of Alan Turing. These aren’t illustrations as such, but Turing-inspired works of imagination in a somewhat schematic pop art style (schematic here being descriptive, not pejorative), which is not surprising considering that Paolozzi is widely considered the godfather of pop art and created an image that is acknowledged to be the first true example of that form, I Was a Rich Man’s Plaything (which actually incorporates the word “pop”), below.

I Was a Rich Man's Plaything, Eduardo Paolozzi (1952), Collage mounted on card support: 359 x 238 mm, Tate Collection

Paolozzi was also a founding member of the Independent Group, an assortment of artists (in various media) and critics who, among other things, are sometimes credited with introducing mass cultural objects into high art, although I would say they expanded rather than introduced this trend, given earlier work by Dadaists and Surrealists.

Paolozzi’s Turing images incorporate brightly coloured shapes, some distinguishable as objects and some not (and some seeming to be at first, but turning out on closer inspection not to be), surrounded in the border by text that appears to be from Turing’s own work. Here are two examples.

Turing Image by Paolozzi

Turing Image by Paolozzi

As you can see, the images range from the relatively rectilinear and mechanical (first image) to flowing shapes reminiscent of Peter Max and the animations in Yellow Submarine (the second image).

Here is an instance — as has arisen many times before and surely will many times again — where an artist has been drawn into Turing’s world. A combination of scientific genius, inestimable military service (that happens also to serve the better instincts of humanity by assisting in a victory over an evil ideology), and human drama will do that to you.

You can find commentary on the Paolozzi images on this page from Andrew Hodges’ excellent site. If you’re of a mind to, you can buy prints of thePaolozzi Turing images from Print Editions here.)

Turing’s Legacy — Art: Turing Goes to Hollywood!

Days to Centenary: 255

Nikki Finke‘s very reliable blog Deadline Hollywood announced yesterday that Warner Brothers has bought Graham Moore’s spec script The Imitation Game, based on the life of Alan Turing, for an unspecified amount in the seven figures. The report is here.

Why the high price tag for a first-time screenwriter’s script about a figure who, after all, is relatively unknown outside science geek circles?  WB reportedly outbid several independent studios because some guy named Leornardo DiCaprio is desperate to star in the movie, hoping that it might finally help launch the career he’s always dreamed of. Also Ron Howard,who has directed several science-related films including Apollo 13 and A Beautiful Mind (the latter about mathematician John Nash) is interested in directing.

I smell Oscar bait!  (A Beautiful Mind won four Oscars, including Best Picture, Ron Howard has two, and that DiCaprio guy was nominated for three, although he hasn’t won any yet.)

The ghost of Alan Turing adjusts to life in Hollywood after learning of a biopic to be based on his life.

First-time producers Nora Grossman and Ido Ostrowsky own the rights to Andrew Hodges’ definitive biography Alan Turing: The Enigma and Finke reports that they “worked with Moore for more than a year to get the script just right.”

Finke’s bottom line on the script?  She hasn’t read it but says that:

“[p]eople I trust tell me The Imitation Game is the best script they’ve read in years — and they read a lot of scripts.”

Now, scripts are known to fly around Hollywood in a fairly uncontrolled fashion, and occasionally to escape into the wilds of the internet.  If anyone has found a copy of the script for The Imitation Game, please send it to me immediately at nas@homoartificialis.com.  If I can find a copy I’ll update this post with some details.  (I’ll attempt to keep it spoiler-free, although what constitutes a “spoiler” in a movie based on the well-documented life of a man who’s been dead since 1954 is an open question.)

What isn’t noted in Finke’s report is that there is already a film called The Imitation Game (IMDB link here) related to Turing.  It’s a science fiction short film (running time: 8:00) by director Calvin Swaim about two scientists who test a synthetic human they’ve built — a homo artificialis — to determine whether or not it can pass the Turing test.  It’s a fun little film, so enjoy!

Turing’s Legacy — Art: Codebreaking Sculpture on Display in Guildford

Days to Centenary: 258

In previous posts I’ve highlighted elements of Alan Turing’s legacy in spheres as diverse as philanthropy and humour. Now, on to the arts.

A sculpture commemorating Alan Turing’s codebreaking work has just gone on display in Guildford, England where he once lived.

The sculpture consists of a large array of lights which in aggregate represent the Wernicke’s Area of the human brain, which along with Broca’s Area is identified with language. Wernicke’s Area is specifically involved in decoding written and spoken language.

Turing Sculpture in Guildford, England

The light display incorporates a secret code, which changes every twenty-four hours, just as the Enigma code used by the German military did during World War II. Members of the public can gain clues to the code by texting messages to the sculpture, then use the information they’ve gleaned to try to break the code.

The sculpture was created by Amenity Space, an art, architecture and design firm whose name derives from the architectural terms for the interstitial spaces that fall between those areas that are clearly designed for a particular use — as the firm’s site puts it, spaces where one is “not contained within a building, stuck on a transport network, or farming the land.”The new artwork stands outside the G Live entertainment complex, which includes seminar rooms, a café and an auditorium with a capacity of 1,000 seated guests or 1,700 standing and seated.