Wednesday, March 10, 2010

When Kurt met Tazio

It is August 1930, and Tazio Nuvolari has journeyed with Alfa Romeo designer, Vittorio Jano, to Vienna after contesting the Linthal-Klausenpass hillclimb. Here, within the Ringstrasse, lies the intellectual and cultural hub of the city: a network of elegant coffee-shops, furnished with marble-topped tables, in which patrons are provided with newspapers, reference books, writing materials, and the atmosphere to discuss and develop the pressing political and philosophical issues of the day.

Within the Cafe Griensteidl sits the young Viennese logician Kurt Godel, an untouched glass of water before him on the tabletop. Wiry and bespectacled, his head tilts down towards the glass, and a permanent frown appears to crease his brow. Across the table sit Jano and Nuvolari, each nurturing a cup of coffee.

The introductions complete, and the small-talk exhausted, a brief silence plays over the background noise, (a cacophonous and symphonous medley of chatter in the coffee-shop, merging melodiously with the sound of a distant waltz, and the vaporous exhalations of a locomotive surging out of Westbahnhof station).

"Signor Nuvolari, please tell me about what you understand by the concept of the limit," asks Godel, without lifting his head.

Nuvolari exchanges a wary glance with Jano. "The limit? Well, suppose I begin driving at a certain speed, and judge that I am a certain distance from the limit of a vehicle's adhesion. I can divide that distance in half, and take myself to that midpoint. I am then going faster, yet I have still not reached the limit of the vehicle. I can then take the new distance that separates me from the limit, divide it in half again, take myself to that next level, and so on, ad infinitum, going faster every time, but never actually reaching the limit of the vehicle. That is what I understand by the limit: it is the boundary of my performance; it restricts me, yet I play with it and manipulate it, see it and feel it, but I can never attain it."

"I see," says Godel. "The possibility of infinite perfectibility within a finite limit interests me. But how do you know this limit is there, if you never attain it?"

"By exceeding it," replies Nuvolari flatly.

Godel finally raises his head, and stares unblinkingly at Tazio. "Vienna is the home of the unconscious, Signor Nuvolari. How much do you think you know about yourself when you're driving?"

"I know that there are things about myself as a racing driver which I could never know, if that's what you mean? If I knew everything there is to know about myself, then I would need to know that knowledge in turn, and then I would need to know that I know that knowledge, ad infinitum. Hence, I would never be able to know myself completely without being infinite."

"Quite," replies Godel with a wry smile.

In September 1930, Godel will go on to raise the possibility at a conference in Konigsberg that there are logically true propositions which cannot be proven. In 1931, he will publish his incompleteness theorems, thereby destroying the 'formalist' programme which sought to establish that all mathematical truth could be obtained by applying syntactical rules of deduction to axiomatic systems. Godel and Nuvolari, however, will never meet again.


Marvin Caldwell-Barr said...

I can’t tell you how pleased I am to have found this blog about one of my favorite subjects.

It’s a privilege to have all this erudite thinking at my beck and call, merely by clicking a mouse. I’m steadily working my way up from December 2006, and loving every moment of it.

XiXiDu said...

No system can understand itself for that the very understanding would evade itself forever. A bin trying to contain itself.

Gordon McCabe said...

Cheers Marvin.

XiXiDu said...

It's an awesome blog indeed. Probably my favorite. Except that I don't care about motor sport :-)

Gordon McCabe said...

Thanks XiXiDu!

Virtually everyone who compliments me on this blog, adds the qualification that they hate the motorsport stuff!

Logically, I should have one blog about motorsport, and one about philosophy of physics. But on the other hand, the blog was designed to reflect the contents of my own mind, not the existence of any particular audience...

XiXiDu said...

Just saw this. You need one of those in your bedroom :-)

Gordon McCabe said...

Now THAT, is awesome!