And they say complexity has no philosophical implications
From these lecture notes by Harvey Friedman comes one of the best metamathematical anecdotes I’ve ever heard (and yes, I’ve heard my share). Apparently Friedman was attending a talk by the “ultra-finitist” Alexander Yessenin-Volpin, who challenged the “Platonic existence” not only of infinity, but even of large integers like 2100. So Friedman raised the obvious “draw the line” objection: in the sequence 21,22,…,2100, which is the first integer that Yessenin-Volpin would say doesn’t exist?
Yessenin-Volpin asked Friedman to be more specific.
“Okay, then. Does 21 exist?”
Yessenin-Volpin quickly answered “yes.”
“What about 22?”
After a noticeable delay: “yes.”
“23?”
After a longer delay: “yes.”
It soon became clear that Yessenin-Volpin would answer “yes” to every question, but would take twice as long for each one as for the one before it.
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Comment #1 July 23rd, 2006 at 2:22 pm
That should be Alexander Yessenin-Volpin, not Yessenin Volpin.
Comment #2 July 23rd, 2006 at 3:04 pm
Thanks — fixed.
Comment #3 July 24th, 2006 at 2:25 am
What a beautifully clever way to respond to such a line of questioning!
Comment #4 July 24th, 2006 at 5:24 am
that’s really inspiring. After reading it, I’ve just started to think to become a finitist.
Comment #5 July 24th, 2006 at 6:47 am
Actually this story could be an inspiration of a new philosophy. Something like “finitary in every fixed frame of mind” (as a fixed frame of mind is limited in time and space). I wonder whether a philosopher more accomplished than I could use this story to write a whole book 🙂
Comment #6 July 24th, 2006 at 8:26 am
Hillarious 🙂
Comment #7 July 24th, 2006 at 9:38 am
2^100 seems much too small for this sort of attitude. I have more atoms than that.
Comment #8 July 24th, 2006 at 11:01 am
I think the number of atoms in the universe is estimated to be around 2^x where x
Comment #9 July 24th, 2006 at 3:04 pm
2^100 seems much too small for this sort of attitude.
Yeah, I was thinking exactly the same thing. 2^1000 would work better.
Incidentally, the number of atoms in the human body is on the order of 2^93. The number of atoms in the visible universe is on the order of 2^266.
Source: Google.
Comment #10 July 24th, 2006 at 3:47 pm
Incidentally, the number of atoms in the human body is on the order of 2^93. The number of atoms in the visible universe is on the order of 2^266
Oops, you are right. The exponent I was remembering was for base 10.
Comment #11 July 24th, 2006 at 5:09 pm
So, who wins the coveted triple A (Aaronson Anthropicism Award)? Miss Universe was declared today–a pale, paltry prelude to the AAA.
Comment #12 July 24th, 2006 at 11:24 pm
In fact the largest number is about 45 billion.
Comment #13 July 25th, 2006 at 12:29 am
So, who wins the coveted triple A (Aaronson Anthropicism Award)?
Oh, were you asking about the AAAAAAAAAAAAAAAA (Allegedly Annual, Although Actually an Aberration, AAronson Award Appreciating Amusing and Artfully-Articulated Anthropic Assertions)?
Comment #14 September 6th, 2006 at 5:09 am
Anonymous said…
What a beautifully clever way to respond to such a line of questioning!
Well, one should remember that Alexander Yessenin-Volpin (listed in Wikipedia as Esenin-Volpin) was one of the founding fathers of the Soviet human rights movement and spent many years in prisons, exile and psychiatric hospitals. He knows a thing or two about interrogations; in 1968, he wrote and circulated via Samizdat the famous “Memo for those who expects to be interrogated”, much used by fellow dissidents.
The story about 2^1, 2^2, 2^3, … is so wonderful that I will perhaps write more about it in my own blog. Watch
http://www.maths.manchester.ac.uk/~avb/micromathematics/