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.

14 Responses to “And they say complexity has no philosophical implications”

  1. Greg Kuperberg Says:

    That should be Alexander Yessenin-Volpin, not Yessenin Volpin.

  2. Scott Says:

    Thanks — fixed.

  3. Anonymous Says:

    What a beautifully clever way to respond to such a line of questioning!

  4. prunus Says:

    that’s really inspiring. After reading it, I’ve just started to think to become a finitist.

  5. Eldar Says:

    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 :-)

  6. jyby Says:

    Hillarious :)

  7. Anonymous Says:

    2^100 seems much too small for this sort of attitude. I have more atoms than that.

  8. Anonymous Says:

    I think the number of atoms in the universe is estimated to be around 2^x where x

  9. Scott Says:

    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.

  10. Anonymous Says:

    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.

  11. Anonymous Says:

    So, who wins the coveted triple A (Aaronson Anthropicism Award)? Miss Universe was declared today–a pale, paltry prelude to the AAA.

  12. Anonymous Says:

    In fact the largest number is about 45 billion.

  13. Scott Says:

    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)?

  14. Alexandre Borovik Says:

    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/