Home > Friday, Science & Technology > Guest post by Lucas:  Kurzweil, “exponential thought”, and gee-whiz numbers

Guest post by Lucas:  Kurzweil, “exponential thought”, and gee-whiz numbers

March 27, 2008

Ok, you can call me pedantic, but this article on Ray Kurzweil (link at end) has an error which should have been caught at the copyediting stage:

“But Kurzweil had a special confidence that grew from a habit of mind he’d been cultivating for years: He thought exponentially. To illustrate what this means, consider the following quiz: 2, 4, ?, ?.

“What are the missing numbers? Many people will say 6 and 8. This suggests a linear function. But some will say the missing numbers are 8 and 16. This suggests an exponential function. (Of course, both answers are correct. This is a test of thinking style, not math skills.) ”  [It’s probably more a test of how much experience the reader has with computers. -LW]

“Look at it this way: If the series of numbers in the quiz mentioned earlier is linear and progresses for 100 steps, the final entry is 200. But if progress is exponential, then the final entry is 1,267,650,600,228,229,400,000,000,000,000. Computers will soon be smarter than humans.”

Based on that mistake, maybe not.  He probably calculated this in some calculator program, which gave him a result in scientific notation.  Instead of just saying “…is approximately 1.26*10^(whatever),” he decided to write that the entry is that number.  This number is clearly divisible by 10, and no power of two is divisible by 10.  Of course, his computer did *exactly what he told it too*, and nothing more. It wasn’t smart enough to realize “Oh, I’m being asked this so that my owner will have a lengthy number to write down verbatim to prove a rhetorical point.  I surmise that he wants this number in arbitrary precision rather than the customary approximation I would normally give his feeble human mind.”

According to my Python interpreter, the correct answer is exactly:

Wait, “L” isn’t a number.  Oh well, I guess the computer knows what it’s doing…  (L stands for “long”, the data type Python uses to handle integers that are longer than a certain number of bits.)

I swear, every article written about Ray Kurzweil pisses me off.  The blog that linked to it had this quote:

“Many computer scientists take it on faith that one day machines will become conscious. Led by futurist Ray Kurzweil, proponents of the so-called strong-AI school believe that a sufficient number of digitally simulated neurons, running at a high enough speed, can awaken into awareness. Once computing speed reaches 10^16 operations per second — roughly by 2020 — the trick will be simply to come up with an algorithm for the mind.”

The blogger commented: “Which is a bit like saying “once we have the technology to travel to another galaxy, all we have to do is get there”.”  Not the best analogy, since it makes it sound like computers are like the technology to travel to another galaxy.  I would say that this is more like saying “Once we can make enough aluminum to build a rocket, we can go to the moon.”
- Lucas



  1. March 27, 2008 at 21:25 | #1

    I thought the directions for the book signing at that event were a little odd. It mentioned there will be no personal signings and you are not supposed to say anything to him. Just go up, hand the book to the person standing next to Kurzweil, and walk to the person that grabs the signed book from Kurzweil. I said happy Birthday to him and smiled as he signed my book. He smiled back and the whole experience felt odd. I was just happy he didn’t have some intelligent machine sign the books for him…  ;-P

    For as genius as Lucas is when it comes to Math it doesn’t surprise me that articles mentioning mathematics would aggravate him. I get the same when when non-technical people write technology articles.

  2. March 27, 2008 at 22:27 | #2

    I was just happy he didn’t have some intelligent machine sign the books for him…

    Well when you think about how little “he” was doing at the signing, how do you know he didn’t?

  3. Ted
    March 28, 2008 at 08:57 | #3

    Well, normally my TV does the thinking for me, but even that seems tiring.

    I, for one, welcome our SKYNET overlords. (What do I care; I’ll be dead. Suuuuckers!)

  4. March 28, 2008 at 21:21 | #4

    I had the opportunity to hear Kurzweil speak on 14 February, and he was really interesting.  He’s done a lot of good in the world.  But he’s nuts… he’s trying to take enough pills to stay alive until robots take over the world or something.  Seriously: he has a guy hired to do nothing but dispense his pills for him.  I don’t know what it means to say “computers will be smarter than humans”, by the way.  We don’t even know how to measure human intelligence yet, let alone machine intelligence.

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