From mvandine@shore.net Mon Dec 9 00:47:50 1996
To: "'Al Van Dine'" , "'Gib Van Dine'" ,
"'Lynn Van Dine'" ,
"'Joan'" , "'Barb'" ,
"'Dan Mushalko'" <72060.3523@CompuServe.COM>
Cc: "'propp@math.mit.edu'"
Subject: The Self-Referential Aptitude Test Revisited
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All -
I'll start by saying that I am a smart son of a bitch and don't let =
anyone tell you any different.
About a week ago I forwarded the following quiz to Al, Gib, and a friend =
of mine who does a syndicated radio show on science ("The Amazing =
Science Emporium"), Dan (Dan and I also worked together on a radio =
comedy show at Penn State). It was funny ... a multiple choice quiz =
about ... itself! Al summed it up perfectly, "I assume this whole thing =
is a spoof on IQ tests -- probably composed by someone who has just been =
rejected by MENSA ... I think it's pretty funny, but 5 or 10 questions =
would have been enough."
What I couldn't shake was the author's claim that the puzzle's solution =
was unique. During a business trip to New York last week, I spent both =
sides of the shuttle trip studying the thing to see if I could spot a =
set of logic tricks or something (a hopeless crusade ... I always give =
up on the problems in Martin Gardner's books).
And then I recalled the email discussion we had about Richard Dawkins.
Friday night, while sitting with Allie and Carol watching TV, I wrote a =
Delphi program similar to the algorithm that Dawkins describes in 'The =
Blind Watchmaker' (Chapter 3 ... 'Accumulating Small Change') ... a sort =
of simple genetic algorithm that 'evolves' a solution based on a =
measurable goal state. The program starts with a random string of =
twenty characters, one for each question in the quiz, each a letter from =
A to E representing an answer to one of the questions in the quiz. The =
program scores the answers (right or wrong), and then spawns a brood of =
'child' strings from the original ... 50 kids per generation, with a =
slight probability that each character may be copied incorrectly (the =
rule I used was that characters were copied correctly about 85% of the =
time). I'd score all of the 'child' answer sets. The high score (or an =
equal score if none were higher) becomes the parent of the next =
generation of kids. I ran this for as many as 750,000 generations (try =
THAT on a Mac, you pagans).
And by God it worked! Well, almost ... there were some bugs in my =
program that had gone undetected which caused the scoring algorithm to =
not work perfectly ... that's when my VanDIne Sense of Humor saved me. =
As I watched the potential solutions scroll past, I couldn't help but =
notice how often the five letters A through E would spell out a word, =
like 'DAD' or 'BED'.
I was running a simulation that was scoring 17 out of 20 about midway =
through the run, when I realized that the answers spelled out:
DAD BEDDED A BAD BAD BABE
That's one of the best operative definitions of a unique solution that I =
can imagine. I checked the answers by hand and confirmed it was 20 out =
of 20 (and found my program bugs in the process!) The final, and best =
joke is that, of course, the last question, the only one that seems to =
ask a question not answered by the quiz itself, suggests that =
Standardized Tests are to Intelligence as a Barometer is to anything but =
what it actually measures.
Mom, I'm sure the answers weren't meant to be taken personally. :o)
mark
From: Mark VanDine/OneSource
Date: 12/03/96 01:13:19 PM
Subject: SELF-REFERENTIAL APTITUDE TEST
SELF-REFERENTIAL APTITUDE TEST
by Jim Propp (propp@math.mit.edu)
The solution to the following puzzle is unique. You may now begin
work.
1. The first question whose answer is B is question
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
2. The only two consecutive questions with identical answers are
questions
(A) 6 and 7
(B) 7 and 8
(C) 8 and 9
(D) 9 and 10
(E) 10 and 11
3. The number of questions with the answer E is
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
4. The number of questions with the answer A is
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
5. The answer to this question is the same as the answer to question
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
6. The answer to question 17 is
(A) C
(B) D
(C) E
(D) none of the above
(E) all of the above
7. Alphabetically, the answer to this question and the answer to the
following question are
(A) 4 apart
(B) 3 apart
(C) 2 apart
(D) 1 apart
(E) the same
8. The number of questions whose answers are vowels is
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
9. The next question with the same answer as this one is question
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
10. The answer to question 16 is
(A) D
(B) A
(C) E
(D) B
(E) C
11. The number of questions preceding this one with the answer B is
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
12. The number of questions whose answer is a consonant is
(A) an even number
(B) an odd number
(C) a perfect square
(D) a prime
(E) divisible by 5
13. The only odd-numbered problem with answer A is
(A) 9
(B) 11
(C) 13
(D) 15
(E) 17
14. The number of questions with answer D is
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
15. The answer to question 12 is
(A) A
(B) B
(C) C
(D) D
(E) E
16. The answer to question 10 is
(A) D
(B) C
(C) B
(D) A
(E) E
17. The answer to question 6 is
(A) C
(B) D
(C) E
(D) none of the above
(E) all of the above
18. The number of questions with answer A equals the number of
questions with answer
(A) B
(B) C
(C) D
(D) E
(E) none of the above
19. The answer to this question is:
(A) A
(B) B
(C) C
(D) D
(E) E
20. Standardized test : intelligence :: barometer :
(A) temperature (only)
(B) wind-velocity (only)
(C) latitude (only)
(D) longitude (only)
(E) temperature, wind-velocity, latitude, and longitude
=20
From AVDZZZ@aol.com Mon Dec 9 20:21:51 1996
To: mvandine@shore.net, GibVanD@aol.com, lvandine@ix.netcom.com,
JoanMore@aol.com, barb@ide.com, 72060.3523@compuserve.com
cc: propp@math.mit.edu
Subject: Re: The Self-Referential Aptitude Test Revisited
Yes, you are a smart son of a ***** (you'd better ease up on that bad bad
babe).
And I tried, I really tried, to follow the steps of your genetic algorithm.
The only one I didn't understand was the first one:
<< The program starts with a random string of twenty characters, one for each
question in the quiz, each a letter from A to E representing an answer to one
of the questions in the quiz. The program scores the answers (right or
wrong), and then spawns a brood of 'child' strings from the original
......etc >>
What I don't understand is how you've established "right" answers for the
program to score against at the outset, before all the creative devolution
can commence.
Note from Jim Propp: Mark Vandine, in private communication, suggest that
people who want to know more on the theme of `The Blind Watchmaker` that
inspired his approach to the SRAT should read Richard Dawkins' recent book
'Climbing Mount Improbable' (published 1996 by W.W. Norton & Co., Inc., ISBN
0-393-03930-7); Mark calls it "well written and thought-provoking". Also,
he writes:
>I wrote the program in Borland Delphi. If you think anyone would be =
>interested in the source code, they can email me, or you could add it to =
>your Web page as well (it's a short program). Depending on how much =
>time you put into this, there are also several interesting Web sites on =
>Dawkins, and genetic algorithms in general ... I can track down a list =
>for you if you're interested.