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 MIME-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: quoted-printable 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.