The Journal of the Mega Society

Number 67

January/February 1992



Rick Rosner

5139 Balboa Blvd #303

Encino CA  91316-3430

(818) 986-9177


This issue, I hope, marks the beginning of a more regular and reliable publication schedule.  Chris Cole has replaced my sputtering modem with a complete PC.  Now, publication depends not on phone lines but on my questionable ability to learn Microsoft Word (and on the U.S. Mail, through which I'll send Chris the disks containing the completed issues).


Jeffrey Wright sent in a set of analogies, which were printed in Noesis 66.  Here're the answers:

15 : Christopher Sly (Taming of the Shrew--Sly only thought he had slept 15 years.)

20 : Rip Van Winkle

57 : Epimenides

100 : Sleeping Beauty







The past issues of Noesis are in hand.  Thank you.


The issue of my being eligible for admission to the Noetic Society is purely academic.  My sleep pattern will not be affected.  My retirement pay will not be different.  My family will still own me.  And furthermore, if I were to hit one of the local inhabitants of my quaint village over the head with a Noetic, they would not be impressed--so there.


My reason for testing the waters is that the MD head of the ATU section of St Joseph's Hospital in Wichita gave me a psychological test upon admission and, upon noting my score, suggested that I. in the parlance of Armed Forces Recruiting, see what I can be.  So far Mensa and TNS have granted me membership.


I, too, have done some research.  The college wherein I took the ACE test had a fire in the administration building some time after the 40's.  They were able to unearth the enclosed photo page of the test explanation.  The mentioned pages following, listing alphabetically those taking the exam, are not to be found.  My score was taken from my personal record.


My forte is not of statistics but I do note that the possible score on my test was 200.  You made mention of the ACE of your note having a possible maximum score of 309.


Regardless of the outcome of my quest--my sincere thanks for your time and efforts in investigating my case.


Ave, atque vale,

William Archer


[Editor's comments:  Mr. Archer has asked for admission to the Mega Society on the basis of a score he received on the 1940 edition of the American Council on Education Psychological Examination for College Freshmen, by L . L. Thurstone and Thelma Gwinn Thurstone.  I did a little library research and discovered that earlier editions of this test used a strange scoring scale, ranging from 10 to 309 (or else I completely misunderstood the data).  Mr. Archer has submitted a report showing that the test he took had a range of from 0 to 200, which I tend to believe more than the results of my own research.  However, no information is available on national means and standard deviations.


So, can anyone help us out?  What was the mean and s.d. of the 1940 ACE?]





Dear Mr. Rosner,


Here's my $10 for 6 issues of Noesis.  Enclosed is an updated version of a piece I submitted to ISPE's Telicom.


Some bio data:  Age 41, tech writer, engineer.  B.A. Physics.  Interests: scientific speculation, computer, music, inventing, chess.


Yours Truly,

Glenn A. Morrison



by G. A. Morrison


The builders of the chess computer "Deep Thought" predict that when their machine is speeded up by a factor of 1000 in a year or two, it will attain a rating of 3400, allowing it to defeat the human champion in 96% of games played.  Others including champion Gary Kasparov himself, insist that human ability and creativity will prevail, and that he will defeat the computer.


With data provided by Computer Chess Reports Quarterly editor Larry Kaufman, I've arrived at rating predictions for the future Deep Thought computer, the random player, and the perfect player.  The ultimate maximum rating should be about 3700, the random player, -1650, the future Deep Thought, about 3020.  Also included is a rating formula for use with home chess computers.


A player who defeats another in 76% of games has a rating 200 points above the other player's rating.  The average tournament player has about 1500 points.  A master has 2200 or above, and Kasparov 2900, all on the U.S. Chess Federation scale.


Playing over some games in Euwe's "Chess Master vs. Chess Amateur," I was able to guess about 55 - 60% of the master's moves.  This was odd, considering that in a typical master-master game, I could guess only about 35%.  It seems that the fact that the master in Euwe's book was playing an amateur must be significant.  The better the players, the more subtle and difficult are the positions arising in the game, and the harder it is to find the absolute best move.


Rating differences are found for small differences of depth, then added up to get the total rating.  First, I calculated the probability p(k, D) of a depth D player finding the kth best move in a position from a "perfect game," using p(k, D) = c(D) k ^ -aD, a = .16, c(D) = normalizing constant, with 45 moves per game and 20 move choices to get 10 ^ 60 possible game sequences.  (The choice of this function comes basically from Occam's Razor.)  Next, find the probability p'(k, D) of a depth D player making the kth best move (judged by the perfect player) in a game between itself and an equal opponent.  A good candidate is p'(k, D) = (1 - .95exp(-.137D)) (k ^ -u(D)) which approaches p(1, D) asymptotically for k = 1 and large D, and satisfies the requirement that when p(1, 5) = .35, p'(1, 5) = .55, and that p'(1, 0) = p(1, 0) = .05.  u(D) is, like c(D), a normalizing constant ensuring that for any D the sum of probabilities from k = 1 to 20 is 1.


Then find for each successive pair of depths D and D+1 the probability, using p'(k, D) and p'(k, D+1), that the value of the average move for D+1 would exceed the value for the average move for D.  To find this, figure the value K of k for depth D for which the probability of a better move is 1/2.  For example, for D = 0, K is 10.5.  The find the probability for D+1 that moves with values of k greater than K will be chosen.


This was converted to standard deviations, then to differences in rating points W(1).  Next, the win record for games of n moves would be, by a basic statistical rule, a factor of square root of n higher: W(n) = SQR(n) W(1).  After depth vs. rating was plotted using the PC (a math coprocessor is helpful here), the following formula was seen to fit the resulting data closely:



This gives the future Deep Thought a rating around 3020 (computer vs. computer), and with, say, 30 points software improvement, 3050.  Rating for a player making random legal moves comes out at about -1650.  Larry Kaufman has extrapolated grand masters' draw percentages to predict a maximum rating of 3600, in rough agreement with the above.


Evaluating p' implies that 87% of Kasparov's moves in his own games are those of a perfect player.  Evaluating p shows that Kasparov would correctly guess 82% of the moves of a "perfect" game.  Again, if he applies anti-computer techniques, such as keeping the game "closed" and avoiding "sharp" positions, he should be able to just about equal the computer's strength, for a very exciting match.


The assumptions on which these results are derived are admittedly rather ad hoc, but they're the simplest I've found that fit the facts.


An approximate rating vs. time per move formula for use with your home chess computer, based on the above:



where r(180) is the rating for the 180 sec/move (40 moves/2 hours) setting on your computer.  t is time per move in seconds.  This formula works best for ratings above 1000.  Keep in mind that limitations on hash table and memory size may adversely affect computer strength at move times greater than 3 minutes.


[Editor:  Not being chess literate, I asked Glenn for more info on chess ratings, etc.]

Dear Rick,


The formula for the win percentage vs. rating difference is ideally supposed to go like the integral of a normal distribution:



76% corresponds to a rating difference of 200 points, and 500 points gives 96%.  (76% is the probability that a random variable from one normal distribution exceeds that from another such distribution displaced one standard deviation below it.)


Also, the rating distribution of all tournament players is "supposed" to be normal, with the mean around 1500 and 200 points as the standard deviation.  However, Larry K. has informed me that neither of these assumptions actually holds exactly in practice:  they are rough approximations.  Larry is in charge of USCF ratings, so I guess I'll take his word for it.


It is remarkable that in chess the s.d. from the rating diff. vs. win percentage is about the same as that of the player rating distribution.  This does not generally seem to be the case in other measures of human attributes and sports abilities.


The way the ratings are actually determined is without reference to any particular pdf or distribution.  For example, if a player wins, his rating is adjusted as follows:


new rating = old rating + 16 + .04[minimum of 350, R(s) - R(w)]


where R(s) = rating of stronger player, R(w) = rating of weaker player.


If one beats an opponent 350 or more points higher, one gains 30 points.


I hope this clarifies things a bit.


Yours Truly,

Glenn A. Morrison






Dear Rick,


I am grateful to you and Chris for keeping Noesis in publication, and for providing the subscribers to it, known by whatever name for having met whatever standard, a means by which to affiliate with one another.  For awhile, it looked as though we might no longer have that.


However, I must protest your having decided arbitrarily to exclude statements by contributors whose sentiments you regard as unbefitting serious displays of intellectual facility.  As interested as I am in the more utilitarian applications of our giftedness--masturbation, fake I.D.'s, and sitcom families at speed approaching that of light--I am fascinated by the notable respects in which we are not exceptional from people in possession of more nearly normal intelligence.


Aside from the notion that a high IQ is equivalent to genius, probably no IQ society delusion is more fatuous than that which holds we are abler than "the rest" to subdue emotionality in favor of rationality--that our strength of mind frees us of the egomaniacal encumbrances which make more difficult an earnest pursuit of knowledge.  Contrariwise, so frequently do we see simple, determinable truths more quickly and certainly than do most people we encounter in our daily lives, we can easily become so arrogant as to preclude our accepting criticism of our views on highly complicated questions, even when offered in the most civil of tones.


None of us is but human in  this organization, and those of us who wish to demonstrate their foibles as such should be free to do so without interference by a pious publisher.  I am giving you the benefit of the doubt, Rick, in that this is the first real controversy with which you have had to deal as editor.  J'accuse.  As a long-time bouncer and adventurer of sorts, you relish a long, dirty, finished fight over a spilt beer as much as I do.  Your function as editor, however, is not to make us take it outside.


Can anyone but Ron and Kevin, who clearly cannot agree on anything, recount the specifics of their disputes?  I cannot, nor do I care to; but how hilarious it is to watch them engaged in battle, each of them wishing momentarily that he had spent more time cultivating his polemical skills, each of them occasionally landing a soft blow. 


Yes, Noesis should contain primarily essays on matters philosophical, puzzles and problems, comments, reviews, and autobiographies; but for every three or four Raging Bulls's, a Pink Flamingos is perfectly appropriate.


Otherwise, more than pleased,


Eric Erlandson


P.S. Note that I have avoided the much-abused "censorship" in the above.  The word has come to identify the user if it as some kind of bone-headed Free Speech purist, which I am not.  Should one of us submit for publication an actual method by which anybody could enrich plutonium using only things found around the average home, I would expect you not only not to publish such a thing, but immediately to turn his name and work over to the CIA.  Now,  that would be fun!


[Editor:  O.K., no more omitted passages, at least until I receive something really awful.  The omitted Hoeflin & Langdon passages were actually pretty mild.]


more from Eric Erlandson:


I submit, for your pleasure (undoing?), a number series designed by Dr. N. G. DeBruijn.  It is infinite and follows a very simple rule; but, since, my cracking it in about nine days very much impressed Paul Erdos, I suppose to do it in a week would be truly outstanding.  Because I've not had a chance to discuss with Dr. DeBruin how dear the thing is to him, I don't feel comfortable having the secret actually published.  I do know that it has been passed around quite a bit by now, so I would be fine with discussing or corresponding about it on a one-to-one basis.


Eric Erlandson

2051 Worthington Ave

Lincoln NE  68502

(402) 475-5746


I have sent Rick the first 2000 terms of the series, but it wouldn't make much difference if he were to publish only 1000 of them. [We'll see. Ed.]  I hope he can get away with Xeroxing the page.  [Nope.]  The numbers in the left margin indicate position, and the text has been blocked for more convenient reference.  [maybe]


The problem is stated in various ways, but I like the following: Let F(n) = the number in position n.  What is the smallest n, such that F(n) = 100?


[1 - 100] 

0 0 1 0 1  2 0 1 2 0  1 3 2 0 1  2 4 3 0 1  2 4 3 0 1  4 2 3 5 0  1 2 6 3 5   4 0 1 2 5  3 4 7 0 1  2 5 3 7 4 

6 0 1 2 8  3 6 4 0 1  5 2 7 3 6  4 9 8 0 1  2 3 6 9 4  7 5 0 1 2  9 3 8 4 7   5 0 1 2 6  8 3 4 11 10  7 5 0 1 2

[101 -200]

6 3 10 4 7   9 5 12 0 1   6 2 10 3 4   9 12 5 11 6   0 1 2 3 9   7 4 11 5 8   10 6 0 1 2   12 3 7 4 5

8 10 14 13 6   0 1 2 9 3   7 4 14 10 5   12 6 0 1 2   7 3 14 4 13   10 8 5 12 6   9 11 0 1 2   7 3 4 8 5

16 15 6 11 9   0 1 2 3 10   12 4 8 15 5   14 11 6 13 0

[201 - 300]

1 7 2 10 3   15 4 8 14 5   11 9 6 17 16   0 1 12 2 3   14 8 4 18 5   1316 9 6 15   12 7 0 1 2   3 8 4 11 13

5 9 15 6 12   19 18 7 0 1   2 3 8 4 11   5 9 19 6 12   14 17 10 7 0   1 2 3 13 11   4 15 19 18 5  

9 17 6 14 10   16 7 0 1 2   8 3 18 4 9   5 14 12 6 16   21 10 7 13 0

[301 - 400]

1 2 8 3 17   4 9 5 12 20   16 6 19 10 7   13 15 0 1 8   2 22 3 20 4   14 9 12 5 6   10 15 7 22 21  

17 11 0 1 2   3 14 4 9 12   5 18 23 6 10   15 13 7 20 11   8 0 1 2 14   16 3 4 18 22   5 21 10 6 20

13 7 11 24 8   23 0 1 2 3   12 9 4 5 20   15 10 6 13 24   19 7 11 22 16   8 18 0 1 2

[401 -500]

12 3 9 4 15   5 24 10 13 6   22 7 11 16 21   14 8 0 1 2   25 3 9 4 17   15 5 19 10 6   21 7 11 18 14

25 8 20 0 1   2 9 3 15 22   4 5 10 21 6   25 16 18 11 7   14 20 23 8 12   0 1 2 9 3   27 4 13 25 5  

24 6 16 20 11   14 7 8 12 17   19 0 1 2 3   4 13 10 5 18   16 23 20 6 11   28 7 22 26 8

[501 - 600]

19 12 15 21 0   1 9 2 3 13   4 23 18 10 5   27 6 26 14 11   7 19 17 8 12   21 15 0 1 28   2 3 18 20 4

10 5 22 25 6   11 7 24 17 21   29 12 8 15 27   23 9 0 1 2   13 3 16 4 10   5 14 6 24 11 19 28 17 7 27  

12 8 26 20 9   0 1 2 16 3   30 10 4 24 28   5 14 19 6 17   7 26 15 12 8   20 31 18 22 9

[601 -700]

13 0 1 2 3   10 4 27 14 5   21 11 6 23 7   15 12 25 29 8   18 28 9 13 16   0 1 2 3 10   4 19 14 32 5  

17 30 11 6 29   25 7 12 20 22  18 8 24 27 13   9 32 0 1 2   21 3 23 4 29   17 5 11 6 28   15 20 7 12 18  

24 33 8 31 16   13 30 9 21 0   1 2 10 3 14 4 28 5 11 6   22 20 15 24 7   12 30 8 26 16

[701 - 800]

13 9 23 19 0   1 25 2 10 14   3 17 4 5 11   22 20 6 15 30   18 7 26 29 8   16 21 13 34 28   9 19 25 32 0

1 10 2 3 4    22 30 11 5 15    6 18 29 12 7    34 33 8 21 32   13 25 19 9 27   17 0 1 2 3   24 4 35 11 5

15 18 6 12 28   7 23 21 16 25   8 13 27 9 36   17 35 14 10 0   1 2 20 3 26   4 11 32 5 18

[801 -900]

28 6 31 12 23   7 16 30 8 13   34 9 33 17 24   22 14 10 0 1   2 3 4 11 15   5 23 6 25 12   35 30 7 27 16

19 8 13 29 9   22 17 26 14 20   10 0 1 2 36   3 18 4 15 23   5 30 34 21 6   12 33 16 7 19   29 8 24 22 38

9 36 31 14 35   10 0 1 2 3   15 11 4 27 5   6 12 29 16 19   7 37 24 13 8   22 31 35 17 9

[901 - 1000]

20 14 10 0 1   18 2 27 3 11 4 21 38 32 5   12 6 16 7 24   26 13 28 8 34   17 20 9 30 14   33 39 10 23 18

0 1 2 15 3   11 4 5 12 19   6 26 24 34 7   22 13 8 39 30   17 38 20 9 37   14 25 27 36 23   10 18 29 0 1

2 11 3 4 34   5 19 12 16 28   6 22 7 30 13   8 17 20 36 32   25 9 14 23 29   10 21 15 31 0

[1001 - 1100]

1 2 11 3 4   24 19 5 16 12   37 6 36 7 13   17 8 27 25 29   9 40 39 18 31   10 21 38 15 0   1 2 28 3 24

4 30 16 5 12   22 6 32 42 35   7 13 20 17 25   8 39 23 34 14   9 18 21 37 10   15 26 28 0 1    11 2 3 19 42

4 41 16 5 35   6 39 27 7 13   17 34 8 23 37   14 9 18 21 36   43 10 26 15 30   24 40 0 1 2

[1101 - 1200]

32 3 22 4 12   5 38 27 6 25   20 13 7 23 8   42 33 14 41 9   18 28 26 30 10   15 35 32 11 0   1 2 3 16 4

12 29 5 44 25   31 6 20 17 13   7 36 33 40 8   14 28 21 18 9   35 24 10 15 19   11 0 1 2 16   3 4 31 12 25

5 20 40 6 17   13 7 39 8 35   30 14 21 18 32   9 44 24 43 42   10 34 37 19 22   11 27 0 1 2

[1201 -1300]

3 25 4 12 33   5 39 23 6 17   13 35 7 28 30   43 26 8 21 14   18 24 9 37 34   15 10 40 19 27   36 11 0 1 2

46 3 12 4 20   5 38 17 6 30   13 32 7 26 41   21 8 14 18 24   40 9 15 29 10   22 27 19 44 33   11 43 16 0 1

2 35 3 12 4   23 5 28 17 32   6 13 26 7 40   21 47 8 14 45   36 44 9 29 31   15 22 10 19 42

[1301 -1400]

25 35 11 16 0   1 2 20 3 12   4 47 5 40 46   26 6 21 7 24   39 18 14 8 31   29 9 27 22 15   19 10 25 41 48

11 16 46 37 30   0 1 45 2 3   34 4 17 5 39   13 6 21 24 7   18 31 14 8 33   38 27 9 35 22   15 19 25 19 45   37 40 30 11 28   23 20 0 1 2   12 3 26 4 17   5 42 13 6 24   49 48 31 38 7   18 41 14 8 45

[1401 - 1500]

22 9 15 19 44   10 32 30 43 34   16 11 23 20 36   0 1 2 12 3   17 4 5 13 24   33 6 29 45 35   18 7 27 14 44   8 37 22 9 19   15 32 30 10 39    48 28 42 16 23   11 20 26 0 1    12 2 3 4 33   21 5 13 44 6   40 18 7 14 43

50 8 22 48 25   32 39 9 15 42   28 10 23 16 20   11 26 0 1 31   2 17 3 35 29   4 21 50 5 13

[1501 - 1600]

37 27 6 18 7   47 14 39 22 8   25 34 30 19 9   15 28 45 41 10   38 23 16 20 11   50 33 31 35 12  

0 1 2 24 3   21 4 13 5 42   6 7 14 34 22   25 30 36 8 19   28 15 9 38 50   44 49 10 26 16   20 40 33 43 11   47 29 12 0 1   2 21 3 27 4   13 5 45 18 6   32 51 36 30 7   44 49 8 19 48   15 9 40 23 47   10 33 35 20 16

[1601 - 1700]

37 11 29 42 24   17 12 0 1 2   3 50 4 13 32   5 36 18 44 6   25 22 38 14 7   28 8 19 43 40   15 9 23 35 46

26 31 10 20 16   42 51 29 11 50   24 17 12 21 0   1 2 3 4 13   18 5 25 6 22   43 14 7 54 53   19 8 35 15 9

23 26 31 50 45   10 39 16 29 11   48 24 41 27 17   21 12 32 0 1   2 3 30 4 18   52 5 40 22 6

[1701 - 1800]

28 14 7 50 19   33 8 45 15 31   23 9 20 10 16   41 11 24 47 34   36 27 17 21 38   12 43 51 0 1  

2 40 3 13 4   25 5 28 6 45   49 14 33 7 19   31 8 26 15 44   9 29 53 20 47   10 16 36 34 24  

11 32 46 21 17   50 40 12 30 0   1 2 3 13 4   22 5 37 56 33   55 6 14 39 7   44 26 52 8 15   29 9 20 36 43   16 10 38 24 32 

[1801 - 1900]

27 40 11 21 17   30 45 12 42 55   54 0 1 2 18   3 13 22 4 33   39 5 47 6 14   41 19 7 26 23   8 15 50 46 43

36 9 20 34 16   57 10 24 55 45   54 11 21 48 17   12 52 37 25 28   0 1 2 22 13   3 4 41 5 14   6 19 26 7 23   29 8 49 38 34   54 20 9 32 53   16 27 24 10 42   52 30 11 17 44   37 35 12 25 28   33 41 0 1 2

[1901 - 2000]

13 3 56 31 4   55 5 14 6 19   23 36 7 53 34   40 15 8 48 20   9 27 16 10 51   30 47 44 21 11  

57 17 50 56 33   25 12 55 46 22   18 0 1 2 3   4 5 26 14 36   19 6 48 23 34   7 42 15 8 51   20 59 58 9 24   44 16 30 10 37   39 35 21 11 54   17 46 33 25 12   53 22 18 0 1   13 2 3 45 38 4 26 5 29 14   23 6 42 7 32


more from Eric:


I really like Chris's idea, and I'm very eager to get a shot at the first crop of problems.  A nicely mixed metaphor, don't you think?  Publish whichever of these you care to in the next issue, if only one per issue is allowed, and save the other for next time.  I'll send others as they occur to me.


[The questions are part of the "short form" test below.  An unlimited number of problem submissions per issue is allowed.]







Dear Editor:


I hereby resign my office of Ombudsman and suggest that the office be left vacant or merged with the office of Editor.  I viewed my role as a mediator, but from what I see in Noesis 65 and 66 people are quite capable of complaining and reaching agreement on their own.


I like Kevin Langdon's discussion of his and the Mega Test.  His, I believe, is suitable for bright polymaths who may or may not be lazy or difficult to inspire.  When I was taking his test I would ask myself "What pattern can I find in this problem which would make me feel stupid if it were explained to me, and I hadn't seen it myself?"  That helped a lot.  By contrast, I hit on the answer to one of the Mega Test's number series and thought "How arbitrary and obscure!  I haven't got the patience or perseverance to search around for patterns like this!" 


A friend of mine is of the opinion that the Mega Test does not really measure intelligence, because he knows people who are, in his opinion, good at library-usage and mathematics, but not extremely intelligent, who do very well on the Mega Test.


I. e. Langdon coaxes intelligent answers out of you, while Hoeflin presents you with a stone wall which he dares you to climb.


I'm disappointed my "Joy List" wasn't indented when published the way I intended.  I meant the indentation to be reminiscent of the indentation of structured (computer) programming, as if an if-then-else list.  I consider it the smallest of operating systems.  It is as if Jesus said, "Follow me, and I will make you a system architect of men."  You see, pyramids and hierarchies are small at the top, so the highest level specification of the joy of life should be small too.  As Jesus might put it, "Which is easier to say, 'the meaning and purpose of life,' or 'the joy of life'?"


Very truly,


Robert Dick




by Robert Dick

13 Speer Street

Somerville, NJ  08876

(908) 722-6949


Say there are two objects, A and B, motionless with respect to each other, but far apart, in interstellar space.  Assume that all gravitational fields along the line between them are everywhere small compared to one (Earth) G.


An intrepid astronaut boards a spaceship at object A, which is initially at rest with respect to A (and B).  The spaceship then heads straight for B at an acceleration that feels like a steady one G to the astronaut.  This goes on for one year ship time.  Then the ship flips and decelerates at what feels like one G for one additional year ship time, whereupon the ship is at B.


Question 1:  How far apart are A and B?  Newton would say about a*t*t = about (10 meters/sec/sec) * (3*10**7 sec/year)**2 = about 10**16 meters apart.  But what would Einstein say?  If acceleration slows as the speed of light is approached, so does ship time.  Therefore could it be that Newton is right about the distance?


Clearly relativity is involved, since after one year Newton would say v = a*t = about (10 meters/sec/sec) * 3*10**7 seconds = 3*10**8 meters/sec = about the speed of light, c.


Question 2:  Given a return trip conducted in the same fashion immediately upon arrival at B, how much time will have elapsed according to an accurate clock held stationary the whole time at point A?  Must it not be considerably longer than four years?  But why?  A clock sitting on a shelf at one G on Earth the whole time surely should register the same time as the ship's clock, which was also subjected to a steady one G the whole time.  How can this be?


[Editor's comments:  With my snazzy new set-up, I oughta be able to print Robert Dick's "Joy List" indented properly.  Here it is:




They who

live small

honor their father

feel sorry

get new joy


renew the world

try hard to do right

grow new strength

give help

get new help

aim for just one thing

see the One newly

give joy

are like a new

child of the One

do right even though

they get hurt for it

honor their father


About gedankenexperiment question 2--this is just a wild guess, but aren't you mixing special and general relativity when you talk about an earthbound clock ticking at the same rate as a clock being accelerated on a rocket?  Doesn't general relativity have a different set of rules for time dilation?  While we're discussing relativity--S. Woolsey wrote and reminded me that the symbol for the speed of light is little c, not capital C.]






Dear Rick,


I had just bought a money order when I found issues 65 & 66 of Noesis in my mailbox.  So here's the money to join Mega and for however many issues of whatever you decide to call the newsletter.  I am hoping that you will send me a cute certificate to impress my friends.


Unfortunately, being an involved Mega member is not a high priority right now.  My problem solving skills have not proved extremely marketable lately and you are all so few and far flung that Mega doesn't look terribly useful for job networking as I'm in Canada and most (all?) of you are not.


[Sorry, no cute certificate.  However, there are some Mega members who aren't flung so far from you.  Richard May lives in Buffalo, NY, Hughes Gervais lives in Charlesbourg, Quebec, and other current or former members live in Canada, Michigan, or New York.  Also, many members, more computer literate than I, communicate through email.  There may even be computer-mediated employment opportunities.--Ed.


On the other hand, I see you may have a niche for test scorers, and possibly some use for test development.  I have a PhD in psychology (cognitive) with lots of background in statistics, factor analysis, test theory, etc., etc. (Resume enclosed--don't publish it, but if anyone could use it, send it on.)


[If you're interested, let me know, & I'll send you a copy of Dr. Clifton's resume.--Ed.]


So if there is any monetary reward available for either test scoring or helping with test preparation (norms, reliability, validity, factor analysis, discriminant analysis, etc.) I might be interested.  Some years ago I did a small analysis on the item by item scores provided in the Omni Mega Test results brochure, but I never did anything more than submit it for a course assignment (42 individuals is an awfully small group.).  Maybe I'll write a bit more about it if anyone cares.  Incidentally there seemed little evidence to support separate numerical and spatial factors, but the verbal vs. math/spatial distinction seemed to be warranted.


One of the reasons for my application for membership last summer was, not to put too fine a point on it, to meet intelligent people (especially men).  However, this is no longer an issue.  I now have a "significant other" (who would like to see me gainfully employed).  A comment is in order here for all you "sensitive" men.  How do (would) your "significant others" feel about you belonging to an organization they can't join?  How would you feel if you had a female significant other who belonged to a group like Mega if you could not join?  There may be a double standard which is not overt, or even acknowledged.  I think such subtle pressures (which may even be largely self-imposed or imagined) may keep your female membership low and/or dormant.  (Please note: I am only addressing one issue here; why women seem not to obtain very very high "IQ" test scores in proportion to their numbers is another can of worms altogether.)  I any case, I can always justify this contribution in terms of seeking employment.


I do find some of the problems presented in Noesis challenging and interesting (just in case you were wondering if I had no interest at all in intellectual stimulation for its own sake).  However, sometime I would like to find the answer to something which someone else had not created already, in short discover or prove something new even if not "useful".  For me the appeal of actually doing tests has paled somewhat.  The results generated by groups of people may still interest me though.


I'm not sure what IQ or intelligence is (Who is?) nor what I should have in common with other people who are good at these sorts of tests.  I'm pretty sure that the numbers called IQ scores are almost meaningless in the extreme ranges.  I have one theory about high IQ societies and this may explain my reluctance to be very involved with them.  High IQ societies are essentially collections of


For years it has been argued that many, if not all, IQ tests "discriminate" against children (and adults) who are not from the dominant culture, who are poor or who have language difficulties, etc., etc.  Culturally disadvantaged is one tag sometimes used in this context.


Clearly, people who belong to high IQ societies DON'T have this problem, and do well on standard IQ tests (or e.g. Ron Hoeflin's tests which require a fair knowledge of English, classical mythology and so on.  Even the LAIT requires good English and familiarity with modern Western conventions for representing spatial perspective).  Further, I'd be willing to bet that the membership of Mega and similar groups is heavily loaded with Caucasians, many of Northern European background (This describes me too).  The names of your contributors support this.  Rosner, Harding, Hoeflin, Sweeney, Price, Pomfrit, Cole, Langan, Dick, Inman, Langdon, May, O'Brien, Van Vleck, Skinner, Wright, Hvatum--culturally advantaged may be an accurate descriptor.


Now for the underachiever part.  Have you ever been asked, "If you're so smart, how come you're not rich?  How come you haven't found a cure for cancer?" etc.  These are, of course, not really fair questions, but it does need thinking about.


There are a lot of people out there who are very intelligent, but who don't join high IQ societies.  Some of them have made important intellectual and artistic contributions.  Perhaps they have on psychological need for further intellectual stimulation but perhaps they also have no psychological need to belong to an organization to validate their intelligence.  They can say, "I've done this, and this, and that, and I don't need to spend my time fussing about whether I'm more intelligent than 98%, 99%, 99.97% . . . of people.


Take John Sununu, for instance (shades of "Take my wife . . . please!)  The comments in my letter so far should alert you to the fact that my political opinions are rather dissimilar to Mr. Sununu's.  The point I want to make is that he scored very high on the Omni Mega Test, but didn't have an interest in joining any high IQ group (at least that's the impression I got from one newsletter) at that time.  He probably had lots of other things to do and although that test result may have added to the general journalistic impression that he is a very bright man, it certainly wasn't one of his major accomplishments.


So, do we all join because we can't figure out what else to do with ourselves?  Are a disproportionate number of members people who don't "fit in" or are perhaps "underachievers"?  Is this a self-selection bias, or is society hard on or difficult for the extremely intelligent person?


Now I've probably offended everybody: even if you haven't already heard these arguments from others, I think they are still worth considering and developing a response to.  Perhaps this lady is protesting too much, nonetheless I could not join without expressing my reservations.  I have been led to believe that I qualify for membership and I will be happy to stay and may occasionally voice all sort of politically incorrect opinions.  On the other hand I may become dormant.  I'm pleased Rick Rosner welcomed everyone to "this slightly silly vessel;" it leads me to hope that some of you may want to challenge yourselves by thinking about why this organization exists as well as who can join.  Of course, you can always stick to doing analogies.


Best wishes,


Jane Clifton


Please edit this if anything looks libelous or particularly troublesome.  I don't think there's any personal invective that should bother some readers more than others.


[Editor's comments:  Though Dr. Clifton said not to publish her resume, I do want to tell interested readers that it lists her proficiency in four computer operating systems, nine software packages, including four statistical software packages, and seven computer languages.  About her comments concerning culturally advantaged underachievers--I think I fit her profile better than most Mega members, but I'd guess that the average achievement level among all members is higher than that of the general population and also higher than the average level of other high-IQ societies.  Many members are highly educated and some are very successful in a traditional sense, both materially and in terms of being married, raising families, living lives that look more or less normal to the average casual observer.


Mega members might be underachievers when compared to other people with the same average level of education; most people today earn degrees to make money.  I think all Mega members have heard arguments along the lines of "If you're so smart, why aren't you rich?"  I used to not be bothered by such questions, my unstated response to them being "If you're so stupid, why don't you kiss my ass?" but traditional pressures in my life have forced me to start asking myself "Why can't you get it together and make some bucks?"  I can't even get in the National Enquirer as smart but screwed up.  An interesting book about  William Sidis, a smart guy who frittered his life away, is The Prodigy, by Amy Wallace.  Sidis is my worst-case scenario.]









Dear Rick,


I just received Noesis 65 and 66.  Enclosed is $10 . . . .


Regarding Chris Harding's letter on page 4 of issue 65, I think our operations are too small-scale for us to be hauled into court for violating some impending international regulations regarding "tests produced by amateurs."  I am told that the American Psychological Association already prohibits tests that are untimed and unsupervised in its ethical code for American psychologists although I've never personally confirmed this.  But since I don't belong to that organization, I am not bound by its rules.  I have seriously considered getting a second doctorate in psychometrics, by the way, but so far lack of funds presents an insuperable barrier.


Regarding Robert Dick's letter on page 11 of the same issue, I doubt if there is a clear demarcation between "aptitude" and "achievement."  But one reason I am developing a third major test, the Ultra Test, is so that the spatial problems from all of my tests--Mega, Titan, Ultra, etc.-can eventually be put together into a single "culture-fair" test that could be translated into foreign languages, which is not possible for the verbal analogies portions of my tests (with the possible exception of verbal analogies that rely entirely on international scientific vocabulary such as Billion : Giga- :: Billionth : ?).


Regarding your renewed comments on fake ID cards in issue 66, page 1, I recall that your own autobiographical remarks in previous issues indicate that you yourself have faked your own ID several times, as when you repeated your senior year in high school, not to mention your having taken the SAT for other people, as you mentioned in your appearance on the Morton Downey, Jr., TV show a few years ago.  I think this obsession with impersonation betokens what used to be known as an "identity crisis."  I believe the psychologist Erik Erikson has written entire books on the problem of achieving one's own identity.  Great impersonators (as people with so-called multiple personalities) perhaps tend to have high fluid intelligence which makes it possible for them to shift their thinking into an alternate identity.  Actors and actresses are putting this sort of talent to some constructive use.  I guess the same could be said for detecting fake ID cards, except that in this case you are being constructive by detecting other people's fake impersonations rather than assuming a fake ID of one's own, as a spy or actor would.




Ron Hoeflin


P. S.  I'd like you to publish a full list of the new Mega Society's members' names and addresses (omitting those who are non-member subscribers).  But I believe Marilyn vos Savant prefers that her address not be published any longer by the high-IQ societies.  She probably should get a P.O. box so that people can have some standard way of contacting her without arousing (legitimate) paranoia.


P.P.S.  Regarding Kevin Langdon's remark on page 8 of issue 66, which I belatedly came upon, to the effect that I am "up to [my] old tricks again," I should point out that the idea of merging the Mega and Noetic societies and of using only my tests for admission purposes was definitely not mine.  I believe Chris Cole and Jeff Ward, representing the Noetic and Mega societies, respectively, came up with this whole plan.  I correctly predicted that the plan would result in a lot of howling of disapproval from Langdon and others.  The merger does not benefit me in any way and I was perfectly happy to see the two groups go their separate ways.  My personality is more akin to Chris Harding's than to Kevin Langdon's in that I tend to avoid interpersonal conflicts.


P.P.P.S.  Regarding Ed Van Vleck's remarks in issue 66 p. 12, on the lack of "peer review" for the Mega Test, there is (or will shortly be) a 4-page review of the test by a professional psychometrician in volume 8 of a publication called Test Critiques.  I can supply Mr. Van Vleck with a copy, if he wishes.  The review was not especially favorable, perhaps in large part because the test is untimed and unsupervised, but those "flaws" also apply to the Langdon tests and other "home brew" tests.  Van Vleck thinks I am unwilling to look at criticisms of my tests.  I suppose I could reply to this view with two mutually contradictory arguments:


(1)  I am an artist--a "test-designing artist," if you will--and an artist has already put his all into his work of art.  If the work of art is still flawed, so be it.  The artist has done his best and can do no more.


(2)  I am a hard-headed pragmatist.  I'll go on with the use of my Mega Test, Titan Test, etc., because they get the job done.  If they are imperfect, so what?  There is no human creation that is perfect.  Imperfections should serve as an impetus to future creators to do a better job!  Each stage builds on and improves what went before.  Newton and Leibniz invented the calculus, but their reasoning was certainly not letter-perfect by future standards.  Yet we still honor them for having made a good beginning.



[Editors comments:  Hoeflin, as he stated, did not have anything to do with any of the (ill-advised) provisions of the merger.  It was part of my considerations not to offend him, because I want his continuing input, but he was not consulted.


About fake ID and an identity crisis--I've been having what I call "a rolling nervous breakdown" since I was 17 and decided to acquiesce to societal norms as I perceived them, becoming  a slightly monstrous amalgamation of regular slob and savant.  But you know that.  Suffice to say that anything Hoeflin theorizes about my psyche is likely to be true.]



Dear Rick,


I entered this essay into an essay competition, but I don't think it matters if you publish it in a journal as small as  Noesis.  You can also publish the longer essay, "Metaphysics and Personality," any time you wish, if you wish.  This essay may be of more interest to the members.  It's also a bit shorter (3000 words vs. 500 or so), which means you could probably squeeze it into a single issue of Noesis.




Ron Hoeflin


P.S.  If you do list members in a future issue, I'd prefer to be classified as "founder" or as "non-member subscriber" or omitted entirely from the list rather than be classified as a "member."


My definition of the Mega Society's admission standard:


The Mega Society is a society that seeks to select members whose intelligence is at or above the 99.9999 percentile--the one-in-a-million level.  Any admissions that have previously been made or that may in future be made whereby any person or persons gain admission without having this level of intelligence shall in no way subvert the society's goal of adhering to this standard with as much accuracy as it can. Any member may legitimately question the effectiveness of the Society's admission procedures, but no member may question the goal of adhering to this admission standard without automatically disqualifying himself or herself from further participation.  Such persons should form a new group at whatever new admission level they deem suitable.  My only means of enforcing this declaration shall be to remove myself and my tests from any further participation in or use by the Society if any member challenging this admission goal of the Society is not immediately removed from further participation.  I'm sorry if this sounds dogmatic, but to me a "Mega" Society that does not seek as its bedrock aim to stick to a one-in-a-million admission policy is a joke and a sham.  We have plenty of constructive things to discuss and debate, so that the loss of this one topic should not be any great loss but instead may help us to more effectively share in a common purpose.   If we cannot adhere to even this one simple goal, we will be like a rudderless ship.  I prefer purposeful enterprises to purposeless ones.


Ron Hoeflin







This paper contends that the four general trends in American philosophy during its so-called "Golden Age," as outlined by Paul Kurtz in his article, "American Philosophy," for The Encyclopedia of Philosophy, correspond to the four "philosophical tendencies" discussed by Ralph Barton Perry in his 1912 book, Present Philosophical Tendencies, which in turn were discussed under different labels by Stephen Pepper in his 1942 book, World Hypotheses.  In his final book, Concept and Quality, published in 1967, Pepper devised a metaphysical system he called selectivism, based on the "root metaphor" of a purposive act.  I argue that the structure of a purposive act can be analyzed in such a way as to integrate into one coherent system not only Perry's "philosophical tendencies" and Pepper's "world hypotheses" but also the major solutions to the problem of induction outlined by Max Black in his article, "Induction," for The Encyclopedia of Philosophy.





In his article, "American Philosophy," for The Encyclopedia of Philosophy Paul Kurtz has a section on the "Golden Age of American Philosophy" covering the period from 1880 to 1940.  This section is divided into three main subsections titled "Pragmatism," Realism," and "Naturalism," with a brief addendum titled "Recent Idealism and Rationalism."


Perhaps not by coincidence, these four subsections correspond almost precisely to the four "philosophical tendencies" that Ralph Barton Perry examined in his book, Present Philosophical Tendencies, which bears the lengthy subtitle, A critical Survey of Naturalism, Idealism, Pragmatism and Realism, together with a Synopsis of the Philosophy of William James.  Present Philosophical

Tendencies was first published in 1912, almost exactly at the midpoint of the sixty-year period that Kurtz identifies with the "Golden Age" of American philosophy.


These four "philosophical tendencies" are also mentioned in a book by Andrew Reck titled The New American Philosophers: An Exploration of Thought Since World War II.  In his discussion of the philosophy of the American philosopher Stephen C. Pepper (1891-1972), Reck notes that Pepper's 1942 book, World Hypotheses, discusses four principal metaphysical systems of "world hypotheses," as Pepper called them, designating them "formism," "mechanism," "contextualism," and "organicism."  Pepper makes no mention of Perry's 1912 book in World Hypotheses, but Reck spots the parallels between the two books, pointing out that "Pepper's four principal world hypotheses match those which Ralph Barton Perry believed to be the present philosophical tendencies: organicism is idealism, mechanism is naturalism, contextualism is pragmatism, and formism is realism."  But unlike Perry, Pepper tried to show that each world hypothesis derives its organization and unity from a central guiding model or analogy that he called a "root metaphor," such as the idea of a machine for mechanism.  In Chapter VII of World Hypotheses he entertains the notion that it might be possible to integrate all four major world hypotheses under a single root metaphor, but in his closing chapter he abandons this possibility as unworkable.


In his final book, Concept and Quality, published in 1967, Pepper proposed a new world hypothesis he called "selectivism" based on the root metaphor of "a purposive act."  He schematized a typical purposive act roughly as follows:


D            A1                                                                                                               G1            Q

A2                                                                            G2

A3                                              G3

        . . .                  . . .

An           Gn


This schema has four main components: (1) the drive, D, such as thirst or hunger; (2) anticipatory sets, A1 through An, such as the anticipation that eating a hamburger will satisfy one's hunger,  A1, that hamburgers can be obtained at a fast-food restaurant, A2, that fast-food restaurants require money in exchange for hamburgers, A3, and that money can be obtained in a variety of ways such as by getting a job, An; (3) goal objects, Gn through G1, corresponding to each of the anticipatory sets, such as a job, Gn, money, G3, a fast-food restaurant, G2, and a hamburger, G1; and (4) the quiescence of the drive, such as the satisfaction of hunger by eating a hamburger or the quenching of thirst by drinking water.


I toyed with Pepper's schema and came up with a slightly different way of looking at it.  I found that it can be analyzed into five segments or phases, with each of which one can associate a common-sense question that expresses the sort of problem one faces at that stage:


(1)  From D to A1 the central issue seems to be, What should I do?, e. g., given the feeling of hunger, D, what proposed action, A1, would assuage it?


(2)  From A1 to An the key problem seems to be, How should I do it?, i. e., what series of proposed actions would lead up to the primary action, A1, if that primary action, e. g., eating hamburgers, cannot be put into effect immediately?


(3)  From An to Gn the general problem might be expressed by asking, Will my anticipations bear fruit?, will a proposed action, An, yield the anticipated result, Gn?


(4)  From Gn to G1 the problem might be expressed, What will be the consequences?, i.e., having attained one goal object, Gn, will the remaining ones follow according to plan?


(5)  And from G1 to Q the key problem seems to be, Will I be satisfied?, e. g., will eating this hamburger actually satisfy my hunger drive?  If the meat is spoiled or poisoned, it may not.


At this point I made the completely unexpected discovery that the five phases and their common-sense questions correspond to five of the traditional branches of philosophy:


What should I do? seems to express the central issue for ethics.  For example, in The Language of Morals, by R. M. Hare, one reads:


It would be when, knowing all the relevant facts of a situation, . . . faced with choices or decisions between alternative courses of action, between alternative answers to the question 'What shall I do?' [emphasis added], that [one] would reveal in what principles of conduct he really believed.


This statement links my common-sense question for the first phase of purposive act to conduct, and Pepper defines "ethics" as "the study of the criteria of good and bad conduct," where "conduct" is said to mean "voluntary action."  And indeed, it does seem reasonable to suppose that one would not ask oneself what one should do unless one felt that one did indeed have a choice in the matter, i.e., that the proposed action is voluntary.  So ethics might be regarded, in effect, as the branch of philosophy concerned with issues that arise in the first phase of a purposive act, namely, issues concerning choice or voluntary action.


How should I do it?, my common-sense question for the second phase, is the central issue, I believe, for induction.  Consider the following three sentences from Pepper's 1958 book, The Sources of Value, in which he first examined the notion of a purposive act in depth:


A docile organism with a strong drive in action, like hunger or thirst, when faced with a novel environment would be at a loss what to do, if it were not for the instinctive technique of trial-and-error activity that automatically goes into gear at such a time. . . .

. . . My view is that the peculiarity of docile behavior is precisely the lack of a cognitive element in the crucial gap between a drive and its goal, and what is learned is the cognitive anticipatory reference that was previously lacking. . . .

The inductive methods of experimental science are essentially systematized trial-and-error.  [Emphasis added.]


As the words I have underlined indicate, the second sentence links anticipatory sets--and hence the second phase of a purposive act--to docile behavior, the first sentence links docile behavior to trial-and-error behavior, and the third sentence links trial-and-error behavior to induction.  These three crucial sentences are scattered across four pages, so it was only years after I discovered the connection between the second phase and induction that I realized, through these sentences, that Pepper had himself already definitely made this linkage.  How should I do it? might, in effect, be construed as a call for a quest, a quest that inherently involves anticipatory, docile, trial-and-error and hence inductive behavior.


Will my anticipations bear fruit? evidently expresses the central problem not just for the third phase of a purposive act but also for epistemology.  For this question can be reworded: Will my knowledge claims be true?, where "knowledge claims" replaces "anticipations" and "be true" replaces "bear fruit."  Since "epistemology" is simply another word for theory of knowledge, we might say that this branch of philosophy is essentially concerned with the same issues we encounter in the third phase of a purposive act, namely, issues of knowledge, i.e., whether a certain claim is true or a certain anticipation bears fruit.


What will be the consequences?, my common-sense question for the fourth phase, appears to express the basic problem for deduction or deductive logic.  For to deduce is to find the consequences of.  Furthermore, the fourth phase, from Gn to G1, in a sense just reverses the direction of the second phase, from A1 to An, just as induction and deduction are often thought of as arguments in the "reverse" direction to one another, in some sense of "reverse."  Last, we might associate some inductive generalization, An, with the major premise of a syllogism, as exemplified by "All men are mortal," and we might associate some perceived goal object, Gn, with the minor premise, as exemplified by "Socrates is a man," so that the next goal object, such as G3, would correspond to the conclusion of this syllogism, as exemplified by "Therefore, Socrates is mortal."  (For a relevant discussion, see Donald Williams' The Ground of Induction, in which the major premise is definitely associated with induction and the minor premise with something that is "directly verifiable by perception.")  Hence, the issue proper to the fourth phase is that of drawing a correct conclusion from a major and minor premise, the latter two representing the work accomplished in the second (inductive) phase and the third (epistemological) phase, respectively.


Last, Will I be satisfied?, my common-sense question for the fifth phase, seems to express the core problem of aesthetics.  For example, Pepper, a noted authority on aesthetics, defined "positive aesthetic value," commonly known as beauty, as "satisfaction in felt quality."


I made the further discovery that each of the major types of metaphysical orientation examined by Pepper and Perry emphasizes a distinctive phase of the purposive act:


Pragmatism, which Pepper called contextualism, I believe can be regarded as a metaphysical emphasis on the first phase of a purposive act.  For example, Perry quotes a leading pragmatist, F. C. S. Schiller, as having written that "Our ultimate metaphysic must be ethical," which Perry says means that "the knowledge process is essentially practical."  I take this to mean that pragmatism, like ethics, focuses on issues of conduct or voluntary action, the same issues that are central to the first phase of a purposive act.


Empiricism, as I prefer to call it, which Pepper calls mechanism and Perry calls naturalism, I associate with the second, inductive phase.  For example, David Prall, whom Pepper mentions in connection with mechanism, wrote that "all knowledge is science, empirical science, based on the unavoidable principle of induction," arguing that "the fact that we learn aptitudes is the fact that we generalize our responses," and "The formal expression of this fact is the inductive principle. . . ."  Here what Prall calls "aptitudes" seems to correspond to what Pepper calls "anticipatory sets."


Rationalism, as I prefer to call it, which Pepper calls organicism and Perry calls idealism, I associate with the fourth, deductive phase.  Spinoza's Ethics seems typical of rationalism in that its approach seems to be modeled after the deductive approach of Euclid's Elements.  On the other hand, Pepper regarded the chief proponents of what he called organicism to be Hegel and his followers.  Nevertheless, deduction seems to be as central to organicism as to rationalism.  Consider the following remark by Pepper concerning organicism:


The theory of truth [of organicism] is known as the coherence theory. . . .  Coherence is ordinarily confused with consistency, which is, as we know, but the formal shadow of coherence.  For consistency is mere formal non contradiction, whereas coherence is the positive organic relatedness of material facts.


Deductive conclusions would be useless unless there were material facts to exemplify them.  It appears to be the deductive relatedness of material facts--illustrated, for example, by the overlapping circles known as Venn diagrams--upon which organicists and rationalists alike are chiefly focused, a relatedness corresponding to that among the fourth-phase goal objects of a purposive act.


Formism, evidently named after Plato's theory of forms, I associate with the fifth, aesthetic phase.  Pepper suggested "similarity" as the root metaphor for formism.  Two objects are similar if they exhibit the same quality or qualities, roughly speaking.  As mentioned before, Pepper defined positive aesthetic value as "satisfaction in felt quality."  But in his first book on aesthetics he goes so far as to say that "The aesthetic field is that of the quality of events.  Great beauty is great enhancement of quality."  It seems to me, then, that qualities are the central concern of formism and aesthetics alike.


Last,  selectivism, Pepper's own metaphysical theory, he appears to have construed epistemologically.  In Concept and Quality he remarks, for example, that the "mind-matter problem . . . becomes a quality-concept problem."  He associated the left or "concept" half of a purposive act with mind and the right or "quality" half with matter.  The meeting place of these two is what I call the third, epistemological phase of a purposive act.  My own interpretation of selectivism is, of course, much broader.


We can now turn to the problem of induction.  In his article, "Induction," for The Encyclopedia of Philosophy Max Black has a section titled "Types of Solution under which he has six subsections titled: "Rejection of induction," "Inductive support for induction," "A priori defenses," "Deductive reconstruction," "Pragmatic defenses," and "Justification as a pseudo problem."


I would suggest that each phase of a purposive act is constantly enmeshed in each of the others, like an airline pilot or circus aerialist who must constantly be aware of all phases of his flight.  But even in less arduous tasks one is typically aware of what part of the task has already been completed and what part remains to be accomplished.  So each phase of a purposive act can be viewed from the perspective of each of the others.  Induction therefore can in principle be viewed from five different perspectives, if we include its perspective on itself.  This insight suggests a concise way to sort out Black's various types of solution to the problem of induction.


We find that Black has not arranged his six types of solution in a way that would suggest that he had any inkling of their connection to the structure of a purposive act.  "Pragmatic defenses" should come first, being the first phase's perspective on the second.  "Inductive support for induction" should come second, being the second phase's perspective on itself.  And "Deductive reconstruction" should come fourth, being the fourth phase's perspective on the second.


Black's three remaining types of solution are not quite so immediately recognizable in terms of the phases of a purposive act.  His discussion of "A priori defenses" is just one short paragraph.  If we delve a little deeper, however, we find that one advocate of this approach, Roy Harrod, says there is "a [modern-day] tendency to overthrow the traditional dichotomy of deduction and induction in favour of a new canonical scheme, constituted by the trinity of hypothesis, deduction and verification"; but Harrod goes on to say that "In certain cases a single verification may endow the hypothesis with high probability," whereas "In other cases a large number of verifications will only endow the hypothesis with low probability," so that what is needed is a "fourth process" of assessment," which for Harrod appears to be the key aspect of induction; and it soon becomes apparent that Harrod associates assessment  with similarity, as when he says, "By induction we argue directly from observed similarities in experience to wider generalizations."  It is clear, then, that in terms of the phases of a purposive act what Harrod calls "hypothesis" corresponds to the second phase, "deduction" to the fourth phase, "verification" to the third, and "assessment" to the fifth, bearing in mind that we have already seen that Pepper identified similarity as the root metaphor of formism, which we have previously classified in the fifth phase.  Since similarity is the crucial factor for Harrod, we can conclude that his "a priori defense" of induction is, in fact, a fifth-phase perspective on the second.


Under "Rejection of induction" Black includes the views of those, such as Karl Popper, who reduce induction to a "hypothetical-deductive" approach where, according to Black, "Inference enters only in the control of hypotheses by the verification of their observable consequences: negative instances strictly falsify a hypothesis, whereas positive instances permit its use, pending further experimental tests, as a plausible, if unproved, conjecture."  Here, the emphasis on verification marks this as an epistemological, third-phase perspective on the second phase.


In "Justification as a pseudo problem" Black offers his own solution to the problem of induction.  He argues that even to use language to discuss the problem of induction is to tacitly accept induction as a fact, rendering attempts to "justify" induction rather pointless.  The present essay suggests, however, that such attempts do, in fact, form a meaningful pattern, each type of justification corresponding to a different phase's perspective on the second.


[Editor's comments:  I didn't include Ron Hoeflin's source citations, 'cause I just didn't want to deal.  If you want the full footnoted version, let me know & I'll send a copy.  It seems to me that Ron is attempting a Grand Unified Theory of philosophy.  Is this an accurate interpretation?]




Chris Cole


As of this writing, five members have submitted questions for the "short form" high ceiling test that Rick and I proposed in previous issues.  Rick and Eric Erlandson submitted two related questions, which I guess is okay, but I think we should try to keep to one question per issue.  I know the Rand Corporation dictum that "quantity begets quality," but I don't want to inundate potential solvers and thereby discourage solving participation.  The quality of the test will very much depend upon how thoroughly screened the questions are.  SO PLEASE TRY TO SOLVE THESE QUESTIONS.


I have spent some time examining solution approaches to the Mega and Titan tests, have listened to criticisms of these tests, and have thought about which questions really tested for a cohesive body of intellectual weight and which merely tested for "doggedness."  Ron has mentioned elsewhere that the PAIN : RUE :: BREAD : ? analogy seemed to be impossible to solve by reference work.  The annual Putnam Mathematics Examination, which has an enviable record of selecting the most productive mathematicians, similarly has evolved from a grind-it-out test to an "aha!" test.  This, I propose, should be the goal of a question for the "short form" test.  In other words, the submitted questions should not be exercises in grueling library searches, combinatorial details, or lengthy calculations.  On the other hand, I see no reason to confine the questions, as Ron does, to "elementary" mathematics, physics, biology, etc.  So, with that said, let me assure the reader that at least some of the following questions can be answered with flashes of inspiration.  SO PLEASE TRY TO SOLVE THESE QUESTIONS.



1.  Six squares can be joined edge-to-edge to form a two-dimensional shape.  Some of these shapes can be folded and joined along the squares' edges to form complete cubes.  How many different arrangements of six squares can be folded into cubes?  (Count reflections as distinct, but not rotations.) (Rick Rosner)


2. Eight cubes can be joined face-to-face to form a three-dimensional shape.  Some of these shapes can be folded and joined (fourth-dimensionally) along the cubes' faces to form hypercubes.  How many different arrangements of eight cubes can be folded to form hypercubes?  (Again, reflections, but not rotations, are distinct.) (Rick Rosner)


Hints:  I know the answer to the first problem, but the second is brutal.  You don't need to be able to think in 4D's to solve it, however.  Each member of the set of six-square shapes that can be folded into cubes may be transformed into any other member through a series of 90-degree rotations of its constituent squares around the squares' corners.  180-degree rotations are not allowed.

Similarly, each member of the set of eight-cube shapes that can be folded into tesseracts may be transformed into any other member through a series of 90-degree rotations of its constituent cubes around the cubes' edges.  Again, 180-degree rotations aren't kosher.  Any legal rotation produces a member of the set.  All you have to do is find one unfolded tesseract; the rest is just finding legal rotations in three dimensions.


There are as many ugly problems of this type as there are unfolded polyhedra and hyperpolyhedra.  The set of unfolded tetrahedra is trivial, and the set of unfolded octahedra is easy, (Is it equivalent to the set of unfolded cubes?  I forget.) as is the set of unfolded hypertetrahedra.  The sets of unfolded icosohedra and dodecahedra are nasty (but equivalent?).


3.  0, 1 ,7, 2, 5, 8, 16, 3, 19, 6, 14, 9, 9, 17, 17, 4, 12, 20, 20, 7, 7, 15, 15, 10, 23, 10, ?  (Eric Erlandson)


4.  10, 10, 171, 186, 2748, 3258, 43981, 56506, 703710, 974010, 11259375, ?  (Eric Erlandson)


5.  BODY : HOLE :: MAX : ?  (Mike Price)


6.  You are lost in a half-planar forest, bounded on one side by a linear road.  The forest is too dense for you to be able to see the road until you walk right up to it.  You know that you are within one mile of the road, but are unable to determine the direction to it.  What is the length of the shortest path that will guarantee your reaching the road?  (Dean Inada)


7.  If  what does  ?  (Chris Cole)