Noesis

The Journal of the Mega Society

Issue #177        June 2005

Contents

About the Mega Society/Copyright Notice		2
Editorial	Kevin Langdon	3
First Report on Online Testing	Dean Inada	4
Option Theory: What I Knew and When I Knew It – Part I	Edward O. Thorp	7
Nature Versus Nurture	Chris Cole	10
Musings on Relativity	Michael C. Price	11
rec.puzzles Meets the Titan Test	Glen Wooten	14
Terra Linda	Kevin Langdon	16
The Indefensible Position: Road Rage Is Good	Rick Rosner	20
A Challenging Endgame Problem	Glenn Morrison	21
The World Puzzle Championship	Ron Yannone	22
Argument in Favor of the Proposed Constitutional Amendment	Chris Cole	23
A Belated Discovery	Richard May	23

About the Mega Society

The Mega Society was founded by Dr. Ronald K. Hoeflin in 1982. The 606 Society (6 in 10⁶), founded by Christopher Harding, was incorporated into the new society and those with IQ scores on the Langdon Adult Intelligence Test (LAIT) of 173 or more were also invited to join. (The LAIT qualifying score was subsequently raised to 175; official scoring of the LAIT terminated at the end of 1993, after the test was compromised). A number of different tests were accepted by 606 and during the first few years of Mega’s existence. Later, the LAIT and Dr. Hoeflin’s Mega Test became the sole official entrance tests, by vote of the membership. Later, Dr. Hoeflin’s Titan Test was added. (The Mega was also compromised, so scores after 1994 are currently not accepted; the Mega and Titan cutoff is now 43—but either the LAIT cutoff or the cutoff on Dr. Hoeflin’s tests will need to be changed, as they are not equivalent.)

Mega publishes this irregularly-timed journal. The society also has a (low-traffic) members-only e-mail list. Mega members, please contact the Editor to be added to the list.

For more background on Mega, please refer to Darryl Miyaguchi’s “A Short (and Bloody) History of the High-IQ Societies,”

http://www.eskimo.com/~miyaguch/history.html

and the official Mega Society page,

http://www.megasociety.org/

Noesis, the journal of the Mega Society, #177, June 2005.

Noesis is the journal of the Mega Society, an organization whose members are selected by means of high-range intelligence tests. Jeff Ward, 13155 Wimberly Square #284, San Diego, CA 92128, is Administrator of the Mega Society. Inquiries regarding membership should be directed to him at the address above or:

ward-jeff@sbcglobal.net

Dues for members of the Mega Society and subscriptions to Noesis for non-members are currently two U.S. dollars per issue (but we are considering elimination of dues and the paper version of Noesis). One free issue for each issue containing your work as long as dues are charged. Your expiration issue number appears on your mailing label. Remittance and correspondence regarding dues and subscriptions should be sent to the Aministrator, not to the Editor.

Opinions expressed in these pages are those of individuals, not of Noesis or the Mega Society.

Editorial

Kevin Langdon

Members of the Mega Society are being sent individual authentication numbers along with this issue, to be used in casting ballots in the society election on the proposed Constitutional amendment printed in Noesis #176. Those that receive Noesis by e-mail are being e-mailed authentication numbers and those who receive Noesis by snail mail are being sent authentication numbers along with their printed issues.

Use of authentication numbers makes e-mail voting feasible. The numbers are generated by the Editor and only a list of valid numbers is transmitted to the Administrator, for use in authentication of ballots and duplicate-ballot control.

Please read the text of the proposed amendment in Noesis #176 and Chris Cole’s argument in favor of it in this issue, then send your “yes” or “no” vote, with your authentication number, to Jeff Ward, Administrator, 13155 Wimberly Square #284, San Diego, CA 92128; ward-jeff@sbcglobal.net . The deadline for receipt of ballots by the Administrator—and for the next issue of Noesis--is July 31, 2005.

When I printed Part I of “About the Author,” from To Unscrew the Inscrutable [the title has been changed to The Encyclopedia of Categories; this is a much more intriguing and informative title—screw the inscrutable ;-) ], by Mega Society founder Ronald K. Hoeflin, I didn’t realize that the whole article had already been printed in Noesis #162. Instead of reprinting the remaining two-thirds of this long and interesting article, it would make sense to simply put #162 online, with some minor additions that Ron has made to the introduction. Assistance in this project is solicited.

No argument in opposition to the proposal to make Noesis an online-only publication has been received, but we may be leaving our founder behind in taking this step. Ron has indicated that he will drop out of Mega and found another 99.9999th-percentile society if we go to online-only publication. Although I wish that Ron would join us in the 21st century, I don’t see an alternative to passage of the proposed amendment; no one has volunteered to publish a print edition of Noesis. (A print version of Noesis could be made available at http://www.lulu.com/ for about $5 per copy.)

Due to the delay in publication of this issue we are right on the deadline (June 16) to enter the U.S./Canadian qualifying round of the World Puzzle Championship (see page 22). Those for whom we have an e-mail address will receive this issue just in time to enter if they wish to do so. I apologize for reaching print subscribers too late.

Cover: 3-D Perspective of Ovda Regio, Venus, from the Magellan spacecraft (NASA) http://www2.jpl.nasa.gov/magellan/image11.html

Back Cover: An image generated with “Eclipse,” a routine in Hallucinations™, by Kevin Langdon

First Report on Online Testing

Dean Inada

Basic Operation

I have implemented a preliminary online testing site at http://www.mental-testing.com/. Users log in with email and password. Unrecognized email addresses are redirected to a registration page, which, after retype confirmation of email address, emails a randomly generated password which can be used to log in initially, and which can be changed later.

Once logged in, a user can start answering questions.

Users start with a flat distribution for their estimated rank within the population of test takers. Since we’re using rank within the test-taking population as our abscissa, the sum of all the user distributions will just be a flat distribution representing the entire test taking population. Before answering any questions, we have nothing to distinguish any of the users, so their initial priors will all be the same. The only way identical priors can sum to a flat distribution is if each of the initial priors is flat.

For each question, we record the probability of answering that question correctly as a function of the user’s rank within the population of test takers so that when a user answers a question we get a new Bayesian estimate for the user’s rank. This is displayed to the user as a graph that looks like this.

The question to be asked next is randomly chosen, with a weight proportional to the square of the amount of information about the user’s distribution that we can expect to get if the user answers that question. The ideal question would be one that is always answered correctly by someone in the top half of the user’s distribution, and always answered incorrectly by someone in the bottom half of the user’s distribution. The expected information gain from answering a question is proportional to the integral of the slope of the question graph times the area of the user graph to the left times the area of the user graph to the right.

Before a user answers a question, the user is informed of the proportion of users who have attempted the question and correctly answered it, both as a function of rank within the population of test takers. This is displayed as a graph that looks like this:

The user may opt to skip a question. The question will be automatically returned to later when the user asks for a new question.

After a question is answered, a new estimate of the user’s likely rank within the test taking population is displayed

Anti-Cheating Measures

We encrypt the question identifier in the URL so that users cannot view questions other than those we choose for them.

To make it difficult for users to log in with multiple user IDs and guessing different answers to the same question until they get it, each question has multiple variants. For the questions that can be answered with a formula, we generate different parameters for the formula. For the word questions, the words are randomly selected from a pool.

We noticed that one person who had a perfect score had logged in from the same IP address as 36 other high scoring users with similar email addresses, most of which appeared to be bogus, who had all registered within a short period of time. Noticing this was one of the reasons we decided it was time to implement our postponed plan to use the registration email address to send the user information necessary to log in to take the test.(until then we had only used it to send new passwords to those who had forgotten them). While it is still possible for someone to obtain 37 different email addresses or even 37 different IP addresses, we hope that most people would not bother, and that most who do will still leave detectable patterns. (Identical passwords could also suggest a common user, but we can’t detect similar passwords since we only store a hash of the password.) Unfortunately, I accidentally deleted the log file which recorded the times and IP addresses of all registrations and logins, so it would not be easy to go back and review the patterns used by this user.

The likelihood that a skipped question will be returned to is proportional to the expected information gain from the question. This has the effect that it is difficult for users to get to hard questions unless they have answered easy questions correctly. This mitigates the problem of users randomly answering questions and contaminating the distribution for harder questions.

Technical Details

User sessions are maintained by storing user information in all the URLs they click on. The CGI code on the site is written in Perl. The graphics are generated with an ImageMagick command. The parameters used for the questions, as well as the user’s answers, are stored in a MySQL database. At first, I used a different table for each user, but the user base grew, along with our disk usage and my understanding of MySQL, so I changed userid to an index in a single table.

At first we cached the .gif images of the user graphs, but this took too much space, so we decided to regenerate them from the histograms each time they were viewed. The histograms eventually also took too much space, even after we changed them from ASCII to packed 16 bit integers, so we are now recomputing them from the set of questions answered correctly and incorrectly.

Statistics

As of March 2005 we are storing 29188990 bytes of data for 33445 users’ answers to 20 questions.

Future Directions

Timestamps on questions and answers might also help to spot patterns of use, and could tell us more about how persistent users are being, but we’re currently only time stamping logins and registrations.

I’d rather let the user retype the password to confirm, and email a link to click on to activate it. I’d also like to check the addresses against RFC-822, and make sure the host can be looked up in the DNS MX records before sending the mail.

I do not address the question of estimating a person’s rank within the general population, but Ron Hoeflin has done work on estimating the probability of taking a test as a function of rank within the general population.

Ideas for new questions are welcome; they should be parameterizeable, and not easily looked up on the Internet, preferably with a sharp threshold where users below a certain intelligence have a low probability of finding the answer, and users above the threshold have a high probability of finding the answer.

Option Theory: What I Knew and When I Knew It – Part I

Edward O. Thorp

Member Ron Lee has obtained the author’s permission for us to reprint several of his columns from Wilmott magazine under the title “A Mathematician on Wall Street.” This is the first of those columns.

One of the themes of this column will be how and to what extent markets are inefficient, and how you might profit from this.

Let’s begin by going back in time to the early days of quantitative finance. Paul Cootner’s book, The Random Character of Stock Market Prices, M.I.T. Press, 1964, presented much of the work that had been done on the random walk theory of stock prices and on the problem of warrant pricing. The warrant valuation problem was essentially the problem of valuing options and, more generally, derivatives. Progress was substantial but the Black-Scholes breakthrough would not appear until 1973.

Meanwhile, in 1965 Eugene Fama proposed that markets were well described as “efficient,” with all-knowing rational participants who acted quickly on their information, causing securities prices to properly and rapidly adjust to correctly reflect current knowledge.

I arrived on this scene with a unique perspective. In 1959-60, I had discovered that the casino game of blackjack could be beaten, and I devised and demonstrated a mathematical system to do so, based on keeping track of which cards had been played. Announced in December of 1960 and in January of 1961 (Proc. N.A.S.) and published in detail in my Beat The Dealer (1962; revised 1966), the system showed that the blackjack “market” was “inefficient.”

In a similar investigation of other gambling games, I discovered how to beat roulette by physical prediction (1955-61) and, with Claude Shannon (of Information Theory fame) built the first wearable computer (1961), whose function was to successfully predict roulette outcomes. The predictions of the computer gave us the huge positive expectation of 44%. Shannon and I then used the computer successfully in Las Vegas to win small sums. The casino gambling “market” had yet another “inefficiency.” For more, see Thorp (1969, 1998) and http://www.media.mit.edu/wearables/lizzy/timeline#1966a.

I investigated several other gambling games with some additional successes, and by 1964 I began to consider the greatest gambling game of all time, the stock market. Whereas I thought of card counting in blackjack as a million dollar idea, my stock market explorations would lead to a hundred million dollar idea. Here’s a brief history of what happened.

1964

I spent an intensive summer