The Journal of the Mega Society
Issue #177 June 2005
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,”
and the official Mega Society page,
journal of the Mega Society, #177, June 2005.
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:
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
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.
Copyright © 2005 by the Mega Society. All rights reserved. Copyright
for each individual contribution is retained by the author unless otherwise indicated.
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
Noesis by snail mail are being sent authentication numbers along with their
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.
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;
The deadline for receipt
of ballots by the Administrator—and for the next issue of Noesis--is July 31, 2005.
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
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.
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.)
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
they wish to do so. I
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
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.
logged in, a user can start answering questions.
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.
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.
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.
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:
user may opt to skip a question. The question will be automatically returned to later when the user asks for a new question.
a question is answered, a new estimate of the user’s likely rank within the test taking population is displayed
encrypt the question identifier in the URL so that users cannot view questions other than those we choose for them.
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.
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.
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.
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.
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.
of March 2005 we are storing 29188990 bytes of data
for 33445 users’ answers to 20 questions.
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.
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
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.
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
– Part I
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.
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
causing securities prices to properly and rapidly adjust to correctly reflect current knowledge.
I arrived on this scene with a unique
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
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
I investigated several other gambling games with some additional successes, and by 1964
to consider the greatest gambling game of all time, the stock market. Whereas I
thought of card counting in blackjack as a million
my stock market explorations would lead to a hundred
million dollar idea.
Here’s a brief history of what happened.
spent an intensive summer introducing myself
to the markets, investments and finance.
discovered, and in some cases rediscovered, curious minor technical patterns in stock prices.
Copyright © 2001 by Edward O. Thorp. All rights reserved.
Reprinted by permission of the
author and Wilmott magazine.
the start of the summer I
intensive study of the market and discovered warrants. I
understood at once that there was a qualitative link between the price behavior of a warrant and its underlying
stock and that it could be more or less quantified and that it could likely be an exploitable market inefficiency. (See
Chapter 2, Beat the Market).
I met economist Sheen Kassouf
in the fall of 1965 when we both arrived as founding faculty members at the new Irvine campus of
the University of
California. Kassouf was already hedging warrants and we collaborated,
publishing much of our work in Beat the Market. We understood static hedging, dynamic hedging, and
delta hedging, in particular market neutral delta hedging. We
documented a historical market inefficiency: warrants with two years or less to expiration tended to be very overpriced.
We used a static hedge to simplify historical
simulations for the reader. We used dynamic hedging in our own portfolios, making adjustments in moderate
sized steps both to limit risk and to limit the cost of doing so.
In practice my hedge ratio, or “delta,” was determined both by the macrostructure of the payoff
(wide range of protection against large price changes in
either direction) and the microstructure (market neutrality against small changes).
became increasingly clear to me
as I thought and invested during 1966-1968 that the clearest proof of an exploitable market inefficiency is to construct
a low (ideally zero) risk (hedged) package that has little covariance with the market, yet produces a
substantial “risk adjusted excess return.”
Beat the Market appeared. Kassouf and I
ended our collaboration with the completion of Beat
the Market in late 1966, and went our separate business ways. I
had become familiar with Cootner’s
1964 book and various warrant valuation models based on integration. I
had earlier concluded that using the log normal distribution for stock price changes and
computing the expected terminal value of a warrant, led to a reasonable candidate
for a warrant formula. I
learned from reading Cootner
that several people had already attempted this, in various ways. The version I
liked, which I
give in Thorp (1969), was, as I
learned only in 1975 from Larry Fisher, first derived by Boness.
However I do not see this in the Boness
paper that is in Cootner, nor
elsewhere in my copy of Cootner (the original 1964 hardcover), but did note Sprenkle’s related attempt (Cootner page
“My” formula had a growth rate for the stock and, in the case where the warrant or option short sale proceeds are credited to the account at once, a discount rate d for the present value.
Note: 2/2, where is the drift parameter and is the volatility.
is the expected value of the stock at time if is
the initial price.
I puzzled over the two parameters and and
speculate that in a risk neutral world I
can set them both equal to the riskless rate corresponding to the time until expiration (which, as it happens, gives
the future Black-Scholes formula). I
also note that a continually adjusted “delta neutral” hedged portfolio is riskless and so should
value discounted at the rate This also suggests the simple idea
of just setting and both
equal to I
mention a couple of these 1967 arguments long after the fact in Thorp (1975).
Occam’s razor and these plausibility arguments suggested to me
that if there was
a simple formula, this (the future Black-Scholes formula) is it.
I didn’t see how to prove
the formula but I
decided to go ahead and use it to invest, because there was in 1967-68 an abundance of vastly overpriced (in the sense of Beat the Market) OTC options. I
used the formula to sell short the most extremely overpriced. I
had limited capital and
margin requirements were unfavorable so I
shorted the options (typically at two to three times fair value) “naked,” i.e.,
without hedging with the underlying stock. As it happened, small company stocks were up 84% in 1967 and 36% in
1968 (Ibbotson), so naked shorts of options were a disaster. Amazingly, I
ended up breaking even overall, on about $100,000 worth of about 20 different options sold short at various times from late ’67 through
’68. The formula has proven
itself in action.
I estimated volatility
from the values
of log(H / L) where and are
the monthly highs and lows, using the last twelve months which were easily and quickly obtained from my library of S&P monthly stock guides. A previously published math paper (Anderson, 1951?)
gives properties of this volatility
estimator, including expected value and standard deviation.
My recollection as I
write now is that the expected value of,
was where is the volatility
parameter in the assumed underlying lognormal distribution.
The use of the volatility
estimator log(H / L) prefigures a 1977? paper on this by
Parkinson and a 1980 paper by Garman. Garman combines this and other volatility
estimators into a grand overall estimator.
My naked calls sold short were probably the world’s first
actual investment use of the future BS formula.
Black, Fisher and Myron Scholes. “The Pricing
of Options and Corporate Liabilities.” J.
Political Economy 81, 1973, 637-54.
Cootner, Paul (editor), The Random Character of Stock Market Prices, M.I.T.
Thorp, Edward O. “Fortune’s Formula: A Winning Strategy for
Blackjack.” Notices of the American Mathematical Society, Dec.
_____. “A Favorable Strategy for Twenty-One.” Proceedings of the National Academy of Sciences, 47, No.
1 (1961) :110-112.
_____. Beat The Dealer. New York: Random House, 1962.
_____. Beat The Dealer, 2nd Ed. New York: Vintage, 1966.
_____. “Optimal Gambling Systems for Favorable Games.” Review of the International
Statistical Institute, 37, 1969, 273-293.
_____. “The Invention of the First Wearable Computer.” Proceedings
of the Second International Symposium on Wearable Computers, Pittsburgh, PA,
October 19-20, 1998.
Thorp, Edward O. and S.T. Kassouf. Beat the
Market. New York: Random House, 1967.
Nature Versus Nurture
the March 2005 issue of National Geographic, there is a
stunning picture of a happy
baby nestled on the coils of a curled up
python. The text surrounding the picture explains that researchers have determined that monkeys raised in captivity have no innate fear of snakes, but that when they
are shown movies of wild monkeys recoiling from snakes, then they
become frightened by snakes too. So this seems to support the “nurture” side of the “nature versus nurture” debate. But the article goes on to reveal that when the researchers altered the movies to show the wild monkeys recoiling from flowers, the captive monkeys did not
become frightened by flowers. So this seems to support the “nature” side of the “nature versus nurture” debate.
It’s not mentioned
in the article, but this result with monkeys is similar to earlier results with pigeons. Are
these results surprising?
don’t think so. I
don’t see how the idea
of a snake could be represented in the DNA of a monkey. I
don’t see how the idea
of an animal could be represented in the DNA. I
don’t even see how the idea
of an external object could be represented in the DNA, although here I
might be willing to concede that the DNA might encode instructions for a building a brain that has a predisposition to conceive of external objects. So how can it be that you can teach
a monkey to fear snakes but not flowers?
It seems to me
there must be some kind of intermediary mechanism for tagging things
as useful to fear. There is a lot of talk about organs like the amygdala, but I’m
not going to be that precise. I’m
just pointing out that there must be some mechanism for deciding that some things are worth worrying about, and others are not. And
whatever this mechanism is, in monkeys it tags snakes as
worrisome and flowers as not a problem.
is a lot of folklore about the brain that needs to be unlearned. For example, I
was taught as a child that cats and dogs are
colorblind. That turns out to be false. They
have rods and cones just like we do. Apparently, the researchers who
are colorblind performed some kind of experiment to see if they
would react to color differences, and made the
incorrect assumption that if the color
difference made a difference to the animal (such as in getting food), then the animal would make that distinction if it could. But it must be more complicated than that. A brain is a hard thing to get to work. Just because the sensory apparatus exists, even in the presence of selective
pressures to use it in certain ways, it may not be possible because the intermediate mechanisms may need to work some other way.
is a cautionary tale about implicit assumptions in science, and how they
can mess you up. Brain science is a
area for implicit assumptions.
Musings on Relativity
Michael C. Price
is the centenary of Einstein’s publication of Special relativity, part of his annus
mirabilis that also included fundamental work on the atomic basis of Brownian motion and the
existence of photons. This got me
thinking, a couple of months ago, about General relativity,
gravity and curvature. Special relativity is quite straightforward to understand, but General relativity is a real tough nut to crack.
Special relativity when I
was 19 from a textbook, Special Relativity, by A.P. French. The way Special relativity is presented in the media is quite shocking. For instance we are told that relativity means that “everything is relative to the observer”, and
is the jumping off point as a mystical theory with all sorts of mushy, philosophical implications.
In fact Special relativity is quite the reverse—it’s about the
things that don’t depend in the viewpoint of the observer,
which is exactly what you would expect from any classical physical theory. A better description of relativity (both Special and General) would be a “theory of invariance.”
first myth to overturn is that Einstein invented relativity. He
didn’t. Galileo invented the notion,
three centuries earlier. It was Galileo who
first enunciated the principle of invariance or relativity when he observed that someone confined to the cabin onboard a ship
cannot tell, without looking out of a port hole, how fast the ship is traveling. And Newtonian
mechanics has this property that Newton’s
laws are still valid
to an observer in a state of constant motion. Or, put another way; no Newtonian experiment can determine the velocity of your laboratory;
therefore Newtonian mechanics, including gravity, conforms to the principle of Galilean relativity. Newtonian
physics is invariant under a Galilean velocity boost.
centuries later, after the mid 1800s, James Clark Maxwell
codified our knowledge of electricity, magnetism and optics into
what we now call Maxwell’s equations (although their
present mathematical compactness is due to Oliver Heaviside and others). The problem with Maxwell’s equations was that they
predicted a definite, precise speed for light (and other forms of electromagnetic
radiation). This seemed to conflict with Galilean relativity—how can light travel at the same speed in different laboratories moving themselves at different speeds? Maxwell’s equations were not
invariant under a shift in velocity; they
violated Galilean relativity! The conventional route out of this was to propose the
existence of an ether for the light to travel through—although
this didn’t really solve the problem completely.
was imagined by the ether proponents, would only be valid
when at rest with respect to the ether, and would need some modification in the more general situation when
we are moving through
the ether. Since we are in orbit around the sun and the center of the galaxy, we would expect to nearly always be in motion with respect to the ether; an “ether wind” blows through
us. Maxwell, who
recognized the conflict between “his” equations and Galilean relativity /
Newtonian physics, died
young and so was not able to complete this work.
Lorentz, Fitzgerald and others had made much progress with
the ether theory by the time Einstein emerged. Lorentz had already noted that Maxwell’s equations were invariant under the
transformations that are now named after him. Fitzgerald
proposed that the ether wind contracted electromagnetic systems along the axis of the wind. Poincaré had speculated about the speed of light being a limiting velocity. Sound familiar?
took a different tack, though,
and decided to regard the invariance of the ether-free version of Maxwell’s equations, as they
presently existed, as sacrosanct. Einstein, working independently, and not aware
of the other post-Maxwellians, was the first to realise that the Lorentz
transformations (as we now call them) should
be viewed as saying something about how space and time relate together, about
the geometry of space-time itself. Einstein guessed that the invariance of Maxwell’s equations applied
not just to electromagnetic objects, but was a property of space-time, and therefore was a
constraint on all objects, since they
all exist within space-time.
It was Einstein who
reformulated Newtonian mechanics to make them compatible with Maxwell’s work. Viewed in this light, then, Special relativity is the natural consequence of the merging of Newtonian mechanics with Maxwell’s
electromagnetism. As an aside I
should point out that in the popular accounts of the origins of Special relativity it is usually stated that the Michelson-Morley experiment, which reported the invariance of the speed of light in different directions with respect to the hypothetical ether wind, was the
jumping off point for Special relativity; that Einstein pondered on Michelson-Morley’s null result.
However Einstein was probably unaware of this experiment in 1905—he denied
knowledge of it early in his career. Only much later, when perhaps his memory of early events would naturally be suspect, did he claim prior knowledge of the Michelson-Morley experiment.
relativity is another similar, although not as simple, story. Here Einstein found another
invariance in nature—that the laws of physics look the same to someone falling down a
lift shaft as they
do to someone
floating in outer space; that acceleration and gravity are
indistinguishable, on a small scale. To turn this insight into precise mathematical laws Einstein had to call upon his tutor, Marcel Grossmann, to teach
him the tricks of tensor calculus and Riemannian
curvature. Tensor calculus is a subtle subject—I
never really understood it beyond the superficial level at college; getting to grips with this has kept me
occupied the last couple of months. Basically tensors are a set
of tools that enable you to shift from one general coordinate frame to another and still retain the same laws. If you write
down a tensor equation valid
in one frame then it is automatically valid
in all other coordinate frames; the coordinate frame
invariance of tensors is called “covariance”. (By “all other frames” I
mean any full coordinate system or map—they
may be non-Cartesian or warped cords; hence the term “general”.) You can do wonderful things with tensors—in fact they
are so powerful that it is sometimes hard to see where the maths
ends and the physics starts. Assumptions are made within General
relativity, and sometimes it is not immediately clear whether
they have any physical significance.
instance the covariant derivative (a derivative that transforms like a tensor) of the metric field (= the
gravitational field, which defines the distance between objects) is assumed to be zero. Why? Because it makes the theory simple? No, it turns out that curvature can only be defined with respect to the metric—simply because there is
nothing else to define curvature with respect to; hence the metric has to be “flat” in some sense; this is ensured by setting the covariant derivative of the metric to
zero. So this assumption turns out to be no more than merely definitional.
simplifying assumption Einstein initially made was that one of the components of the covariant derivative (the
“connection”) was symmetric. I
shan’t try to explain the details, but assuming a symmetric connection leads to the simplest version of General relativity. A
more general version of General relativity relaxes this symmetry whilst still retaining the covariance of the equations, making different experimental predictions. General
relativity with this non-symmetric “torsion” could really be called general General
relativity, although I
suspect that the name won’t catch on!
Anyway, that’s where I
am now, working
my way through
the torsion version of General relativity. My suspicion is that the torsion is a bit like the cosmological constant—both torsion and the cosmological constant complicate the minimally consistent version
of General relativity. The cosmological constant (a covariantly constant term in Einstein’s equations that provides an extra impetus to the
expansion of the universe) is currently back in favour with
astronomers, after being rejected in the 1920s. First the cosmological
constant was in because Einstein assumed the universe wasn’t expanding, then with
Hubble’s observations that the distant galaxies are receding it was hastily
dropped. Now it
seems the Hubble expansion is not de-accelerating as previously thought, and the cosmological constant is back in vogue again. I
suspect that torsion, because it also is covariantly consistent with General relativity, also has some truth to it.
I hope to move on to supersymmetry
every physicist seems to believe
yet the evidence for it is scanty. Why? I
my responses to some of the statements by posters to the rec.puzzles newsgroup. Although some of the posted answers on that site are incorrect and entertaining, and even though most of the posted answers are to easier questions, if this
will lead to the
desuetude of the Titan test.
they want people to thing of them as smart, which I
don’t blame them for, then they
ought to go do something that indicates they
really are smart.
we want people to “thing” of us? Until a
better measure of intelligence comes along, I.Q.
tests are the best measuring devices we have. The notion
that one must win a Nobel prize to prove
smartness is pure
folly. Too many factors are at play here. Specialized knowledge, creativity, intelligence, happenstance,
collaboration, personality type, and knowing people can all play a role in deciding who
will win a prize. Not all Nobel winners have genius I.Q.
scores and an I.Q.
above a certain level may actually be a hindrance. I
also don’t view it as our job to “perform” for people.
So what is the Mega Society looking for? Potential great accomplishments or
simply the $30.
is a false dichotomy. It assumes we could have no other purpose—such as the investigation of the upper limits of measuring intelligence or friendship and communication
with individuals of a similar disposition. Not every tall person wants to be a basketball player and not every intelligent person wants to be the next Einstein. Einstein
himself once said that if he had
life to live over again he would choose to be a plumber. Would he have been less intelligent? No, just less famous.
neither deep knowledge nor broad knowledge is a necessary
consequence of intelligence, can you enlighten me
on just what exactly _is_ a consequence of intelligence and how the Titan test
consequence of intelligence is an ability to understand. The problems on the Titan test require an individual to understand patterns and relationships and
make objective decisions.
These are all important skills in the real world.
do you have to start somewhere? Why don’t you document those who
you are intending to exclude. Is your club only for those who
have a Liberal Arts education?
suggesting we start nowhere! If we
documented people we intended to exclude, that would be starting somewhere. To my knowledge, Mega Society members are well-educated in most areas, not just liberal arts.
is trivia whether
source is pop culture or Liberal Arts. If you’re so smart, tell us how that correlates to intelligence.
is not trivia when it
comes to psychometrics. Knowing the original colors in a box of Crayola
crayons and knowing the capital of Canada are not of equal value. An intelligent person is expected to know general knowledge an inquisitive mind would have acquired through
what is the correlation? Are you trying to say a philosopher who
can’t program a computer is more intelligent than a computer programmer who
doesn’t know Wittgenstein from a hole in the ground?
show positive correlations as high as .8 or better. Having a certain job doesn’t guarantee one is smarter than other people. Without question, a certain athlete may be smarter than a certain physicist.
Further, it’s unclear why knowledge acquisition and
retention are evidence of “intelligence” at all! A CD can be burned with the contents
of an encyclopedia—does this mean the CD is highly intelligent? (Certainly, the CD doesn’t know
are worthwhile, yet the contents
represent a broad inquiry into human knowledge!)
not unclear at all. Studies have been going on since the inception of intelligence tests and they
confirm the correlation. Consider an intelligent dog that grows up with an intelligent baby. Even if the dog is exposed to the exact same environment as the baby, the dog will not acquire the same knowledge due to its limited mental capacity.
The baby, however, will acquire knowledge very rapidly. A CD may contain knowledge but it understands
nothing and thus has no intelligence.
Linda” is Latin/Spanish for “beautiful land,” and the valley of that name is indeed beautiful—but it was more beautiful before it got excessively built-up, after the time to which this account refers, the mid-to-late 1950’s (even the signature oak at the freeway exit is long gone).
spoken about moving to the suburbs, but I
was shocked when my mom and dad told me
that we were moving from our house on Rockdale Drive in San Francisco to Marin
County, north of San
Francisco, across the Golden
This would uproot my whole life, except
and a few family
and I was both apprehensive and excited about the prospect at the same time.
of attending Aptos Junior High School in San Francisco I
would be in the 7th grade in a K-8
country school which had suddenly become a transplanted city school, because most of the kids belonged to families who
had moved in to this new subdivision of tract homes.
we moved in construction was still going on. I
remember seeing bulldozers rumbling by where back fences had not yet been built behind our
house. There was dust everywhere. It was a joke
around Terra Linda that the name meant “pretty dirty.”
was an overwhelming presence for our
first few months in the valley, not only at home but at school and in the surrounding area where we kids used to play. The construction sites and large equipment
exerted a certain fascination, alongside our social microcosm
and the natural world of the creek, the fields, the trees,
and the hills. Some of us just played around the new construction but other kids vandalized it.
small country school was a shock, with several grades together in
one classroom. There was only one eighth-grader, Tom Hurwitz, and some fifth- and sixth-graders along with the four
or five of us seventh-graders. At the rehearsal for the graduation ceremony at
the end of the first year, I
tied Tom’s shoelaces together. When he got up to give his speech he moved his feet in tiny little steps and everybody laughed (especially
Tom). Incredibly, I
didn’t get in trouble. Tom went on to be the star of the
golf team at San Rafael
Dennie B. Willis, the sadistic principal of the school, doubled as a part-time classroom teacher. He was unfair,
punitive, and vindictive (and a lousy teacher, too). I
hated his authoritarian rule and rebelled against it at every opportunity. But I
a “traffic boy,” charged with keeping kids safe going to and from our school. It was interesting
work and I
father was President of the school board for that small suburban district.
The school district was having severe growing pains and he felt that he needed to get involved. He was a hospital administrator and had very strong organizational skills. Under his direction the problems began
to get resolved.
dad wanted my sister and me
a less urban lifestyle, and he definitely succeeded in that. I
have many memories of roaming
the hills, lying in the grass, and rafting in the creek, where
frogs were everywhere. Sometimes I
explored the area with some of the other kids but most of the time I
was alone. This gave me
lots of time for reflection.
was still a working
farm on one side of the creek. A couple of times some of us got into the large barn where there was some machinery that ran on tracks, for moving supplies around. We played with the
machinery but we didn’t do any damage.
Among the kids my age, there were two who
were particularly physically able
and charismatic and two groups formed around them. I
was in the group surrounding Joe Melton, the son of an Air Force officer. The other group centered around Ralph “Biff” Moore and tended to be more rebellious. (It certainly wasn’t
typical of me
to be on the more conservative
team anywhere, but I
was in this case.)
that time, the Air Force had a stunt-flying team called the Sabre Knights.
I saw them perform at Hamilton Air Force Base, just a few miles up Highway 101 (this base was closed many years ago). Joe organized some of us into a group, also called “the Sabre
Knights,” which rode bicycles in formation. We practiced quite a bit and got pretty good at it (but, of course, the
wild wheels-off-the-ground maneuvers common today were practically unknown then).
during that period were Joe’s sister Pam and Toni Guerrero. I
took Toni to a dance once but I
never really got anywhere with either of them. Such were the trials of a young nerd. Toni became Biff’s girlfriend and Pam got involved with Tom Rundberg,
who lived across the street from us.
was a vacant house not far from Toni’s house where the
kids used to hang out. Some of those who
had coupled up used to kiss and make out there. In addition to
Biff and Toni and Tom and Pam, Joe was involved with Toni’s sister Ramona (“Mo”). I
had no partner and was the odd
man out. Because of this, on a day when the rest of the kids were there but Pam
hadn’t arrived yet, someone
had the bright idea
of sending me to fetch Pam.
walked over to the Meltons’ house. When I
got there and asked
for Pam, her mother asked
me what was going on. I
by the situation, especially being sent to fetch a girl I
liked for another guy. I
remember my exact words: “Joe’s kissing Mo, Biff’s
kissing To, and Tom’s waiting impatiently to kiss Pam.” “Well, he can keep on waiting!” replied Mrs. Melton. The other kids were mad at me
for a while but they
knew they’d had it coming and the incident was soon forgotten.
and I were friends, too. We used to get together to play and invent games. Tom’s father and mother were Swedish
immigrants. Per Rundberg, the father,
was a loud,
who went to parties and hit on the women; my dad saved him from getting punched out for it on more than one occasion.
What I didn’t know but found out one evening was that when he got drunk enough he groped children too. I
got out of there very quickly. In retrospect, I
should have gone to the police.
I was visiting Tom in front of his house. He had a
basket flimsily attached to the front of his bike with some wire. I
was trying to fix the wire so that the basket would be attached more securely but I
cut the wire in the wrong place and it came loose. Tom started to cry and just then his father
came out the front door. He asked
Tom what was going on and he said, “Kevin cut my bike wire!”
that, Per hauled off and hit me
on the side of the head. I
got up and told him to fuck himself.
He came toward
me again and I
ran across the street to my house. As I
ran in the front door I
heard him raging at my mom and dad and they
told him to stick it, too, in
somewhat more polite language. After we’d discussed the situation, my dad said that I
shouldn’t have used such bad language but that he was proud
of me for standing up to Mr. Rundberg.
After that, I
wasn’t allowed to play at the Rundbergs’
any more. Once again, I
should have gone to the police.
Later, after they
grew up, Tom and Pete became Scientologists and had their
parents declared “suppressive persons” by the Church of Scientology.
had two very satisfactory cats in Terra Linda, Pussy Willow, a
female tabby, and Furry Purry, a part-Persian grey neutered male
with long thick grey hair. Pussy Willow was
a fearsome huntress and brought
home many of her trophies; Furry Purry was a lover,
not a fighter.
we lived in Terra Linda, my dad bought a 28-foot cabin cruiser. It was his pride
and joy and the family
would go boating on many weekends, weather
permitting. I hated it. I
was afraid of being at close quarters with my dad for hours on end (because he would sometimes get mad at me
and I’d have no place to get away from him; he was never abusive, just strict, and sometimes wrong according to my perceptions at the time, some of which seem more accurate than others in retrospect), often seasick, and
out of my mind. It
took a lot of boring maintenance work, too.
were two “bad” girls, Cathy and Barbara, in our school. They
fought and cursed and were rumored to do other things. One day Cathy had a fit over something and climbed up to the top of the
water tower on the hill near our school and threatened to jump to her death. The
sheriff’s department and the fire department came out in force. It was quite a circus and Cathy had her day in the center ring.
next day, Barbara did the exact same thing.
One day Tom’s brother Pete and I
around in the hills. Cathy’s brother Brian and two of his friends were in the same general area and they
vandalized some construction equipment. They
were apprehended by the sheriff’s department. Brian told them that we had done most of the damage and they
were just following our lead, and Pete
and I were picked up by a sheriff’s car.
were two deputies in the car and they
tried to pressure us into “confessing.” “Those other boys were man enough to confess,” said one of the deputies, and Pete Rundberg
started to cry. I
didn’t feel like crying. I
was angry at this injustice. The deputies released us into the custody of our parents.
That evening it developed that a friend of our family, Dorothy Brown,
the mother of my sister’s and my friends Craig and Bonnie, had seen the whole thing out her kitchen window. Brian was exposed as the liar he was, and Pete and I
were vindicated (naturally, the pigs didn’t apologize).
next day, Craig and I
were riding our bicycles when we spotted Brian on his bike. We chased the little rat a couple of miles to the cemetery, where he gave us the slip. Then, that evening, my mom got an angry call from Brian’s mom; it seems that he’d ridden his bicycle several miles further and then called her to pick him up. Oddly enough, my mom wasn’t very sympathetic to the mother of the rat.
we lived in Terra Linda we attended Mass at Blessed Sacrament Church. The pastor was a
priest with a fondness for liquor. My father called him Father Red Nose and made fun of his hypocrisy and
stupidity, as when he railed about the people who
didn’t come to mass on Sunday to the people who
the years went by my dad became more and more cynical about religion and he
eventually abandoned it altogether.
I could see his point about the external form, but that wasn’t what interested
felt something in church, something that I
couldn’t explain, but it was the stirring
of what later became a search for something greater than my ordinary day-to-day experience
and led to a number of interesting
discoveries beyond the scope of this account.
graduated from the 8th grade in 1956 and
I was off to San Rafael High School. Our family moved from Terra Linda to Lucas Valley,
the next valley north, an Eichler development which had avoided some of the mistakes that had been made in Terra Linda (overdevelopment,
poor construction, inferior floor plans, etc.).
Road Rage Is Good
Reprinted from the May 2005 issue of Esquire by permission of the
In Flannery O’Connor’s “A Good Man Is Hard to Find,” The Misfit explains, “She would of been a good woman if it had been
somebody there to shoot her every minute of her life.” The same goes for bad drivers. They
need constant harassment.
You try not to hate them. You think, “Who
am I to judge?” You tell yourself that anger hurts your heart and your karma and makes driving more dangerous. That’s gutless and wrong. Danger and bad karma lie in surrendering to selfish drivers. One-third of drivers shouldn’t be driving. Some are too old or drugged or dumb to drive, but here in L.A., where the sun always
shines on your Xterra (leased), most lousy drivers are simply too smug to pay attention.
the sword of petty and ineffective vengeance. I
honk, sneer, curse, flip the bird, try to block drivers who
use the shoulder to sleaze past traffic. My anger rarely fazes the targets of my wrath, but it focuses me.
I’m alert, hunting for the next object
of scorn—an actor, script propped on his steering wheel, doing 25 on Ventura or an old blonde, corgi on her lap, going the wrong way in the Trader Joe’s parking lot. Anger is my conscience. I
can’t rage at some tool’s shitty maneuver, then pull the same move myself.
And anger is instructive for my ten-year-old daughter, who
gets a dime for each bad driver she spots.
Bluetooth, BlackBerry, DVD
player, in-dash navigator—so many new distractions. Drivers won’t learn
to use them safely unless we savagely diss drivers who
don’t. C’mon—drive angry. Pass judgment on jerks. They’ve
already judged you a nonentity. And don’t worry about giving yourself a heart attack. Beta-blockers can keep your BP at 100 over 60 even as you scream at that dick in the Denali
tapping away on his PDA.
Copyright © 2005 by the Hearst Corporation. All rights reserved.
A Challenging Endgame Problem
What is the best move?
This is a position from Mengarini-Evans,
1951 US Championship. Black to play and win(?). Although on the surface it may appear easy, this position requires analysis more than 50 ply (total moves) deep, beyond the ability of computers
to directly fathom. It
turns out that white has strong defensive resources here and a win by black is at least very difficult and may be impossible.
Grandmaster Evans (black) won the actual game, which included less than perfect moves by both players, especially his
opponent, as revealed by the program Shredder 8, which performs at world championship level on a fast PC.
Next: A tantalizing, tentative attempt at a solution!
The World Puzzle Championship
may not be 1-in-1-million questions, but the time-constrained (2.5 hour) online U.S./Canada
Qualifying test could be really exhilarating—for some of the members and non-member subscribers. The top 2 U.S. scorers get to be on the U.S./Canadian team for the “World Puzzle Championship.”
test will be administered online June 18 at 1 p.m. (see
and website for more information).
winners will be notified within 5 days of the Test. Results will be posted on the website no later than Saturday, June 25. The answers to the test
will be posted no later than one day after the Test.
top two U.S. contestants will be selected for the U.S. Team to compete at
the World Puzzle Championship in Hungary in October, 2005.
know I can’t “work this fast”—but someone like Bill Corley would be able to! Bill tackled the Mega test
while proctoring a college exam in about 2 hours (got something like a 35/48)!
World Puzzle Championship
“Random House World-Class Puzzles from the World Puzzle Championships”
2004, ISBN: 0-8129-3586-1
Father’s Day weekend marks the traditional timing for the U.S. Open golf tournament. And over the past
several years puzzlers across North America have also marked their
calendars for the same weekend—in anticipation of the U.S. and Canadian Qualifying
Test! In 2002, the test was administered via the Internet. The day
before the test, contestants were able to download the encrypted puzzles from the U.S. team web site. They
the actual instructions to all 23 puzzles for the 2½-hour test, in order to familiarize themselves with the challenges that lay ahead. Only the puzzle artwork was kept secret. Then at
precisely 1:00 p.m. Eastern time the password was given, and the contestants were off and running.
Argument in Favor of the Proposed
are some points that that I
think are in favor of the proposition:
1. All the active members have email and Web access.
Probably the same is true of inactive members.
Web publication allows us to eliminate subscription fees.
The elimination of subscription fees may entice some inactive members to become
Web publication makes the members’ submissions available to a wider audience.
We have no volunteer to publish Noesis in hard copy.
I‘m a highly perceptive
person, so I
was quite disconcerted to discover about a week ago that I
been dead for more than two years. Apparently I never really noticed that had I
because I was so distracted by sending myself
e-mails, irradiating my brain with cell-phone EMF, having my Volvo tattooed
It’s really a life-altering experience
to suddenly learn
that you have been dead for years. None of my closest friends noticed my passing
either. Perhaps they
had also deceased and were too busy making a living. It’s never very clear these days, I
guess. Naturally I
just continue to do everything as usual.
Sometimes you don’t get serious about life until you’re dead, but maybe not immediately even then.
no need to hurry. Now I
take a little more time to smell the dead flowers.
not an ontological wanna-be. It’s not that I
wish that I
had ever been, but occasionally for a moment I
may wish that I
wished that I
had been. At least nothing has really changed, since I
In fact I haven’t noticed any difference at all.
2005 by Polymath Systems. All rights reserved.