NoesisThe Journal of the Mega Society Issue #176 February 2005 |
Contents
About the Mega Society/Copyright Notice |
|
2 |
Editorial |
Kevin Langdon |
3 |
Some Thoughts from Glenn Morrison |
|
4 |
How Many Quarters? Bayesian Reasoning V |
Chris Cole |
6 |
Rockdale |
Kevin Langdon |
9 |
The First Wearable Computer |
Edward O. Thorp |
12 |
Technically Advanced Ancient Civilizations? |
Chris Cole |
20 |
About the Author, Part I |
Ronald K. Hoeflin |
22 |
Valentine’s Moment |
Richard May |
29 |
Proposed Constitutional Amendment |
Kevin Langdon |
30 |
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, #176, February 2005.
Noesis is
the journal of the Mega Society, an organization whose members are selected by
means of high-range intelligence tests. Jeff Ward,
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). 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.
Copyright © 2005 by the Mega Society. All rights reserved. Copyright for each individual contribution is retained by the author unless otherwise indicated.
EditorialKevin Langdon
Ron Yannone has resigned as Editor and Publisher of Noesis. Thank you, Ron, for your service to the Mega Society. As the only candidate for Administrator to respond to the call for candidates for society office was Jeff Ward, the only candidate for Internet Officer was Chris Cole, and the only candidate for Editor was Kevin Langdon, we are all, according to the Mega Constitution, automatically elected.
As none of us really has the time to deal with producing and mailing hard-copy issues, it has been proposed that Noesis become a Web-only publication and that we eliminate membership dues (see the proposed Constitutional amendment contained in this issue). What is proposed is that issues be both e-mailed to those who wish to have them available on their own computers and displayed on our website (this is the same way that Ron's last few issues have been handled). We’ll take a vote after members have had a chance to discuss the proposed changes.
If we don’t have a current e-mail address for you, please write to one of the Mega officers to let us know where we can reach you if we change over to Internet-only publication. We’d also like to try to reach our lapsed members. If you’re in touch with Mega members who aren’t currently participating in society affairs please let us know.
This issue and the next one will be produced in hard copy by me, with the cost of these issues generously underwritten by Chris Cole. Thank you, Chris.
There are about five people who are paid up for more hard-copy issues than would be published under this proposal, and that will have to be taken into account also. We'll need to refund some unearned dues/subscription money to these people if the proposal passes, and find a way of funding the refunds
So far, only Ron Hoeflin’s website and mine are listed on the society’s home page. Please consider adding yours. Write to Internet Officer Chris Cole <chris@questrel.com>.
As usual, we need interesting and thought-provoking material for publication in Noesis. Please write something, respond to something in this issue or previous issues, or look for something suitable for publication in your files.
The deadline for #177 is April 1.
Cover: Jupiter from Galileo (NASA)
Back Cover: An image generated with “Whorlflower,” a routine in Hallucinations™, by Kevin Langdon
Some Thoughts from Glenn Morrison
Below is a shot of the electric vehicle I recently designed and built using off-the-shelf parts found on the internet. It has a 35-mile range on 0.56 kwh lead-acid battery storage, 19 mph max speed. The thing on the top is a 100 watt tiltable solar panel made from photovoltaic cells cemented onto rigid foam type house insulation.
I started designing it in July 03, and finished the basic vehicle to the point of usability in Jan 04. By June 04 I’d installed the solar panel. Over that period I probably spent 30 hours actual “tool time,” 30 in front of the computer, and 100 just idly thinking about it. Total cost came to approx $3900.
It serves as cheap practical neighborhood transport and at the same time as a concept test platform for further development.
Early in the design stage I checked with the vehicle authorities. They follow the Federal guidelines which state that an electric vehicle with max speed below 20 mph is regarded as equivalent to a bicycle and does not require a license or registration.
Soon after I began operating the vehicle the cops stopped me and told me I needed better visibility. So after a bit of research, I installed a yellow strobe on the rear strut, along with one of those fluorescent orange triangles for slow vehicles. Seems to have solved the problem, since cars give me a wide berth and there’ve been no further objections from the local constabulary.
Plans are in the works for a second version with aerodynamic shell enclosure, 40 mph max speed, 200 mile range using 6 kwh of juice from lithium ion polymer battery. Will keep you posted if and when this project gets seriously underway.
The recent tsunami started me wondering how often in history we get huge natural disasters like this, or worse. One good data point:
1. In 535 AD a huge volcanic eruption (probably Krakatoa, according to investigator David Keys) blanketed the earth with atmospheric dust for 2-3 years, causing the nuclear winter effect, leading to famine, pestilence and regime changes including the rise of Islam and the fall of several important civilizations.
An article by David Keys on global warming and extreme weather appears at:
http://www.newint.org/issue319/cat.htm
And here are links to some stories on Dr. Keys’ work:
http://www.laweekly.com/ink/01/27/summer-Ihara2.php
http://www.lakepowell.net/sciencecenter/catastrophic.htm
http://www.iol.co.za/index.php?set_id=1&click_id=31&art_id=qw974926261574E162
For much more on this subject, see: http://www.sciencedaily.com/news/earth_climate/global%20warming/
2. The other day I was looking up the source of the quotation a prophet has no honor in his own country, and lo and behold, the very next verse (Luke 4:25) reads: “. . . in the days of Elijah, when the heavens were shut up for 3 years and 6 months, when there came a great famine over the land . . .”
Sounds like a fair description of the good old nuclear winter effect, right? So looking up the days of Elijah, it turns out to be circa 850 BC. A possible second data point.
If these points are both valid, it suggests that this type of catastrophe happens at 1000-2000 year intervals on the average. Not holding my breath, but it does kind of put everything else in perspective.
Bayesian Reasoning V
Chris Cole
This is the fifth in a series of articles. The previous articles were:
Noesis 26 (May 1988): Bayesian Regression
Noesis 28 (July 1988): The Principle of Insufficient Reason
Noesis 40 (July 1989): Applications to Famous Problems
Noesis 59 (March 1991): The Principle of Insufficient Reason II
If we define “most difficult” as “answered correctly by the smallest proportion of Mensa members,” then the most difficult puzzle in the Mensa Genius Quiz-A-Day Book by Abbie Salny (and the members of Mensa) is the entry for May 14:
You have fifty coins totaling $1.00. You drop one down an open drain while tossing the coins in your hand. What is the chance that you have dropped a quarter?
Only 15% of Mensa members were able to do this puzzle, which might make it or something like it a good candidate for a high range test. Here is the solution given in the book:
There are two ways you can have fifty coins totaling $1.00: two dimes, forty pennies, and eight nickels; or two dimes, forty-five pennies, two nickels, and one quarter. These arrangements are equally probable, so there is a one-half chance you had a quarter to begin with. The probability that you dropped that quarter from all the coins in your hand is one fiftieth. Therefore, the total probability that you lost a quarter is one half times one fiftieth, or one one-hundredth.
The flaw in this solution is the assumption that the arrangements are equally probable. This is not given as part of the puzzle statement, and cannot be inferred from any of the information given in the puzzle statement. We know nothing about how the coins that are in the arrangements were selected, so we cannot know that the arrangements are equally probable.
The assumption that the arrangements are equally likely may be an invocation of something we’ve discussed before in this series: the Principle of Insufficient Reason (also called the “Principle of Indifference”). This Principle is not valid and should not be relied upon. It is not valid in the sense that it is not logically implied by the mathematics underlying Bayesian inference. That it should not be relied upon requires a little explanation.
There are two major schools of thought about what we mean by probability statements, the subjective school and the objective school. The subjective school holds that probability is an expression of our degree of belief in a statement. The objective school holds that probability is a feature of nature and is equal to the frequency of successful outcomes in a series of experiments. The Principle should not be used by adherents of either school, as we’ll now show.
It
may seem strange for a subjectivist to say that the probability of something is
unknown, but in real life there are things we have a good idea of, like the
odds of rolling seven or eleven in craps, and here are things we don’t have a
good idea of, like the price of tea in
The
Principle, however, would have us eliminate uncertainty by simply assuming that
all unknown outcomes have equal probability. If we know that the price of
tea in
The objectivist, on the other hand, thinks that probability is the ratio of favorable states to total states. Unfortunately, nature does not divide the world into states for us. For example, suppose there are two balls in an urn. We know that each ball is either black or white. What is the probability that the balls are both white? Some people think the possible states are {white-white, white-black, and black-black}. Other people think the possible states are {white-white, white-black, black-white, black-black}. In the first case the probability of both white is 1/3; in the second case it is 1/4. Which is right?
It might be hoped that in the limit of a large number of experiments, the law of large numbers will determine the probabilities by taking the frequencies to the limit. There are two problems with this conclusion, though. First, the law of large numbers cannot solve the problem of the correct states into which to partition nature. Second, symmetries are continuously broken and it is unclear that the law of large numbers has time to catch up. The universe is far from equilibrium, so determining which probabilities are at their limit is hopeless. Every raindrop is a broken symmetry.
On a less technical note, the intuitive objection to the Principle is that it tries to get something for nothing. How can it be that knowing that the prior probabilities are equal does not change the answer? It seems intuitive that this is a valuable piece of information. And yet, according to the Principle, we don’t need it. We can merely assume it.
Returning to the May 14 puzzle, let’s see how realistic the assumption that the arrangements are equally likely is. Let’s assume it’s true and see where this leads in a realistic scenario. Let’s assume that we reach into a jar of coins and count out fifty coins. If the two arrangements are equally likely, then we can roughly estimate the frequency of each denomination in the jar. Pennies are selected 85 times out of 100 for a probability of .85; nickels have a probability of 10 out of 100 or .1, dimes have a probability of 4 out of 100 or .04, and finally quarters have a probability of 1 out of 100 or 0.01.
What is the probability of randomly picking a hand worth $1.00? The probability of picking the hand with no quarter is:
The probability of picking the hand with one quarter is:
Both arrangements are very unlikely, even given these highly tuned abundances of coin denominations. If this were an experiment, I think we’d conclude that someone purposefully selected coins that total $1.00. Once we realize this, how could we possibly conclude that the two arrangements are equally likely? We might be willing to estimate the likelihood of the outcome of some natural process, but not of a selection process involving intention. I don’t think anyone who faced this question in the real world would be well-advised to assume that the arrangements are equally likely.
So, where does this leave us? If the solution given in the book is an application of the Principle of Insufficient Reason, it is invalid because the Principle is invalid. If on the other hand the solution is supposed to be based upon a realistic scenario, a simple analysis of the situation reveals that it is impossible to know the relative likelihood of the two arrangements because the arrangements were apparently intentionally selected. So, in conclusion, the correct answer to the puzzle is that the probability that the lost coin is a quarter lies somewhere between zero and two percent.
Since presumably none of the Mensa members who tried this puzzle before the book was published actually answered it correctly, perhaps this would make a good high range test item.
Editorial Comment: I looked at it still another way. I assumed that the person with the change in his pocket knew what he had and that there’d be no reason to consider the probability that the dropped coin was a quarter if he hadn’t had at least one quarter. That reduced it to one case and a probability of two percent—except that the probability of dropping the quarter, in the real world, would be less because it’s bigger. . . .
Rockdale
Kevin Langdon
We lived in other places before that—one of them was 1515 25th Avenue—but the place where I first ventured out on my own, as a child of five or six, was our house on Rockdale Drive, at the foot of Mount Davidson, in San Francisco. I’m sure there was danger even then but I was never aware of anything more dangerous than the neighborhood bullies and I wandered around within a mile or so of our house in all directions.
The
summit of
My memories of the time before Rockdale are less placed within an organized framework and most of them have a somewhat dreamlike sense of moments outside time. There is light, my mother and father, some recollection of the “look and feel” of the flats we occupied, memories of my mother taking me out to the park, around the city, and to many interesting places. There are also some darker memories, not of abuse but of a sense of my ignorance of the world and the principles on which it is constructed and states of existential angst, as early as age one.
Rockdale
drive is joined in a Y formation by Chaves. We were a few houses up the outside
of the right branch of the Y. The foot of the Y is a dead end and on our side
of the street the houses back directly onto
This was a magical time for me, the early 1950’s.
My folks had a large room built for me in the basement. I loved the isolation; in my room I felt free to indulge my creativity in various ways—building with my blocks and my erector set, drawing and painting, telling myself elaborate stories illustrated with toy soldiers, blocks, marbles, and whatever objects were at hand, playing games by myself and inventing new games, reading, etc.
My dad used to get down on the floor and play with the me. He taught my sister and me many games and both my mom and dad read us stories, and made some up too.
My sister and I were supported in many ways by my parents. We were stimulated, amused, protected, given emotional support, disciplined, and challenged. My father’s ego collided with mine over disciplinary matters, and I’m sure that contributed to the extreme distaste for authority I’ve had since I was a boy. But I’m very grateful for the preparation for living I got from my parents.
A neighbor across the street from us and slightly up our branch of the Y was very fond of children and used to invite us in for games and refreshments. I remember many games of cards and dominoes in her dining room. She took a special interest in me and encouraged my interest in playing and inventing games.
Even
though we went to several separate schools there was a strong sense of
community among the kids in the neighborhood. We played at one another’s
houses, we played in the street, on the sidewalks and in the back yards, and we
played in
We played cowboys and Indians, spacemen, and other ruleless fantasy adventures, as children do, and also competitive games with more formal rule sets. The neighborhood kids got together almost every afternoon. I have fond memories of playing Kick-the-Can by twilight, waiting for the calls to dinner that would end the game.
My sense of time now had an orientation. I was growing up—excruciatingly slowly but it was clear that I’d probably be a grown-up someday. I wasn’t prepared for what a rocky ride it was to be, but few children are.
There was an order to the day, the week, the month, and the season. Easter, the Fourth of July, Halloween, Christmas, and other holidays colored home, neighborhood, and school environments in cyclic progression. Each holiday was celebrated in a special way. The Fourth and Halloween were particularly neighborhood affairs. (Having heard tales from another generation of a time when Trick or Treat was taken seriously, I was a little disappointed that by the time my generation inherited the tradition it was all treats and the really fun part wasn’t being practiced any more.)
All was not sweetness and light. There were bullies that beat me up on my way to school (I had a serious physical disability that made me easy prey). And there were such cruel delights (common in boys of a certain age) as blowing up insects with fire crackers. School itself was frustrating to me, as it seemed that everything moved in slow motion and left off just where it might have started to get interesting, and I acted out a lot. There was “good” and “bad” in my life, but many of my social needs were being met by the generally-very-understanding children that I’d known for many years.
Later, when we moved north 30 miles to a suburban development, I was without this social safety net. Some of those kids were crude and mean (though there were some very nice ones too) and I had a hard time adjusting to my new social environment.
During my Rockdale period, I was fortunate to have five “best friends”: Chuckie, Edward, Stan, Ralph, and Diane.
My
sister Valerie is 3.3 years younger than I am; Chuckie
is right in between our ages and was a close friend of both of us. He lived
three doors up the street. We played mostly physical games. Sometimes we ganged
up on my sister. I remember chanting with Chuckie,
“We’re big men and she’s a little girl!” Later, Chuckie
and his family moved to
Edward is about three years older than me. We had great fun playing all kinds of elaborate indoor and outdoor games. Edward and I created elaborate imaginary worlds. We mapped the neighborhood, including all the back yards and secret places to hide or make our way from one to another, and sometimes we’d organize games involving all the neighborhood kids.
Stan and Ralph were in my class in school. I got together with each of them after school frequently and played games. Stan and I invented a variation on Monopoly, a game we particularly liked. Sometimes a game would go on for days. Stan and I were part of a larger circle of friends who used to play in a wild area not far from Stan’s house. There was an exhilarating sense of freedom in roaming around with the other boys, amusing ourselves with whatever was at hand or on our minds. And the minds of this particular circle of boys were, on the whole, quite innocent. Ralph was in the same class but was less connected with this group, more introspective, and I remember him being with us in our outdoor adventures only infrequently.
Diane was my main female friend among my classmates. She was very kind and protective of the shy kid that I was then. She excelled in academics and we shared many intellectual interests.
How little these words convey. These people were important to me during a certain period of my childhood and touched me deeply. I’ve been in touch with all of these friends of my childhood except Chuckie since I’ve been what is called “grown up,” but I’ve found it difficult to really reconnect with people I’ve known in the past in general; I think people are very sensitive to “relationship overload” and jealous of the time it takes to keep a relationship going, and this causes an unconscious aversion to extending oneself to do so. I intend to persevere in reconnecting with my old friends. I think there is deep value in thus honoring the bonds of friendship.
I graduated from Miraloma Elementary School in 1954 but instead of going to Junior High the next year, I attended a K-8 country school (suddenly almost exclusively occupied by transplanted city kids) when our family moved north to Marin County, the next chapter in my life.
The Invention of the
First Wearable Computer
Edward O. Thorp
Edward O. Thorp & Associates
Thanks to member Ron Lee for arranging
publication of Dr. Thorp’s article.
Abstract
The
first wearable computer was conceived in 1955 by the author to predict
roulette, in a joint effort at M.I.T. with Claude Shannon in 1960-61. A
final operating wearable computer was tested in
Claude
and Betty Shannon, and Vivian and Ed Thorp, tested the computer in
We kept the method and the existence of the computer secret until 1966.
1: The idea - 1955
In the spring of 1955 I was finishing my second year of graduate physics at U.C.L.A. One Sunday afternoon on a study break, my head filled with physics equations, I got into a discussion with my friends as to whether it was possible to beat the roulette wheel. Was there a mathematical system? A theorem said it existed for equally likely outcomes and independent trials. Could croupiers control the ball well enough to affect the odds? This was unknown to us (I would later show “no”). What about biased (defective) wheels? We didn’t know. (Al Hibbs and Roy Walford had successfully and sensationally exploited one in Reno in 1949-50, but wheels now usually do not have exploitable imperfections.) I believed that roulette wheels were mechanically well made and well maintained. With that, the orbiting roulette ball suddenly seemed like a planet in its stately, precise and predictable path. This led me to the idea of measuring the position and velocity of the ball and rotor to predict their future paths and from this where the ball would come to rest.
Note that the system requires that bets be placed after the ball and
rotor are set in motion and somehow timed. That means that the casinos
have a simple, perfect countermeasure: forbid bets after the ball is
launched. However, I have checked games throughout the world, including
For camouflage I planned to have an observer standing by the wheel recording the numbers that came up, as part of a “system.” This is common and doesn’t seem out of place. But the observer would also wear a concealed computer device with timing switches. His real job is to time the ball and rotor. (Much later we settled on toe-operated switches, leaving both hands free and in the open.) The computer would make the prediction and transmit it by radio to the bettor. The bettor, at the far end of the layout, would appear to have no connection to the observer-timer. The bettor would have a poor view of ball and rotor and would not pay much attention to them. To further break any link between timer and bettor, I would have several of each, with identical devices. They would each come and go “at random.”
The important bets have to be placed after the ball is launched. A bettor who only bet then, and who consistently won, would soon become suspect. To avoid that, I planned to have the bettor also make bets before the ball was launched. These would be limited so their negative expectation didn’t cancel all the positive expectation of the other bets. I became a licensed radio amateur (W6VVM) when I was 13 so I thought I could build the radio link and other electronic gadgetry.
2: First Efforts 1955-60
I began research and development late in 1955. Confident that the idea would work, I began work on the radio link concurrently with the physics experiments. In 1958 I studied a cheap half scale wheel by making movies of the wheel in action, and to time each frame the picture included a stopwatch that measured in hundredths of a second. By studying the film and plotting orbits from this data, I learned that my wheel and ball were very irregular and that their defects prevented predictability.
But full-sized wheels were not like that. In December 1958, partly to study real casino wheels, I made my first visit to the casinos. I observed several regulation wheels and found that the ball moved smoothly on its tracks. Also the tracks were a pair of flat-beveled, carefully-machined surfaces, not a tube. When I saw how good the casino wheels were, I was more convinced than ever that prediction was possible. But I needed a full-sized wheel and some good laboratory equipment to continue.
Ironically, on this same trip, I happened to try out a recently published blackjack strategy by Baldwin et al [1]. This led quickly to the conviction that that I could devise a winning blackjack card counting system and now I set to work on this intensely. Then in March or April of 1959, twelve man years of blackjack calculations arrived, courtesy of Baldwin, Cantey, Maisel and McDermott, and I pushed the roulette project aside.
I moved from U.C.L.A. to M.I.T., in the summer of 1959, where I wrote my blackjack computer programs. From late 1959 through mid 1960 my computer production runs produced the basic results that gave me the five-count system, most of the ten-count system and the ideas for the ultimate strategy. I also made the computer runs and worked out the methodology so that all of today’s so called “one parameter” blackjack systems could be readily devised by anyone versed in the use of computers. The expectation of plagiarism and worse (an expectation fulfilled) led me to seek quick publication. I chose the Proceedings of the National Academy of Sciences. I needed a member of the Academy to communicate (i.e., approve and forward for recommended publication), so I sought out the only mathematics member of the Academy at M.I.T., Claude Shannon.
I was able to arrange a short appointment early one chilly November
afternoon. But the secretary warned me that
Feeling awed and lucky, I arrived at
I decided to spill my other big secret and told him about roulette. Ideas about the project flew between us. Several exciting hours later, as the wintery sky turned dusky, we finally broke off with plans to meet again on the roulette project.
3: Teaming up with Claude Shannon
Shannon lived in a huge old three story wooden house once owned by Jane
Addams on one of the
Our work continued there. We ordered a regulation roulette wheel from
3.1: Analyzing the motion
My original plan was to divide the various motions of ball and rotor into the following simpler stages and analyze each separately:
· The ball is launched by the croupier. It orbits on a horizontally oriented circular track on the stator until it slows down enough to fall from this (sloped) track towards the center rotor. Assume from first that (a) the wheel is perfectly level, and (b) the velocity of the ball determines how many revolutions it has left before falling off. This means that by timing one revolution of the ball on the stator, we could tell how many more revolutions and how much more time remained until the ball left the track. If these assumptions turned out to be poor, we would modify the analysis.
· Next analyze the portion of the ball orbit from the time the ball leaves the track until it crosses from the stator to the rotor. If the wheel is perfectly level and there are no obstacles, then it seems plausible that this would always take the same amount of time. (We later learned that wheels are often significantly tilted. This tilt, when it occurs, can affect the analysis substantially. We eventually learned how to use it to our advantage.)
There are, however, vanes, obstacles, or deflectors on this portion of the wheel. The size, number, and arrangement vary from wheel to wheel. On average, perhaps half the time these have a significant effect on the ball. Sometimes they knock it abruptly down into the rotor, tending to cause it to come to rest sooner. This is typical of “vertical” deflectors (ones approximately perpendicular to the ball’s path). Other times they “stretch out” the ball’s path, causing it to enter the rotor at a more grazing angle and to come to rest later, on average. This is typical of “horizontal” deflectors (ones approximately parallel to the ball’s path).
· Assume the rotor is stationary (not true), and predict that situation first. Reasoning: if you can’t beat a stationary rotor, you can’t beat the more complex moving rotor. Even a stationary rotor introduces uncertainty due to the ball being “spattered” by the frets (the dividers between the numbered pockets). Sometimes a ball will hit a fret and bounce several pockets on, other times it will be knocked backwards. Or it may be stopped dead. Occasionally the ball will bounce out to the edge of the rotor and move most of a revolution there before falling back into the inner ring of pockets. Thus, even if we knew where the ball would enter the rotor, the “spattering” from the frets causes considerable uncertainty regarding where it finally stops. This tells you that there is no possible reliable “physical” method for predicting ahead of time exactly which pocket the ball is going to land in, unless the wheel is grossly defective or crooked. Thus the roulette method “used” in the movie “The Honeymoon Machine”, where the players forecasted the exact pocket, is an impossibility. It also tells you that successful physical prediction can at best forecast with an advantage which sector of the wheel the ball will end in.
· Next, assume the rotor is spinning. The ball and rotor are spun in opposite directions increasing their relative velocity. This increases the relative number of revolutions and “stretches” the forecast probability distribution, decreasing predictability. A moving rotor also increases the ball “spattering”. On a given play, friction decreases the velocity of the rotor very slowly, so it is possible to predict with high accuracy its position when the ball leaves the stator.
I will now sketch a simplified version of what we first tried to do.
3.2: Timing errors
First, consider the motion of the ball on the track. The actual function x(t), which describes the number of remaining revolutions x versus the remaining time t, is theoretically very complex.
Our first problem, and the key one, was to predict when and where on the stator the ball would leave the track. This problem was key because once we knew this, everything else except rotor velocity was a “constant.” And rotor velocity is easy to measure in advance and incorporate into the prediction, as we shall see. Our method was to measure the time of one ball revolution. If the time was “short”, the ball was “fast” and had a long way to go. If the time was “long”, the ball was “slow” and would soon fall from the track.
We hit a microswitch as the ball passed a reference mark on the stator. This started the electronic clock. (There are many such “marks” available on all actual casino wheels.) When the ball passed the reference mark the second time we hit the switch again, stopping the electronic clock. The clock measured the time for this revolution.
The switch flashed a strobe as well as starting and stopping the clock. The flash “stopped” the ball each time the switch was hit. This let us to see how much the ball was off the reference mark. Since we knew the ball velocity, we could tell how much we were early or late in hitting the switch. This let us correct times recorded on the clock, making the data much more accurate. The visual feedback also trained us to become much better at timing.
With practice our timing errors fell from r.m.s. values of about 0.03 seconds to about 0.01 seconds. Later we trained our big toes to operate switches in our shoes and do almost as well.
The total prediction error comes not only from timing but from the complex
dynamics of the system, the “spattering” of the ball on the rotor pocket
dividers (frets), the deflection of the ball by metal obstacles as it spirals
down the stator, and the possible tilt of the wheel. Assuming the total
error was approximately normally distributed, we needed a standard deviation of
about 16 pockets (
0.42 revolutions) or less to get positive
expectation for both best single number and best octant bets. We actually
achieved an expectation of about 44% for the best single number and about 43%
for the best octant, corresponding to a standard deviation of about 10 pockets
or 0.26 revolutions.
3.3 A time of fun and ferment
Claude Shannon and I worked intensely from November 1960 to June of 1961
designing and building the roulette computer.
For bet sizing in favorable games,
The Kelly strategy showed that it was worth trading a little expectation for a
large reduction in risk by betting on several (neighboring) numbers, rather
than a single number, if feasible. We settled on “octants”, groups of
five neighboring numbers, which covered every number once and the green 0 and
00 twice. We also considered
4: Design and construction of the computer: 1961
Several months of experiments and consideration of a wide range of designs led us to a final version of the computer which had twelve transistors and was the size of a pack of cigarettes. We input data using two microswitches in our shoes, operated by our big toes. One switch initialized the computer and the other timed the rotor and the ball. Once the timing switch was hit twice to time the rotor, the computer started transmitting a musical scale which matched the passage of rotor octants past the reference mark. By tuning a pair of variable resistors, the computer was “set” earlier to match the wheel and ball and optimize prediction for a specific number of ball revolutions to go. We usually chose the range between 3 and 4 revolutions. When the timing switch was first hit for the ball, the tone sequence shifted and played faster. As the timing switch clocked the ball for the second time, the tones stopped. The last tone heard named the octant on which to bet. If the timer misjudged the number of ball revolutions left, the tones would continue and the bettor would not get a prediction. Note that the prediction, if sent, was simultaneous with the last input. The compute time was zero!
In April of 1961 I went to
We each heard the musical output through a tiny loudspeaker in one ear canal. Thin wires connected the computer and the speaker. We painted the wires to match our skin and hair and affixed them with “spirit gum”. The wires were the diameter of a hair to make them inconspicuous but copper broke constantly. We finally located hair thin steel wire which seemed adequate. The wearable version of the computer was complete and operational in June of 1961.
5: The computer in
An attractive offer took me away from M.I.T. in the summer of 1961 but
Betty and Claude Shannon and my wife Vivian and I met in
Claude generally stood by the wheel and timed, and for camouflage seemed to record numbers like just another “system” player. I sat away from the wheel at the far end of the layout. We acted unacquainted. Once I saw a lady next to me look over in horror. I left the table quickly and went to see what she had seen. The speaker was peering from my ear canal like an alien insect.
What prevented us from moving to large scale betting on this trip were the wires to the speaker. They broke frequently, leading to tedious repair and rewiring of ourselves.
Except for the wire problem, the computer was a success. We could solve this with larger wires and growing hair to cover our ears, a conspicuous style at the time, or persuade our reluctant wives to “wire up”. We adjourned to consider.
6: Afterward: 1962-98
For reasons such as the difficulties of working together at a distance and the opportunity cost from our other activities, we never continued the project. In 1961 I also built a “knockoff” to predict the “wheel of fortune” or “money wheel” [4]. It used the toe switch for input, the speaker for output, and a single unijunction transistor, and required only one person. The matchbox sized computer worked well in the casinos but the game had too little action to conceal the late bets and the spectacular consequences.
Finally in 1966, I publicly announced our roulette system because it was clear
now that we weren’t going to exploit it [8]. I published more details
later in [10, 11, 12]. I was then called by a member of the future Eudaemonic Pie group, to whom I outlined our work and
results in detail. They went on to build an operational wearable roulette
computer in the ‘70’s using the next generation of technology. They also
reported a 44% positive expectation but we were ultimately frustrated by
hardware difficulties, as reported in [2]. Other groups also launched
secret roulette projects, several of which (including the “Romeo Project”)
reportedly led to substantial casino wins. Shannon and I discussed
building a simple wearable blackjack computer but I found mental card counting
easier so we passed. However, Keith Taft and others built and marketed
them. Finally on May 30, 1985 the
7: References
[1] Baldwin, Roger; Cantey, Wilbert; Maisel, Herbert and McDermott, James, “The Optimum Strategy in Blackjack,” Journal of the American Statistical Association, Vol. 51, 1956, pp. 429-439.
[2] Bass, Thomas A., The Endaemonic
Pie, Houghton
[3] Kelly, J.L., “A New Interpretation of Information Rate,” Bell System Technical Journal, Vol. 35, 1956, pp. 917-926.
[4] O’Neil, Paul, “The Professor Who Breaks the Bank,” Life, March 27, 1964, pp. 80-91.
[5] Thorp, Edward O., “A Favorable Strategy for Twenty-One,” Proceedings of the National Academy of Sciences, Vol. 47, No. 1, 1961, pp. 110-112.
[6] Thorp, Edward O., “A Prof Beats the Gamblers,” The Atlantic Monthly, June, 1962.
[7] Thorp, Edward O., Beat The Dealer,
Random House,
[8] Thorp, Edward O., Beat The Dealer, 2nd
Edition, Vintage,
[9] Thorp, Edward O., “Optimal Gambling Systems for Favorable Games,” Review of the International Statistical Institute, Vol. 37, 1969, pp. 273-293.
[10] Thorp, Edward O., “Systems for Roulette I,” Gambling Times, January/February 1979.
[11] Thorp, Edward O., “Physical Prediction of Roulette I, II, III, IV,” Gambling Times, May, July, August, October 1979.
[12] Thorp, Edward O., The Mathematics of
Gambling, Lyle Stuart,
[13] Thorp, Edward O., “The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market,” Paper presented at the 10th International Conference on Gambling and Risk Taking, Montreal, June 1997. Finding the Edge: Mathematical Analysis of Casino Games, Vancura, Eadington and Cornelius, editors, Univ. of Nev., Reno, 1998. On the web: http://www.bjmath.com/bjmath/thorp/paper.htm
Technically Advanced
Ancient Civilizations?
Chris Cole
I had lunch with Jeff Ward recently, who is a very well-traveled guy and therefore a student of history. Or maybe it is vice versa. Anyway, the issue of whether there could have been ancient advanced civilizations came up. If there were large stone monuments built, say, 500,000 years ago, would any trace of them remain today? We think not. This led to the question: can we disprove that ancient advanced civilizations existed? Proving a negative is hard, but that just makes it more fun. So here are some thoughts I’ve had since the lunch that I hope fellow Mega members can improve upon.
The fossil record is pretty consistent about the tools used by our immediate ancestors from say a few hundred thousand years ago to a few million years ago. As far as I know, every time we find fossilized humanoid bones, we find associated with them in the same strata tools made of flint and rock that are evidence of a “stone age” technology. Although details of these tools differ, they all share the same basic evidence of no metals and no advanced technology. I’m not sure if the absence of metals means much, because perhaps refined materials will tend to break down over that time frame. Plastics, for example, have a lifetime in the tens of thousands of years. Perhaps metal has a similar lifetime. Does anyone know? But it is not the absence of metals that is critical to the argument; it is the presence of stone tools. Surely it is a stretch to argue that every fossilized human happened to be a collector of ancient stone tools.
One possibility is that there was an advanced civilization during this period, somewhere on Earth, of which no trace remains. This would imply that this civilization co-existed with the primitive peoples of the time, and did not interact with them. The modern record of “first world” civilization indicates that it tends to spread evidence of itself