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CHANCE News 6.12

(10 October 1997 to 9 November 1997)

Prepared by J. Laurie Snell and Bill Peterson, with help from Fuxing Hou, and Joan Snell, as part of the Chance Course Project supported by the National Science Foundation.

Please send comments and suggestions for articles to jlsnell@dartmouth.edu.

Back issues of Chance News and other materials for teaching a Chance course are available from the Chance web site:

http://www.geom.umn.edu/locate/chance
or

Note: We got Bible code fever and fell behind. We will send out part 2 of Chance News 6.12 later.

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DNA neither knows nor cares. DNA just is.
And we dance to its music.

Richard Dawkins
River Out of Eden p. 133

Contents of Chance News 6.12 Part 1

• 1. Chance lectures.

• 2. Every probability is 50-50.

• 3. There are codes in War and Peace too.

• 4. The jungles of randomness.

• 5. Prenatal care better at HMOs, study finds.

• 6. AIDS researchers drop placebo plan.

• 7. Star watch: Gum wrapper astrology.

• 8. Schedule for Chance lectures.

• 9. Two books from the computer of Joan Garfield.

• 10. Student ratings of professors

• 11. How to raise your I.Q.

• 12. GOP just wants to check whether anybody likes the IRS.

• 13. Ask Marilyn: Chance of being struck by lightning.

• 14. Personal accounts and folded paper.

• 15. Colleges look for answers to racial gaps in testing.

• 16. Buy a house, lose your job?

• 17. Compromise found on census sampling.

• 18. We really can tell if we are being watched.

• 19. Ask Marilyn: The infamous two boy problem.

The Chance project is devoted to the use of current news items in the teaching of probability and statistics. The goal of this lecture series is to bring together experts in a variety of subject areas which regularly appear in Chance news. We've asked the speakers to present the basic ideas of their subjects in a manner which will be accessible to an inquisitive and intelligent audience with "newspaper knowledge" of their area. The lectures will eventually be put on the Chance web site and are intended to be an educational resource.

This Lecture Series is supported in part by the National Science Foundation.

Schedule for Chance Lectures
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Bob Hayden writes:

Your Chance acquaintances may be interested to hear that I found the hard cover version of Tainted Truth for $4 in a Book Warehouse. They had MANY copies. Presumably this means it is out in paperback, which may also be of interest.

TED KOPPEL: Dr. Andrews, I'm sure you have heard such cautionary advice before so on what basis is the assumption being made that this is the one that's going to have the kind of impact on southern California in particular that's being predicted?

RICHARD ANDREWS: Well, in the business that I'm in and that local government and state government is in, which is to protect lives and property, we have to take these forecasts very seriously. We have a lot of forecasts about natural hazards in California and we have a lot of natural events here that remind us that we need to take these forecasts seriously. I listen to earth scientists talk about earthquake probabilities a lot and in my mind every probability is 50-50, either it will happen or it won't happen. And so we're trying to take the past historical record, our own recent experience of the last, two of the last three years and make the necessary preparedness measures that can help protect us as much as we can from these events.

Maya also sent us an English translation of the following article on the bible codes that appeared in Galileo, a Hebrew science journal. You will be able to obtain this translation from web version of this issue of Chance News.
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There are codes in War and Peace too.
Galileo, vol. 24, November-December 1997
Maya Bar-Hillel, Dror Bar-Natan, Brendan McKay

This article reports on new work related to the Witztum, Rips and Rosenberg (WRR) paper on Bible codes (also called Torah codes) that appeared in Statistical Science 1994, Vol, 9, No. 3, pp 429- 438 (Chance News 6.07). We shall refer to the authors of the Galileo article as BBM and the authors of the Statistical Science article as WRR. WRR reported on the following experiment.

The names of 34 famous Rabbis, born long after Genesis was written, were chosen from an encyclopedia of famous Rabbis. For each Rabbi, WRR chose a set of names and titles that would identify the Rabbi and a set of dates that represent the date of birth or death of the Rabbi.

WRR then considered a Hebrew version of Genesis as a string of 78,064 Hebrew letters with no spaces. They defined an equi-letter- skip (ELS) word as a word whose letters occur in this string of letters of Genesis, separated by sequences of letters of equal length. An elementary probability calculation shows that we can expect, just by chance, that most of the names and dates of the Rabbis will be ELS words.

WRR then defined a notion of distance between two ELS words and hypothesized that the names and dates of the Rabbis would be closer together than could occur by chance. This hypothesis was tested and the results were highly significant (p = .000016).

The referees suggested that the authors choose a completely new set of famous Rabbis and test their hypothesis again. They did and again obtained highly significant results. Finally the referees asked the authors to test their hypothesis in the Hebrew version of another work of similar size. They did so, using the first 78,064 letters of the Hebrew translation of War and Peace. The Rabbis' names and dates again appear as ELS words but the degree of closeness of their names and dates was not significant. On the basis of these tests the referees accepted the paper for publication in Statistical Science.

We have now a situation very similar to a well designed experiment in extra-sensory perception with highly significant results that a skeptic just doesn't believe. What does the skeptic do? He looks for something in the experiment that was not done quite right. MBB play the role of skeptics. They believe that recent experiments, carried out by Dror Bar-Natan and Brenden McKay, cast considerable doubt on the claims of Witztum and that the choice of names and dates to use for the Rabbis was made before any consideration of where the names and dates occurred as ELSs in Genesis. WRR claim, in fact, that they (WRR) did not even make these choices, but rather they were made by other historical scholars for them.

So what did Bar-Natan and Brenden McKay (BM) show? They showed first that, whoever chose the names and dates to use for the Rabbis for the WRR article, made a significant number rather arbitrary choices--especially for names of the Rabbis. BM then asked if they could find a significant result in War and Peace if they were allowed to make judicious choices to help their cause. BM considered the second list of Rabbis chosen by WRR at the suggestion of the referees. They kept the same dates but made modifications in the choice of names. Specifically they dropped 20 of the names from the 90 names used by WRR for the Rabbis and added 30 new ones. The new names were ones that research suggested to BM could equally well have been chosen by WRR. With these changes, BM found the same kind of significant results in War and Peace that WRR found in Genesis.

The authors conclude that one explanation for the significant results of WRR is that they "cooked" their data. The authors report on additional evidence for this cooking. They state that almost every one of the apparently quite arbitrary choices WRR made in choosing the names, increased the significance of the result. Of course, this itself could be considered evidence of divine intervention.

Well, that leaves us with the familiar ESP situation: the believer continues to believe and the skeptic continues to be skeptical. (See the reports by Jessica Utts and Ray Hyman (Chance News 5.04) as they assessed the research on extra sensory perception sponsored by the Defense Intelligence Agency during the cold war.

DISCUSSION QUESTIONS:

(1) Harold Gans, former senior cryptologist with the Department of Defense, took the names of all 66 Rabbis and replaced the various spellings of dates of birth or death of the Rabbis used by WRR by the spellings of the cities where the Rabbis were born or died. Gans again obtained a highly significant result (p < 1/143,000). If you were asked to referee papers by Gans, purported to confirm the WRR results, or by BM purporting to show how the WRR results could have been flawed, how would you decide whether one or both of these papers should be accepted?

(2) What would you estimate to be your apriori probability for the hypothesis proposed by WRR before their experiment? How would the results of WRR change this apriori probability?
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Another skeptical look at the Torah Codes has been provided by Barry Simon of California Technology. Simon is one of the countries leading mathematical physicists and himself an Orthodox Jew. His article "A skeptical look at the Torah codes" will be published in the March issue of Jewish Action. A preliminary version is posted on the web Barry Simon on Torah Codes.

Simon has an interesting discussion, based on his considerable experience as an editor of a scientific journal, about the overstated claims regarding the WRR article that have been made, especially by religious groups, based on acceptance of this work by Statistical Science and supporting comments by leading mathematicians.

Simon discusses some of the same issues raised by MBM in their Galileo article. Another concern Simon mentions is that the definition of distance between EDLs provided by WRR is extremely complicated and not a natural definition that other mathematicians would have been likely to choose. The statistical significance of the WRR could be quite sensitive to the form of this definition and Simon suggests that, without even realizing it, WRR could have been influenced by what works in choosing this rather unnatural definition of distance.

DISCUSSION QUESTION:

Simon says that he believes it would be impossible to disprove the WRR claim that the Torah has hidden codes. He writes:

I explicitly asked Professor Rips this question and he admitted it was an interesting question to which he didn't have an answer. If it isn't possible to disprove, then the hypothesis is not a scientific hypothesis. This is not to say that statistical analysis can't be a valid way to analyze what might be going on, but without the possibility of disproving a hypothesis, that hypothesis is outside the realm of science as we understand it.

Satinover is a psychiatrist who is currently studying physics at Yale. His book is meant to be a complete story of the search for Bible codes from the point of view of a "believer" with an "open" mind. We were rewarded by reading this book in finding ourselves quoted as saying: "the Chance course at Dartmouth College is designed to train students to be suspicious of what look like Œmeaningful coincidences¹ when careful statistical analysis will show they are not meaningful at all." This appears in a discussion of how things will change if the claim of the existence of Torah codes becomes widely accepted by the scientific community.

DISCUSSION QUESTION:

What evidence would be needed to convince the scientific community of the existence of Torah codes?
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Finally, what about Michael Drosnin's best seller book "The Bible Code" suggested by the work of WRR (Chance News 6.07). Barry Simon remarks "at one point was on the top ten best sellers list simultaneously in New York, London, Paris and Rome.

This book has been ridiculed by everyone, including Witztum and Rits, except Warner Brothers who have signed the book up saying that it has the potential for a fine movie. Perhaps the most amusing put down of this book resulted from a challenge made by Drosnin:

When my critics find a message about the assassination of a prime minister encrypted in Moby Dick, I'll believe them. (Newsweek, Jun. 9, 1997)

DISCUSSION QUESTION:

Closeness of two ELSs is shown, at least informally, as follows: Imagine putting the whole text of Moby Dick (without spaces) on a single page. Then ELSs appear as lines, vertical, horizontal, or slanted somewhere on this page. The text can appear on the line in either of the two possible directions. Two ELSs are considered close if you can choose the line length of the page containing the entire text so that these two ELS lines are confined within a rectangle that is small compared to the rectangle (page) containing the entire book. For example, by a judicious choice of line length, McKay finds "Kennedy" and "shoot" in Moby Dick within a 32 by 15 rectangle of letters. McKay also finds five other words including "rifle" and "coffins" or phrases including "has been so killed" within this same rectangle that could be associated with Kennedy's assassination!

(1) If you find two ELSs by searching in a single string of letters representing Moby Dick, how would you decide if you could choose a line length that would make them appear in a relatively small rectangle?

(2) Using the full text of Moby Dick, Albin Jones provided us with the following distributions for the occurrences of the 26 letters in Moby Dick.

A: 75566  (8.169677%)
B: 16413  (1.774461%)
C: 21755  (2.352001%)
D: 37243  (4.026457%)
E: 113660 (12.288139%)
F: 20286  (2.193183%)
G: 20265  (2.190913%)
H: 60966  (6.591225%)
I: 63761  (6.893402%)
J: 1043   (0.112762%)
K: 7843   (0.847931%)
L: 41683  (4.506480%)
M: 22700  (2.454168%)
N: 63918  (6.910375%)
O: 67454  (7.292663%)
P: 16631  (1.798030%)
Q: 1494   (0.161521%)
R: 50466  (5.456037%)
S: 62477  (6.754584%)
T: 85524  (9.246268%)
U: 25874  (2.797319%)
V: 8344   (0.902096%)
W: 21546  (2.329406%)
X: 998    (0.107897%)
Y: 16417  (1.774893%)
Z: 629    (0.068003%)

If a book with about a million letters is written, with letters chosen randomly according to this distribution, what is the expected number of times that the ESL "Kennedy" would appear in the book? Would it be reasonable to use the Poisson approximation to estimate the probability that this ESL occurs at all?

(3) See if you can find another estimate for the distribution of the frequency of letters in a typical English text. See for example, "Secret and Urgent" by Fletcher Pratt, Bobbs-Merrill, 1939. Is this second estimate reasonably consistent with the distribution found from Moby Dick? If not, why not? (If you know of a better source of letter frequencies please let us know about it).
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The jungles of randomness.
Ivars Peterson
Wiley, 1997
ISBN 0471164496
$24.95

We often say that probability plays a key role today in almost every field of knowledge. On the other hand, reading a typical probability book, you would never realize this. It has taken mathematician-science writer Ivars Peterson to show us that, what we have been claiming on some kind of blind faith, is really true.

This final paragraph of the preface sets the stage and the tone of the book.

The trek through the jungles of randomness starts with games of chance. It proceeds across the restless sea of life, from the ebb and flow of human concourse to the intricacies of biological structure and the dynamics of flashing fireflies. It wanders into the domain of sounds and oscillations and the realm of fractals and noise. Glimpses of gambling lead to a lifetime of chance.

The middle third of the book is centered around the many manifestations of oscillations. We learn how studying "the bounds of a kangaroo, the graceful leaps of a gazelle, the rocking gait of a cockroach and the slithering of a snake" can help us build robots that will wander over the surface of Mars. Another marriage of probability and mathematics is presented with the discussion of the solutions of Mark Kac's problem: Can you hear the shape of a drum?

The study of the synchronous behavior of the lights of fireflies provides us with a dramatic example of interacting particle systems; a major branch of modern probability theory.

The fact that Peterson is a science writer (mathematics and physics editor at Science News www.sciencenews.org) makes him aware of most recent developments in science that use probability concepts. We found his discussion of the recent applications of Levy flights and of the new ways to let nature provide us with truly random numbers completely new to us and sent us off to the library to look up the references provided for these topics. References are given by chapter at the end of the book.

Even though this book surveys many areas, Peterson provides a level of detail that makes the reader become involved in the phenomena being discussed. Even in reading about such a mundane object as a slot machine, we learn that the spinning wheels of the old slot machines determined the random final combination and told us if we had won a prize, but, with the modern electronic slot machines, before the wheels even start spinning the random number generator has determined where they should stop. The wheels are there just for nostalgia!

Each year in June we have spectacular displays of fireflies in our back yard. In future years watching these displays will remind us of our enjoyment reading this fascinating book.
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Prenatal care better at HMOs, study finds.
The Boston Globe, 21 October 1997, pA12
Associated Press

This article reports on a review of 8000 birth records for babies born in the Seattle area during 1992-3. Half the babies were born to women in an HMO and half to women in private insurance. The study found that women enrolled in HMOs were 40% less likely to receive inadequate prenatal care and 30% more likely to give birth to a baby weighing more than 5.5 lbs -- usually a marker for good health.

On the other hand, the article points out that "for reasons not understood" HMO patients with no obstetrical risk factors were 40% more likely to have labor and delivery complications. However, the authors of the report stressed that the incidence of complications was less than one percent in both groups, affecting only a few of the 8000 patients in the study. Moreover, the differences might be attributable to more thorough record-keeping at HMO hospitals, so that details on complications would be more likely to be found there.

DISCUSSION QUESTIONS:

(1) What do you suppose constitutes "adequate" prenatal care? How would you interpret the claim that HMO patients are "40% less likely to receive inadequate prenatal care"? What else do you need to know?

(2) If anything near 1% of the 8000 had complications, wouldn't you regard this as more than "a few" patients? Why do you think the result was reported in this way?

(3) If the number of complications really is small, why didn't the authors simply state that the differences might represent chance variation?

(4) What do you think of the explanation that HMO hospitals are doing more thorough record-keeping?
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AIDS researchers drop placebo plan.
The Boston Globe, 24 October 1997, pA1
Richard A. Knox

This updates a story from Chance News 6.11, where we reported on the ethical controversy surrounding the use of placebo in a study of "short course" AZT treatment to prevent mother-to-fetus transmission of HIV. The present article reports that Johns Hopkins University researchers have dropped plans to use the placebo design in Ethiopia.

However, according to Dr. Joseph Saba, who oversees the studies worldwide, the decision is not a response to the criticism. There are five studies currently underway in Africa and Asia, and he insists that these are not unethical. If, however, these begin to show positive results, then the newer trials would have to be stopped prematurely. Dr. Jack Killen, of the National Institutes of Allergy and Infectious Diseases, adds that it had been part of the larger plan all along to rethink the design if positive results started to appear.

US advocacy groups are pressuring the US Dept. of Health and Human Services to end placebo use in any further studies of mother- infant studies funded by the US. They maintain that 1993 studies in the US already demonstrated that the short course is better than no treatment at all. Dr. Saba and other officials dispute this interpretation of the data.

DISCUSSION QUESTION:

The article does not actually say that positive results have appeared so far. If none do, do you believe it will be feasible to start new trials with placebos?
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Star watch: Gum wrapper astrology.
The Boston Globe, 3 November 1997, pC6.
Alan M. McRobert

McRobert points out that the horoscopes in today's "Globe" actually derive from ancient interpretations of gods walking among the constellations. Yet astrologers don't seem to mind that the positions of the constellations have changed in the last 2000 years, due to the astronomical phenomenon of precession. So it's likely that a person classified today as a Gemini was actually born while the sun was in Taurus. So why aren't Geminis complaining about inaccuracies in their horoscopes? Because, says McRobert, there's no way to notice: any horoscope will work for you as well as any other!

Any piece of advice, he explains, can make you look at your life in a new way, thereby leading you to some insight. He claims that, when people are shown several personality readings based on Zodiac signs, they can't pick their own more often than would be expected by chance. Similarly, if key words in a person's forecast are replaced by their opposites, the modified ones will be rated as being just as insightful as the originals. He doesn't provide references for these results, but the results suggest some interesting activities for student projects for a CHANCE course.

The title of the article is a reference to the comics that appear on the inside of Bazooka bubble gum wrappers. The author recalls how he and his childhood friends would pick up wrappers they found discarded on playgrounds and try to interpret the comics as parables about their lives. It always seemed to work.

DISCUSSION QUESTION:

How would you design an experiment to test whether switching words with their opposites affected people's feelings as to how "insightful" their horoscopes are?
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