Marilyn vos Savant

Marilyn vos Savant (born Marilyn Mach on August 11 1946) is an American magazine columnist, author, lecturer and playwright who rose to fame through her listing in the Guinness Book of World Records under "Highest IQ." Since 1986 she has written Ask Marilyn, a Sunday column in Parade magazine in which she answers questions from readers on a variety of subjects.

Biography
Born in St. Louis to Mary vos Savant and Joseph Mach, vos Savant opposes the tradition of children taking their father's surname, instead using her mother's maiden name. She is of Austrian ancestry. She attended Washington University, but dropped out to pursue a career in writing and investing.

Marilyn's listing in the 1986 Guinness Book of World Records brought her widespread media attention. Among the periodicals profiling her was Parade, which followed its article with a selection of questions and her answers to them, the popularity of which launched a regular question-and-answer column, Ask Marilyn. In the column she solves mathematical and logical puzzles and answers questions on a wide range of subjects, including philosophy, physics, politics, education, and human nature, as well as responding to more traditional requests for personal advice. The column has also provided a basis for many of her books.

Vos Savant lives in New York City with her husband, artificial-heart pioneer Robert Jarvik, whom she married in August 1987. She has two children by the first of her two previous marriages. She is the Chief Financial Officer of Jarvik Heart, and assists her husband with cardiovascular disease research and prevention. She has also served on the Board of Directors of the National Council on Economic Education and on the Advisory Boards of the National Association for Gifted Children and the National Women's History Museum, the last of which gave her a "Women Making History" award in 1998 "for her contribution to changing stereotypes about women." She was named by Toastmasters International as one of the "Five Outstanding Speakers of 1999," and in 2003 received an honorary doctorate of letters from The College of New Jersey.

IQ
It is generally acknowledged that Marilyn vos Savant has an extremely high IQ, and she has belonged to Mensa, Prometheus, and other high-IQ societies (Thompson 1986). However, there is much confusion over its actual value, with different data and calculations yielding different numbers: 167+, 186, 218, 228, and 230. These will be examined below, but the measurement of extremely high IQs is an inexact science, subject to problems including small sample sizes (because so few people have IQs at this level), ceiling bumping (because many tests are not designed to measure such high IQs), and a fat tail (because there seem to be more high IQs than a normal distribution would predict), as well as to the controversy over IQ in general.

Vos Savant was listed in the 1986 to 1989 editions of the Guinness Book of World Records under "Highest IQ." Subsequent editions do not include this category, and her column now reports that she is listed in the Guinness Hall of Fame. The book mentioned her performance on two intelligence tests: the Stanford-Binet (taken when she was a child) and the Mega Test (taken when she was an adult).

Her Stanford-Binet score is discussed in a 1989 New York magazine article by Julie Baumgold (Baumgold 1989). Vos Savant took the Stanford-Binet when she was ten years old; this was the Second Edition of the test, published in 1937. The Stanford-Binet at that time yielded ratio IQs: scores obtained by dividing mental age (as assessed by the test) by chronological age, and multiplying by 100. Vos Savant says she first took the test in September 1956, at the age of 10 years and 0 months, and achieved the ceiling mental age of 22 years and 10 months, yielding an IQ of 228. This was the score listed by Guinness, this is the score she gives in interviews, and this is the score shown in the "About the Author" section of her books. Rounding it up produces the value of 230 which sometimes appears.

The figure of 167+ comes from a school record cited by Baumgold indicating that vos Savant took the Stanford-Binet in March 1957, at the age of 10 years and 8 months, and achieved a mental age of "17-10+" (meaning at least 17 years and 10 months). It is unclear how the recorded chronological age was derived; dates in March are six or seven months from her August birthday, not eight. It is also unclear how this record relates to the account given in the previous paragraph. The Stanford-Binet at that time had two forms (Form L and Form M), so one possibility is that Marilyn took the test twice.

The figure of 218 was informally derived by test-designer Ronald K. Hoeflin, using a chronological age of 10 years and 6 months, and a mental age of 22 years and 11 months. This figure seems to have no obvious rationale. The ceiling of the Second Edition of the Stanford-Binet was 22 years and 10 months, not 11 months (Terman 1937), and a chronological age of 10 years and 6 months corresponds neither to the age in Marilyn's account nor to the age in the school record cited by Baumgold (although it could fit a March test date).

The second intelligence test mentioned by Guinness is the Mega Test, designed by Hoeflin and taken by vos Savant as an adult in the mid-1980s. The Mega Test yields deviation IQs: scores obtained by multiplying the testee's normalized z-score (the rarity of their raw score on the test) by a constant standard deviation (in this case 16) and then adding 100. Marilyn's raw score was 46 out of 48, corresponding in the latest norming of the test to a z-score of 5.4 and therefore an IQ of 186, a percentile of 99.999997, and a rarity of 1 in 30,000,000 (Hoeflin 1989).

Assertions that vos Savant's IQ dropped from 228 as a child to 186 as an adult are confused: the two numbers represent different types of IQ. For the upper half of the population, ratio IQs seem to follow a log-normal distribution, with a standard deviation of 0.15 for the natural logarithm of the ratio of mental age to chronological age (Scoville). Consequently, vos Savant's Stanford-Binet ratio IQ of 228 corresponds to a deviation IQ of 188, and her Mega Test deviation IQ of 186 corresponds to a ratio IQ of 224.

It is safe to say that Marilyn has one of the highest IQs tested and recorded. More extravagant claims&mdash;that she is the smartest person in the world (Schmich 1985), or is more or less intelligent than such-and-such a child prodigy, historical genius, or famous intellectual&mdash;should be treated cautiously. Marilyn herself values IQ tests as measurements of a variety of mental abilities, but believes that intelligence itself involves so many factors that "attempts to measure it are useless" (vos Savant, 2005).

The Monty Hall problem
Perhaps the most famous event involving Marilyn vos Savant began with the following question in her 9 September 1990 column:

"'Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, the others, goats. You pick a door, say #1, and the host, who knows what's behind the doors, opens another door, say #3, which has a goat. He says to you: 'Do you want to pick door #2?' Is it to your advantage to switch your choice of doors?' &mdash;Craig F. Whitaker, Columbia, Maryland"

This question, named "the Monty Hall problem" due to its resemblance to situations on the game show Let's Make a Deal, existed before Marilyn addressed it, but was brought to nationwide attention by her column. Marilyn's answer, that you should switch because door #2 has a 2/3 chance of winning whereas door #1 has only a 1/3 chance, provoked thousands of letters in response, nearly all arguing that she was wrong and that the doors are equally likely to win. A follow-up column affirming her answer only intensified the debate, which soon spread through the media, even reaching the front page of The New York Times. Among the ranks of her opponents were hundreds of academics with Ph.D.s, some of them professional mathematicians scolding her for propagating innumeracy.

Despite the criticism, Marilyn's answer was correct under the most common interpretation of the question, in which the host always opens a losing door and offers a switch; see Monty Hall problem for details. (In other interpretations, the host may open a door at random, or offer a switch only if your initial choice was correct. The question says only that the host knows what is behind the doors, but Marilyn specified in her original answer her understanding that the host "will always avoid the one with the prize", noting in a follow-up that "anything else is a different question.")

After a second follow-up in which Marilyn explained in more depth her reasoning and the conditions on which it was based, many readers, including academics who had previously argued against her, wrote to admit that she was right. She also called on school teachers across America to simulate the problem in their math classes. In a final column, she announced the results: out of more than a thousand schools which had performed the experiment, nearly 100% had found that it pays to switch. A majority of readers now agreed with her answer, and half of those whose letters had been published wrote to retract their arguments.

Fermat's last theorem
Less favorable to Marilyn was the outcome of the controversy following the publication of her book The World's Most Famous Math Problem in November 1993, a few months after the announcement by Andrew Wiles that he had proved Fermat's Last Theorem. The book, which surveys the history of the theorem, drew criticism for its discontent with Wiles' proof; Marilyn was accused in making her case with misunderstanding mathematical induction, proof by contradiction, and imaginary numbers (cf. Boston & Granville, 1995). Especially contested was her view that Wiles' proof should be rejected for its use of non-Euclidean geometry. Specifically, she argued that because "the chain of proof is based in hyperbolic (Lobachevskian) geometry," and because squaring the circle is considered a "famous impossibility" despite being possible in hyperbolic geometry, then "if we reject a hyperbolic method of squaring the circle, we should also reject a hyperbolic proof of Fermat's last theorem".

Critics pointed to differences between the two cases, distinguishing the use of hyperbolic geometry as a tool for proving Fermat's last theorem, from its use as a setting for squaring the circle: squaring the circle in hyperbolic geometry is a different problem from that of squaring it in Euclidean geometry. She was also criticized for rejecting hyperbolic geometry as a satisfactory basis for Wiles' proof, with critics pointing out that axiomatic set theory (rather than Euclidean geometry) is now the accepted foundation of mathematical proofs and that set theory is sufficiently robust to encompass both Euclidean and non-Euclidean geometry.

In a July 1995 addendum to the book, Marilyn retracts the argument, writing that she had viewed the theorem as "an intellectual challenge&mdash;'to find a proof with Fermat's tools,'" but that she is now willing to agree that there are no restrictions on the tools to be used.

Works

 * 1985 - Omni I.Q. Quiz Contest
 * 1990 - Brain Building: Exercising Yourself Smarter (co-written with Leonore Fleischer)
 * 1992 - Ask Marilyn
 * 1993 - The World's Most Famous Math Problem: The Proof of Fermat's Last Theorem and Other Mathematical Mysteries
 * 1994 - More Marilyn: Some Like It Bright!
 * 1994 - "I've Forgotten Everything I Learned in School!": A Refresher Course to Help You Reclaim Your Education
 * 1996 - ''Of Course I'm for Monogamy: I'm Also for Everlasting Peace and an End to Taxes
 * 1996 - The Power of Logical Thinking: Easy Lessons in the Art of Reasoning…and Hard Facts about Its Absence in Our Lives
 * 2000 - The Art of Spelling: The Madness and the Method
 * 2002 - Growing Up: A Classic American Childhood

In addition to her published works, Marilyn has written a collection of humorous short stories called Short Shorts, a stage play called It Was Poppa's Will, and two novels: a satire of a dozen classical civilizations in history called The Re-Creation, and a futuristic political fantasy, as yet untitled.