Chance News 27

Quotation

I could prove God statistically. Take the human body alone - the chances that all the functions of an individual would just happen is a statistical monstrosity.

George Gallup

This is from an ineresting article about the life of George Gallup: "The Human Yardstick", Williston Rich, Saturday Evening Post January 21,1939, p. 71. The article ends with:

His greatest delution is that he can forecast the stock market. his greatest fear, that a competitor will enter his field and be dishonest with the figures. His greatest devotion, to his family, his home and his church. He says "I could prove God statistically--.

Submitted by Laurie Snell

Forsooth

The following Forsooths were in the May 2007 RSS News:

The Times leader of 28 February tells us that taking regular dose of certain vitamins 'can actually increase the risk of mortality by five per cent'. Since the "risk of mortality' is already 100 percent this is very worrying.

AWF Edwards
Cambridge

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Da springen drei Rosen, Halb rot und halb weiß

19. Die schöne Müllerin
Franz Schubert,

Submitted and sung by Laurie Snell

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How to own a random number

God created the integers; all else is the work of man, Leopold Kronecker

AACS is the copy protection technology used on HD-DVD and Blu-ray discs. The consortium that owns this technology are apparently trying to stop websites and newspapers publishing a specific 128-bit integer that, with suitable software, enables the decryption of video content on most existing HD-DVD and Blu-ray discs. As part of this effort, they have claimed ownership of the encryption key, which means that you cannot use, without written permission, that particular 30-digit integer (in base 10) and several million other unknown keys that they apparently are claiming ownership of. Not only that, but the numbers in question were chosen randomly so there is no simple way of knowing if your random choice conflicts with theirs, even if their choices were public knowledge.

Further reading

• How to own a random number, BoingBoing blog, 7 May 2007.
  
• You Can Own an Integer Too — Get Yours Here, Ed Felten, May 7, 2007 — this professor of Computer Science and Public Affairs at Princeton University suggests a way that you too can own your own random integer. He even suggests a use for your number:

Did we mention that a shiny new integer would make a perfect Mother’s Day gift?

Submitted by John Gavin.

Two probability problems

IBM has a monthly "Ponder this challenge" which is often a probability problem. The April 2007 Challenge was the following random walk problem.

This month's puzzle concerns a frog who is hopping on the integers from minus infinity to plus infinity. Each hop is chosen at random (with equal probability) to be either +2 or -1. So the frog will make steady but irregular progress in the positive direction. The frog will hit some integers more than once and miss others entirely. What fraction of the integers will the frog miss entirely? You may consider the answer to be the limit as N goes to infinity of the fraction of integers between -N and N a frog starting at -N and randomly hopping as described misses on average. An answer correct to six decimal places is good enough.

You might also want to the Puzzle for February 2007 which provides another example of the occurence of the Golden Mean:

Consider the following two person game. Each player receives a random number uniformly distributed between 0 and 1. Each player can choose to discard his number and receive a new random number between 0 and 1. This choice is made without knowing the other players number or whether the other player chose to replace his number. After each player has had an opportunity to replace his number the numbers are compared and the player with the higher number wins. What strategy should a player follow to ensure he will win at least 50% of the time?

Why have Americans stopped growing?

Bad Health Care, Deficient Welfare Keep Americans Short, Spiegel Internaional, 22 May 2007.

This on-line article, one in a series, claims that US citizens were the tallest in the world up to World War II but since then, US heights have stagnated while Europeans have been getting taller. Furthermore, the average American is now between two and six centimeters shorter than his European counterpart. The article cites a new study which conjectures that this phenomenon might be explained by differences between health care and the social network systems in various countries. It also suggests a similar result for life expectancy.

The underlying academic paper studies long-term trends in the heights of the US population by combining the results of cross-sectional surveys. The authors analysis is based on the complete set of NHES and NHANES data collected between 1959 and 2004. They used regression analysis to estimate the trend in U.S. heights stratified by gender and ethnicity, holding income and educational attainment constant.

The article asks why the historical correlation between height and wealth is breaking down

The correlation between wealth and height has long been understood, the most recent example coming as Eastern Europeans shot up following the collapse of communism. But why, in the richest country in the world, should growth rates (in height) be stagnating?

This academic study argues that politics may offer an answer. The paper claims that the US average is pulled down by those who struggle to get by, in a country with drastic differences between rich and poor. It claims

whereas in the US, some 15 percent of the population has no health insurance and those on welfare can barely get by, almost all citizens of northern and western European countries enjoy universal health care and a generous social net. The result is that even those children dependent on welfare in Europe have a sufficient living standard.

The paper mentions that taller people have higher incomes, on average, but is unsure about the direction of causation. Is spite of this, the US population height has been stable since 1950 even though prosperity contined to rise, something that will require further work to explain, according to the authors:

Quite a bit more needs to be done to determine the relationship between social standards and height. In short, the richest are neither the tallest nor the healthiest. Why that is so must be explained.

Questions

• Today, Americans are between two and six centimeters shorter than the Dutch but in the mid-19th centuary the reverse was the case. How reliable do you think data from 150 years is, in this case? What questions might you ask to ensure that any comparisons between cross sectional studies, over such a long period of time, are fair? How large do you think the samples sizes might have to be to justifty such claims?
• The authors claim an association between height and health but also mention an association between health and life expectancy. Height is easy to measure and fixed (between ages 20-50) but life expectancy appears not to be. Is it plausible to speculate on what average height might tell us about average life expectancy? Might it be easier for health educators and policy makers to focus on height as a simplier and more transparent measure of health than life expectancy?
• Similar to the previous question, there is a negative correlation between population height and population illiteracy and population height and income inequality. Would height serve as a good proxy for the overall well-being of a population? If so, why aren't trends in population height used by policy makers more often?
• Other factors that might influence the relation between height and health, such as nutritional intake, incidence of disease and availability of medical services, were not felt to be material in developed countries. Why might this be? Might these factors have been more relevant in the past? How difficult do you think it would be to reliably extract such measures from historical data?
• The paper briefly mentions a negative association between population height and population density, allowing for social status. Speculate on how you might investigate such a relationship.
• If height seems like an attractive proxy for health, how might you handle the fact that a population's average height grows with age between 0 and about 20 and shrinks with age above about age 50? Without such adjustments, is it necessary to wait 20 years for each generation's final height to stabilise before drawing conclusions about their future health and life expectancy?
• For future studies, speculate on how genetic information might gradually replace height as a proxy for future health. What are genetic's relative merits compared to height?

Further reading

• Underperformance in Affluence: The Remarkable Relative Decline in U.S. Heights in the Second Half of the 20th Century, Komlos, Benjamin E. Lauderdale (2007), Social Science Quarterly 88 (2), 283–305 (another link to the pdf). This new study published in the current issue of the Social Science Quarterly by researchers from Princeton University in the US and the University of Munich in Germany indicates that the difference may have to do more with politics than biology.
• America's Middle Class Has Become Globalization's Loser, Gabor Steingart, Speigel International, 24 Oct 2006 -- excerpted from the German best-seller World War for Wealth: The Global Grab for Power and Prosperity by Speigel editor Gabor Steingart.
• Poor People in Rich Nations: The United States in Comparative Perspective, Timothy Smeeding, Syracuse University.
• Blogs discussing this story, via Technorati.

Submitted by John Gavin.

A short film exploring relative sizes

On the topics of visualisation and scaling, this short film - once loaded, click on Top Ten then Powers of ten - visualises the size of 'things' and the effect of then adding a zero to the scale. Every second the view is 10 times wider starting with one meter - a person lying on the ground - to 10^24 - the univerise. It then reverses the view down to a subatomic particle, 10^-14. A journey of 40 powers of ten.

Submitted by John Gavin.