Belgian Astronomers and Exercise Machines

October 6, 2010
By

(This article was first published on R-Chart, and kindly contributed to R-bloggers)


In the twisting paths of human discovery, you never quite know what intellectual enterprise is going to result in a world changing discovery.  For instance, the mathematical notion of expected value did not grow up in a sterile, academic environment.   In 1654 Blaise Pascal was approached by Chevalier de Méré who was interested in gambling problems.  Pascal corresponded with Fermat and thus the mathematical theory of probabilities was born.

In recent days reports on economic upheaval have often cast financial industries as institutions based upon greed and power that contribute nothing of value to society.  Defenders of the free market are quick to respond with the immediate economic benefits provided by such institutions as they mitigate risk and serve as "middle men" in modern financial markets.  What is seldom considered is that discoveries in one area often find application in a separate area of life that was never considered during the initial investigation.  And so one day, perhaps Wall Street calculations might be put to non-financial use that benefit mankind in other ways.  There is historical precedent.  For instance, interests in the insurance industry served to popularize and apply a 19th century Belgian calculation in a manner that is now used on modern exercise machines.

A Belgian Astronomer: Adolphe Quetelet
Adolphe Quetelet (1796–1874) was a Belgian mathematician, astronomer and statistician.  While studying astronomical activities in Paris he interacted with Joseph Fourier (1768–1830), Siméon Poisson (1781–1840) and Pierre Laplace (1749–1827).   He went on to put his new found appreciation of probability to practical use in the study of the human body (a subject he had initially approached as a painter and sculptor).  One calculation he created, dubbed the Quetelet Index, is a number that expresses a relationship between a person's height and weight.  Quetelet was not specifically interested in the use of his index for health purposes, but simply for defining the characteristics of "normal" or "average" man.

The Financial Industry
In the mid 20th century actuaries observed increased mortality in overweight policyholders.  And so in an effort to construct more accurate mortality tables the relationship between weight and cardiovascular disease became the subject of epidemiological studies.  Weight tables were first used to predict life expectancy as far back as 1913.  But tables of ideal or desirable weight were developed by the Metropolitan Life Insurance Company in the 1940's.  In the 1960s, a small group insurance industry experts began to use the Quetelet Index.  But it remained for a an American scientist to perform a comparative study of available indices and rename the Quetelet Index to the form that we know it today where it has become a subject related to health and nutrition.

An American Oceanographer, Biologist, and Physiologist
Ancel Benjamin Keys was a scientist who wrote an article for the July 1972 "Journal of Chronic Diseases" that coined the phrase "body mass index" or BMI as a modern designation for the Quetelet Index.  Interestingly enough, Keys early studies culminated in a B.A. in economics and political science in 1925.  His first Ph.D. was in oceanography and biology but his later work was related to his second Ph.D. focused on physiology.  He is best known for two dietary contributions - the K-Ration and the Mediterranean Diet.

Keys (and others today) considered the tendency in the insurance industry to equate relative body weight with excess risk of death to be somewhat simplistic.  There is worldwide variation according to diet and physical activity habits. In most industrial countries people in the middle range of body weight are healthier than those at an extreme.

Because of these types of concerns, BMI is often considered along with other concerns that can indicate potential health risks.  Specifically:

  • A BMI in the overweight category along with certain diseases 
  • A BMI of less than 25 and a waist size above the standard (35 for women or 40 for men) 

The actual BMI ranges considered healthy or at risk are still being debated.  In 1998, the U.S. National Institutes of Health changed U.S. definition of normal from 27.8 to 25 to conform to World Health Organization Standards.  In addition, other countries in the world are encouraging the upper limit for BMI to be even lower than 25.

BMI and R
One’s optimal weight can be derived using the BMI and height as follows:

optimal_weight = function (height, bmi){
  round((height**2 * bmi) / 703)
}

A grid, similar to one found here and the chart above can be constructed a script found at GitHub.

For example:

> create_bmi_dataframe(bmi_end=30)
    19  20  21  22  23  24  25  26  27  28  29  30
60  97 102 108 113 118 123 128 133 138 143 149 154
61 101 106 111 116 122 127 132 138 143 148 153 159
62 104 109 115 120 126 131 137 142 148 153 159 164
63 107 113 119 124 130 135 141 147 152 158 164 169
64 111 117 122 128 134 140 146 151 157 163 169 175
65 114 120 126 132 138 144 150 156 162 168 174 180
66 118 124 130 136 143 149 155 161 167 173 180 186
67 121 128 134 140 147 153 160 166 172 179 185 192
68 125 132 138 145 151 158 164 171 178 184 191 197
69 129 135 142 149 156 163 169 176 183 190 196 203
70 132 139 146 153 160 167 174 181 188 195 202 209
71 136 143 151 158 165 172 179 186 194 201 208 215
72 140 147 155 162 170 177 184 192 199 206 214 221
73 144 152 159 167 174 182 190 197 205 212 220 227
74 148 156 164 171 179 187 195 203 210 218 226 234
75 152 160 168 176 184 192 200 208 216 224 232 240
76 156 164 173 181 189 197 205 214 222 230 238 246
77 160 169 177 186 194 202 211 219 228 236 245 253
78 164 173 182 190 199 208 216 225 234 242 251 260
79 169 178 186 195 204 213 222 231 240 249 257 266
80 173 182 191 200 209 218 228 237 246 255 264 273

There is some variation with the government site – perhaps related to rounding.

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