Galton Institute Home Page September 1999 Newsletter Contents Newsletter Index

Who Is Sir Francis Galton?

Gary E Pittman

III. The Lecture Part 2

Galton’s Inventions

During his early forties, Galton was interested in mechanical devices that performed both mathematical and graphing functions, and were called “computers”. As you might expect, novel concepts were used in their construction. There is a listing of Galton's inventions in Appendix I of D W Forrest’s biography of Galton. I am continually in awe of the amazing number of different things that he became involved with. In this listing, the reader will find some surprising inventions ahead of their time, and also some humour.

Fingerprints

Francis Galton is also responsible for the development of a reliable system of recording and identifying fingerprints. We still use his system today, more than 100 years after he wrote Finger Prints (1892). At that time Galton was 70 years old. A necessary contribution was the development of detailed methods for taking the fingerprint and recording it, an example of Galton's practical approach, and also his willingness to work tirelessly on details, something not necessarily expected of a man who also thought in grand sweeping concepts. In his autobiography, Francis Galton says that his fingerprint classification system should be able to accommodate 20,000 sets of prints. In 1964, the FBI had 173 million sets of fingerprints.

Galton's Fingerprints

Statistical Thinking

Some of the events and discoveries of statistical thinking go back centuries, and involved the astronomers. In fact, astronomers have played major roles into the nineteenth century. This is because the accuracy of measurements was so important to them.

The table above lists three men who were important pioneers, who were astronomers, yet who are known more for their contributions to statistical thinking.

Early astronomers were reluctant to share information, each claiming to have the best methods and equipment for precise measurements. Later, when measurements were shared, it was discovered that there were large differences for which it was difficult to find obvious causes. So these differences were attributed to “errors”. But when combined, these observations formed a frequency distribution having a shape that was then called the “Law of Error”. Later, this shape was found to be due - not to errors - but to the way that many and varied “small causes” (Ref. Francis Galton, Memories of My Life, 1908, p. 310) in a stable system effect the output of that system - a point to which I shall return in a later article. This shape or curve became known as the “normal curve”, and a mathematical equation, which fits the curve exactly, was developed by the great German astronomer and mathematician Karl Gauss. The 10 Deutsche Mark bill has his likeness, a graph of the normal distribution, and the formula for the curve, the formula being both simple and elegant at the same time. So in Germany, there is today an awareness of the significance of Gauss' contributions.

Pierre Simon De La Place (1749-1827)

French Astronomer & MathematicianTheory of Probability

Karl Friedrich Gauss (1777-1855)

German Astronomer & MathematicianDirector of Gottingen ObservatoryTheory of Electricity & Magnetism

Adolphe Jacques Quetelet (1796-1874)

Belgian Astronomer & Statistician

Director of the Royal Observatory

The Normal Distribution

In Francis Galton's first major scientific work titled “Hereditary Genius”, published in 1869 , there is a table on page 378 with numbers provided by Quetelet, the Royal Astronomer of Belgium. When these numbers are made into a graph, we get the beautiful shape above.

I include this reference to a book published more than 125 years ago, because it is important to understand that the phenomenon of the Normal Distribution has been studied by eminent men of science for a long time, and does not represent some new idea that just hatched yesterday. The way of thinking that has developed over many years has been completely validated, and when used properly, is a true representation of the laws of nature. This is the way things really are, whether we would like to think so or not.

When this shape (or distribution) is found to occur with regard to the output of a system, the implications for the system producing it are often profound. Let us see what Francis Galton had to say about it.

“I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the “law of error”. A savage, if he could understand it, would worship it as a god. It reigns with severity in complete self-effacement amidst the wildest confusion. The huger the mob and the greater the anarchy, the more perfect is its sway. Let a large sample of chaotic elements be taken and marshalled in order of their magnitudes, and then, however wildly irregular they appeared, an unexpected and most beautiful form of regularity proves to have been present all along. Arrange statures side by side in order of their magnitudes, and the tops of the marchalled row will form a beautifully flowing curve of invariable proportions; each man will find, as it were, a pre-ordained niche, just of the right height to fit him, and if the class-places and statures of any two men in the row are known, the stature that will be found at every other place, except towards the extreme ends, can be predicted with precision.”

Here Francis Galton tells us about the effect which the Normal Distribution has had upon his understanding of the “cosmic order” which is present amidst apparent chaos. Can anyone tell me what he means by “a beautifully flowing curve”? I'll give you a clue. It is not the curve of the normal distribution. I'll tell you what it is in the next article.

Francis Galton delivered the Huxley Lecture of the Anthropological Institute on October 29, 1901; while discussing the distribution of human talents, he says, “The frequency distribution (of human talents) follows certain statistical laws, of which the best known is the Normal Law of Frequency.”

The Quincunx (see the first article in this series) is a machine which demonstrates the output of a stable system controlled by many small causes. When we take a large sample of values from the Quincunx and plot them on a graph, we see the characteristic shape of the normal distribution.

We see the symmetry about the average value, and the inflection point on both sides of the average. This inflection point locates the value of what is called the standard deviation, an index of the dispersion or range of values in the distribution. We can also say that this representation of the Normal Distribution is a frequency distribution; that is, how many things can be counted in each interval of interest within a total distribution? We will see this in simple form in the next article in the series, in which we will explore how Francis Galton sought to represent frequency distributions to gain even clearer insight into their interpretation.