One of the reasons I disliked public school so much is that is was boring and I never learned a damn thing past first grade.
In college I took a class in statistics and remember thinking, "Who the hell figured out the standard deviation is the square of the variance?" I could have never done it myself. It took me forever to get through that class. But then, I'm not a polymath. I'm not even gifted in math. I just slogged my way through.
What happened to polymaths, anyway?
This is from Wikipedia.
Sir Francis Galton, FRS was an English Victorian progressive, polymath, sociologist, psychologist, anthropologist, eugenicist, tropical explorer, geographer, inventor, meteorologist, proto-geneticist, psychometrician, and statistician. He was knighted in 1909.
Galton produced over 340 papers and books. He also created the statistical concept of correlation and widely promoted regression toward the mean. He was the first to apply statistical methods to the study of human differences and inheritance of intelligence, and introduced the use of questionnaires and surveys for collecting data on human communities, which he needed for genealogical and biographical works and for his anthropometric studies.
He was a pioneer in eugenics, coining the term itself and the phrase "nature versus nurture". His book Hereditary Genius (1869) was the first social scientific attempt to study genius and greatness. As an investigator of the human mind, he founded psychometrics (the science of measuring mental faculties) and differential psychology and the lexical hypothesis of personality. He devised a method for classifying fingerprints that proved useful in forensic science. He also conducted research on the power of prayer, concluding it had none by its null effects on the longevity of those prayed for.
As the initiator of scientific meteorology, he devised the first weather map, proposed a theory of anticyclones, and was the first to establish a complete record of short-term climatic phenomena on a European scale. He also invented the Galton Whistle for testing differential hearing ability.He was cousin of Douglas Strutt Galton and half-cousin of Charles Darwin.
Galton was born at "The Larches", a large house in the Sparkbrook area of Birmingham, England, built on the site of "Fair Hill", the former home of Joseph Priestley, which the botanist William Withering had renamed. He was Charles Darwin's half-cousin, sharing the common grandparent Erasmus Darwin. His father was Samuel Tertius Galton, son of Samuel "John" Galton. The Galtons were famous and highly successful Quaker gun-manufacturers and bankers, while the Darwins were distinguished in medicine and science.
Both families boasted Fellows of the Royal Society and members who loved to invent in their spare time. Both Erasmus Darwin and Samuel Galton were founding members of the famous Lunar Society of Birmingham, whose members included Boulton, Watt, Wedgwood, Priestley, Edgeworth, and other distinguished scientists and industrialists. Likewise, both families were known for their literary talent: Erasmus Darwin composed lengthy technical treatises in verse; Galton's aunt Mary Anne Galton wrote on aesthetics and religion, and her notable autobiography detailed the unique environment of her childhood populated by Lunar Society members.
Galton was by many accounts a child prodigy – he was reading by the age of two; at age five he knew some Greek, Latin and long division, and by the age of six he had moved on to adult books, including Shakespeare for pleasure, and poetry, which he quoted at length. Later in life, Galton would propose a connection between genius and insanity based on his own experience. He stated, "Men who leave their mark on the world are very often those who, being gifted and full of nervous power, are at the same time haunted and driven by a dominant idea, and are therefore within a measurable distance of insanity"
Galton attended King Edward's School, Birmingham, but chafed at the narrow classical curriculum and left at 16. His parents pressed him to enter the medical profession, and he studied for two years at Birmingham General Hospital and King's College London Medical School. He followed this up with mathematical studies at Trinity College, University of Cambridge, from 1840 to early 1844.
According to the records of the United Grand Lodge of England, it was in February 1844 that Galton became a freemason at the so-called Scientific lodge, held at the Red Lion Inn in Cambridge, progressing through the three masonic degrees as follows: Apprentice, 5 February 1844; Fellow Craft, 11 March 1844; Master Mason, 13 May 1844. A curious note in the record states: "Francis Galton Trinity College student, gained his certificate 13 March 1845". One of Galton's masonic certificates from Scientific lodge can be found among his papers at University College, London.
A severe nervous breakdown altered Galton's original intention to try for honours. He elected instead to take a "poll" (pass) B.A. degree, like his half-cousin Charles Darwin. (Following the Cambridge custom, he was awarded an M.A. without further study, in 1847.) He then briefly resumed his medical studies. The death of his father in 1844 had left him financially independent but emotionally destitute, and he terminated his medical studies entirely, turning to foreign travel, sport and technical invention.
In his early years Galton was an enthusiastic traveller, and made a notable solo trip through Eastern Europe to Constantinople, before going up to Cambridge. In 1845 and 1846 he went to Egypt and travelled down the Nile to Khartoum in the Sudan, and from there to Beirut, Damascus and down the Jordan.
In 1850 he joined the Royal Geographical Society, and over the next two years mounted a long and difficult expedition into then little-known South West Africa (now Namibia). He wrote a successful book on his experience, "Narrative of an Explorer in Tropical South Africa". He was awarded the Royal Geographical Society's gold medal in 1853 and the Silver Medal of the French Geographical Society for his pioneering cartographic survey of the region This established his reputation as a geographer and explorer. He proceeded to write the best-selling The Art of Travel, a handbook of practical advice for the Victorian on the move, which went through many editions and is still in print.
In January 1853 Galton met Louisa Jane Butler (1822–1897) at his neighbour's home and they were married on 1 August 1853. The union of 43 years proved childless.
Galton was a polymath who made important contributions in many fields of science, including meteorology (the anti-cyclone and the first popular weather maps), statistics (regression and correlation), psychology (synaesthesia), biology (the nature and mechanism of heredity), and criminology (fingerprints). Much of this was influenced by his penchant for counting or measuring. Galton prepared the first weather map published in The Times (1 April 1875, showing the weather from the previous day, 31 March), now a standard feature in newspapers worldwide.
He became very active in the British Association for the Advancement of Science, presenting many papers on a wide variety of topics at its meetings from 1858 to 1899. He was the general secretary from 1863 to 1867, president of the Geographical section in 1867 and 1872, and president of the Anthropological Section in 1877 and 1885. He was active on the council of the Royal Geographical Society for over forty years, in various committees of the Royal Society, and on the Meteorological Council.
James McKeen Cattell, a student of Wilhelm Wundt who had been reading Galton's articles, decided he wanted to study under him. He eventually built a professional relationship with Galton, measuring subjects and working together on research.
In 1888, Galton established a lab in the science galleries of the South Kensington Museum. In Galton's lab, participants could be measured to gain knowledge of their strengths and weaknesses. Galton also used these data for his own research. He would typically charge people a small fee for his services.
During this time, Galton wrote a controversial letter to the Times titled 'Africa for the Chinese', where he argued that the Chinese, as a race capable of high civilisation and (in his opinion) only temporarily stunted by the recent failures of Chinese dynasties, should be encouraged to immigrate to Africa and displace the supposedly inferior aboriginal blacks.
The publication by his cousin Charles Darwin of The Origin of Species in 1859 was an event that changed Galton's life. He came to be gripped by the work, especially the first chapter on "Variation under Domestication," concerning the breeding of domestic animals.
Galton devoted much of the rest of his life to exploring variation in human populations and its implications, at which Darwin had only hinted. In so doing, he established a research program which embraced multiple aspects of human variation, from mental characteristics to height; from facial images to fingerprint patterns. This required inventing novel measures of traits, devising large-scale collection of data using those measures, and in the end, the discovery of new statistical techniques for describing and understanding the data.
Galton was interested at first in the question of whether human ability was hereditary, and proposed to count the number of the relatives of various degrees of eminent men. If the qualities were hereditary, he reasoned, there should be more eminent men among the relatives than among the general population. To test this, he invented the methods of historiometry. Galton obtained extensive data from a broad range of biographical sources which he tabulated and compared in various ways. This pioneering work was described in detail in his book Hereditary Genius in 1869. Here he showed, among other things, that the numbers of eminent relatives dropped off when going from the first degree to the second degree relatives, and from the second degree to the third. He took this as evidence of the inheritance of abilities.
Galton recognised the limitations of his methods in these two works, and believed the question could be better studied by comparisons of twins. His method envisaged testing to see if twins who were similar at birth diverged in dissimilar environments, and whether twins dissimilar at birth converged when reared in similar environments. He again used the method of questionnaires to gather various sorts of data, which were tabulated and described in a paper "The history of twins" in 1875. In so doing he anticipated the modern field of behaviour genetics, which relies heavily on twin studies. He concluded that the evidence favoured nature rather than nurture. He also proposed adoption studies, including trans-racial adoption studies, to separate the effects of heredity and environment.
Galton recognised that cultural circumstances influenced the capability of a civilisation's citizens, and their reproductive success. In Hereditary Genius, he envisaged a situation conducive to resilient and enduring civilisation as follows:
The best form of civilization in respect to the improvement of the race, would be one in which society was not costly; where incomes were chiefly derived from professional sources, and not much through inheritance; where every lad had a chance of showing his abilities, and, if highly gifted, was enabled to achieve a first-class education and entrance into professional life, by the liberal help of the exhibitions and scholarships which he had gained in his early youth; where marriage was held in as high honour as in ancient Jewish times; where the pride of race was encouraged (of course I do not refer to the nonsensical sentiment of the present day, that goes under that name); where the weak could find a welcome and a refuge in celibate monasteries or sisterhoods, and lastly, where the better sort of emigrants and refugees from other lands were invited and welcomed, and their descendants naturalised.
Galton invented the term "eugenics" in 1883 and set down many of his observations and conclusions in a book, Inquiries into Human Faculty and Its Development He believed that a scheme of 'marks' for family merit should be defined, and early marriage between families of high rank be encouraged by provision of monetary incentives. He pointed out some of the tendencies in British society, such as the late marriages of eminent people, and the paucity of their children, which he thought were dysgenic. He advocated encouraging eugenic marriages by supplying able couples with incentives to have children. On 29 October 1901, Galton chose to address eugenic issues when he delivered the second Huxley lecture at the Royal Anthropological Institute The Eugenics Review, the journal of the Eugenics Education Society, commenced publication in 1909. Galton, the Honorary President of the society, wrote the foreword for the first volume. The First International Congress of Eugenics was held in July 1912. Winston Churchill and Carls Elliot were among the attendees.
Galton conducted wide-ranging inquiries into heredity which led him to challenge Charles Darwin's hypothetical theory of pangenesis. Darwin had proposed as part of this hypothesis that certain particles, which he called "gemmules" moved throughout the body and were also responsible for the inheritance of acquired characteristics. Galton, in consultation with Darwin, set out to see if they were transported in the blood. In a long series of experiments in 1869 to 1871, he transfused the blood between dissimilar breeds of rabbits, and examined the features of their offspring. He found no evidence of characters transmitted in the transfused blood.
Darwin challenged the validity of Galton's experiment, giving his reasons in an article published in "Nature" where he wrote:
Now, in the chapter on Pangenesis in my Variation of Animals and Plants under Domestication I have not said one word about the blood, or about any fluid proper to any circulating system. It is, indeed, obvious that the presence of gemmules in the blood can form no necessary part of my hypothesis; for I refer in illustration of it to the lowest animals, such as the Protozoa, which do not possess blood or any vessels; and I refer to plants in which the fluid, when present in the vessels, cannot be considered as true blood." He goes on to admit: "Nevertheless, when I first heard of Mr. Galton's experiments, I did not sufficiently reflect on the subject, and saw not the difficulty of believing in the presence of gemmules in the blood.
Galton explicitly rejected the idea of the inheritance of acquired characteristics (Lamarckism), and was an early proponent of "hard heredity" through selection alone. He came close to rediscovering Mendel's particulate theory of inheritance, but was prevented from making the final breakthrough in this regard because of his focus on continuous, rather than discrete, traits (now known as polygenic traits). He went on to found the biometric approach to the study of heredity, distinguished by its use of statistical techniques to study continuous traits and population-scale aspects of heredity.
This approach was later taken up enthusiastically by Karl Pearson and W.F.R. Weldon; together, they founded the highly influential journal Biometrika in 1901. (R.A. Fisher would later show how the biometrical approach could be reconciled with the Mendelian approach. The statistical techniques that Galton invented (correlation, regression) and phenomena he established (regression to the mean) formed the basis of the biometric approach and are now essential tools in all the social sciences.
The method used in Hereditary Genius has been described as the first example of historiometry. To bolster these results, and to attempt to make a distinction between 'nature' and 'nurture' (he was the first to apply this phrase to the topic), he devised a questionnaire that he sent out to 190 Fellows of the Royal Society. He tabulated characteristics of their families, such as birth order and the occupation and race of their parents. He attempted to discover whether their interest in science was 'innate' or due to the encouragements of others. The studies were published as a book, English men of science: their nature and nurture, in 1874. In the end, it promoted the nature versus nurture question, though it did not settle it, and provided some fascinating data on the sociology of scientists of the time.
Sir Francis was the first scientist to recognise what is now known as the Lexical hypothesis. This is the idea that the most salient and socially relevant personality differences in people's lives will eventually become encoded into language. The hypothesis further suggests that by sampling language, it is possible to derive a comprehensive taxonomy of human personality traits.
Galton's inquiries into the mind involved detailed recording of people's subjective accounts of whether and how their minds dealt with phenomena such as mental imagery. To better elicit this information, he pioneered the use of the questionnaire. In one study, he asked his fellow members of the Royal Society of London to describe mental images that they experienced. In another, he collected in-depth surveys from eminent scientists for a work examining the effects of nature and nurture on the propensity toward scientific thinking.
Core to any statistical analysis is the concept that measurements vary: they have both a central tendency, or mean, and a spread around this central value, or variance. In the late 1860s, Galton conceived of a measure to quantify normal variation: the standard deviation.
Galton was a keen observer. In 1906, visiting a livestock fair, he stumbled upon an intriguing contest. An ox was on display, and the villagers were invited to guess the animal's weight after it was slaughtered and dressed. Nearly 800 participated, but not one person hit the exact mark: 1,198 pounds. Galton stated that "the middlemost estimate expresses the vox populi, every other estimate being condemned as too low or too high by a majority of the voters", and calculated this value (in modern terminology, the median) as 1,207 pounds. To his surprise, this was within 0.8% of the weight measured by the judges. Soon afterwards, he acknowledged that the mean of the guesses, at 1,197 pounds, was even more accurate.
The same year, Galton suggested in a letter to the journal Nature a better method of cutting a round cake by avoiding making radial incisions.
Studying variation, Galton invented the quincunx, a pachinko-like device, also known as the bean machine, as a tool for demonstrating the law of error and the normal distribution.
He also discovered the properties of the bivariate normal distribution and its relationship to regression analysis.
In 1846, the French physicist Auguste Bravais (1811–1863) first developed what would become the correlation coefficient. After examining forearm and height measurements, Galton independently rediscovered the concept of correlation in 1888 and demonstrated its application in the study of heredity, anthropology, and psychology. Galton's later statistical study of the probability of extinction of surnames led to the concept of Galton–Watson stochastic processes. This is now a core of modern statistics and regression.
Galton invented the use of the regression line and was the first to describe and explain the common phenomenon of regression toward the mean, which he first observed in his experiments on the size of the seeds of successive generations of sweet peas. He is responsible for the choice of r (for reversion or regression) to represent the correlation coefficient. In the 1870s and 1880s he was a pioneer in the use of normal distribution to fit histograms of actual tabulated data.
Galton went beyond measurement and summary to attempt to explain the phenomena he observed. Among such developments, he proposed an early theory of ranges of sound and hearing, and collected large quantities of anthropometric data from the public through his popular and long-running Anthropometric Laboratory, which he established in 1884, and where he studied over 9,000 people. It was not until 1985 that these data were analysed in their entirety.
Galton's study of human abilities ultimately led to the foundation of differential psychology and the formulation of the first mental tests. He was interested in measuring humans in every way possible. This included measuring their ability to make sensory discrimination which he assumed was linked to intellectual prowess. Galton suggested that individual differences in general ability are reﬂected in performance on relatively simple sensory capacities and in speed of reaction to a stimulus, variables that could be objectively measured by tests of sensory discrimination and reaction time. He also measured how quickly people reacted which he later linked to internal wiring which ultimately limited intelligence ability. Throughout his research Galton assumed that people who reacted faster were more intelligent than others.
Galton also devised a technique called "composite portraiture" (produced by superimposing multiple photographic portraits of individuals' faces registered on their eyes) to create an average face. In the 1990s, a hundred years after his discovery, much psychological research has examined the attractiveness of these faces, an aspect that Galton had remarked on in his original lecture. Others, including Sigmund Freud in his work on dreams, picked up Galton's suggestion that these composites might represent a useful metaphor for an Ideal type or a concept of a "natural kind" such as Jewish men, criminals, patients with tuberculosis, etc.—onto the same photographic plate, thereby yielding a blended whole, or "composite", that he hoped could generalise the facial appearance of his subject into an "average" or "central type".
This work began in the 1880s while the Jewish scholar Joseph Jacobs studied anthropology and statistics with Francis Galton. Jacobs asked Galton to create a composite photograph of a Jewish type. One of Jacobs' first publications that used Galton's composite imagery was "The Jewish Type, and Galton's Composite Photographs," Photographic News.
Galton hoped his technique would aid medical diagnosis, and even criminology through the identification of typical criminal faces. However, his technique did not prove useful and fell into disuse, although after much work on it including by photographers Lewis Hine and John L. Lovell and Arthur Batut.
In a Royal Institution paper in 1888 and three books, Galton estimated the probability of two persons having the same fingerprint and studied the heritability and racial differences in fingerprints. He wrote about the technique (inadvertently sparking a controversy between Herschel and Faulds that was to last until 1917), identifying common pattern in fingerprints and devising a classification system that survives to this day.
The method of identifying criminals by their fingerprints had been introduced in the 1860s by Sir William James Herschel in India, and their potential use in forensic work was first proposed by Dr Henry Faulds in 1880, but Galton was the first to place the study on a scientific footing, which assisted its acceptance by the courts. Galton pointed out that there were specific types of fingerprint patterns. He described and classified them into eight broad categories: 1: plain arch, 2: tented arch, 3: simple loop, 4: central pocket loop, 5: double loop, 6: lateral pocket loop, 7: plain whorl, and 8: accidental.
In an effort to reach a wider audience, Galton worked on a novel entitled Kantsaywhere from May until December 1910. The novel described a utopia organised by a eugenic religion, designed to breed fitter and smarter humans. His unpublished notebooks show that this was an expansion of material he had been composing since at least 1901. He offered it to Methuen for publication, but they showed little enthusiasm. Galton wrote to his niece that it should be either "smothered or superseded". His niece appears to have burnt most of the novel, offended by the love scenes, but large fragments survived.