Wednesday 16 February 2022

Sir Francis Galton (16 Feb 1822 - 17 Jan 1911)

Today marks the 200th anniversary of the birth of Sir Francis Galton. He lived from 16 February 1822 to 17 January 1911.

Sir Francis Galton
Image from Wikipedia

He was a cousin of Charles Darwin, and like many educated Victorian gentlemen, dabbled in many different areas of learning. Among Galton's interests were anthropology, genetics including eugenics (the idea of improving the human race by genetic selection), exploration, geography, invention, meteorology and statistics. He was knighted in 1909. He actually invented the term eugenics, and is considered the first person to use the expression "nature versus nurture".

Galton's wide range of interests led him to publication of over 340 papers and books during his lifetime. But it is his mathematical contributions, particularly in the field of statistics, that we are interested in. He created the statistical concept of correlation and widely promoted regression towards 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 used in his genealogical studies and his analyses of the behaviour of people, anthropometrics.

So Galton's contributions were considerable and, in some cases, revolutionary. But some of his ideas were also highly controversial, even for the time in which he lived. He attempted to draw up a 'Beauty Map' of the British Isles, and for this he classified passing girls into three categories: attractive, indifferent and repulsive, surreptitiously making pin-pricks in paper stored in his pocket as a means to build a database.

Eugenics itself is today considered a brutal concept. The practices involved in favouring certain families deemed genetically superior was practised by some governments during the early years of the 20th century, resulting in deprivation and a loss of human rights for millions.

Galton's book, Hereditary Genius (1869), was one of the first scientific attempts to study genius and greatness. It demonstrates some of the statistical techniques that Galton would develop through his life, but it is steeped in language that is far from acceptable in today's scientific literature, such as "idiots" and "imbeciles".

He founded psychometrics (the science of measuring mental faculties) and devised a method for classifying fingerprints that was later used in forensic science. He also conducted research on the power of prayer, concluding it had none, because of the fact that those prayed for lived no longer than those not prayed for.

Finally Galton was a pioneer of scientific meteorology. He devised an early weather map, proposed a theory for the formation of anticyclones, and was the first to establish a complete record of short-term climatic phenomena on a European scale.

Francis Galton was truly a great British eccentric, whose ideas were often controversial, but whose contributions to statistics and science in general cannot be ignored.

Monday 31 January 2022

Happy 50th Birthday to the HP35

Finally! I've got my hands on an HP 35 calcula...
The HP-35 scientific calculator
Image via Wikipedia

1st February 1972 marked a birth that would revolutionise mathematics education across the world. This was not, this time, the birth of a great mathematician, but of a machine. The first scientific hand-held calculator (HP-35) was introduced to the US market, and later to the UK. Costing $395, it was made by Hewlett-Packard and its name came from the fact that it had 35 keys.

The HP-35 measured 79 x 147 x 34 mm, pretty chunky by today’s standards, but ultra-sleek in its day, when a computer still filled a small room. It ran on rechargeable batteries, and its electronics used several integrated circuits. ‘Scientific’ meant the calculator was able to perform logarithmic and trigonometric functions with one keystroke. It featured a red LED display which could give scientific notation up to 10 digits, with 2 digits for an exponent (power of 10).

The price was reduced several times, eventually to $195 in the US. But this was, of course, still too high for the HP-35 to become a mainstream part of classroom teaching. Production of the HP-35 was stopped in Feb 1975, 3 years after its launch. 300,000 units had been sold.

The numbers and functions for calculations were entered in "Reverse Polish Notation". This would seem very strange to today’s maths students, since the operator always appears last: a calculation such as 3+5 was performed by typing “3 5 +”. It avoided the need for parentheses or an "=" key.

Further models from HP followed. The introduction of the HP-35, its descendants and similar scientific calculators by Texas Instruments soon brought about the demise of the slide rule in the classroom.

The appearance of the calculator gave rise to the “should we, shouldn’t we?” debate in the media and among educators, with some feeling strongly that the introduction of a calculating device would bring about a decline in students’ own calculating abilities. These arguments had little real relevance in the early days, since the cost, fragility, and short battery life of these early machines meant the calculator had limited use in the classroom, and was certainly not available to every pupil.

By the early 1980s, those deterrents began to decline. Solar-powered scientific calculators began to appear, with hard cases, costing around £20. The UK exam boards bowed to the inevitable and made them a standard piece of equipment in O-Level and A-Level mathematics. The calculator was here to stay.

Later, the first hand-held calculators appeared that could graph functions. Like their simpler counterparts, these calculators were too expensive to be widely adopted when they first appeared, but today many schools encourage their use, although they are still not all tolerated within examinations.

Nowadays, the line between a calculator and a handheld computer is very blurred. Some calculators such as the TI-89, the Voyage 200 and HP-49G are able to differentiate and integrate functions, solve differential equations and run word processing software. Other handheld devices can, of course, connect to the Internet. Whether such devices will ever be used in our exams, only time will tell.

An emulation of the HP-35 is available for the Apple iPad.