Devon Perspectives

George Parker Bidder

The phenomenal mental calculation prodigy from Moretonhampstead

Humble beginnings

George Parker Bidder age 9

George was Born in Moretonhampstead on June 14th, 1806, the third son of stonemason William Bidder by his second wife Elizabeth Parker. Despite receiving little formal schooling it wasn't long before his family realized that George had a remarkable facility for memorizing and manipulating large numbers in his head; William capitalized on his son's extraordinary gift by presenting George as the Calculating Prodigy in local fairs. As the boy's reputation spread he was exhibited across the country, often to gatherings of distinguished establishment figures including Queen Charlotte, wife of George III, who witnessed his powers at first hand when George was only eight. His composure and charming demeanour endeared him to audiences; the rapidity and accuracy of his answers astonished them.

George's prodigious talent gains a wider audience

Anecdotal evidence suggests that Bidder had honed his mental calculating skill to such a level of speed and accuracy by age seven that it began to be noticed outside the family.

The incident which first brought his talents into notice was a dispute between two neighbours about the weight and price of a pig which one was selling. George Bidder, then about seven years old, who was playing near, suddenly ceased his game, and going up to them, said, " You are both wrong," naming at the same time the correct price, to the great surprise of the disputants[4].

Having heard that the seven year old George had a peculiar talent for combining numbers, the local Baptist minister Jacob Isaac decided to question the boy in order to determine for himself the measure of his ability, and hopefully to establish his method. The result of this examination was published as a letter to The Monthly Magazine dated January 19th, 1814[note1]. This letter is of particular interest because it illustrates that aside from his prodigious talent in mental arithmetic, George was, as Isaac put it, as ignorant as uneducated children of his age commonly are.

Jacob quickly established that the boy was unable to read from his school copy of the New Testament, nor did he recognize the numbers of the verses from 1 to 10. Isaac then gave him a selection of easy arithmetic tasks which were answered correctly without delay, before setting some slightly more challenging calculations.

I then asked him how many days are in two years? But here he was at a stand - he did not know what a year is, or how many hours are in a day; but having the terms explained, he soon made out the hours in a week, in a month, in 12 months. When asked how many inches are in a square foot, he soon signified he knew neither of the terms, nor how many inches a foot contains; but with the aid of explanation he soon made out the number 1728* and when desired to multiply this by 12, he complained the number was too large; but having time, about two minutes, he made out the number 20,736: and by close attention and examination, I discovered that, in the first place he multiplied the thousands, hundreds, tens, and units in rotation, and added them together, to find the above amount.
* Isaac evidently gave the wrong explanation of a square foot, this being the number in a cubic foot.
The letter continues with these misguided observations, the first in reference to George's method of multiplication, the second assuming the unfounded correlation between prowess in mental arithmetic and mathematical ability.
I was glad to make this discovery, as once we find he has a method of his own, however wrong, we hope that he may be taught the true one, without injuring his retentive faculty.
His physiognomy is not bad, his features pretty good, and his symmetry without fault. Were he under the guidance of a proper master for a few years, it should seem to me that at a very early age he might be made a good mathematician.

While still in his seventh year George was able to complete complex arithmetic tasks entirely in his head with such rapidity and exactitude that his reputation soon spread far beyond Moretonhampstead. A later edition of the Philosophical Magazine gave this instance of George's burgeoning arithmetical talent at that early age as the first example to attract wider attention.

George Parker Bidder as a child
George, whose time was employed as country children's are, went to a three-halfpence a-week school till seven years old, when the first proof he gave of his extraordinary abilities was in reckoning the nails in a horse's four shoes, and by degrees doubling them from a farthing 32 times. [2]
a poster publizing George Bidder's appearance at Oxford in 1817

After demonstrating the boy's ability at local events, it wasn't long before his father was promoting him for financial reward beyond Devon.

His reputation soon increased so much that he was taken by his father to all parts of the country to exhibit his extraordinary gift. In April 1815, he was presented to Her Majesty Queen Charlotte by the Bishop of Salisbury, and on that occasion solved various intricate questions with great rapidity and precision[4].

Pamphlet giving Examples of Mental Calculations by G. Bidder

By 1815 newspaper reports of George's appearances began to appear, and pamphlets were published listing some of the arithmetic posers set, usually giving the time it took him to answer them. The questions often took an elaborate form but this didn't faze Bidder who immediately pared them down to their essential arithmetic elements, and he had no difficulty handling conversions between the quirky imperial units used to measure weights and distances at this time.





Here is a representative sample of questions from a popular contemporary pamphlet[8]
If a coach-wheel is 5 feet 10 inches in circumference; how many times would it revolve in running eight hundred million miles? Answer, in 50 seconds -- 724,114,285,704 times, and 20 inches remaining.
If two ships of 83 guns each exchange at sea, and they continue in action five hours, forty-three minutes, seven seconds, each firing a broadside every 2½ minutes; how many shot will they each fire? Answer, in 20 seconds -- 11,391 each.
Suppose a snake to crawl from Gloucester to Land's End, Cornwall, a distance of 239 miles, 6 furlongs, 38 poles, 7 feet, in 1,010 days; at what rate does he travel each day? Answer, in 1 minute -- 417 yards, 2 feet, 11 inches, 2 barley-corns.
What is the interest of £4,444 for 4,444 days, at 4½ per cent. per annum? Answer, in 2 minutes -- £2,434 16s. 5¼d.
Multiply 72,468 by 87,468. Answer, in 1½ minute -- 6,338,631,024.
What is the square root of 119,550,669,121? Answer, in half a minute -- 345,761.
How many pounds weight are there in 232 hogheads of sugar, each weighing 12cwt 1qr 22lb? Answer, also in half a minute -- 323,408lb.

The Morning Post of April 3rd, 1815 carried this report on Bidder's encounter with Queen Charlotte at Windsor:-

On Thursday, Master George Bidder, the wonderful calculating boy, who is only eight years of age, was introduced to the Queen and Princesses by the Bishop of Salisbury, when he gave specimens and proofs of his surprising powers.
The rapidity and precision of his answers to the questions of considerable intricacy put to him by the Queen and Princesses, and others of the Royal Party, and also Messrs. Knights, who were present, are scarcely to be credited; the following were among them:-
What number multiplied by itself will produce 36,372,951? Answer 6031; he answered this in eighty seconds. The next question was, How many minutes in forty-nine years, answer 25,754,400; answered in two seconds[note3]. Multiply 4698 by 4698, answer 22,071,204. From 3,287,625 subtract 2,348,756, answer 943,869. Multiple 5 eight times by itself, answer 1,793,125.
Missing from this report, but included in [8], is the following question from the Queen :-
From the Land's End, Cornwall, to Farret's Head, in Scotland, is found by measurement to be 838 miles; how long would a snail be creeping that distance, at the rate of 8 feet per day? Answer -- 553,080 days.
This question for Bidder reported in the Royal Cornwall Gazette, Falmouth Packet & Plymouth Journal of October 7th, 1815 referenced a momentous event from June of the same year, but even for moon dwellers the last echoes of gunfire must have faded long since. Did young George actually visit Margate, or was this piece a spoof? Given that the stated answer is correct (by my reckoning), I'm inclined to accept it as genuine despite failing to find any reference to Margate among the towns George was said to have exhibited in.
George Bidder, the celebrated calculating boy of Moreton Hampstead, is now at Margate, astounding the salt-water drinkers at that fashionable bathing-place. One of the Stock Exchange brokers asked the following question:- Suppose the moon be distant from the earth 123,256 miles, and sound to travel at the rate of four miles in a minute, how long would it be before the inhabitants of the moon could hear the battle of Waterloo? Answered by the the boy in two minutes:- 21 days, 9 hours and 34 minutes!

With most of George's time spent touring the country, inevitably his general education was being neglected. Fortunately the astronomer John Herschel and others at the University of Cambridge took an interest in the boy and arranged for him to attend Wilson's Grammar School, Camberwell all expenses met. This wasn't to last, and within a year his father took him back on the road.

This travelling about the country, for the purpose of exhibiting his son's powers proved so agreeable and profitable to his father, that the boy's education was entirely neglected. Fortunately, however, amongst those who witnessed his public performances were some gentlemen who thought they discerned qualities worthy of a better career than that of a mere arithmetical prodigy. The Rev. Thomas Jephson[note2], Fellow and Tutor of St. John's College, Cambridge, and the late Sir John Herschel (then Mr. Herschel) visited Moreton in the autumn of 1817, to see the "Calculating Boy" and they were so much impressed by his talent and general intelligence that before the vacation was over Mr. Jephson and his Cambridge friends agreed to defray the expenses of his education. His mother was delighted with such a prospect for her boy: she was a good woman, possessed of a great deal of character, and capable of looking beyond the temporary interruption of gain for her son's ultimate advantage. All who knew her, spoke of her as a very pleasing person, and her son George held her memory in most affectionate reverence. The father's consent having been, with much difficulty, obtained, he was placed with the Rev. W. Jephson, master of the Grammar School at Camberwell. There he remained for about a twelvemonth, when his father insisted on removing him, for the purpose of resuming the exhibition of his talents. The boy was accordingly taken from Camberwell, and set forth again, with a sad heart, on further journeys[4].

Bidder's education resumes in Edinburgh

George Parker Bidder age 13

During a visit to Edinburgh for an exhibition around the time of Bidder's thirteenth birthday he came to the notice of a benevolent figure of the Scottish establishment who was to become his friend and mentor: Sir Henry Jardine, the King's Remembrancer for Scotland, raised a public subscription to put the boy's education on a firm footing, and George was assigned a personal tutor prior to his enrolment at the University of Edinburgh. It is there that he met Robert Stephenson (son of locomotive builder George) who was to become his life-long friend and civil engineering partner. Mindful of what had transpired at Camberwell, Sir Henry compensated William Bidder for the loss of income from George's public exhibitions. Bidder remained in Edinburgh until he was 18 when Jardine found him a trainee position with the Ordnance Survey. From there his career as a civil engineer progressed rapidly until he was rubbing shoulders with titans of the Industrial Revolution including Isambard Kingdom Brunel. He made good use of his exceptional powers of mental arithmetic throughout his working life.[note4]

Bidder returned to Devon in his fifties, buying a property in Dartmouth in 1860 giving him the opportunity to pursue his love of sailing.

Much later, Bidder recalls his formative years

George Bidder delivering his 1856 lecture On Mental Calculation
In contrast with many child prodigies, Bidder retained his extraordinary mental arithmetic prowess throughout his life and put it to good use in a distinguished career as a civil engineer. Bidder was also unusual in providing in a formal setting a detailed description of how he performed rapid mental computations: I have reproduced in full his remarkable lecture entitled On Mental Calculation, delivered to the Institute of Civil Engineers[1] during 1856 when Bidder was 50[note5]. In this extract covering his early years he explains how he taught himself to carry out multiplications as a purely mental exercise without knowing the meaning of the word multiply, or how numbers were represented symbolically.
As nearly as I can recollect, it was at about the age of six years, that I was first introduced to the science of figures. My Father was a working mason, and my elder brother John pursued the same calling. My first and only instructor in figures was that elder brother. The instruction he gave me was commenced by teaching me to count up to 10. Having accomplished this, he induced me to go on to 100, and there he stopped.
Having acquired a certain knowledge of numbers, by counting up to 100, I amused myself by repeating the process, and found, that by stopping at 10, and repeating that every time, I counted up to 100 much quicker than by going straight through the series. I counted up to 10, then to 10 again = 20, 3 times 10 = 30, 4 times 10 = 40, and so on. This may appear to you a simple process, but I attach the utmost importance to it, because it made me perfectly familiar with numbers up to 100; they became as it were my friends, and I knew all their relations and acquaintances.
You must bear in mind, that at this time I did not know one written, or printed figure from another, and my knowledge of language was so restricted, that I did not know there was such a word as "multiply;" but having acquired the power of counting up to 100 by 10 and by 5, I set about, in my own way, to acquire the multiplication table. This I arrived at by getting peas, or marbles, and at last I obtained a treasure in a small bag of shot: I used to arrange them into squares, of 8 on each side, and then on counting them throughout. I found that the whole number amounted to 64: by that process I satisfied my mind, not only as a matter of memory but as a matter of conviction, that 8 times 8 were 64; and that fact once established has remained there undisturbed until this day, and I dare say it will remain so to the end of my days. It was in this way that I acquired the whole multiplication table up to 10 times 10; beyond which I never went; it was all that I required.
At the period referred to, there resided, in a house opposite to my Father's, an aged Blacksmith, a kind old man who, not having any children, had taken a nephew as his apprentice. With this old gentleman I struck up an early acquaintance and was allowed the privilege of running about his workshop. As my strength increased, I was raised to the dignity of being permitted to blow the bellows for him, and on winter evenings I was allowed to perch myself on his forge hearth, listening to his stories. On one of these occasions, somebody by chance mentioned a sum, whether it was 9 times 9 or what it was I do not now recollect; but whatever it was, I gave the answer correctly. This occasioned some little astonishment; they then asked me other questions, which I answered with equal facility.
They then went on to ask me up to two places of figures: 13 times 17 for instance; that was rather beyond me, at the time, but I had been accustomed to reason on figures, and I said 13 times 17 means 10 times 10 plus 10 times 7, plus 10 times 3 and 3 times 7. I said 10 times 10 are 100, 10 times 7 are 70, 10 times 3 are 30, and 3 times 7 are 21; which added together give the result, 221; of course I did not do it then as rapidly as afterwards, but I gave the answer correctly, as was verified by the old gentleman's nephew, who began chalking it up to see if I was right. As a natural consequence, this increased my fame still more, and what was better, it eventually caused half-pence to flow into my pocket; which I need not say, had the effect of attaching me still more to the science of arithmetic, and thus by degrees I got on, until the multiple arrived at thousands.

notes

1.
Much of Isaac's letter concerning Bidder and a critique of it are given in [5]. For the full text of the letter, see page 104 of the The Monthly Magazine, Volume 37, 1814. available from Google as a free ebook here (Google account sign-on required). [return]
2.
This is the same Thomas Jephson who was the defendant in a celebrated homosexual offences trial in 1823 in which the jury found in his favour, giving him the benefit of their doubt following the direction of the judge; there is no suggestion of impropriety in Jephson's dealings with Bidder. [return]
3.
When asked to give the number of minutes in 49 years, Bidder's recorded response time of two seconds seems remarkably quick - I have seen 2 seconds quoted for this answer elsewhere (in the Phreno-mnemotechnic Dictionary, for example†), so it wasn't a transcription error in the newspaper report I quoted. The answer he gave - 25,754,400 - is the product of 49x365x24x60. The Gregorian Calendar, in which the leap year was introduced, has been in continuous use in England since 1752, so George overlooked the extra day in each leap year. In mitigation, maybe no-one had told the 8-year-old boy about leap years. [return]
† there is a discrepancy between this work and the newspaper report insofar as the time for Bidder's answer to the previous question - What number multiplied by itself will produce 36,372,951? - is given by the Phreno-mnemotechic Dictionary as eight seconds, not eighty.
4.
Bidder's considerable accomplishments as a civil engineer are well covered in the biographies and obituaries listed in the bibliography section of this article; I have chosen not to include them as my intention was to concentrate on his childhood years. [return]
5.
The gift of rapid mental calculation rarely goes hand in glove with mathematical distinction; indeed, Bidder referred to his own mathematical limitations in his On Mental Calculation lecture, assuring his audience that 'in no respect have I ever been distinguished for mathematical pursuits'. Notwithstanding this humble self-deprecation, it should be mentioned that he was awarded the 1822 prize for the study of higher mathematics while enrolled at the University of Edinburgh.
One notable exception was the distinguished mathematician Professor Alexander Aitken who was also a renowned mental calculator. In a lecture titled The Art Of Mental Calculation; with Demonstrations given to the Royal Society of Engineers in 1954 in which he describes his own mental processes he paid homage to Bidder referring to his 1856 presentation as:
..the locus classicus on the topic, the most detailed and straightforward account in existence, and by a professional man of standing.

bibliography

1.
On Mental Calculation by G.P. Bidder. Minutes of Proceedings of the Institute of Civil Engineering Volume XV p251-280, London, 1856. The full proceedings are available from Google as a free ebook here (Google account sign-on required). [return]
2.
3.
GEORGE PARKER BIDDER, 1806-1878. This concise but well-written biography of Bidder is distilled from The Calculating Boy by E.F. Clark(Bidder's great-great-grandson) and J.J. Linfoot, KSL Publications, 1983.
4.
OBITUARY of GEORGE PARKER BIDDER (1806-1878) , Minutes of Proceedings of the Institute of Civil Engineers, Volume 57, Part 3, 1879. (Free access as a pdf file from the ICE Virtual Library).
5.
Section 46, BIDDER, George Parker in Prince's "Worthies Of Devon" and the "Dictionary Of National Biography" Part II by W. Pengelly, Report and Transactions of the Devonshire Association, Vol. XVIII, Plymouth, 1886.
6.
7.
George Parker Bidder: The Calculating Prodigy by Joyce Linfoot, The Institute of Mathematics and its Applications March/April/May,1987, Volume 23, p68-71.
8.
The full title of the 1820 pamphlet is: A Short Account of George Bidder, the Celebrated Mental Calculator; With a Variety of the Most Difficult Questions Proposed to him at the principal Towns in the Kingdom and his Surprising Rapid Answers!. A selection of of the questions are given here.

acknowledgements

The photo of the portrait of George Bidder as a child reading at a desk (painter unknown) is reproduced from the ICE Image Gallery.
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