#### Humble beginnings

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.

^{[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.

^{*}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.

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.

^{[2]}

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

^{[4]}.

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.

^{[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:-

^{[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.

^{[8]}, is the following question from the Queen :-

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.

^{[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

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]}

#### Much later, Bidder recalls his formative years

*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.

#### notes

*The Monthly Magazine, Volume 37, 1814.*available from Google as a free ebook here (Google account sign-on required). [return]

*What number multiplied by itself will produce 36,372,951?*- is given by the Phreno-mnemotechic Dictionary as eight seconds, not eighty.

*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.

*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:

*locus classicus*on the topic, the most detailed and straightforward account in existence, and by a professional man of standing.

#### bibliography

*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]

*The Calculating Boy*by E.F. Clark(Bidder's great-great-grandson) and J.J. Linfoot, KSL Publications, 1983.

*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.

*George Parker Bidder: The Calculating Prodigy*by Joyce Linfoot, The Institute of Mathematics and its Applications March/April/May,1987, Volume 23, p68-71.

*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.