Bidder, George Parker
President of the DA 1869-70.
Published in DA Transactions, 1879.
George Parker Bidder was a native of Moretonhampstead, in this county, and was brought into public notice at a very early age through the wonderful power of mental calculation which he developed without having received any instruction. He was born in very humble circumstances, his father being a stonemason; and at the age of seven, when his talent first became apparent, he did not know the meaning of the word “multiplication”, nor could he read the common numerical symbols.
An elder brother had taught him to count up to one hundred, and he had some treasures, such as marbles, shot, &c., which it was his favourite amusement to arrange in rows of different numbers, such as nine rows of nine, seven of five; then counting them, he fixed in a singularly retentive memory the results of these combinations, and in this way, numbers being his playthings, he acquired a marvellous facility in realizing and dealing with them, and was unconsciously led on to the most complicated arithmetical processes. He was a great favourite with the kindly old village blacksmith, in whose workshop the neighbours would gather to hear little George solve the most difficult questions they could devise, as he sat perched by the forge fire.
His father now took him all over the country to exhibit his wonderful powers. In 1815 he was presented to Queen Charlotte by the Bishop of Salisbury, and on one occasion was brought into competition with Zerub Colburn, when he far surpassed the young American. George Bidder is said to have been a singularly bright and prepossessing boy, and when visiting Edinburgh he attracted the notice of Sir Henry Jardine, who long held the office of King’s Remembrancer for Scotland, and who was so much struck by the lad’s talents, and altogether taken with him, that, with the aid of some friends, he undertook to have him properly educated. In 1819, when in his fourteenth year, George was accordingly placed at the University of Edinburgh, where he remained till the beginning of 1824, fully realizing by his industry and success the hopes formed by his friends.
When first asked to extract the square root, he did not know what the term meant; but when this was explained by saying, as 400=20 x 20 that 20 is the square root of 400; and similarly, as 8=2 x 2 x 2 that 8 is the cube of 2, and 2 the cube root of 8, he at once devised his own system for performing the operation, with a rapidity and accuracy which astonished his questioners. With equal ease he mastered the difficulties of compound interest; but although the original processes by which he arrived at these results are interesting, their details would exceed our limits.
Mr. Bidder never forgot the deep debt of gratitude then incurred, and in after years he connected a grateful tribute to his Alma Mater with the name of his venerable friend and benefactor, by founding a bursary or scholarship of £40 per annum for the aid of poor students at Edinburgh University, to be called “the Jardine Bursary.” On leaving Edinburgh, a post was obtained for him in the Ordnance Survey, where he soon obtained promotion, and assisted in making the trigonometrical survey of his native county.
In April, 1825, he quitted the Ordnance Survey, and was engaged as assistant to Mr. H. R. Palmer, civil engineer, thus entering the profession of which he became a distinguished member. It is worthy of remembrance that George Bidder’s first care when starting in the world was to provide for the education of his two younger brothers, and for that purpose this lad of eighteen stinted and saved, denying himself all but the barest necessaries; and at one time undertaking the duties of an insurance clerk* besides his daily employment, in order to supplement the scanty means which were all he could at first command. In 1833, under Messrs. Walker and Burgess, he superintended the construction of the Brunswick Wharf, Blackwall; and in 1834 he joined the staff of Messrs. George and Robert Stephenson, with whom he was engaged for many years, taking part in the construction of the London and Birmingham, the South Eastern, North Kent, London and Blackwall, Norwich and Yarmouth, Northampton and Peterborough, Trent Valley, North Staffordshire, and many other railways.
* At the Royal Exchange.
The most implicit confidence existed between the two Stephensons and Mr. Bidder. Robert had been his classmate at Edinburgh, and their close and unbroken friendship is well known. Mr. Bidder was the engineer of the Norwegian Trunk Railway; and, with Robert Stephenson, was engineer to the Danish State Railway. He was also for many years consulting engineer to the Delhi, Scinde, and Punjaub lines. He was connected with most of the lines in the Eastern Counties, and was the originator of the system of swing bridges, now so largely used for crossing rivers, &c., where sufficient headway cannot be given, having erected the first of the kind over the river Wensum, near Norwich.
Long experience with railways enabled him to see the value of electric communication between stations. He introduced it on the Blackwall and Yarmouth Railways, and his belief in its capabilities caused him to be one of the principal founders of the original Electric Telegraph Company. He continued to be the engineering adviser of the Company until the Government purchase of the telegraph system in 1870.
In hydraulic engineering his chief works were the construction of Lowestoft Harbour and the magnificent Victoria Docks at North Woolwich. The latter, and indeed the whole of the now populous district adjoining, were the creations of his mind. He was called mad for proposing to construct docks away from London, in what were then marshes and water meadows; but he had formed a just estimate of the capabilities of the position, and not only carried out his ideas by the construction of the docks (a work of great engineering skill), but had such confidence in their future that he persuaded the Dock Company to buy at the time sufficient land to treble their original size, which extension is now being carried out.
Mr. Bidder was consulted by the Chancellor of the Exchequer upon certain very ingenious alterations in taxation, and as one of a committee by the Admiralty with reference to the best types of ships of war. In connection with the latter subject, he took a warm interest in the experiments of his valued friend, the late Mr. W. Froude.
He was also a member of the Government Committee on Explosives, and was Lieut.-Colonel Commandant of the Engineer and Railway Volunteer Staff Corps, a body of considerable importance for the transport of troops and for the aid of the reserve forces of the kingdom. Space will not allow more than this brief mention of his principal engagements; but his advice was frequently in request, and he has been well described as one whose memory nothing escaped, and from whom a valuable opinion could always be obtained.
Mr. Bidder took a distinguished part in the great parliamentary contests which attended the establishment of railways. His wonderful memory, his power of instantaneous calculation, his quick perception and readiness at repartee, caused him to be dreaded by hostile lawyers, one of whom made a fruitless application before a committee in the House of Lords that Mr. Bidder should not be allowed to remain in the room, because “Nature,” he said, “had endowed him with qualities that did not place his opponents on a fair footing.”
A remarkable instance of Mr. Bidder’s wonderful readiness and power of mental numeration occurred in connection with the passing of the Act for the North Staffordshire Railway.
There were several competing lines, and the object of Mr. Bidder’s party was to get rid of as many as possible on Standing Orders. They had challenged the accuracy of the levels of one of the rival lines; but upon the examination before the Committee on Standing Orders, their opponents witnesses were as positive as those for the North Staffordshire, and apparently were likely to command greater credence.
Fortunately Mr. Bidder was present, and when the surveyors of the opposing lines were called to prove the levels at various points, he asked to see their field books, which he looked at apparently in the most cursory manner, and quietly put down without making a note or any observation, and as though he had seen nothing worthy of notice. When the surveyors had completed their proofs, Mr. Bidder, who had carried on in his own mind a calculation of the heights noted in all the books, not merely of the salient points upon which the witnesses had been examined, but also of the intermediate rises and falls noted in the several books, suddenly exclaimed that he would demonstrate to the Committee that the section was wrong. He then went rapidly through a calculation which took all by surprise, and clearly proved that, if the levels were as represented at one point they could not possibly be as represented at another and distant point.
The result was that the errors in the levels were reported, and the Bill was not allowed to proceed.
But if adversaries in public life have shrunk before his outspoken frankness and ready wit, no one who enjoyed his intimacy could fail to appreciate the simplicity of his character, his warmth of heart, and superiority to all narrow feeling; and there are many who can bear witness to the disinterested zeal with which he threw himself into the affairs of others, and who know that in him is lost a faithful counsellor, a steadfast friend. Mr. Bidder joined the Devonshire Association in 1868, and presided at the meeting held at Dartmouth in 1869. Always retaining a warm affection for his native county, it was to Devonshire that he returned when compelled by failing strength to relinquish all professional engagements.
For the last twelve months his life hung on the frailest tenure, though his mental powers remained in full vigour to the last, and he accepted his growing infirmities and the restrictions they imposed with a cheerful serenity which the near approach of death could not disturb.
He was always a great lover of nature, and an earnest enquirer after truth, both in science and religion; nor did he shrink from encountering the difficulties raised by modern scepticism. But his acute intellect and clear judgment found no incompatibility between the revelations of Scripture and those of Science; it was his happiness to recognize in both the hand of a merciful God, and with humble confidence to repose a sure hope for all men on the merits of their Saviour.
He died rather suddenly, from disease of the heart, on September 20th, 1878, aged 72.
From W. Pengelly: “Prince’s Worthies of Devon and the Dictionary of National Biography. Part II” ( Transactions 1886. Vol. 18 pp. 269-369)
46. BIDDER, George Parker. The article in the Dictionary (v. 12–13) on this distinguished Devonian not only confirms the Obituary Notice of him in the Trans. (xi. 48–52), but adds a few facts of interest to which, as well as to a few from other sources, attention may be here directed. The earliest notice of Bidder which I have met with is the following letter, dated “Moretonhampstead, Jan. 19, 1814”, signed “J. Isaac”, and printed in the Mon. Mag. (xxxvii. 104.) “Sir — Having heard that George Parker Bidder, seven years of age” [He was really seven years and seven months old at the date of the letter, as he was born 14 June 1806] “has a peculiar talent for combining numbers, … I sent for him, and … desired him to read a few verses in the New Testament, his class book in a school supported by Richard Holland, Esq., and found he could scarcely do it even by spelling many words; and knew not the numbers of the verses from one to ten” [Mr Isaac then asked him several questions in the first four rules of Arithmetic, the most difficult of which involved the multiplication of 21 by 96, and the division of 200 by 12, to each of which “he replied correctly and readily”. He proceeds to say] “I then asked him how many days are in two years? But here he was at a stand – 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 be multiplied the thousands, hundreds, tens, and units in rotation, and added them together, to find the above amount. … Not one of the terms used above does he understand, without explanation; and on every other topic, he is as ignorant as uneducated children of his age commonly are. … Were he under the guidance of a proper master for a few years it would seem to me that at a very early age, he might be made a good mathematician. …” This interesting letter contains one or two points which invite comment.
(1) Mr. Isaac is not quite correct in his statement of Mr. Bidder’s mode of calculation. It is quite true that in multiplying any such number as 1,728 by any other number he began with the thousands, not with the units; but he did not perform all the successive multiplications first and then make one addition sum of all the products. His method, fully explained in his lecture on “Mental Calculations” delivered 19 February 1856 (See Proc. Inst. C. E. xv. 251–280), was intended to tax his memory as little as possible. He had of course to remember the digits and the order in which they stood in the multiplicand and the multiplier respectively. Thus, in the case mentioned above, 1,728 took in his memory the algebraic form of 1000 + 700 + 20 + 8, and he proceeded with the multiplication thus: 12 times 1000 are 12,000, and 12 times 700 are 8,400 and these products added make 20,400; with this sum he charged his memory for the time, but dismissed for ever the 12,000 and the 8,400; next, 12 times 20 are 240, which with the remembered 20,400 make 20,640; with this he again charged his memory temporarily, but dismissed the 20,400 and the 240, for which he had no further use; finally he said, or rather saw, that 12 times 8 are 96, which with the 20,640 make 20,736, and this he at once pronounced as the answer, forgetting every thing else connected with the work.
(2) Mr. Isaac no doubt believed that every good mathematician was necessarily a good computist, and that a good computist would develop into a good mathematician under suitable conditions. This belief is by no means uncommon, and was held by others as well as by Mr. Isaac with regard to Bidder (see Combe ii. 502); nevertheless, I have no doubt of its being utterly incorrect, and believe there have been more than a few eminent mathematicians who were wretched computists, and splendid computists who never could have been made to understand Euclid or to solve a quadratic equation. Among my own pupils, I remember one who was invariably and deservedly at the head of the class in Mental Arithmetic, but as certainly at the bottom of it in everything else.
It may be doubted whether Mr. Isaac was competent to form an opinion on the question. He obviously believed, and taught little Bidder to believe, that what was really a cubic foot was a square foot; and that a square foot contained 1728, instead of 144, square inches.
The following paragraph in the Dictionary respecting Mr. Bidder’s education is fuller than that on the same subject in the Trans.: “Fortunately for him his powers attracted the attention of several eminent men, by whom he was placed at school, first at Camberwell, and afterwards at Edinburgh. His education was completed at the university of Edinburgh, where, in 1822, he obtained the prize given for the study of the higher mathematics by the magistrates of Edinburgh.”
Still more complete are the following passages from a Memoir of Mr. Bidder in Proc. Inst. C. E. (lvii. Part 3, pp. 294–309): “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, 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 to defray the expenses of his education. … 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.
“ … Among other places, he was taken to Edinburgh, where he attracted the notice of Sir Henry Jardine … Sir Henry was so pleased with the boy’s disposition, and so satisfied with his capabilities, that with the assistance of Sir William Rae, Sir George McKenzie, and some other friends, he raised a sufficient subscription, and became responsible for his education. Bidder was then placed with the Rev. A. Stewart, a private tutor; and afterwards, in 1819, he attended the classes at the University of Edinburgh, where be fully realized the expectations of those who educated him, and in the spring of 1822 obtained the prize given by the Magistrates of Edinburgh for the study of the higher mathematics. … He quitted Edinburgh in 1824.”
The Lit. Gaz. (iv. 110) contains the following paragraph: “GEORGE BIDDER, the boy whose wonderful powers in calculation have attracted so much notice, has been rescued, by a public subscription at Edinburgh, from the degraded situation of a common show, and a fund raised to give him a liberal education. He is now thirteen years of age; and the progress of his mind will be watched with philosophical care, by some of the learned members of the university where he is placed, and of the Royal Society” (the Roy. Soc. of Edinburgh is probably meant).
Finally, Combe remarks (ii. 502), “Mr. George Bidder, when a mere child, displayed such astonishing talent as a mental calculator, that several gentlemen in Edinburgh were induced to take charge of his education; and, on the supposition that his abilities extended to mathematical science generally, selected for him the profession of an engineer. Having heard of this intention, and having observed that in his head the organs of the geometrical faculties were not developed in any extraordinary degree, I inferred that his eminence as a geometrician would not equal that which he had attained as a calculator, and communicated this conviction in writing to Principal Baird, one of his patrons. Mr. Bidder subsequently pursued the study of geometry; but at the end of two years, both he himself and Professor Wallace informed me, that he was not distinguished for more than common ability in the class.” This, it may be remarked, is fully borne out by Mr. Bidder’s statement in the Lecture alluded to above. “As regards mathematical aptitude”, he says, “I cannot be mistaken, for when I was associated with large classes, I experienced considerable difficulty in maintaining a fair position, and in no respect have I ever been distinguished for mathematical pursuits.” Proc. Inst. C. E. xv. 253.)
Some of the achievements with which Mr. Bidder is credited are certainly very astonishing; for example, in an article on “Calculating Boys”, in Belgravia (xxxviii. 459) the following passage occurs: “When thirteen years old, in dealing with the question, What is the cube root of 897,339,273,974,002,153? He obtained the answer in 2 1/2 minutes, viz., 964,537. I do not believe one arithmetician in a thousand would get out this answer correctly, at a first trial, in less than a quarter of an hour.”
Again, Andrews having described some of the calculating feats of Jedediah Buxton, a Derbyshire lad, was led on to write of Mr. Bidder’s achievements, and to give “a few of the principal questions solved by him.” The eleventh of these questions (p. 215) is “What is the cube of 1,178,420,165,015,625?” Stated in other words it is a modest request to multiply a number consisting of sixteen significant figures by itself, and then to multiply the result by the original sixteen figures. It will be observed that two consecutive multiplications are proposed. The result of the first would contain 31 figures, and this number is to be again multiplied by the original 16 figures, which would produce a result having 46 figures.
While shrinking from asserting that these statements are incredible, I am compelled to hesitate before accepting them by the following passages in Bidder’s Lecture already referred to. “As a great effort,” he says, “I have multiplied 12 places of figures by 12 places of figures; but that has required much time, and was a great strain upon the mind. Therefore in stating my conviction that mental arithmetic could be taught, I would desire it to be understood that the limits within which it may be usefully and properly applied should be restricted to multiplying 3 figures by three figures.” (Proc. Inst. C. E. xv. 256.)
Returning to this subject in the same Lecture, he said “On one occasion ‘I went through the task of multiplying 12 places of figures by 12 figures; but it was a great and distressing effort.” (Ibid. p. 259.)
As I understand the foregoing quotations, Mr. Bidder when in his 50th year, and little likely to surpass his accomplished feats, stated, either explicitly or implicitly, that his greatest achievement in mental multiplication was multiplying 12 significant figures by 12 significant figures; that it was performed “on one occasion” only; that it “required much time”, and “and was a great and distressing effort”; and, so understanding, I am constrained to hesitate as to the credibility of the statement that he once multiplied 16 significant figures by 16 significant figures, and at once multiplied the product, consisting of 31 significant figures, by 16 significant figures, and that the ultimate product, consisting of 46 significant figures, was correct in every particular.
Nor do I find it easier to believe that the extraction of the cube root of the number mentioned above would be a less difficult feat. In performing it with writing materials in the ordinary way about 550 calculations would have to be made and written, as against about 800 in the specified multiplication question, but the process would be so much more complicated as to lead me to believe that the performance of the question in Evolution would be a greater achievement than that in Multiplication.
I cannot conclude this topic without enriching my Note with the following statement, compiled from the Memoir of Bidder in the Proc. Inst. C. E. (lvii. 309). On 26 September 1878, being then in his 73rd year, he was conversing with a mathematical friend on the subject of Light, when, it having been remarked that “36,918 pulses or waves of light, which only occupy 1 inch in length, are requisite to give the impression of red”, the friend “suggested the query that, taking the velocity of light at 190,000 miles per second, how many of its waves must strike the eye and be registered in one second to give the colour red; and producing a pencil, he was about to calculate the result, when Mr. Bidder said, ‘You need not work it; the number of vibrations will be 444,433,651,200,000.’”
The calculation which he made required the continued multiplication of the number of waves in an inch, the number of inches in a mile, and the velocity of light in miles per second, = 36,918 x 63,360 x 190,000. It is unnecessary to say that the factors may be taken in any order, and experience would have taught the computist which order was for him most expeditious and least fatiguing. Taking the order given above, and omitting the terminal ciphers until the multiplication was finished, the final multiplication would be 233,912,448 x 19; or, beginning with the first and third, the last multiplication would be 701,442 x 6336; or, beginning with the second and third, he would finally have 120,384 x 36918; that is he would have the choice of multiplying nine figures by two, or six figures by four, or six figures by five.
The feat was undoubtedly a very remarkable one; and, though it fell far short of multiplying 16 figures by 16 figures, and their product by 16 figures again, it was the more note-worthy, when it was remembered that Mr. Bidder had long been an invalid, as showing that neither age nor illness had impaired the remarkable faculty which first made him famous. He died rather suddenly 20 September 1878, the second day next after the achievement just mentioned.