Jan. 15, i88cT 



NATURE 



253 



The topic to which I especially wish to direct attention, 

 is the innate and hereditary tendency of certain persons 

 to see numbers in definite and constant arrangements or 

 schemes, whose various characters will be easily under- 

 stood from the extracts I am about to give and by the 

 accompanying illustrations, which are reductions to a 

 small scale of the pictures I have received, with a 

 necessary sacrifice of detail in a few cases. 



The simplest instances do not seem to be the com- 

 monest ; thus, I have very few indeed that could be 

 classed with the following : — 



8. When a child, I counted by means of imaginary cards 

 from ace to ten. My little boy in the same way, used an 

 imaginary domino. 



Or this :— 



9. I picture numbers in group?, thus 5 is sometimes [•'. , 

 sometimes • ••, S is :: , 7 is I j , 100 is ten rows of ten. 



I may as well give the remainder of this communication 

 here ; it is written by a lecturer upon mental philosophy. 

 He says : — 



10. The numerals 1, 2, 3, 4, &c, from the part they play in 

 the multiplication table, have been personified by me from child- 

 hood. 9 is a wonderful being of whom I felt almost afraid, 

 S I took for his wife, and there used always to seem a fitness in 

 9x9 being so much more than S x S. 7 again is masculine; 

 6, of no particular sex but gentle and straightforward ; 3, a feeble 

 edition of 9, and generally mean ; 2, young and sprightly ; I, a 

 common-place drudge. In this style the whole multiplication 

 table consisted of the actions of living persons, whom I liked or 

 disliked, and who had, though only vaguely, human forms. 



The schemes in which numerals appear are usually 

 fantastical and sometimes very elaborate. I will (by 

 permission) give the name of the writer of the first 

 instance about to be adduced, on account of the hereditary 

 interest that is attached to it. It is by Mr. George Bidder, 

 Q.C., a son of the late eminent engineer, who was known in 

 early life as the calculating boy. Mr. George Bidder 

 inherits much of his father's marvellous power of mental 

 arithmetic, being able, though not with equal precision 

 and rapidity, to mentally multiply fifteen figures by 

 another fifteen figures. This faculty has been again 

 transmitted, though in an again reduced degree, to the 

 third generation. (See letter in the Spectator, December 2S, 

 1878, also the early numbers of that paper in 1S79.) 



He writes to me as follows : — 



11. One of the most curious peculiarities in my own case, is 

 the arrangement of the arithmetieal numerals. I have sketched 

 this to the best of my ability. Every' number (at least within 



the first thousand, ami afterwards thousands take the place of 

 units) is always thought of by me in its own definite place in 

 the series, where it has if I may say so, a home and an indi- 

 viduality. 1 should, however, qualify this by saying that when 

 I am multiplying together two large numbers, my mind is 

 engrossed in the operation and the idea of locality in the series 

 for the moment sinks out of prominence. You wdl observe 

 that the first part of the diagram roughly follows the arrangement 

 of figures on a clock-face, and I am inclined to think that may 

 have been in part the unconscious source of it, but I have 

 always been utterly at a loss to account for the abrupt change at 

 IO and again at 12. 



It occurs to me that the change is probably due to the 

 wrench given to the mental picture of the clock dial in 



order to make its duodecimal arrangement conform to the 

 decimal system, and that the same action is repeated at 

 no. 



The next diagram exhibits the most compact of all 

 the mental schedules which I have as yet received : — 



12. The representation I carry in my mind of the numerical 

 series is quite distinct to me, so much so that I cannot think of 

 any number but I at once see it (as it were) in its peculiar place 

 in the diagram. My remembrance of dates is also nearly 

 entirely dependent on a clear mental vision of their loci in the 

 diagram. This, as nearly as I can draw it, is the following : — 



'«$& 



0& 



It is only approximately correct (if the term " correct " be at 

 all applicable). The numbers seem to approach more closely 

 as I a-cend from 10 to 20, 30, 40, &c. The lines embracing a 

 hundred numbers also >eem to approach as I go on to 400, 500, 

 to 1,000. Beyond 1,000 I have only the sense of an infinite 

 line in the direction of the arrow, losing itself in darkness towards 

 the millions. Any special number of thousands returns in my 

 mind to its position in the parallel lines from I to 1,000. The 

 diagram was present in my mind from early childhood j I re- 

 member that I learnt the multiplication table by reference to it, 

 at the age of seven or eight. I need hardly say that the impres- 

 sion i~ not that of perfectly straight lines, I have therefore used 

 no ruler in drawing it. 



Some writers have somewhat rashly asserted that our 

 idea of numbers is always based on our ten fingers and 

 ten toes. There are, however, other forms in use by 

 various nations than those of decimal arithmetic, and the 

 last paragraph of the foregoing seems sufficient to show 

 that the finger and toe hypothesis is not universally true. 

 This opinion was strongly maintained by the lady writer 

 of the following remarks, whose imagery dates beyond 

 her earliest recollections : — 



13. The annexed column [a portion only of it is represented 

 here] represents how I see the numbers from I to 

 140. There is no break up to 30, and none from 

 90 to 130, but I think this is because the three 

 figures at 100 make a sort of break of themselves. 

 After 140 they go on regularly, but farther off. 

 The figures are not one above the other, as they 

 appear in the diagram, but are one beyond the 

 other, stretching away into space. They are about 

 half an inch long, of a light grey colour on a 

 darker and brownish grey ground. 



The next example is very curious ; the 

 diagram which accompanies it is carefully 29 30 

 and minutely drawn on a large sheet of 28 

 paper and looks like a detailed route survey 27 

 made by a careful traveller. I have been &c. 

 obliged to treat it much as a map maker Fig. 3. 

 would treat such a survey. 



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