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Updated: May 21, 2025
She could never follow the order of the twelve months of the year, nor master a single arithmetical figure, nor count a sum of money, nor reckon the price of a thing. A month's instruction was not enough to give knowledge of the hours of the day on the dial-plate. The words she used were often the direct opposites of the words that she meant to use.
The examiner should be careful to ask questions adapted to the station of life of the supposed lunatic; a man is not necessarily mad because he cannot perform simple arithmetical operations, or does not know about things with which his questioner is well acquainted.
Practically, people rarely play upon any except the three first- named chances, and they will be sufficient for my explanation. Now a very simple arithmetical calculation will show you, that the chances against your naming one number out of the five drawn is eighteen to one; against your predicting two, four hundred to one; and against your hitting on three, nearly twelve thousand to one.
In precisely analogous fashion, beans, shoe pegs, and counters may be helpful aids to a realization of numerical relations, but when employed except as aids to thought the apprehension of meaning they become an obstacle to the growth of arithmetical understanding. They arrest growth on a low plane, the plane of specific physical symbols.
There is a meta-physical impossibility implied in the attempt to extend its application to persons. It is possible, we admit, to ordain by local law that four and four make ten, but such an exercise of legislative wisdom could not overcome certain arithmetical prejudices innate in our minds, or dethrone the stubborn eight from its accustomed position in our thoughts.
The attempts to perfect the construction of his arithmetical machine seem especially to have worn out his delicate frame, and to have laid the foundation of the nervous prostration from which he more or less suffered all his life afterwards. “From the age of eighteen,” she says in a significant passage that her brother “hardly ever passed a day without pain.
I then threw myself on the couch, and endeavoured to dispose myself to sleep; but it was in vain that I used every effort to compose myself that I lay without movement of finger or of muscle, as still as if I had been already a corpse that I endeavoured to divert or banish disquieting thoughts, by fixing my mind on some act of repetition or arithmetical process.
Several subjects of teaching and education highly important to the all-round harmonious development of a man seemed to me thrust far too much into the background, treated in step-motherly fashion, and superficially worked out. The results of the arithmetical teaching astounded me, yet I could not follow it into its larger applications and wider extent.
To the latter the world is indebted for the introduction of decimal fractions, which completed our arithmetical notation, and formed the second of the three steps by which, in modern times, the science of numbers has been so greatly improved; and yet both of these men believed in the most childish absurdities at least in enough of them to die without their orthodoxy having ever been questioned.
With these cautions, the method here alluded to will be found to be of very great advantage in many studies; for example, all the arithmetical tables may be recited in this way; words may be spelled, answers to sums given, columns of figures added, or numbers multiplied, and many questions in history, geography, and other miscellaneous studies answered, especially the general questions asked for the purpose of a review.
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