Mathematics in Court. [Letter to the Editor, signed as "V. X." The Nation 5.116 (19 September 1867): 238.] ³⁶

To the Editor of The Nation:

The question of forgery is involved in the “Howland Will Case,” and it is contended that two signatures must have been traced.

Mr. Crosman was engaged in examining different signatures of various individuals with reference to the question of signatures repeating themselves. He “stated at great length the result of the comparison of these signatures; that he found many of them to cover much better than the signatures of Miss Howland to the second pages and to the will; that in one case both lines, ‘ Tour obedient servant ’ and ‘ Joseph B. Spear,’ covered much better than the two signatures of Miss Howland.”

The whole case was closed by the testimony of Prof. Benjamin Peirce upon the doctrine of chances. I quote from this testimony as follows:

“In the case of Sylvia Ann Howland, this phenomenon could occur only once in the number of times expressed by the thirtieth power of five or more—exactly, it is once in two thousand six hundred and sixty-six millions of millions of millions of times, or 2,666,000,000,000,000,000,000. This number far transcends human experience. So vast an improbability is practically an impossibility.” How then to account for “Your obedient servant, Joseph B. Spear,” and other duplicate signatures?

Now, I would ask if all this testimony of Prof. Peirce’s is not irrelevant? The signatures that do correspond, and are not forgeries, are facts, and by the side of this doctrine of chance they seem to prove that figures cannot always be trusted. It appears to me that the case in question is not amenable to the laws of chance. It is always a person’s intention to make the signature similar to others as nearly so as possible every time. The elements of will and desire unfit it for judgment by such laws. Figures can be prostituted to prove almost anything, and were it not for Prof. Peirce’s high position, one might be led to think his evidence nothing more than a special plea. And the tone of his testimony is arrogant and positive, as if he were charging the judges.

I doubt very much whether “all the mathematicians of the world” will instantly recognize the correctness and applicability of this doctrine.

V. X.

[Mr. Crosman’s testimony does not in any way conflict with Professor Peirce’s, for the conclusion of the professor’s testimony is not that there may not or do not occur exact coincidences in the signatures of certain persons, but that in the case of Sylvia Howland such a coincidence would be a most extraordinary event, unless designedly produced by tracing or other form of forgery. The evidence on which this conclusion is founded is a minute comparison of about fifty signatures of Miss Howland each with all the others. So irregular were the signatures found to be that a coincidence so close as that of the alleged forgery ought not to be expected more than once in 2,666,000,000,000,000,000,000 cases of comparison. This calculation is not affected by the fact that other people write more regularly than she; it is based simply on an investigation of her habits of writing. This investigation might be called in question as being in the nature of things somewhat arbitrary so far as determining what are and what are not cases of coincidence. No two individuals of any species whatever could be found exactly alike if examined with sufficient minuteness. It was accordingly necessary to resort to the practical judgment of common sense to determine the data for this calculation; and the value of the calculation, which is a very simple one, depends wholly on the judgment used in observation, and is not a mathematical question at all. The procedure was substantially this: The thirty down-strokes of Miss Howland’s signature were chosen as test objects. In comparing any two signatures, as many of these lines were made to coincide with corresponding ones as in the judgment of the observer could be made to do so. The coincidences, or what in the judgment of the observer were deemed coincidences, were counted, and the whole number of coincidences in the 1,250 comparisons was found to be to the number of non-coincidences as one to four nearly, or to be about one-fifth of the whole. The relative frequency of the occurrence of different numbers of coincidences in single comparisons followed the law of chance very closely, showing that the several coincidences were independent, accidental events, and hence, for the whole thirty to occur (the independent chance of each being one-fifth), there is only the chance measured by one-fifth to the thirtieth power. This conclusion is not invalidated by the fact that in the signatures of other persons exact coincidences do happen, unless it can also be shown that these persons generally write as irregularly as Miss Howland did. The effect of a person’s intention to make all signatures alike, which “V. X.” refers to, is fully taken account of in the investigations of the person’s habits. There is nothing whatever in what “V. X.” says about the “elements of will and desire.” His comment on the tone of Professor Peirce’s testimony is hardly just. Mr. Peirce has a not very wise way of putting his testimony in the most paradoxical and at the same time positive form he can devise, thereby making it very much less effective on the minds of common folks. If he appears arrogant, it is probably from a desire to make up in the earnestness of his statements the lack of convincing clearness—to supply his audience with a lively faith in default of a clear understanding. He is a little too much given to impute a certainty to the results of mathematical computation which only belongs to the processes and not to the data of the computation. The value of the present testimony depends wholly on the judgment of his son in estimating coincidences, and does not depend on the judgment of either father or son as mathematical experts.—Ed. Nation.]