The Anthropological Review

Mental Calculation.* All the performances of Colborn, Buxton, and other celebrated calculators, appear insignificant when compared with those of our contemporary, Zacharias Dase, of Hamburg. Having had ample opportunities to witness his extraordinary performances, I shall first describe what took place on the 12th, 15th, and 19th of January, and subsequently add what I have observed in my daily personal intercourse with him.

Dase commenced by casting a rapid glance on twelve ciphers written by a spectator on a board, and reciting them forwards or backwards. He then invited any person to multiply the number with any single number, and immediately named the multiplicator on the product being communicated to him.

At the third representation, Dase recited 188 ciphers, forwards and backwards, stating at the same time how often and at what place each number occurred. I subjoin a few of the questions and answers.

Q. What is the product of 354783293 multiplied by 5423957? A. (1½ minutes) 1924329325550401.

Q. What is the product of 6529710840352 divided by 98? A. (instantaneously) 66629710840352.

Q. 684028396281753, divide by 6541325. A. (2½ minutes) 104570312 138353/6541325.

Q. Divide 423339075240048565 by 708346795. A. (after five minutes) 597643807.

Q. Tell the square root of 582169. A. (immediately) 763.

Q. What is the cubic root of 318611987? A. 683.

Q. Tell the 19th root of 7093585369945932256195429028464404423 A. (after three minutes) 87.

Q. The steeple of the Nicolay Church being 180 feet high, how many such steeples must be towered upon each other before the last reaches the moon, assuming the distance to be 50,000 German miles? A. (immediately) 6666666 and two-thirds.

Q. What time would a snail require to perform this journey, assuming that it covers two inches and three-sevenths in a minute? A. (after a few minutes) 5929411764 12/17 minutes; 98823529 7/17 hours; 4117647 1/17 days; or, 11281 years and 82 1/17 days.

At the end of his representations. Dase gave some specimens of what he calls his "surveying glance." Thus, he mentioned at once the number of a handful of peas or beans, the number of books on the shelves, or the pieces in a bundle of firewood without a moment's hesitation. If ever he commits an error, he instantly corrected it. Thus, he estimated the number of a handful of peas to be 242, but he immediately corrected it by saying that he had probably counted two peas twice.

The most difficult tasks which Dase performed were the extraction of the 52nd root of a number of 97 ciphers, and the multiplication of two sums, each consisting of 100 ciphers, which he accomplished at Munich, in 8¾ hours.

He stated that during this calculation, the conversation of the spectators rather entertained him, and that neither noise nor loud conversation disturbed him in the least.

On my questioning him how far he thought he might go in multiplication of sums, he replied that he could not tell, but be had no hesitation in saying that he could undertake the multiplication of sums of 300 ciphers, and might probably require 100 hours mentally to accomplish the task.

From the experiments it resulted that he solved the multiplication of 8 ciphers in ¾ of a minute; 12 in 2¼ minutes; 20 in 6-8 minutes; 40 in 40 minutes; 60 in 3 hours; 100 in 8¾ hours.

Zacharias Dase, the son of a publican, was born at Hamburg, June 23, 1824. He was sent to an infant school at the age of two and a half years, and entered a popular school in his sixth year. Up to his fifteenth year he received instruction in reading, arithmetic, writing, geography, history, and the German language. He was always the first in arithmetic, nor was there any book published on this subject in Hamburg which he had not studied through. He says of himself:—"Originally I occupied myself more with written than with mental calculation, and I am therefore justified in asserting that, though my calculating capacity may be innate, it has been developed by undeviating industry. My mind never becomes fatigned by calculations. I may continue them for the whole day and am as fresh to begin again in the evening." From his early childhood Dase suffered from a spasmodic affection of the stomach, and epileptic attacks. Speaking of his moral character, he says:—"I am not passionate nor sensual; I am indifferent to the fair sex; I avoid spirituous liquors; I am good natured, tolerant, companionable, a man of peace, and make no distinction in my intercourse with may fellow beings, whether they be of high rank or not; I am fond of children, and am rather economical." With regard to his mental faculties, he complains that he could make no great progress is mathematics, that he had no memory for form and space. Nor did he make much progress in the highest branches of arithmetic, his great skill being limited to the extraction of roots, the calculation of factors and logarithms. He could give no exact account of the process by which he arrived at his results; but he seems to proceed in his mental calculations as if he were performing them on paper or a slate. In multiplying, all the numbers are plainly visible to him; he multiplies the multiplicands successively with the multiplicator, placing the sums mentally beneath each other. He further states that besides this capacity for number, he possesses order and locality in an eminent degree, so that in large towns he soon finds his way. He complains of possessing neither the faculty of ambition nor wit, but, on the other hand, much patience.

* Versuch einer Wissenschaftlichen Begründung der Psychologie. Von Professor Dr. P. Jessen. Berlin: 1865.

Comment from Oleg Stepanov.

Real source: P. Jessen, "Versuch einer wissenschaftlichen Begründung der Psychologie". Berlin: Veit & Comp., 1855.