CH. XIll] CALCULATING PRODIGIES 277 



geometry and any language but German he remained ignorant 

 to the end of his days. He was trustworthy and filled various 

 small official posts in Germany. He gave exhibitions of his 

 calculating powers in Germany, Austria, and England. He died 

 in 1861. 



When exhibiting in Vienna in 1840, he made the acquaint- 

 ance of Strasznicky who urged him to apply his powers to 

 scientific purposes. This Dase gladly agreed to do, and so 

 became acquainted with Gauss, Schumacher, Petersen, and 

 Encke. To his contributions to science I allude later. In 

 mental arithmetic the only problems to which I find allusions 

 are straightforward examples like the following: — Multiply 

 79,532,853 by 93,758,479 : asked by Schumacher, answered in 

 54 seconds. In answer to a similar request to find the product 

 of two numbers each of twenty digits he took 6 minutes ; to 

 find the product of two numbers each of forty digits he took 

 40 minutes; to find the product of two numbers each of a 

 hundred digits he took 8 hours 45 minutes. Gauss thought 

 that perhaps on paper the last of these problems could be 

 solved in half this time by a skilled computator. Dase once 

 extracted the square root of a number of a hundred digits in 

 52 minutes. These feats far surpass all other records of the 

 kind, the only calculations comparable to them being Buxton's 

 squaring of a number of thirty-nine digits, and Wallis' extrac- 

 tion of the square root of a number of fifty-three digits. Dase's 

 mental work however was not always accurate, and once (in 

 1845) he gave incorrect answers to every question put to him, 

 but on that occasion he had a headache, and there is nothing 

 astonishing in his failure. 



Like all these calculating prodigies he had a wonderful 

 memory, and an hour or two after a performance could repeat 

 all the numbers mentioned in it. He had also the peculiar 

 gift of being able after a single glance to state the number (up 

 to about 30) of sheep in a flock, of books in a case, and so on ; 

 and of visualizing and recollecting a large number of objects. 

 For instance, after a second's look at some dominoes he gave 

 the sum (117) of their points; asked how many letters were in 



