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562 SWEDENBORG AS A MAN OF SCIENCE. [Doc. 199.
desired a calculation of greater extent and of a more diffi
cult arrangement
, which would afford him an opportunity
for displaying the greatness and power of his understanding,
and his deep penetration. He accordingly desired to know
if there was one number which included as well a cube, as a
square, and which also by halving could be reduced to one.
Sixty- four was proposed, which is the square of eight and the
cube of four, and which by even numbers could be halved to
number one. We did not fail to remind him , that this
number was too high, too difficult, and almost unmanageable.
Because, if number sixty -four was to be reached by single
numbers, and then only the change into two numbers was to
be instituted, and if these numbers were to be changed sixty
four times, i. e. if sixty -four times sixty-four (or 4096) was to
be reached before three numbers were to be used, in this
case in all computations therewith and especially in multipli
cation and division that difficulty would have to be faced, that
a multiplication-table consisting of 4096 numbers would have
to be borne in mind instead of the usual one, which consists
only of eighty or ninety numbers. But the greater the diffi
culties that were raised, the more his desire to make the
trial increased and to prove the feasibility of a matter which,
we maintained, required too deep reflection to be brought into
order and to be accomplished in a short time. His Majesty
himself therefore undertook to elaborate and project this
method of counting.
The very next day he sent us his project elaborated on a
whole sheet with new characters and new names ; the sixty
four numbers above-named he had there divided into eight
classes, and each class was distinguished by a peculiar mark
from the others. Upon closer investigation it was found that
these distinctive marks were all taken from the initial or
final letters and from the characters of the numbers which
he had introduced; and it was all done in such an ingenious
and compendious manner, that after the first eight numbers
were known, no difficulty was experienced in learning the
numbers following until sixty -four. New names also were
given to each class, and to each of the numbers in the first
class, which names could be easily remembered ; and the rest
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