--| Re: The Atomistic Conception of Numbers |--- 

in the Middle Ages... Arithmetic was not taught as the abstraction of
today, but as the entity expressed in the mystery of numbers. Number
itself was looked upon differently from how it is done today. I will
give you a trifling instance of this.

How does one picture 1, 2, 3 to oneself today? It is done by thinking of a
pea, then of another pea, and this makes two; then another is added and
there are three. It is a matter of adding one to another Ñ piling them up.
In olden days one did not count in this way. A start was made with a unit.
And by splitting the unit into two parts one had 2. Thus 2 was not arrived
at by adding one unit to another. It was not a putting together of units,
but the two were contained in the one. Three was contained in the one in a
different way Ñ four again in a different way. The unit embraced all
numbers and was the greatest. Today the unit is the smallest. Everything
today is atomistically conceived. The unit is one member and the two is
added to it, this is all imagined atomistically. The original idea was
organic. There the unit is the greatest and the following numbers always
appear as being smaller and are all contained in the unit. Here we come to
quite different mysteries in the world of numbers.

These mysteries in the world of numbers give the merest intimation that
here we are not concerned with what merely lives in the hollow of Man's
head. (I say the hollow of his head because I have often shown it really
to be hollow from the spiritual point of view.) In the relations of number
we can come to perceive the relations of the objectivity of the world. If
we always just add one to one naturally this is something that has nothing
to do with the facts. I have a piece of chalk. If beside it I place a
second piece of chalk this has nothing to do with the first. The one is
not concerned with the other. If, however, I presuppose that everything is
a unit and now pass to the numbers contained in this unit, I get a two in
a way that is a matter of some consequence. I have to break up the piece.
I then get right into reality. 


Rudolf Steiner, The Alphabet, An Expression Of The Mystery Of Man,
Dornach, December 18, 1921, GA 209.

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