378 HERMANN VON HELMHOLTZ 



Helmholtz proceeds to the questions that are so important and 

 interesting in physics, of physical equality, and the commutative 

 and associative laws of physical relations, defining addition in 

 a somewhat extended form as a relation of magnitudes of the 

 same kind, the results of which do not alter by exchanging the 

 terms for equal magnitudes of the same kind. So that Helm- 

 holtz maintained for arithmetic, or for the transcendental con- 

 ception of time in relation to its axioms, the same standpoint 

 which he took up in opposition to Kant in his investigation 

 of space. 



Helmholtz's house had been for more than ten years the centre 

 of the most enlightened minds of the new capital of the Empire: 

 here, to their mutual advantage, both mental and spiritual, the 

 most profound thinkers met the most talented artists, not on 

 neutral ground, but on a soil ripe to receive all that was good 

 and beautiful. Moltke's pupils and Bismarck's disciples came 

 together under the Olympic peace of the great investigator 

 and his distinguished wife, who here developed her transcen- 

 dent gift of bringing the most unlike minds into contact. 

 External position counted for little with her if it were not 

 accompanied by intellectual distinction or a fine artistic 

 temperament : 



1 1 have set myself all my life against a low level of social 

 environment, and kept it away wherever it was not imposed 

 upon me. I have held good manners, and a mental equipment 

 superior to my own in some aspect, or interesting at the least, 

 to be the first requirement of social intercourse. In this 

 respect one cannot afford to be modest, unless one means to 

 drop into mediocrity/ 



The migration to the new Presidential dwelling in Charlotten- 

 burg did but provide a 'more intimate and perhaps even 

 more harmonious setting for these social relations '. 



