AND ITS SELF-COKSEKVATION. 103 



Again, zero is commonly defined as a symbol which, 

 when standing alone, expresses no value. That seems 

 simple enough. And yet on further examination the 

 symbol represents, even in its very lowest term, a 

 product of very abstract thinking. It really represents 

 the negation in thought of all reality. That is, its 

 subjective meaning may be said to be greatest when 

 its objective meaning is least. Or if, as is sometimes 

 done, we take the term "objective" to mean valid, 

 true, then we would have to change the mode of our 

 expression, and say that the objective significance of 

 the term zero in its ultimate abstraction consists pre- 

 cisely in its subjective character. For in its ultimate 

 abstraction the term zero represents a perfectly valid 

 concept to which there is no corresponding reality other 

 than the concept itself. It represents just that nega- 

 tive concept which consists in the recognition that 

 beyond reality there is absolutely no limitation, for 

 limitation is itself a mode of reality, or, if the technical 

 reader prefers, a mode of actuality. 



But still further, in concrete science zero represents a 

 multitude of values on occasion. In the higher geometry 

 a right line is represented by an equation, of which one 

 member is 0. Again, in physics zero of temperature (Cen- 

 tigrade) represents that balancing of the molecular attrac- 

 tions and repulsions in water, the slightest disturbance of 

 which one way or the other will (under given conditions 

 of pressure) cause the water to assume the solid state or 

 assure its remaining liquid. But this is by no means all. 

 The theoretical "absolute zero" (273 below Centi- 

 grade) gives a scale in which Centigrade is found to 

 represent an "absolute" positive temperature of 273. 



