286 
PLATO 
When Socrates’s interlocutor speaks of the use of astronomy 
for distinguishing months and seasons, for agriculture and 
navigation, and even for military purposes, Socrates rallies 
him on his anxiety that his curriculum should not consist 
of subjects which the mass of people would regard as useless: 
‘ it is by no means an easy thing, nay it is difficult, to believe 
that in studying these subjects a certain organ in the mind 
of every one is purified and rekindled which is destroyed and 
blinded by other pursuits, an organ which is more worthy 
of preservation than ten thousand eyes; for by it alone is 
truth discerned/ 1 
As with astronomy, so with harmonics. 2 The true science of 
harmonics differs from that science as commonly understood. 
Even the Pythagoreans, who discovered the correspondence 
of certain intervals to certain numerical ratios, still made 
their theory take too much account of audible sounds. The 
true science of harmonics should be altogether independent 
of observation and experiment. Plato agreed with the Pytha 
goreans as to the nature of sound. Sound is due to concussion of 
air, and when there is rapid motion in the air the tone is high- 
pitched, when the motion is slow the tone- is low; when the 
speeds are in certain arithmetical proportions, consonances or 
harmonies result. But audible movements produced, say, by 
different lengths of strings are only useful as illustrations; 
they are imperfect representations of those mathematical 
movements which produce mathematical consonances, and 
it is these true consonances which the true dp/xoviKos should 
study. 
W.e get on to easier ground when Plato discusses geometry. 
The importance of geometry lies, not in its practical use, but 
in the fact that it is a study of objects eternal and unchange 
able, and tends to lift the soul towards truth. The essence 
of geometry is therefore directly opposed even to the language 
which, for want of better terms, geometers are obliged to use; 
thus they speak of ‘ squaring ‘ applying (a rectangle) 
‘ adding &c., as if the object were to do something, whereas 
the true purpose of geometry is knowledge. 3 Geometry is 
concerned, not with material things, but with mathematical 
1 Rep. 527 n, e. 2 Ih. 531 A-c. 
3 lb. vii. 526 d-527 b.