216 PHYSICAL SCIENCE IX THE MIDDLE AGES. 



mire in the Alexandrian philosophy, he declares that they were incapa- 

 ble of treating scientific questions. The extent to which this is true is 

 well illustrated by the extract which he gives from Plotinus, on the 

 question, " Why objects appear smaller in proportion as they are more 

 distant." Plotinus denies that the reason of this is that the angles of 

 vision become smaller. His reason for this denial is curious enough. 

 If it were so, he says, how could the heaven appear smaller than it is, 

 since it occupies the whole of the visual angle ? 



2. Mystical Arithmetic. It is unnecessary further to exemplify, 

 from Proclus, the general mystical character of the school and time to 

 which he belonged ; but we may notice more specially one of the forms 

 of this mysticism, which very frequently offers itself to our notice, es- 

 pecially in him ; and which we may call Mystical Arithmetic. Like 

 all the kinds of Mysticism, this consists in the attempt to connect our 

 conceptions of external objects by general and inappropriate notions of 

 goodness, perfection, and relation to the divine essence and govern- 

 ment ; instead of referring such conceptions to those appropriate ideas, 

 which, by due attention, become perfectly distinct, and capable of be- 

 ing positively applied and verified. The subject which is thus dealt 

 with, in the doctrines of which we now speak, is Number ; a notion 

 which tempts men into these visionary speculations more naturally 

 than any other. For number is really applicable to moral notions to 

 emotions and feelings, and to their objects as well as to the things of 

 the material world. Moreover, by the discovery o the principle of 

 musical concords, it had been found, probably most unexpectedly, that 

 numerical relations were closely connected with sounds which could 

 hardly be distinguished from the expression of thought and feeling ; 

 and a suspicion might easily arise, that the universe, both of matter and 

 of thought, might contain many general and abstract truths of some 

 analogous kind. The relations of number have so wide a bearing, that 

 the ramifications of such a suspicion could not easily be exhausted, 

 supposing men willing to follow them into darkness and vagueness ; 

 which it is precisely the mystical tendency to do. Accordingly, this 

 kind of speculation appeared very early, and showed itself first among 

 the Pythagoreans, as we might have expected, from the attention which 

 they gave to the theory of harmony : and this, as well as some other of 

 the doctrines of the Pythagorean philosophy, was adopted by the later 

 Platonists, and, indeed, by Plato himself, whose speculations concern- 

 ing number have decidedly a mystical character. The mere mathe- 

 matical relations of numbers, as odd and even, perfect and imperfect, 



