166 
there is little here but what we can get from 
others. But here it is, well and clearly ordered 
and expressed, and abundantly furnished with all 
sorts of guide-posts for those in quest of still 
more information or discussion. 
The bibliographical lists are astonishingly good, 
without pretending to ‘“‘completeness.” The one, 
for instance, which is appended to the first section 
of our volume is of a general kind, and covers 
some seventy pages; it pilots the student to the 
texts of Diels, Mullach, and others; to works on 
the history of philosophy, Greek and other, from 
the days of Ritter and Preller to Zeller and Burnet 
and Diels; and ends with a capital account of the 
historians of mathematical, astronomical, and 
physical science, from Bailly, Montucla, and 
Delambre, to Allman and Zeuthen, and Moritz 
Cantor and Paul Tannery and Sir Thomas Heath. 
There may be mistakes, for aught I know, in this 
learned and compendious book, but I have neither 
found them nor sought for them. It was one of 
Pythagoras’s sayings (or Dr. Johnson tells us so) 
that a friend should not be chidden for little faults. 
Pythagoras is one of the great figures of the 
world, and many and many a scholar has had a 
predilection for him. Sir Thomas Browne loved 
him; Plato was steeped in his doctrine; and 
whole books of Euclid are ascribed to his teaching. 
Those who knew least of him could always quote 
him, as Shakespeare did, and Dr. Johnson, and as 
Goldsmith quoted Ocellus Lucanus. But the 
more we read about Pythagoras the less we know 
of him for sure and certain; and it is just herein 
that his peculiar fascination lies. For he is one 
of those shadowy figures who stand on the border- 
land between history and fable, between fairyland 
and reality: like King Arthur and Thomas of 
Ercildoune and King Solomon and Caliph Haroun 
al Raschid. We know that one of his legs was of 
gold, that Apollo was his father, that heavenly 
messengers flew down to him on golden arrows, 
and that his face shone like the faces of the 
Shining Ones. In more sober statement he seems 
to represent the continuity, unbroken but dwindled 
to a thread (a thin but indispensable thread), 
between one civilisation and another, between the 
beginning of Greek thought and the decline of 
learning in a remote but erudite antiquity. To 
the student trying to prefigure so strange and 
so elusive a personality there is a choice of ways. 
If he keep to sober and critical consideration of 
the meagre facts at hand, he will probably arrive 
at the conclusion that there is ho evidence for 
Pythagoras having learned anything worth speak- 
ing of upon his travels or having inherited any 
load of learning from pre-Hellenic science and 
philosophy. So it is commonly held by many men 
of the soundest classical learning that no foreign 
influence can be traced in the school of Pytha- 
goras, and that his “philosophy and institutions 
contain nothing but what might easily have been 
developed by a Greek mind exposed. to the ordi- 
nary influences of the age.” Dr. Allman held, 
with all due caution, that we must be “struck with 
the Egyptian character of the geometrical work 
attributed to Pythagoras”; but Prof. Burnet 
NO. 2453, VOL. 98] 
NATURE” 
[NOVEMBER 2, 1916 
asserts that all the mathematics of the Egyptians 
consisted of a few rules of thumb by which to 
measure the area of a field or the height of a 
pyramid, and denies that Egypt had anything to 
teach Pythagoras that was worth the learning or 
the borrowing. : i 
On the other hand, there is ample room for 
others, of a more imaginative disposition, to grope 
among the ruins and the misty darkness of pre- 
Hellenic civilisation, to put two and two together 
wheresoever they can, and to apply themselves. 
(for a while at least) to the ingenious art of fanci- 
ful reconstruction. Dr. Naber’s curious book, 
“Das Theorem des Pythagoras,” is of the latter 
kind. The ground on which he leads us is some- 
times dangerous, as when he depends on Piazzi 
Smyth for his facts as well as his theories of the 
pyramid; but for all that he weaves a fascinating 
and instructive story. He brings together a pro- 
digious mass of curious lore about the triangle and 
the pentagon, and the Sacred Letter, and the 
Symbol of Health, and Abracadabra, and the 
sacred lotus and mallow-flower; he touches on a 
hundred things which the: early students of the 
triangle must (in all likelihood) have observed and 
discovered by the way; and he suggests with no. 
less ingenuity the lines of tradition along which 
such knowledge ran, from far-away antiquity even. 
to the artists and cathedral-builders of the Middle 
Ages. 
If we be inclined to see in Pythagorean mathe- 
matics not the discoveries of a single lifetime but. 
fragments of the learning of a preceding age, so 
also in his philosophy may we be inclined to recog- 
nise parts of a great edifice the scattered stones of 
which confront us in unexpected places, built into 
the fabric of old but less ancient walls. We have 
often heard that there is a curious link or bond 
between the Cabbalists and the Pythagoreans; 
and now again, in a recent Hibbert Journal, 
an article by the Chief Rabbi on ‘Jewish Mysti- 
cism” suggests, though it does not assert, this 
view. The “opinion of Pythagoras” regarding 
metempsychosis, wholly absent from Bible and 
from Talmud, is fundamental to the teaching of 
the Cabbala. In Cabbalistic as in Pythagorean 
philosophy the ten numerals, or Sefiroth, contain - 
the possibilities of all things, and, with the help 
of language, represent the Spirit of God; the mys- 
tical number Ten is the material universe, God’s 
kingdom made visible; wisdom and understand- 
ing, mercy and justice and harmony are among 
the concepts which other numbers represent or 
embody; and the mystical One is the mystery of 
mysteries, which in the beginning filled all space 
and was all space. Then “En Sof contracted Him- 
self in order to leave an empty space for 
creatures”; just as, according to Pythagoras, 
érecdyerOar 8 ex Tov dmeipov Xpovoy Te Kal TVvOnV Kal TO 
xevov. The Pythagorean, or Platonic, or Jewish 
concept of Number is a hard saying to the un- 
poetic, non-mystical modern and Western world; 
and many a way is found to show that Plato and 
Pythagoras meant something prosy and common- 
place after all. But to some it is still as plain as 
ever that Number is the clue to the greatest of 
