idea said to be dimly prefigured in mythology?
The universal belief in the sacredness of numbers is an instinctive
faith in an immortal truth; it is a direct perception of the soul, akin
to that which recognizes a God. The laws of chemical combination, of the
various modes of motion, of all organic growth, show that simple
numerical relations govern all the properties and are inherent to the
very constitution of matter; more marvellous still, the most recent and
severe inductions of physicists show that precisely those two numbers on
whose symbolical value much of the edifice of ancient mythology was
erected, the _four_ and the _three_, regulate the molecular distribution
of matter and preside over the symmetrical development of organic forms.
This asks no faith, but only knowledge; it is science, not revelation.
In view of such facts is it presumptuous to predict that experiment
itself will prove the truth of Kepler's beautiful saying: "The universe
is a harmonious whole, the soul of which is God; numbers, figures, the
stars, all nature, indeed, are in unison with the mysteries of
religion"?

FOOTNOTES:

[67-1] Buckingham Smith, _Gram. Notices of the Heve Language_, p. 26
(Shea's Lib. Am. Linguistics).

[68-1] I refer to the four "ultimate elementary particles" of
Empedocles. The number was sacred to Hermes, and lay at the root of the
physical philosophy of Pythagoras. The quotation in the text is from the
"Golden Verses," given in Passow's lexicon under the word ~tetraktys:
nai ma ton hametera psycha paradonta tetraktyn, pagan aenaou physeos~.
"The most sacred of all things," said this famous teacher, "is Number;
and next to it, that which gives Names;" a truth that the lapse of three
thousand years is just enabling us to appreciate.

[68-2] Ximenes, _Or. de los Indios_, etc., p. 5.

[68-3] See Sepp, _Heidenthum und dessen Bedeutung fuer das Christenthum_,
i. p. 464 sqq., a work full of learning, but written in the wildest vein
of Joseph de Maistre's school of Romanizing mythology.

[69-1] Brasseur, _Hist. du Mexique_, ii. p. 227, _Le Livre Sacre des
Quiches_, introd. p. ccxlii. The four provinces of Peru were Anti, Cunti,
Chincha, and Colla. The meaning of these names has been lost, but to
repeat them, says La Vega, was the same as to use our words, east, west,
north, and south (_Hist. des Incas_, lib. ii. cap. 11).

[69-2] Humboldt, _Polit. Essay on New Spain_, ii. p. 44.

[70-1] This custom has been oft