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SCIENCE 



[N. 8. Vol. XXXVII. No. 963 



the great conception — mathematically pre- 

 cise yet mystical withal and awful in its 

 limitless reaches — which is ever ready to 

 form itself, in the normally educated mind 

 and there to stand a deep-rooted conscious 

 conviction regarding the shape and the size 

 of the all-embracing world. 



Is the conception valid? Does the con- 

 viction correspond to fact? Is it true? It 

 is not enough that it be intelligible, which 

 it Is ; it is not enough that it be noble and 

 sublime, which also it is. No doubt what- 

 ever is noble and sublime is, in some sense, 

 true. For we mortals have to do with more 

 than reason. Yet science, science in the 

 modern technical sense of the term, having 

 elected for its field the domain of the ra- 

 tional, allows no superrational tests of 

 truth to be sufficient or final. We must, 

 therefore, ask: are the dimensions and the 

 figure of our space, in fact, what, as we 

 have seen, Pascal asserts and the normally 

 educated mind believes them to be? Long 

 before the days of Pascal, back yonder in 

 the last century before the beginning of 

 the Christian era, one of the acutest and 

 boldest thinkers of all time, immortal ex- 

 pounder of Epicurean thought, answered 

 the question with the utmost confidence in 

 the affirmative. I refer to Lucretius and 

 his " De Rerum Natura. ' ' In my view that 

 poem is the greatest and finest union of 

 literary excellence and scientific spirit to 

 be found in the annals of human thinking. 

 I maintain that opinion of the work despite 

 the fact that the majority of its conclu- 

 sions have been invalidated by time, have 

 perished by supersession; for we must not 

 forget that, in respect of knowledge, "the 

 present is no more exempt from the sneer 

 of the future than the past has been." I 

 maintain that opinion of the work de- 

 spite the fact that the enterprise of Lucre- 

 tius was marvelously extravagant; for we 

 must not forget that the relative modesty 



of modern men of science is not inborn, 

 but is only an imperfectly acquired lesson. 

 "Well, it is in that great work that Lucre- 

 tius endeavors to prove that our universe 

 of space is infinite in the sense that we 

 have explained. His argument, which 

 runs to many words, may be briefly para- 

 phrased as follows. Conceive that, start- 

 ing from any point of space, you go out 

 in any direction as far as you please, 

 and that then you hurl your javelin. 

 Either it will go on, in which case there is 

 space ahead for it to move in, or it will not 

 go on, in which case there must be space 

 ahead to contain whatever prevents its go- 

 ing. In either case, then, however far you 

 may have gone, there is yet space beyond. 

 And so, he concludes, space is infinite, and 

 he triumphantly adds : 



Therefore the nature of room and the space of 

 the unfathomable void are such as bright thunder- 

 bolts can not race through in their course though 

 gliding on through endless tract of time, no nor 

 lessen one jot the journey that remains to go by 

 all their travel — so huge a room is spread out on 

 all sides for things without any bounds in all 

 directions round. 



Such is the argument, the great argu- 

 ment, of the Roman poet. Great I call it, 

 for it is great enough to have fooled all 

 philosophers and men of science for two 

 thousand years. Indeed only a decade ago 

 I heard the argument confidently employed 

 by an American thinker of more than na- 

 tional reputation. But is the argument 

 really fallacious? It is. The conclusion 

 may indeed be quite correct — space may 

 indeed be infinite, as Lucretius asserts — 

 but it does not follow from his argument. 

 To show the fallacy is no difficult feat. 

 Consider a sphere of finite radius. We 

 may suppose it to be very small or inter- 

 mediate or very large — no matter what its 

 size so long as its radius is finite. By 

 sphere, in this part of the discussion, I 

 shaU mean sphere-surface. Be good enough 



