April 17, 1914] 



SCIENCE 



561 



be viewed as any meehanieally demon- 

 strable or fundamentally necessary law of 

 nature. Whether nature is a mechanism or 

 not, energy, according to the kinetic theory, 

 runs down hill as it does for statistical and 

 not for mechanical reasons. Energy need 

 not always run down hill; and in fact 

 would not do so if there were present in na- 

 ture any persistent tendency, however in- 

 perfeet, towards a suitable sorting of mole- 

 cules. Maxwell suggested in his image of 

 the demons sorting the atoms of a gas, how 

 such a tendency might make energy run up 

 hill instead of down, without the violation 

 of any mechanical principle. 



More recently Boltzmann, in his further 

 development of Maxwell's hypothesis, 

 pointed out how the theory of probability 

 itself requires that, in the course of very 

 vast intervals of time, there must occur 

 some occasional concentrations of energy 

 and some sensible unmixings — some rever- 

 sals of the diffusion of gases, in ease indeed 

 the kinetic theories are themselves true. 

 And still more recently Arrhenius has sug- 

 gested that the nebulae may furnish the con- 

 ditions for the occasional if not the general 

 reversal of the second law of the theory of 

 energy. Of such speculations I can of 

 course form no judgment. They interest 

 us here only as examples of the logic of the 

 statistical view of nature. 



In sum, all these investigations have 

 tended to this general result: If a law of 

 the physical world does not appear con- 

 sistent with the mechanical view of nature 

 so long as you confine your attention to a 

 single system of bodies, whose individual 

 movements you follow and compute, this 

 law may still become perfectly intelligible 

 when viewed as the expression of the aver- 

 age behavior of a kinetic system complex 

 enough to give an opportunity for the ap- 

 plication of statistical laws, and for the use 

 of the conception of probability. 



VIII. THE CANONICAL FORM OF SCIENTIFIC 

 THEORIES 



All the foregoing instances may appear 

 to you merely to suggest that, in dealing 

 with mechanisms too complicated to be the 

 object of a direct computation, our igno- 

 rance may force us to make use of statistical 

 modes of computation. These statistical 

 methods, you may say, are convenient 

 devices whereby we neutralize, for certain 

 special purposes, the defects of our mechan- 

 ical knowledge. 



If the insurance actuaries — so you may 

 say — could use a sufficient knowledge of 

 the world's mechanism, they would com- 

 pute the precise time when each individual 

 man is to die, just as the astronomers com- 

 pute the eclipses. An almanac of mortality 

 would take the place of the present naut- 

 ical almanac. Everybody's funeral would 

 be announced, if that were convenient,- 

 years in advance ; and life insurance would 

 appear to be a blundering and awkward 

 substitute for scientific prediction. Because 

 and only because, as a fact, no knowl- 

 edge of the differential equations of the 

 precise movements of matter, and no exact 

 measurements of the accelerations or of the 

 other rates of change in these movements 

 gives us the power to predict the phenom- 

 ena of nature in their detail, including the 

 movements which determine life and death, 

 we are obliged to substitute a statistical 

 definition of the probable tendencies of a 

 definable proportion of great numbers of 

 men to die, in a way which varies with 

 their numbers and their ages, for the pre- 

 cise knowledge of the hour of each man's 

 death which we should all regard as a scien- 

 tific ideal, if we could know the mechanism 

 of life and death. The statistical view is a 

 mere substitute for a mechanical view 

 which our ignorance makes us unable to 

 use, in the individual case, with sufficient 

 accuracy. Such may be your comment. 



