200 THE PRINCIPLES OF SCIENCE 



Mendel's laws do not permit us to predict the characteristics of 

 the plant that will grow from a given seed of known hybrid pedigree. 

 This check does not much stir us: lacking knowledge of the exact 

 "state" of the seed concerned, of course we cannot predict. And in 

 microphysics, too, it was argued by Planck and others that a pre- 

 cisely analogous incapacity for prediction derives from a precisely 

 analogous deficiency in practice of knowledge conceivably attainable 

 in principle. Today most physicists reject this view, contending that 

 microphysical indeterminacy is no matter of what we don't know 

 but, rather, what we can't give meaning to even in principle. Precise 

 knowledge of the initial state of a microphysical system is impossible 

 for the simple reason that the defining parameters of state are irre- 

 duciblv statistical in nature. Thus statistical variation of results, 

 leaving the individual event substantially uncertain, arises not from 

 our ignorance of the initial state of the system, but from that state 

 as such. 



Let us concede this widely accepted opinion. What then? This 

 conception leaves entirely unshaken the dominance by determinism 

 of the kind of large-scale events already known reducible to deter- 

 minist order. Moreover, as Margenau observes, we can still say some- 

 thing meaningful about the initial states even of microphysical 

 systems. 



... if the condition of the particle is unspecifiable by statements say- 

 ing where it is and how fast it is going; if it is found sometimes here 

 and sometimes there, then an aggregate of measurements must be 

 performed, and the interesting infonnation is the relative frequency, 

 i.e., the probability, with which it is found here or there. It is difficult 

 to see why an observable should lack the fitness to serve as a variable 

 of state if its determination requires more than one measurement. 



Even at the microphysical level the initial state of a system can thus 

 be defined, in statistical terms, and so of course we can make predic- 

 tions for statistically large numbers of events. I have now no basis 

 for predicting when some one particular radioactive atom will decay. 

 But I easily predict, and with great exactness, the time required for 

 decay of some given fraction of a very large number of such atoms. 

 E\'en in microphysics, then, determinism is a far from total loss. 

 But what of causality: can we still aspire to know the how of micro- 

 physical phenomena involving parameters only statistically signifi- 



