192 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1950 



answer depends on the nature of the rewards. Three different kinds 

 of reward will illustrate the three kinds of statistics. 



(a) The two rewards are two memorial coins with portraits of New- 

 ton and Shakespeare respectively. The teacher may give Newton 

 either to Tom or to Dick or to Harry, and Shakespeare either to Tom 

 or to Dick or to Harry. Thus there are 3 times 3, that is 9, different 

 distributions (classical statistics). 



(b) The two rewards are two shilling-pieces (which, for our pur- 

 pose, we must regard as indivisible quantities) . They can be given to 

 two different boys, the third going without. In addition to these three 

 possibilities there are three more: either Tom or Dick or Harry re- 

 ceives 2 shillings. Thus there are six different distributions (Bose- 

 Einstein statistics). 



(c) The two rewards are two vacancies in the football team that is 

 to play for the school. In this case two boys can join the team, and 

 one of the three is left out. Thus there are three different distribu- 

 tions (Fermi-Dirac statistics). 



Let me mention right away: the rewards represent the particles, 

 two of the same kind in every case ; the boys represent states the par- 

 ticle can assume. Thus, "Newton is given to Dick" means : the par- 

 ticle Newton takes on the state Dick. 



Notice that the counting is natural, logical, and indisputable in 

 every case. It is uniquely determined by the nature of the object — 

 memorial coins, shillings, mejnberships. They are of different cate- 

 gories. Memorial coins are individuals distinguished from one an- 

 other. Shillings, for all intents and purposes, are not, but they are 

 still capable of being owned in the plural. It makes a difference 

 whether you have 1 shilling, or 2 or 3. There is no point in two boys 

 exchanging their shillings. It does change the situation, however, 

 if one boy gives up his shilling to another. With memberships, neither 

 has a meaning. You can either belong to a team or not. You cannot 

 belong to it twice over. 



Experimental evidence proves that statistical counts referring to 

 elementary particles must never follow the pattern (a), but must fol- 

 low either (6) or (c). Some hold that for all genuinely elementary 

 particles (<?) is competent. Such particles, electrons for instance, cor- 

 respond to membership in a club; I mean to the abstract notion of 

 membership, not to the members. Any person eligible to membership 

 in that club represents a well-defined state an electron can take on. 

 If the person is a member, that means there is an electron in that par- 

 ticular state. According to Pauli's exclusion principle, there can 

 never be more than one electron in a particular state. Our simile 

 renders this by declaring double membership meaningless — as in most 

 clubs it would be. In the course of time the list of members changes. 



