136 COLLIGATWE RELATIONS AND SCIENTIFIC LAWS 



greater number of initial conditions. With a statistical relation, on the 

 other hand, we may find that no such increase in the number of spec- 

 ifications of the state of the particular system suffices to increase the 

 reliability of our prediction of the one particular event. Dealing with 

 a statistical relation, we find only one way to improve our perform- 

 ance: we must limit our predictions to comparatively large numbers 

 of events, and the improvement in predictive reliability is in pro- 

 portion to the increase in the number of events. We are powerless to 

 predict the result of a single throw of a well-balanced die, but we 

 predict with confidence that in a long series of throws each of the 

 faces will turn up very nearly one-sixth of the time. 



Often a statistical relation leaves us profoundly unsatisfied: for 

 example, each man seeks one specific item of prediction no statisti- 

 cal table of life expectancies can ever yield him. In exactly the same 

 way, the Mendelian laws leave undetermined whether a given seed 

 —with a given genetic heritage— will produce a white or a pink 

 flower. But when we work with large numbers of seeds the laws 

 permit us to make excellent predictions of the ratio of white and 

 pink flowers. The table shows Mendel's own results for seven sets of 

 monohybridizations conducted with sweet peas. 



Total 



14949 



5010 



2.98 : 1 



The relation so clearly evident in the table is one of very broad 

 generality. It applies with equal facility to a great number of differ- 

 entiating characteristics displayed by a great variety of plants and 

 animals; and it furnishes a secure predictive guide of profound im- 

 portance to plant hybridists and others who work on a large scale. 



