154 ANNUAL REPORT SMITHSONIAN INSTITUTION, 19 32 



of physical quantities we are imparting knowledge as to the response 

 of various external indicators to its presence and nothing more. 

 A knowledge of the response of all kinds of objects would determine 

 completely its relation to its environment, leaving only its un-get- 

 at-able inner nature which is outside the scope of physics. Thus if 

 the system is really isolated so that it has no interaction with its 

 surroundings, it has no properties belonging to physics but only an 

 inner nature which is beyond physics. So we must modify the 

 conditions a little. Let it for a moment have some interaction with 

 the world exterior to it; the interaction starts a train of influences 

 which may reach an observer; he can from this one signal draw 

 an inference about the system, i. e., fix the value of one of the symbols 

 describing the system or fix one equation for determining their values. 

 To determine more symbols there must be further interactions, one 

 for each new value fixed. It might seem that in time we could fix 

 all the symbols in this way so that there would be no undetermined 

 symbols in the description of the system. But it must be remem- 

 bered that the interaction which disturbs the external world by a 

 signal also reacts on the system. There is thus a double conse- 

 quence; the interaction starts a signal through the external world 

 informing us that the value of a certain symbol p in the system is 

 Pxi and at the same time it alters to an indeterminable extent the 

 value of another symbol q in the system. If we had learned from 

 former signals that the value of q was q^^ our knowledge will cease 

 to apply, and we must start again to find the new value of q. Pres- 

 ently there may be another interaction which tells us that q is now 

 ^2; but the same interaction knocks out the value p^ and we no 

 longer know p. It is of the utmost importance for prediction that 

 a paired symbol and not the inferred symbol is upset by the inter- 

 action. If the signal taught us that at the moment of interaction 

 p was px but that p had been upset by the interaction and the value 

 no longer held good, we should never have anything but retro- 

 spective knowledge — like the chemistry lecturer whom I described. 

 Actually we can have contemporaneous knowledge of the values 

 of half the symbols, but never more than half. We are like the 

 comedian picking up parcels; each time he picks up one he drops 

 another. 



There are various possible transformations of the symbols and the 

 condition can be expressed in another way. Instead of two paired 

 symbols, the one wholly known and the other wholly unknown, we 

 can take two symbols each of which is known with some uncertainty ; 

 then the rule is that the product of the two uncertainties is fixed. 

 Any interaction which reduces the uncertainty of determination of 

 one increases the uncertainty of the other. For example, the posi- 



