SCIENCE (and common SENSE ) 53 



grasp of the concepts of weight and distance, which are not "given" 

 in experience, and we have further supposed their denotations at 

 once estabhshed with contrivance of auxihary experimental tools like 

 the meter stick and the equal-arm balance. A further element of 

 fantasy develops around just such tools. In a real inquiry, directed 

 toward the discovery of a relation not already known, the clean un- 

 complicated beam and fulcrum with which we began would appear 

 not at the beginning but very near the end. We specified as the beam 

 a light, straight, rigid body— e.g., a segment of a giraflFe's shinbone. 

 But this prescription is not "given" us. A priori we might as well have 

 picked the jawbone of an ass, a subject much less suitable for the dis- 

 covery of the law of the lever. Starting with a simple device, and 

 concepts, suitable for the solution of a problem already clearly for- 

 mulated, we began with more than half the battle already won. 



Perhaps the greatest element of fantasy in my sketch has yet to be 

 noted. I assumed measurements that lead to the law of the lever. 

 These were synthetic measurements; actual measurements do not 

 yield the simple equality of weight and distance ratios indicated in 

 the law. The weights are, after all, not the only weighty objects in 

 the system: the beam itself has weight. Neglecting this we neglect 

 an essential element of the situation. What to do? We cannot simply 

 introduce the highly sophisticated concept of a "center of gravity"; 

 this surely will not have occurred to us before we have even grasped 

 the law of the lever. Perhaps we might think to stipulate use of a very 

 light beam and very heavy weights. But then a dijfferent complica- 

 tion sets in when the beam begins to bend. 



Ultimately there are three major courses open to us. First: we 

 might complicate our statement of the law of the lever to allow for 

 the weight of the beam, its rigidity, the lengths by which it projects 

 on either side of the fulcrum, etc. Such an expedient is repugnant to 

 science and to common sense alike; we arrive then at an awkwardly 

 complex expression difficult to think about and difficult to use as a 

 predictive device. Second: we might say our results are "good 

 enough" to justify statement of the uncomplicated law of the lever 

 as a rough working rule. This would be the course followed in com- 

 mon sense. Third: we might adopt a course characteristically that of 

 science. We postulate an ideal lever: a straight, rigid, weightless 

 beam— essentially equivalent to a Euclidean straight line— borne fric- 

 tionlessly on an ideal fulcrum. Feeling we understand why our actual 



