THEORIES AND MODELS 249 



as delusive (e.g., is the something that travels a wave or a particle?), 

 as well as to questions obviously nonsensical {e.g., does the some- 

 thing put on its rubbers before coming out?). We can, of course, 

 found a science of geometric optics on a much less ambitious prem- 

 ise: In a homogeneous medium an illuminated point and a point-light 

 are joined by a straight line. The formally superfluous explanation is 

 then suppressed, and with it the delusive and nonsensical questions 

 as well. But alas, the valuable first question, and others like it, are 

 also suppressed: all these questions are suggested by the same ex- 

 planation. 



Torricelli's model is "superfluous." For the correlation of his data 

 a less speculative, more purely descriptive premise would have suf- 

 ficed: e.g., bodies behave as though subject to a force approximating 

 one ton per square foot of surface in contact with air. Torricelli's sea- 

 of-the-air analogy was then formally superfluous, a "pointless" effort 

 to explain the origin of the premised force.* But the heuristic power 

 of Torricelli's concept derives entirely from the selfsame analogy. 

 Only through that analogy does Pascal come to conceive the Puy de 

 Dome experiment. If we live at the bottom of a sea of the air, ascent 

 through that sea should bring us to regions of progressively dimin- 

 ishing pressure. The experiment leads to genuinely new knowledge: 

 we find a relation between altitude and atmospheric pressure earlier 

 unsuspected. The idea of an atmospheric sea further suggests the 

 possibility of pumping air much as we pump water. Thus efforts to 

 produce a laboratory vacuum derive directly from Torricelli's anal- 

 ogy, and experiments on and in vacua yield a rich harvest of new 

 discoveries. Of course the analogy could also produce misconcep- 

 tions: taking it too literally, Pascal is led to ask at what altitude one 

 will emerge through a clearly defined "surface" of the atmospheric 

 sea. But the futility of this question is obviously of trivial importance 

 compared to the multitude of worthy questions evoked by the same 

 model— all of which are lost if the model is suppressed. 



Basis for the development of aerostatics, the hydrostatic analogue 



* Even if only an explanation, may this not still be essential? Without it would 

 Torricelli (or anyone else) have considered for even a moment a premise that 

 demands each of us to assume himself wholly unaware of a total compressive force 

 of some 15 tons exerted on the surface of his body? No small implausibihty in- 

 deed! Given Torricelli's analogy we at least see some way around the difficulty: 

 after all, fish live and move at substantial depths in water, apparently unaffected 

 by the great pressures to which they are there subject. 



