572 Electronic Computers /3! :2 



If basic differential equations can be developed (which is true in the 

 foregoing examples), then in principle one can sit down with a pencil 

 and paper and solve by numerical methods each specific problem. In 

 practice, this is not too easy because there are often certain parameters 

 (such as kinetic rate constants) for which values must be chosen in order 

 to make the theory fit the data. If it takes two years to solve the problem 

 for each choice of parameters, it might take several human half-lives to 

 find the answer. Some problems which are only a little too time-con- 

 suming for pencil and paper solutions can be hastened by the use of 

 mechanical aids such as slide rules, desk calculators, and tables of 

 logarithms. However, the mathematics of most problems amenable to 

 solution with desk calculators has been worked out rather thoroughly. 

 The most challenging problems remaining are too complex for these 

 methods. All of the problems referred to in the previous paragraph 

 would require many human lifetimes, if attacked with a desk calculator. 



Automatic computational devices, which are far more rapid than the 

 desk calculator, have become important physical tools used in biological 

 research. There are two general types of automated computers. One 

 type, the analog computer, solves problems by analogies between the 

 elements of the real physical system and other physical variables, such 

 as the potential across certain resistors or the torques on various shafts. 

 The other type, the digital computer, carries out the same types of 

 operations as does a desk calculator (of course, very much more rapidly) ; 

 in addition, the digital computer can make logical choices. 



2. Analog and Digital Computers 



Analog computers operate by setting up analogies to physical problems. 

 Many such problems occurring within the realm of biophysics and 

 physiology cannot be solved mathematically in an exact closed form. 

 Many of the analog computers used in physiological research involve 

 complex physical equipment combined in imaginative fashions; as such, 

 they belong in the part of biophysics concerned with physical techniques 

 used in biology. 



The use of analogies in biology is by no means restricted to analog 

 computers. For example, temperatures are measured in terms of the 

 length of a column of fluid. And pressures are often measured in terms 

 of the height of a column of mercury. In analog computers, this process 

 is carried slightly further; completely unrelated variables such as the 

 concentration of hydrogen peroxide and the voltage across a given 

 resistor are said to be analogs. In this case, the circuit is so designed 



