THE TEN PILLARS 9 



For subsequent use in the introductory phases of biophysics we now de- 

 fine ten conveniently grouped concepts. Since most of this is review, the 

 presentation is cryptic. Since only the language and the logic, and not the 

 operations, are necessary for future use in this book, we follow the principle 

 so aptly stated by Lord Dunsany: "Logic, like whiskey, loses its beneficial 

 effect when taken in too large quantities." 



THE TEN PILLARS 



1. The Variable 



If so'me entity — it may be a physical property or some other combination 

 of length, mass and time — changes under the influence of a force, that entity 

 is called a variable. There are dependent and independent variables in nature. 

 The value of the independent can be chosen at random, but any variable de- 

 pendent upon that choice is thereby fixed in value. 



The ideal gas law, PV = nRT, illustrates this. In a closed vessel of vol- 

 ume V, containing n moles of gas, the independent variable (on the right- 

 hand side of the equation by convention) is the temperature, T. The tem- 

 perature can be chosen at will. However, once T has been fixed, the pres- 

 sure, P, dependent upon T in this case for its value, has also been fixed. 



2. The Function 



Further, it can be said that P is proportional to T, or varies directly as 7", or 

 P & T; that P vanes inversely as V, or is proportional to 1/F, or P <* \/V. 

 The constant number, R, which serves to equalize the dimensions or units on 

 the two sides, never varies with experimental conditions, contains all our 

 further ignorance of this relationship expressing the equivalence of thermal 

 and mechanical energy, and is one of the universal constants of nature, (7r, the 

 value of the quotient of the circumference of a circle and its diameter is 

 another example). There are constants other than the universal ones — they 

 are simply variables held constant over the course of a particular changing 

 situation. V in the preceding paragraph is an example. They are called 

 "constants of the system." 



A relationship between two variables, such that a choice of a value for one 

 fixes the value of the other, is called a functional relationship. In general terms, 

 if we do not know the exact relationship between two variables, y and x say, 

 but we know that one exists, we can say y varies with x, or y is a junction of x, 

 or in shorthand (ormy = f(x). 



Nowjy = f(x) is so general that it could describe any functional relation- 

 ship between y and x. In nature we find both rational and transcendental 

 functions. Rationals can be expressed as a sum of simple terms, transcen- 

 dental cannot. Three examples of the former functions are: (a) linear, 



