7/3 DESIGN FOR A BRAIN 



(6) A stone, falling through the air into a pond and to the 



bottom, would meet resistances varying similarly. 



(7) The temperature of a match when it is struck changes in 



step-function form. 



(8) If strong acid is added in a steady stream to an un- 



buffered alkaline solution, the pH changes in approxi- 

 mately step-function form. 



(9) If alcohol is added slowly with mixing to an aqueous 



solution of protein, the amount of protein precipitated 

 changes in approximately step-function form. 



(10) As the pH is changed, the amount of adsorbed substance 



often changes in approximately step-function form. 



(11) By quantum principles, many atomic and molecular 



variables change in step-function form. 



(12) The blood flow through the ductus arteriosus, when ob- 



served over an interval including the animal's birth, 

 changes in step-function form. 



(13) The sex-hormone content of the blood changes in step- 



function form as an animal passes puberty. 



(14) Any variable which acts only in ' all or none ' degree shows 



this form of behaviour if each degree is sustained over a 

 finite interval. 



7/3. Few variables other than the atomic can change instan- 

 taneously ; a more minute examination shows that the change 

 is really continuous : the fusing of an electric wire, the closing of a 

 switch, and the snapping of a piece of elastic. But if the event 

 occurs in a system whose changes are appreciable only over some 

 longer time, it may be treated without serious error as if it oc- 

 curred instantaneously. Thus, if x — tanh t, it will give a graph 

 like A in Figure 7/3/1 if viewed over the interval from t = — 2 

 to t = +2. But if viewed over the interval from t — — 40 to 

 t = -|- 40, it would give a graph like B, and would approximate 

 to the step-function form. 



In any experiment, some ' order ' of the time-scale is always 

 assumed, for the investigation never records both the very quick 

 and the very slow. Thus to study a bee's honey-gathering flights, 

 the observer records its movements. But he ignores the movement 

 caused by each stroke of the wing : such movements are ignored 

 as being too rapid. Equally, over an hour's experiment he ignores 



82 



