REGULATING THE VERY LARGE SYSTEM 13/21 



achieves the whole selection in the fewest steps is selection by 

 successive dichotomies, so that the early selections are between 

 group and group, not between elements. This method is much 

 faster than the method of examining the A^ one by one, seriatim. 

 And if A'^ becomes very large, the method of selecting among groups 

 becomes almost incomparably faster. Lack of space prohibits an 

 adequate treatment of this important subject, but it should not be 

 left until I have given an example to show something of how 

 enormously faster the dichotomising method is. 



Let us consider a really big selection. Suppose that, somewhere 

 in the universe (as visible to the astronomer) there is a unique atom; 

 the selector wants to find it. The visible universe contains about 

 100,000000 galaxies, each of which contains about 100000,000000 

 suns and their systems; each solar system contains about 300000 

 bodies like the earth, and the earth contains about 1,000000,000000 

 cubic miles. A cubic mile contains about 1000,000000,000000,000000 

 dust particles, each of wliich contains about 10000,000000,000000 

 atoms. He wants to find a particular one! 



Let us take this as a unit of very large-scale selection, and call it 

 1 mega-pick; it is about 1 from 10 ''3. How long will the finding 

 of the particular atom take ? 



Two methods are worth comparing. By the first, the atoms are 

 examined one at a time, and a high-speed electronic tester is used 

 to examine a million in each second. Simple calculation shows that 

 the number of centuries it would take to find the atom would require 

 more than the width of this page to write down. Thus, following 

 this method dooms the selection to failure (for all practical purposes). 



In the second method he uses (assuming it possible) the method of 

 dichotomy, asking first: is the atom in this half or that? Then, 

 taking what is indicated, is it in this half or that?. And so on. 

 Suppose this could be done only at one step in each second. How 

 long would this method take? The answer is: just over four 

 minutes! With this method, success has become possible. 



This illustration may help to give conviction to the statement that 

 the method of selection by groups is very much faster than the 

 method of searching item by item. Further, it is precisely when the 

 time of searching item by item becomes excessively long that the 

 method of searching by groups really shows its power of keeping 

 the time short. 



13/21. Selection and reducibility. What does this mean when a 

 particular machine is to be selected? Suppose, for definiteness 

 that it has 50 inputs, that each input can take any one of 25 values, 



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