make sure that the computing units are as numerous as possible, let's suppose that each one is no larger than the least voluminous object known, the single neutron.
How many computing units would the machine contain?
A neutron is only one-ten-trillionth of a centimeter in diameter. One cubic centimeter—which is equal to only one-sixteenth of a cubic inch—will, therefore, contain 1013 x 1013 x 1013 or 1039 neutrons, if these were packed in as tightly as possible. (We assume the neutrons to be tiny cubes rather than tiny spheres, for simplicity's sake.)
Now light travels at the rate of 3 x 1010 centimeters per second. There are about 3.16 x 108 seconds in a year. A light-year is the distance traversed by light in one year, and is, therefore, 3 x 1010 x 3.16 x 108 or about 1019 centimeters in length. Our computing machine which is ten billion (1010) light-years along each edge is, therefore, IO29 centimeters long each way and its volume is 1029 x 1029 x 1029 or 1087 cubic centimeters all told. Since each cubic centimeter can contain 1039 neutrons, the total number of neutrons that can be packed into a cube a thousand times the volume of the known universe is 1087 x 1039 or 10126.
But these "neutrons" are computing units, remember. Let us suppose that each computing unit is a really super-mechanical job, capable of testing a billion different amino-acid combinations every second, and let us suppose that each unit keeps up this mad pace, unrelentingly, for three hundred billion years.
The number of different combinations tested in all that time would be about 10155.
This number is still approximately zero as compared with the hemoglobin number. In fact, the chance that the right combination would have been found in all that time would be only 1 in 4 x 10464.
But, you may say, suppose there is more than only one possible hemoglobin combination. It is true, after all, that the hemoglobin of various species of animals are distinct in their properties from one another. Well, let's be unfailingly generous. Let's suppose that every hemoglobin molecule that ever possibly existed on Earth is just a little different from every other. It would then be only necessary for our giant computing machine to find any one of 1050 possibilities. The chances of finding any one of those in three hundred billion years with 10126 units each turning out a billion answers a second is still only 1 out of 10414.
It would seem then that if ever a problem were absolutely incapable of solution, it is the problem of trying to pick out the exact arrangement of amino acids in a protein molecule out of all the different arrangements that are possible.
And yet, in the last ten years, biochemists have been making excellent
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