Foreknowledge by Joel Hayes - Library of Theology

The exceeding smallness of the lack of certainty here expressed is beyond all conception. To gain
some idea of it compare the smallest animalcule a million of which may have abundance of room to live and
sport in a drop of water, with the volume of the sun and all the visible fixed stars and all the space between
them. We do not know the distance of the farthest fixed star visible to the naked eye, but we suppose in this
comparison that it is so great that it would take light 50,000 years to reach the earth, traveling at the rate of
185,000 miles in a second. Suppose all the space extending from the earth for this distance in every
direction to be filled with matter. Then think if possible how much smaller than this large mass is the
animalcule. Repeat this; that is, suppose another large mass as many times larger than this mass, the
volume of the star-space, as this mass is larger than the animalcule. To gain some conception of the
magnitude of this second mass, suppose a point moving so slowly that it would take it 50,000 years to
traverse the semi-diameter of the smallest animalcule. Then imagine, if possible, how long it would take
such a slow-moving body to move from the earth to the farthest fixed star. It would take light with its
immense velocity just that length of time to traverse the semi-diameter of this second large mass. And yet
the lack of certainty expressed by a fraction, numerator one and denominator 161 figures, is more than a
million times smaller compared with unity than the animalcule is, compared with this mass. That is, taking
this large mass to represent certainty the probability of the righteousness or wickedness of at least 100 out
of 1,000 on the basis of 1/2 would be represented by the same mass with a millionth part of the animalcule
taken from it.
This for the probability of the righteousness or wickedness of at least 100 out of 1,000. To express
the lack of certainty of that of at least 100,000 out of 1,000,000, we should have to repeat this process
(supposing a third large mass as many times larger than the second as the volume of the star-space is
larger than the animalcule, then a fourth mass the same number of times larger than the third, etc.) 2,076
times, and then compare this last mass thus conceived of with less than
1/10,000,000,000,000,000,000,000,000,000 of the animalcule; while to express that of at least 1,000,000
out of 10,000,000 the process would have to be repeated 20,763 times and the mass thus imagined
compared with a part of the animalcule 1,000,000,000,000,000,000,000 times smaller still. We do not much
blame Dr. Whedon for gracing such probabilities as these with the name of certainties. They are not perfect
certainties, however; they lack just a little.
On the same basis, the chances of the righteousness or wickedness of at least one out of four are
15 in 16, those of at least 25 out of 100 are all but about 1 in 10,596,000. The lack of certainty of that of at
least 250 out of 1,000, numerator one and denominator 59 figures; 2,500 out of 10,000, numerator one and
denominator 574 figures; 25,000 out of 100,000, numerator one and denominator 5,703 figures; 250,000
out of 1,000,000, numerator one and denominator 57,000 figures; 2,500,000 out of 10,000,000, numerator
one and denominator 569,980 figures. To express the last two lacks of certainty, the process in the
preceding paragraph would have to be repeated respectively 740 and 7,4000 times, and the mass thus
imagined compared with less than the animalcule. 278
On the same basis, the chances of the righteousness or wickedness of at least one out of three are
seven in eight; those of at least 34 out of 100 are about 539 in 540; the lack of certainty of that of at least
334 out of 1,000, numerator one and denominator 28 figures; 3,334 out of 10,000, numerator one and
denominator 252 figures; 333,334 out of 1,000,000, numerator one and denominator 24,920 figures;
3,333,334 out of 10,000,000, numerator one and denominator 249,180 figures.
On the same basis, the chances of the righteousness or wickedness of at least 2 out of 5 are 13 in
16; those of at least 40 out of 100 are about 51 in 52; those of at least 400 out of 1,000 are all but about 1
in 22,390,000,000; the lack of certainty of that of at least 4,000 out of 10,000, numerator one and
denominator 44 figures; 40,000 out of 100,000, numerator one and denominator 417 figures; 400,000 out
of 1,000,000, numerator one and denominator 4,143 figures; 4,000,000 out of 10,000,000, numerator one
278
The process repeats every 77 figures.
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