An Estimate of the Number of Shakespeare's Atoms

in a Living Human Being

I. The General Mathematical Analysis

W ith reasonable assumptions, it is possible to estimate the number of atoms in one's body that originated from within William Shakespeare. There are three sources of Shakespearean atoms: (i) those produced at the time of his death, (ii) those breathed out during his lifetime and (iii) and those that exited in the form of solid, liquid and gaseous waste (Please avoid imaginative thought here) while he was alive. It turns out that source (i) is considerably smaller than sources (ii) and (iii). Let S be the total number of atoms that originated from Shakespeare and entered the environment.

Most of these source atoms are rapidly dispersed. For example, winds and weather thoroughly mix atmospheric molecules around the world within a few months. Any atoms entering the ocean are probably thoroughly distributed within a few years. The same is true of waste that is processed by microbes. Rain, evaporation and other natural processes also lead to molecular exchanges among oceans, land and air.

Let E be the total number of atoms in the environment. Then the probability P that such an atom came from Shakespeare is

P = S/E

N = P B = S x B/E (1)

in

out

in

out

p = A/B

r out p = r A/B (2)

r in P = r S/E (3)

A = S x B/E

II. Estimating the Numbers

T o determine N, we need estimates for S, B and E. Take the mass of a human to be about 80 kilograms. Since each mole (6 x 10 23 atoms = N A = "Avogadro's number") weighs about 12 grams (the molar mass of a carbon atom), there are 80,000 x (6 x 10 23 )/12 atoms in a human body:

B = 4 x 10 27

18

21

A

44

24

47

44

E = 1.4 x 10 47

23

22

30

26

30

S = 7 x 10 30

N = 2 x 10 11

III. Conclusions, Comments and Other Interesting Facts