An Estimate of the Number of Shakespeare's Atoms
in a Living Human Being

I. The General Mathematical Analysis

With 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

It turns out that the oceans are the biggest component of E. See below. Hence, they have the greatest "diluting" effect on Shakespeare's atoms.
     A human being is created from the material in its environment, be it indirectly from the mother during the gestation period or directly from food, water and air after birth. During the rest of one's life, one continues to take in environmental atoms so that even if one started out with none of the playwright's atoms in one's body, they would be acquired through intake processes and accumulate. Let B be the number of atoms in one's body. Then the number N of atoms that start out in one's body that originated from Shakespeare is expected to be about

N = P B = S x B/E            (1)


     One might expect to accumulate even more Shakespearean atoms through breathing and consumption during one's life. However, this is not the case: Let rin be the rate at which atoms (of any type) are taken into the body in units of atoms per day. Likewise, let rout be the rate at which they are exiting. Then since a person's weight is more or less stable, it must be true that rin is rout. Let r denote this common rate.
     Let A be the total number of Shakespearean atoms that have accumulated in the body at some point during one's life. Then the probability p that an atom in the body originated from Shakespeare is

p = A/B

Hence, each day the number of his atoms exiting one's body is

rout p = r A/B            (2)

while the number entering is

rin P = r S/E            (3)

     At "equilibrium", the two rates in equations (2) and (3) are equal. This leads to

A = S x B/E

which is the same value of A as the starting number N. If at some point A becomes bigger than N, then the exodus of Shakespearean atoms as given by (2) is bigger than the intake of Shakespearean atoms as given by (3) and A will decrease until it becomes N. Likewise, if N is less than A, A will increase and, given enough time, will become equal to N.
     There is an easy way to understand this result. The ratio B/E is the probability that an atom in the environment comes from Shakespeare. However, since a person is part of the environment (in the sense in which the word is used in our analysis), the probability that an atom in a human body comes from Shakespeare must be the same and hence S/E too. The multiplying by the number of atoms B in a human body produces the result.

II. Estimating the Numbers

To 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 1023 atoms = NA = "Avogadro's number") weighs about 12 grams (the molar mass of a carbon atom), there are 80,000 x (6 x 1023)/12 atoms in a human body:

B = 4 x 1027

     The environment in which Shakespeare's atoms are dispersed consists of the troposphere (the lower portion of the atmosphere that makes up 75% of its weight), the oceans, and surface landmass and biota. Since the weight of the atmosphere is known to be about 5.3 x 1018 kilograms and each mole of atmospheric atoms weighs roughly 15 grams (the approximate average molar mass of nitrogen and oxygen atoms), there are 0.75 x (5.3 x 1021) x NA/15 = 1.6 x 1044 atoms in the troposphere. The mass of the oceans is 1.4 x 1024 kilograms, from which one deduces that there are about 1.4 x 1047 atoms there. Let H be the average depth of soil and biota in which the playwright's atoms might be imbedded on land. The number of atoms in this top-layer region of Earth is about 4 x 1044 x H/(one meter). Since H is likely to be a few meters, the number of atoms in the environment is dominated by those in the oceans:

E = 1.4 x 1047

     To determine S, we must estimate the three sources (i)-(iii) mentioned above. Suppose that 0.01% of the mass of the playwright's body escaped entombment and entered the environment. This loss corresponds to about 8 grams or 4 x 1023 atoms. The origin of these few grams could be evaporation of bodily fluids, the processing of decaying parts by bacteria or the breaking off of skin and hair and other surface tissues before the bard's burial. One might even perhaps throw in the contribution coming from one last expiration of air.
     The value for source (ii) is estimated as follows. Assume that somewhat less than a liter of air enters and exits the lungs during each breath. Then, since one-quarter of this actually exits or enters the body (the nitrogen is immediately exhaled), one can determine that about 1.25 x 1022 atoms are exchanged during one breath.
     Like all of us, William Shakespeare did a lot of breathing during his lifetime. He died at the age of 52. If he exhaled 15 times a minute, he breathed about 400 million times during his lifetime! (If that seems like a large number, then do the calculation.) Therefore, the literary master exhaled about 5 x 1030 atoms during his life. In other words, a lot more than just well-constructed sentences came out of the playwright's mouth.
     Now we come to the messy part of the analysis: source (iii). A human eats and drinks about 2 kilograms of food and fluids daily. That translates into 1026 atoms consumed each day. A person also loses about the same number of atoms through perspiration, urination and defecation. During Shakespeare's 52-year-long life, he shed almost 2 x 1030 atoms by these means.
     Adding the above three numbers, one gets

S = 7 x 1030

So there are this many of Shakespeare's atoms dispersed throughout the environment. The literary master certainly has made his presence felt. To be or not to be – that used to be the question. Now the question is "where am I?" "Am I here or there?"
     Plugging these estimates into equation (1), one finds

N = 2 x 1011

Thus there are about 200 billion Shakespearean atoms in each of us. We all have quite a bit of Shakespeare in us. Of course, if some of the bard's waste did not disperse, higher concentrations of his atoms are likely to be located in the United Kingdom. Hence, Brits can claim to have more Shakespeare in them, which seems reasonable from social and biological points of view anyway and should make them jolly happy. Not to intentionally deflate their egos, however, pigs and other grazing animals of the United Kingdom should be able to claim to have even more of the Shakespeare's atoms in them. And of course, a few choice atoms do not a genius make.

III. Conclusions, Comments and Other Interesting Facts

It straightforward to determine the number of Shakespeare's atoms that enter a person each day through breathing, drinking and eating. The result is almost 20 billion. That means that, even if one's body were cleansed of the playwright's atoms, it would only take about 10 days to return to "normal." If you live to 75 years, some 500 trillion of his atoms enter you during your life. After we've lived a while, our direct knowledge of Shakespeare is rather substantial, which proves the statement that education is a lifelong endeavvor. The only reason why you have just 200 billion of his atoms in you is that you are also losing his atoms at virtually the same rate as you are gaining them, as the analysis on equilibrium in Part I above makes clear.
     More than half the atoms of the literary master are acquired through breathing. Time for English exercises: Breathe in, hold it there, enjoy the Shakespeare, breathe out. Aaaah. Repeat!
     The number of "dead Shakespearean atoms," that is, atoms only from source (i), in each of us is still substantial. Using 4 x 1023 for S, gives about 10,000 atoms. Of course, this result is sensitive to the number of grams of Shakespeare's body that escaped entombment. If the 8 grams is changed to 80 grams, then we have 100,000 of his dead atoms in us and if it is 0.8 grams, we only have 1,000.
     Our analysis not only applies to Shakespeare but also to anyone (and any living thing including animals, insects and microbes) who has previously died. So there's also a little Buddha in all of us. That should all make us feel wiser. So there's a little ant in us and that should make us feel humbler. What's bad, however, is that we all have some Hitler in us too (God darn us). So the evil cometh with the good. And there's no use in trying to cleanse your body of Hitler either: As the above analysis shows, in about 10 days he'll be back.
     There's more "bad news." About one in seven of the Shakespearean atoms in your body originated from his excrement. And if you respond, "Hey, I don't want those; I'm getting some of the worse part of Shakespeare," you have no choice. You're stuck with them; it's tough luck. Of course, if you react this way, you're probably the type of person for whom English literature leaves a bad taste in the mouth.
     Actually, the above conclusions are a little unfair. Molecules and atoms in the biotic environment are recycled so much that any one particular atom cannot be attributed to any particular person or specific source type.
     This concludes the analysis. Now if we could only figure out how those fanatically typing monkeys managed to reproduce Hamlet.


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