# Counting Critters

This picture allows us to set a lower bound on the number of creatures that ever lived of \~4.

We recently had a big book sale [1] here in town where books were being
sold for about a quarter. Needless to say, I bought far more than I’ll
probably ever need or read. One of the books I bought was called
*General Paleontology* by A. Brouwer [2]. Anyways, I didn’t really make
it too far in the book. In fact, I only made it to the first sentence of
the second paragraph of the first chapter, when I encountered this line:
*“The number of individuals which has populated the Earth since life
began is beyond estimation.”* * Horse feathers, I say! Horse Feathers!
The number of things that ever lived may very well be unknowable*, but
it’s certainly not beyond estimation. So below, Alemi and I each provide
an estimate for the total number of creatures that have ever lived on
Earth. We flipped a coin and I lost, so I guess I’ll go first. My
estimation will be a genuine guess-y kind of estimate that doesn’t draw
too heavily on too many physical considerations. Instead, I will
formulate a series of assumptions and base my final answer on that. So
assuming my assumptions are valid, the answer should give a reasonable
estimate to the total number of creatures that have ever lived. My
assumptions are as follows: (1) The number of individuals that have ever
lived will be almost entirely dominated by the number of bacteria that
have ever lived on Earth. So to leading order, all the life that has
ever lived on Earth is bacteria (or something similar). (2) Life began
at some time, T, in the past and immediately spread to all places on
Earth. Hey, man, it’s the power of geometric progression! (3) The
majority of life is found within h = 1 m from the surface of water. I
picked this number since it’s roughly (order of magnitude) how far down
I can see in really clear water. Most of the life will be photosynthetic
and thus need a fair amount of sunlight. (4) The number density of
organisms in water is n \~ 10^5. I have no real justification for this.
(5) The average lifetime of an organism is t \~ 1 hr. Alright, so if
these assumptions are valid (a big if [3]), then the following
prediction should be fairly accurate. So the total volume in which these
creatures may live is just the shell of the Earth down to about a meter:

*all*the moments. So I will take the total number of “generations” to be the time life has been around divided by the average lifetime of a given organism. Putting this all together gives

Click for the full Jimmy Johns experience

To explain these scribbles, I now cede the floor (and the mic) to Alemi.
[ SEAMLESS TRANSITION ] So, when Corky posed this question to me while
we ate some tasty sandwiches, another approach came to mind. Namely, I
wanted to try to estimate the number of critters that have ever lived by
putting some kind of energy bound on the number. Ultimately, all
critters come from the sun. That is, all life on Earth is only able to
exist in so much as it consumes energy, and for almost all life
[ignoring the under ocean heat vent guys], the energy they consume, one
way or another comes from the sun. So, let’s estimate the number of
critters in three parts (1) We need the energy the Earth recieves from
the sun. (2) We need to estimate the energy density of life (3) These
two things, combined with a characteristic length or volume scale for a
critter would enable us to figure out the rate at which the Earth could
produce critters. (4) Assuming this rate and a time scale for how long
life has been around on the Earth would give us a total number of
critters. Let’s begin (1) Energy from the sun. Corky and I happen to
know that the solar flux on the sun is roughly 1000 W/m^2. Multiplying
this by half the surface area of the earth gives us a rough total solar
flux

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