# Human scale

I’ve always been intrigued by how long we live compared to the age of the universe.  At 14 billion years, the universe is only a factor of $10^8$ older than a long-lived human.  In contrast, it is immensely bigger than us.  The nearest star is 4 light years away, which is a factor of $10^{16}$ larger than a human, and the observable universe is about 25 billion times bigger than that.    The size scale of the universe is partly dictated by the speed of light which at $3 \times 10^8$ m/s is coincidentally (or not) the same order of magnitude faster than we can move as the universe is older than we live.

Although we are small compared to the universe, we are also exceedingly big compared to our constituents. We are comprised of about $10^{13}$ cells, each of which are about $10^{-5}$ m in diameter.  If we assume that the density of the cell is about that of water ($1 {\rm g/ cm}^3$) then that roughly amounts to $10^{14}$ molecules.  So a human is comprised of something like $10^{27}$ molecules, most of it being water which has an atomic weight of 18.  Given that proteins and organic molecules can be much larger than that a lower bound on the number of atoms in the body is $10^{28}$.

The speed at which we can move is governed by the reaction rates of metabolism.  Neurons fire at an average of approximately 10 Hz, so that is why awareness operates on a time scale of a few hundred milliseconds.  You could think of a human moment as being one tenth of a second.  There are 86,400 seconds in a day so we have close to a million moments in a day although we are a sleep for about a third of them.  That leads to about 20 billion moments in a lifetime. Neural activity also sets the scale for how fast we can move our muscles, which is a few metres per second.  If we consider a movement every second then that implies about a billion twitches per lifetime.  Our hearts beat about once a second so that is also the number of heart beats in a lifetime.

The average thermal energy at body temperature is about $10^{-19}$ Joules, which is not too far below the binding energies of protein-DNA and protein-protein interactions required for life.   Each of our  cells can translate about 5 amino acids per second, which is a lot of proteins in our lifetime.  I find it completely amazing that  a bag of $10^{28}$ or more things, incessantly buffeted by noise, can stay coherent for a hundred years.  There is no question that evolution is the world’s greatest engineer.  However, for those that are interested in artificial life this huge expanse of scale does pose a question –  What is the minimal computational requirement to simulate life and in particular something as complex as a mammal?  Even if you could do a simulation with say $10^{32}$ or more objects,  how would you even know that there was something living in it?

The numbers came from Wolfram Alpha and Bionumbers.