It’s difficult to visualize big numbers. As a professor, I throw out big numbers to my students all the time, but without something to visualize, they are really hard to appreciate. For example, simple cells formed 3,600,000,000 years ago. That’s three billion, six hundred million. How can we picture that?

I tried to think of something big that people had some experience with, and thought of a swimming pool. If the water in a pool represented the time since the beginning of life, when simple cells first developed, we can look at more recent events and ask how much pool water it takes to represent the amount of time since they happened. We can do some quick calculations to give us a feeling for the vastness of time.

If an average pool holds 375,000 liters of water, human evolution diverged with chimpanzee evolution between 5 and 7 million years ago, which is about 520 liters of water. That's about two big bathtubs.

Anatomically modern humans appeared about 200,000 years ago, which is only 20 liters of water, or about 10 two-liter bottles of soda's worth.

The dawn of agriculture was about 10,000 years ago, which is just one liter or water.

A human lifespan of 80 years is a mere two teaspoons of water in the great big pool of life.

Think about that as you swim this summer.

Pictured: A pool at the University of Stirling. From Wikimedia Commons

Here is the python code, if anybody wants to play with it:

# Calculator for how much, out of a pool of water, is human history.

# some numbers

# Simple cells formed 3.6 billion years ago
SimpleCells = 3600000000.0

# Our divergence from chimps happened about 5 to 7 million years ago.
ChimpDivide = 5000000.0

# Anatomically modern humans came into existence about 200k years ago
ModernHumans = 200000.0

# The dawn of agriculture happened about 10k years ago
Agriculture = 10000.0

# Typical swimming pools are about 25m x 10m x 1.5m deep.
# One cubic meter of water has 1000 liters
Pool = 375000.0

# Human lifespan
lifespan = 80

print "If a typical swimming pool held water (", Pool, " litres) representing time since simple cells developed,"
print "then how much water in it would represent (in litres)...\n"

print "\n"
print "the time since the human line diverged from the chimapzee line (", ChimpDivide, " years ago.)"
x = (ChimpDivide * Pool) / SimpleCells
print x

print "\n"
print "the time since anatomically modern humans appeared (", ModernHumans, " years ago.)"
x = (ModernHumans * Pool) / SimpleCells
print x

print "\n"
print "the time since the dawn of civilization (agriculture, ", Agriculture, " years ago)?"
x = (Agriculture * Pool) / SimpleCells
print x

print "\n"
print "human lifespan ( ", lifespan, " years ago)?"
x = (lifespan * Pool) / SimpleCells
print x

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