# Back-of-the-Envelope Calculations: Earth History Timeline

## Summary

Question

The Earth is about 4.6 billion years old. Let's try to get a perspective on how long that really is. A roll of good quality toilet paper has 1000 squares. If the roll of toilet paper represents the entire history of the Earth, how many million years is represented by each square? Suppose you were to reel off the toilet paper. Where would some of the important events in the history of the Earth fall along the unrolled toilet paper?

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## Assessment

One square is about 4.6 million years. One good, arm-length pull on the roll reels off about 10 squares. Here are a few events:

10-12 arm-length pulls to get to oldest rocks on Earth
9 more pulls to first fossil evidence of life on Earth
30 more pulls to breathable atmosphere on Earth
37 more pulls to life with fossilizable hard parts
7 more pulls (66 squares) to first dinosaurs (Paleozoic is about 65 squares long)
4 more pulls (39 squares) to extinction of dinosaurs (Mesozoic is 39 squares long)
Cenozoic is remaining 14 squares
hominids (e.g., Lucy) roamed East Africa roughly 4" from end of last square
Pleistocene ended about 0.01" from end of last square
recorded human history fits easily in last 0.002-.003" of the last square

## References and Resources

This SERC page describes the use of Back of the Envelope Calculations

A View from the Back of the Envelope: This site has a good number of easy simulations and visualizations of back of the envelope calculations.

The Back of the Envelope: This page outlines one of the essays in the book "Programming Pearls" (ISBN 0-201-65788-0). The book is written for computer science faculty and students, but this portion speaks very well to back of the envelope calculations in general.