Earth Day

Significant and Insignificant

April 22nd is Earth Day. Since there is no practical way to determine otherwise, let's call it Earth's birthday. The best scientific estimate for the age of the earth is about 4.55 billion years, plus or minus 70 million years. This estimate was calculated from the work of an Iowan, Clair Patterson, in 1953. See the Bill Bryson book, “A Short History of Nearly Everything” (p.149-160) for more information.

From what I can tell, what we would call human beings (homo sapiens) have existed on the earth for about the last 250 000 years. Of course this is a rough estimate but it gives the opportunity to do some interesting math. Large numbers are not easily understood by anyone. In one of my earliest posts (October 30th, 2007), I mentioned that one million seconds is about 11.5 days while one billion seconds is about 31.7 years.

Using the above numbers, 4.55 billion years for the age of the earth and 250 000 years for the time human beings (homo sapiens) have been on earth, there are a few ways to show the relative insignificance of man's time on earth compared to the time that earth has been in existence. One way to do this is to compress the entire age of earth into one 24 hour day. Based on that, how long have human beings existed on earth?

The easiest way to solve this would be to use a proportion:

4 550 000 000 years : 250 000 years = 24 hours : X hours

Solving for X we get about .001318681319 hours

Multiply that by 60 min./1 hour and by 60 sec./ 1 min. (which are forms of one)
and we get about 4.747252747 seconds.

Therefore in the 24 hour history of earth, human beings have been on the scene about the last five seconds. Most people would find that pretty stunning.

Another interesting thing to do with the information is more appealing to students on a visual level. Assume that the average sized man has a wing span (arms stretched out wide), from the tip of the fingernail on the middle finger of one hand to the tip of the fingernail on the middle finger of the other hand, of six feet or 72 inches. Assume that length of 72 inches is all of earth's history. What part of that length would represent the length of human beings time on earth? Again set up a proportion:

4 550 000 000 years : 250 000 years = 72 in. : X in.

Solving for X we get about .003956043956 inches which is very close to .004 inches, or about 1/250 of an inch. In the Bryson book (p.337), one of the authors he cites says, “... a single stroke with a medium-grained nail file [would] eradicate all of human history.”
That is a pretty good visual for students to see that the 1/250th of an inch scraped off one of those middle finger nails would represent all of human beings' time on earth.

Another visual way to look at that would be to imagine that the 4.55 billion years of earth be represented by a 100 yard football field. What would the 250 000 years of human beings be on that field?

4 550 000 000 years : 250 000 years = 100 yards : X yards

Solving for X we get about .005494505495 yards. Multiply by 36 in./1 yard you get about .197802197 inches or about 1/5th of an inch. Imagine looking at a football field from one goal line to the other goal line and realizing that the time of human beings would only be about 1/5th of an inch. That is pretty stunning too.

The very bright student may realize that some of these numerical answers can be obtained from the other numerical answers. Time could be spent on that for those interested. For example, the football field (100 yards) is fifty times as long as the wing span of 6 feet. Multiply 1/250th of an inch times fifty and you would get 1/5th of an inch.

I love math!