June, 2006

Adventures In Time And Space 1: Powers Of Ten

Powers of Ten (1977)

Powers of Ten (1977)

One of the things that makes science so awesome is knowing that all of the wonders of the universe exist all around us but we can notice only a small part of it. We humans are trapped in both time and space by the limitations of our senses. We go about our daily lives using measurement scales that range (in time) from about a second to about a year and (in space) from about a millimeter to about a kilometer.

But events in the universe occur at much smaller and at much larger measurement scales than within these normal human ranges. Science has had to establish a common framework in order to make sense of a far more detailed universe. We use a scale of numbers with a fixed ratio called an order of magnitude.

To make it easy on us, we express the orders of magnitude in factors of ten, i.e., ten multiplied by itself a certain number of times. Each order of magnitude is either ten times larger or ten times smaller than the one next to it, e.g., if a number differs from another number by one order of magnitude, then it is ten times different than the other number; if they differ by two orders of magnitude, then the numbers differ by a factor of 100.

We can use scientific notation to show the order of magnitude in an easy way. If the order of magnitude of a number, say, 2300 is three, then we can express this as 2.3 x 103. If the number was 23000 instead, then it would be 2.3 x 104 and have an order of magnitude of four.

Why bother? Because doing it this way helps us handle very large and very small numbers and gives us a way to compare the scale of things.

The designers Charles and Ray Eames wanted to show this relative scale of the universe. They made a film using the orders of magnitude in factors of ten. They started with humans (naturally) and zoomed outwards from Earth towards the edge of the observable universe. They then zoomed inward towards a single atom and the quarks inside it. In 1977, their film Powers of Ten: A Film Dealing with the Relative Size of Things in the Universe and the Effect of Adding Another Zero was their awesome result:

Powers of Ten (for length)
The examples given are sizes that are within the range of lengths that exist between each order of magnitude. For example, the sizes of elephants, FM radio waves, and humans fall in descending order between one decameter (ten meters) and one meter.

10−18 attometer (quintillionth of meter)
0.000,000,000,000,000,001 (e.g., quark)

10−15 femtometer (quadrillionth of meter)
0.000,000,000,000,001 (e.g., uranium nucleus, proton, neutron)

10−12 picometer (trillionth of meter)
0.000,000,000,001 (e.g., carbon atom, x-rays, gamma rays)

10−9 nanometer (billionth of meter)
0.000,000,001 (e.g., virus, DNA, visible light)

10−6 micrometer (millionth of meter)
0.000,001 (e.g., human hair, white blood cell, bacterium)

10−3 millimeter (thousandth of meter)
0.001 (e.g., rice grain, ant, sand grain)

10−2 centimeter (hundredth of meter)
0.01 (e.g., hummingbird, chicken egg, penny)

10−1 decimeter (tenth of meter)
0.1 (e.g., baseball bat, basketball, cell phone)

100 meter (one meter)
1 (e.g., elephant, FM radio waves, human)

101 decameter (ten meters)
10 (e.g., football field, blue whale, house)

102 hectometer (hundred meters)
100 (e.g., Eiffel Tower, Boeing 747 airplane)

103 kilometer (thousand meters)
1,000 (e.g., Grand Canyon, AM radio waves)

106 megameter (million meters)
1,000,000 (e.g., Jupiter, Earth, Texas)

109 gigameter (billion meters)
1,000,000,000 (e.g., Deneb, Arcturus, Sun)

1012 terameter (trillion meters)
1,000,000,000,000 (e.g., Stingray Nebula, Kuiper Belt)

1015 petameter (quadrillion meters)
1,000,000,000,000,000 (e.g., Orion Nebula, Oort Cloud)

1018 exameter (quintillion meters)
1,000,000,000,000,000,000 (e.g., Large Magellanic Cloud, Tarantula Nebula, Eagle Nebula)

1021 zettameter (sextillion meters)
1,000,000,000,000,000,000,000 (e.g., Local Group, Milky Way Galaxy)

1024 yottameter (septillion meters)
1,000,000,000,000,000,000,000,000 (e.g., Virgo Supercluster)

1027 zennameter (octillion meters)
1,000,000,000,000,000,000,000,000,000 (e.g., observable universe)

Incidentally, 10100 is the number googol. Mathematician Edward Kasner’s nine-year-old nephew coined the word and Edward mentioned it in his 1940 book Mathematics and the Imagination. Of course, this power of ten was the inspiration for the name of the company Google.

The Powers of Ten film from the Office of Charles and Ray Eames was a landmark film. It even became a 2004 couch gag on the opening sequence of The Simpsons (The Ziff Who Came to Dinner):

If we want to show the relative scale of events and not of sizes, then we can use the powers of ten to get a sense of how long events take. We can show how fast atoms react with each other and then go towards larger and larger time scales until we reach the grand age of the observable universe:

Powers of Ten (for time)
The examples given are events that occur within the range of times that exist between each order of magnitude.
For example, the time between normal human heartbeats takes between one decisecond (tenth of second) and one second.

10−18 attosecond (quintillionth of second)
0.000,000,000,000,000,001  (e.g., transfer of electron between atoms)

10−15 femtosecond (quadrillionth of second)
0.000,000,000,000,001  (e.g., chemical reaction time)

10−12 picosecond (trillionth of second)
0.000,000,000,001  (e.g., lifetime of hydronium ion in water)

10−9 nanosecond (billionth of second)
0.000,000,001  (e.g., light travels 30 centimeters or one foot)

10−6 microsecond (millionth of second)
0.000,001  (e.g., strobe light flash)

10−3 millisecond (thousandth of second)
0.001 (e.g., wing flap of honey bee)

10−2 centisecond (hundredth of second)
0.01 (e.g., camera shutter speed)

10−1 decisecond (tenth of second)
0.1 (e.g., human eye blink)

100 second (one second)
1 (e.g., time between human heartbeats)

101 decasecond (ten seconds)
10 (e.g., )

102 hectosecond (hundred seconds)
100 (e.g., )

103 kilosecond (thousand seconds)
1,000 (e.g., class period, movie, concert, football game)

106 megasecond (million seconds)
1,000,000  (e.g., calendar month, grading cycle)

109 gigasecond (billion seconds)
1,000,000,000  (e.g., human life span)

1012 terasecond (trillion seconds)
1,000,000,000,000 (e.g., complete cycle of the equinoxes)

1015 petasecond (quadrillion seconds)
1,000,000,000,000,000 (e.g., length of geologic period)

1018 exasecond (quintillion seconds)
1,000,000,000,000,000,000 (e.g., age of universe)

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My version of the famous cartoon by Peter Steiner that was published on July 5, 1993 in The New Yorker. Here it goes!