Perspectives in Time: The Toilet Paper Timeline

William P. Blair, Johns Hopkins University

Version 1.1, Updated March 2010

(Version 1.0, February 2004)

Communicating the immense numbers used in astronomy, whether in distance or in time, is always a challenge when talking to public audiences. The concept of Powers of Ten is useful for making "big" numbers manageable, but the immensity of numbers like millions and billions (let alone trillions!) tends to get lost. One idea I have used numerous times to bridge this gap with audiences of all ages is to use a roll of toilet paper as a timeline, changing the scale as needed to cover various time frames of interest. Here is one example of how this can be done. You can adapt the complexity up or down for a given audience.

I like to use "1000 sheet" rolls of TP because of its nice tie-in to powers of ten. Let's say I've just described how the dinosaurs died away 65 million years ago, likely because of an asteroid impact on the earth, and I want to put this into perspective. I pull out a roll of TP where scaling has been marked at 10,000 years per sheet of TP. (I usually mark out to, say, 1 million years, which is 100 sheets in--a bit of a pain, but it adds to the effect.) Note, in a classroom setting, unrolling and marking the TP every 100,000 years can be part of the fun.)

Now I just unroll 10 sheets or so and describe how everything we really know about (e.g. recorded history) is on the first sheet. (Even the pyramids of Egypt at, say, 2000-3000 BC or 5000 years ago, are only a half sheet back.) I usually highlight the cave paintings in France, dated at 20,000 years ago or so, as representing "cave men" (e.g. when Fred Flintstone lived, if the audience remembers the Flintsones!). For more sophisticated audiences, I may pause at 100,000 years or so and highlight the emergence of Cro Magnon man (basically, the arrival of modern homo sapiens on the scene. Then I start unwinding to find the dinosaurs at 65 million years.

The clever reader will have already figured out, however, that at 1000 sheets per roll and 10,000 years per sheet, there are only 10 million years on a single roll. It will take 6.5 rolls of TP end-to-end to get back to when the dinosaurs disappeared. (Obviously you don't have to unroll the whole roll of TP to make the point...) It can also be pointed out how ridiculous it is that Fred Flintstone had a dinosaur for a pet!

(Since we are on the dinosaurs, with some audiences it might be instructive to highlight just how successful the dinosaurs were. They came on the scene about 225 million years ago and only went away after some 160 million years, and even then it apparently took an asteroid collision to do it! Now 160 million years is 16 full rolls of TP end-to-end, compared with the generous 10 sheets of TP (100,000 years) for the human species. And what with the things we are doing to the earth's environment, one has to wonder whether we will even make it for one more sheet of TP. But that's a different story...)

The scaling aspects can now be used to advantage to get to times meaningful for many astronomical purposes, like the five billion years back to the birth of the solar system, or even the estimated 13.7 billion years back to the Big Bang. Take out a second roll of TP, marked with 10 million years per sheet. Thus each sheet on this roll corresponds to an entire roll of TP in the previous example! To keep a long story short (so to speak), the solar system formed 500 sheets back (half a roll) on this second TP roll, and the entire roll only gets back 10 billion years, or only about 3/4ths of the way back to the Big Bang.

I hope this gives some inkling of how to use this idea. Of course, one can work many variations on this theme depending on the subject being discussed. It is very flexible, depending on the time scale per sheet to be used and the subjects one wants to work in after using this as an introductory demonstration. It would also be feasible to use the TP roll to discuss large distances, say the relative distances of planets from the sun (on out to the next nearest star or whatever). Ideas for distance scalings are given in my companion document, Size Scales in Astronomy.

Another very effective mechanism for communicating the vastness of cosmic time is the use of the Cosmic Calendar, where all of time since the Big Bang is collapsed into a single calendar year, and then one looks at the date and time that various things happened. (I can tell you that the solar system doesn't form until September 9th of the Cosmic Year!) As far as I am aware, this concept was first put forth by Carl Sagan in his book "The Dragons of Eden," but many versions of this are now available on-line as well. Here are a couple of links of possible interest:

Carl Sagan's Cosmic Calendar on YouTube.
The Universe in One Year from the American Museum of Natural History.
Cosmic Calendar on Wikipedia.

If you find this document useful, or if you have suggestions for improving it, please let me know through one of the following channels:

Snail mail: Dept. of Physics and Astronomy, Johns Hopkins University,
  3400 North Charles Street, Baltimore, MD  21218-2686
William P. Blair