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How big is a phone book, and other ways of illustrating size

In terms of representing scale, one of the most powerful mechanisms I find useful is to use examples people can grasp in meaningful terms. In the Boston seminar, ET uses the "amount of data in a phone book" as one of those conceptual hooks. I think I caught him say that a typical phone book contains 38,000 characters. Did I hear that right?

And, while I raised the topic, do you have other credible examples of this kind of metric? For example, I'm trying to explain to people how much a terabyte of data is; the best example I have found so far is that the entire Library of Contents is estimated to be about 10 terabytes of data. That's a good way to make that staggering number real.

And, today, I heard another one, that there are about a billion bags checked for air travel, world wide, in a year.

I'm curious if anyone else has some favorite ways of representing scale in concrete, understandable terms.

-- Mark Palmer (email)

Something I was told twenty-five years ago (when RAM was a dollar a byte) was that the Bible was 5Mb as unformatted text. There are a million seconds in (roughly) eleven-and-a-half days, and a terabyte of seconds in something around 32,000 years.

However, a good-quality large art book (ignoring file compression) could have half-a-gigabyte of illustrations, and a collection of maps as image files easily larger, so a terabyte would be somewhere around the fine art section of a big-city bookstore, or a reasonably sized personal library in a private house that included maps or illustrated books. "Library of Congress" may only be good guide if you leave out formatting and illustrations.

A terabyte is not big at all. If I could contain all the information I know about one other person in one byte, and their information about me similarly, then two people's knowledge of each other equals two bytes. Three people's knowledge is six bytes (factorial 3). By the time you reach fifteen people you are past a terabyte.

If, rather than a byte, you take a terabyte as the information you know of any person - one percent of a brainful say (estimates of the number of information connections in the brain vary from say a hundred terabytes to a terabyte squared) - and say six billion people on earth each knowing one hundred other people, then a terabyte is to the sum of human knowledge as a single atom is to the square of the number of atoms in the known universe - give or take a few.

-- Martin Ternouth (email)

A colleague told me once that it was his habit to start a lecture with the words "I plan to talk for about a microcentury". A microcentury is actually about 53 minutes, and a nanocentury is about 3 seconds -- perhaps surprisingly long for a period that sounds so short. Alternatively, taking a typical lifetime as three-score years and ten, a millionth of a lifetime is about 37 minutes, and a billionth is about 2 seconds.

-- Athel Cornish-Bowden (email)

Telephone book, double-page spread = 36,000 characters, or 18,000 characters per page. Note these are PAGE counts.

There's detailed information about character densities in the essay "The Cognitive Style of PowerPoint," in chapter 8 on data density in The Visual Display of Quantitative Information, and in chapter 2 in Envisioning Information.

-- Edward Tufte

When I was teaching high school, and needed to describe a large quantity I found that using the local stadium (Riverfront to be exact) as a reference provided a good comparsion since most of the students had been there and could visualize it easily. It was also handy in that it held just over 50,000 (52,000 & change) - so the math was easy!

-- Ed Mullin (email)

My favorite example of this sort is Grace Hopper's nanosecond:

Grace Hopper is famous for her nanoseconds. People (such as generals and admirals) used to wonder why satellite communication took so long. She started handing out pieces of wire which were cut just under 1 foot long, which is the distance that light travels in 1 nanosecond (1 billionth of a second). The reason satellite communication is so slow is that the signal must travel for many nanoseconds on the way up, and then many nanoseconds on the way down. Even generals and admirals could understand this explanation. Later she used the same pieces of wire to illustrate why computers had to be small to be fast. At many of her talks, she handed out nanoseconds to everyone in the audience.
from wikipedia

-- Carl Manaster (email)

When discussing with a coworker the deplorable lack of general knowledge in a recent group of college graduates I lamented:

"He thought Hiroshima happened right after Pearl Harbor."

To which my collleage replied:

"In terms of geologic time he was right."

Finding universal points of reference isn't easy....a standard element for all theatrical drafting elevations used to be a human figure (normally drawn at 6'). This is rarely found in scenographic drawings anymore - but it is crucial for all lighting sections (to show where the light is directed- the person's head- not their feet). You will find ground plans for television with cameras and camera operators depicted. This helps show the camera angles as well as giving a better idea of scale. John Lee Beatty (Tony award winning Broadway set designer) likes to make 1/4" models of the set- because moving your finger through the model takes up about as much space as a person would on the actual set.

-- Ziska Childs (email)

Slightly off-topic but very interesting, UC Berkeley's "How Much Information?" study was recently updated. Among many other things it says 5 exabytes of stored data were created in 2002 and 18 exabytes of transmitted data (98% of this in phone calls). I like their answer to "how big is 5 exabytes?", basically that it's half a million Libraries of Congress.


-- Matt Fell (email)

Check out Guy Ottewell's "THE THOUSAND-YARD MODEL, or The Earth as a Peppercorn."

"Instructions for using common objects such as nuts to make a solar-system model, over a distance of 1000 yards. It could be called a Model, Walk, or Happening. Tested many times with groups of children, who invariably are spellbound by the incredible distances. Since it also leads to a vivid grasp of light-years, star sizes, etc., it is an ideal opener to any astronomy course. ?????? This description was twice printed in magazines, and was revised and reprinted as a booklet because there are so many requests for copies of it. The exercise is now performed annually or monthly by some astronomy clubs and at the American Museum of Natural History, New York; has been proposed as an installation in the city of Portland, Oregon; and we know of it being done in Peru, Guadeloupe, Iceland, and along a kilometer of the Great Wall of China."

The book is available from his site at:


an online description is available at:


-- Michael Ivester (email)

The link on solar system scaling is excellent.

-- Edward Tufte

For what it's worth, once you remove their extra text, the Project Gutenberg plaintext (ASCII) copy of the King James Bible (Old and New Testaments) is 4.13MB in size, or 4,332,914 bytes or 34,663,312 bits. Not a handy number to work with.

Since this is ascii, each character is represented by one byte, so there are about four and one third million characters in the bible. This is a little easier to work with.

There are almost exactly 100,000 words in this version of the bible, which is a lot easier to work with. So divide whatever you want to express by 100,000 and say "if each of these were a word, you would have this many bibles."

The "with twelve zeroes" type talk some folks use is just confusing since it's hard to comprehend that each zero makes it ten times more.

What about the "for every man, woman, and child" notation people use?


-- Stephen Foskett (email)

A sense of scale - petroleum reservoirs

My work deals with the internal dynamics of oil and gas reservoirs, and it's important to have a realistic sense of scale to understand why physical cause and effect can take months or years to play out in the subsurface.

One popular trick is to overlay a field outline map over a city map. This should be familiar to your audience - maybe the city they live in, or the capital city of the country where the field is. The field I'm working on right now is comparable in scale to Houston inside the Sam Houston Tollway, or London inside the M-25 orbital motorway. Stratigraphic cross sections scale nicely against pictures of buildings with maybe 30 stories (the relevant scale here being the thickness of the oil-bearing beds). Again, you need to choose a familiar landmark for the best effect.

Of course, when you flash this confection up on the screen, you need to make sure your audience understand why they're looking at a map of their home town and not the oilfield they came to hear about!

-- Brian Davies (email)

Excellent work by Chris Jordon, who uses images to indicate quantities--somewhat in the style of the Vietnam Veterans Memorial:


-- Edward Tufte

How big is a megalitre?

Here in the UK water industry, we quote leakage in the distribution system in megalitres per day. In order to illustrate the megalitre, we point out that when you see a typical "Olympic-sized" swimming pool on television, or at your local sports centre (say 50 × 25 × 1.6 metres), you're looking at about two megalitres of water (I say about, even though those dimensions come to exactly 2 Ml, because the pool may not be exactly those dimensions).

Now the British are pretty used to the litre by now, so why do they need an illustration of a million of them? Because (I believe) knowing a quantity does not mean knowing many thousands, or thousandths of that same quantity. All it means after the first few zeroes is "a lot".

That's why I disagree with the estimable Mike Dickison of Duke University, who in an entry in his blog, Pictures of Numbers, insisted on replacing Astronomical Units in the scale of a solar system graph with millions of kilometers. I argue that the astronomical unit is a more intuitive unit for the solar system than the "million kilometers"; people don't grasp the latter just because they grasp the metre and the kilometre, but I could very quickly show someone an AU (or 0.71AU, which is close) by showing them Venus in the sky at maximum elongation, and reminding them that they're seeing a right-angled triangle whose other two sides are 1.00AU to the sun and 1.23AU to Venus. I don't know of a way to place a hundred million kilometres before someone's very eyes that wouldn't involve a similar effort.

-- Derek Cotter (email)

Followup to How big is a megalitre?

Incidentally, googling for the swimming pool analogy, I see the Australians have got themselves in a bit of a pickle over it. Somehow the factor of two has been dropped, and many authorities incorrectly quote 1Ml=1 O.S.P. Other, more skeptical Australians get upset about this and insist that the O.S.P. is a bogus measure in any case, and propose the "million tinnies", where a tinnie is 375ml, the size of an Australian beer can, or the hectare-metre or acre-foot, because more Australians (or is it just that particular guy?) watch rice paddies than watch Olympic swimming.

For the first, I just repeat my argument about how knowing a thing isn't knowing a million of them, or Chris Jordan's pictures that E.T. refers to above wouldn't be necessary. For the second, I think that commentator is taking the analogy twice out of its original context. First, when he insists everyone else use an analogy that suits his profession, instead of one that more urban Australians are likely to have seen, and second when he fails to look into the history of the O.S.P. as a unit, because I suspect the Australian water authorities picked it up from the British, and most of us certainly wouldn't have an easier time imagining the supply needs of a rice farmer (hint: we have less of a need for artificial irrigation, being a country blessed with rain, and we also grow crops that require not to be waterlogged. Ultimately, the hectare-metre in Britain would be most apparent to the maintainers of reservoirs, i.e. the very water industry our megalitre started in, that we were trying to translate out of!.

-- Derek Cotter (email)

Followup to How big is a megalitre?

Sorry, each comment I make today seems to spawn another. Re: my point that size analogies should match the audience's experience, the late Stephen Jay Gould had a hilarious essay called "The Case of the Creeping Fox Terrier Clone", on the origin of the mysterious "fox terrier" size comparison for the extinct horse ancestor Eohippus, wondering why it was repeated in textbook after textbook when hardly anyone owns or has seen a fox terrier. It turns out that the original author of the comparison was writing for a nineteenth century upper-class English audience who presumably would be familiar with fox hunting, and the (now-disappeared) habit of carrying a special breed of terrier on horseback to dig foxes out of the earth when they hide. As well as selecting for various practical features in the breed, relating to its work, the breeders had selected for the entirely humorous physical resemblance to a miniature horse, so that the hunter was carrying what looked like a horse on a horse. But no-one nowadays knows anything about this, so the repeated statement that "Eohippus was about the size of a fox terrier" doesn't mean a lot. They might as well say it was about the size of a poodle (toy, not standard), as at least we've all seen one in the park.

PS googling to find the title and location of Gould's essay, I find them on a site by Leonard Richardson, who points out what Gould implied, that the size comparison itself is an instance of an evolutionary phenomenon: despite not being selected for, it has persisted simply because so few textbook writers take the trouble to select against it when writing their own book, and think about a more apt comparison for today. It's junk DNA in the popular science literature.

Richardson says the essay is in Gould's collection Bully for Brontosaurus. Hmm, I've actually got that book; I think I'll reread the essay when I get home.

-- Derek Cotter (email)

To the other direction of size, the "human hair" size comparison for everything diffcult to see unaided by magnification. What an inadequate catch all, considering the variability of human hair sizes, yet it persists due to its universality.

Years ago before our manufacturing was shipped overseas, the Quality Control group had a deceptively simple way to measure surface roughness on machined components, in micro-inches or micro-millimeters. A stainless steel cylinder with different surface roughness bands exhibited colour differences: technically structural colour dependant on the wavelength of surface roughness, similar to the anisotropy discussed in the 'images on steel' thread. The inspector would take a sample component and the cylinder over to the window and compare them for colour reflectance, if so the component passed visual inspection.

-- Donald (email)

Earlier in this thread, Martin Ternouth noted:

"A terabyte is not big at all. If I could contain all the information I know about one other person in one byte, and their information about me similarly, then two people's knowledge of each other equals two bytes. Three people's knowledge is six bytes (factorial 3). By the time you reach fifteen people you are past a terabyte."

However, this isn't the case. If we visualized this example as a graph, each person would be a node, and known information about other people would be an edge between two nodes.

In the provided example, a complete graph (in other words, a connection between each node on the graph -- see http://en.wikipedia.org/wiki/Complete_graph) of 15 nodes, would not be 15! bytes (over a terabyte) as the author states, but would simply be 15(15-1), or 210 bytes. The author appears to have assumed this number would grow at a factorial rate since his example of three nodes satisfies this equation: 3! = 3(3-1), however at 15 this is not the case: 15! > 15(15-1).

-- Julius Schorzman (email)

Here's a visceral example of time, in this case using the calculated color of the sky over Chicago from 1998 to 2022, by Jason Salavon. The image represents 9149 days of sunrises and sunsets.

-- Rob Simmon (email)

From our thread on 3D scaling of 2D images:

Here is a lyrical and moving story by Primo Levi,
with overtones of Italo Calvino's Cosmicomics,
on the words for scaling astronomical objects.
The story is so intense that I read one paragraph at a time
and then took a break before the next paragraph

Primo Levy, "A Tranquil Star," The New Yorker, 12 February 2007

-- Edward Tufte

Re: Venus at maximum elongation

Unfortunately I got my numbers wrong: the correct figures for Venus are Venus-to-Earth 0.53AU; Venus-to-Sun 0.72AU (54.0°). The corresponding figures for Mercury are Mercury-to-Earth 0.78AU; Mercury-to-Sun 0.39AU (26.3°). The figures in degrees are angular distance.

I'm not sure how to do it, but I'd like to label up this APOD image of Venus and Mercury at max. elongation at the same time, in April 2004. The Sun is frustratingly far below the horizon, though.

-- Derek Cotter (email)

Dear ET,

here is a system of weights and measures published by Donald E. Knuth in a school magazine in 1957 under the title "Potrzebie System of Weights and Measures." In it, he defined the fundamental unit of length as the thickness of MAD magazine #26, and named the fundamental unit of force "whatmeworry."

MAD magazine liked it so much they bought the article and published it in the #33, June 1957 issue.

Here it is. A higher resolution image is here (http://upload.wikimedia.org/wikipedia/en/5/52/Potrzeb.jpg)


-- Matt R (email)

The American Museum of Natural History recently published "The Known Universe" video. From the accompanying description on Youtube:

The Known Universe takes viewers from the Himalayas through our atmosphere and the inky black of space to the afterglow of the Big Bang. Every star, planet, and quasar seen in the film is possible because of the world's most complete four-dimensional map of the universe, the Digital Universe Atlas that is maintained and updated by astrophysicists at the American Museum of Natural History. The new film, created by the Museum, is part of an exhibition, Visions of the Cosmos: From the Milky Ocean to an Evolving Universe, at the Rubin Museum of Art in Manhattan through May 2010.

-- Chris Pudney (email)

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