Most of you have probably recognized my obsession with matters of scale – the idea that our brains are wired to prevent us from being able to grasp orders of magnitude. Whether it be atomic particles measured in Planck lengths, galaxies measured in light years, or even our difficulty estimating the number of grains of sand on a beach, I’ve been pondering the impossibility of genuine comprehension. Can we only deceive ourselves into* thinking* we can comprehend such numbers and distances?

As a child visiting the American Museum of Natural History in New York, I was impressed by the timeline of life on Earth laid out as a wall mural, and I was impressed by the fact that mankind occupied such a small section of it, compared to the history of all life. But then, I noticed that the scale had changed to give more space to humanity than its proportionate share, as if children wouldn’t be able to handle the relative insignificance of humanity, if we saw the real thing. I don’t know if that mural has been redone since the 1960’s, but the Museum still offers for sale what they call “The Big History Timeline Wallbook” for $19.95. Their website describes the six foot long timeline as “divided into 12 sections covering both natural history as well as the history of human civilizations.” As I see it, giving human civilization one twelfth of a timeline of all existence is bound to leave kids with an inflated sense of the importance of humanity.

I’ve been trying to make things (spreadsheets, videos, books, diagrams) which don’t employ collapsing scales in order to appease our need to see the importance of ourselves.

For example, I recently tried to get a feel for the height of Mt. Everest compared to the size of the planet as a whole. I’d seen plenty of diagrams in books and on the internet which show mountains on the surface of the Earth, but if the whole Earth itself was represented, the images have always been labeled with the caveat, “Not Drawn to Scale.” The reason, of course, is that the diameter of the Earth is so much greater than the height of Everest that for an image of the Earth to appear on one page of a book, Mt. Everest would only be as high as a human hair is wide. Such problems drive illustrators to resort to deception. If the people at the American Museum of Natural History didn’t resort to collapsing scales, their six foot long diagram of history since the big bang would leave less than two feet for the history of all life on Earth, about 1/1,000^{th} of an inch for the history of homo sapiens, and about a 1/100^{th} of that for what we think of as human “civilization.”

Every picture of Earth’s cloud-studded atmosphere I’ve seen has made it seem to extend quite far above the surface of the Earth – far higher, say, than Everest. And we’ve all wondered why, hurtling through space at sixty-seven thousand miles per hour, the Earth’s atmosphere isn’t torn to shreds. But when I looked, I couldn’t find an image showing me the thickness of the atmosphere compared to the thickness of the Earth. It occurred to me that perhaps an Excel Spreadsheet might be a handy tool for giving me a better understanding of what I wanted to grasp. So I made such an image myself, using Excel. Starting at the center of the Earth, I added a kilometer to the next row of the spreadsheet, then I copied that increment and dragged it down the page the requisite number of kilometers. The image so drawn enabled me to “see” the picture that resulted – *but only sort of.* Specifically, holding my finger down on the scroll bar continuously, the kilometers from the Earth’s center to its surface sped by in a blur that lasted about twenty seconds or so. Then, suddenly, Everest and the atmosphere flashed by —so fast I couldn’t see them at all.

Never again will I forget that our atmosphere is a thin film barely coating the surface of the planet. Hurtling the Earth through space has as much chance of disrupting our atmosphere as a pitch toward home plate would have of wiping the grass stains off a baseball.

In any case, a couple of years ago, I became determined to figure out a way to represent the history of life on Earth, giving mankind no more than our due space within the whole. I wanted a timeline that did not vary in scale. I wanted to express the place held by humanity not only with the “knowing” that our brains are capable of, but through the more real “experiencing” that I believe gets us closer to genuine understanding of very large numbers. How might I use an *experience* to enhance my intellectual understanding?

One early idea was to use ping pong balls threaded together in a very long string, with a person having to actually walk the length of the string to experience how long it would be. I wanted each ping pong ball to represent a length of time that a human being might actually understand. I thought perhaps a thousand years – the time since William the Conqueror – might be such a number, to be represented by a single ping pong ball. The math was easy – at that scale, I would only need four million ping pong balls to represent the four billion years of life on Earth. But the idea of someone walking the length of the string came to an end when I realized that, leaving a 10 mm space between each 40 mm diameter ball, a string of four million such balls would be more than a hundred and twenty-four miles long. Few people would be willing to walk such a length to “experience” that amount of time, so I felt compelled to change my approach.

Marbles would be too tough to string together. Lead fishing weights would be smaller and easy to crimp onto a long fishing line. But the combined weight of four million fishing weights became a prohibitive factor.

So I turned from ping pong balls and fishing weights to the idea of making a sound or video recording. But it was quickly apparent that an hour-long video couldn’t express the concept meaningfully. What if such a video counted off the history of life on Earth in increments of a thousand years each? It would be pointless if the numbers on a screen were simply a blur; each would have to be visible for, say, half a second, even to be recognizable. But at two thousand years per second, it would take a person over sixty years, watching continuously, to see such a video. The video idea went the way of the ping pong balls.

The more ideas I considered, the more I felt myself inching closer to understanding the length of time involved, but the more it seemed that real understanding of such huge durations was impossible, as a practical matter. We can say the words, “Life has been on Earth for four billion years,” and we can multiply and divide numbers, but does any of that mean we can really appreciate how long four billion years is? By writing characters on a blackboard, we can manipulate decimal points and zeros to deceive ourselves into a false sense of “understanding” such large numbers. We have also developed whole systems of math that make perfect logical sense of the so-called “imaginary” numbers like the square root of negative two. We make calculations and even practical use of them, but none of us really “understands” them. I think big numbers are the same. Math helps us deceive ourselves into a feeling of understanding when no real understanding exists.

Still, we probably get by more efficiently in this real world precisely because our brains *can’t *comprehend such immensity.

I remain keen on distinguishing between mere intellectual “understanding” (aka self-deception) and true experiential understanding. Obviously, we can’t actually experience a duration as long as the four-hundred-billion-year history of life on Earth . But try counting down that history, even a million years at a time, from four billion years ago, and see how far you get. “Four billion. Three billion, nine hundred and ninety-nine million. Three billion, nine hundred and ninety-eight million. Three billion…” It would be like singing yourself all the way through “100 Bottles of Beer on the Wall” ten thousand times in a row. If we can’t bring ourselves even to *say* the numbers, even if we’re counting a million years at a time, then how can we think we really understand them?

In any case, while my string of ping pong balls will never see the light of day, my effort to put the life span of humanity into perspective has finally resulted in something real – a book titled “It’s Been Four Billion Years: The Story of Life on Earth a Million Years at a Time.”

It’s at the printer’s now, and will be available on Amazon.com and other retailers in September. The retail price is $19.95 – same as the History Museum’s deceptively skewed timeline. (Needless to say, my book maintains a constant scale, all the way through.)

The best part of it is that in appreciation for your having subscribed to this blog, I am willing to send you a free copy when they come out next month. If you send me an e-mail with your snail-mail address, I’ll be able to send you one.

In the mean time, I’m thinking of doing another book, trying to express extremes of distance and size….

Until then, peace to you all.

I want a copy! How long will it take to read or understand….less than billion…million…thousand…hundred…ten…week…hours….minutes….of….

Just want to know since this pandemic we are spending more time at home I want to be able to fit it into my very busy schedule of doing practically nothing. This should help fill the void!

If you just look at the pictures, maybe only five minutes or so. Considering how busy you are, maybe you should read the text, including the timeline at the bottom of each page. In fact, you needn’t even wait for a copy of the book. Just start counting the years now. “Four billion. Three Billion, Nine Hundred and ninety-nine million. Three billion, nine…” When you get to the present day, let me know, and I’ll have the book ready for you, along with a few sequels…

Thank you Joe for your thoughtfulness and for sharing it with us on a regular basis.

Looking forward to it! This link may help on scale … http://jamescarvin.com/2020/08/07/large-numbers/