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Three decades ago a hundred Cornell University undergrads sat glassy-eyed in their lecture hall as a weary old professor told them about a very large number.
The students, including 19-year-old me, were mostly communication and business and history majors trying to complete our science requirements without thinking too hard. The professor had earned several advanced degrees and was far too qualified to teach a class derisively called “Physics for Poets.”
And the very large number was Avogadro’s Number. I won’t try to explain this number (which is sometimes less glamorously called a mole), because the reason it’s important to physicists and chemists matters much less to me now than its enormous size.
Our professor spent an hour impressing upon us the sheer size of Avogadro’s Number. It is very, very big. 602,000,000,000,000,000,000,000, give or take. That number is so long that you’ll mostly see it written as 6.02x10^23 — which how scientists write numbers when they’ve removed several dozen digits to save time. Put another way, Avogadro’s Number is just over 600 sextillion. It’s the better part of a trillion trillions.
Not surprisingly, an entire lecture of decimal places and twenty-third-powers didn’t stick to my juvenile brain. Which is why I had to look all that up.
But one thing did stick: The fact that Avogradro’s Number of M&Ms would cover the earth to a depth of 25 miles.* That would mean M&Ms piled on Manhattan more than 100 Empire State Buildings tall. That’s almost five Mount Everests of M&Ms dumped on top of the actual Mount Everest. That’s nearly a marathon of M&Ms on top of every square inch of land and sea. It’s a lot of M&Ms. And that fact — those images — are the reason why I still have Avogadro’s Number lodged in my skull decades later.
Numbers are hard to remember, especially when they contain 26 digits. Even when people remember big numbers, they don’t always comprehend what those big numbers mean. But I’ll remember that 25 miles of M&Ms for the rest of my life.
I thought of this while reading Making Numbers Count by Chip Heath & Karla Starr. The book contains fantastic advice, despite the authors’ frustrating willingness to sacrifice accuracy in favor of a good story. (It’s possible to offer both!)
In particular I second their recommendation to “convert abstract numbers into concrete objects.” Like the example in their book that explains a millisecond by showing the 984 feet of wire that electricity can travel in that time. Or by explaining an unimaginably large number by encouraging your audience to imagine M&Ms.
* At least, 25 miles is the number I recall, and it’s also the number in this questionable slideplayer presentation. For some reason it’s hard to find a more reliable source for this crucial calculation.
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