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The high vantage point provide perspective. In the view from the top of a tree / building / mountain, or from an airplane, one can see the lay of the landscape. Can see the shape of forests, where only trees were visible from ground level.

Trees are important. Details are important. But it is often in backing away from them, blurring them, that connections, patterns become visible. And it is often far easier to learn and understand details, once one has seen the big picture. Once one sees how the details fit together.

The back of the envelope is fundamentally about scale. If details were always crucial, if everything was always a close call, everything about the same size, lots of explanations similarly plausible, then there would be no back of the envelope. Its approximation and estimation would not work. But instead the universe has a broad breadth of scale. There is both the very big, and the very small. Often along side each other, providing contrasts so dramatic, that blurring the pieces doesn't change the picture. Explanations, seemingly plausible, that a moment's rough reflection reveals are not even close to fitting. The rough is often sufficient, and should always be the prelude to worrying about detail.

So what is this "back of the envelope"? I know the phrase from engineering and science, but I don't know its origins. The idea is that when thinking, it often helps to scribble. In reflection or conversation, driven by the need to explore, to clarify, to capture, to explain, one reaches for whatever paper is at hand. Be it table cloth, or napkin, or the back of an envelope. To rough out your ideas. To sketch and visualize. To do quick plausibility checks. It is these rough sketches which sometimes grow up to be companies, and hardware designs, and works art.

So what is this site? There is a kind of rough calculation which is both powerful and accessible. I would like to encourage its greater use.
Powerful because it can handle the breadth of the big picture. Can provide a framework for knowledge. Can simplify things by allowing you to choose just the right amount of numberness. (Too little is like trying to find a house when no one will tell you the address or street names. Too much, like being hosed with useless trivia.) And because it actually works, can actually be used to answer one's own questions.
Accessible because it uses a simple kind of number, in an easy way. Any age, any one, who can add and subtract 1 through 10, can make it work. With perhaps the biggest obstacle being trying to use a tool based on understanding, in an environment where it is so hard to find really good descriptions, or people who really understand how something works.

My intent was once merely to collect pointers to existing resources, for people who had already encountered these ideas. But I found even people who knew this stuff might not fully appreciate it (myself included), and that existing resources were just a start (as are these pages). So now this site is a mish-mash of introduction and obscure `here is a random neat idea explained so poorly that it only makes sense if you already know it'. It's a start.

I suggest you begin by looking at Counting by powers of ten.
Then there are various loosely organized topics,

• the details on how to do rough math,
• how to use it to answer questions, (Fermi Questions, Landmarks, ...)
• some examples of big pictures, (`Power of Ten' scales, ...)
• some thoughts on understanding, and on applicability to education.

Or you can just take a look at a few pages I find particularly fun.

Please pardon the mess.
Mitchell Charity

History:
 1997.Aug.01  First draft.