A View from the Back of the Envelope top

"What order of magnitude is ...?" game
On Being Approximate
Counting by powers of ten
Rough Draft
getting a feel for magnitudes

"About how many chairs are in your room? Is it more like 2, or 7, or 15?"
You probably didn't really need to count. Just looking at things, you have a feel for whether there are "a couple", or "a few", or "a dozen". You have done it enough times that you now have a feel for it, an intuition.

"How many people have you talked with today? Is it more like 1, or 10, or 100?"
"How much time have you spent reading this? Is it more like 1 minute, or 10 minutes, or 100 minutes?
"How far away is home? Is it more like 1 mile, or 10 miles, or 100 miles?"
"How tall is that building? Is it more like
(a) one foot, or
(b) ten feet, or
(c) a hundred feet, or
(d) a thousand feet, or
(e) ten thousand feet?"

Lets do that last one together.
Hmm... could it be 1 foot? Well, unless it's a doll-house building, it has to be a lot bigger than 1 foot. So (a) is out. Could it be 10,000 feet? Well... isn't a mile only a few thousand feet? It doesnt seem the building could be a mile tall. So it has to be less than 10000 feet. So it's (b), (d), or (e). Could it be 10 feet? What do we know thats about 10 feet big? Hmm... how tall are people? So if the building is a couple of people high, (b) sounds good. Oh, but that means (d), 1,000 feet, would be how high? 100 people high!? That doesnt sound right. Except maybe for a skyscraper. So it looks like (b) or (c), depending on how tall the building is.

A process of "Well, if it's (q), what does that mean? Ok, but we know mumble mumble. So it can't be (q), thats too way too big! So it has to be between (m) and (r). Lets see, what else do we know? Well, if it's (m), what does that mean? Ok...". "So, to wrap up, we have concluded it has to be between (o) and (p)."

"How many cats and dogs live near you? Is it more like
(0) 1
(1) 10
(2) 100
(3) 1000
(4) 10000
(5) 100000"

So you see, you can also come to have a feel for what order of magnitude (how many zeros) things have.


This form of the game inspired by [Hofstadter].

Better examples and `how to' would be nice.

A View from the Back of the Envelope
Comments encouraged. - Mitchell N Charity <mcharity@lcs.mit.edu>