A friend once gave me a sweatshirt with e painted on it (a portion of its decimal representation, followed by an ellipsis). Wearing it led to people asking what it meant. I usually gave an example using compound interest:

Imagine that a bank account pays 100% interest in a year. With simple interest (a 100% dividend at the end of the year), a $1 balance becomes $2 after a year. With interest compounded semianually, $1 becomes $1.50 after six months and $2.25 after a year. Compounding quarterly gives $2.44. Compounding daily gives $2.71. Shortening the compounding period increases the ending balance but never by a factor greater than e.

People get the idea, but to really get it requires understanding limits. There is a plethora of different (but equivalent) ways to define e but most of them involve a limit, derivative, or integral. Here's one that doesn't:

A group of men go to a party, each man wearing a hat. At the party, they throw their hats into a box. They shake the box and each man takes a hat from the box before leaving.

How many ways can the hats be distributed? For n men and n hats, this is counting permutations; the answer is n! (n factorial).

How many ways can the hats be distributed such that every man leaves with a different hat than the one he came with? This is counting derangements, and a formula for counting them is less obvious. Examples:
 n  permutations derangements
11! = 10
22! = 21
33! = 62
44! = 249
55! = 12044
66! = 720265
77! = 50401854
The number of derangements of n objects turns out to be n!/e, rounded to the nearest integer. (A proof is beyond the scope of this blog posting.) This provides a suitable basis for defining e:
e is the unique real number such that n!/e rounded to the nearest integer is the count of derangements of n objects for all positive integer values of n.
This is a somewhat lengthier illustration of e than the complex interest example but it is notable for not involving any calculus concepts.
bee on Erythrostemon gilliesii, this morning
Lepus californicus (a few days ago)
I saw an eclipse of the sun in Mexico in 1991. People were jazzed during the initial partial phases of the eclipse. Excitement was in the air. After totality, the same partial phases happened in reverse but no one cared. Everyone went inside to have lunch.

Most climbers are more interested in climbing up than down. After climbing a route, we lower ourselves with rope or walk back to the base of the rock on a trail.

Squirrels and lizards both climb my Joshua tree. They run away if I draw near which of course requires first getting down off the tree. Squirrels climb down the way they went up, whereas lizards jump off. This is the difference between squirrels and lizards.
My allowance was 25 cents a week when Mad magazine raised their price from 25¢ to 30¢. I remember going back to my mom and asking for more when the price went up. (I don't remember her response.) I see from covers of Mad on the web that the 30¢ price started with the June '65 issue. Ergo, I was reading Mad when I was five years old.

New York had 2% sales tax at the time. The state published a tax table that didn't round up when tax would be ½¢, i.e. there was no sales tax on a 25¢ purchase but there was a penny tax on 26¢ to 75¢.

Someone in Australia once sent a letter (or postcard, can't remember) to Mad's offices in New York City with just a stamp on it and a drawing of Alfred E. Neuman. It got there.
Lepus californicus
Another day, another earthquake. Today's was bigger than yesterday's. I'm fine, nothing's damaged. Wikipedia page.
puzzlement at first, then excitementThere was a magnitude 6.4 earthquake this morning centered about 70 miles from me. It didn't feel strong at my house but it lasted a while.

The USGS has a web page for people to describe what they felt at their location. The question to the right was my favorite.
Ammospermophilus leucurus, Yucca brevifolia
Squirrels climbing my J-tree this morning to get the fruit.
N842BA (and a B-2, serial number unknown) at about 25,000' MSL
Yesterday afternoon. KC-46 tankers like this one went into service this year and have been practicing in my area.
reflected (with diffraction) off an integrated circuit
Sunlight on the ceiling this morning.
Last summer I posted pics of a prototype Toyota Supra. Toyota has since announced the new Supra model and made it available to reviewers. Toyota claims the Supra has a lower center of gravity than the Toyota 86, which would be remarkable because the 86 has a flat‑four engine that sits close to the ground and the Supra has an inline‑six. Some reviewers parroted Toyota's claim as fact, i.e. without saying "according to Toyota".

Car and Driver magazine reported today that the Supra's CG is not lower than the 86's but rather 1.5" higher. I found it fun to guess what procedure they used to determine the CG location. (They didn't toss the car in the air and watch what point it rotated about.)

The name "86" refers to (among other things) the car's engine specs: bore and stroke are both 86mm.
cell phone pic, it was drizzling
Yesterday evening.
this

FAQ
search
contact
rss/xml
atom/xml
spam notice
terms of use
warrant canary


sundries

xkcd
skippy
Sroyon
pylduck
Woolly Days
TYWKIWDBI
Futility Closet
Language Log
Yastreblyansky
Bruce Schneier
Dinosaur Comics


archive