Geekiness

I just love numbers. Whatever I'm doing, there's always some cipherin' going on.

I am fascinated by units of measure that are based on observerable phenomena, like the month based on the time from one full moon to the next, etc. They connect me to my ancestors and to history in general, and I often try to make up my own. In this I am the very personification of the title of this blog. I am certain that I am coming up with units of measure that have been independently developed a hundred times all around the world.

So, once I was hiking along a trail in New Mexico and wanted to be able to count my steps and figure out how far I had gone. My biggest problem is that counting, say, 2000 steps is hard to do and be able to enjoy the scenery at the same time.

I was walking with a staff (another thing I enjoy, that hunt for a good staff on a trail... that's another post). I noticed that my staff hit the ground every four steps. I have a course that I walk that is exactly 2 miles. I counted my steps on that course and came up with 3980, or 1980 steps per mile. That's close enough to 2000 (within 1%!) for me. I determined that 500 hits with my staff would constitute, to a reasonable degree of accuracy, one mile!

500 Staves (as I immediately dubbed my new unit of measure) are much easier to count than 2000 steps. I only had to count to four repeatedly, and that comes very naturally for me from my musical background (one, two, three, ONE; one, two, three, TWO; one, two, three, THREE; etc). I could even be "aware" of four steps without even having to count them, and soon I got to where counting the Staves was all I had to do. Awesome!

I prefer doing math in my head when I can, and the 500 staves per mile made it very easy to convert any number of steps directly to miles, to whit:

(staves x 2) / 1000 = miles

So, say, 137 staves equals (137 x 2) = 274 / 1000 = .274 miles. How cool is that?

Yes, I know I could just divide by 500, but this formula is easier to do in your head.

Which brings us to... significant digits! Significant digits, in practical use, are a measure of accuracy. The more digits that are significant, the greater the accuracy. This means that 2.00 is more accurate than 2. Zeroes between the last digit and the decimal point don't count, so 4, 40, 400 and 4000 all have one significant digit. That last digit is where the innacuracy lies, so 2.00 really means that you're somewhere between 1.995 and 2.004. 2 means that you're between 1.5 and 2.4. Big difference.

Like I said, I like to do math in my head when I can, which forces me to limit significant digits. Usually one, but sometimes as high as three if I'm feeling particularly hot.

So today I was wondering how fast I was walking. A 20 second count of my steps resulted in 44 steps, so my sun-bright mind immediately determined that I was walking at 2.2 steps per second. To convert to miles per hour I did it in two significant digits and one significant digit, just because I'm that cool.

Two Significant Digits

So, given:

2.2 steps per second, 500 staves per mile, 4.0 steps per stave (or is it staff? I haven't decided yet)

1 step = .25 staves

.25 x 2 / 1000 = .0005 miles

2.2 steps x .0005 = .0011 miles per second

.0011 x 3600 seconds per hour = 3.96 miles per hour

Since we are using two significant digits we must round this to 4.0 mph.

One Significant Digit

2 steps per second, 4 steps per stave

Yeah, 1 step = .25 staves, but we must stay true to the digits, so 1 step = .3 staves

.3 x 2 / 1000 = .0006 miles.

2 steps x .0006 miles = .001 miles per second

again, 3600 seconds per hour, but we must be consistent, so 4000 seconds per hour.

.001 x 4000 = 4 mph!

Now, with two digits we're talking between 3.95 and 4.04 mph, while with one digit we're talking 3.5 to 4.4 mph. A much broader range, but dig this: I have walked at exactly 4 miles an hour on a treadmill, and it's too fast for me. With fewer significant digits, I have, in one sense, been more accurate!

Also, there is another method of rounding where when you round from .5, instead of automatically rounding up, you round to the nearest even number. I would have rounded .25 steps per stave to .2 instead of .3, resulting in an end result of 3 mph instead of 4. So, between 3 and 4 mph is about as close as you can get. Not bad, and good enough for head work.

How cool is that?

I know I lost you a long time ago, but that's cool. It's all part of the fun.