This one constantly bothers me. Somebody out there help.
I walk from the bus station to work every day. Coffee and graffiti aside, normally I walk three blocks east and three blocks south. Total walk: 6 blocks (3+3).
Sometimes I take “shortcuts” through the side-streets where I walk 1 block east, 1 block south, and so on until I get to work. Total walk: 6 blocks (1+1+1+1+1+1).
Let’s say I could go through the buildings and make this even more jagged. So now I walk 1/2 block east, 1/2 block south, and so on. My total walk would still be 6 blocks. (1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 )
And let’s say I did that to the infinite limit such that I was taking a millionth of a block walk east and a millionth of a block south. My total theoretical walk would still be 6 blocks. (1/1,000,000 + etc.)
Here’s my conundrum. At that point, it’d pretty much be a straight line to work.
And since it’s a 45degree angle and each leg is 3 blocks the total straight line distance is
- which is 4.24 blocks.
So which is it? 6 blocks or 4.24 blocks? This plagues me every day of my life. Someone talk me down from the cliff.
(cricket)
San Demos High School Football Rules.
Macroscopic physics says that once your fractions of blocks east and south are shorter than your own feet, your calculation of distance has to accommodate that fact. (Math is nothing without physics! Muhahaha.)
ReplyDeleteAnother way of looking at it: even before your fractions of blocks get shorter than your feet, you are likely to be losing distance by not taking strict 90 degree turns - and that means for every turn you take, you shave a little bit off your distance. So your zigzag shortcuts are in fact shortcuts, if only marginally.
Nope. Still plagued. But we should talk more, I miss that.
ReplyDelete