Business Miles Addition

The simple version of this story is that 400 + 300 = 700. We want you to walk away agreeing that there must be more to it than that.

In vector everything, we say that we never just add numbers. Every term in a summation must be attached to something that is quantifiable (like quarters and Bavarian cream donuts).

So what we have above is really 400 miles + 300 miles = 700 miles.

OK, that’s better, but we need one more thing. Every number-thing combination must actually be a difference.

When you took 50 dollars out of your bank your wallet went from $30.00 to $80.00 and the bank’s balance went from $10,000,000,090.00 to $10,000,000,040.00.

If you look at the picture you can piece together that the story is

(700 miles – 300 miles) + (1400 – 1100) = 700 miles

Hopefully it is clear that 300,700,1100,1400 are odometer readings contributing to this story.

It probably feels like we are taking something simple and making way too complicated. Yes, but…

Later on in physics when you see something like we want you to interrogate and make swear under oath that the number 700 is attached to units and that it is actually a first number minus a second number–that is to say, it is a difference.

If 700 coughs and stutters and then says that it is just an odometer reading (like the 300, 700, 1100, 1400) then the judge will order the bailiff to escort him out of the court room and he will be charged with “Contempt of Vector Calculus”.