Numbers v. Units

In a previous post, I argued that numbers and units are born together.

As we deal with quantities of increasing sophistication, we often have a choice between using more sophisticated units or more sophisticated numbers.

If we wish to deal with uncustomarily large lengths, we either start to use suitably large length units, or we learn to deal with uncustomarily large numbers.  If we start to deal with unfamiliarly small weights, we can employ suitably small units, or we can start incorporating some kind fractions into our number system.  If we start to discuss bidirectional quantities, we can use an opposed pair of units---e.g. debit and credit---or we can learn to use negative numbers.  If we need to use quantities in the plane, we can use directional units like north, south, east, and west, or we can learn to use right and left (aka $\pm\sqrt{-1}$), and the other numbers of the plane (aka complex numbers).

Doesn't make sense yet?  In subsequent posts, I hope to spill all the details. 

For now, remember that increasingly sophisticated kinds of numbers can be understood by playing with increasingly sophisticated kinds of units.  Also, notice that technical usage of the quantities convention supports real numbers, or at least ragged reals.  It does not really support complex numbers.  We shall require a broader view of quantities than is provided by customary usage of the quantities convention.