And so, my dear pupils, it is time for another foray into the deep effervescent thoughts of that most delightful system of measurement, the Mike Unit.
Now, as a brief refresher, remember that a Mike Unit is a specific unit of measure. That is to say, if you pour liquid into a cup and you measure the volume of the liquid in the cup, you’ll find that it is one Mike Unit. If you measure how hot the liquid is in the cup, you’ll find that it is one Mike Unit. If you measure the pressure of the liquid in the cup, again, one Mike Unit.
As a corollary then, if you measure the volume of liquid in another cup, you will again find it is one Mike Unit. But if you then pour this one Mike Unit of liquid into the other cup which already contained one Mike Unit, you would now find that you had one Mike Unit of liquid in the cup you poured into. Curiously enough, you would also still have one Mike Unit of liquid remaining in the seemingly empty cup.
The key here is that performing any operation on Mike Units results in a Mike Unit. So one Mike Unit plus one Mike Unit equals one Mike Unit. One Mike Unit minus one Mike Unit equals one Mike Unit. The same is true for times, divided by, raised to the power of, et cetera.
In my previous post, I mentioned that you can’t cancel Mike Units, so moving from 1MU + 1MU = 1MU to the seemingly identical expression 1MU - 1MU = 1MU is actually quite difficult. Let’s look at what would happen with normal numbers:
1 + 1 = 2
1 + 1 - 1 = 2 - 1
1 + 0 = 2 - 1
1 = 2 - 1
Here we subtracted 1 from both sides because subtraction is a special kind of operation that preserves equality when it is applied to both sides of an equality relationship. Then because 1 - 1 is 0 and something + 0 is the something, we wind up where we expected to be, namely that 1 + 1 = 2 implies that 1 = 2 - 1. The fact that we can apply an operation to both sides that in effect reduces one of the operands to zero is what we refer to as canceling.
Now let’s break down what happens if we try to follow the same logic with Mike Units:
1MU + 1MU = 1MU
1MU + 1MU - 1MU = 1MU - 1MU
1MU + 1MU = 1MU - 1MU
1MU = 1MU - 1MU
Notice here that subtraction is again equality preserving, so we were able to subtract the 1MU from both sides and still have equality. But on the next line, notice that we did not reduce that 1MU to zero. Instead, it remained one Mike Unit. Then we used the fact that 1MU + 1MU = 1MU to wind up with the final equation. But we never canceled by taking something to zero.
This is because there is no zero in Mike Units, there is only the 1 Mike Unit. Even when there is seemingly no Mike Unit, if it can be measured, it can be shown to be 1 Mike Unit. Fascinating, isn’t it?
Posted with : Bare with Me