Ask Cool Daddy Nothing
Dear Cool Daddy: Back when you were talking about infinite Earned Run Averages, you mentioned you couldn’t divide by zero. And come to think of it, when paying the bills or doing my taxes, I don’t think I ever had to. But why can’t you exactly? …From Zeno, Square Root City
Dear Zeno: To be honest with you, I got help from Stolf on that one…he’s the numbers guy on this blog, the college boy. Stolf, do you mind being a guest lecturer here?
Hey, don’t sell yourself short. Weren’t you working on a Mixology Degree from the Sam Houston Institute of Technology?
Yeah, I was, but it was mail-order, and the postman kept drinking my homework.
Oh, well anyway, you’re right, I have a B.S. in Philosophy, with a minor in Math. But it was tough, because mathematicians hate philosophers. In fact, the worse insult a mathematician can hurl at a colleague is: “Oh, now you’re talking like a philosopher!” The reason is, unlike any other discipline, be it humanities, the sciences, engineering and technology, medicine, fine arts, hospitality, anything…only mathematics operates on a basis of absolute certainty. They don’t like people peaking behind the curtain to see why it is they believe what they believe. And that’s the job of philosophy, hence the hostility. What does this have to do with anything? I’ll get to that.
Now if you try dividing by zero on a calculator, you get ERROR. And there are 2 standard ways to explain why that is. Take 8 ÷ 2. Below, in the top section, you have 8 smiley faces. You can either ask: If you divide the 8 into 2 groups, how many are in each group? And we see, that’s 4. Or you can ask, as in the bottom section: If you divide the 8 into groups of 2 each, how many groups would you have? Again, it comes out 4.
But now, try doing it with 0 instead of 2. If you divide the 8 into no groups, how many are in each group? Or…If you divide the 8 into groups of 0 each, how many groups would you have? In either case, there’s no way to give any meaning to it. You come close with: divide the 8 into one group…or divide the 8 into groups of one each…but that’s still not the same as “no groups”…or “groups of zero each.” Thus math assigns the tag “undefined” and simply rules it out.
The second way to look at it is to say that division is a way to reverse or undo multiplication. In the blue boxes above, 8 ÷ 2 = 4 means the same thing as 4 x 2 = 8. But what happens in the orange boxes, when you try 0 instead of 2? Anything times 0 is 0…there’s nothing that times 0 can equal 8…so 8 ÷ 0 can’t be anything.
And it’s right about here that philosophy throws a penalty flag, benches clear, and punches are thrown. Philosophy wonders why it is you can take something as straightforward as numerals (above, in the red box), which represent numbers or quantities of things…then combine and compare them in various comibnations, using symbols (in the green box)…but you get stuck with one of the numbers and one of the symbols…0 doesn’t work with division. It’s as if you could add any 2 numbers together, except for 33…anything added to 33 gave a meaningless answer that had to be declared “undefined.” It makes no sense, and while mathematicians are happy to sweep this discrepancy under the rug, philosophers aren’t allowed to be so cavalier.
And there is a solution: If 0 were a symbol instead of a numeral, division by 0 would not be a problem…it would never even be an issue, any more than dividing a number by any symbol would be… like “8 ÷ =”…or even “8 ÷ ÷”. Of course, we would still need a symbol that indicated nothing in the ones’ place, nothing in the tens’ place, nothing in the hundreds’ place, etc. It would be better if “0” as a symbol were retired…too much old baggage…and a new placeholder symbol be adopted…
…thus, above top left is a list of “current” numbers, followed by 7 possible ways that a post-zero world might look. It would take some getting used to, but we would…and division by zero would be a thing of the past. Cool Daddy, does that answer the question?
I’m sorry, Stolf, what did you say after “Hey, don’t sell yourself short”?
shame + less + plugsh – h = …
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