Tuesday, March 22, 2011

How To Divide By Zero

Ever since elementary school, I was always told that you can't divide by zero.  After all, zero designates nonexistence, and you can't divide by nothing.  But as of today, I am convinced otherwise.  As my thoughts wandered a bit at work (as they often do), I wondered if there is some way that zero can be divided by, even if it's some lame excuse.  And believe me, I'm great at lame excuses.  Once I even found two different (and quite lame) ways to justify adding two and two and getting five.  It was in trying to come up with a lame excuse that I found the answer.  It was more a problem of logic than anything.  And it's something we do all the time and just never realize it.

To understand how to divide by zero, one must first understand the absolute basics of what division is.  Division is taking a certain quantity and evenly distributing said quantity to a number of locations.  Simple as that.  Now when one only uses whole numbers and doesn't split any of the components into smaller pieces, one often ends up with remainders.  For example, if you have 42 apples and want to put them evenly into five baskets, each basket would have eight apples with a remainder of two.  Now here's where it gets a little weird.  What if you couldn't find the baskets to put the apples into?  Then 42 apples not split into any baskets (basket quantity = 0), then the per-basket quantity is zero with a remainder of 42.

Now let's put it into somewhat practical use.  Twenty school children at recess want to play a game of football.  It doesn't matter if it's American Football or International Football (Soccer).  They are just going to play some sort of football.  Now don't pick nits.  Anyway, we can assume that there will be two teams, as football (any type) tends to be played.  So we know that, after the teams are chosen, that each team should have ten players.  But what about before the teams are picked?  How many are on each team?  To find out, we take the total number of players (20) and divide it by the number of teams which have players currently allotted to them (0), thus getting the number of players on each team (zero with a remainder of 20, or 0R20).

When dividing a given quantity by zero, the answer will always be zero with a remainder of the quantity to be allotted.  Dividing by zero is the ideal means of calculation when fractions and decimals are inappropriate (whole pieces must be distributed), even distribution is required, and either the source quantity has no destination or the quantity is less than what is needed for the destinations.  For example, four apples divided evenly into five baskets is still zero with a remainder of four.  If the destinations can't fit into the distribution "pool" then they can't exist in said pool (quantity of zero).

Since division is about allocation, then anything which is not allocated must be assumed as being divided by zero.  And since there will always be categories which any item will not fall into, it must be assumed that all things, in one form or another, is divided by zero, until it is actively allotted in one way or another.  Any thing in a normal state of being is divided by zero, and any non-zero division would suggest change.  Therefore, it is not only possible to divide by zero, but it would seem to be the natural order of things.

This moment of mathematical bliss was brought to you by workplace boredom.

You now know how to divide by zero.  Impress your friends.

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