Comments on: Override

By: Peter Joes

Peter Joes — Wed, 03 Jun 2009 22:40:54 +0000

To talk about a percentage increase from zero is gibberish.

I guess next we will be talking about the increase in gubernatorial veto overrides of the state budget – - again infinite according to some – - but ask any Republican and they’ll tell you its insignificant.

By: Bokweb

Bokweb — Wed, 03 Jun 2009 22:18:39 +0000

But we don’t get into these infinite fractional divisions because, in our statistical problem, we’re dealing with an irreducible unit of 1, and 0 just happens to be the starting point. Thus, there were 531 times more millionaires in 2007 than in 2000 – which is a 53,100% increase.

Your example of the New York Times – dividing the increase by the original amount – happens to work; it doesn’t work here, where the starting amount is 0. My approach happens to work here, as it provides a result that more or less accurately expresses the increase in millionaires without getting bogged down a sideshow wrestling with infinity – but I wouldn’t claim that it would be useful in more complicated calculations (and I’m still uneasy with a zero in the picture).

All of which suggests to me that neither of us is using the best math for this kind of problem.

By: PBremser

PBremser — Wed, 03 Jun 2009 15:31:23 +0000

The Sunday New York Times will now cost $6 at my local convenience store. Last week it cost $5. To compute the percentage increase, I take the increase ($1) and divide by the original amount ($5) to get 0.20, meaning 20%. Since it’s a relative measure, it has no units. (Doesn’t matter if I’m talking dollars or pennies or pesos — it’s still 20%.)

So the reader who said the increase in the number of millionaires is infinite is correct, in the sense that we’re trying to divide 531 by 0 (the original number of millionaires) here. That is, we’re looking for a number p such that 0 times p is 531. But 0 times anything is 0, so finding that p is an unsolvable problem. So what happens if you divide 531 by smaller and smaller numbers?
If you take 531 and divide it by 1/2, you get 1062;
divide 531 by 1/4 and you get 2124;
divide 531 by 1/8 and you get 4248;
divide 531 by 1/100 and you get 53,100, etc.
Fixing the numerator at 531 and letting the denominator get closer and closer to 0 gives you numbers that are growing without bound, and that’s where infinity comes in.

By: Bokweb

Bokweb — Wed, 03 Jun 2009 12:59:53 +0000

I thought of the whole zero thing – any increment over zero, however tiny, theoretically being an infinite percentage increase – but I wasn’t in the mood for flights of mathematical fancy.

I stand by my post: it’s a 53,100% increase. At least since the 14th Amendment was ratified, any tabulation of persons greater than zero is a positive integer. Thus, for purposes of these statistics, all of those pesky (and infinite) fractions have been factored out of the calculation.

The larger fallacy of the infinity argument, however, is that it assumes that the difference between zero and 1 is (infinitely) greater than the difference between 1 and 2. While pondering that notion, it’s worth remembering that while Zeno ruminated over his paradoxes, Achilles did, in fact, overtake the tortoise.