So, say you have a big negative number, such as, oh, I dunno, a negative 1 trillion, and say that that number measures something. And say that you measure that thing a year later and it now measures out at a negative 900 billion. Is that second number smaller or bigger than the first number?
On one hand the second number is closer to zero than the first number, which means that the second number is closer to being a positive number, which means that the second number is bigger, right?
But on the other hand the second number is smaller in its negative-ness than the other number, which means that the second number is smaller, right?
Such is the mind of a middle-schooler coming to grips with negative numbers.
Well, I am pretty sure that we’re all taught that the first explanation — the one that says that negative 900 billion is bigger than negative 1 trillion — is the correct one.
And let’s not even get started on what happens when you multiply negative numbers (no, let’s not do that . . . or should I say, yes, let’s not do that?) or fractions or, heavens to murgatroyd, the situations in which you should add exponents together or multiply them. And, no oh no, please, no fractional exponents in the mix.
* * *
I bring this up because we recently had an annual update to a series of very big negative numbers that are pretty directly impacting our lives, and because, what with all the electioning going on our there, the update didn’t make much of a splash in the media.
I speak of the federal deficit for fiscal year 2012 (which ends September 30th, right before the SCOTUS kicks into gear). The deficit for FY2012 was $1.089 trillion, down from $1.3 trillion, a decrease in the size of the deficit relative to the prior year of 16% (as always, your trusty FRED has all the federal deficit numbers going all the way back to 1901). Most would call that a step in the right direction.
Here are the numbs for the past three decades or so (my apologies to small-screen readers for the discombobulate you’ll see of this table; here is a pdf for you):
in Deficit Over
in Deficit Over
Now, if those double negatives and interactions don’t make your head hurt, you aren’t paying attention. Plus, if I had more time I could make it an easier set of numbers to follow.
For now I make but three points:
1. The deficit for this past year was not as big as the year before. And that is the correct direction you want to see it going in over the long-run (though many would differ about whether this is a good thing in the short-run).
2. The rest is a Rorschach Test. Choose your favorite president and see what was going on with the direction of the deficit during his (no hers in this group!) tenure. How’d the numbs do, and, either way, is he blameworthy/praiseworthy? Why?
3. As is often the case, a simple series of numbers, delta’ed and otherwise cogitated and sifted and manipulated, yields some weird results. A simple percentage calc in the table above gave two aberrant results, in instances where the negatives swung to positives and such. I haven’t the time to look into it, but I think the formula would need to be a bit more if/then oriented to truly generate smart results. As it is, I had to hardwire the results, i.e., override the simple percentage calc when it gave a couple’a negs which should’ve been positives.
Like I said, double negs and such. Ain’t the numeric universe grand . . .
681 words, and lots of numbs
(a seven minute read — but
a lotmore minutes if you
want to cozy up to