What Does It Mean When Big Negative Numbers Get Smaller?

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):


Fiscal Year
Ending On
30th of:
in Deficit Over
in Deficit Over
1981 (78,968) (5,138) (7%) JEC/RWR
1982 (127,977) (49,009) (62%) RWR
1983 (207,802) (79,825) (62%) RWR
1984 (185,367) 22,435 11% RWR
1985 (212,308) (26,941) (15%) RWR
1986 (221,227) (8,919) (4%) RWR
1987 (149,730) 71,497 32% RWR
1988 (155,178) (5,448) (4%) RWR
1989 (152,639) 2,539 2% RWR/GHWB
1990 (221,036) (68,397) (45%) GHWB
1991 (269,238) (48,202) (22%) GHWB
1992 (290,321) (21,083) (8%) GHWB
1993 (255,051) 35,270 12% GHWB/WJC
1994 (203,186) 51,865 20% WJC
1995 (163,952) 39,234 19% WJC
1996 (107,431) 56,521 34% WJC
1997 (21,884) 85,547 80% WJC
1998 69,270 91,154 417% WJC
1999 125,610 56,340 81% WJC
2000 236,241 110,631 88% WJC
2001 128,236 (108,005) (46%) WJC/GWB
2002 (157,758) (285,994) (223%) GWB
2003 (377,585) (219,827) (139%) GWB
2004 (412,727) (35,142) (9%) GWB
2005 (318,346) 94,381 23% GWB
2006 (248,181) 70,165 22% GWB
2007 (160,701) 87,480 35% GWB
2008 (458,553) (297,852) (185%) GWB
2009 (1,412,688) (954,135) (208%) GWB/BHO
2010 (1,293,489) 119,199 8% BHO
2011 (1,299,595) (6,106) 0% BHO
2012 (1,089,353) 210,242 16% BHO


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
the numbs)


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