November 25, 2008 | 10 Comments

## Which combination of President and Congress spent the most?

We’re probably getting tired of this topic (I am), but many people requested that we look at the same data but take into account the influence of Congress.

This is the same inflation-adjusted (to 2008) average yearly per capita spending, broken by Presidential, House, and Senate Parties (see yesterday’s post for a more complete description). There are 8 possible combinations (D President, R House, R Senate, and so on). These are arranged from highest to lowest average spending.

President Senate House Outlay
R R D \$8300
R D D \$6000
R D R \$5600
D D R \$5500
D D D \$4200
R R R \$2000
D R D \$1000
D R R none

That chart is kind of busy, so here is the same thing condensed by Presidential party and whether the House and Senate are completely aligned (all parties the Same), or one house the opposite (Mixed), or both houses opposed (Opposite).

I’m not sure how much we can read into this: these charts obviously ignore the time series nature of the data, the changing definitions of what a “R” and “D” mean. The strongest argument is those “R”s and “D”s are just letters to put after a name.

President Support Outlay
D Same \$4200
D Mixed \$1000
D Opposite \$5500
R Same \$2000
R Mixed \$5900
R Opposite \$6000

Still no GDP. Will get to it if I can.

November 24, 2008 | 11 Comments

## Which president spent the most?

Just for fun, here’s another way to look at the same data we’ve been playing with (in this post and this one.)

First thing is to calculate the inflation-adjusted spending per capita. Then total up the entire amount spent under each president. We could rank presidents this way, but it’s unfair to people like FDR who spent a lot longer in office then did, say, Ford. So I divided the total (inflation-adjusted per capita) by the number of years in office.

This gives a ranking based on who on average had the highest yearly spending. Everything is in 2008 dollars. Democrats in blue and Republicans in Red as usual.

Everybody is guessing, as we mentioned last week, but if the guesses are close, then Obama will top this list with \$9400 per citizen per year.

 Bush II 8900 Bush I 8200 Clinton 8000 Reagan 7500 Carter 6600 Ford 6200 Nixon 5400 Johnson 4600 JFK 4000 Truman 3400 Eisenhower 3400 FDR 2200 Wilson 700 Harding 500 Hoover 400 Coolidge 300 T Roosevelt 200 Taft 200

As was pointed out, this list does not take into account Congress.

November 23, 2008 | 4 Comments

## Government per capita spending revisted

Reader Stephen Dawson, a writer from Australia, has twice tried to show me where I made a bone-headed error in two of the figures from the original government per capita spending article from a couple of days ago. This time I was smart enough to listen and so reproduce those corrected figures below. They are also now correct in the original article too, but I haven’t changed any of the analysis there.

The first picture is this one:

(If you’ve visited this page before, be sure to hit “Reload” to make sure you aren’t using an old image from cache.)

This is dollars spent per citizen adjusted to 2008 dollars. The caveats about our inability to precisely measure inflation, plus the partial confounding of inflation and population growth still hold. What changes from the original is the y-axis is now properly adjusted for inflation (in the original, I multiplied where I should have divided—one of my favorite idiotic errors).

The story for the correct figure isn’t too much different than for the incorrect one. Spending was relatively constant until the first World War hit, where it jumped dramatically. It came down a bit in the post-war years, but started rising again after the Great Depression and the installation of FDR. Then another big jump for the Second World War, this time shown in its proper scale. After the war, we have the same depressingly exponentially increasing trend. What might be surprising, however, is that trend briefly reversed itself during the Clinton years. Also remember that the dark blue section is for Obama, and that these numbers are wild guesses.

The second picture is this one:

This is the annual change in dollars spent per citizen adjusted to 2008 dollars. Numbers less than 0 mean that the budget decreased per person in that year, numbers greater than 0 mean that the budget increased per person. Note the logarithmic scale on the y-axis. This figure is useful to see what happened on a year-to-year basis, but the overall trend is still in the first picture.

Start with 2001, Bush II’s first year in power. He decreased the budget. Then came the wars in Afghanistan and Iraq, and spending increased. Then also came a host of social spending programs. As said above, the picture for Clinton is more flattering. Two years he increased per capita spending, but six years he decreased it. Bush I also increased spending. Working backwards, we see that the opposite pattern held for Reagan. Even Carter decreased per capita spending for one year. Nixon split, but ended with more spending than he started with: that is, his increases were larger than his decreases. The rest is easy to see.

Who tended to increase spending more, Democrats or Republicans? Not in dollars, but in trend: that is, who had more up than down years? Ignoring the upcoming Obama years, Republicans had 25 years with increased per capita spending, and 35 down years. Or, they increased spending about 42% of the time. Democrats had 20 years with increased spending, and 31 years with decreased years; or they increased per capita spending about 39% of the time. Thus, both parties have roughly the same proclivities towards increasing the per capita spending (especially if you consider Obama has promised to increased spending—who knows whether he will—but if he does, then Democrats will have increased spending about 44% of the years).

That crude analysis obviously ignores all subtleties, such as total cost increase or decrease. It turns out that, over this period, Democrats increased net per capita spending by about \$5500, and Republicans increased the net by \$4000.

If you are fan of one party over another, these figures are nothing to crow about.

Thanks again to Steve Dawson for keeping us straight!

November 21, 2008 | 25 Comments

## Stock market crash, hearing aids, F-train music, and the boom-chhh Combinatoric Theory of Finite Musical Variety

The stock market is crashing and may have even bottomed out. Naturally, people are beginning to look around for buying opportunities. I have the perfect one.

Hearing aids.

Any company that sells or markets hearing aids is positioned for rapid growth over the next ten to thirty years. My scientific estimate is that a dollar invested today will bring twenty a few years from now. I give you this hot tip for free, my friends, just for being a loyal reader of this blog. You simply cannot go wrong.

My evidence for this stunning opportunity is based on my experiences commuting via the F train. My insight arrived suddenly, when yesterday I was surrounded by at least seven people wearing Thinking Suppression Devices (TSDs). I had to give up on reading James Fitzjames Stephen because each commuter’s device was louder than the others’. Everybody was wearing earphones, but even still, I was assailed by various booms and crashes which were clearly audible to anybody—to anybody not wearing a TSD themselves. These people are obviously going to lose a significant part of their hearing, if not go deaf, hence my advice about buying stock in hearing aid companies.

But I decided to make this an opportunity instead of despairing and following my usual approach of looking at my fellow passengers like they had just stepped in what they were listening to.

Now, the only distinct sounds I could make out—and I listened attentively—were various combinations of booms and chhhs (electronic cymbal crashes). This was my first important clue.

I asked the guy sitting next to me, who was fiddling with his TSD, “How many songs does that thing hold?” He said a number in the thousands, and that he had just about filled it up and was looking into getting a better model. I asked, “Got any Duke Ellington on it?” When he said “Who?”, I had my second clue, and realized that my boomchhh observation was not an accident. I therefore told him that he didn’t need a larger device, because there were only about 100 pop songs in the world anyway.

“Yes,” I sagaciously intoned, “based on my scientific measurements of your music—this is only an estimate, to be confirmed later, mind you—there are only about 100 possible songs that can be made. You don’t need a more expensive device. Think of the money I have just saved you!”

The look he gave me told me he was deeply aware of my genius. The fact that he edged toward the door as fast as he could, so that he could jump out at the next stop told me how excited he was to pass on his new knowledge to his friends and family.

It was on that train ride that I devised the Combinatorial Theory of Finite Musical Variety. This theory states that there are exactly, and only, 124 possible pop songs. Here is how it is proved.

Our first piece of evidence is that every popular song is comprised solely of combinations of booms and chhhs. There are other trivial elements, related to the outmoded and ancient theories of melody, harmony, point and counterpoint, and lyricism, but these can be, like they now always are, ignored.

The second piece of evidence is that, to build a pop song, you must have either three, four, or five booms and chhhs in combination and that at least one of these must be a special boom. Examples:

• boom boom chhh
• boom boom boom chhh
• boom chhh chhh boom chhh

Ready? Let’s start counting. Begin with the three combination, with one mandatory boom. Suppose first that the boom is at the end. The other two slots must be filled with booms and chhhs. We could have two booms, two chhhs, or one of each with either leading the way. That’s 4 possibilities. But then we remember that we have the mandatory boom at the end, which could be placed in any of the three available slots (it could have come first, second, or third), and then the other booms and chhhs would fill in the other two slots. This makes 3 x 4 = 12 possibilities.

What if there were 4 slots and one mandatory boom? Suppose again that the regulated boom is at the end, and the booms and chhhs fill in the other three slots. They could all be booms or all chhhs, or various combinations. We could list them all, but that gets to be a pain, so let’s use some math. We have three slots and we could put 0, 1, 2, or 3 booms in those slots, with chhhs filling in the blanks.

There is a formula for this called choose. If we say “3 choose 0”, we say we have three slots and we choose no booms to go in them. The choose formula tells you the number of ways we can do this. It should be obvious to you that the only way to place no booms out of three is 1; namely, you choose no booms. Formally, the answer is

n!
—————–
(n-k)! k!

where n! is read “n factorial” and means “n x n-1 x n-2 x … x 2 x 1”. In our example, n = 3 for three slots. At first, k = 0 for no booms. The formula works out to be

3 x 2 x 1
———————–
(3 x 2 x 1) x 0!

where you have to know that “0! = 1” (there are good, technical, mathematical reasons for this, which I’ll skip). There answer equals 1. Then you work this formula out for k = 1, k = 2, and k = 3 because we want to know how many different booms go into the 3 slots for each possible number of booms.

The answer turns out to be 1 + 3 + 3 + 1 = 8 for k = 0, k = 1, k = 2, and k = 3. But again we have to remember that one mandatory boom could have gone into any of the four slots, so we have to multiply the answer by 4 to get 32.

Thus far, we have 12 + 32 = 44 possible songs, but we still have to calculate the number of possibilities if there were 5 slots and one mandatory boom. The math is exactly the same, except n = 4, and k = 0, k = 1, k = 2, k = 3, and k = 4. But it turns out that there is a simplification when you sum up all possible combinations of 2 things (booms and chhhs). The sum of “n choose 0” + “n choose 1” + … + “n choose n” = 2n, which is very easy to calculate.

If n = 4 then 24 works out to 16 different songs with the mandatory boom at the end, but there are 5 possible places for that boom, so we have 5 x 16 = 80 combinations.

In total, then, we have 12 + 32 + 80 = 124.

That’s it, friends! There are only 124 possible pop songs. I was therefore right to harangue my train-mate with this wisdom so that he would not waste his money on a device that holds more than this. It is therefore a matter of great curiosity how people could not have recognized this before now, a fact which can only tell us of the deleterious effect of pop music on the brain.

Incidentally, a corollary to the theory is: Each pop song must be played as loudly as possible, not only to annoy those around you, but to destroy your hearing as quickly as possible.

Incidentally, incidentally, I cannot vouch that the math here is 100% accurate. This is because, as I write this, the beaujolais nouveau arrived in stores this afternoon, and I am liberally sampling this year’s offerings.