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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-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.

November 19, 2008 | 34 Comments

On the growth of government spending: who benefits, the rich or poor?

UPDATE: Reader Stephen Dawson has kindly shown where I made a very stupid error. This error caused me to label the y-axis incorrectly in the third picture below. It also causes the fifth picture to change dramatically. I will leave my original analysis untouched, except to indicate in bold where it is wrong. See the post from 23 November 2008 for an update on these two important figures, where I will give the proper interpretation. Thanks again to Dawson.

It’s obvious that, as time has gone on, the Federal Government has spent more and more and more money. Since a reasonable proxy of government control over the lives of its citizens is the outlay of funds from its treasury, a sane observer might wonder about this increasing trend.

A raw plot of the Federal outlay by year will not do as a measure, however. At least two adjustments have to be made.

A government ruling over 1000 people will obviously have to spend more than one ruling over 10 people, so we have to adjust by population size, which has also been increasing. We can be reasonably sure we are measuring population to, say, the nearest million, which is close enough. The budget is also reasonably well measured.

Then there is inflation, the phenomenon whereby a loaf of bread costs $1.00 ten years ago becomes $1.89 this year. But inflation is difficult to measure because of many reasons. For one, that loaf of bread probably isn’t the same as the loaf now: it has different ingredients, uses changed baking technology, improved packaging—who knows what has changed in that ten years. The population, too, which has increased over this period also tends to drive prices higher because it makes certain commodities scarcer. Plus, nobody knows which are the ideal items to track to measure cost increase: bread? cars? Eliot Spitzer’s hobbies? We’ll use inflation adjusted dollars in some of the plots, but we have to remember that these pictures are a lot more uncertain.

The first picture is the Outlay per Capita: that is, the dollars spent per citizen since 1901 (data from the US Budget Office and the US Census).
Outlay per capita
I have also colored the years red for Republican presidents, and blue for Democrat presidents. The years from 2009-2012 are obviously projections, so should not be taken too seriously. Not too much can be noticed, except for the obvious exponential increase in government control, plus the two blips for World Wars I and II.

Since the rate of increase is exponential, we can see things clearer by showing the picture on a logarithmic scale:
Outlay per capita
The two war-time era increases now pop out, with WW I showing the biggest increase. The after-war decreases are also more obvious. And we can see the small blip for the Korean war and a smaller build-up for Vietnam (all these increases are in the blue areas). The steady increase after Vietnam is also clear: where you can see a higher rate of increase in George W. Bush’s years because of the Iraq/Afghan wars, but certainly not a giant surge. Of course, I do not parse how much of any spending is due to military and civilian funding.

The big, but maybe not so obvious. point is that 2008 spending is about $10,000 per person. That means the government is spending $10-grand per head. That also means, in some loose sense, that if you pay more than this in taxes—if your personal bill is more than $10k—then you are paying more than your equal share. This implies, then, that if you are paying less than $10k you are not paying your equal share. You are requiring those that are better off to support the bulk of the government.

Now, if you are a Lefty, then you probably like this idea. “Let the rich pay their ‘fair’ share!” But to say this ignores Briggs’s Doctrine of Unintended Consequences. To see what I mean, let’s look at the same picture adjusted for inflation. The inflation adjustment index is from Oregon State University.
Inflation-adjusted Outlay per capita in 2008 $
This is adjusted to 2008 dollars. Suppose I were to declare that every citizen had to pay $10 to the treasury. If you, for example, were Dad and the only worker in a family of four, your bill would be $40. The last time this happened was in the 1940s (remember: this is 2008 dollars, not 1940 dollars, so $40 was affordable).

This analysis is broadly correct, but the y-axis was off. You can see that the cost in 1940 was about $700 per head, or $2800 per family of 4 (all in estimated 2008 dollars). Still affordable, but to as many families as $40.

Everybody can afford this (with the trivial exception of a handful of people). Everybody would contribute an identical amount and would, morally at least, be entitled to an equal say in government. “But, wait! The rich will still have more money, and with money comes influence!” Yes, true. It is a tautology to say the rich will have more money, and it is obvious that with more money comes more influence. But this is not a good argument, my Lefty friend. Because look at 2008, where the bill is $10k per head. Only a small percentage of the population (about 5%) can afford this. Those 5% of course have more money. They further are aware of where that money is going. They will therefore have plenty of motivation to control the outflow, which means controlling the laws, rules, and regulations—controlling the government—which say where the money is to go. This small minority will use their money to align the government to their views.

Now, the rich certainly would have done this to some extent had everybody had to pay the same share, but they will have orders of magnitude more motivation to do it when they are paying nearly all the bill. And—here’s the kicker, so pay attention—they will still have plenty of money left over to have the same influence over other non-governmental matters, influence they already had before this tax structure started asking more of them.

About the only thing this confiscatory tax policy will do is to take enough money from the just-rich, to make them no longer rich. Thus, more control will flow into the hands of fewer and fewer people. This is inevitable. And it’s happening at an exponential pace. The noble idea of having those with more pay for those with less guarantees that those with more will have even more, and those with less will have even less, plus they will suffer a corresponding loss of influence and control over government.

Disproportionately taxing the rich to grow government, and doing so at an increasing, exponential pace, thus guarantees the creation of a oligarchic ruling class. Supporting these tax laws, then, will have the exact opposite effect of your intent.

I use the term “Lefty” not to indicate “Democrat”, as will be clear in the next two pictures:
Change in Outlay per capita in 2008 $
These are the year-to-year change in outlay per captia. The first is unadjusted, the second is adjusted to inflation.

The unadjusted shows the blips due to the wars, plus the accompanying decreases in the budgets after the wars ended. Most of the wars, WW I, WW II, Korea, and Vietnam happened under Democrat administrations. But there was only moderate growth until Nixon was president in 1969, then the increases began with real vigor, and it has rarely abated since (only one year in Reagan’s presidency did the budget not increase significantly).

The scarier picture is this one, adjusted by inflation:
Inflation-adjusted change in Outlay per capita in 2008 $
This shows the contest between R and D more clearly. Nixon (R) had a modest rate of increase, but Carter (D) really showed how it was done with a stellar increase. Reagan (R) did his best, but could never match Carter. Clinton (D) was also just an average player. Bush (R) beat them all. No taxpayer left behind. Again, Obama’s (D) tenure is just a wild guess by the budget office; however he has often boasted of increasing taxes on “the rich”, so we can guess that his rate will be Carter-like.

My comment below about my not being an economist is right on: I am not and made a fundamental error here. The new figure shows the changes more clearly—they bounce around 0 a lot more than I originally thought. Be sure to see the 23 November 2008 post for more on this Figure.

I am not historian or economist enough to say why the rapid increase in government control really got going with Nixon, but we have some hints in his social spending policies. The funny thing is the opposite of common wisdom appears to be true. Most, but not all, of the increases in spending for the military have come from Democrats (the wars just mentioned); and most, but not all, of the increase in spending on social causes have come from Republicans. Each side, as we all know, is continuously accusing the other of the opposite! It might be a case of projected guilt all politicians feel (at some level; I cannot really guess why this is so).

Even if you don’t agree with me on anything, it must be clear that this rate of increase cannot continue indefinitely. It cannot even continue for very much longer. Roughly, every 20 years brings an order of magnitude increase in government control. So in 40 years, in the trend continues, the bill will be about $1 million per head, an impossibly high number. Power would be coalesced into the hands of a very, very few.

I don’t know about you, but I plan a two-pronged strategy: (1) to never vote for anybody, D or R, who I think will raise taxes, and (2) to be one of those who can afford the tax, because I’d rather have the control than not.

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Signed copies: update

Update: to get a signed copy you must email me at with SIGNED COPY in the subject line. I’ll then contact you for payment details. Cost is $32.00. You can order the book below, but it won’t be signed. If you did buy from below thinking it would be signed, send me an email and I’ll let you know where to mail the book to get it signed. Sorry for any confusion. Thanks.

Got another batch of books in last night and I’ll mail them out this morning.

This takes care of all the orders I have received so far.

Perhaps one of the wisest men to ever live has said this about the book:

[T]he book is very good. I am enjoying it thoroughly.

Buy one now. Perfect Christmas gift for that brainiac you know. You won’t be disappointed, and neither will they.

Small book cover
Click here to order.

November 17, 2008 | 15 Comments

Statistic of the day

In today’s New York Post comes a startling new research finding, bulleted in this graphic:
NY Post

In case you can not see the picture, it says that 29% of women “Care about partner’s appearance” and that 63% of men do.

Internationally renowned researcher Dr. H. Harrister was quoted as saying, “You know what that means, don’t you?”

“It means that 37% of men are lying.”