The Spectre of Math

February 29, 2012

Devil’s in the details

Filed under: Politics — jlebl @ 8:40 pm

It seems that not only did some democrats vote in the Michigan republican primary, satan himself also voted. Check the primary results in Mackinac county (e.g. on http://elections.msnbc.msn.com/ns/politics/2012/Michigan/Republican/primary at least this was the data on wednesday)

The final result in that county was very close. It was by one vote for Romney, but you should check how many votes did Santorum get:

Romney: 667 (41%)
Santorum: 666 (41%)

February 22, 2012

Exponential growth (and CEO pay)

Filed under: Economics,Mathematics,Politics — jlebl @ 11:17 pm

So CEO salary has increased by approximately 9.7% adjusted for inflation every year between 1990-2005 [1] (that is approx 300% increase over that time, so 4 times what they had in 1990). Anyway, that has a doubling time of \frac{\log 2}{\log 1.097} \approx 7.5 years. Now median CEO (among the top 200) made approximately 10 million a year in compensation in 2010 [2]. In 2009 there were about 8.3 trillion dollars in existence [3]. Anyway, approximately a CEO makes a 1 millionth of the money in the world, or in other words, if we had a million CEOs we’d exhaust our money supply. It takes about \log_2 1000000 \approx 20 doublings to get a million. Hence in 20\times 7.5 = 150 years one CEO will make all the money in the world. And this is all inflation adjusted.

But we don’t have to go so far to get into trouble. Now we did talk about the top 200, so when would the top 200 make all the money in the world. Well that requires only \log_2 \frac{1000000}{200} \approx 12.3 doublings so 12.3 \times 7.5 \approx 92 years. OK, so in less than 100 years, the top 200 CEOs will suck out all the money in the universe.

Anyway, the problem is the following: The companies are not rewarding an individual CEO for good performance. They are rewarding all future CEOs. The thing is, that there is no “starting salary.” A CEO that just started is (statistically) making about the same as the one who’s been around for quite a while. If you would start all CEOs at a base salary, then one particular CEOs salary could rise at 10% a year because he’d be with the company only a fixed number of years, the problem would be manageable. Now to whatever extent there is anything like a “starting salary” the increase an individual CEO makes is even higher than 10% a year. Essentially the starting salary is increasing at 10% a year.

Let’s look at even a more realistic example of how quickly do we get into trouble. The CEO salary can easily be even 1% of the revenue for the company [4]. In fact some small private colleges are paying 1% of their budgets to their university president, a group where similar thing has happened. Well, now think about this doubling. If it is 1% now, it will be 2% in 7.5 years, 4% in 15 years, 8% in 22.5 years, 16% in 30 years, 32% in 37.5 years, 64% in 45 years, and we get 100% at less than 50 years. So in less than 50 years the entire revenue would have to support the CEO. Now you say, well but the revenue is also growing. Not so fast, the 10% pay increase is overall, that includes companies that did badly and those that did well. One would think that the growth of revenue on average (including failed companies) is not that much more than inflation. And this is adjusted for inflation. In any case CEO is definitely growing a lot faster than the economy (and hence your average revenue), and hence you hit the wall sooner or later. Even if we lob off another 2% to adjust for growth, the doubling time for CEO pay is still 9 years.

Of course a problem would appear a lot earlier than in 50 years. So it’s not only the “rich get richer” and “things are not fair” argument. This state of affairs is actually unsustainable even in relatively short period of time (within our lifetimes). I think people don’t understand that exponential growth is really really fast. That’s why pyramid schemes never work. It’s why Ponzi schemes usually fail far quicker than the perpetrator hoped. 10% increase a year does not seem like much (just like 10% return on investment doesn’t seem like that terribly much).

[1] http://www2.ucsc.edu/whorulesamerica/power/wealth.html (better sources exist, but I am too lazy to search further).

[2] http://www.nytimes.com/interactive/2011/07/03/business/20110703-executive-pay-revisited-even-higher-than-it-first-seemed.html

[3] http://money.howstuffworks.com/how-much-money-is-in-the-world.htm

[4] http://yourperspective.org/index.php?action=read&value=16a2b99e-4847-102d-bdde-00065b3be33a

February 6, 2012

Diffy Qs notes at 20000 downloads

Filed under: Mathematics,Teaching,Technology — jlebl @ 12:31 am

So the differential equations textbook just reached 20000 downloads from unique adresses. The real analysis textbook is close behind (despite being a year younger) at around 19200. The rate is growing, it started out at around 200 per week for both in the fall and is now pushing 400 a week. As an overwhelming percentage of the hits come from google I think google might have ranked the pages higher. So if you want to help out with the project of free textbooks: link to the books on your blog, page, whatever. And press those social buttons on the page, I guess that also does it.

It’s also interesting to see how ipv6 is doing. So far, 82 ipv6 adresses looked at the real analysis book and 43 for the diffyqs. As ipv6 was active for about half a year on the server, it’s still a very tiny percentage. There were about 6-7 thousand ipv4 addresses looking at the diffyqs book during that time frame and about 8-9 thousand for the real analysis book. But at least someone is using ipv6 (if I could get an internet provider that offered ipv6, I’d use them, but I didn’t find such in Madison).

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