Older blog entries for vicious (starting at number 311)

Exponential growth (and CEO pay)

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 years 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 managable. 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


Syndicated 2012-02-22 23:17:39 from The Spectre of Math

Diffy Qs notes at 20000 downloads

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).


Syndicated 2012-02-06 00:31:34 from The Spectre of Math

When will the beheading start

It is always good to know when will other people want to cut off your head. Let us look at when were most heads cut off: that was probably the French revolution. OK, what made people want to cut off other people’s heads? Extreme inequality. OK, what was the Gini coefficient? Well, one estimate is 59 [1]. OK, so if we look at the US Gini coefficient it seems to be rising approximately linearly since 1980. In particular, US Census Bureau (via Wikipedia [2]) has the following data:

1980 40.3
1990 42.8
2000 46.2
2009 46.8

Let us do linear regression to obtain:

2020 50.0
2030 52.4
2040 54.8
2050 57.1
2058 59.0
2060 59.5
2070 61.9
2080 64.3

So, I guess people will start trying to cut other people’s heads off around 2058. We’re all safe till then.

[1] Christian Morrison, Wayne Snyder The income inequality of France in historical perspective, European Review of Economic History, 4, 59-83.

[2] Wikipedia.org, Gini Coefficient.


Syndicated 2012-01-21 22:40:35 from The Spectre of Math

Biking

So, it was -15 celsius (barely positive farenheit) and snowing this morning, actually it’s still -15 and still snowing. Surely only a complete moron would bike to work today. Actually the ride was pretty good. Yesterday it was -18 and I think I can tell the difference (though it was not snowing). The downside of biking in this weather is that the gears are refusing to shift. The levers just sort of stick and nothing happens. Fortunately, I’m in a reasonable gear right now.

Another downside is that I have these cool hybrid tires on the mountain bike. Sort of like road tires with spikes only on the sides, which is reasonable in terrain and much smoother than regular mountain bike tire on the road. They were really good at the UCSD campus (San Diego) where I’d go off road often and it never snowed. Because they kind of suck on snow.


Syndicated 2012-01-20 22:02:19 from The Spectre of Math

Newspapers will be half the size on wednesday

With the Wikipedia blackout, what will journalists do? There will be a lot less in the wenesdays edition, though on the plus side it will have a better chance to be correct or at least original. Also, all school essays that were due wenesday will be turned in a day late.


Syndicated 2012-01-17 22:53:23 from The Spectre of Math

New chapter in real analysis notes

I finally posted a new version of the real analysis book with the new metric space chapter, it weighs in at 192 pages now (with 12pt font though). It also fixes a now record number of errata; though my standard for what is an erratum rather than just a simple obvious typo has dropped slightly. One thing that makes me feel better about errata is that it seems Rudin’s 3rd edition of principles still has some errata that is essentially the same as what I did (independently, not that I really worry about taking credit for errata:).

The differential equations book nowadays seems to be hitting fewer and fewer problems: 6 errata in the past year, 2 of which have been in new stuff added before the summer. This is despite several people using the books and one ongoing partial translation. So I guess they are rather “correct” by now.

My goal right now is to get them to be correct rather than perfect. So I haven’t really been reordering things or rewriting things that could be improved. I’ve been at most doing small improvements in exposition. The main thing is that I want to spend time doing other things too of course:)


Syndicated 2011-11-18 23:17:13 from The Spectre of Math

Wisconsin

On the way to Madison we were trying to see what the Wisconsin ski resorts look like. Seems like the toughest runs are rated double-black-bunny.


Syndicated 2011-08-27 02:29:50 from The Spectre of Math

No more overheating

Pissed off about the CPU overheating, I wrote a simple daemon. It monitors the core temperatures and sets the cpufreq governor to powersave when temperature in either core is above 90 deg celsius, and sets it back to ondemand when it gets below 75 in both cores (those numbers I pulled out of my ass, they might need tuning). It simply polls the temperature every 2 seconds. There is no configuration or anything, simply change code and recompile. It’s all the neurons I’m willing to commit to this problem.

Yes I know performance might suffer since the CPU can go even further, but I don’t care about performance, I care about the machine not turning off randomly. I guess ondemand is actually better poewr (and heat) wise when everything is normal, but when then heat is high, powersave does come to the rescue.

Here is the code for those that want to do something similar. You might need to modify it heavily. I called it noverheatd.c, I simply compile the thing with something like gcc -O2 -Wall noverheatd.c -o noverheatd, placed the resulting binary in /root and then in /etc/rc.local I added /root/noverheatd &. The parts that need modification is set_policy where you need to set the number of cpus your kernel thinks it has, and then in the main loop you need to set the right coretemp paths for all the coretemps you have. I had to run “sensors-detect” as root from the lm_sensors package to obtain those guys.


Syndicated 2011-07-12 19:15:44 from The Spectre of Math

Books

About a week ago I finally added those new extra exercises I’ve been promising on the webpage (almost 150 new exercises) to my differential equations book. These are now with solutions. I did not want to add solutions to existing exercises. I still feel that it’s better to not have solutions. But I guess having some exercises with solutions does make the students feel better. Plus it seems this was an argument against using my book in at least department (not enough exercises and no exercises with solutions). So there. Some of the new exercises are interesting, many are just simple plug and play exercises to get students going. I’ve added all of them as exercises numbered 101 and above so that I would not change existing numbers. I suppose the “even/odd” thing is the common theme, but this has the added advantage that I can have fewer exercises without solutions.

As for the real analysis book. After having taught with Rosenlicht at UCSD (because my book doesn’t have metric spaces), I decided I will use my book at Madison this coming fall. This requires that I write up some metric space stuff. So I will be adding a Chapter 7 to the book. It will probably not be completely polished by the fall, so I might keep it separate even for the fall and only add it once all the bugs are caught after teaching with it. The plan is to do first everything on the real line and then do metric spaces. I found that metric space stuff was a bit too abstract for the students if I jumped right in. It might be better to do first sequences and continuity with real numbers only. I will skip some other material such as series though, and cover other material more lightly, due to time constraints. As for other news on the book: It is now (in slightly modified form) the standard book at University of Pittsburg.


Syndicated 2011-06-27 22:42:25 from The Spectre of Math

We have to kill you to save you

This is funny in a very dark sort of way. Let’s do some numbers: Suppose that after some time about 100 people a year die from extra radiation exposure due to all these scanners. That’s a fairly low number, it would be impossible to
even notice this number from the cancer statistics. Given the millions of people that get scanned every year and that spend sufficient time near those scanners, that’s a tiny percentage. Now let’s see, let’s suppose we take the last 50 years of plane travel before 2001 and we notice that number of people killed in terrorist attacks including 2001 is a little more than 3000. That’s about 60 a year. Let’s suppose that no terrorist attack ever happens again (yeah right). Still we’d be killing almost twice as many by our security measures.

I wish my granddad were alive, this is what he did (nuclear hygiene). It would be nice to ask if 100 is a reasonable estimate.


Syndicated 2011-06-27 22:01:37 from The Spectre of Math

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