eon

Posted by tpc at June 6th, 2010

Yesterday (5th June) was World Environment Day. I wouldn’t say I’m a green fanatic but I do try my best to recycle, use the air conditioner only when it is unbearable and bring my own non-plastic shopping bags whenever I know I was going shopping. According to this webpage, a total 17,291 species are known to be facing extinction.

I wonder what is the source of the number. If you google World Environment Day 17291, 17 of the first 20 webpages has a variation of that same sentence. Out of these 17 only this one suggests that the number is not exact. I quote (emphasis mine)
“In totality, there are roughly 17,291 species that are on the threatened list”

The number 17291 stood out for me. It turns out to be prime! In fact wolfram alpha tells me it is a twin prime. No prizes for working out which is its twin. Of course, 1729 is the famous Ramanujan Taxicab number. Perhaps that’s why it looked familiar.

Update 1: Google’s spider is amazing. I just googled 17291 and this post has been indexed within 13 minutes.

Update 2: The source seems to come from The IUCN Red List of Threatened Species and this blog post has a breakdown. So the number does appear to be exact at least at a certain point in time.

Posted by tpc at May 21st, 2010

If for some reason, you wanted the values of certain mathematical constants to a few billion digits, numberworld.org might be a site for you. Well known ones like are all there to billions of digits. Not much is written about the what and the how of the computations so you’ll have to take the author’s word for it. Incidentally do not make the mistake of confusing A.J. Yee, computer scientist and author of the website with A.J. Yee, the combinatorist.

Posted by tpc at February 28th, 2010

while a rose by any other name may smell as sweet, a mathematician might just be discriminated by his/her name. The perceived ability of a mathematician (as well as most academics) is by publications. There are two norms in listing authorship of joint work. One adopted by mathematics and economics is to list the authors alphabetically, regardless of amount of contribution. On the other hand, for disciplines like psychology and biology, the norm is to list the author in terms of contributions. It’s an interesting phenomenon, because I’ve seen biology papers with many authors. It seems that if you are in a lab which publishes 10 papers, chances are high that you get your name in every one of them, maybe as the 7th author. Perhaps, I can get my name as the 8th author by just walking past the lab! In a sense, as long as the main author’s name is first, he probably wouldn’t mind sharing credit with people, maybe in the hope that the favour is reciprocated.

I must say both practices have their pros and cons. Suppose you are a young person writing with an established guy, people would tend to think the established person did the work, unless you put your name first. On the other hand, a co-authorship might result in A providing an idea and B doing all the work. Now, who should deserve more credit? The one who did the work? Not really. A good idea is usually hard to come by. Plus it can be touchy to always have to establish who should get main credit. I suspect the relationship wouldn’t last or at least be as cordial. Compare that to the Hardy-Littlewood rules for collaboration.

I’m not one to want to upset the established order, so I stick to the alphabetical routine. As my surname is in the last quartile of the alphabet, I’m always the second or third author. I do have this nagging suspicion that this might have impact on how people perceive your contribution. This was confirmed when I read superfreakonomics. That book mentioned the following paper in Economics that concluded that there is some bias towards academics with names arriving later in the alphabet. Here’s the reference if you are interested.

What’s in a Surname? The Effects of Surname Initials on Academic Success, Liran Einav and Leeat Yariv, Journal of Economic Perspectives - Volume 20, Number 1—Winter 2006—Pages 175–188.

One main point is that tenured faculty in the top 5 economics departments in the US have surnames arriving earlier in the alphabet than junior faculty. But the bias disappear as the data is expanded to the top 20 or 35 departments. So perhaps the impact of that bias is not as great as things like race, gender and other forms of discrimination.

Posted by tpc at October 12th, 2008

In the midst of recession and oil prices falling from $145 to below $80, the ridiculous power company announced that electricity prices are going up by 21%, based forward oil pricing. The best thing is that our electricity are generated through natural gas, not crude oil!

Even more ridiculous is the following quote taken by the report written by one Liaw Wy-Cin.

The scope for savings is high considering that power consumption patterns show that 40 per cent of households, from one-room flats to landed properties, use more than the monthly average, said Mr Khoo (Chin Hean, EMA chief executive.) EMA is the electricity and gas industry regulator.

Well, if the report was accurate, the statement defies common sense! By the very definition of average, 50% of every household would use more! I’m guessing the 40% comes because they banded the average consumption into ranges. (I made a terrific blunder here, see the comments.)

Another report from Reuters said

People who take long spells of sick leave at least once in three years face a higher risk of early death,…

What a magnificent revelation, almost as strange as rooster crows leading to a higher chance of the sun coming out. Come on, which part of ’sick’ in sick leave do you not understand? People suffering from serious ailment take sick leave and have a high chance of premature death. Common sense tells you that. Again, either it was a worthless paper in the British Medical Journal or it’s the reporters missing the point.

Posted by tpc at June 3rd, 2008

Most people tend to confuse randomness with uniformly distributed. They believed that if you toss a coin 100 times you would get 50 heads and 50 tails. Lots of people have discussed this, gave examples of how they detected pseudo randomness. I would like to add my very own example.

I have 1600 exam scripts ordered by student matriculation numbers, divided into 16 piles. A total of 11 students asked to checked their scripts. One would think the 11 would come from different piles right? Here’s the actual stats: number of scripts (from pile number)

2 (1), 1 (4), 1 (6), 2 (7), 2 (9), 3 (14).

Posted by tpc at August 4th, 2007

I read in the local newspaper that 54.2% of bioengineering graduates last year found jobs not related to their field of study. Ha, great fodder for me to attack the crazy obsession with life sciences. But since we live in a google age, I thought I better check the data. Turned out that there are only less than 50 per cohort so that 54.2%. So there are two ways to interpret this.

1) only about 25 people found non bio related jobs. This is a small number and could reflect just diverse interest or better opportunities in business and finance. (These days every other study want to go into finance.)

2) then again for such an exclusive club. 50 out of the 1300 engineering graduates, you would think that these students are the creme de la creme, specially honed with tender loving care into bright future stalwarts of the life science industry. Surely, the industry could squeeze out 50 jobs?

Posted by tpc at January 21st, 2007

A headline in a local newspaper read “Want higher salary? Get master’s degree”

Woe is me, for a master’s I possess not. The reporter wrote based on a ministry of manpower study which I tried in vain to locate. So I can’t compare what was implied by ministry versus what was implied by the newspaper reporter.

The reporter wrote: “Getting a master’s degree is the most financially rewarding - with each year of study, wages climb by 23.1 per cent. It even beats getting a PhD, which will earn one a wage hike of only 14.7 per cent.”

I have no problem with the statistics. If you count an MBA as a master’s then it is clear why this is true. Finance professionals earn astronomical pay compared to academics. Along the way, highly successful managers like to get their MBA. My point being, these people earn more before getting their masters and not the other way around.

Here’s a local version of the news report.

Posted by tpc at July 27th, 2006

A very nice guardian article on how the British used statistics to count German tanks. (via Mathforge.) I particularly like this bit:

The statisticians believed that the Germans, being Germans, had logically numbered their tanks in the order in which they were produced.

Posted by tpc at July 2nd, 2006

The latest advertising campaign of a local internet service provider is tauting their service as the Fat Green Pipe. (Allusions to Super Mario Bros?) It is classical Darrell Huff.

The numerical data states 95% vs 65% which is measured by the length of the pipes. Yet, in the illustration, their own green pipe is at least 4 times as wide as the competition’s.

Related: An article on Huff and his book. Linked via wiki.

Posted by tpc at April 9th, 2006

Honestly, I know next to nothing about statistics. It’s no wonder that I have not heard of this book, and most of the actors in the stories within. This is a good book that tells the tales of the origin of statistical studies and should be a must-read for all statistics majors. One major flaw was that he was writing too much for a layman, and most of the details are hidden behind some general explanation. While this is alright for a brief history of the subject, I sincerely believe that anyone who is willing to read a 300 page book on statistics, would like to see a deeper discussion. Another gripe is that the author seem to come across as one who is very critical of those who are only interested in pure theory/mathematics. That aside, the book is filled with gems.

I particularly like this delightful quote attributed to R. A. Fisher

A scientific career is peculiar in some ways. Its raison d’etre is the increase of natural knowledge. Occasionally, therefore, an increase of natural knowledge occurs. But this is tactless, and feelings are hurt. For in some small degree it is inevitable that views previously expounded are shown to be either obsolete or false. Most people, I think, can recognize this and take it in good part if what they have been teaching for ten years or so comes to need a little revision; but some undoubtedly take it hard, as a blow to their amour propre, or even as an invasion of the territory they have come to think of as exclusively their own, and they must react with the same ferocity as we can see in the robins and chaffinches these spring days when they resent an intrusion into their little territories. I do not think anything can be done about it. It is inherent in the nature of our profession; but a young scientist may be warned and advised that when he has a jewel to offer for the enrichment of mankind some certainly will wish to turn and rend him.

Posted by tpc at March 23rd, 2006

by Steven D Levitt and Stephen Dubner. A local bestseller that attempts to find the hidden answers from (not necessarily economic) data. The answers presented are controversial to say the least, but yet not quite far fetched. That’s I guess the main selling point of the book.

The following passage is from the book. It has nothing much to do with the theme/thesis proposed by the authors. But when I read it, I began thinking whether or not it was mathematically consistent.

The ECLS project surveyed roughly one thousand schools, taking samples of twenty children from each. In 35 percent of those schools, not a single black child was included in the sample. The typical white child in the ECLs study attends a school that is only 6 percent black; the typical black child, meanwhile, attends a school that is about 60 percent black.

Another completely unrelated thing. Simpson’s paradox. A google search will reveal several good write-ups.

Posted by tpc at February 22nd, 2006

My previous job was doing operations research in a big logistic company. The problem of the day was making accurate forecasts. For example, the amount of work fluctuated significantly from day to day and we needed an accurate gauge of the manpower requirements for the next day to give us time to make adjustments.

While the people on the ground have been doing the forecast manually based on their years of experience, the management wanted us the techies to make the process scientific. Honestly, it was a lost cause to begin with. And the biggest reason for failure was that there was no accurate benchmarking of our forecasts compared to the manual prediction.

In real world situations, I don’t really think it is possible to make any reliable forecast. Yet, you see the economists and financial analysts telling you the dow jones will hit 12000, google’s stock price will hit $450. Mostly, we the silly people laps up their predictions but nobody bothers to check how good they were.

As an experiment, I tabled the GDP forecast by the Singapore Government Statistics Board. These were the official figures, not those dime a dozen ones given by analysts, as reported in the newspapers. So the combined wisdom of the Singapore Chief Statistician and his minions told us:

Jan 2005: 3% to 5%
Apr 2005: Low end of 3% to 5%
May 2005: 2.5% to 4.5%
Aug 2005: 3.5% to 4.5%
Nov 2005: 5%
Feb 2006: Accurate figure 6.4%

So despite the fact that they were continuously revising their figures as more data came in, they were still completely way off. One might argue that they chose to err on the side of caution but I honestly think that I might have done better by picking a figure at random. Random walk theory I guess.

Posted by tpc at March 23rd, 2005

One headline of the local newspaper reads “Living Room is the Most Dangerous Place for Kids”. In the report, they quoted a study which showed that 30% of accidents involving children occurred in the living room. This is a classic case of sensational reporting and abuse of statistics. There is a really simple reason why most accidents occur in the living room - children spend more (active) time there. So what are we to make of the report? Overreact and ban our children from the living room? From now on, the kids are confined to the staircase because the report showed there are 10 times less accidents at staircases than in the living room.