Math


So Al Gore, who invented the internet, says the earth is warming quickly and we’re on the cusp of passing the point of ecological no return and dying a horrible, hot, death.

Enter stage left: Christopher Monckton, who “…advised Margaret Thatcher, FRS, on scientific scams and scares”, lays out how the U.N. has possibly cooked the books regarding the warming trend so many are alarmed about.  Specifically, “…the UN had minimised the sun’s role in changing past and present climate, persisted in proven errors and used unsound data, questionable graphs and meretricious maths to exaggerate future warming threefold.”  Wow.  Not holding much back, is he?  [Note to self: I’ve got to add meretricious maths to the next performance report I write.]

Not content with that, he then lambastes the proposed solution of spending 1% of the world’s GDP in order to “avert disaster”.  The likely outcome?  “They are also coy about what value our $500 billion a year would buy us. They say that if the world stabilises atmospheric CO2 at about 485 parts per million we’ll have spent 1 per cent of GDP to get – er – a 1.1 per cent fall in consumption.”

Not being an environmental scientist, I can’t really say whether global warming is something to be worried about or not.  I’m convinced it’s real, but I’m not convinced it’s as bad as people think.  Call me a skeptic, but until the models can predict the temperature 5 and 10 years down the road (hasn’t been done yet), then it’ll be more likely I buy into the global warming panic.

I’m all for environmentally friendly buildings, power, cars, and more.  However, I’m for those things because the Mrs. has introduced the concept of ‘frugality’ into my life and I’ve taken a liking to it.  If I can save some money by changing the light-bulbs to LEDs and having an energy efficient house, then maybe she’ll reward my efforts by funding one of these.  Plus, I’m a big fan if independence.  So, being independent of middle-eastern oil is good and being independent of aging U.S. power distribution systems is better.  Go green!

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I’m down south for a while (the lower-48 for those not familiar with the Alaskan terminology) and find I have more time than usual for reading.  Right now I’m in the middle of Fermat’s Enigma by Simon Singh.  It’s the story of a several hundred year-old theorem that resisted proof by the greatest mathematical minds during that time and has only recently been solved.

I was amused by Pascal’s view of religion,

 Pascal was even convinced that he could use his theories to justify a belief in God.  He stated that “the excitement that a gambler feels when making a bet is equal to the amount he might win multiplied by the probability of winning it.”  He then argued that the possible prize of eternal happiness has an infinite valaue and that the probability of entering heaven be leading a virtuous life, no matter how small, is certainly finite.  Therefore, according to Pascal’s definition, religion was a game of infinite excitement and one worth playing, because multiplying an infinite prize by a finite probability results in infinity.

There are many paths to faith.

That said, I recommend the book.  I’ve been a fan of Singh since discovering The Code Book several years ago.

Talk about applied math!  Here’s a little trick that can open all 5-key keyless vehicles in 3129 key strokes (usually less).  Neat stuff…if you don’t own a vehicle with keyless entry.  One more reason to love my mid-90’s Jeep, if only I could stop the driver’s side door from rusting off…

The easy way for car-makers to make this a non-issue is to require an action (another key press like ‘Enter’ or attempting to open the door) in order for the combination to be accepted and simultaneously reset the keys.  That would significantly increase the time it takes to run through all the combinations and defeat the economies the system gains with each sequence building one number at a time from the previous sequence.

(H/T Bruce Schneier)

Love is like pi – natural, irrational, and very important.

– Lisa Hoffman

One of my favorite brain teasers is asking someone to describe a shape with an infinite circumference but finite area. The answer is a fractal (an object or quantity that displays self-similarity) called the Kock Snowflake.

It is built by starting with an equilateral triangle, removing the inner third of each side, building another equilateral triangle at the location where the side was removed, and then repeating the process indefinitely. The area converges to eight-fifths of the original triangle while the circumference grows infinitely. The figure below shows the first three iterations.

Koch Snowflake

Source: Weisstein, Eric W. “Koch Snowflake.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/KochSnowflake.html

So for those who were curious, the by-line at the top of the blog is the beginning description of a Markov sequence or Markov chain. It’s a sequence of random variables X1, X2, X3, … with the property that, given the present state, the future and past states are independent. While that may not sound very interesting, the Wikipedia entry notes that Markov chains are used in Google’s PageRank, speech recognition, generating random numbers, and in Bayesian inference. The last one is the email tie-in because of its use in sorting out bulk spam emails from the emails you want to get.