Posts Tagged ‘books’

Mike Brown, Planet Killer: “Mercury is Pissing Me Off”

December 19, 2010

Mike Brown is famous for discovering Eris, a dwarf planet larger than Pluto orbiting out on the far edge of the solar system. Ultimately, Eris’ discovery led to the redefinition of the word “planet” and the eradication of Pluto from children’s lunchboxes.

Brown’s new book, How I Killed Pluto and Why It Had It Coming tells the story of his team’s discovery of a complete menagerie out past Neptune – a place most astronomers thought held little but hydrogen, comets, and a few bits of rock that occasionally get flung out there by gas giants.

In an interview from last Wednesday, December 15, Brown told me that his most scientifically-important discovery was not Eris, but Sedna, a large object lying so far away from the gravitational perturbations of Jupiter and friends that its orbit can be traced back to the beginning of the solar system, and whose existence has challenged astronomers’ conception of how the planets formed.

Brown also showed me the sonograms of his embryonic daughter (now 5 years old) to compare side-by-side with photographs of Venus taken by the Venera Lander, and commented on the gravitational influence of my mother.

Part 1 (17 minutes: Hate mail, the process of writing, science of the early solar system)

Part 2 (31 minutes: More science, more writing, international intrigue, Pluto’s appeal and wimpiness)

Median of a Very Long List of Primes

December 21, 2008

This morning I read a short review of a new popular math book, the conceit of which will be obvious from the title:
The Unimaginable Mathematics of Borges’ Library of Babel

Using Amazon’s search feature, I got as far as reading the following passage, in which the author attempts to describe why it would be difficult to evaluate the expression “the median of the prime numbers less than 10100“:

By the famous prime number theorem – which we’ll outline in a moment – there are 1097 prime numbers smaller than 10100. This number may sound manageable, but 1097 is trillions of times larger than the number of subatomic particles in our universe. There simply isn’t any imaginable way to list and keep track of 1097 numbers, which precludes the possibility of finding the median

However, you don’t need to keep track of all the numbers to find their median. A simple algorithm will do the job.
Just look from prime numbers from both ends of the spectrum. Find one small prime number, then one big prime number, then one small prime number, etc, until the two paths either meet or cross. Then you’ve got the median. At any point, you only have to remember what number you’re building up from at the low end of the range, and what number you’re counting down from at the high end. Not only do you not need to remember the entire list of prime numbers, you don’t even need to remember how many prime numbers you’ve found.

To illustrate the method, find the median of all prime numbers less than 100:
Small Primes: 2 3 5 7 11 13 17 19 23 29 31 37 41
Big Primes: 97 89 83 79 73 71 67 61 59 53 47 41

Now that both lists have reached 41, you know that is the median. Even as I write this I don’t know how many primes there are between 1 and 100. And, although all the primes are listed on the lines I just wrote out, I don’t remember them off the top of my head.

It wouldn’t be fast to find the median prime when the top of the range becomes 10100. It gets increasingly harder to evaluate whether a number is prime when you start tacking on digits, and, as the author pointed out, there are a lot to go through. But storage space is no problem.