John Borwick’s blog

A snowflake has approximately 10^15 unique characteristics. The birthday problem’s generalized solution is

Pr(k, s) = 1 - ( s! / ( ( s-k)! * s^k ) )
k is sample size.
s is the number of possibilities.

I need to know two things:

1. For what minimal k does Pr(k, 10^15) exceed 0.5?
2. How many snowflakes have ever fallen in history?

Unfortunately, I don’t really know how to find the answers to either question. My math is rusty about how to deal with factorials, and I have a hard time visualizing how many snowflakes are in one cubic foot of snow. Help, anyone?

Update

Mass of a snowflake is 3 x 10-6 kg. The density of snow ranges from about 50 to 300 kilograms per cubic meter. Therefore one cubic meter of snow has around 10^7 snowflakes.

Russia has 16,995,800 square kilometers of land mass. Let’s make that 1.7*10^7 km^2, which you have to multiply by 10^6 to get cubic meters = 1.7 * 10^13. Assume that all the snow that has ever fallen in the world is at least equal to covering Russia with one meter of snow… that gives us 1.7 * 10^20.

If a snowflake has 10^15 unique characteristics, then we have definitely had a lot of identical snowflakes. Even if a snowflake has somewhere in the range of 10^21 unique characteristics, I think the birthday problem will show that the probability is that we have seen at least two identical snowflakes.

I missed this one, but apparently

During the 5 October 2004, debate between United States candidates for the office of vice president, the incumbent Vice President Cheney responded to an issue by referring viewers to ‘factcheck.com’. Mr. Cheney apparently intended to refer viewers to factcheck.org instead of factcheck.com.

Here’s what’s awesome:

Name Administration re-directed those visitors to a website relevant to U.S. politics. Name Administration chose the website of investor, philanthropist, and political activist Mr. George Soros, because his website is well-funded, does not seek to raise funds from visitors, and had greater capacity to absorb the load of visitors, reaching over 100 visitors per second during peak times after the debate.

George Soros is one of the most-donating liberals evah and his goal is to get George Bush out of office. High quality.

I’m off work again this week. I just watched the end of Oz season four.

Oh yeah! Only one more season (on DVD) (that I know of) to go!

Armistice Day (now Veterans’ Day) is November 11. I’ve meant to take a minute of meditation/reflection at 11 AM on November 11 for many years, and I’m hoping that this year I’ll remember.

I’ve heard stories that during WWII the German and Allied forces had an informal cease-fire on November 11, but I don’t know that for sure.