John Borwick’s blog

I just finished categorizing all my entries, back to when I started blogging in 2003.  My blog taxonomy is a little unwieldy, perhaps because I was making it up as I went along.  Here they are, by category (please note one entry can be in multiple categories):

Technology: 199
Entertainment: 157
Politics: 100
Links: 53
Winston-Salem: 38
Self-Improvement: 32
Tweets: 21
Work: 18
Language: 17
Science: 17
Travel: 14
Writing: 8
ITSM: 6
Religion: 3

Some problems: “Technology” is such a large category as to be useless; and technically everything on here should be able to go under “Entertainment.”

I feel like I need a “re-balancing” algorithm, where if a category is more than N times as big as the average category size then it gets sub-divided or re-assesed.  Conversely if a category has fewer than 1/N of the average size maybe it should be re-factored into other categories.

Arguably, to be an effective blog I should have some theme under which most of my posts reside.  Oh well.

Filed under “Science” and “Self-Improvement.”

Today is the winter solstice! Sunrise here was at 7:28 AM!

I think Thoreau once argued that, given a nearby city he had to travel to, the ordinary person would earn their wages for coach fare and travel the next day, whereas Thoreau would just walk and get there.

The only flaw with Thoreau’s thought is that some time is more valuable than other time. For example, if I had to get to the nearby city to catch a friend before they left, I might be willing to take out a loan.

I’ve been playing Urban Dead, a zombie game. As a human, you can search for ammo or you can attack with melee weapons. The balance is that it takes you a long time to find ammo and load it into your weapon, so the urbandead wiki argues this is a “stored action.”

More than that, I think that the idea of “stored action” can be applied to preventative maintenance. For example, if you fuel up your car when it’s not an emergency, you have more time freed in case of emergency.

Is exercise a way of storing your actions (because you live longer)?

Professor Libbrecht from Caltech was kind enough to explain the snowflake problem to me, and to give me permission to quote him.

Let’s make the numbers a bit smaller to make things clearer. Say a snowflake contains just 10,000 molecules, and these lined up in a straight line. Most of these are ordinary water molecules, but let’s say 100 are heavier isotopes.

Then the question is, how many ways can you arrange these 100 heavier molecules in this linear crystal? Well, the first heavy molecule could go at position 1, or 2, or any position up to number 10,000. Thus there are 10,000 places to substitute the first heavy molecule.

Similarly, the second heavy molecule has 9,999 possible locations. If you placed just two heavy molecules in the crystal, there are already 99,990,000 different ways to do it. By the time you place all 100, there are nearly 10^400 different ways to arrange things.

Since 10^400 is a very large number, there is basically no chance you would place 100 molecules in the same way twice.

The same logic applies to snow crystals, except all the numbers are much, much larger.

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.

You know how they say that every snowflake is unique?

Have you heard the proof about how if 30 people are all in a room, the odds are that two will have the same birthday?

Can’t you put the two together to prove that, somewhere in the course of history, there have been two identical snowflakes?

Some of the Slashdot geeks are talking about the Atkins Diet. I really don’t know how such logical people can think it’s a good idea to eat slabs of meat.

Atkins diet rebuttals:

• Atkins Diet Alert, from the Physicians Committee for Responsible Medicine
• The Guardian: Atkins diet is ‘pseudo-science’, say experts
• Big Fat Fake: The Atkins diet controversy and the sorry state of science journalism
• Atkins diet banned in Scottish hospitals

update: I posted on Slashdot for the first time.

The UK’s government has officially warned people about the Atkins diet.

From the Christian Science fair winners:

1st Place: “Life Doesn’t Come From Non-Life”

Patricia Lewis (grade did an experiment to see if life can evolve from non-life. Patricia placed all the non-living ingredients of life - carbon (a charcoal briquet), purified water, and assorted minerals (a multi-vitamin) - into a sealed glass jar. The jar was left undisturbed, being exposed only to sunlight, for three weeks. (Patricia also prayed to God not to do anything miraculous during the course of the experiment, so as not to disqualify the findings.) No life evolved. This shows that life cannot come from non-life through natural processes.

The Guardian reports, Long odds for massive meteor impact. My favorite part:

Bookmakers William Hill say that they are happy to take bets at odds of 909,000/1 that the asteroid will hit Earth on March 21 2014 and wipe out life on the planet. “On the principle that if the asteroid does wipe out life on Earth we probably won’t have to worry about paying out to winning customers we will happily take all such bets - although one customer who placed a bet on the world ending said that he would collect his winnings in heaven,” said Graham Sharpe, a spokesman for William Hill.

I like media that understands humor.