Meet π’s cousin, φ

So what’s that symbol, you ask? It’s the Greek letter Phi (pronounced FEE).

We’ve all heard of the (in)famous π, or 3.14159265358… Our math teachers pounded this into our heads every year, and the nerds would always hold competitions to see who could recite the most digits of pi. So far, computers have sputtered out over 5 trillion digits of pi.

But another number, just as beautiful as pi, is relatively unknown to the masses. That number is phi, or 1.61803399… It is the number that satisfies the following algebraic equation: (a+b)/a = a/b.

There are many ways of expressing this golden number:

As an infinite series,

As a continued fraction,

As a continued square root, which bears striking resemblance to the above:

But wait, there’s even more:

φ^2 = φ + 1,

and even more surprisingly,

1/φ = φ – 1. Wow!

If that surprised you, this will truly give you a shock:

φ to the nth power is equal to the sum of the previous two integer powers of φ. Check this out:

• φ^3 = φ^2 + φ^1
• φ^4 = φ^3 + φ^2
• φ^n = φ^(n-1) + φ^(n-2)

The same thing goes with negative powers! Try it out!

Thought it couldn’t get even more fascinating? WRONG!

Compare the digits after the decimal point in this table:

n	phin	phi-n
1	1.61803398875	0.61803398875
3	4.23606797750	0.23606797750
5	11.09016994375	0.09016994375
7	29.03444185375	0.03444185375
9	76.01315561752	0.01315561752

Lo and behold, the decimal parts in the latter 2 columns are exactly the same! Also notable: this relationship does not exist if n is an even number.

For those of you who are still reading, there is a special link between phi and the Fibonacci series:

Let F_(n) = 1, 1, 2, 3, 5, 8, 13, …

WHOA! Who knew?

Bored of video games? Try this.

I stumbled across this website a few days ago while I was flipping through the pages of Scientific American. The name of the website is “Old Weather“, and it’s a project that aims to fill the holes in the earth’s climatic record between the years of World War I and World War II.

Now you may ask, who the heck cares about weather that’s 100-or-so years old? The fact is, between the two World Wars, we have a paucity of climate data, because weather recording was affected by the wars.

Then how do we get the data if it’s missing?

While ground-based weather stations lacked sufficient records, there were numerous ships at sea that kept records of weather on a day-to-day basis. OldWeather.org is a treasure trove of these ship logbooks, which typically contain six weather reports per day taken at four hour intervals. Unfortunately, the handwriting in these logbooks is almost impossible for a computer to read without horrendous mistakes. And that’s where the power of the HUMAN BRAIN comes in. Or rather, 550-thousand-plus human brains.

What is the “paranormal”, really?

As the name suggests, it’s something that’s unusual, strange, or simply not normal. The word “paranormal” most often refers to ghosts, spirits, or anything ethereal.

There’s a reason why most people have superstitions about the paranormal: it “shouldn’t” exist. When we were young, our minds could fathom basic things, like “if the stove is red, then it is hot,” or “the sun’s shining outside, it’s warm outside.” We couldn’t yet fathom why magnets attracted to each other, or how salt “disappears” in water. We would think of these as “weird”, “paranormal”, and “supernatural.”

Philosophy gone wrong

If 5 o’clock sharp and 5 o’clock flat mean the same thing, then why isn’t a sharp the same thing as a flat?

and

If going UP to Seattle means the same thing as going DOWN to Seattle, then why isn’t UP the same as DOWN?

Or maybe UP is the same as DOWN, which means:

Orionid Meteor Showers this Wednesday… who’s watching?

Right: An Orionid meteor photographed on Oct. 21, 2008, by amateur astronomer Rich Swanson of Sierra Vista, Arizona.

I’m watching! Historically, the only meteor showers I’ve ever watched are the Perseids, around August 12, but every time, I miss them. This year, I woke up at 2AM that day, and looked up at the sky. Nothing but light pollution from Seattle, and the sky was cloudy. BOO.

According to NASA (article here), the Orionid meteor showers this year “could be a very good show.” Year after year, I miss these showers, which come from Halley’s comet’s debris, but thanks to Twitter, I’m up to date.

The best time to see the meteor shower is before sunrise on Wednesday, October 21st. Lucky for me, I wake up before sunrise every day Monday – Friday. The ZHR (Zenithal Hourly Rate) is 60, which means on average one can expect to see sixty meteors shooting through the sky per hour. That’s about one per minute, but hopefully, the skies are clear and the meteors are bright.

If you’re going to watch them, wake up around 5AM or 5:30, and look south-east towards Orion. You can’t miss it.

UPDATE: Nope. It was cloudy today . Couldn’t see a darn thing. I’ll see if I can catch any meteors tomorrow (October 22nd, also the day when Windows 7 is released!)

The answer to “If humans evolved from monkeys then why are there still monkeys?”

Earlier this month I asked this question on my blog to see if anyone would be able to answer it. One person wrote and guessed that humans evolved smart enough to preserve monkeys, and that this was a rare instance. But that’s not the answer.

The answer is simple enough: humans didn’t evolve from monkeys!

So yes, this was a trick question, and it took me 30 seconds to realize that.

Humans and monkeys shared a common ancestor as they are both hominids. That doesn’t mean they evolved from each other. It’s like saying “if I evolved from my cousins, then why are my cousins here?”