Thursday, March 29, 2012

Money for (almost) Nothing

Five Hundred Mega Dollars, to be precise.
(Image from Wikipedia)
I am not typically interested in lotteries.  They seem silly and I am seriously beginning to question their usefulness in bringing about a good harvest.  But this morning I read in the news that the Mega Millions lottery currently has a world record jackpot up for grabs.  In fact, the jackpot is so big...

Tonight Show Audience:  HOW BIG IS IT?

It is so big that I decided to do a little bit of analysis on the expected returns.  Zing!

Wednesday, March 14, 2012

Pi storage

Let me share my worst "best idea ever" moment.  Sometime during my undergraduate I thought I had solved all the world's problems.

You see, on this fateful day, my hard drive was full. I hate it when my hard drive fills up, it means I have to go and get rid of some of my stuff.  I hate getting rid of my stuff.  But what can someone do?

And then it hit me, I had the bright idea:
What if we didn't have to store things, what if we could just compute files whenever we wanted them back?
Sounds like an awesome idea, right?  I know.  But how could we compute our files?  Well, as you may know pi is conjectured to be a normal number, meaning its digits are probably random.  We also know that it is irrational, meaning pi never ends....

Calculator Pi

There is a very fast converging algorithm for computing pi that you can do on a desktop calculator.
  • Set x = 3
  • Now set x = x + sin(x)
  • Repeat
This converges ridiculously fast, after 1 step you get 4 digits right, after 2 steps you get 11 correct, in general we find:

A Clarification

As there seems to be some confusion among my fellow Virtuosi, I wanted to point out that Pi day occurs on July 22nd or, in the year 4159, on January 3rd.

Today is in fact Seventh Power Day.


Fun fact:  pi squared is very close to 10.  How close?  Well, Wolfram Alpha tells me that it is only about 1% off.

I first realized this fact when looking at my slide rule, pictured to the left (click to embiggen), just another reason why slide rules are awesome.

It turns out I use this fact all of the time.  How's that you ask?  Well, I use this fast to enable me to do very quick mental arithmetic.

Moving Pi-ctures

My TV celebrates without me.
Today, as I'm sure you're aware, is Pi Day - a day for the festive consumption of pies and quiet self-reflection.  In the spirit of the holiday, I'd like to present a point for discussion:

Everyone has a great talent for at least one thing.

That this is true for at least some people is seen through even a cursory glance at a history book:  George Washington was really good at leading revolutions, Michelangelo was an outstanding ceiling painter [1], and Batman was the best at solving complex riddles (especially in English, pero especialmente en espaƱol).

But I'm certain that this holds for everyone.  What's your talent? Mine, as those of you who read this blog should know very well by now, is certainly not doing physics.  Nope, my talent is watching TV.  Seriously guys, I watch TV like a boss [2].  In light of this talent, I thought I would describe a few instances in which I have seen pi represented (for better or for worse) in TV and movies.

A Very Small Slice of Pi

Rhubarb pie (Source: Wikipedia)
Some people know a suspiciously large number of the digits of pi.  Perhaps you have met one of these people.  They can typically be found hiding behind bushes and under the counters at pastry shops, just... waiting.

At the slightest hint of a mention of pi, they will jump out and start reciting the digits like there's a prize at the end.  After rattling off numbers for a few minutes they abruptly come to an end, grin like an idiot, and walk away.  It is an unpleasant encounter.

The sheer uselessness of this kind of thing has always bothered me, so I'd like to set a preliminary upper bound on the number of digits of pi that could ever possibly potentially kind of be useful (maybe).  For those following along at home, now would be a good time to put on your numerology hats.

Primes in Pi

Recently, I've been concerned with the fact that I don't know many large primes.  Why?  I don't know.  This has led to a search for easy to remember prime numbers.  I've found a few goods ones, namely

But then I remembered that I already know 50 digits of pi, memorized one boring day in grade school, so this got me wondering whether there were any primes among the digits of pi

Lo an behold, I wrote a little script, and found a few:

Found one, with 1 digits, is: 3 Found one, with 2 digits, is: 31 Found one, with 6 digits, is: 314159 Found a rounded one with 12 digits, is: 314159265359 Found one, with 38 digits, is: 31415926535897932384626433832795028841

I think it's usual for most science geeks to know pi to at least 3.14159, if you're one of those people, now you know a 6 digit prime! for free!

Monday, March 12, 2012

F-91 Revisited

Farmer Uncle Sam...with a rifle.
(Image Credit: Wikipedia)
Today was a sunny exception to the grey overcast rule of weather in Ithaca.  I should be overjoyed by this anomaly, spending the day outside flying a kite or playing frisbee with a border collie in a bandanna.

Unfortunately, today was also the beginning of Daylight Savings Time (DST) - my least favorite day of the year.  For my colleagues unfamiliar with this temporal travesty (I'm looking at you Arizona), let me briefly explain DST.  

Once a year, the time lords steal a single hour from us and place it in an escrow account for future disbursement, presumably in some elaborate scheme to gain the favor of hat-throwing farmer-clock hybrids (see image left).  The details are a bit murky, but the net result is that today I had one less hour to do my very favorite thing in the whole wide world - sleep.

It also means that I have to set my watch, so I figured I'd check in and see how well my previous model for time-loss in my watch has held up.

Tuesday, March 6, 2012

Proofiness: A look into how mathematics relates to American political life

Dearest readers,

This is my first post on The Virtuosi, so I thought I’d take a moment to introduce myself.  I’m a first year physics graduate student at Cornell, recently joined after 2 years working as an engineer first at a private firm and then at a national lab.  I myself have had lots of fun following the exploits of my estimable colleagues here on The Virtuosi, and I thought I could bring a new angle to the content here.   I would like to use this space to discuss how science interacts with everyday life in a cultural sense. How does science appear in popular culture?   How do political or social issues relate back to science? Those sorts of questions.  (I understand that there are plenty of other resources elsewhere that offer far more intelligent insight into these matters than I can, but in the very least this will give people a chance point them out to me as they yell at me in the forum below.)

Enough intro, here begins my very first blog post:

Being interested in how science is communicated to the public, I am an avid reader of popular science.   While academic types sometimes dismiss this kind of writing as shallow or otherwise uninteresting, I think science writers perform a very important function serving as a way to convey information about conceptually challenging topics to a general audience.   At their best, I find that these books serve as examples for how I can communicate my own ideas better, and in addition challenge my understanding of how science relates back to society in general.