Professor Kruskal pointed out to my class a few years ago that someone had written a paper about how pi is wrong: http://www.math.utah.edu/~palais/pi.pdf
The author points out that if pi were 6.28, things might be simpler or more elegant...
For example, when you took trigonometry you learned that one full rotation of a circle is 2*pi. Thus that cyclical graph we know as sin(x) and cos(x) would look the same but the x-axis would just be multiplied by a factor of two. After all, humans invented pi and the value. Maybe it's tacky to suggest that one circle should allow pi(in radians)=pie(shape). Or maybe we gave it a number before we really understood what pi was really about. Let's dig a little deeper and explore some other things Mr. Palais points out:
Currently: cox(x+pi) = -cos(x)
If pi=6.28: cos(x+pi) = cos(x)
Currently: roots of unity e^(2*pi/n) = 0, 1, ..n-1
If pi=6.28 roots of unity e^(pi/n) = 0, 1, ..., n-1
And my all time favorite (the most beautiful equation ever written):
e^(pi * i) = -1
Now if we let pi = 6.28 we get:
e^(pi * i) = 1
Yes, we've improved the amazing.
So, while the mildly mannered geeks all celebrate today as pi day, I'll be waiting until June 28th to sit down and read "The Joy of Pi" http://www.joyofpi.com/
Monday, March 14, 2011
Thursday, March 3, 2011
Fun with Google's Latest Visualization Tool: Ngram Viewer
Late last year Google released another free tool called 'Ngram Viewer' http://ngrams.googlelabs.com/. It's similar to Google Trends but we're no longer limited our search to the last decade or so. Google may not have existed in 1800, but they're now able to show how many times a particular word or phrase was in text by year. When your spare time hobby is to scan in every book every written you can do interesting stuff.
Want to know how many times the word 'fuel' was written between 1800 and 2008? Try it out, you'll some interesting things.
Linked are some I found interesting:
The Future is No Longer Now, it has been replaced with the Past:
http://ngrams.googlelabs.com/graph?content=future%2Cpast&year_start=1800&year_end=2010&corpus=0&smoothing=3
But we like to write about the years:
http://ngrams.googlelabs.com/graph?content=1800%2C+1850%2C+1900%2C+1950%2C+2000&year_start=1800&year_end=2008&corpus=0&smoothing=3
Political Parties:
http://ngrams.googlelabs.com/graph?content=republicans%2Cdemocrats%2Cwhigs&year_start=1800&year_end=2008&corpus=0&smoothing=3
Some of the presidents:
http://ngrams.googlelabs.com/graph?content=Roosevelt%2CNixon%2CReagan%2CBush%2CCarter%2CKennedy%2CLincoln%2C&year_start=1800&year_end=2008&corpus=0&smoothing=3
Academic Subjects (stolen from Ben Shneiderman):
http://ngrams.googlelabs.com/graph?content=chemistry%2Cphysics%2Cbiology&year_start=1800&year_end=2008&corpus=0&smoothing=3
Burger King IS King:
http://ngrams.googlelabs.com/graph?content=McDonalds%2CHardees%2CTaco+Bell%2C+Burger+King&year_start=1800&year_end=2000&corpus=0&smoothing=3
Want to know how many times the word 'fuel' was written between 1800 and 2008? Try it out, you'll some interesting things.
Linked are some I found interesting:
The Future is No Longer Now, it has been replaced with the Past:
http://ngrams.googlelabs.com/graph?content=future%2Cpast&year_start=1800&year_end=2010&corpus=0&smoothing=3
But we like to write about the years:
http://ngrams.googlelabs.com/graph?content=1800%2C+1850%2C+1900%2C+1950%2C+2000&year_start=1800&year_end=2008&corpus=0&smoothing=3
Political Parties:
http://ngrams.googlelabs.com/graph?content=republicans%2Cdemocrats%2Cwhigs&year_start=1800&year_end=2008&corpus=0&smoothing=3
Some of the presidents:
http://ngrams.googlelabs.com/graph?content=Roosevelt%2CNixon%2CReagan%2CBush%2CCarter%2CKennedy%2CLincoln%2C&year_start=1800&year_end=2008&corpus=0&smoothing=3
Academic Subjects (stolen from Ben Shneiderman):
http://ngrams.googlelabs.com/graph?content=chemistry%2Cphysics%2Cbiology&year_start=1800&year_end=2008&corpus=0&smoothing=3
Burger King IS King:
http://ngrams.googlelabs.com/graph?content=McDonalds%2CHardees%2CTaco+Bell%2C+Burger+King&year_start=1800&year_end=2000&corpus=0&smoothing=3
Monday, February 28, 2011
GirlTalk and Computer Science, what more could a guy ask for?
Yes, it's no secret I love Girl Talk. Who doesn't love this musical magician? I swear he's using a computer program of some sorts to identify which music to use and how to blend it. No mortal could EVER be that good.
It's also no secret I love computers. I love technology (more than Kip I swear) and I'd hope the pursuit of my PHD in computer science is such an indication. This semester I am taking Information Visualization taught by Ben Shneiderman. Thus is was as if the stars aligned when one of my buddies sent me a link that has a nice visualization of the latest Girl Talk album 'All Day':
http://mashupbreakdown.com/
Finally I can see what song is being played at what point. A few of the items are slightly off but I think this is a nice way to view Girl Talk's implementation. It's insane to think he occasionally mixes up to 7 songs at a time.
Insane.
It's also no secret I love computers. I love technology (more than Kip I swear) and I'd hope the pursuit of my PHD in computer science is such an indication. This semester I am taking Information Visualization taught by Ben Shneiderman. Thus is was as if the stars aligned when one of my buddies sent me a link that has a nice visualization of the latest Girl Talk album 'All Day':
http://mashupbreakdown.com/
Finally I can see what song is being played at what point. A few of the items are slightly off but I think this is a nice way to view Girl Talk's implementation. It's insane to think he occasionally mixes up to 7 songs at a time.
Insane.
Subscribe to:
Posts (Atom)
