Sunday, September 12, 2010

Fun with Data Fitting


Holy page hit batman.    I will readily admit that I am a curmudgeony luddite when it comes to twitter.  The format perpetuates what I see as a disturbing trend towards shortened attention spans and disinterest in depth or subtlty. …or even knowing how to spell subtlety.  To be honest, though, my feelings may also stem from the question “What has twitter ever done for me?” 

Well, this has been a big week for me in the educyberbloggerinterwebmathsphere.  Firstly, I was really excited to meet three—count ‘em three—bloggers that I follow at an evening professional development get together where I may or may not have actually made the comment “One-half is not equal to two-fourths.”  It’s a long story that may or may not deserve a separate post, but somewhat related to Simpson’s Paradox. I had already put a face to Dan because I was blown away by his presentation last winter at CMC-North and, frankly, he’s sorta’ famous in that “famous within a specific subset of a specific field” sort of way. Nonetheless, it was great shaking his hand (ok, the handshake was actually just ok, but subsequent conversations were great).  I had not had a chance, though, to put a face to Jason or Sophgermain (although M. LeBlanc might be more appropriate).   

It appears that I also owe Dan and, begrudgingly, twitter a big thanks because my recent post about mathematical habits of mind was “picked up” via twitter by The O’Reilly Radar (and I thought they just wrote nerdy computer science books) and kottke.org (which I had never heard of, but it appears that other people have).  Anyway, the table below says it all.

Date
Page hits
Friday, August 20th
4
Friday August 27th
10
Friday, September 3rd
33
Friday, September 10th
6449

It’s growing exponentially!!  And by exponentially, I mean fast.  And by fast, I mean something completely different from exponentially.

So don’t fall for that malapropism.  With a little data fitting, you can instead see that these numbers fit the function:

f(t) = 1063t3 -6368t2 + 11670t - 6361 (with a little rounding)

where t is the number of weeks after August 13th and f(t) is the number of page hits.

What does this mean? The table below says it all.

    
Date
Page hits
Friday, August 20th
4
Friday August 27th
10
Friday, September 3rd
33
Friday, September 10th
6,449
Friday, September 17th
25,634
Friday, September 24th
63,964
December 31st, 2010
6,181,370
December 31st, 2014
12,266,700,000

Since this is greater than the United Nation’s projection of the world population at the end of 2014, this is unequivocal proof of either:
1.     Extraterrestrial intelligent life in the universe that will be reading my blog
2.     A tea party landslide in the 2010 midterm elections leading to a universal ban on contraception
3.     Bad math

I’ll let you decide.

6 comments:

  1. Well, I'm glad I had a chance to meet you before you become world famous, and impossible to meet!

    I really did laugh out loud when I got to that 12 billion.

    I've had two big spikes. (Neither as big as this.) One when Peter Gray, who blogs on the Psychology Today site, mentioned my blog. And one when the video of my math salon went up. The trick is keeping people coming back. I'll anticipate more delightful mathematical humor (and great stuff like the habits of mind post), as you attempt to do that.

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  2. Simpson's Paradox brings back memories! Thanks for taking me back to my days as a statistician, and discussions I had with certain members of the company R&D department who didn't seem to get the idea that experiments needed to be designed - not just done, data-ed and papered!

    As for the unequivocal-proof list, I'd go for option (4) The product of an over-active imagination!

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  3. You know you're really big when non-math people are adapting your list:

    http://www.ritholtz.com/blog/2010/09/10-habits-of-mind-for-investors/

    And Soph has a blog here: http://abrandnewline.wordpress.com/

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  4. Sorry. Typo. Try again:

    oh and the quote as I remember it is, "One-half is never equal to two-fourths."

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  5. @Sue: Don't worry. I won't change. :) You also shouldn't worry too much because the average person (I again blame twitter) only spent 30 seconds on the site. So there are either a hoard of speed readers now reading my blog or...

    @Jason: I will neither confirm nor deny that quote. :) I will say that I'm spending an inordinate amount of time thinking about how I want to approach ratios later in the semester.

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