Archive for the ‘math’ Category
Budget Proposal 2011
February 2nd, 2010
The New York Times has a lovely interactive infographic detailing the proposed 2011 budget.
Nomograms
January 10th, 2010
Nomograms (or sometimes nomographs) are graphical single-purpose analog computing devices. They range from the very simple – like the above BMI calculator – to the (often beautifully) complex. Once upon a time they were commonly used for navigation, astronomy, surveying, and countless other things. Now, what with cheap omnipresent digital computers, they’ve fallen into disuse.
Like beautiful math? Need a calendar for 2010? Download a copy of Ron Doerfler’s Graphical Computing Calendar.
We Know You’re Out There, Spiderman
November 22nd, 2009
Abstract
Using absolutely bulletproof science, we demonstrate that 35.3 spidermen are created annually and that hundreds live secretly among us.
Introduction
Prompted by arguments about the possibility of radioactive spidermen living among us, Mr. Harman and I decided to use science to determine how many spidermen (if any) exist on Earth. It’s difficult to extrapolate from the single known instance of a spiderman (hereafter the SKI), but following the example of the Drake equation we’ve developed a predictive formula. Behold the incontrovertible majesty of the Harman-Schwartz equation:
Our equation states that:
N = Pe × fs × fr × fl × fp × fg
where:
Total Population
Note that by using the above formula we’ve only calculated the number of spidermen being generated each year and not the total number of spiderman living on earth at any given time. This can be calculated by the following equation:
Ntot = N(<Ad> – <Ac>)
where:
- Ntot
- is the total number of spidermen living on earth at any given time.
- <Ad>
- is the expected age at which a spiderman dies.
- <Ac>
- is the expected age at which a spiderman is created.
Plugging in the Numbers
- Pe
- The population of the Earth is around 6.67 billion.
- fs
- We estimate that about 1.66 × 10-3% of people are bitten by a spider each year.
- fr
- Between Chernobyl, Hiroshima/Nagasaki, and assorted other tests and accidents, about 2.55% of the land area of the Earth has been irradiated to some degree. We can use this as fr if we assume an evenly distributed spider distribution.
- fl
- The vast majority (about 99.9%) of people survive spider bites, but obviously irradiated spiders are more deadly. Let’s set fl to 50%.
- fp
- Working off the SKI, we’d have to assume that this is 100%. Let’s be conservative, though, and say only a tenth of people bitten by radioactive spiders develop superpowers.
- fg
- We’re totally guessing here and saying that 25% of superpowered radioactive spidermen will dedicate their lives to doing good.
Plugging those figures into the equation, we estimate that on average, 35.3 spidermen are created annually.
- <Ac>
- The median age in the world’s population is 27.5 years, which is what we’re using.
- <Ad>
- This is a controversial term. For the purposes of our study, we’ve made the simplifying assumption that spidermen have an average lifespan equal to the human average (73.1 years). It could be argued for the that spidermen are especially prone to an early violent death, but following the example of the SKI we argue that the rates of violent death and cloning are approximately equal, thereby sidestepping the whole issue.
By plugging these numbers into our final equation, we find that at any given time on Earth, on average there are 1,609 radioactive spidermen living secretly among us. ☐
Quines
July 21st, 2009
Named after the American philosopher and logician W.V.O. Quine, a quine is a program whose only output is its own code. Here’s a neat example in Lisp/Scheme, taken from the wikipedia article:
((lambda (x) (list x (list 'quote x)))
'(lambda (x) (list x (list 'quote x))))
computer science, language, math, old dead white guys | No Comments »
MIT GEB Lectures
June 4th, 2009
For the last few years, MIT has been putting the course materials for many (about 1,900) of its classes online for free as part of its OpenCourseWare project. Most of them are really fantastic, and the site is worth browsing through. Of particular interest to me is the series of lectures for a course devoted to Douglas Hofstadter’s Gödel, Escher, Bach. Which, if you haven’t read, you should; these lectures might help you along if you’ve found it a bit difficult.
Incidentally, the course is taught by an undergrad math major! The guy’s teaching style is a little rough, but he’s actually laudably competent.
books, computer science, language, math, science, video, web | No Comments »
Wolfram Alpha’s Launching Tonight
May 15th, 2009

At 8 PM Eastern time, Wolfram Alpha is going live. If you haven’t yet seen the screencast, you should, because it looks terrific. I doubt it will be more than a few weeks until Google comes up with an equally incredible product, but still, pretty neat.
See above for a totally authentic screenshot of the new software. IT KNOWS EVERYTHING
computer science, language, math, science, video | No Comments »
The Open Problem Garden
May 10th, 2009

Obviously mathematicians have a great job. In fact, according to the Wall Street Journal, they have the best job. If you, too, would like to share in all the respect, leisure time, money, and sexual desirability that inevitably results from a career in academia, all you need to do is solve a few of the puzzles at the Open Problem Garden. Your illustrious mathematical career awaits!*
* Reward yourself with a trophy!
An Impossible Proof
March 26th, 2009

I like proofs that claim to prove obviously false statements. They are the best puzzles.
This delightful series of operations demonstrates that all triangles are equilateral. Have fun finding the flaw!
Benford’s Law
March 24th, 2009

It turns out that in statistics and lists, the digit “1″ appears almost three times more often than it should. Benford’s Law describes this wacky phenomenon.
Another good find by Mr. Harman. He keeps coming up with awesome material, but never updates his blog! Soon I’m going to make him write a few guest posts here.


