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Humanity has built enough roads to cover the distance from the earth to the moon over 80 times*.
* This value will change - Wolfram|Alpha calculates the moon’s current distance from the Earth, which varies as it moves through its monthly orbit.
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[Flash 10 is required to watch video] Music generated with Otomata!
Continuous variation in the parameter “a” starting at a = 0
Unknown code parameters : r, a(final), s
Visuals created with Mathematica code:Manipulate[ Graphics[ Line[ Table[ {-r^n*Sin[n*a], r^n*Cos[n*a]}, {n, 0, s}]], PlotRange -> .01], {r, .1, 1}, {a, 0.001, 4*Pi, .00001}, {s, 1, 10000, 1] -
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I know voronoi is a parametric cliché, but its an attractive one. Burning time at work…
(via un)
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Beyond Between Good and Evil
- “Adults have to deal with moral grey areas”
- “I’m not liberal or conservative, I guess I’m somewhere in the middle”
- “On a sliding scale from 1 to 10, how happy are you with life?”
- “The truth lies somewhere in between”
People talk about “grey areas” as if [0,1] is so much more sophisticated than {0,1}. I find such rhetoric limiting. After all, the convex combinations of black and white are totally ordered, completely linear, and only one-dimensional! A painting in B&W couldn’t display much variation. (Not that it couldn’t be interesting.) We deal everyday with things more complicated than “a grey area” because the world is 3-D and colour is Lab (3-D nonlinear). Add in texture and smell and you’ve increased the psychological dimensionality manyfold.
The metaphor is insufficiently rich. Adult situations don’t fall on a straight line. Political viewpoints don’t sit neatly next to each other in 1-D. Moral ambiguity is certainly more colourful and convoluted than the path from
#000000to#FFFFFF.Me, I’m more interested in 2.7-dimensional hornspheres, quartz crystal spires, hot-air balloons with a row of golden rings piercing the spine, and quasi-polar negatively bent inside-out torii-cum-logcabins. Or even just something as “pedestrian” as a mountaintop pine forest, which is already much more intricate than, cough cough, the unit interval [0,1].
So—back to my original point—I think moral ambiguity resembles a cell complex more than a line segment. Real situations—the layered tragedies, ironies, comedies, and lengthy mediocrities that desirous, egocentric humans instinctively generate—have a much more interesting shape than “the span between 0 and 1.”
I guess I shouldn’t be so critical. The people using the grey-area metaphor probably don’t avail themselves of the whimsical thought-gardens in which more exciting shapes live. Sorry there, I was just feeling constricted.
I hope you’ve enjoyed these drawings by Robert Ghrist from his (free) notes on homotopy.
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Portraits of Albert Einstein and Stephen Hawking from Illustration Now’s book Portraits.
(via freshphotons)
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The “Most Important Algorithm Of Our Lifetime” Could Change This Modern World
Math breakthroughs don’t often capture the headlines—but MIT researchers have just made one that could lead to all sorts of amazing technological breakthroughs that in just a few years will touch every hour of your life.
Here’s a quickie explainer: Fourier transforms are a mathematical trick to simplify how you represent a complicated signal—say the waves of sound made by speaking. They work by reducing the complex wave pattern to a simple and pretty short list of numbers that, when run through the system again, result in a very good approximation of the original signal. FFTs (Fast Fourier Transforms) are simply a way of making this magic happen in a digital computer, but the combination of math and machine means the FFT has revolutionized science and many industries that have technology at their core. Which is why it’s been labeled the “most important algorithm of our lifetime.”
Now, you should remember that sound waves, and both picture and video signals, are all handled by processors in your TV, PC, and phone, and that the radio waves that whizz through the air to keep us all connected to the Internet need digital processing too. That’s every compressed sound signal that you listen to as an MP3 or similar format, most every image that you snap with your smartphone or DSLR, every image frame in the video you’re watching on your TV streamed over the Net, many images—such as those from an MRI—your doctor uses to diagnose your disease and every burst of radio that connects your cell phone to the nearest tower or your PC to its Wi-Fi router.
So calculating FFTs up to ten times faster is a big deal. It means that if you use existing hardware to do the math, it’ll be quicker at solving the problem you’ve set—so you need less compute time to do the task. If you’re talking about a portable computer like the one in your smartphone, that means it can spend more time doing other things instead. And with the valuable computing and battery resources of these portable devices under such pressure (you wouldn’t want your phone to be laggy now, would you?) that’s a good thing.
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An LED attached to a self-guiding bullet illustrates changes in the projectile’s trajectory.
The prototype bullets were developed for the U.S. military by Sandia National Laboratory, owned by Lockheed. They have been tested at distances up to 2,000 meters.
(via edisonsdesk)
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SpongeBob’s “Pineapple” Under the Sea and Fibonacci Numbers
Apparently Nickelodeon is defying the laws of the universe by claiming that SpongeBob Squarepants lives in a pineapple under the sea. Why?
Besides the fact that his pants are not actually square, he doesn’t live in a pineapple. He can’t. Pineapple patterning follows a classic mathematical sequence: the Fibonacci numbers.
Watch as the spirals of a pineapple are counted and be amazed at nature’s natural order. you can find this patterning in pinecones, flowers and artichokes, too!
Your move, Nickelodeon!
(by Vihart)
(via un)
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111,111,111 x 1,111,111,111 = 123,456,789,987,654,321
Number are amazing.
