There are plenty of great domino cascades on YouTube, but this is one of the best. There are a couple of obvious cuts, but using multiple takes is more than made up for by the perfect coordination with the A-Trak tune. Enjoy:
That's all for this week. See you again on Monday!
Think of a number. Now multiply it with itself. Now add the number you first thought of. Multiply the result with itself. Again add the number you first thought of. Keep repeating that process. If the number you have keeps getting larger and larger, the number you first thought of is not part of the Mandelbrot Set. (For example, starting with 0.5 you get 0.75 -> 1.0625 -> 1.628 -> 3.153 ... and so on off to infinity, so 0.5 is not part of the Mandelbrot Set.)
You can also let the number you think of be a complex number of the form (a, b), where "a" is called the "real part" and b is called the "imaginary part". The only difference is that (a, b) multiplied by itself is (a2-b2, 2ab), so the next step in the sequence is (a2-b2+a, 2ab+b), but otherwise the game is much the same. (This Jonathan Coulton song explains the rules in lyrical form.)
The trick is that you can use (a, b) as the X and Y coordinates on a 2-dimensional chart. Color the chart black if (a, b) is in the Mandelbrot Set, and otherwise color it according to the number of steps it takes to get the complex number at those coordinates to get above size 2 (5 steps in our example for 0.5 above). Then, you get the beautiful and familiar representation of the Mandelbrot Set. (You can easily write a program to do this in the R language, since it support complex arithmetic natively.)
One of the amazing things about the Mandelbrot set is that it's infinitely complex: as far as you zoom into its crenellated edges, it never smooths out. This video enlarges the Mandelbrot Set as much as expanding a proton to the size of the Universe -- and then billions and billions of times more.
That's all for this week. See you back here on Monday!
Today is a day of joy for math geeks in the USA, and a day of bemusement for maths geeks everywhere else: Pi Day. (If only April had 31 days!) In fact, today is a very special once-in-a-century Pi day: at 9:26:53.5898 this morning was a "pi instant" where the time and date read out pi to 10 significant digits.
I'm celebrating Pi day on a cooking weekend with friends on an island getaway in Puget Sound. We began with pi-ella:
and of course, finished with apple pi:
Happy pi day everyone, and we'll see you back here on Monday.
This is a great reminder that the light that enters our eyes is not the absolute determinant of what we see. Our brain gets involved too: it formulates models based on our knowledge and experience of the world around us, and chooses the one that best fits what our senses are telling us. (Our brains are Bayesian.) But sometimes, two models are equally good interpretations: take for example the classic Necker Cube illusion.
You may see this as a cube with its front face pointing to the left and down, or perhaps one facing to the right and up. If you stare at it long enough, it will probably even flip between the two states. The brain, supplied with ambiguous information, switches back and forth between the two models.
I suspect that's what's happening with this dress: a white and gold dress, or a blue and black dress, are equally valid models for what we see in the photo. But how can such wildly different appearances both be valid? The reason is color constancy: our brains have evolved to see objects in a fixed color, even though lighting conditions routinely change the color of photons reflecting from the object into our eyes. (Without color constancy, the world would appear to change color schemes every time a cloud passed overhead.) It's like the reverse of the Cornsweet illusion: even though the top and bottom segments of this object have the same pixel color (check with an RGB tool, or just hold your finger of the seam), we see them as two entirely different colors: white and black.
In this illusion, the horizon and shadows give us strong clues about the lighting, which causes our brain to interpret the panels as two different colors. In the case of the dress, we have few clues about the actual lighting environment (the photo is a tight closeup), so our brain makes a guess. Some of us subconsciously assume the photo was taken a dark indoor environment with bluish lighting, making the dress appear white and gold. Others assume bright yellow daylight lighting, which makes it appear blue and black. (Anecdotally, it seems the lighting environment in your room where you look at the picture influences the version your brain sees. Try looking at it near a sunlit window.) As always, xkcd explains it perfectly in cartoon form. The center panel is from the actual dress photo; the cartoon dresses in both the left and right panels are the same (RGB) color.
For the record, while I can see the dress as nothing but white and gold, the actual dress is blue and black. (Check out the reviews in that Amazon listing!)
That's all for this week (but you can check out our Because it's Friday series here). See you back here on Monday!
If you're a foodie (or know people who are particular about their food) and enjoy a good laugh (and don't mind some NSFW language), then you should definitely check out the new web-series The Katering Show.
This is the funniest thing I've seen in a long time. The Katering Show was produced with the support of the Australian Government. As an Australian, I've never been prouder.
The World Cup of Cricket starts this week. (C'mon Aussie!) Cricket isn't well-known amongst many of my American friends or colleagues, so when I'm asked about it I usually point them to this video, which gives a good sense of the game:
Actually, this Vox article and this ESPN video do a much better job of describing the game. One thing the ESPN video doesn't mention (besides not listing all 11 ways to be out) is the possibility of a draw. In test match cricket, it's entirely possible for a match lasting five days to end without a winner. The reason is that a test match lasts four innings (each team gets to bat twice), and is also limited to five days. If the time limit ends before both innings are complete, and the trailing team is still at bat, the game is declared a draw. (The idea is that the trailing team may have caught up if only the game could continue.) The strategy for the trailing team, if they don't think they can achieve outright victory, is to instead play for time and go for the draw. (The winner of a test series is the the team with the most wins over five five-day test matches.)
Playing for five days without a definitive outcome can try the patience of the modern sporting fan, so one-day cricket was born. Here, there are just two innings per game, each team is given a fixed number of overs (balls) with which to score, after which the innings is automatically over and the other team has an opportunity to bat. As the name suggests, the game is over in a day and one team or the other will be declared the winner (unless there is an exact tie in scores).
There's an interesting statistical angle here, which is related to interruptions in the game. Let's say we're halfway through the second innings and Australia is at bat with 142 runs to England's 204. Normally, Australia would need to score 63 runs (the "target") to win. Now suppose it starts to rain, and the game is suspended for an hour. To keep the game from running long, Australia will be given fewer overs to bat, and their target will be reduced as well. But the target isn't reduced in exact proportion to the overs removed, to reflect the fact that more runs are generally scored in the latter part of an innings. The exact calculation is based on statistical analysis of cricket games, and is a great example of censored data analysis. (The basic idea is to be able to forecast what the final score would have been in games that are interrupted.) The calculation is known as the Duckworth-Lewis method, named after the two British statisticians that devised it. People often talk about statistics and baseball in the same breath, but this is the only example I can think of where statistical modeling is such an important part of a sport. (If you can think of others, let me know in the comments!)
Well, that's all for this week — I'm off to watch the cricket! See you back here on Monday.
Ever wondered why rivers take such meandering paths on their way to the sea? Minute Earth explains in this short video:
This process goes on all the time: unless the banks are reinforced (as they are usually as they flow through big cities), the river's path will keep on changing over time. Vox recently featured this animated gif (from the Time Timelapse site, which has several other cool animations), showing the path of Peru's Ucayali River from 1982 to 2012.
Incidentally, much the same process is behind the formation of river deltas. As the river reaches the sea and slows down, it deposits sediment. The river's shifting position acts much like a random walk, and the sediment creates the triangular shape of the delta.
That's all we have for this week. Join us back here on Monday for more from the Revolutions blog.
Secret sharing time (no, not this one): my first trip to the United States was to play pinball. I'd played a lot of pinball in my youth and I thought I was pretty good. So I booked a flight to Chicago in the mid-90's (I can't remember exactly when) to compete in the PAPA World Championships ... and promptly got my clock cleaned. Take a look at this Reddit AMA to find out what it takes to be a pinball champion — that, sadly, was not me.
Pinball has declined since its peak in the 60's and 70's (as you can see in the Tableau chart below, by Paul Banoub), and most of the manufacturers had closed up shop by the turn of the century. Nonetheless, pinball has enjoyed a recent resurgence thanks to ageing hipsters (like me) looking to relive their youth, and a younger generation looking for a tactile experience you just can't find in a video game.
That said, pinball is also enjoying a renaissance in the virtual arena. Over the past few years, the Pinball Arcade has reproduced many of the pinball tables of days past (including many of my favourites, like Twilight Zone) for play on tablets and consoles. But my favourite of all is Pro Pinball Timeshock, a completely custom virtual table developed for PCs in the 90's, and now just re-released for iOS:
If you squint closely, there below the left flipper, you can see my name in the playfield credits. My pinball obsession in the mid-90s led me to a small consulting role on this game when it back was released for PC. It was quite a pleasant surprise to see my name there — I haven't done computer game work for 20 years! — but it's made reliving those memories even more fun. If you want to try it yourself you can find Pro Pinball on the App Store. Even better, this digital pinball table will soon be made into a real-life pinball machine -- after playing so many real tables converted to digital games, I can't wait to see how my favourite digital game translates to the real world.
That's it for this week. See you back here on Monday!