Space is big. Really big. And, surprisingly, is still seems positively enormous even at the speed of light. Hop on this spaceship of the imagination, ignore the effects of time dilation, and follow a photon from the sun to beyond Jupiter in this humbling video by Alphonse Swinehart:

Even travelling at the speed of light, it takes more than 40 minutes to get from the Sun to Jupiter ... and that's peanuts compared entire Solar System, let alone the Milky Way Galaxy. If you have a second monitor, I recommend popping this video on it, putting it full-screen, and enjoying the ride in the background. You might be surprised at what you see along the way.

That's all for this week. See you back here on Monday!

It's nice to see my current favourite Australian band, Boy and Bear, starting to get some traction over here in the States. The single from their latest album, Southern Sun, is excellent — but what I really wanted to share is the music video:

I'd originally assumed it was shot in the Australian Alps (yes there's such a thing and yes, there's snow), but it was actually filmed near Queenstown, New Zealand. Either way, the scenery is gorgeous.

That's all from us this week. Enjoy the weekend, and we'll see you back on Monday!

Check out this visualization (via notreble) of the bassline in Ain't No Mountain High Enough, featuring Marvin Gaye and Tammi Terrell:

The visualization of legendary Motown bassist James Jamerson is by Vulfpeck's Jack Stratton.

That's all for this week. Have a great weekend, and we'll see you on Monday!

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 (a^{2}-b^{2}, 2ab), so the next step in the sequence is (a^{2}-b^{2}+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.

Clearly these divers are underwater. But what are they extracting with their drills and ... a wheelbarrow?

It's always interesting how strange things can look with a twist in perspective! And don't worry, the wheelbarrow was recovered from the bottom of the amazingly clear Lake Saarijärvi in Finland.

That's all for this week. We'll be back on Monday — see you then!

The internet is agog over this picture of a dress, which appears white and gold to some, and blue and black to others:

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.

That's all for this week — see you on Monday!

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.