Helen Friel - “Here’s Looking at Euclid” (paper sculptures of mathematician Oliver Byrne’s illustrations of Euclid’s Elements, 2012)
Byrne’s illustrated Euclid is one of my favorite vintage science reads (you can leaf through it online for free!) and the fact that the Mondrain-esque artwork has been made into paper sculptures makes me happier than I can verbalize.
What if the Autobots recruited a new bot called a Fourier Transformer and he was several smaller bots that came together into a much more powerful bot that was the sum of the lesser bots’ powers, but was, like, really assymmetrical and fell over a lot and none of the other bots could ever quite figure him out?
Aatish Bhatia on the math trick behind MP3s, JPEGs, and Homer Simpson’s face … AKA Fourier Transforms.
You’re probably thinking “there’s no way that could be interesting”, but you’re wrong.
Previously we saw this trick (is it a trick?) in action to draw famous faces using only mathematical functions.
At Slate, Ben Blatt has analyzed Waldo’s location in each puzzle of the seven main Where’s Waldo books, applied some statistical analysis and … unlocked a pattern to where Waldo usually is. I’m not going to spoil it, but I think he’s on to something.
It’s the finest use of data analysis that I’ve seen in recent memory. Of course, I don’t have a very good memory, but I’m pretty sure I’m right.
Waldo books aren’t the largest and most airtight data set, but they were put together by a human being, and it’s not unlikely that there’s an unconscious pattern at play in the striped wanderer’s usual hiding place. I suspect these might not be gold-medal winning statistics, but it’s a really fun analysis all the same. Go check out the full rundown, and get ready to impress your friends with your Sherlockesque powers of perception!
Now if only he could give me some tips for those magic eye puzzles …
A plague on both the axes!!
As Strogatz says, the ebb and flow of love and passions truly redefines the “many-body problem”.
Circling the Earth in 20 Golden Steps
Via Futility Closet, Jo Niemeyer’s land-art project 20 Steps takes us around the world in just that: 20 steps. It is a lesson in nature’s (seemingly) natural proportions and the extremes of logarithmic progression. More on ratios down below, but let’s first take a trip to Finland.
Picture a line, originating in the frigid Finnish lapland, that stretches 40,023 kilometers (one circumference) of the Earth, returning again to where it began. Niemeyer traced this path using only twenty metal poles to mark the way, erected in various countries stretching from northern Europe to Russia to China to Australia … and back to Finland. Why only twenty? There was a very particular method to this madness.
The poles were spaced out along this circumference line according to the golden ratio, or φ (1.61803398875). The first two were only 0.458 meters apart. The distance to the third was φ beyond the first two, or just under 3/4 of a meter. So on and so on … over the logarithmic horizon. Walking along this path, we will pass twelve of them before we leave Finland. By the fifteenth, we have left Europe and find ourselves in Russia. Number eighteen finds us in China, and to find nineteen we must travel to Australia. By twenty, we have arrived at our starting point.
The golden ratio, employed in sculpture and painting, seems at first glance inherent in nature’s forms, from quantum physics to flower petals. But is it really natural? It has fascinated artists, builders and scientists for ages, so much so that many in ages past declared it “divine”. But science tells us that no gods and spirits are at play in this math, that no design revealed via its ubiquitous appearance.
It begs the question nonetheless: Is this merely a numerical coincidence or the fingerprint of a deeper natural property at play? Are we just seeing phi where we want to see it and ignoring the rest?
The answer appears to revolve around efficiency. For things that grow in turns, spirals, or ordered stacks, like so much of nature does, phi isn’t magic, it’s just the best way to fit things in. Take the sunflower, for instance: turning 0.618 times before adding a new seed is just the best way to add seeds so that you don’t leave gaps between them. Visit Math is Fun for an interactive tool that lets you “build” flowers with different “natural ratios”.
It may seem that deducing the mathematics behind nature’s patterns diminishes their beauty. For me, art is made a little bit richer by it. We have taken a nod from the natural world to create pleasing creations by our own hands, and if you ask me, that’s universally beautiful.
What do you think?