Hyperreal numbers: infinities and infinitesimals - "In 1976, Jerome Keisler, a student of the famous logician Tarski, published this elementary textbook that teaches calculus using hyperreal numbers. Now it's free, with a Creative Commons copyright!" (pdf—25mb :) [more inside]
"A Truncated Story of Infinity," a short film about the infinite possibilities contained in a day. [more inside]
This is what happens when you build a cube out of one-way mirrors. From an industrial design collective called Numen/For Use.
Closing in on the twin prime conjecture (Quanta) - "Just months after Zhang announced his result, Maynard has presented an independent proof that pushes the gap down to 600. A new Polymath project is in the planning stages, to try to combine the collaboration's techniques with Maynard's approach to push this bound even lower." [more inside]
How To Fold a Julia Fractal. A beautiful interactive introduction to complex numbers, fractals and waves. (Requires WebGL). To Infinity And Beyond is a similar introduction to calculus.
What happens to comics if newspapers go away? Garry Trudeau imagines a terrifying void. Webcomic artists think Garry Trudeau is silly. But if you, too, fear the vast abyss of a world without newspaper funnies, and lack the patience to search for all the treasures of the webcomic world, what you want is a comic that never ends. Pandyland and Mezzacotta each offer an infinite supply of three-panel comics, so that you'll never have to go without a brief moment's amusement. Sure, 99% of the comics you see might be crap, but there are gems amidst all the rubbish.
Are there as many odd numbers as there are all numbers? Can one infinity be bigger than another? TED Ed and Minute Physics both take a look at some of the mind boggling realities of Infinity.
Donald in Mathmagic Land is a 27-minute Donald Duck featurette released on June 26, 1959. As Walt Disney said, "We have recently explained mathematics in a film and in that way excited public interest in this very important subject." (Wiki)
“I’m going to divide the universe into Planck-sized regions, and put a monkey in each one. You will ask what the monkey is made of, when nothing can be smaller than the Planck scale, and I will say that it is not made of anything – it is a single, fundamental monkey particle. One in every Planck sized region of space. These regions are very small - there will be nearly as many monkeys inside the space occupied by a single atom as there are atoms in the universe. And there will be monkeys in the spaces not occupied by atoms too. And they will type faster. How fast can a thing happen? Just as there is a shortest possible distance, there is a shortest possible time, and it’s called the Planck time." A look at the idea of an infinite number of monkeys at an infinite number of typewriters. [more inside]
"L'infinito": Infinity. Infinity. Infinity. Infinity. Infinity. Infinity. Infinity. Infinity. Infinity. Infinity. Infinity. Infinity. Infinity...
You may think it's a long way down the road to the chemist's, but that's just peanuts to the Mandelbrot
Want a forest but don't have the space? Get a tree and four mirrors and make your own Unlimited Urban Woods
Sure, big numbers are fine. But infinity (in the set theoretic sense) is where the fun really starts. Developed almost entirely by one man in the late 19th century, set theory now forms the foundation of modern mathematics. Cantor showed that not all infinite sets are the same size. Notably, while there are just as many integers as rational numbers, there are more real numbers than integers. These results, along with others that soon followed like the axiom of choice, led to several fascinating consequences: [more inside]
If the universe is a hologram and the healthy human brain a valve of consciousness then where'd this mental infinity come from? Are we simply living the simulacrum? Or does Pi protect us all, forever, infinitely?
Find out how many radio stations in your area are owned by the same company. Here in Dallas Texas Clear Channel owns six. Then there's four other radio stations owned by Susquehanna Radio which used to be owned by AM/FM Incorporated but they merged with *guess who* Clear Channel last year. So it looks like Clear Channel either directly or indirectly controls almost a dozen radio stations in north Texas alone. How much control do they have over your airwaves? Ever wonder why radio stations all sound the same? Cuz they ARE the same!