From Fish to Infinity I have a friend who gets a tremendous kick out of science, even though he’s an artist. Whenever we get together all he wants to do is chat about the latest thing in evolution or quantum mechanics. But when it comes to math, he feels at sea, and it saddens him. The strange symbols keep him out. He says he doesn’t even know how to pronounce them. In fact, his alienation runs a lot deeper. Crazy as it sounds, over the next several weeks I’m going to try to do something close to that. So, let’s begin with pre-school. The best introduction to numbers I’ve ever seen — the clearest and funniest explanation of what they are and why we need them — appears in a “Sesame Street” video called “123 Count With Me.” Children learn from this that numbers are wonderful shortcuts. As adults, however, we might notice a potential downside to numbers. Viewed in this light, numbers start to seem a bit mysterious. The creative process here is the same as the one that gave us numbers in the first place. Notes:

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Vi Hart: Math Doodling Remember that video about doodling dragons and fractals and stuff? I finally finished part 2! Here is a magnet link so you can dowload it via torrent. Here it is on YouTube: You can tell I worked on it for a long time over many interruptions (travelling and other stuff), because in order to keep myself from hating what was supposed to be a quick easy part 2, I had to amuse myself with snakes. Part of working on part 2 was working on part 3 and other related material, so the next one should go faster. Here was part 1, via Torrent or YouTube. The Hilbert Hotel In late February I received an e-mail message from a reader named Kim Forbes. Her six-year-old son Ben had asked her a math question she couldn’t answer, and she was hoping I could help: Today is the 100th day of school. He was very excited and told me everything he knows about the number 100, including that 100 was an even number. He then told me that 101 was an odd number and 1 million was an even number, etc. He then paused and asked: “Is infinity even or odd?” I explained that infinity is neither even nor odd. Kim replied: Thank you. Although something got garbled in translation (infinity is neither odd nor even, not both), Ben’s rendering hints at a larger truth. At the time, Cantor’s theory provoked not just resistance, but outrage. My goal here is to give you a glimpse of this paradise. It’s always booked solid, yet there’s always a vacancy. For the Hilbert Hotel doesn’t merely have hundreds of rooms — it has an infinite number of them. First he does the doubling trick.

Khan Academy How To Slice A Bagel Along A Mobius Strip — And Why In the weeks before Doug Sohn closed down his legendary Chicago sausage joint Hot Doug’s, people were literally walking in the door and offering him a million dollars to stay open. This week on The Sporkful podcast, we’re featuring part one of our live show at the Taste of Chicago. I talk to Doug about why he walked away from all that money, and one of the top chefs in the world reveals his favorite candy bar. As part of our live show I also interviewed mathematician Eugenia Cheng, author of How To Bake Pi: An Edible Exploration of the Mathematics of Mathematics, who sliced a bagel along a Mobius strip live on stage. A Mobius strip, as you probably forgot, is a surface with only one side. If you were to start drawing a line down the middle of the strip and just keep going, you’d cover all the paper and end up right back where you started, without ever flipping it over. How did that make the bagel more delicious? “Well, it’s basically completely ridiculous,” Cheng explains.

On the Nature of Mathematics One of the oldest of all fields of study is that now known as mathematics. Often referred to, used, praised, and disparaged, it has long been one of the most central components of human thought, yet how many of us know what mathematics really is? Many have likened it to a language, while others claim it is a science, and a few more an art. At the simplest level, mathematics is a vast symbolic logic system possessing a few simple postulates from which an unimaginable, though finite, number of statements can be proven or disproven. Most of the symbols used in mathematics have been inspired by the real world. Most of us tend to assume that the rules we apply to these symbols are some sort of natural laws, but they too have been chosen arbitrarily. This brings up an important point. In many ways, mathematics is like an art. Mathematics, rather than being a science in its own right, is the foundation of all other sciences. As mentioned, mathematics is also a kind of language.

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