Triangles on Earth Exceed 180 Degrees

The idea that space and time can be curved or warped is fairly recent. For more than 2,000 years the axioms of Euclidean geometry were considered to be selfevident. As those of you who were forced to learn geometry at school may remember, one of the consequences of these axioms is that the angles ot a triangle add up to 180 degrees. However, in the last century people began to realise that other forms of geometry were possible in which the angles of a triangle need not add up to i8o degrees...

 How Rules Make Games Pleasurable and Encourage Self-Regul...

Picture a child poised excitedly at the starting line of a footrace, ready to run down the track, breathlessly awaiting the starting signal. Rather than giving in to her intense desire to leap from the starting line, she waits for the signal that the race has begun. What's going on here? Why does our player anxiously hold back when she really desires to run? Developmental psychologist L. S. Vygotsky notes that "Play continually creates demands on the child to act against immediate impulse, i...

 Redundancy of English language is a Goldilocks zone for C...

In Shannon’s terms, the feature of messages that makes codecracking possible is redundancy. A historian of cryptography, David Kahn, explained it like this: “Roughly, redundancy means that more symbols are transmitted in a message than are actually needed to bear the information.” Information resolves our uncertainty; redundancy is every part of a message that tells us nothing new. Whenever we can guess what comes next, we’re in the presence of redundancy. Letters can be redundant: be...

 Euclid's Elements as a Game

"If video games had been around in 350 BC, Euclid would have made a video game," Devlin told me. The thirteen books of Euclid's Elements would have been the supplemental material, a PDF file that you could read if you wanted to. "People think I'm joking—I absolutely mean that. Euclid would not have written a textbook, he would have designed a video game." Peek at any of his proofs, Devlin said, and you'll quickly find that the great Greek mathematician, often called the father of geometry, ...

 Feminist Portrayal in Sir Arthur Conan Doyle's Writing

All day the memory of this interview haunted him. He felt that he had come very badly out of it. She had showed herself to be his superior on his own pet subject. She had been courteous while he had been rude, self-possessed when he had been angry. And then, above all, there was her presence, her monstrous intrusion to rankle in his mind. A woman doctor had been an abstract thing before, repugnant but distant. Now she was there in actual practice, with a brass plate up just like his own, comp...

 Anecdote of Shamans Responding to Star Trek

DI for documenting his journey to shamanism in the 1994 book Of Water and the Spirit: Ritual, Magic, and Initiation in the Life of African Shaman. He writes about the proverbial dive into the rabbit hole as he was studying with the elders of his community and balancing his newfound wisdom with his Western education. Some paints a picture of a different path to knowledge that contradicts the norms of Western conventions. According to him. the Dagara have no word for the supernatural. "For us, ...

 Beyond Three Dimensions

“In One Dimensions, did not a moving Point produce a Line with two terminal points? In two Dimensions, did not a moving Line produce a Square wit four terminal points? In Three Dimensions, did not a moving Square produce - did not the eyes of mine behold it - that blessed being, a Cube, with eight terminal points? And in Four Dimensions, shall not a moving Cube - alas, for Analogy, and alas for the Progress of Truth if it be not so - shall not, I say the motion of a divine Cube result in...

 The Social Network Political Bubble

In the growing social media space, most users encounter a mix of political views. But consistent conservatives are twice as likely as the typical Facebook user to see political opinions on Facebook that are mostly in line with their own views (47% vs. 23%). Consistent liberals, on average, hear a somewhat wider range of views than consistent conservatives – about a third (32%) mainly see posts in line with their own opinions. But that doesn’t mean consistent liberals necessarily embrace ...

 The Zoku Jewel

‘Volition is a funny thing,’ Zinda says. ‘The jewels don’t just respond to what we want, but what we would want if we were wiser or smarter or knew more. The zoku as a whole tries to extrapolate what you really need, rather than just what you are asking for, and in line with everybody’s volition. I’ll give you an example. Tell me something you really like. A food, or something.’ Mieli hesitates. ‘This is pointless.’ ‘Come on. Don’t take it so seriously!’ Mieli sighs...

 Humans Are Abstraction Masters

What distinguishes us from cavemen is the level of abstraction we can reach. Abstraction enabled humans to move from barter to money, and from gold coins to plastic cards. These days, what's left of "money" is often just an account record we read on a computer screen, and soon it could just be a line of code in a bitcoin ledger. Today, abstraction is all around us — and math is the language of abstraction. In the words of the great mathematician Henri Poincare, mathematics is valuable beca...