How could medieval maps be so accurate?

In the 13th century, so-called “portolan maps” appeared that are so accurate, they could be used in navigation today.  But it has been a mystery how they were made and how, given the limits in technology of the time, they could be so accurate.  (This is another example of how the notion that people from other times were unintelligent is just untrue, as in the myth that people in the Middle Ages thought the earth was flat.)  A mathematician has figured out at least part of the answer of why these hand-drawn maps are so good, with even their limitations pointing to a startling sophistication. [Read more...]

Happy Super Pi Day: 3.14.15

Today is “Pi Day,” the 14th day of the 3rd month (3.14).  Not only that, it is “Super Pi Day,” with the rest of the date giving the next two numbers: 3.14.15.  Pi is the ratio of the circumference of a circle to its diameter.  Though circles are everywhere, their numeric ratios can never be exact.  The mysterious number represented by the Greek letter π has been proven to be an “irrational number,” one which has an infinite number of non-repeating decimals.  And, yet, the ratio has to be used in all kinds of common calculations, from figuring the area of a circle to analyzing subatomic and astronomical phenomena.

After the jump, an excerpt and a link to an essay on π and pi day by Cornell mathematicisn Tara S. Holm.  Do go to the link for an account of the history of our knowledge of the concept, including a government attempt to regularize it at 3.2 by passing a law.  My favorite part is how Prof. Holm is celebrating the day:  Getting her family together at 9:26 and 53 seconds (the next five numbers) and eating a piece of pie. [Read more...]

What else Turing did

The movie The Imitation Game focused on how mathematician Alan Turing broke the German “Enigma” code, a major contribution to the Allied victory in World War II.   Those interested in artificial intelligence talk about the “Turing test,” the goal of making it impossible to tell whether a machine or a human being is responding to questions.  But  Turing’s most enduring contribution is not known so much.  He wrote a paper about 0′s and 1′s and computable numbers that basically invented the concept of software. [Read more...]

The God of multiple infinities

There are an infinite number of numbers.  But there are also an infinite number of numbers between any two numbers!  In fact, there are more numbers between numbers than there are countable numbers, even though both are infinite!  (Mind blown yet?)  George Cantor, the father of Set Theory and a devout Christian, proved that.  Joel Bezaire shows what the concept of “multiple infinities” can do to our sense of the infinity of God. [Read more...]

Why non-conformists look the same

A mathematician took up the topic of hipsters.  Specifically, why different individuals who try not to conform to what is seen as normal end up looking and acting very much like each other.

After the jump, read the details, link to the math, and consider my thoughts on the matter, which offers a different account of non-conformists and sort of a defense of hipsters. [Read more...]

The NSA’s encryption-busting quantum computer

The NSA is working on the development of a quantum computer that could foil all public encryption systems.  The description of this technology, after the jump, combines weird physics, weird mathematics, and weird surveillance. [Read more...]


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