tingilinde

what are the odds

Notes on methods of studying and calculating coincidences... (pdf)

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Coincidences abound in everyday life. They delight, confound, and amaze us. They are disturbing and annoy- ing. Coincidences can point to new discoveries. They can alter the course of our lives; where we work and at what, whom we live with, and other basic features of daily ex- istence often seem to rest on coincidence.
Let us begin with a working definition. A coincidence is a surprising concurrence of events, perceived as mean- ingfully related, with no apparent causal connection. For example, if a few cases of a rare disease occur close to- gether in time and location, a disaster may be brewing.

The definition aims at capturing the common language meaning of coincidence. The observer's psychology enters at surprising, perceived, meaningful, and apparent. A more liberal definition is possible: a coincidence is a rare event; but this includes too much to permit careful study.

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false visual proofs

I was familiar with the first two.  The third is subtle indeed

teaching math with computer graphics

A Bell Laboratories piece from the mid 1960s..

what's known about math education

It's a mess..  we all have our own ideas.  I think the Finns were on the right track when they elevated the teaching profession a decade  A highly-trained, well-paid teaching profession has made a difference.  Of course society has to agree to care about kids and on the idea that an education is a good thing.

 

 

 

1000000000000066600000000000001

Belphegor's prime - a palindrome prime.

 

 

fun piece on ffts

a surprise bit on the long forgotten original discovery..  I learned of it some years ago when Andrew Odlyzko casually mentioned it.

 

knots

Why they're interesting in math and beyond.

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Knot theory began as an attempt to understand the fundamental makeup of the universe. In 1867, when scientists were eagerly trying to figure out what could possibly account for all the different kinds of matter, the Scottish mathematician and physicist Peter Guthrie Tait showed his friend and compatriot Sir William Thomson his device for generating smoke rings. Thomson — later to become Lord Kelvin (namesake of the temperature scale) — was captivated by the rings’ beguiling shapes, their stability and their interactions. His inspiration led him in a surprising direction: Perhaps, he thought, just as the smoke rings were vortices in the air, atoms were knotted vortex rings in the luminiferous ether, an invisible medium through which, physicists believed, light propagated.

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something neat about the ny subway

Greg pointed out a fantastic segment on Radiolab.. it starts around 56 minutes (the interface is terrible.  start it and then go to the bottom of the page for the progress bar .. or find the episode elsewhere)

 

 

very cute proof I ran into

 

Proof that 1+2+4+8+⋯+2ⁿ = 2ⁿ⁺¹−1

Expressing the sum in binary we have 111…111 (n+1 1's)

Adding 1 to this number we get 100…000 hence 2ⁿ⁺¹

 

 

a classic problem is solved

Quanta offers nice non-specialist pieces on math and the science.  Here's one on the triple bubble problem.

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The bubble problem is simple enough to state: You start with a list of numbers for the volumes, and then ask how to separately enclose those volumes of air using the least surface area. But to solve this problem, mathematicians must consider a wide range of different possible shapes for the bubble walls. And if the assignment is to enclose, say, five volumes, we don’t even have the luxury of limiting our attention to clusters of five bubbles — perhaps the best way to minimize surface area involves splitting one of the volumes across multiple bubbles.

Even in the simpler setting of the two-dimensional plane (where you’re trying to enclose a collection of areas while minimizing the perimeter), no one knows the best way to enclose, say, nine or 10 areas. As the number of bubbles grows, “quickly, you can’t really even get any plausible conjecture,” said Emanuel Milman of the Technion in Haifa, Israel.

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