The Monty Hall Problem explained

Imagine that you’re on a television game show and the host presents you with three closed doors. Behind one of them, sits a sparkling, brand-new Lincoln Continental; behind the other two, are smelly old goats. The host implores you to pick a door, and you select door #1. Then, the host, who is well-aware of what’s going on behind the scenes, opens door #3, revealing one of the goats.

“Now,” he says, turning toward you, “do you want to keep door #1, or do you want to switch to door #2?”

Statistically, which choice gets you the car: keeping your original door, or switching? If you, like most people, posit that your odds are 50-50, you’re wrong...

This counterintuitive and often-debated problem is discussed in detail at Priceonomics.

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17th century wearable technology

This is a relic of the Chinese Qing Dynasty, and is made of pure silver. Inlaid in a ring like a decoration, the size of the abacus is 1 cm × 0.5 cm. It has seven rods and on each rod there are seven beads. With a diameter of less than 1mm, the little beads are not made of filamentary silver, because they have no seams even when being examined under a microscope. More surprisingly, the beads can be moved easily and smoothly along the silver rods. For operating this tiny abacus, fingertips are too big. It seems that the beads can only be moved by small tools such as pins. However, this is no problem for this abacus’s primary user—the ancient Chinese lady, for she only needs to pick one from her many hairpins.

More on the history of the abacus and examples of unusual ones at China Culture.

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Displaying three variables on a 2-dimensional graph

In this case, movie ratings from three sources (IMDb, Rotten Tomatoes, and Metacritic).  To avoid the necessity of a third z-axis, one set of data is presented using a color code.

The graph itself has little useful information except to display a general concordance; the identification of selected outliers serves no useful purpose.  Posted to illustrate the concept of displaying a third variable using color.

Discussed at the Dataisbeautiful subreddit.

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Math puzzle

Who else would give you a math puzzle for Christmas morning? 

Solve/simplify/reconstitute this mathematical construct into what might be considered a more "elegant" expression.

For those who long ago swore that they would never again have anything to do with natural logarithms, the answer is below the fold:

Image cropped for space (and source lost):

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A "hundred" used to mean 120

A reminder that the English language evolved at a time when the counting system involved a "long hundred" equal to 120.

The long hundred, a unit of count = 120, appears to have arisen out of an ancient Germanic way of counting, one which is echoed in modern English. The “teen” suffix, as in four-teen, six-teen, etc, is not applied to one plus ten or two plus ten (they aren't one-teen and two-teen). Eleven and twelve are treated the same way as the first ten numerals; the break is after twelve, not ten... Note that this is not a duodecimal numeric system.

The use of the word in this manner lingered for a long time in England:

This reckoning of one hundred as six score still holds good (or did to my knowledge ten years ago) in Leighton Buzzard, Beds. If one ordered there 100 plants, for example, one received, and also had to pay for, 120: a hundred being always reckoned as six twenties. If one required simply 100, it was necessary to order five score.

So also here in Cardigan and around, taking eggs, for example, the dealer picking up three eggs in each hand, reckons that twenty times this makes one hundred.

Emily M. Pritchard (writing on 21 July 1906).
Archaeologia Cambrensis. 6th series, vol. 6, page 352.

Learned from a recent podcast of No Such Thing As A Fish (thank you, elves).

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