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Carl Sagan Explains the Drake Equation

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YouTube / Davies Robinson

Professor Frank Drake proposed an equation that could be used to estimate the number of detectable extraterrestrial civilizations in the Milky Way galaxy. The equation was deemed important for his work at the National Radio Astronomy Observatory in Green Bank, West Virginia (which I've driven by many times -- their huge telescope is quite a sight!). In essence, Drake decided to define a series of limiting factors, so that we could take the total number of observable stars, then scope way down to get to some estimate for how many might have civilizations that we could contact. The resulting Drake Equation is one of the most exciting bits of math I've ever seen. Wikipedia explains it like so:

The Drake equation states that:

where:

N = the number of civilizations in our galaxy with which radio-communication might be possible (i.e. which are on our current past light cone);

and

R* = the average rate of star formation in our galaxy

fp = the fraction of those stars that have planets

ne = the average number of planets that can potentially support life per star that has planets

fl = the fraction of planets that could support life that actually develop life at some point

fi = the fraction of planets with life that actually go on to develop intelligent life (civilizations)

fc = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space

L = the length of time for which such civilizations release detectable signals into space

If that's too math-heavy for you, just watch Carl Sagan explain it in this eight-minute video:

Where it really gets interesting (and frustrating) is when you start to figure how many of these detectable civilizations are actually currently broadcasting during a time period when we might actually contact them or receive their broadcast (adjusted, of course, for the massive lag time to get the broadcast from point A to point B). Sagan touches on part of this problem in his discussion, but doesn't get into the details. Read more about all this at Wikipedia, or check out this detailed lecture:

A review of the Drake Equation from RiAus on Vimeo.

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History
When Math Discoveries Led to Banned Numbers
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iStock

The literature world has seen more than its share of controversy. The best stories tend to provoke the strongest reactions—both positive and negative—in readers, which is why so many classic books have been banned at one point or another. But even a more objective field like math isn’t immune to conflict. In its new video, TED-Ed rounds up the numbers that caused such a stir when they were introduced that they were banned in math circles.

One of the earliest examples comes from ancient Greece. A mathematician named Hippasus was having trouble solving certain equations with fractions and whole numbers alone, so he came up with irrational numbers to make these values easier to express. The ruling school of thought at the time dictated that everything in nature could be explained elegantly with the numbers that already existed. Threatened by Hippasus’s new notion, his fellow mathematicians rejected the irrational numbers and had him exiled.

Other numbers have been banned for legal reasons. When Arab traders brought their positional number system, which included zero, to Italy in the Middle Ages, Florence banned it from record-keeping fearing that they would be easier to forge than Roman numerals. The Arabic way of counting also led to the rise of negative numbers, which were regarded with disdain by many experts into the 19th century. For more banned numbers, including some that are prohibited today, check out the full story below.

[h/t TED-Ed]

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Euclid
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Live Smarter
An Ex-Google Engineer Just Reinvented the Measuring Cup
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Euclid

Recognizing a problem most people didn’t even know they had, former Google and Facebook software engineer Joshua Redstone has made a bold claim for his recent Kickstarter venture: He’s developed a better measuring cup.

According to the Boston Business Journal, Redstone spent four years tinkering with a solution to something that had long annoyed him as an amateur chef: Traditional measuring cups, which are stocky and not very well tapered, don’t do a great job of accurately measuring their own contents. Redstone believes the shape of a cup determines its success, particularly when a cook overfills a liquid or solid by a tiny amount. The smaller the volume, the more the problem is magnified.

Euclid

Redstone’s cup, Euclid, resolves the issue. According to the Kickstarter page: “With traditional measuring cups, the smaller the amount, the harder it is to measure accurately. The culprit? The shape. Straight sides magnify errors when measuring lower down in the cup. Some have tried to solve this problem with conical measuring cups, but their results fall short of Euclid’s by up to 60 percent. Euclid is the only measuring cup with a mathematically optimal, tapered design for consistent accuracy across amounts.”

Euclid is just about ready to overshoot its $30,000 Kickstarter goal. Backers can pay $24 for the cup now, or wait until it’s available at retail for a slightly higher price to be determined. The cup is scheduled for release in May 2018.

[h/t Boston Business Journal]

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