After a long day of toil and trouble, there’s nothing quite like a cold, refreshing beer.
As you take your first pull from the bottle or glass, your worries immediately drift away, and as you set your vessel down, you begin to lose yourself in the effervescence of it all, just as the bubbles slowly and continually rise to the top.
That is, of course, unless you’re drinking a stout, such as the popular Irish drink of choice, Guinness. That's where science comes into play. Just like beer, science is often more fun when it’s shared. . . .
Carl Sagan said that "extraordinary claims, require extraordinary evidence." In a stunning display of mathematical logic vs common sense, David Spiegel of Princeton University and Edwin Turner from the University of Tokyo published a paper last summer that turns the Drake equation upside down using Bayesian reasoning to show that just because we evolved on Earth, doesn’t mean that the same occurrence would necessarily happen elsewhere; "using evidence of our own existence doesn’t show anything" they argue, "other than that we are here."
For decades, biologists have debated whether individuals sacrifice themselves to save those who share their genes or in effect to benefit the whole group. University of Vermont researcher Charles Goodnight has shown through mathematical models that the two views of altruism, kin selection versus group selection, are in fact equivalent behaviors.
The research sheds new light on fundamental issues in evolutionary theory.
"Children know many math concepts through early play. As infants they know that they are small and their mother and father are big even though they do not know the words. Toddlers know that if they put one block on top of another, they will have two even though they do not know the words. They know that if they have 2 blocks and you have 10, you have more and they want them..."
Every few days, a new study decrying the sorry state of the mathematical aptitude of American students is published and the powers that be, particularly those in education, wring their hands in exasperation before advocating some new trendy way of...
"This is an application that has me excited in so many ways that I think it’s a can’t miss for any mathematics teacher using a computer. Calling itself a dynamic geometery application, Sketchometry http://sketchometry.org/ is really something to play around with."
The great physicist and populariser of science, Carl Sagan, on whose book the film is based, next demonstrates how a shared universal mathematics and rules of logic can be extended to a common lexicon able to convey complex information. For example, the alien versions of the statements
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