Not for the faint of art. |
Complex Numbers A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number. The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi. Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary. Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty. |
Today's article, from SciAm, is an ad. Though it's for a book, which I've repeatedly insisted is appropriate here (much as movie previews are appropriate ads before movies), I just wanted to state that up front. Can Scientific Thinking Save the World? A physicist, a philosopher and a psychologist are working together to bring better, smarter decision-making to the masses As I've also repeated, my default answer to any binary headline question is "no." I mean, I'd like it to be "yes," but the world stubbornly refuses to conform to my wishes. Spurred by what they saw as a perilously rising tide of irrationality, misinformation and sociopolitical polarization, they teamed up in 2011 to create a multidisciplinary course at the University of California, Berkeley, with the modest goal of teaching undergraduate students how to think—more specifically, how to think like a scientist. Seeing that now, 13 years later, that particular (red) tide keeps rising, I'd say the world stubbornly refuses to conform to their wishes, too. Now the three researchers are bringing their message to the masses with a new book, Third Millennium Thinking: Creating Sense in a World of Nonsense. Like I said: ad. And their timing is impeccable: Our world seems to have only become more uncertain and complex since their course began, with cognitive biases and information overload all too easily clouding debates over high-stakes issues such as climate change, global pandemics, and the development and regulation of artificial intelligence. Perhaps they're just pissing into the ocean. Scientific American spoke with Perlmutter, Campbell and MacCoun about their work—and whether it’s wishful thinking to believe logic and evidence can save the world. The rest of the adarticle is in interview format. I find it interesting, which shouldn't be surprising, given that the disciplines in question are ones I've discussed here on numerous occasions. But no point in rehashing points. Instead, since the subhead up there cries out for it, I'll attempt to make up a joke: A physicist, a philosopher and a psychologist walk into a bar. Bartender says, "What'll it be?" The physicist says, "The answer depends on the level of our knowledge of all the prior states of the system." The philosopher says, "The future is unknowable; we just have to wait to find out." The psychologist says, "I'll have a beer. These two chucklefucks want wine." ...I didn't say it would be a good joke. |