Roger Penrose likes complex numbers. The renowned physicist Roger Penrose has written several excellent books on mathematical physics aimed at the interested layperson - these include the classic The Emperor's New Mind and his newest book The Road to Reality. What I like about Penrose is that he's easy to read, and he explains things as if he actually wants and expects you to understand them. I'm slowly working my way through TRTR right now. As in TENM, Penrose provides a lot of information on the role of complex numbers - numbers that have a "real" part and an "imaginary" part. Imaginary numbers are multiples of i, the square root of -1. (As we all know, -1 doesn't have a square root. That's why they're called "imaginary" numbers. No, really.) For Penrose, one of the key concepts in the development of mathematics (and science in general) has been the process of generalizing a useful concept to provide new insights. For example, transcendental numbers like pi - also called "irrational" numbers because they can't be expressed as the quotient, or "ratio", of two integers - were viewed warily in the Pythagorean world. But once mathematicians started allowing themselves to work with these numbers, many important discoveries were made. "In many instances, this drive for mathematical consistency and elegance takes us to mathematical structures and concepts which turn out to mirror the physical world in a much deeper and more broad-ranging way than those that we started with."
And so, the introduction of the concept of seemingly impossible imaginary numbers allows us to gain amazing new insights. Picture imaginary numbers on a "number line" of their own - at right angles to the familiar "number line" of real numbers. (And speaking of the number line, remember when you first learned about negative numbers? Up until then, you'd been taught that you couldn't have any number less than zero, and you couldn't subtract a bigger number from a smaller number. And then ... well, you see what RP is talking about.) So just for fun, we're turning the old number line into a grid, and now we can plot complex numbers (some real number + some imaginary number) on this grid. Now what happens if we add these numbers? Or multiply them? (Remember, i times i is minus one.) And now the real fun begins. You gotta read Penrose to find out the rest.
Volcano discovered on Titan. Space.com reports: 'Scientists think they've spotted a large volcano on Saturn's smoggy moon Titan. The mountain could be pumping methane into the atmosphere, which would explain the perplexing presence of the chemical that helps create Titan's dense atmospheric shroud. The new study, announced today [June 8], also adds to mounting evidence showing there are no widespread methane oceans on Titan, as scientists had predicted prior to the Cassini mission.' The volcano could help explain the presence of methane in Titan's atmosphere, as new evidence makes the presence of widespread methane oceans on the planet look increasingly unlikely. Frequent volcanic eruptions, with lava flows, would also account for the smooth appearance of Titan's surface.
Space enthusiast Maryam interviewed. Big news! Maryam, aka Kuwaiti Girl, is interviewed by Mister Ghost at In T Views. Read her thoughts on her interest in the space program, the Arab world, the Iraqi invasion of 1990, black holes, string theory, and (naturally) Sergei Kirkalev.
