This is a bit of an extension/update to my previous post about TV and science inspiration. It turns out that Wolfram Research, the makers of Mathematica math-analysis software, are now the official math consultants of the CBS cops/FBI show "NUMB3RS". The premise of this show is that a mathematician helps an FBI group to catch the bad guys. What's especially cool about the Wolfram connection is that with each episode, the math advisors now write up an episode webpage linked with CBS's NUMB3RS webpage, which explains in much more detail the math topics discussed in that week's story. The one for episode #401 that I read was a very nice introduction to set coverage and optimization (which in fact relates to some of the sensor coverage research my department at APL does). It included script snippets, graphics, and even interactive demonstration applets using the new Mathematica Reader that can be downloaded for free from Wolfram. (That Reader is also used to play the wonderful online Demonstrations Project applets on the Mathematica website.) The episode writeup was really interesting for a scientist/mathematician guy to read, and I'll definitely come back to read them for future episodes. But unfortunately it was far from readable by the general public, having equations and jargon after the introductory paragraphs. Perhaps that will change as the series goes on, and meanwhile it's a start. I'm still absolutely amazed that Hollywood is doing a partnership like this -- wow! ...
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We happen to have a cute little baby at home, and some of her baby toys are cooler than others. Take for instance this great rattle of hers. I figure chances are pretty good that its designers didn't intend it to be a functioning, trinary, two-digit abacus, but that's exactly what it is. Check it out, I've taken a sequence of pictures showing how to use the thing to count from 0 to 8 in trinary...
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Far out, have you heard about this? The Oklo region in Gabon, Africa contains an ancient uranium deposit that used to be a naturally occurring nuclear reactor a couple billion years ago. Scientists know this by analyzing samples of the isotopes mined from the deposit. There was in fact an article recently in Physics Today, a technical magazine of the American Institute of Physics, by some researchers who study Oklo. Their interest is in comparing the decay rate of uranium billions of years ago with the decay rate measured today. Theoretically that rate should be exactly the same over the eons, being a physical constant. But the focus of this article was "hey, here's a chance to check this constant over billions of years - could it drift very slightly in that time?"...Read more

I was just reminded about this yet again by a schoolteacher I met on the bus. My 4th grade teacher managed to get my scientist Dad's hackles up periodically from misinformation she taught us in her science class. It was mostly little things, like when I answered a class question that a "lightyear" is a unit of distance, and she wrongly insisted it's a unit of time. But the thing that really pushed Dad over the edge was when we received a new issue of our Weekly Reader one spring day, and in the science section was a blurb telling us about the Equinox Egg Effect. You may have heard of this myth, it’s a strange one that has snuck into all sorts of funny places to be described as a scientific fact. Well, so our teacher thought this would make a neat class project.

The Equinox Egg Effect myth says that at the exact moment of the vernal equinox in the spring, you can balance an egg perfectly on its end without it falling over. The vernal equinox is the time of year when the tilted axis of Earth’s rotation is facing 90 degrees away from the Sun. Equinoxes happen twice a year actually, the other time being the autumnal equinox. The equinoxes fall halfway between the summer and winter solstices, which are the dates when the Earth’s tilted axis points directly toward or away from the Sun. In the US is the solstices and equinoxes are chosen as the beginnings of the seasons, but that’s only a matter of convention. Perhaps the most familiar example to us of a different convention is the “midsummer’s night” of Shakespearean fame, which was another name for the summer solstice. There’s nothing particularly scientifically interesting about these dates, outside of the fact that at that time the days and nights are equally 12 hours long. Anyway, popular explanations as to why an egg should stand on its end at the exact moment of the vernal equinox are usually very vague, and generally cite something about gravity from the Sun being somehow momentarily stronger or more directed during the equinox...Read more

Around 2nd grade I became really interested in codes and desperately wanted to be able to solve these cipher puzzles still found today in Games magazine.  So one morning I was pestering Dad to no end about I-don't-remember-what, and he finally said "Enough!  So you wanted to learn about these ciphers right?  Well it's all about knowing how often certain letters appear in the English language. So now go get your Hardy Boys book there and count up the number of times each letter of the alphabet appears in all of chapter one, and jot your numbers down on this piece of paper here.  And don't pester me till you're all done!"  So off I went into my room and started counting diligently, and by that night I'd made it up to the N's or something, and by the end of the next day I had it.  And I remember being really puzzled at Dad's surprised look when I came back to him with my sheet of numbers.  But after two days of peace and quiet he was happy to show me what to do with those numbers and I then was off and going on my cipher puzzles.Read more

The same black and white TV on which I watched the Six Million Dollar Man was the source of other inspiration during my fifth year. In the summer of 1976 (I was born in 1971) the Viking 1 probe landed on the surface of Mars, the first ever landing on another planet. This was a big deal. I remember excitedly watching with Mom as the first photographic image from Mars appeared slowly, strip-by-strip, on the TV screen as it was shown on the Today show. Looking back on it, I’m not sure why the image appeared strip-by-strip – the data rate from Viking would have been far too slow to show this image live, and it certainly wouldn’t have been much effort to piece the image together before showing it on TV. But the strips, which were the individual tall/skinny photos that in montage formed the full landscape photos...Read more

This one's in response to another high-school student's question: What's the difference between "centripetal" and "centrifugal" force? Why do we say this has something to do with relativity?

Well, defining centripetal force is easy. Centripetal force is what pulls a rotating object towards the center of what it's rotating around. For example, if you swing a ball on a rope around horizontally over your head, the centripetal force is your pulling on the rope so the ball doesn't fly away. Or in the case of the Moon rotating about the Earth, the centripetal force is the force of gravity constantly pulling the Moon toward the center of the Earth, otherwise the Moon would fly away in a straight line too. Remember Newton's First Law - a body in motion wants to stay in motion in a straight line at a constant speed unless something else (gravity or friction or whatever) specifically acts to change that motion. Anyhow, so centripetal force points toward the center of the rotating system.

The definition of centrifugal force on the other hand, and its difference from centripetal force, is a little more involved; it's ironic that it is the term more familiar in popular usage. From popular usage we at least know that centrifugal force has something to do with rotation and with getting thrown off merry-go-rounds. But before I define centrifugal force and compare it to centripetal force, I have to take a second and talk about different "frames of reference" so the rest makes sense...Read more

From a high school student: I read somewhere that time gets all messed up because of the theory of relativity or something. What's up with that?

Well, the theory of relativity was a new physics idea developed in the early 1900's by Albert Einstein, radically generalizing ideas from electromagnetism at the time (e.g. invariance of Maxwell's equations in different reference frames). It says that the old laws of kinematics and dynamics - motion and forces - by Newton and Kepler and all those guys who we learn about in school are in fact only approximations to what really happens. The equations we learned early on, like "distance equals speed multiplied by time", work just fine for daily life things like cars and airplanes and bowling balls, and are still important for those describing things. But when we deal with objects that move at close to the speed of light, or that are near large gravity fields, our traditional equations and experiences are way off, time and space don't act like you would expect, and we need to use more complicated equations to describe the motion...Read more