Base 10 Birthday

Later this week I’ll celebrate another birthday.  It will be one of those “decade” birthdays, where the first digit in your age moves up a notch and the last digit in your age cycles to zero again.

Let’s face it:  decade birthdays are somewhat annoying.  Just because our culture long ago settled on a “base 10” number system — presumably because the ancient Egyptians realized that we’ve got ten fingers on our hands, and chose to build mathematics around the concept of ten as the path of least resistance — doesn’t mean there should be any special significance to celebrating a birthday when your new age divided by ten produces a whole number rather than a fraction.  It’s just another year added to the ledger, and the turn of the calendar page doesn’t mean you should feel or act any different.

And yet, everybody treats the “decade” birthdays as if they are some hugely significant milestones.  Sure, 13 and 18 and 21 have their own special elements, but the decade birthdays can actually define you as a person.  Suddenly you’re “in your twenties” or “in your thirties,” and people expect you to behave in a certain way.  And as those decades creep upward, the age-related expectations tend to become even more fixed.

So I’ve got another decade birthday coming up.  So what?  The decimal system doesn’t define me.  In fact, I’m going to pretend that we’ve got a base 8 culture and ignore it.

After 100 Years, It’s All Relative

This year marks the 100th anniversary of Albert Einstein’s theory of general relativity.  First published in 1915, covering the intersection of gravity, space, time, and the speed of light, and supported by a mass of hard-core mathematics beyond the ken of most mortal beings, general relativity stands with evolution as one of the most well-known, universally recognized scientific theories in history.

80619-004-9b9d0d26Even though the theory of general relativity has hit the century mark, it’s still the subject of some controversy — including whether it’s the exclusive brainchild of Einstein, or whether it was the product of ideas and concepts contributed by a group of scientists and physicists.  A recent piece tracks the history, and the controversy, and the potential contributions by others.  It’s a fascinating tale.

What’s most interesting about the theory in my view is that it began as a thought experiment that captured Einstein’s imagination, in which he considered whether, if he were seated in a windowless, doorless box, he would be able to tell the difference between being subject to gravity or being exposed to the sensations of acceleration.  It tells you something about Einstein that he even came up with such an idea in the first place, but that curious thought experiment ultimately produced a theory that predicted the bending of light by gravitational bodies, was confirmed by measurements conducted during an eclipse a few years later, and helped to make space flight feasible.  The theory of general relativity, coupled with his trademark unkempt mane of hair, made Einstein the most famous scientist in the world.

Since 1915, the theory of general relativity has withstood countless tests and challenges and experiments.  It’s still pretty spry for a 100-year-old.

 

How Best To Avoid The Raindrops?

For years, physicists and mathematicians have debated a simple question:  when it’s raining and you’re without an umbrella, will you stay drier if you run or walk?

Each position is supported by a logical argument:  if you walk, you’re out in the rain for a longer time, but if you run you hit more raindrops.  Dozens of scientific papers have addressed the issue and discussed factors like wind speed.  Now Professor Franco Bocci has weighed in, arguing that prior efforts have not adequately taken into account factors like the human shape.  He says past calculations have assumed human beings are like thin sheets or upright, rectangular boxes — and you tend not to see many such shapes in today’s super-sized world.  He concludes that, for the most part, the best approach is to run through the rain as fast as you can.

I wonder whether Professor Bocci’s analysis adequately considers the length of the rainy space to be crossed, its condition, and the condition of the person trying to stay as dry as possible.  Not many people wearing business suits are going to successfully sprint 500 yards through a downpour, no matter what mathematical models might say.  And if you’re making a mad dash down a city street trying to avoid a good soaking, you’re far more likely to charge through an undetected puddle or be splashed by a passing car and get even more soaked.  The better course often is to evaluate the topography and availability of awnings and overhangs, and then plot a carefully calibrated zig-zag course that affords maximum cover while not requiring heroic running performances.

Or, better yet, have the foresight to carry an umbrella.

Peace Of Pi On Tau Day

You will remember pi, of course.  It is the mathematical constant whose value is the ratio of any circle’s circumference to its diameter.  Pi also is the ratio of a circle’s area to the square of its radius.  Simply by writing those two sentences I have caused most readers to grit their teeth, remember their high school geometry and higher math courses with a grim shudder, and thank their lucky stars that they never have to use such concepts in their jobs.

Pi is probably the most important mathematical constant, and it is also the point at which math begins to reveal its dark, kinky soul.  Pi is an irrational number that starts as 3.14 and then trails off into an endless series of numbers that do not repeat.  Some friendless, misguided people celebrate March 14 — that is, 3.14 — as pi day and do things like bake pies with the value of pi to a certain number of decimal places along the rim of the pie crust.

Given the celebration of pi, and its weird irrationality, in the math community, who would have suspected that there is an anti-pi contingent?  But there is, and yesterday was their dayThese friendless, misguided math enthusiasts propound tau as the preferred alternative to pi.  Tau is a mathematical constant that is twice as large as pi; hence tau is 6.28 and change, and tau day is June 28.  Why do the tau proponents dis pi and tout tau?  They say that tau is a more natural, convenient way to express the mystical qualities of circles, because circles really are about radii — that is, the distance from a circle’s center to the points along the circle — not diameters.

Now that tau day is over, we can gratefully return to our daily lives.

As Simple As Rubik’s Cube

Researchers using supercomputers have figured out that any scrambled Rubik’s Cube can be completely solved in no more than 20 moves.  (And I’m happy to report that one of the people involved, who is quoted in the linked article, is a mathematician at Kent State University, here in Ohio.)  Why were supercomputers needed, you ask?  Because Rubik’s Cubes can be put into 43 billion billion different starting positions.  The vast majority of these can be solved within 15 to 19 moves.  In 100 million combinations, exactly 20 moves are needed to solve the puzzle.

20 moves!  Just what I needed:  something else to remind me that I was clueless when it came to figuring out a Rubik’s Cube, or one of those bent nails puzzles.

I had a friend once who got so frustrated with the apparently unsolvable Rubik’s Cube that he steamed the colored squares off the plastic underneath and re-glued them so that he could brag to friends that he figured it out.  Of course, he might have done better if he’d been helped by a supercomputer or two.