Are there any imponderable that you find you cannot stop pondering?
I don’t know about you, but there are some things I find hard to stop doing, some ideas I find hard to stop mulling, and some thoughts I find hard to stop thinking (I used to be indecisive, but now I'm not so sure).
Just the other day, for example, my son Joseph presented me with some candies (sweets in England) that I still find difficult to describe. They weren't too big and they weren't too small. They had hard-ish chewy exteriors coupled with slimy chewy interiors. They had a taste that was hard to put one's finger (or tongue) on. They managed to be both interesting and disgusting at the same time. Just one of these candies would have sufficed for a lifetime, yet I couldn’t stop eating them to make sure that each new one was as bad as I thought it was going to be.
Or take the poem The Road Not Taken by Robert Frost (see also my column Two Roads Diverged In a Yellow Wood (Yellow?)). Now, don’t get me wrong, I love this poem, but at the end of the day it's about someone who has brought dithering to a fine art, and who would probably drive you insane it you were to actually meet them.
The bottom line is that the person telling the tale was wandering through a wood when he (or she) came to a fork in the path. Both branches were identical. He equivocates and vacillates until you want to pull your hair out, eventually choses one, and then witters on about how this choice "made all the difference." On a first read, you get the impression that he's now old and tired and approaching the end of his life, reflecting on how different things might have been had he taken the other path. When we re-read it, however, we see:
I shall be telling this with a sigh
Somewhere ages and ages hence...
It's the "ages and ages hence" that galls me. Now I'm left with the impression that he's still in the prime of his life. He took his walk only that morning, and now he's sitting in his armchair on the afternoon of the same day, smoking his pipe, drinking a cup of tea, and waffling on to anyone who will listen about the momentous decision he made. If I were there, I'd want to shake him by the scruff of the neck and scream "Go back and walk down the other $#%! path and put us all out of our misery, for goodness sake!"
And then there's the book Contact by Carl Sagan (the book is much better than the movie of the same name). The book is great. I love it. We receive a message from the stars that tells us how to build a weird machine. Five people get in the machine and are transported to the center of the Milky Way where they have all sorts of wonderful experiences and learn all sorts of interesting things.
When they eventually return, they discover that no time has passed on Earth, that all their video footage has been erased, and that nobody believes that they went anywhere. Our heroine, Ellie, ends up devoting the rest of her life to compute the digits of Π to heretofore-unprecedented length. Once again, I love this book, but I'm still left thinking "That's it?"
All of which brings me to the point of this column (of course there's a point, do I look like a man who doesn’t have a point?). Earlier today, my chum Jay Dowling pointed me at this video on YouTube.
This was created by Matt Parker, who used to be a math teacher in Australia, but who left the unfinished continent Down Under to move to London, England, where he works both as a math communicator and a stand-up comedian. Now that I come to think about it, you don’t see as many Australian math-communicator-comedians around as you used to when I was a lad, but we digress...
This is a great video. Very thought provoking. Matt sets out to calculate the value of Π based on random numbers that he generates using two d120 dice (the one-hundred-and-twenty-sided d120 is based on a polyhedron known as the disdyakis triacontahedron, and is described as "The ultimate fair die allowed by Mother Nature").
The video is 24 minutes long. At around the 15:30 mark, Matt triumphantly calculates the value of Π as being ~3.05. Hmm, "close, but no cigar," as they say. On the other hand, this is only off by ~2.8% and I'm still jolly impressed. I'm also reasonably confident that Matt will improve on this value in the remaining eight and a half minutes of the video, but I'll have to watch that part later.
Now I'm left ruminating and cogitating on the mystery that is Π. This little rascal is woven into the very fabric of time and space and it pops up everywhere. In all the multiverse (or meta-universe), could there be space-time regions in which Π has different values? What would this mean? My head hurts!
How about you? Are there any imponderables that you find you cannot stop pondering, or am I one of a kind? (My mother always used to say I was special. I foolishly took this to be a complement. It was only recently that I thought "Just a minute...")
write the first three prime numbers twice each 113355
The only problem is that isn't the first three prime numbers, which would be 223355. It is the first three odd numbers. It is a good formula, but if you are stranded on a desert island with a calculator without Pi and need to use Pi in an equation to help signal for rescue (not sure how that would happen, but I can't think of how else to make your life depend on Pi) then you will end up with 1.5919 and some very wrong answers.
@perl_geek: ...This whole experiment sounds like a variation on "Buffon's needle"...
Yes -- that's another one that amazes me.
I'm a bear of little brain -- I can understand the relationship between Pi and the circumference or a circle or the volume of a sphere -- what I find hard to wrap my brain around is how Pi pops up in so many other places.