The Fibonacci Sequence

1, 1, 2, 3, 5, 8, 13, 21, 34, 55…

At first, it just seems like a string of numbers, perhaps one of those “what’s the next number in the sequence?” questions you remember from SAT or IQ tests from your school days. But these numbers, I assure you, are something completely different.

Although the interesting properties of this sequence were first noticed by a Sanskrit writer called Pingala around 500BC, it was Italian mathematician Leonardo of Pisa (also known as Fibonacci) who first studied them in the West in the early 1200s. Because of Leonardo’s work, the numbers are now known as “Fibonacci numbers” or a “Fibonacci sequence”. The pattern is created, simply enough, by adding the two previous numbers in the sequence to make a new number, and adding that new number to the previous one in the sequence and so on.

But why is this interesting? Because the Fibonacci sequence is literally everywhere in nature. According to Wikipedia, the “branching patterns of leaves in grasses and flowers, branching in bushes and trees, the arrangement of pines on a pine cone, seeds on a raspberry, and spiral patterns in horns and shells” are all done in Fibonacci sequences. The genealogy of male bees follows a Fibonacci sequence. I can personally tell you from my days in Liberal Arts Math that, with the exception of 2 or 3 oddball varieties, every species of daisy has a number of petals that follow the Fibonacci sequence.

But wait – there’s more! If you divide a Fibonacci number by the one that precedes it, you’ll notice an interesting pattern starting to take shape. The result of the equation always remains close to 1.618, which is also known as the Golden Ratio. The Golden Ratio is considered (in the West, anyway) to be one of the most aesthetically pleasing forms around. The facade of the Parthenon is based on the Golden Ratio. The shape of most books and cereal boxes is based on the Golden Ratio. Read up on this stuff… it’s really interesting!

The Mysterious “Voynich Manuscript”

You know how I love history’s mysteries? Well, one of the best there is is the mysterious “Voynich manuscript”, a book now owned by Yale University. The book is around 240 pages (out of an estimated original 272), and is thought to be from between 1450 and 1520AD. The book is handwritten on vellum and is chock full of illustrations (albeit none as fancy as most other European manuscripts). What makes the Voynich manuscript such a mystery is that it’s written in a completely unknown language. There are approximately 170,000 unknown glyphs in the text, yet there are many curious facts about the glyphs: they appear to follow some sort of grammar (certain glyphs appear in combination with other glyphs, just as English has common letter combinations like “ie” or “th”). The text seems to follow Zipf’s Law (which is a word frequency analysis; for example, Zipf’s Law states that “the” will probably be the most common word in an English language text). And the glyphs themselves seem to have been written in a flowing, graceful hand (which suggests familiarity with the language). On the other hand, the “language” of the Voynich manuscript seems to be a mish-mash of European and Arabic. For example, some glyphs appear only at the beginning or end of a “word” (like Arabic, but unlike European languages), yet there are no words longer than 10 characters nor are there any with just one or two characters (unlike either Arabic or European). The origin of the text is unknown. Some suspect that it’s the work of Roger Bacon or John Dee (among others). Many scholars think it’s an outright 600 year-old hoax. But the sheer amount of work that went into the book – not to mention the thought about grammar and letter frequency, which were barely understood by most people in the Middle Ages – makes me think that it’s not a hoax. In any case, the Voynich manuscript has befuddled some of the best cryptographers in the world – even the wunderkids from Bletchley Park.

Read more about the Voynich manuscript here.

Candy Jones, Super Spy

One movie that totally exceeded my expectations was George Clooney’s Confessions of a Dangerous Mind. The movie, based on the “autobiography” of television personality Chuck Barris, deals in large part with Barris’ allegations of being a hit man for the CIA. Now I haven’t read the book, but the movie leads one to ask all kinds of questions. At first glance, it’s easy to think that Barris is either pulling a fast one on us or is simply crazy. But his stories are so rich in detail yet so simple in their nature that one almost stops and wonders if he was indeed hired by the CIA to carry out all kinds of nasty deeds. And then there’s the question of motive… Barris was already a household name when his book came out; as far as I know he didn’t have any projects coming out that might have benefited from the book’s publicity. Why would someone make a story like that up?

But then you have the twisted tale of Candy Jones. Born Jessica Wilcox in Atlantic City, New Jersey, on December 31, 1925, the future Miss Jones had a rough childhood. Her father left when she was three (but not before reportedly crushing her fingers in a nutmeg grater), while her mother was a cold disciplinarian that locked poor Jessica alone in her room for long stretches at a time. To combat the loneliness, Jessica invented several imaginary friends, one of whom – a cold, calculating girl named “Arlene” – would never quite go away.

Continue reading Candy Jones, Super Spy

Woo-Hoo – I entered the 21st Century!

OK, so… I’ve gone and installed WordPress on my site, and have big plans to convert the entire site over to it. Yes, it’s finally time to ditch FrontPage, so those of you out there who have given me grief about using FrontPage (and you know who you are)… you can now shut up about it!

I have no idea of how long it’s gonna take to convert the old site over (months, I’m guessing), so I’ll be running a “split site” in the mean time – just go to jimcofer.com and click on the link to the old site, and you’ll be able to get all the old info there. Nothing new should be posted over there, but you never know. Perhaps the WordPress thing will be a complete disaster. Or a smashing success. Who knows?

In the meantime… enjoy!