The drive to adorn our bodies is pretty close to universal.

Clothing, for example, serves the triple purpose of protecting our skin, keeping us warm, and making us look good. Well, some of us. I'll admit up front that I have a fashion sense that, if you were to rank it on a scale of one to ten, would have to be expressed in imaginary numbers. But for a lot of people, clothing choice is a means of self-expression, a confident assertion that they care to look their best.

Then there are tattoos, about which I've written here before because I'm a serious fan (if you want to see photos of my ink, take a look at the link). Tattooing goes back a long way -- Ötzi the "Ice Man," a five-thousand-year-old body discovered preserved in glacial ice in the Alps, had no fewer than 61 tattoos. No one knows what Ötzi's ink signifies; my guess is that just like today, the meanings of tattoos back then were probably specific to the culture, perhaps even to the individual.

Then there's jewelry. We know from archaeological research that jewelry fashioned from gems and precious metals also has a long history; a 24-karat gold pendant found in Bulgaria is thought to have been made in around 4,300 B.C.E., which means that our distant ancestors used metal casting for more than just weapon-making. So between decorative clothing, tattoos, and jewelry, we've been spending inordinate amounts of time and effort (and pain, in the case of tattooing, piercing, and scarification) altering our appearances.

Why? No way to be sure, but my guess is that there are a variety of reasons. Enhancing sexual attractiveness certainly played, and plays, a role. Some adornments were clearly signs of rank, power, or social role. Others were personal means of self-expression. Evolutionists talk about "highly conserved features" -- adaptations that are between common and universal within a species or a clade -- and the usual explanation is that anything that is so persistent must be highly selected, and therefore important for survival and reproduction. It's thin ice to throw learned behaviors in this same category, but I think the same argument at least has some applicability here; given that adornment is common to just about all human groups studied, the likelihood is that it serves a pretty important purpose. What's undeniable is that we spend a lot of time and resources on it that could be used for more directly beneficial activities.

What's most interesting is that we're the only species we know of that does this. There are a few weak instances of this sort of behavior -- for example, the bowerbirds of Australia and New Guinea, in which the males collect brightly-colored objects like flower petals, shells, and bits of glass or stone to create a little garden to attract mates. But we seem to be the only animals that regularly adorn their own bodies.

How far back does this impulse go? We got at least a tentative answer to this in a paper this week in *Science Advances*, which was about an archaeological discovery in Morocco of shell beads that were used for jewelry...

... 150,000 years ago.

"They were probably part of the way people expressed their identity with their clothing," said study co-author Steven Kuhn, of the University of Arizona. "They’re the tip of the iceberg for that kind of human trait. They show that it was present even hundreds of thousands of years ago, and that humans were interested in communicating to bigger groups of people than their immediate friends and family."**************************************

Mathematics tends to sort people into two categories -- those who revel in it and those who detest it. I lucked out in college to have a phenomenal calculus teacher who instilled in me a love for math that I still have today, and even though I'm far from an expert mathematician, I truly enjoy considering some of the abstruse corners of the theory of numbers.

One of the weirdest of all of the mathematical discoveries is Euler's Equation, which links five of the most important and well-known numbers -- π (the ratio between a circle's circumference and its diameter), e (the root of the natural logarithms), i (the square root of -1, and the foundation of the theory of imaginary and complex numbers), 1, and 0.

They're related as follows:

Figuring this out took a genius like Leonhard Euler to figure out, and its implications are profound. Nobel-Prize-winning physicist Richard Feynman called it "the most remarkable formula in mathematics;" nineteenth-century Harvard University professor of mathematics Benjamin Peirce said about Euler's Equation, "it is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth."

Since Peirce's time mathematicians have gone a long way into probing the depths of this bizarre equation, and that voyage is the subject of David Stipp's wonderful book *A Most Elegant Equation: Euler's Formula and the Beauty of Mathematics*. It's fascinating reading for anyone who, like me, is intrigued by the odd properties of numbers, and Stipp has made the intricacies of Euler's Equation accessible to the layperson. When I first learned about this strange relationship between five well-known numbers when I was in calculus class, my first reaction was, "How the hell can that be true?" If you'd like the answer to that question -- and a lot of others along the way -- you'll love Stipp's book.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support *Skeptophilia*!]