The structure is usually long and narrow with each component strand functionally equivalent in zigzagging forward through the overlapping mass of the others. More complex patterns can be constructed from an arbitrary number of strands to create a wider range of structures (such as a fishtail braid, a five-stranded braid, rope braid, a French braid and a waterfall braid). The simplest and most common version is a flat, solid, three-stranded structure. Braiding has been used to style and ornament human and animal hair for thousands of years in various cultures around the world. An Egyptian child with a 'Lock of Youth' plait hairstyleīraids (also referred to as plaits) are a complex hairstyle formed by interlacing three or more strands of hair. For other uses, see Braided hair (disambiguation). Morning sunlight illuminated John Preskill’s lecture notes about Caltech’s quantum-computation course, Ph 219.'Braided hair' redirects here. I’m TAing (the teaching assistant for) Ph 219. I previewed lecture material one sun-kissed Sunday. Pasadena sunlight spilled through my window. So did the howling of a dog that’s deepened my appreciation for Billy Collins’s poem “Another reason why I don’t keep a gun in the house.” My desk space warmed up, and I unbuttoned my jacket. I underlined a phrase, braided my hair so my neck could cool, and flipped a page. The phrase concerned a mathematical statement called “the Yang-Baxter relation.” A sunbeam had winked on in my mind: The Yang-Baxter relation described my hair. The Yang-Baxter relation belongs to a branch of math called “topology.” Topology resembles geometry in its focus on shapes. Topologists study spheres, doughnuts, knots, and braids. Scientists are harnessing this physics to build quantum computers. Alexei Kitaev largely dreamed up the harness. Alexei, a Caltech professor, is teaching Ph 219 this spring.

1 His computational scheme works like this. We can encode information in radio signals, in letters printed on a page, in the pursing of one’s lips as one passes a howling dog’s owner, and in quantum particles. Imagine three particles on a tabletop.Ĭonsider pushing the particles around like peas on a dinner plate. You could push peas 1 and 2 until they swapped places. The swap represents a computation, in Alexei’s scheme. The diagram below shows how the peas move. Imagine slicing the figure into horizontal strips. Each strip would show one instant in time. Letting time run amounts to following the diagram from bottom to top. Let’s recap: You began with peas 1, 2, and 3. You swapped 1 with 2, then 1 with 3, and then 2 with 3. The peas end up ordered oppositely the way they began-end up ordered as 3, 2, 1. You could, instead, morph 1-2-3 into 3-2-1 via a different sequence of swaps. That sequence, or braid, appears below.Ĭongratulations! You’ve begun proving the Yang-Baxter relation. You’ve shown that each braid turns 1-2-3 into 3-2-1. The relation states also that 1-2-3 is topologically equivalent to 3-2-1: Imagine standing atop pea 2 during the 1-2-3 braiding. You’d see peas 1 and 3 circle around you counterclockwise. You’d see the same circling if you stood atop pea 2 during the 3-2-1 braiding. That Sunday morning, I looked at John’s swap diagrams. I looked at the hair draped over my left shoulder. “Yang-Baxter relation” might sound, to nonspecialists, like a mouthful of tweed. It might sound like a sneeze in a musty library. But an eight-year-old could grasp the half the relation. When I braid my hair, I pass my left hand over the back of my neck. The braidings would look identical to a beetle hiding atop what had begun as the middle hunk of hair.Ī quantum corkscrew (“twisted worldribbon,” in technical jargon)īut I could have passed the right hand first, then the left. Like the corkscrews formed as I twirled my hair around a finger. I hadn’t realized that I was fidgeting till I found John’s analysis. I gave up on his lecture notes as the analogy sprouted legs. What computation might it represent? What about the French braid? You begin French-braiding by selecting a clump of hair. You add strands to the clump while braiding. The addition brings to mind particles created (and annihilated) during a topological quantum computation.Īncient Greek statues wear elaborate hairstyles, replete with braids and twists.

Could you decode a Greek hairdo? Might it represent the first 18 digits in pi? How long an algorithm could you run on Rapunzel’s hair?Ĭall me one bobby pin short of a bun. But shouldn’t a scientist find inspiration in every fiber of nature? The sunlight spilling through a window illuminates no less than the hair spilling over a shoulder.

Eloquent hair braiding