With hot weather currently making me sweat down here in Australia, it’s nice to fantasise about winter. Everyone’s heard the old adage “No two snowflakes are alike”, but how true is it? Clearly, checking every single snowflake on Earth would be impossible, so how can we be sure? Well, by using mathematics, of course. Complex snowflakes are made up of six symmetrical spokes, each extraordinarily detailed. Each tiny change in these details counts as new design of snowflake, and these small variations result in a staggeringly huge amount of possible combinations. To understand the math, let’s think about a smaller number for a moment. Let’s say you have 15 books—how many possible ways can you arrange them on your bookshelf? You can decide on 15 different spots for the first book, then 14 for the second, 13 for the third, 12 for the fourth…and all the way down to just 1 for the fifteenth book. These numbers are multiplied out to get the number of possible combinations, and although there are only fifteen numbers, multiplying them out gives you 1,307,674,368,000—i.e., over a trillion ways to organise just fifteen books. If you had 100 books, the combinations rocket up to a number a thousand times larger than the total number of atoms in the universe. A complex snowflake easily has one hundred separate features, so the math behind it is similar—the number of possible combinations is enormous, so the probability that there have ever been two identical snowflakes is so small that it’s indistinguishable from zero.
If you approached the rim of a volcano and looked down into it, you might expect to see a lava pool, but if the volcano previously erupted and then the top of it collapsed into a huge bowl-shaped crater, or caldera, then what you might see when you peer over the rim is a beautiful crater lake. Sometimes the water is acidic and the lake has a bright greenish hue. Other times the water is a cloudy turquoise color, yet other times the lake may appear to be a very deep shade of blue. Crater Lake, Oregon, is one of the most well known, but crater lakes can be found all over the globe. If the volcano has been dormant for a long time, the water can be extremely clear because no river or streams flow into with sediment deposits. In some cases, water may have filled up an impact crater to form a lake, but this is less common. A few crater lakes were created by man via an atomic blast, but an artificially-created crater lake is the least common of all. All crater lakes were once a place where the earth experienced great violence, but now are a place of great beauty … even though the volcano can become active and violent again.
“A human being is a part of the whole called by us ‘the universe,’ a part limited in time and space,” wrote Einstein in 1950. “He experiences himself, his thoughts and feelings, as something separate from the rest—a kind of optical illusion of consciousness.” It’s a brilliant and fascinating perspective, and science tells us that it’s true. Our eyes inform us that there is a definite boundary between us and the world around us, and so we perceive ourselves as entities separate to the wider universe—as individuals just making our home in this vast place. But when we take a step back, we can see that we’re molecular machines built from a specific arrangements of atoms—atoms that existed before we were born and will continue to exist after we die. They were recycled from the dust of dead stars, and we’re only their temporary custodians. Fundamentally, each of us is just a tiny individual expression of an enormous singular entity—so we are the universe perceiving and studying itself. The idea that the individual and the universe are inseparable is a humbling, counter-intuitive and ultimately awe-inspiring idea—there’s a mad kind of beauty in knowing that we do not live in the universe, but rather we are the universe. As Feynman wrote: “I…a universe of atoms…an atom in the universe.”
Meet Kelvin Doe, a 15-year-old completely self-taught engineering whiz from Sierra Leone who was given the chance to visit and study at MIT. His story is inspiring and remarkable – showing that inspiration and innovation can spring from anywhere. Kelvin’s drive to teach himself electronics and help his community by reverse-engineering radios, generators and other devices from what 99.9% of the population would consider trash is a moving reminder of that fact.
Plants aren’t typically known for their speed, but the carnivorous Venus flytrap can close its jaw-like leaves in the blink of an eye. Charles Darwin once referred to the Venus flytrap as “one of the most wonderful plants in the world.” But despite the plant’s notoriety, its closing mechanism remains a mystery 250 years after its discovery.
Biophysicists at the Ecole Polytechnique Universitaire de Marseille, in France, are investigating the cellular process behind the Venus flytrap’s rapid response to prey. The researchers have already thrown out one popular explanation for the Venus flytrap’s quick motion, that water movement within the plant makes its jaw snap. They announced this finding in San Diego at a meeting of the American Physical Society’s Division of Fluid Dynamics.
“This is the first time someone has looked at how Venus flytraps move on the cellular level,” said biophysicist and lead researcher Mathieu Colombani. “We are looking for an explanation that’s both biologically and physically possible.”
Venus flytraps are native to the coastal bogs of North and South Carolina. The bogs’ soil lacks the proper nutrients — particularly nitrogen and phosphorus — for plants to grow. The plant manages to survive in this tough environment by trapping and digesting insects in order to fulfill their nutritional needs. [continue reading] | image: Mathieu Colombani (via Inside Science)
Benoit Mandelbrot was a mathematician who coined the term fractal: a geometric figure that repeats itself on progressively smaller scales. He spent much of his career at the IBM Watson Research Center, and in 1978 he was the first to use a computer to construct a graphical representation of a set of numbers, now known as “The Mandelbrot Set.” It is a fractal because it displays self-similarity at magnified scales with an infinite level of detail, but it’s also an infinitely complex representation because the small-scale details aren’t always exactly the same as the whole image. The Mandelbrot set is generated quite simply using iteration, which is to repeat a process over and over again. In mathematical terms this just means it’s generated from a equation that involves complex numbers (numbers that have a real part and an imaginary’ part, i.e. 3+2i). It is one of the most widely recognised fractals, and its beautiful, fascinatingly intricate structures reflect nature itself.