In a post just over a year ago, I presented data on earth activity (in particular earthquakes, volcanic eruptions, and tropical storms). Given all the buzz on the internet about an increased earth activity over the past several years, I was curious to see this for myself, so I downloaded and analyzed some publicly available data. Surprisingly, though, the data showed no such increase at all. In the current post, I present the updated data for up until the end of 2016, which still shows no sign of any unusual behavior. Judge the plots below for yourself…

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The historic city of Graz, in south-eastern Austria, was designated a UNESCO world cultural heritage site in 1999 for having “the best preserved city center of Central Europe”. It combines renaissance, gothic, baroque, and also modern architecture, and has some wonderful natural beauty nearby as well. I recently spent four days exploring this fascinating city and its surroundings, combining culture and nature with a lot of walking.

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Spirals are common in nature. We’ve all admired the beautiful spirals that occur on sea shells, we can find spirals in plants, and even in the arms of galaxies or weather patterns. There are also situations in which spirals aren’t a result of slow growth, but occur spontaneously in biological or chemical systems. A famous example from chemistry is the Belousov-Zhabotinsky (BZ) reaction: when several chemicals are mixed together in a petri dish, the resulting solution forms changing spiral patterns. In biology a particular slime mould, called dictyostelium discoideum, gives rise to similar patterns. Spontaneous spiral wave formation in such systems can be reproduced and studied with simple mathematical models known as cellular automata.

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Charles Darwin’s theory of evolution by natural selection is one of the most profound scientific theories to have ever been developed. However, there were several questions about evolution that Darwin himself could not answer. Not that he wasn’t smart enough (in fact, his intuition often pointed in the right direction), but the answers to those questions required sophisticated mathematical insights that were not developed far enough, or even available yet, in Darwin’s time. One such problem was the evolution of altruism. If evolution by natural selection is all about competition and survival of the fittest, how can altruistic behaviour (which, by definition, lowers the altruist’s fitness and increases the receiver’s fitness) ever evolve?

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Evolution is still all too often (but wrongly) downplayed as “just a theory” in public discussions. This is partly due to an unfortunate misunderstanding of what a theory means in science, as opposed to its common language meaning. Evolution by natural selection is much more than just a hypothesis, and is as much a valid and well-accepted scientific theory as the theory of gravitation. What Darwin did for biology is on par with what Newton did for physics — and mathematics plays an important role in both theories.

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Last night a rare event happened: the summer solstice and a full moon at the same time. So I went up Kahlenberg, a hill above the city of Vienna, to have a good view of this special full moonrise. Unfortunately my cheap little point-n-shoot camera is almost useless in low-light conditions, but I got a few halfway decent shots anyway. Click each pic to see a larger version.

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I’ve made a short movie showing autocatalytic sets arising in a dynamical simulation of a simple polymer model. It shows how autocatalytic subsets appear, one after another, and then grow in concentration. This provides a nice visual and dynamical example of our usually more graph-theoretical analyses. Continue Reading