500,000 years and more in the future. Disused satellites and space debris orbit around the Earth. Among these there is a structure that resembles a space station. Suddenly a module detaches and crashes onto the planet. After the explosion, we follow an animal that, from the top of a cliff, spreads its wings and flies to the impact site. From the relatively distant readers' point of view, the flying shadow could be a pterodactyl and the Earth we see, in reality, that of prehistory: even the vegetation and the gigantism of the environment would seem to suggest it. Instead, when we get closer to the impact site, the figure becomes more defined: it is a kind of monkey with wings.
The guides in the exploration of this regressed world of the future are Diego Agrimbau and Lucas Varela and they use a robot, Alpha, as their guide. His job is to assist the terrestrial scientist Robert who, together with his wife June, devised a complex plan to repopulate the Earth with homo sapiens. Robert, in fact, predicting the fate of extinction of human beings, has decided to freeze himself and his wife while waiting for the planet to recover from the ecological disasters left on its surface by the passage of the human race.
posted by @ulaulaman #AlanTuring #mathematics #biology #genetics #ecology
One hundred years ago was born Alan Turing. He was known essentially for his role during the Second World War: he encrypted the Enigma machine. But He is also a brillant mathematichian and today I would try to describe one of his better model, that today biologists are applying to their research field.
A vibrating object tends to vibrate at certain preferred frequencies, called natural frequencies. These frequencies depend on properties such as the density and tension of the vibrating object. Mathematicians and physicists can determine the natural frequencies of an object when they know the values for these other properties. This article describes new work being done to solve the reverse problem - calculation of properties such as density when the natural frequencies of the object are known.
As I was scraping a brass plate with a sharp iron chisel in order to remove some spots from it and was running the chisel rather rapidly over it, I once or twice, during many strokes, heard the plate emit a rather strong and clear whistling sound: on looking at the plate more carefully, I noticed a long row of fine streaks parallel and equidistant from one another. Scraping with the chisel over and over again, I noticed that it was only when the plate emitted this hissing noise that any marks were left upon it; when the scraping was not accompanied by this sibilant note there was not the least trace of such marks.(1)
Some years after Galilei (1680), Robert Hooke
was able to see the nodal patterns associated with the modes of vibration of glass plates.
In 1787 Ernst Chladni repeated Hooke's experiments and published his results in Entdeckungen über die Theorie des Klanges (Discoveries in the Theory of Sound). Finally in 1967 Hans Jenny published Kymatik (Cymatics), a book based on Chladni's work, and cymatics became an interesting science, in particular for artists! For example, Jeff Volk, poet, writes an interesting article about Jenny and the pattern of sound: From Vibration to Manifestation (pdf). In particular he presents an image from Alexander Lauterwasser's Water Sound Images
Pay attention: following Lauterwasser and Volk we could explain the pattern of leopard's coat, but the first explanation come from one of the Alan Turing's paper The Chemical Basis of Morphogenesis(2). In this paper Turing is interested in the formation and development of path in biology (the so called phenomenon of morphogenesis).
Any pattern or shape observed in nature, even though governed by genetics, is most likely produced by an unknown mechanism. Thus, determining these mechanisms that generate pattern and shape in organisms is an important goal of theoretical biologists.(3)
The most used model for this type of systems is the reaction-diffusion system, described by the following formula:
\[u_t = d \Delta u + f (\gamma, u)\]
where $u$is the position of the gene, $u_t$ the diffusion speed, $d$, $\gamma$ real constants. We can write two similar formulas for every morphogene in the system.
Reaction-diffusion models are particularly compelling with regard to their ability to capture complex evolving patterns.(3)
Similar equations are really complex to analyze, due to their local and general phenomena. In an intuitively way, we can see the pattern formation like a challenge between reaction mode and diffusion mode. In his paper, Turing
suggested that a system of reacting and diffusing chemicals (morphogens) can interact to produce stable patterns in concentration (Turing patterns).(3)
Or in a more simple way: we can imagine the presence of an activator molecule of the morphogenesis. This molecule will be produced more and more thanks an autocatalysis process, but the activator will produce also an inhibitor, that will limit the production of the activator. The dynamics between activator and inhibitor will generate the pattern observed in nature (for example tigers' stripes). Tipically the two diffusion velocities are different, so we can explain the great variety of patterns.
