Slime mould finds shortest path to food (in yellow). Photo: Nature
Welcome to the magical maze of the mathematical mind. ... Slime mould is a crowd of amoebas, which assemble in beautiful spiral patterns. ...
Japanese scientists claim that amoeba-like organisms have a primitive form of intelligence, following an experiment where a slime mould found its way through a maze.
Reporting in the journal Nature, Toshiyuki Nakagaki from the Bio-Mimetic Control Research Centre in Nagoya showed that a slime mould negotiated the shortest route between two exits in a maze, avoiding three longer paths.
"This remarkable process of cellular computation implies that cellular materials can show a primitive intelligence," Dr Nakagaki said.
Slime moulds are made up of a mass of protoplasm embedded with multiple nuclei, but no individual cell walls. The adult, feeding stage, called a plasmodium, is a glistening mass of mucus which swarms over and engulfs its food.
The maze was created by laying a maze template down onto a plate of agar. In the first part of the experiment, pieces of slime mould Physarum polycephalum were placed throughout the 3x3cm maze. To grow, the slime mould throws out tube-like structures called pseudopodia, and it soon filled the entire maze.
The maze had four routes through, to get from one exit to the other. Food was placed at both exits, and after eight hours, the slime mould had shrunk back so that its 'body' filled only the parts of the maze that were the shortest route from one piece of food to the other.
The researchers suggest that as the parts of the plasmodium come into contact with food, they start to contract more frequently. This sends out waves to other parts of its body which tell give feedback signals as to whether to grow further or contract. Ultimately, to maximise foraging efficiency, the plasmodium contracts into one thick tube, running through the maze.
There continues to be scientific debate about whether simple cellular organisms, and even individual cells, have intelligence. There is no doubt cells can move: the cell cortex has autonomous domains called microplasts whose movement is controlled by a centrosome. Microtubules mediate between the control centre and the autonomous domains. Cell can also 'see', using a cell structure called the centrioles which can detect near infrared signals and steer the cell towards their source.
Cells may contain a signal integration system that allowed them to sense, weigh and process huge numbers of signals from outside and inside their bodies and to make decisions on their own, according to Guenter Albrecht-Buehler, from the Institute for Advanced Studies, in Berlin, and Robert Laughlin from the Northwestern University Medical School, Chicago.
They argue that if cells are intelligent, future medical treatment may involve 'talking' to cells in their language. "They (cells) should be capable of integrating physically different signals (mechanical, electrical, chemical, temperature, pH, etc) before they generate a response", the researchers said.
http://www.abc.net.au/science/news/stories/s189608.htm
Magical Maze - Lecture Summary
Article by Ian Stewart
Stage:4 and 5
Mathematics is a special way of thinking about the world around us. The universe can be thought of as a maze, built from events that are linked together by paths of cause and effect. Inside our heads there is a second maze of nerve cells: the brain. Our brains have evolved a third maze --- the maze of mathematical truths, whose pathways are logical deductions that link statements to their consequences.
Mathematics is a maze of ideas rather than a maze of things. Yet the mathematical maze in our heads has given humanity a profound understanding of the outside universe. This is not logic: it is magic. The magical link between mind and matter; the same kind of magic that makes sunsets beautiful and distant galaxies awesome.
Welcome to the magical maze of the mathematical mind.
Lecture 1. Mathematics Everywhere
What is mathematics? Is it invented or discovered? How does it relate to Nature? Is it all in the mind, does it exist 'out there' in the real world, or is it something altogether different? Would a dolphin civilisation, or an alien one, necessarily possess some kind of mathematics? Would it have to be much like our own, or could it be wildly different?
To tackle these questions, we'll take a look at how mathematics has opened up human understanding of the universe and influenced our culture. Examples include music, which led the ancient cult of Pythagoreans to believe that the universe rested on numbers; planetary motion, which led Isaac Newton and others to the idea that we live in a 'clockwork universe' ruled by rigid physical laws; and patterns of growth and form in the living world, such as the strange numerology of flowers and the shapes and sizes of animals, which suggest that there is more to life than DNA. We'll discover that nature has deep numerical patterns, but that the true mathematics of nature may well lie deeper still. If so, alien mathematics might not look terribly familiar. After all, why would right angles be important to a dolphin?
Lecture 2. The Pattern of Tiny Feet
Early in 1997 a NASA spacecraft turned a tiny six-wheeled robot loose to explore the surface of Mars. The next Mars robot may well have six legs, like a mechanical insect --- so designers of legged robots are taking some tips from nature. After all, it would be silly to reinvent the leg.
Animals, which have evolved very effective ways to use legs, move in a variety of patterns. A horse can walk, trot, canter, or gallop, for instance. These patterns are called gaits. There are characterstic mathematical patterns in gaits. These patterns are clues to the layout of the circuits in the animal's nervous system that control locomotion. By understanding how these circuits work, we can build better robots.
A similar kind of mathematics can be applied to groups of animals --- herds of bison, flocks of birds, shoals of fish. These also display characteristic patterns of movement. Applications include new methods for modelling the flow of crowds in public buildings, which can help prevent future disasters by making the buildings safer.
Lecture 3. Outrageous Fortune
One of the most useful areas of mathematics is probability theory, which deals with chance. Probability theory is an essential part of statistics, a tool that is widely used for all kinds of decision-making; it is also fundamental to our understanding of risk. But what is probability?
The lecture will explain some of the basics of probability theory by looking at simple examples, showing that our unaided intuition can often lead us astray. Topics will (probably!) include coincident birthdays, sexes of children, DNA fingerprinting, the role of confessions in legal evidence, and the notorious T'onty Hall Problem' involving a game show, a star prize of a car, and goats as booby prizes.
Life, too, is a game of chance. All human actions --- including 'do nothing' --- carry an element of risk. The degree of risk may be large (leaping across a canyon on a motorbike), or small (watching television in your home). Probability theory helps us to understand risk better, and to take more sensible decisions about risky activities.
Lecture 4. Chaos and Fractals
Ian Malcolm, the mathematician in Jurassic Park, is a 'chaos theorist'. His speciality tells him that the Park's complex systems are doomed, right from the start --- but nobody listens until it's too late. But what is chaos theory? The movie doesn't tell us, but the lecture will. It will also explain the role of fractals, beautiful and intricate geometrical shapes that are somehow associated with chaos.
The revolution of scientific thought pioneered by Isaac Newton led to a vision of the universe as some gigantic 'clockwork' mechanism, a point of view known as 'determinism'. This idea has been spectacularly successful in helping us come to terms with the world around us. But now mathematicians and physicists have run into an apparent paradox. Order can breed its own peculiar kind of disorder. Deterministic causes can have effects that seem random. This remarkable discovery --- 'chaos' --- is changing the face of science. It explains why it is so hard to predict the weather, offers new ways to control heart disease, predicts the gaps in the asteroid belt, and even opens up more efficient --- but slower --- routes to get a spacecraft from the Earth to the Moon.
Lecture 5. The Science of Patterns
Mathematics is the science of patterns. A pattern is a landmark in the magical maze. Many common types of pattern are symmetric. The mathematical concept of symmetry was not made precise until the early 1800s, when it was realised that symmetry is not a thing, but a transformation --- a way of moving objects around.
Symmetries are widespread. We find them in kaleidoscopes, allowing us to design bathroom mirrors that don't reverse left and right. We also find symmetries in more unlikely circumstances --- for example, in the migratory habits of slime mould. Slime mould is a crowd of amoebas, which assemble in beautiful spiral patterns. These patterns 'emerge' from mathematical rules that govern chemical signals sent from each amoeba to its neighbours.
The same kind of rotating spiral can be observed in a beautiful chemistry experiment, the Belousov-Zhabotinskii reaction. The mathematics of such patterns, introduced by Alan Turing, also applies to the markings on animals. Many animals --- tigers, zebras, raccoons --- have stripes. Others, such as leopards or giraffes, have spots. Turing suggested that chemical patterns in embryos could lay down a 'pre-pattern' which, when the animal developed, triggered the formation of the markings that we see. The intricate markings on seashells can be explained in this way, and very recently the theory has been applied to the stripes on angelfish --- which move.
So: would a dolphin civilisation invent the concept of a right angle? Would there have to be a dolphin Pythagoras? Or would they base their mathematics on the swirls and vortices of moving fluids? Not calculations with numbers, but a feel for fluid dynamics?
Your guess is as good as mine.
What do you think?
