Two of the most fundamental questions asked by people are how life emerged on the Earth, and whether we are alone in the cosmos. These deeply important questions form the core of a new kind of science, one that recently has been rapidly gathering momentum: astrobiology. Lewis Dartnell explains.
Modern technology has changed many things in our lives, including the way we communicate, travel and entertain ourselves. Electronic instruments and computer simulations have revolutionised science. Mathematics, one of the purest forms of human logic and reasoning, has also been changed by computer approaches. Even art has been undergoing a deep upheaval in the way it is created and appreciated, using the fast processing and graphical output of computers. The boundary between artist, computer programmer, and mathematician is becoming ever more blurred. In this article, Lewis Dartnell leads us through some examples of this exciting new wave of digital art.
Read full article on +plus
In the first part of Simulating the World we saw how simple mathematical models can be built to study everything from the flocking of birds to the collision of entire galaxies. In these examples, a matrix, or a grid of numbers, was used as a convenient way of storing information on all the objects included in the simulation, so that it can be updated each time step as the simulation progresses. In this second article, we’ll take a look at another class of mathematical models; ones where the matrix or array isn’t just a way of storing information during the simulation, but actually is the simulation itself.
Many real-world situations can be simplified as a sequence of objects in a line or an arrangement across a flat space — in other words, they can be faithfully represented by either a list of numbers (a one-dimensional matrix) or a regular grid of cells (a two-dimensional matrix). During the course of the simulation, the objects interact with those near-by according to a set of predefined rules, with the identity of each discrete position on the line or plane changing over time. Such a system is called a cellular automaton model.
Read full article on +plus
Building models forms the core of many areas of scientific and engineering research. Essentially, a model is a representation of a complex system that has been simplified in different ways to help understand its behaviour. An aeronautical engineer, for example, might build a miniaturised physical model of a fighter plane to test in a wind tunnel. In modern times, more and more modelling is being performed by computers – running mathematical models at very high rates of calculations. A computer model of the flow of air over a supersonic wing is incredibly sophisticated, but it is based on very basic principles of program design and simulation. In this article, the first half of a two-part feature on model behaviour, we’ll take a look at how simple computer models can be programmed to study some very interesting natural systems as well as focus on how a few scientists are using similar models in their own front-line research.
Read full article on +plus
Judging by their self-confident lyrics about women and wealth, rappers consider themselves quite a special bunch. And now it’s been proven mathematically that indeed they are, at least as far as their interaction network is concerned. An analysis of the network you get by connecting any two rappers that have performed together shows not only a remarkably close-knit community, but also another feature rarely found in naturally arising networks.
Read full article on +plus
In the last issue Lewis Dartnell explained how chaos in the brain is not only unavoidable but also beneficial. Now he tells us why the same is true for our solar system and sends us on a journey that has been travelled by comets and spacecraft.
Read full article on +plus
Saying that someone is a chaotic thinker might seems like an insult – but, according to Lewis Dartnell, it could be that the mathematical phenomenon of chaos is a crucial part of what makes our brains work.
Read full article on +plus
The word “stealth” is often associated with high-tech bombers built to be invisible to enemy radar. This technology works through the aircraft’s surface being specially designed and having a covering of radar-absorbent skin that ensures minimal radio waves are reflected back to the enemy radar transmitter.
There is another kind of stealth, however, that does not rely on hiding the presence of an object, but on masking the fact that it is moving. If the pursuer approaches along a particular trajectory it appears to remain perfectly stationary from the point of view of the target. The pursuer can use this “motion camouflage” to rush right up to the target before it is perceived as a threat. This technique could be used by missiles to remain undetected for as long as possible, and even appears to have been discovered by nature. There is good evidence that hoverflies and dragonflies have evolved this strategy to fly without being detected.
Read full article on +plus
The world around us is full of relationships, rhythms, correlations, patterns. And mathematics underlies all of these, and can be used to predict future outcomes. Our brains have evolved to survive in this world: to analyse the information it receives through our senses and spot patterns in the complexity around us. In fact, it’s thought that the mathematical structure embedded in the rhythm and melody of music is what our brains latch on to, and that this is why we enjoy listening to it. It is perhaps not surprising then that there is a great deal of overlap between mathematics and the art that our brain finds so pleasing to look at.
This article is a whistle-stop tour of some of the types of art with a strong mathematical component, or conversely where a mathematical visualisation has an astonishing beauty.
Read full article on +plus
The BA (British Association for the Advancement of Science) is a nation-wide organisation dedicated to connecting science with people and promoting openness about science in society. It organises Science Week (11-20 March 2005) and an annual Festival of Science, which was hosted this year by the University of Exeter. Mathematics was well represented at this year’s Festival, with an exhibition of mathematical art, the launch of the National Cypher Challenge, and a morning of fascinating lectures on the Clay Institute Millennium Problems. The three ‘Million Dollar Maths’ problems covered were P vs. NP, the Riemann Hypothesis, and the Poincaré Conjecture.
Read full article on +plus
This article has been reprinted in the February 2005 issue of Mathematics Today (vol.47, no.1), the magazine of The Institute of Mathematics and Its Applications (IMA). Download pdf
Alan Turing is considered to be one of the most brilliant mathematicians of the last century. He helped crack the German Enigma code during the Second World War and laid the foundations for the digital computer. His only foray into mathematical biology produced a paper so insightful that it is still regularly cited today, over 50 years since it was published. In it he described how a set of ‘reaction-diffusion equations’ explain how the wonderful diversity of animal patterns may be generated.
Read full article on +plus
This article has been reprinted in Muse, the YouthAgency magazine. The agency is run by the National Association for Gifted Children and aims to inspire able students to cultivate their abilities. pdf copy of the reprint.
As we saw in the last edition of +plus, mathematical techniques have been applied very successfully to analysing certain types of games. The two examples that we looked at were the simple subtraction game Nim, and the much more complex case of chess endgames. The next step is to see how computers, which are no more than automated maths machines, are being programmed to actually play chess themselves. It is theoretically possible to play chess perfectly, but neither humans nor machines will probably ever accomplish this. Computers have, however, already practically achieved perfection in draughts, and soon may be said to have ‘solved’ the game. Continue reading