Snow flakes, ice crystals, beautiful round baubles — Christmas is the time of symmetry, so here's a few articles to celebrate it!
Everyone knows what symmetry is, and the ability to spot it seems to be hard-wired into our brains. Mario Livio explains how the symmetry we admire in a snow flake might also explain the workings of the Universe.
Through the looking-glass
When Alice stepped through the looking glass in Lewis Carroll's Through the Looking-Glass and What Alice Found There, she would have found that more than just the writing was back to front. The very molecules that made up her body would have been the wrong way around in the looking-glass world, and their
interaction with the looking-glass molecules would have led to a very confusing — and possibly dangerous — adventure!
Maths is a creation of our brains, so how come it describes the world around us so amazingly well? How is it that
ideas from pure maths suddenly find real-world applications decades or even centuries after their discovery? Here are some articles exploring the "unreasonable effectiveness" of mathematics.
When it comes to describing natural phenomena, mathematics is amazingly — even unreasonably — effective. This article looks at an example of strings and knots, taking us from the mysteries of physical matter to the most esoteric outpost of pure mathematics, and back again.
We all take for granted that mathematics can be used to describe the world, but when you think about it this fact is rather stunning. This article explores what the applicability of maths says about the various branches of mathematical philosophy.
You might not have thought it, but while you sit contentedly digesting your turkey and gazing at the telly, your brain is keeping up the hard work, making sure that everything in your body goes according to plan. And to understand this most amazing of nature's creations you need maths. Here are some of our favourite articles on brains, human and animal.
Catching sight of a cockroach tends to make us behave chaotically, what with the running and screaming and throwing of shoes. But it appears that chaos might actually explain how we, and the cockroach itself, behave.
The human brain faces a difficult trade-off. On the one hand it needs to be complex to ensure high performance. On the other hand it needs to minimise what you might call wiring cost — the sum of the length of all the connections — because communication over distance is metabolically expensive. It's a problem well-known to computer scientists. And it seems that market-driven human invention and natural selection, faced with similar challenges, have come up with similar solutions.
Think drug-induced hallucinations, and the whirly, spirally, tunnel-vision-like patterns of psychedelic imagery immediately spring to mind. But it's not just hallucinogenic drugs that conjure up these geometric structures. People have reported seeing them in near-death experiences, following sensory deprivation, or even just after applying pressure to the eyeballs. So what can these patterns tell us about the structure of our brains?
It may be Sunday but that's no excuse for resting your brain. Plus has been grappling hard with the strange weirdnesses of quantum mechanics lately, and we think that you should too. So get ready to be mind-boggled.
With counterintuitive ideas such as superposition and entanglement, quantum mechanics doesn't seem to resemble reality as we know it, yet quantum physics is an incredibly successful theory of how the physical world operates. Plus spoke to Andrew Briggs, John Polkinghorne, Nicolas Gisin, David Wallace, Roger Penrose and Andrea Morello about how we can resolve the mysteries of quantum physics with our experience of reality. And we found out why quantum physics is just like riding a bike...
Quantum mechanics is usually associated with weird and counterintuitve phenomena we can't observe in real life. But it turns out that quantum processes can occur in living organisms, too, and with very concrete consequences. Some species of birds use quantum mechanics to navigate. Studying these little creatures' quantum compass may help us achieve the holy grail of computer science: building a quantum computer. You can also listen to the accompanying podcast.
When it comes to the science of the very small, strange things start happening, and our intuition ceases to be a useful guide. Plus finds out about the crazy quantum world, and spin that a politician would die for.
Over the last few years the words string theory have nudged their way into public consciousness. It's a theory of everything in which everything's made of strings. Find out how these tiny strings offer hope for reconciling quantum mechanics with Einstein's theory of relativity.
One of the many strange ideas from quantum mechanics is that space isn't continuous but consists of tiny chunks. Ordinary geometry is useless when it comes to dealing with such a space, but algebra makes it possible to come up with a model of spacetime that might do the trick.
Whenever you smell the lovely smell of fresh coffee or drop a tea bag into hot water you're benefiting from diffusion. Now researchers have finally found experimental confirmation for the most important concept underlying diffusion theory.
With the weather cold and the nights very dark, it's the perfect time to curl up in front of the fire and do some philosophising. Here are some of our favourite articles on mathematics and the nature of truth ... or lack of it!
Many people like mathematics because it gives definite answers. Things are either true or false, and true things seem true in a very fundamental way. But it's not quite like that. You can actually build different versions of maths in which statements are true or false depending on your preference. So is maths just a game in which we choose the rules to suit our purpose? Or is there a "correct" set of rules to use? We find out with the mathematician Hugh Woodin. Read more...
In the 1930s the logician Kurt Gödel showed that if you set out proper rules for mathematics, you lose the ability to decide whether certain statements are true or false. This is rather shocking and you may wonder why Gödel's result hasn't wiped out mathematics once and for all. The answer is that, initially at least, the unprovable statements logicians came up with were quite contrived. But are they about to enter mainstream mathematics? Read more...
Paraconsistent mathematics is a type of mathematics in which contradictions may be true.
In such a system it is perfectly possible for a statement A and its negation not A to both be true. How can this be, and be coherent? What does it all mean? Read more...
If you like mathematics because things are either true or false, then you'll be worried to hear that in some quarters this basic concept is hotly disputed. This article looks at constructivist mathematics, which holds that some things are neither true, nor false, nor anything in between.