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[GUEST POST] Tony Ballantyne, Author of DREAM PARIS, on Building the Science of a Dream World

tonyballantyneTony Ballantyne is the author of Dream London, Dream Paris, the Penrose series and the Recursion series. He has also written many short stories.

Tony grew up in County Durham in the North East of England. He studied Maths at Manchester University before moving to London where he taught Maths and IT.

His first SF sale was “The Sixth VNM” which appeared in Interzone 138. Since then he has had short stories appear in magazines and anthologies worldwide. He has also written romantic fiction and satirical pieces for various magazines such as Private Eye.

Recursion, his first novel, was published by Tor UK in 2004. He has been nominated for the BSFA and Philip K Dick awards.

He now lives in Oldham with his wife and two children. His hobbies are playing the piano, accordion and cornet. He also enjoys walking and cycling.

Building the Science of a Dream World

by Tony Ballantyne

Just suppose I flew an aeroplane 1000 kilometres north, turned through 60 degrees, flew another 1000 kilometres, turned another 60 degrees and flew another 1000 kilometres. Where would I end up?

If you said back where I started, then you’re thinking in terms of Euclidean Geometry. Perhaps you noticed that I described an equilateral triangle, or perhaps you’d sketched out a triangle on a piece of paper.

But perhaps that was a mistake. If the aeroplane was flying over the Earth, then Euclidean Geometry wouldn’t apply. It doesn’t apply because the Earth is curved – being roughly spherical. An aeroplane following the path described above would end up some distance from its starting point.

Not convinced? Then here’s another question: how can I draw a triangle with three right angles?

The answer is to ignore Euclidean Geometry and to draw the triangle on a sphere.

Again, imagine an aeroplane starting at the north pole, flying down to the equator, turning ninety degrees and flying along the equator for the same distance. It then turns ninety degrees again and flies back to the north pole. You’ve just described a triangle with three right angles, something impossible in Euclidean Geometry.

That’s not to say there’s anything wrong with this Form of Geometry. It’s how we learn to understand the world, it just that it doesn’t exactly describe the real world.

It describes it close enough though, especially when small distances are involved. It’s accurate enough if you’re building a house, or a pyramid. But that doesn’t mean that it’s right.

That’s an important point. We have grown up being taught that the angles in a triangle add up to 180 degrees, we’re encouraged to believe that the maths we’re taught describes the world around us, and it does, but only up to a point. Actually, the world is much stranger than that…

In Dream London, and my most recent novel, Dream Paris, numbers don’t work as they do in our world. There are no fractions, no irrational numbers, there are only whole numbers. Extra numbers have had to pop into existence to deal with this fact, so that red is the number that you get when you half three and (a feeling of fulfillment) is the ratio between the circumference of a circle and its diameter.

The fact that all numbers have a whole number values means that the Dream World operates in a very different way to hours. When pi is a whole number, a circular path is a different length to its equivalent in our world. Things are a different shape on the outside. All sorts of strange effects and coincidences leap into being. Some of them even touch our world. The chapters in Dream Paris are numbered in the Dream World manner and some of the numbers are remarkably appropriate, the chapter numbered pi (in our numbering system) in particular. This was not deliberate!

Strange though Dream Maths is, it’s still not as odd as our Mundane Maths. I still remember how mind blowing the Banach-Tarski paradox was when I first heard about it. Look it up if you don’t believe me, but this is a proof that you can cut a ball into pieces and then put those pieces back together to make two identical copies of the original ball. You could end famine by repeatedly cutting one pea up and sticking it back together as two peas.

Things like that make you question if we need SF. The real world is quite strange enough…

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