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Nature's mathematics

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We can enjoy nature perfectly well without maths and science, so why bother with them. Well, if maths and science tell us things about nature, we are ignoring important aspects if we shut our eyes to these topics. These pages only describe very simple ideas that might arise during a walk in the country. Deeper phenomena, such as population trends and the mechanics of flight, require a lot of work. Then there are all the internal workings, which have a perfection of there own, and the evolution over time. None of this can be known without much study. But the things we can observe for ourselves can give us clues to the beauty and order that are present in even the most "humble" animal or plant. And they must all be quite successful; like us, they are still here.

Don't quit just yet - the maths will not be painful - it will be hardly noticeable. If you do want to quit, please write down this book title first, or click on this URL. The examples in these web-pages are by definition only the simplest ones. The book and others to be cited later describe some subtle and beautiful things.

Life's Other Secret by Ian Stewart - Penguin

ISBN 0 14 025876 0.

Click here for numbers that relate a sunflower to a suspension bridge.

Click here for notes about trees and forests.

Click here for notes about spider webs.

Click here for surface tension.

Click here for engineering curves.

Click here for interference.

Click here for sine and exponential.

Click here for snake curves.

Click here for numerology.

Click here for relationships in maths and science.

When Wordsworth saw a field of daffodils, what he saw made him feel like writing a poem. He felt that he had to put something down on paper about the scene that made him feel so deeply. He certainly didn't think about maths. Another person, such as Monet, might have made a painting.

When you see a large number of bluebells, you probably don't think about maths either. You don't need to, in order to enjoy the scene.

But maths is there, all the same.

Where is it? And why should we be interested?

You actually get involved with maths quite often. Every time you hear music, maths is there. Every flower seems to have maths. If you solved the Rubik cube you used maths.

Suppose you wrote a poem consisting of the word "daffodil" repeated an infinite number of times. It would be highly symmetrical, because it would look the same everywhere.

A real  poem cannot last for ever, and is a little less symmetrical for that reason alone. The symmetry of a real poem is reduced further, because most of the lines, most of the stanzas, and most of the words, differ from one another.

But the rhyming scheme and the rhythm scheme often retain enough symmetry to distinguish poetry from prose. But what about blank verse?

So poetry has  an underlying structure of broken symmetry, just like theories about the physical world. Some kinds of minimalist music are rather repetitive, and have a high degree of symmetry. You might even think that the permutations of the people and relationships in books such as "Jude the obscure" look like an attempt at a symmetrical structure.

The word maths may have already told you that this page is not for you. The problem with maths is that whenever there is a phenomenon to be understood, there must be some pattern to it, and maths is a good language to understand it.

Even if the behaviour is random - guess what - maths is the thing to use.

The problem is that mathematicians and scientists see maths in everything. It's not their fault - there is no other way of describing so many things as concisely. Not using maths would be like not using prose or poetry to communicate - there isn't anything else as convenient.

People don't accuse Wordsworth of reducing daffodils to mere poetry - the daffodils were still there, exactly as before. And mathematicians and scientists don't reduce anything either - they just describe it in ways that are economical and neat. They may feel as deeply as Wordsworth did, but they express themselves differently.

Both art and science can provide abstract depictions of nature. A being from another planet that had no air would not understand a poem about daffodils swaying in the breeze. The poem only makes sense if we have some point of reference and some knowledge. Paintings based on classical mythology are hard to understand if we don't know the stories behind them. A scientific theory is only comprehensible if we have the background to understand the basic ideas in it.

Many people are more familiar with art than science, and many people are more uneasy with abstract art than with representational art. Yet a novel or a poem - words on paper - are completely abstract. A stone statue is about as far as you can get from living, supple, graceful human body. Yet it is so familiar that we accept it.  In fact we are so familiar with this convention that objects such as Oldenburg's soft typewriter were considered weird when created.

We accept a flat picture as pretty realistic, yet your pet dog or cat will seldom recognize a picture or a TV image.

Blake, in his poem about a tiger, asked a very deep question - how could a lamb and a tiger have a common origin? No scientist could have asked the question more beautifully and clearly than Blake. No poet could have answered it as neatly as Darwin and his followers.

What art, music, poetry, maths and science can do is to illuminate. Even if you don't believe what they tell you, they can show you some ways of seeing.

Here is the title of a book that can tell you much, much more than this web-page - 

Life's Other Secret by Ian Stewart - Penguin

ISBN 0 14 025876 0.

In this book, Professor Stewart points out that genes are not enough to specify what happens - they operate within the laws of physics and chemistry. Knowing the rules of chess, which are few and simple, does not allow us to predict, except in general terms, the types of events that can happen in a game - exchanges, pins and forks, yes, beautiful sacrifices - possibly.  

Chess is a little universe inhabited by 32 atoms in a two-dimensional discrete space with 64 locations. There are only six kinds of atoms. And, like the genes, the rules of chess were probably not invented as a single event: no doubt they evolved to produce the right degree of complexity that keeps the game interesting even today, with powerful computers and teams of analysts.

Another part of this website discusses bridges. Here, too, as Malcolm Millais points out, logic alone will not allow you to create the best solution for a given problem: engineering, like art, sport and science, is a creative occupation, an art as well as a science.  Building Structures by  Malcolm Millais - E and FN Spon (Chapman and Hall) - ISBN 0 419 21970 6.

 

Click here for numbers that relate a sunflower to a suspension bridge.

Click here for notes about aliases.

Click here for notes about trees and forests.

Click here for notes about spider webs.

Click here for surface tension.

Click here for engineering curves.

Click here for interference.

Click here for sine and exponential.

Click here for snake curves.

Click here for numerology.

Click here for relationships in maths and science.

Click http://www.mathsyear2000.org/ for some fascinating material.

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