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@ The wonder in the natural world

When I found the 'Euler's Equation', well-known to the knowledgeable, in Ogawa Yoko's novel 'The equation the doctor loved', which was also a hit in the movies, I was surprised and impressed as well at the unexpected result. The 'Euler's Equation', which represents that 'e' multiplied by 'i' plus '1' equals '0', produces lyrical beauty rather than crystal one. It is very regrettable that an equation can not be written in the blog.


By the way, the 'multiplication' is 'how many times the same number is multiplied', and the 'cube of 2' is to multiply 2 two times i.e. the answer is 4 and the 'cube of 2' is to multiply 2 three times i.e. the answer is 8.


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Incidentally, we are apt to carelessly think things in 'addition'; however, in fact, most of events in the natural world vary in 'multiplication = with multipliers'. In other words phenomena in the natural world vary not in linear lines or with velocity but in curved lines or with acceleration such as parabolas and hyperbolas.


Now the 'e', 'I' and '', which appear in the 'Euler's Equation', are keys to the 'wonder in the natural world'.


The 'e' is called the 'Napier's Constant' after its finder, however it was Euler who made the secret of the 'e' clear, and it is mathematically called the 'base of natural logarithm'. Apart from such mathematical details, the 'e' plays an important role when we describe the changes of various phenomena in the natural world.
Unless we can describe the movement in the natural world, I don't say it is entirely impossible, but various types of inconvenience arise when we forecast the weather or fly an airplane well.


The '' is the 'circular constant' as you know it very well. While the discovery or determination of the 'circular constant' has a long past from the Pharaonic era, I have to raise my hat to the efforts of geniuses who have tried to convert a 'circle', one of the 'perfect curved lines = nature, into a 'straight line = human knowledge' at all costs.
Everybody can draw a 'circle' on the ground, the word 'Geometry' was created combining 'ground (Geo)' and 'measuring (Metric)'; however the '' becomes indispensable when we want to match a circle to a building composed of a straight line. After all, the sun and the earth as well is round.


The 'i' is an imaginary figure which is a fictitious one existing in a brain only, while a 'real figure' which can practically be used for counting an apple, two apples and so on by touching or seeing them.
As it is a fictitious figure, it does not seem to be directly related to us. On the contrary the 'i' exists close by our life. For instance, the 'i' always appears in the structural calculation of a reinforced concrete building and makes it possible to construct a safe building on the earth.


The greatness of the 'Euler's Equation' is that it has admirably combined entities which seem to be a fanciful 'sign' only with the most fundamental figures which we can realise immediately, i.e. '1 = the minimum unit of existence' and '0 = inexistence'. Saying '1 and 0', they also compose a 'digital world' which is indispensable to a computer.


Ms. Ogawa Yoko beautifully depicts such great but charming 'figures' as being lurking in the natural world in her 'The equation the doctor loved'. I strongly recommend you to read it.


The attached illustration is super-famous 'The back of waves off the coast of Kanagawa' by Hokusai. His greatness is that he intuitively detected the 'e', '' and 'i', and made them up into a skilful ukiyoe. Was Hokusai a 'transcendental mathematician' or was Euler a 'super-eminent artist'? Probably they were both.


i8/12/2006j
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