15. How chaotic is the universe?

O. E. Rossler

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15. How chaotic is the universe?

O. E. Rossler
O. E. Rossler

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How chaotic is the universe? O. E. Rossler Institutfiir Physikalische und Theoretisehe Chemie, Universitat Tubingen, D-7400 Tubingen, Federal Republic of Germany The title of the chapter is better than anything can possibly follow it. Originally I planned to write something nice and grandiose about Anaxagoras' invention of chaos as an explanation of the universe, and his ideas about transfinite iteration and the subtlety of the single 'immiscible' substance, the mind. Diesel automobile engines, the geyser Old Faithful, X-ray bursters in the sky, and autonomous nerve equations (including a 3-variable FitzHugh equation whose chaotic analogue computer solutions were shown to me by its inventor in late 1976) were then to follow suit—to illustrate the ubiquity of trajectorial mixing in simple differential systems populating the cosmos. Yet, even though it would be tempting to (re-)consider these topics (cf.[13]) in detail, and perhaps to add a disclaimer about the validity of discrete computational models as an exhaustive description of nature (cf.[3]), something less pretentious will be done in the following. Ά return to the mothers' of concrete three-dimensional visualisation is to be proposed once more. Look at a gas at equilibrium — a chaotic 'gas' (an artificial word that means 'chaos') of equal billiard balls. And feel the exhilaration of riding on such a ball like a Baron Munchhausen (or inside it — it makes for a perfect bumping cart). Or even better: lean against the perfect walls of the container of the gas (in a safe little niche) and watch and listen. It is like watching snowflakes fall. It takes a little while to get in tune and see the laws behind the whirling: that I am moving upwards with the ground, at constant speed, for example. If the moving spheres are big enough and slow enough (and you are small enough in your niche to feel awed), you may suddenly 'see' — even if this should turn out false on later analysis — that every ball owns a territory: one Mh of the volume of the whole container is assigned to it. And you 'realise' that each ball is busy

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How chaotic is the universe? O. E. Rossler Institutfiir Physikalische und Theoretisehe Chemie, Universitat Tubingen, D-7400 Tubingen, Federal Republic of Germany The title of the chapter is better than anything can possibly follow it. Originally I planned to write something nice and grandiose about Anaxagoras' invention of chaos as an explanation of the universe, and his ideas about transfinite iteration and the subtlety of the single 'immiscible' substance, the mind. Diesel automobile engines, the geyser Old Faithful, X-ray bursters in the sky, and autonomous nerve equations (including a 3-variable FitzHugh equation whose chaotic analogue computer solutions were shown to me by its inventor in late 1976) were then to follow suit—to illustrate the ubiquity of trajectorial mixing in simple differential systems populating the cosmos. Yet, even though it would be tempting to (re-)consider these topics (cf.[13]) in detail, and perhaps to add a disclaimer about the validity of discrete computational models as an exhaustive description of nature (cf.[3]), something less pretentious will be done in the following. Ά return to the mothers' of concrete three-dimensional visualisation is to be proposed once more. Look at a gas at equilibrium — a chaotic 'gas' (an artificial word that means 'chaos') of equal billiard balls. And feel the exhilaration of riding on such a ball like a Baron Munchhausen (or inside it — it makes for a perfect bumping cart). Or even better: lean against the perfect walls of the container of the gas (in a safe little niche) and watch and listen. It is like watching snowflakes fall. It takes a little while to get in tune and see the laws behind the whirling: that I am moving upwards with the ground, at constant speed, for example. If the moving spheres are big enough and slow enough (and you are small enough in your niche to feel awed), you may suddenly 'see' — even if this should turn out false on later analysis — that every ball owns a territory: one Mh of the volume of the whole container is assigned to it. And you 'realise' that each ball is busy

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