“… whilst the great ocean of truth lay all undiscovered before me.”

CHAOS IN HISTORY

The ancients told of this original state of chaos.

It was included in their myths, of course.

It was seen as a chasm, void, or abyss.

They looked for order out of chaos in ancient Greece.

Later, chaos was pre-creation, a state of disorder,

while cosmos was seen as one of more order.

Egyptian goddess Maat determined order from chaos.

She fought with Isfet to prevent a return, or reverse.

In the Torah, tohu-va-vohu was a void without form.

Divine intervention brought order to this chaotic norm.

In the Tao, hun-tun, or chaos, was the first station,

others would follow on the way to creation.

Then nature would correlate, arrange and regulate.

She was the mother of the universe, who would create.

Pythagoreans said for them—”all is number”— was real.

Plato said cosmology imposed form on formless material.

Aristotle said, “First of all things came chaos to being.”

Chaos was an interval to contain and precede everything.

Christians believed God had to tame primal chaos.

The triumph of good over evil—as a force.

In a cave, on the Mountain of Light, a man from the Arab nation

had a vision when the earth was made from heavenly separation.

Long ago in Greece they believed in the Tetractys, or mystic Tetrad.

They used numbers to disclose the ideas that they had.

A world geometrically, harmonically, mathematically arranged.

With chaos theory only the method has changed.

Tetractys was the root and source of eternally flowing creation.

We may have found this belief, with chaos as the motion.

For chaos theory to emerge, it needed complex calculation.

Computers were the catalyst for the theory’s new direction.

ISAAC NEWTON

He was a great scientist of all ages,

and takes a distinguished seat among sages.

He was self-taught and fascinated by nature and life forces;

but said he did not invent ideas, without work that reinforces.

He researched ancient scholars and their tracts.

And gave his own original meaning to rational facts.

He saw that wisdom from long ago had foresight;

and used ancient teaching with his new insight.

He had an enlightened view into old truths,

and toiled continuously to find the clues.

He followed esoteric learning reflecting on any result;

and, as a loner, didn’t want others around to consult.

A secret written in code, at his own notion.

“It is useful to solve differential equations.”

In Newton’s science there was no chance or free flow.

Was he interested in the — regular/irregular — no.

His genius saw gravity and motion laws.

In non-linear ideas he would have seen flaws,

but linear thought is not enough to reason the universe as a whole.

Chaos can bring different dimensions to that goal.

Isaac’s angle and tangent of thought was authentic,

he was interested in codes, alchemy and magic.

He said there were many ideas as yet undiscovered

and knew future scientists would have them covered.

They would investigate — the great ocean of truth –

and use his methods of a diligent sleuth.

He looked through the lens of truth for many a year.

By the 21st century we would see non-linear was clear.

Whatever we decide what can or cannot be in chaos theory;

Isaac said that the system of the heavens may be founded on good geometry.

WHAT IS CHAOS?

Is it the science of how things change,

or is it about how they rearrange?

What can we gain from our history,

a deterministic system with a past story?

Is it that earlier states affect later ones,

or would they change anyway in the long run?

Are these changes governed by one law,

is there only one effect, no more?

Is it a system that changes with a fixed rule,

can we then call this — dynamical?

Can we track its moving by number,

or does time defeat us and try to encumber?

Can we see chaos in — the butterfly effect —

or does that analogy contain a defect?

Is the movement of a butterfly’s wing,

so eventful as to change anything?

Are the numbers found in chaos flirtation

giving us clues to the nature of creation?

Are fractals the geometry of chaos?

For algebra, could things be any worse?

Do they help with systems that are turbulent

or is this confusion only hell-bent?

Fractal small sections resemble the whole,

does this constant scene affect us all?

The universal characters were elucidated,

by Feigenbaum’s fig tree we were educated.

Each wishbone in the tree has a width,

the same ratio always used forthwith.

It moves in a distance of four decimal seven,

growing narrower along this horizontal direction.

It’s always two decimal five shorter for the height.

The correctness of these numbers is always right.

There are more decimal places if you want to fuss,

but basically, these are constants of chaos.

A state that is attracted by a system?

A natural attraction that brings it back again?

Are there three types of attractors in this range?

Yes, a stable one, a cycle, and a strange.

There is something else about these attractors,

they all contain fractal structures.

The successive states of a dynamical change

can be a curve or discrete dots, that’s the range.

In the orbit diagram, composed of two parts,

the orderly and the chaotic start.

If there is a fractal, you will see,

due to its self-similarity.

The logistic chart with universal features,

shows chaos and real world characters.

A theory of linear chaos may be a fact,

to show how random from chaotic data react.

If you give a chaotic system a nudge,

it would turn to a regular one by that budge.

If tiny variations at first, lead to tall,

then do large ones compact to small?

If systems change over time forwards,

can they be sent to time backwards?

If light can be a wave or a particle,

can time be a flow or stand still?

Is chaos a fraction of fractal factions,

or is it a faction of fractal fractions?

If chaos can all life rehearse,

then maybe it fine-tunes the universe?

WHERE IS CHAOS?

Is it the future or the past,

will it vanish or will it last?

Does it mean that forecasts are uncertain,

or is the answer behind the curtain?

Are there large variations in long-term behaviour,

or smaller varieties held by a saviour?

Is it where a butterfly flaps its wings,

to follow a change that is quite amazing?

Does it give a new idea of dimension,

or do we string it with apprehension?

Does the chaotic behavior use an attractor,

or is it something that fuels the reactor?

Do initial conditions lead to orbits,

or are they first indicators of splits?

Do orbits to a chaotic region converge,

or are they hidden as they merge?

Do attractors arise from a chaotic system,

or are they — strange — as you call them?

Where do you see whether or not chaos has an edge,

is it where order and random are on the same ledge?

Is iteration over and over, the same again,

or is the one before changed in a plane?

Is a transition in chaos anything stable,

or does change put intricacy on the table?

Are very small variations something to tabulate,

or are they a catalyst for a change in state?

Are there signs that chaos is on the way?

Yes, if fractals are there, you can say.

Are there some clues when you see constant folding?

Are there self-similar sections that keep exploding?

Is there a setting where time flows continuously,

or does it advance by stages to flow free?

Is it where the future is influenced by the present,

or is there a fixed law that is sent?

Are these all signs of a chaos theory,

where algebra is beaten by geometry?

FRACTALS

Historically we have been aware of micro and macro.

Fractals have given to those states a mathematical intro.

They vary widely and are said to be scale free.

They are a visual aid, so chaotic dynamics we see.

Fractals are self-similar and they interrelate.

They stretch to surfaces that are not finite.

Mandelbrot gave fractal geometry as his contribution.

We now realize they are central to an act of causation.

Their self-renewal seems to be endless.

They are crucial to the science of chaos.

We use fractal statistics for many systems to unravel.

The research into mysteries of life continues to travel.

In many areas we see that fractals will stretch and fold.

This idea occurred to three men, independently, I’m told.

A strange thing about fractals is their dimensionality.

It lies somewhere between the numerals one and three.

Fractals are not only geometrically static,

in time they can also be erratic.

This fractal geometry has given science allure.

For chaos, fractals are the signature.

Fractals unite life on earth, and maybe the universe.

They have given a crucial key to unlock the diverse.

CHAOS IS…

Chaos is now a challenge, not a curiosity.

It has shown new vistas mathematically.

Chaos is something you find when two close, first states,

rapidly diverge toward different fates.

Chaos is the irregular and non-linear, before ignored.

It now has fascinating features as a reward.

Chaos is used to identify biological rhythms and oscillations;

in future work with health and disease assume revelations.

Chaos is no longer in a deep slumber,

it has emerged to unite nature with number.

Chaos is not a total state of confusion.

It has reached into many areas by diffusion.

Chaos is fractal statistics, dimensions and architecture.

It can see secrets of nature, or tell of the future.

Chaos is a revelation if we can decipher the dynamics;

it could maybe tell us more about celestial mechanics.

Chaos is seeing, learning, touching the eternal,

using logic and mathematics in a strange miracle.

Chaos is displaying laws in far-flung guises,

and showing us that life has many surprises.

Chaos is uncovering creation and giving a status to fate.

Chaos is finding new information to calculate.

Chaos is the focus on insight to follow the clues.

Chaos tells us some settings neither win nor lose.

Chaos is inherent in nature and may be all natural forces;

we still have to track the variety of sources.

Chaos is found in the melding of science and arts;

a fortunate combination with an active counterpart.

Chaos is cognizant that a minute variation,

in the history of the universe has given many a creation.

We are aware that circumstance has material from fate;

that chance, fortune, destiny or accident can create.

Could the music of the cosmos have a song to sing,

that it was the finger of chaos that fine-tunes everything?

In the ocean of truth could Isaac now see chaos theory?

Yes, there is enough evidence, not to make him too wary.

Have I taken too many liberties with science?

Or is this a poet’s forgiven licence?

FOOTNOTE

This statement was reputedly made by Isaac Newton about his life, to his nephew.

“I do not know what I may appear to the world;

but to myself I seem to have been only like a boy,

playing on the sea shore, and diverting myself,

in now and then finding a smoother pebble

or a prettier shell than ordinary,

whilst the great ocean of truth

lay all undiscovered before me.”

I decided to explore what I had learned

about chaos theory in a course from

The Teaching Company given by Professor Steven Strogatz.

Apart from my poetic speculation,

I apologize for any incorrect scientific statements.