6

I meant to say no need to click.

The Mandelbrot cluster has an extraordinary structure, but it is not just any human design. Remarkably, this structure is defined by a rule of simplicity.

The point I want to make is that even Mandelbrot himself, when he first saw the incredible complications in the fine details of the set, had no real preconceptions about the extraordinary richness of the set.

The Mandelbrot set was certainly not an invention of any human mind.

The set is objectively there in the mathematics itself.

If it makes sense to ascribe an actual existence to the set, that entity is not in our minds, because no one can fully grasp the infinite variety and boundless complexity of the set. Nor can its existence lie in the large number of computer outputs that are beginning to capture some of its incredible complexity and detail, as these outputs are at best nothing more than a shadow of an approximation to the set itself.

Yet it has an undoubted robustness; for the closer the same structure is examined—regardless of the computer viewing it—the more subtlety it is revealed in all its perceptible details.

Its existence can only be in the world of Platonic forms.

I can hear you saying, don't start philosophizing again!

I realize that there will be many readers who find it difficult to attribute any sort of actual existence to structures.

Let me ask such readers that they simply expand their understanding of what the term existence might mean to them.

It is clear that the forms of Plato's world do not have the same kind of existence as ordinary objects such as paintings.

They do not have spatial locations; nor do they exist in time.

Objective concepts should be thought of as timeless entities and should not be assumed to exist as soon as they were perceived by the first human.

Certain eddies of the set shown did not acquire their presence when they first appeared on the computer screen.

Nor did the general idea behind the set come when it was first humanly laid out.

Thus, mathematical existence differs not only from physical existence, but also from an existence assigned by our mental perceptions. Yet there is a deep connection with each of the other two forms of existence—physical, mental, and Platonic—as beings belonging to three separate worlds.

Regarding the first of these mysteries, which relates the platonic world to the physical world, I allow only a small part of the mathematical world to be concerned with the workings of the physical world.

Although we are often surprised at unexpected important applications, it is certain that the vast majority of the activities of pure mathematicians today have no clear connection to physics or any other science.

Likewise, it relates to the second mystery in which the mindset emerges with certain physical structures. I do not insist that the majority of physical constructs should introduce mindset. While a cat's brain can really evoke mental qualities, I cannot say the same for a rock. Finally, for the third mystery, I think it's obvious that only a small part of our mental activity should be involved.

absolute mathematical truth! (we are more concerned with the wide variety of ailments, pleasures, anxieties, excitements and the like that fill our daily life) These three truths are represented in the smallness of the base of the connection between each received world and the next world. Everything in the physical universe is governed by mathematical principles in utterly precise detail—perhaps equations as we will learn, or perhaps some future concepts that are fundamentally different from what we would call the term equations today.

If this is true, then even our own actions will be completely subject to control where control may still allow some random behavior governed by strict principles.