Math is crowned king But Chaos Rules
Lorenz was adamant that chaos is deterministic and rightly so. Chaos does not mean an event is causeless. In effect chaos underscores the fact that all events have more than one cause at the same time. In fact the unpredictability that chaos lends to so much of life is due to so many factors contributing to any one event that there is always an uncertainty inherent in all events until they become actualized.
By that I mean that there is not just one chain of cause and effect which brings about any one second of life, but in deed all the chains of cause effect in the universe contribute to create every event; every second. To me that is an astounding realization with vast consequences.
So we can’t just say that an event is completely local anymore. There are local aspects to it, but that’s only a small part of it. The much larger part of any local event is the culmination off all prior events. All events are subject to all of history. How can we assign absolute certainty about what made an event happen? We can’t. But we do the only the thing we can do. We include all the data available to us, and that is usually close enough to assign blame from a specific perspective or gain a particular insight into a particular truth about the event.
That’s why there are so many opinions about any event. Everyone sees events from a different perspective, and each perspective has a history behind it. Not all perspectives are equal, of course. But that just adds to the complexity of the situation.
The bottom line seems to be that even though we may plan something in the greatest detail possible, there is no way to be absolutely certain of what will actually happen when we set our plan into motion. But we all knew that already, didn’t we?
We my walk outside and bump into some one we know. That will change the exact time we arrive at our destination. Those few moments may mean the difference between fulfilling our plan and failing. You may have a flat tire. Even though you pay your electric bill the company may lose the record of payment and cut you off anyway. There is no way to be sure of what will happen from one moment to the next.
Even though every event has a definite history and definite causes, it is fundamentally uncertain due to influences we cannot know about.
Again, this is due to the fact that when we talk about an event we are not talking about one event following another. But in reality all events are caused by dozens of events all influencing the outcome at once. Yet if we could know all of the influences that go into any in event there is no reason to think we couldn’t predict it with absolute certainty. The problem is that there is probably no way to ever take every variable into account due to sheer number and the non-locality of them.
It’s lucky that most of the time we don’t need to know all the variables in order to make a good guess.
The good news is that the laws that govern events don’t change. And that’s how we can discover how things work and see the patterns of existence in absolute terms.
Besides all the rules of physics, what makes a tree look like a tree? It seems like two basic rules of growth: Grow for a while and then divide. Notice also that each time the tree branches, the twigs become smaller. The trunk and first division are large by comparison to the next split, and then the next is smaller still. Even the leaves follow this pattern in their veins. But the smallest branch mimics the largest branch.
As the tree grows, of course, how this growth happens depends on many factors including temperature, rain fall, soil quality, and probably hundreds of environmental conditions over its lifetime.
As an aside, the reason we can draw stick figures to represent humans has always seemed to me to be because really, a human is constructed of lines and joints. It seems that many things in nature follow these same basic rules of growth with only slight variation creating large differences. In art, for example, the picture of a body is often drawn rough out of geometric shapes and then by pulling those shapes a little here and there a human form takes shape.
The small variations and distortions we add to the geometry transform it.
This is the kind of thing is predicted by the Mandelbrot set. As I said, Benoît Mandelbrot devoted his life to discovering why the world was “rough” rather than more geometric. He discovered a way to map chaos through mathematics and discovered fractals.
He took his mathematical set and entered it into a computer. The result is amazing. The patterns themselves are beautiful. But the amazing thing is that if you keep magnifying a small part of the picture you eventually see that every small part contains the whole. You come back to the pattern you started with and can pick any point and magnify it, only to repeat the process infinitely.
This is the same phenomenon we find in holograms. Each part holds the information that creates the whole. This is counter intuitive. One would suspect that a small piece of the whole only holds the information for itself. But this is not the case in holograms, fractals, or biological entities like humans.
Strangely, part of all of us follows this pattern. Our DNA can be found in all our cells, and therefore every cell contains all the information needed to build the entire living organism from scratch.
Many years ago I had the idea that the universe produces replicas of itself in various forms and complexities. This has been borne out by physics over the years. Now we know that the fractal pattern is built into many aspects of nature. Fractals are also responsible for the current state of computer graphics and their life like detail.
In the world of Newtonian physics the world was ultimately predictable. But because of the discovery of fractals and the nature of chaos, it has become obvious that there is a fundamental uncertainty built into nature that we never dreamed of and don’t notice much unless we look.
Isn’t that a bit odd? One would think that with so much uncertainty strange things happening would be the norm. But they aren’t. Why not?
There is another place we hear about the fundamental uncertainty of the universe. That place is physics. One of the reasons this came to be is the fact that even though the half life of a radioactive substance can be measured very accurately, there is no way to know when a specific atom will decay or why it picks the precise moment it does. Though we know there is a cause, there is no way to know what it is in advance.
However, knowing which atom will decay is not necessary. What is most interesting to us is how many will decay in a specific space of time; and that we can do accurately through statistics.
Amazing enough, statistics are the only way we can study the quantum and make brilliantly accurate predictions about it. Quantum mechanics is a tool we use to gather quantum statistics and understand the way the smallest parts of existence behave.
One of the founders of QM was Werner Heisenberg. To his astonishment as much as anyone’s he discovered that it is fundamentally impossible to know both the momentum and the position of a particle at the same time.
He discovered that no matter which way you set up an experiment the nature of the quantum is such that if you measure position accurately, you can not know the momentum with certainty, and if you measure momentum accurately there is always uncertainty about position.
This was counter intuitive for anyone brought up with a classical physics background and hotly debated by many including Einstein who believed that there were hidden variables that accounted for the problem.
Later on Bell formulated a theorem which was testable and proved that the hidden variable theory as it stood is false. There are still those that believe that hidden variables are not completely out of the picture. String theory postulates many dimensions. The many worlds theories so many are fond of postulate many universes to solve the problem. But one wonders what fractals and new deeper understandings of chaos will bring to the debate in the future.
Once the uncertainty principal was formulated it spawned many other additions like Niels Bohr’s energy/time uncertainty principle and Hugh Everett’s entropic uncertainty. It had many more implications then one might think at first glance and has been used to predict the actual state of empty space as being filled with quantum activity that has only recently been proven true. That phenomenon is quantum fluctuation.
The uncertainty principal wasn’t the only source of surprise in the early days of QM. The fact of particle wave duality and quantum entanglement only made the quantum universe stranger and less intuitive by the minute. But each in turn was proven by experiment.
More in part three