I wonder what we might be able to tell about the Big Bang, the tremendous explosion which began the universe as we know it, just by looking at the universe as it is. I am also near-obsessed with the concept of complexity, and the possibility of quantifying it. But, it seems that we do not do well at even defining complexity.
DEFINING COMPLEXITY
I have defined complexity as the total number of levels manifested by a given system. The complexity of any system is not the same thing as the definition of the boundaries of that system. This is because complexity can be defined as the sum total of all factors that may affect the system, in other words the amount of information within the system.
These factors may be either inside or outside the boundaries of the system. As an example, a party held outdoors is more complex than one held indoors because the one outdoors may be affected by rain, even though the weather is not actually an element of the party.
If we are dealing with man-made machines, the boundaries of a system include a definition of what it will be used for. The operation of a refrigerator may be affected if it was taken into outer space with no air and zero gravity. But since it is highly unlikely that the buyers of a new refrigerator intend to take it into outer space, this can be safely excluded when setting the defintition of the system that is the refrigerator.
When considering the factors which may affect a given system, and thus affect it's complexity, we must remember that a factor will only affect the complexity of a system if it changes the total number of levels within that system, but not if it changes what those levels are.
The number of different permutations of the elements of a system which we define may or may not be the number of levels in the system, and thus the complexity of the system. It depends on the relationships between the elements of the system. If the elements of the system are independent of one another, as the planets of the Solar System essentially are, then the complexity is equal to the number of elements. This could be referred to as a "loose" system.
If the planets were closer together, so that the position of a planet was significantly affected by the gravity of the other planets as they orbited the sun at different rates, then the relationship of each planet to each other planet would also be elements of the total system. This could be referred to as a "tight" system and would be much more complex than the loose system. But the complexity is always the sum of information within the system.
THE UNIVERSE IN TERMS OF COMPLEXITY
I find that the concept of complexity, which I would really like us to begin expressing in quantitative terms, sheds valuable new light on the structure of the universe. This will form a link between my complexity theory and my cosmological theory, as described on my cosmology blog.
Let's consider the conservation of complexity, which I described in the posting "Complexity, Patterns And, Energy". We saw there how complexity is like energy in that it cannot be created or destroyed, but only changed in form.
This can only mean that the complexity of the entire universe, and of the many individual systems within the universe cannot exceed the complexity of the Big Bang, meaning the information within it, which began the universe.
Have you ever noticed that all of the fundamental organizational units of the universe; atoms, molecules, stars, solar systems, galaxies and, galactic groups all have roughly the same, relatively low, level of complexity? This does not, however, include living things on earth, which I believe to be the special creation of God.
We must remember that the number of elements in such a system does not affect this universal complexity. Two identical systems are not twice as complex as one such system, but only slightly more complex and this also goes for multiple identical systems. This means that a plutonium atom is only marginally more complex than a helium atom.
There can be repetition of complexity without violating the law of conservation of complexity, but there cannot be interrelationships which would require more complexity because there is only so much information available. This level of complexity, which is found in all of the basic units of the inanimate matter of the universe, is a reflection of the complexity of the Big Bang, which got everything started.
Atoms are the first structural building block of matter in the universe. Stars and planets are the second and, galaxies are the third. Molecules, solar systems and, galactic groups can be considered as three secondary structural elements associated with the primary elements. All have a similar, and relatively low, level of complexity because this repetition of structure lessens complexity and there is only the limited amount of information from the Big Bang available. Complex molecules are synthesized by living things and are not really complex in that they are multiple repetitions of a basic pattern.
What can this level of complexity be except a reflection of the complexity level of the Big Bang?
Boundaries must be maintained between the basic fundamental units of structure in the universe. The positions of electrons in the individual atoms in stars cannot affect the large-scale operation of the star. The internal processes of the star cannot affect the orbits of the planets around the star.
There cannot be a permanent, complex solar system in which all of the planets affect each others' orbits. Moons around planets cannot affect the other planets and their moons. Positions of individual planets in solar systems cannot affect the arrangements of stars or the rotation of the entire galaxy. The rotational positions of individual galaxies in a galactic group cannot affect the movement of the entire group.
If any of the above took place, it would make those systems more complex and so violate the conservation of complexity. The numerical ratios that comprise the structures of the universe, such as how many atoms it requires to make a star and how many stars to make a galaxy, are as they are to avoid violating the conservation of complexity because there is only so much information available. Distances in space are also set to maintain this necessary separation of matter structural elements, in order to keep a limit on the resulting complexity.
(Note-concerning the relative sizes of planets and stars, you might like to read "The Chemical-Nuclear-Astronomical Relationship" on my physics and astronomy blog, http://www.markmeekphysics.blogspot.com/ ).
The extreme complexity of living things is far greater than any of these universal structual elements and does not come remotely close to fitting into this pattern. I say that this complexity of living things must therefore have been introduced from outside the universe, namely by God. The things made by human beings are also highly complex because they are a reflection of the complexity in our brains.
The number of dimensions affects complexity, two dimensions are twice as complex as one. The conventional model of the Big Bang, a simple and sudden explosion, is not complex enough to account for the structures of atoms, molecules, stars, solar systems, galaxies and, galactic groups.
This can only mean that there must be more to the Big Bang, in more than the three spatial dimensions that we can see. My model of the two-dimensional sheet of orphan space folding until the dimensional bonds in one of it's dimensions disintegrated, leaving strings of matter arcoss the universe, gives us just about the right amount of complexity necessary to account for the primary structural elements of matter in the universe today.
Can you see how useful this concept of measuring complexity is? For one thing, it has given us a new way of looking at the fundamental structure of the universe.
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