So far we have only concerned ourselves with the effects of the generating function very far from the origin, as we would experience it being part of the generated world.
We can trace back the values at every point to a single multi-dimensional number at the origin. A nice name for this would be seed as it behaves like the seed value of a pseudo-random number generator, but this invites a naive misinterpretation of the word, by asking who has planted that seed, so we will stick to calling it the initial condition.
The theory of a universe expanding from a single point stems from the 1920ies but the catchy term “big bang” was coined by Fred Hoyle in 1949, at a time when the mind of the public as well as the scientists was on nuclear weapons. The general image conjured up is the big bang as a huge atomic bomb explosion. This is not the only time the Zeitgeist informed the perception of a physics theory. We have already discussed how in the 1970ies, when computers started to become ubiquitous, the concept of cellular automata became popular and some people speculated that the universe is made of basic units of information simulated in a giant computer.
Expanding ordered set
Because the space grows as the generations increase, we as observers inside the universe see that it is expanding.
This is not due to any explosion slowed down by gravity. Instead each dimension grows linearly with increasing generations. It is just a property of the set and has nothing to do with the contents.
The traditional approach of physics has been to consider that massive particles create the space they inhabit, so an expansion or deceleration of space requires attractive or repulsive forces between them.
Here the space is the numerical structure of our ordered set, which expands quite independently of the patterns within it.
The value at the initial condition
We don’t know the exact value of the initial condition, and we will never be able to determine it. We will however be able to discount some starting values that don’t create compexity.
In the introduction we argued that number sequences exist apart from our physical universe. Thus if one exists, for example the natural number, then all other sequences must also exist. This is valid for all generating formulae as well as all initial conditions. Quite clearly this is an application of the anthropic principle since we must live in a universe that allows life. There will be many dead number sets that do not generate sufficient complexity.
Finite versus infinite set
There are many galaxies, but not countless numbers. The reaches of space are far, but not infinite.
The universe is expanding towards infinity, but at this current moment it is finite in size. Does it require finite or infinite calculations to determine a new state? We can answer this question. It depends on the initial condition. If it is an infinitely dimensional number then infinitely many calculations are required for each point, however if the initial point has a large but finite number of dimensions, then we only require a finite number of calculations.
We said earlier that we live in a random combination of generating formula and initial condition. If there are infinitely more finite universes than infinite ones then it is infinitely more likely that we live in a finite one.
At first glance this seems to have a bad impact on free will. If the universe is finite and deterministic then all our actions are pre-programmed. Luckily this is not the case because the value of the initial condition is unknown to us and cannot be found with a finite amount of computation by us.
Fate of the universe
This has another interesting consequence. For every finite number, however large, we can always find more numbers that are larger. Our generating formula is hierarchical, so the effect of the higher dimensions is smaller than the effect of the lower ones.
Let’s say our actual initial condition is an order 7 number and thus has 210 dimensions. For simulations of physics we can approximate this with 30 dimensions. We could even approximate it with 6 dimensions but then we couldn’t model the weak force or gravity.
However we can’t be sure that the initial condition is not actually order 8 with 420 dimensions and that the extra dimensions have just not been significant yet.
In effect our minds are blurred across universes with multiple initial conditions exactly like they are across time lines as described earlier.
This means that as the universe ages, meaning at higher and higher generations removed from the initial condition, we can always find more complexity. Therefore the rumours of the heat death of the universe have been greatly exaggerated.
Classification of life
Another interesting thing this allows is the classification of self-aware life on a grand scale by which orders the consciousness inhabits. My feeling is that we are with 1 perceived time and 3 perceived space dimensions are at the very bottom of the pecking order.