sábado, julio 03, 2004

What restrictions impose the life to any universe capable to hold it

I consider the problem of what conditions has to obey an universe in which a primary intelligence exist. With primary intelligence, I mean the intelligence that is not been simulated by other.

My guess is that a computer simulation creates, step by step, a portion of a space-time manifold, that is, a mathematical construct with many dimensions, being the time one of them. If we assume that initially, all possible universes are possible in all dimensions, each one being a different parallel universe, not only the isomorphic to a manifold generated by a set of equations like –presumably- our own universe, but the universes that are non differentiable, discrete, random, without rules etc. Then, if we assume that all possible manifolds exist, then, a simulation is only the recreation of-a portion of- something already existent. It may be said that every possible simulation already exist and has been already executed no matter that there is no program, at this point in time and maybe never will be, to recreate that universe within our own universe, “in a box” under our own view. No matter that, the result of every simulation already exists, and the consideration mentioned below applies also to simulated universes from the start.

However a simulation must not start from non-intelligent beings. it may start with intelligent ones, and may not have Darwinian evolution. But it appears that this is not the case on our own world.

If an universe is simulated, the question would be: How the intelligence who made the simulation arise?. For a self aware structure to emerge in a universe in which previously didn’t, the only known mechanism is Darwinian evolution and his generalization: the genetic algorithm. But evolution where? The objective is to establish conditions for this universe.

The evolution impose a set of constraints over the universe, highlighted by Max Tegmark in his TOE article Is ``the theory of everything'' merely the ultimate ensemble theory? .These constrains comes from the following pre-requisites:

1 predictability
2 stability
3 complexity

From these requirements, Tegmark deduces some consequences about a inhabitable mathematical universes. If we are completely agnostics and we don’t event start from formal mathematics but from any rational or irrational form of universe, it may be seen that the existence of life and intelligence imposes strict constraints applicable to any world, being mathematical or not, one of them is that it has to have a lot of mathematics inside as I will show.

If we take a look at the three life constrains on the light of the evolutionary biology and his generalization, the genetic algoritms, we can extract some considerations:

1 Predictability is a constraint introduced by the fact that life, in a way or other, is composed of a set of behaviors in order adapt to repeated sequences of events that appear in the environment. Intelligence appears in life to predict complex situations in the future in order to make the organism to be ready for it and to choose the adequate behaviour. Predictability is the seed of Reason and intelligence. If for example, the being inhabits a universe in which Boolean Algebra is not valid, the organism has no such basic tool to predict the future and to accomplish accordingly, so no intelligence can arise in this case. More basic than that, and appearing at an earlier time in evolution, if there is no similar thing like fluid dynamics, and fluids are ever chaotic, the being will never be capable to evolve to swing. That kind of reason can be applied to any physical aspect in which the being has to evolve.

Predictability, under my point of view, rules out any non-mathematical world, and seriously impairs any universe in which there is a paradox, although slight paradoxes which can marginally affect evolution can exist. If we consider that, I may guess, and it is only a speculation, the Russell paradox may be slight mathematical failures in the world we live, although these marginal incoherencies does not precludes –we believe- intelligent life.

2 Stability is related to predictability. Stability is necessary because, for an evolutionary process to achieve results, it is necessary a stable environment along many generations (or iterations, in algorithmic terms). Taking together stability with predictability we can obtain another implication for the mathematical manifold we inhabit and to other possible inhabitable universes:

it is necessary a sort of local causality that permits that the most recent and near events are the ones who most affect the immediate future, while the farter event in time and space produce less events locally in space and time. This requirement of smoothness comes from the fact that for life and intelligence evolution, due to the iterative nature of it, and therefore the implication of relative short life and short reach for any evolvable life form, the most relevant events for the immediate future of the life form have to be in the organism life sperience, that is, if the far space and time events produces frequent events locally, they will be seen as random under the limited experience of the being. Although the innate instincts deal with unknown events and may evolve and generate complex behaviours if the previous generations were exposed to these events, it is necessary a local event that trigger in order to activate this behaviour. This non local causality doesn’t favour evolution. Local causality does.

Also, it is doubtful that intelligence can appear if there is non local causality, since the world would be plenty of random events for which the reason will be irrelevant, and because that, the reason and intelligence would be non-adaptive in these conditions, and, therefore, would never may appear in that kind of universe.

For example, some conditions coming from the far past may be, in the context of a earth like planet, the mountains, due to billions of years of plate tectonics and other long term geological events, but the mountains are environmental conditions, not in any sense events, if we understand an event as something appearing at some instant of time. An earthquake, in the contrary, may be an event due to the same geological reasons. But intelligence -and even life-, can be guessed, may not appear in a world plenty of earthquakes, meteoric impacts and so on. Not to mention elephants appearing and disappearing.

The stability and predictability constraints has far reaching implications: a inhabitable universe must have clear rules (by 1) and these rules have to have local causation (by 2). Obviously it is necessary to elaborate more these implications.

3 complexity-simplicity: complexity is, at first sight, a requirement, since the life and intelligence that we know demand complicated physical and computational architectures. But how complicated the physical-mathematical laws may be? The answer, as we extract from evolutionary theory is: Enough to support life, but not more. Why?. There are two reasons:

a) because high forms of life , candidates to be intelligent beings, needs heavy neural computations for anything: from sound and image recognition, displacement, trajectory calculus, body functions, resource optimizations etc. And, more strongly, intelligence needs a lot of other neural processing, closely associated to certain mathematics. Life evolution is, in a certain way, the instinctive discovery of the -local form- of the mathematical rules of the corresponding universe. If the rules of the universe are too complex, it is more difficult that a being can evolve to master them in order to survive and even have intelligence. If, for example, the rules are plenty of complicated exceptions with implications in the life of the living structure, in a way similar to if-else rule in a simulation, or non derivable singularities in a mathematical manifold, the living being is not capable of "discover" them by evolution in order to perform the life activities like the above mentioned.

b) And this goes to the second reason for simplicity: exceptions not only make the evolution more complex, but hardly achievable, since the evolution process is parsimonious: For example, there is no animal with wheels, because a wheel can never be "invented" by a progressive adaptation. Once the Mutationist school of the Evolutionary Biology is discredited, it is accepted that life forms only progress trough continuous adaptation to the changing environment, so big changes necessary to adapt to environmental complexities are not permitted or very unlikely to be realistic. There is a very highly unlikely that a organism develops an adaptation to a very complex environment without following the intermediate path. That reinforces the conclusions of 3a).

The conclusions advocates for a (1) predictable (mathematical, mostly free of contradictions) (2) with local causality and (3) as simple and smooth as possible universe. So evolution favour the simplest mathematical universe capable of support it.

The best way to refine these conclusions is to study, formally, the restrictions of the mathematical environments considered as possible locations in the corresponding universes which, applying the genetic algorithm, results in a certain kind of evolution, besides that this universe, as a pre-condition, must allow replicable structures.

Computer simulations:

What is said about the primary problem: the origin of everything can be aplied to the, for the secondary problem: the universe generated by an existing intelligence, that is, a computer simulation.