Crackpot ideas
Wolfram’s (not entirely original) central idea in A New Kind of Science is that a science around algorithms (or more likely mappings) is fundamentally different from a science governed by equations.
This is fair enough, you can create something very big and complex, like the universe by iterating an equation more simply than by creating an instruction to make it in one go.
There are ‘equations’ which are very simple, which when mapped onto themselves will create infinite complexity. This infinite complexity implies that all other equations can be created (a universal turing machine), nested within the original.
Cellular automata demonstrating these mappings can be unbelievably simple, i.e. a two state one dimensional systems with a handful of possible rules.
My hunch - adding the parameters of natural selection (variable inheritance within finite constraints), to any information carrying system will create a UTM (information carrying implies ‘bits’ i.e. two states and at least one dimension). Variable inheritance within finite constraints implies a finite universe (at any point in time) and rules which apply in chunks (i.e. like ‘turns’ in a game or metabolic cycles). This implies a universe with ‘information exchange’, even if the universe is made of continuous quantities, information can only be exchanged between systems in discrete quanta, bits.
Defining a system is tricky with being tautological or obvious. But its clear that all systems have boundaries or membranes which allow information to be transferred and filtered. i.e. a system is a partially enclosed macroscopic ‘feature’ in a sea of elements. The membrane acts to channel information flow and possibly process it. These ‘features’ require corresponding partner ‘features’ (which can be nested within the parent or external to it) made up of components of the same type (possibly in turn made up of sub components, determining their absolute granularity) for information to flow using compatible ‘bits’ of the same flavor.
So that’s all you need:
1. Systems comprised of a finite number of bits (the cells in a cellular automaton, perhaps the surrounding ‘environment’ can even be infinite) 2. cycles of interaction between systems (flow of bits), 3. Inherited rules of interaction (any rule, the rules will morph to ‘useful’ ones, under natural selection and perhaps information exchange via the same flavor of bit implies rules, the inheritance is defined by the physics of the systems), 5. Inaccuracy in the rules (so that natural selection can apply).
The inaccuracy in the rules could be as a result of noise in the system (i.e. the environment, consisting of a sum total of other systems than the ones in question). In other words only a truly isolated system would have no variation, and there is no such thing as a truly isolated system.
Since a simple two state system can create a UTM, the ‘meta rules’ which define what the universe of possible rules are might be fixed and simple.
This leaves the only variable, being the level of noise. This might even imply some sort of self organized criticality, where the universe of what existed over time was tuned and lay on a boundary between too much noise and too little.
So all you need for a recipe for the universe is:
Interaction between macroscopic features and time.
Emergent features as a result of acting under natural selection are implicit in the information exchange itself and require no other variables.
rss
June 2nd, 2009 at 3:12 am
When you see ‘things’ like plants buildings or elephants, they look solid. The idea of solidity goes against ‘things’ existing at the boundary between chaos and stability (i.e. a solid is a boundary around a stable enclosed space). But what if the 3 dimensional solidity of everything (not just living things) was due to the folding of a 2 dimensional membrane.
There is some tangential evidence for the above, from the holographic principal, the the empirical data that the fractional dimension of humans lies between 2 and 3 and the fact that we perceive a time dimension ‘edge on’ (unlike other dimensions we can’t see it all at once, but as one slice or edge).
June 4th, 2009 at 2:10 pm
Thinking about the above, things can be solid, but in terms of how a living thing ‘works’ all that is important is the connection of channels, i.e. two dimensional folded structures. The only point where three dimensional solidity matters is how thick a membrane is.
June 4th, 2009 at 2:14 pm
Persistence of any pattern, while things flow through it implies action of a feedback loop or mapping. Think of a whirlpool or knot sliding along a string - the matter that constitutes the knot or whirlpool flows through the pattern it is being replenished via a feedback loop (what goes out comes in).
June 4th, 2009 at 2:17 pm
Actually - the above is not strictly a feedback loop. Not sure what the term is for a self replenishing pattern. A feedback loop may be a special case of this.
November 10th, 2009 at 3:37 am
Evolution as Physics
********************
If you believe the premise that evolution by natural selection (ENS) is more than a feature of biological systems, then there is a physical law that underlies it.
Things like the laws of thermodynamics apply to systems that collectively run down. The local complexity that arises by means of evolution is part of an overall system that runs down.
To fit ENS into the framework of thermodynamics requires a proof that all energy transfer creates local complexity. It may be that this complexity can be described as part of a more fundamental law, such as the idea that systems will self configure to maximize the rate of energy dissipation (The local complexity consists of little entropy machines). In this case we’d need a theory of maximum energy transfer.
More generally, to create a fundamental theory of ENS would require a proof that all information transfer creates local complexity. while the link between energy and information transfer is clearly there in terms of the relationship between thermodynamic and logical entropy, there is no rigorous link between the two.
[to do: the continuum from heat to statistical to information entropy continues with concepts such as Kolmogorov entropy which suggest that entropy measure may be relative to the measuring/measured system pair - perhaps the stuff below about imperfectly closed systems may create a way to talk about systems in some kind of relative way.]
Evolution happens due to the imperfect copying of a system within a finite environment. The mechanism of evolution requires variable heredity, i.e. imperfect information transfer within a constrained environment (a closed system).
Imperfect information transfer is provided by noise, if all systems are not perfectly closed then there will always be noise. In other words, the finite environment constraint is linked to the variation one (the more perfectly closed, the less noise, the lower the ‘mutation’ rate).
What would an experiment look like to prove that evolution was a law of physics?
It would have to show that increasing local order was a feature of information flow between any two systems in an energy gradient (i.e. low to higher entropy). To do this would require the following:
1. It would have to show that the information transfer came in repeated cycles.
2. It would have to show that the information was stored (the state of the system would depend on the message).
3. It would have to show that there was always random noise in the system (no two systems are perfectly closed with respect to the environment).
3 can be considered an axiom, however 1 and 2 require and experimental model.
1. Might be considered an axiom if one assumes (as seems reasonable) that all information has to be digital, consisting of bits. If there are bits then messages come in chunks, therefore if more than 2 bits flow, there are repeated cycles. What’s not clear is how these repeated cycles work - 1 bit -> 2 bits -> n bits.
2. Without external interference (noise) the state of a system after information transfer is dependent on the specific message, therefore information has been stored.
[does 2. require self copying systems that store information permanently or can it be things that are created from scratch each time energy flows, such as cascades of eddies in weather patterns.]
November 10th, 2009 at 4:20 am
The heredity component of evolution requires a birth-death cycle, which in information terms just means individual messages.
This is provided by gaps of pure noise in low entropy energy/information transfer, which in turn is provided by an kind of modulation due to things such as spinning planets or deep sea convection flows around hot vents.