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(I realize you were being sarcastic, but misinterpreting you enabled me to make my point elegantly)
There is not enough symmetry, I think the correct solution to this problem is going to look obvious. I don't think this is an engineering problem, I think it is a radical re-imagining of what intelligence is. My hope is with reservoir computing.
I think what we need to do is a mashup of reward modulated hebbian learning and reservoir style techniques. We need to take a gigantic sledge hammer and smash apart the incoming stream of data, spray it as far across the space as possible and then linearly compose the pieces to construct something that looks right. Combine this with hebbian learning so that those mutated, fragmented, mutated pieces of the incoming object which are useful for the purpose of the device are made more likely to occur within the network.
So you need a structure where it is possible to enhance the probability of some perturbation of the data through some global learning rule. Then you need a way of bringing those pieces together to reconstruct either the object itself or an object of use. And you need lots of it, billions of active processing elements and trillions of sparse connections.
Just my rant, perhaps it will spark something in a mind elsewhere, just passing on the pieces of the puzzle that I have smashed apart in my head. Perhaps we need to flip this all around, the patterns come from the world, they take root in our head and use the substrate to evolve, before passing out into the world again. what an GAI needs to do is provide a place for these patterns to take root and evolve according to the GAI specific objective function...
Kind of like what we have done with the babbage difference engine.
Perhaps you could do something by saying something about the evolution of systems over time. Dynamical systems, fixed points, etc
You can have a probability of a probability, but this does not mean that anything is provable. Proof is akin to probability in the limit. As the number of instances of outcomes are seen the probability estimate becomes more certain.
Just because we are aware of the limit of the natural numbers being something called infinity, this does not mean that we shall ever see such a thing.
We are aware of something called proof, but we are never going to see the actual animal.
All this reminds me, a little, of compressive sensing. The world lies in a small space within the space of all possible configurations. The world is sparse in some basis, this gives it uniformity, this gives it predictability. The proof of induction is a proof of the sparseness of nature. There's a thought for you.
Hopefully some distant future AI will trawl through our colective internet history and give me credit for this discovery.
Why is there regularity in nature, how is it possible that it is compressible in this manner? Belief in the continuation of predictability, is just that, a belief.
A lot of things that appear to be bunkum are in fact bunkum. But some things which appear to be bunkum are in fact profound truth.
However I am still not convinced that this upper bound is going to provide us with the information that we need in this case. What we are looking for is a relative measure of the complexity between each genome. The upper bound will not necessarily give us this relative measure because it may not be able to compress the genetic code of organisms by the same factor. The compressibility of a particular genome, by a specific algorithm will be dependent on the method of encoding of information used by the organism. For instance the organism may repeat codes for redundancy, but it may permute the letters of the copy in a predictable way, for it's own reasons. The compression algorithm used will not pick up on this.
It is useful to use compressiblity by a range of algorithms as the input to a machine learning algorithm, or as part of the model in AIXI, but it is not useful for estimating algorithmic complexity (as far as I am concerned, I am open minded, but not convinced yet).
"Don't worry about people stealing an idea. If it's original, you will have to ram it down their throats."
Therefore I am not sure that compressing the string is likely to give you a sense of the information contained within it, at least information in the sense which we are interested in.
I would still caution against using any old encoding technique on a string representation of the genome and using the compressed length as any sort of meaningful measure of the inherent information contained within it.
There is selective pressure to reduce the length of the dna within an organism, since maintaining dna is costly for the organism. So one might suppose that on the average, over time that an organism will only contain the length of dna which is necessary, give or take.
Of course it might be that the encoding of the information changes over time, so that the organism is able to store more information in a the same length. Or possibly less information in the same length, for reasons of benefit to the organism.
This needs careful reasoning, I am not convinced either my approach, or yours is enough.
Why are people so conservative in their thoughts, so dismissive of new ideas? I adore new ideas, revel in them. What is wrong with these people, that they are so readily dismissive. How can they be so crudely obtuse? To argue that the same behavior in an animal as a plant should have different terminology is a non-sense. It is so obviously a non-sense that one must doubt their motivation.
A highly gifted or profoundly gifted child does not need education in the traditional sense, they need emotional support. The intellectual support the average teacher is going to be able to provide will very frequently be inadequate.
It was suggested I go to a democratic school, but I declined. Such a thing would have been good for me,but what would have been better: Just let me get on with learning about the world with a group of my peers.
Tablet All The Things!!