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Discussion about the use of self-organisation for automatically "programming" networks of processing nodes.

Jorge Luis Borges wrote:

Well, that should save a bit of time!

I need to update what is going on with my paper "Discrete network dynamics. Part 1: Operator theory", which can be found in arXiv at cs.NE/0511027. Yes, it was that long ago and the paper is

I have been getting rather evasive feedback from various people about this paper, and I don't like the sound of what I hear at all. In a nutshell, there is a widespread view that my use of quantum field theory is misguided and/or wrong.

One critic said that I didn't understand quantum mechanics, which I thought was rather odd given that my PhD is in quantum chromodynamics! That comment immediately told me that he had

All I use is operators for creating and annihilating quanta; the model is defined at the level of these quanta, and there is no deeper level of theory. This is where the QFT that I use is a

One can manipulate these creation and annhilation operators by using their algebraic properties to rearrange "operator products" in various ways, and thus break operator expressions apart into a sum of contributions with different combinatoric properties, each weighted by a combinatoric factor that is automatically generated by the algebraic manipulations. These manipulations have the same general structure as the sorts of manipulation that occur in "operator product expansion" calculations in high energy physics; my PhD dissertation is full of this sort of calculation, and some relevant papers that I contributed to can be found by doing a search of the SPIRES database here.

All the above leaves me no choice but to describe what I write about in my paper "Discrete network dynamics. Part 1: Operator theory" as a "quantum field theory".

If you are wondering why there is no news on the ACEnetica front, it's because none of the Four preconditions for civilisation is currently being met.

There is an article by Marcus du Sautoy entitled Burden of Proof in this week's New Scientist, which discusses the issue of whether a computer generated mathematical proof can be considered to actually be a proof, especially since some such proofs are so lengthy that they cannot be checked by a human. An example of this type of proof is the 4-colour map theorem.

My own view on this issue is that a computer generated proof has

The degree of assistence in generating a proof can be taken one stage further by using a computer to implement some or all of the rules for manipulating the symbolic expressions, rather than implementing all of the rules in the human brain. This seems to be a fairly radical step to take, because hitherto the only part of the proof that was "outside" the human brain was its "dumb" representation using pen and paper, whereas the "clever" bit involving the implementation of rules to manipulate this representation was "inside" the human brain.

Let us consider what these rules of manipulation actually are. Effectively, they define a procedure for taking an initial expression constructed out of symbols, and repeatedly operating on it using the rules to eventually generate the required final expression. The cleverness is in the

Use a human to

Interestingly, I wrote a paper (see here)

in which I used a computer (running the symbolic algebra program

I will be on holiday in the south-west of England for the next 2 weeks, and I won't be able to access the internet, so any comments will remain unanswered until I return.

I have just uploaded a paper to arXiv here.

I wrote this paper about a decade ago, and submitted it to Neural Computation on 2 February 1998, but in effect it was not accepted for publication because the referees asked for changes to be made to the paper that I thought (and still think) were unreasonable. Apart from minor reformatting changes, this arXiv version of the paper is

The paper contains material that is based on a preprint that I wrote at the Neural Networks and Machine Learning Scientific Programme at the Isaac Newton Institute in 1997. The Newton Institute preprint number is NI97039, and it is available online on this page of 1997 preprints, or can be accessed directly here.

The main idea in the paper is to optimise a multi-layer density-modelling network so that the

The objective function for optimising the joint probability of the state of all the layers of a network is