The two general principles of MRM

When we speak of mathematical models for biology, we usually refer to formulae (such as the Hardy-Weinberg theorem, or the Lotka-Volterra equations) that effectively describe some features of living systems. In our case, embryonic development is not described by integrals and deconvolutions, and the formulae of the reconstruction algorithms cannot be a direct description of what happens in embryos. There is however another type of mathematical model. The formulae of energy, entropy and information, for example, apply to all natural processes, irrespective of their mechanisms, and at this more general level there could indeed be a link between reconstruction methods and embryonic development. For our purposes, in fact, what really matters are not the formulae per se, but 

In the MRM model, the initial memory matrix is a tabula rasa, a white page that is gradually filled during the reconstruction process, while the reconstructed picture starts with a uniform image, and becomes progressively differentiated in the course of time. A reconstruction with the MRM model, in other words, is a set of two distinct reconstructions that are performed in parallel. The point is that this double reconstruction is necessary for reasons that are absolutely general. 

A picture and its projections are both structures of the real space, and, when projections are incomplete, there is no possibility of perfoming exact reconstructions if information comes only from structures of the real space (or from equivalent structures of the Fourier space). Only in a related but autonomous space we can find genuinely new information, and the memory space is precisely that type of independent world. It is in fact the only space where a system can get the extra information that allows it to increase its own complexity. The MRM model, in other words, leads to a universal concept to the principle that there cannot be a convergent increase of complexity without memory. 

The second fundamental characteristic of the MRM model is that information can be transferred from memory space to real space only by suitable conventions. In order to decrease the number of the unknowns in real space, it is necessary to give a meaning to the structures that appear in memory space, and this too is a conclusion whose validity is absolutely general. Real space and memory space must be autonomous worlds, because if they were equivalent (like real space and Fourier space, for example) they would convey the same information and no increase in complexity would be possible. But between two independent worlds there is no necessary link, and no information can be transferred automatically from one to the other. The only bridge that can establish a link between such worlds is an ad hoc process, i.e. a convention or a code. This amounts to a second universal principle there cannot be a convergent increase of complexity without codes. 

The Memory Reconstruction Method, in conclusion, gives us two general principles that must be valid for all systems which increase their own complexity, and embryos are such systems. The MRM model predicts therefore the existence of biological structures which are equivalent to reconstruction codes and to memory matrices. More precisely, the model leads to the conclusion that in embryos there must be codes and memories which are made of organic molecules, i.e. organic codes and organic memories. At this point, therefore, we can go back to biology and look for the existence of such structures in real life. 

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