Dear Pedro, I think that we should assess the role of formal tools that are already in place.
1. We use the accepted (graph-theoretical + geometry) models of molecules. These models are very powerful and fundamentally simple, but the complexities of their application in molecular biology is very great, requiring computational handling of the data and geometry. Some molecular biologists add features related to physics such as electromagnetic fields and quantum mechanics to these models, and it should be expected that the quantum level will eventually be very important to the structure of molecular biology. 1(a). This is a further comment on 1. In protein-folding we use the basics of model 1, plus elementary modeling of energy and probability of bonding. These models are insufficient to do what Nature does naturally. The models are combinatorial and graph theoretic in nature but they do not address the right issues (what are they?) to impinge on the actualities of protein folding as it happens. The same is probably true about the topological side of protein folding — one can easily construct topological invariants at the combinatorial level (I have written about this) but their use by biologists has not happened yet. At least one researcher (Anti Niemi) suggests a different and more field theoretic approach to protein folding. See https://www.researchgate.net/profile/Antti_Niemi/publications <https://www.researchgate.net/profile/Antti_Niemi/publications> 1(b). There has been a nice success in applying topology via the embedded-graph paradigm for molecules. See DNA Topology <https://www.google.com/search?client=safari&rls=en&q=DNA+Topology&ie=UTF-8&oe=UTF-8> DNA Topology Kauffman and Lambropoulou] <https://www.google.com/search?client=safari&rls=en&q=DNA+Topology&ie=UTF-8&oe=UTF-8#q=DNA+Topology+Kauffman+and+Lambropoulou%5D> It is in this domain, that I became interested in looking at the self-reproduction of DNA as an instance of an abstract self-replication schema. There is much more to be done here in linking this abstraction back to the topology and to the actualities of the biology. The investigation led to a number of analogies with structure of quantum mechanics and this will in turn related to quantum topology. This is in development. 2. Further topological/geometric work is very possible. The sort of thing seen in Pivar could be examined for mathematical problems to be articulated. We are aware that biological forms must arise via self-assembly and this is in itself a possibly new field of geometry! The simplest example of self-assembly as a model is the model of autopoesis of Maturana, Uribe and Varela from long ago. Their model shows how a two dimensional cell boundary can arise naturally from an abstract ‘chemical soup’. 3. While I do not agree with Max Tegmark that Mathematics is identical to Reality, I do believe that the key to actuality is in the essence of relationships. The essence of relationships is often accompanied by a mathematical essence or simple fundamental pattern. This is so striking in the case of DNA reproduction (e.g.) that I cannot help but feel that some real progress can occur in looking at that whole story from the abstract and recursive self-replication to how it is instantiated in the biology. The question in general is: What can we see about the way mathematical models are instantiated in actuality?! I will stop here in the interest of bevity. Best, Lou > On Mar 20, 2016, at 2:04 PM, PEDRO CLEMENTE MARIJUAN FERNANDEZ > <pcmarijuan.i...@aragon.es <mailto:pcmarijuan.i...@aragon.es>> wrote: > > May I suggest that Louis make some further comment on the formal tools for > develop., answering Stan? Then, I think we should derive towards generalizing > on the bio problem and arguing about the existing philosophical gap(s) that a > tentative new phenom of life could fill in... it may be a good opportunity to > focus the entire discussion sessions. Plamen and me could attempt that, of > course Louis in his response to Stan too, irrespective that other parties may > finally plunge into the discussion or not. At least we will have done our > part. > best --Pedro
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