Today comes a very important topic… No, I mean it, it is one that starts a discussion like those questions children use to ask… like “where are babies coming from?”… No, really, it couldn’t be more important… the subject of this evening in called “interactions”… Why is it so important? Well, physicist should know it: interactions make things real. What could you tell about a particle with no interaction whatsoever? Well, that it doesn’t exist! As long as it is a physical object it must represent some form of energy and if that is the case it must interact at least gravitationally… spacetime, what am I saying, geometry itself is a manifestation of interactions. Physicist should know that better than anyone else, right? WRONG! Unfortunately physicists tend to look at interactions in terms of physical objects interacting via some other physical objects… this is rather unfortunate… because this way of looking at reality hides some very important interactions, the logical interactions… the possible results of the coexistence of mathematical structures… and these are widely and wildly ignored by todays physicists… Let me be more specific: at the famous CERN LHC there are (as the name says) hadrons (strongly interacting particles) that collide… when the collision energy is high enough all hell breaks lose! You get interactions that generate all sort of jets and particles and there will be virtually everything, photons, gluons, neutrinos, Higgs’s, particles mediated by weak or strong or e.m. decay and so on, and so on… However, this fact makes physicists rather arrogant… they tend to believe that everything that exists in nature appears because of tiny somethings that interact with one another through tiny other “somethings”… This is utterly incomplete… It is as if you said the universe is a lattice or other nonsense like that… In reality the interactions we see are just an epiphenomenon of other interactions, those between mathematical structures. There, just put a classifying space, a group and an isomorphism together and all hell breaks lose! We wouldn’t even notice that there is lots of jittering at the level of mathematical structure if there were not for something called “quantization prescriptions”… These, especially when involving gravity, allow us to make a point about how mathematical structures interact at a level otherwise unseen… and believe me, the are less restrictions than one could imagine! It is very unlikely that you simply get to restrict the possibilities of mathematics. The information is encoded in the most unexpected ways and it is transmitted from one structure to another by things that also encode some form of information. Even the possible ways in which a structure is mapped into another one can give hints about the desired information. 

What happened to me today? Well, a colleague in my office today spoke to the phone and had to spell the letters of a pretty difficult name. She used the standard method of contextualizing the data: L from Lima, I from Italy etc. I thought: what an amazing thing!!! How does this reflect into some mathematics? Isn’t it amazing that a letter is by itself badly received while put into a known context it becomes a mean of information transmission? Isn’t it amazing that by adding extra structure you facilitate and accelerate the communication in noisy environments? What you actually do is to encode the information of an entity in the structure of a larger object of known properties. Every letter from LIMA makes you think at the first letter L… if you change the first letter: say P instead of L you get PIMA which makes no sense… It is not only a topological information coding… it is more than that… I still have to understand how this reflects on quantum mechanics… 

Isn’t it amazing how a seemingly irrelevant fact can make me think at very interesting things? Well, this is the beauty of the human mind! Not the repetitive performance of tasks! 


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