Information Topology

Video  at CIRM 2017: Information Topology: Statistical Physic of Complex Systems and Data Analysis

The work received the K2 trophy 2017 "mathematic and applications".  Videos of the interviews.... 

”The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful. If nature were not beautiful it would not be worth knowing, and life would not be worth living... What I mean is that more intimate beauty which comes from the harmonious order of its parts, ...” ”Now what is science? ...it is before all a classification, a manner of bringing together facts which appearances separate, though they are bound together by some natural and hidden kinship. Science, in other words, is a system of relations. ...it is in relations alone that objectivity must be sought. ...it is relations alone which can be regarded as objective. External objects... are really objects and not fleeting and fugitive appearances, because they are not only groups of sensations, but groups cemented by a constant bond. It is this bond, and this bond alone, which is the object in itself, and this bond is a relation.” ”Mathematicians do not study objects, but the relations between objects; to them it is a matter of indifference if these objects are replaced by others, provided that the relations do not change. Matter does not engage their attention, they are interested in form alone.” H. Poincaré.

"there is urgency in coming to see the world as a web of interrelated processes of which we are integral parts, so that all of our choices and actions have consequences for the world around us" A.N.Whitehead (in the 1910's ! after he published principia mathematica)

Fashions (in biology) live and die, mathematic stays and evolves. These are the quality most of the people on earth wish for living dynamic. In Paris it was quoted as ''fluctuat nec mergitur'', but this seems on my experience quite a widespread human wish, as notably quoted by ''sustainable development'', or simply ''survival'' according to most of the people, any bacteria and Grothendieck. So may be mathematic can be also usefull, to reveal and promote the harmony of our world, it indeed does so since its early ages.

 Life, energy, space and time, resources, money (…)  are  discrete and finite  in data-measures. But we need  continuous  models to  predict ; Co-homology (discrete-Galois  and  continuous-Lie). "Information theory must precede probability theory and not be based on it. By the very essence of this discipline, the foundations of information theory have a finite combinatorial character." Kolmogorov, 1983

“It is certain that all bodies whatsoever, though they have no sense, yet they have perception … and whether a body be alterant or altered, evermore a perception precedeth operation; for else all bodies would be alike to one another” Francis Bacon 1967: 68-69 (in Monod, Wyman, Changeux, , on the nature of allosteric transition, 1964)

“ Well then - all things feel! ” Pythagoras (attributed to)

Golden Verses

Man ! Free thinker - do you believe that you alone can think

 In this world, where life bursts forth in everything :

 Forces you hold your freedom dispose,

But from all your advices the universe is absent.

<em> Respect in the beast an acting spirit : ...

<em> Each flower is a soul of the bloomed Nature ;

<em> A mystery of love in the metal repose :

 "All things feel !" - And everything on your being is powerfull !

 Fears in the blind wall a glance watching you

 Even to the matter a verb is attached ...

 Do not make it serve to some impuous use !

 Often in the obscure being lives a hidden god ;

And like a nascent eye covered by its lids,

A pure spirit grows under the bark of stones !

Gerard de Nerval, 1853.

What if this poem was a theorem ?

"O Time, thou must untangle this, not I.

It is too hard a knot for me t’untie."

W. Shakespeare.