from physics to biology and society _ 13

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1/19/2015 From Physics To Biology And Society : 13.7: Cosmos And Culture : NPR

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In the rich and novel Galilean relationship between experiments and theories,physical theorizing is meant to provide intelligibility of phenomena as well as

predictability: one first observes and measures, then the theory should produce a

prediction capable of confirming it.

The scientifically expected future was set at the core of the understanding of modern

science. And prediction is done in the space and time of physical events,

mathematically described by the Cartesian analytic representation of space enriched

by Galileo's relativity: the modern space-time of phenomena is born by an analysis on

how to go from one (Cartesian) reference system to another and preserve the physical

laws, inertial movement in particular. In the pre-given space-time of possible

trajectories, the invariants are described as symmetries by Galileo's group.

I would ascribe, though, the turning point towards the myth of a scientific expectation

of apossible (and predictable) future to the early Italian Renaissance.

Therationalinsight into the future,within a given space of possibilities, goes back to

theappreciation of progress, and of possible estimates of it, in Italy, in the XIV and

XV century. This is when both modern technologies began to change the world and

bank creditwas invented.

Lending money was finally allowed, in particular under the form of the "letters of

credit" or early paper money. No more a sin, one could bet on possible future

progress, obtain money from a bank, then invest, expect the return of the money, plus
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interest, and also obtain personal gain.

It was an economic and a conceptual revolution.

There was no magic in the expectation of progress and a foreseeable future, but

rational knowledge. Of course, hazards are possible, but within a perfectly pre-givenspace of possibilities: like throwing dice it is a risk, but within the six possible

outputs, no more, no less. betting is rational: one can compute the probabilities and

evaluate the risk.

And the society of an expected future progress, in apredetermined list of possible

worlds, begins. The society where one can dare to borrow and lend money as well as

construct scientific knowledge within mathematically pre-determined space-time; a

science, where it is possible to predict, by a scientific theory, the output of an

experiment.

Later on, as Stuart Kauffman observed in last week's blog post, Newton and Laplace

gave us the mathematics of modern "state determined systems". Indeed, by solving

equations, Laplace says, "one must be able to predict all future event of mechanics"

(celestial mechanics, but he thinks to the entire physical world).

Pascal's and Laplace's analysis of probabilities scientifically deal also with

unpredictability, but randomness is extraneous to the mathematical determination.

Anyway, for them, unpredictable events happen within the pre-determined Cartesian

space of all possible trajectories and facts.

Much later, quantum mechanics will integrate randomness in the theory, under the

form of intrinsic indetermination. Yet, the space of possible trajectories and events

will still be mathematically predetermined, whether they be infinite or even infinite

dimensional Hilbert and Fock spaces. By a finite axiomatization we give them a

prioriand they may accommodate the most unpredictable quantum event. Now, the

finite descriptionof these possibly infinite spaces, from Descartes to quantum spaces,

is made possible by their regularities: they are given in terms of mathematicalsymmetries (as sets of invariants and invariant preserving transformations).
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These audacious and once fruitful bets on a foreseeable future, in a mastered list of

possibilities, have now become the pure transfer of richness towards the richest, by

the refined mathematics of finance. Its aim is not prediction, but to construct new

possibilities for bets, to shape the unforeseeable markets and to distribute the risk

maximally, so that the Chinese workers will buy the debts of the bets on a totally

unpredictable risks taken by American finance.

The theoretical challenge is thus to invent tools for understanding, not necessarily for

prediction (Darwin's evolution predicts nothing yet it is knowledge). Qualitative

estimates on the effects of an activity may allow us to act on the world, if these

estimates are grounded on criteria of robustness of development, as (increasing)

diversity and adaptability. These words, in a societal context, mean democracy and

justice.

As for biology, in a book and in several downloadable papers, with Bailly and

Montvil, we hinted at novel conceptual (and mathematical) structures which aim at

a better understanding of the physical singularity of the living state of matter: the

change of perspective on symmetries is at the core of our scientific proposal.

Predictability, not even of the space of possibilities, is no longer at the center ofknowledge construction. This construction aims at the understanding of the historical

contingency of life (and, eventually, society), at the awareness of the role of our action

in a totally unpredictable world, where we judge for the better, by making explicit the

perspective (and values) that guide our acts.

Giuseppe Longo has been a professor of mathematical logic and of Computer

Science at the University of Pisa. He is currently Directeur de Recherche CNRS at

the Ecole Normale Suprieure, Paris. He is editor-in-chief of Mathematical

Structures in Computer Science. He recently extended his research interests and

work to the epistemology of mathematics and theoretical biology.

xp. .
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