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Les causes et les possibles,entre physique et biologie

Giuseppe Longo

Centre Cavaillès, CNRS et ENS, Parishttp://www.di.ens.fr/users/longo

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Nécessité et hasard comme aspects de la détermination

Comprendre la nécessité par le hasard

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Le hasard

• Pascal (lettre à Fermat, 1654) : Méthode d’estimation d’un jeu …Une ''modélisation'' du hasard par les probabilités.L’infini (le même pour le hasard) : « on en saisi l'existence, mais on n’en saurait connaître la nature »

• Spinoza (Ethique, 1675): la rencontre de chaînes causalesindépendantes; e. g. un tuile qui se décroche, glisse, tombe sur latête du passant, deux parcours bien déterminés, Pas d’analyse probabiliste, mais une proposition sur la nature:imprédictibilité déterministe, très épistémique ….

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Physico-mathematical Determination and Randomness

Laplace, aux idées claires et distinctes :

A) (equational) determination implies predictability (« on doit pouvoir prédire complètement tout fait de la

mécanique » )

B) determination ≠ randomness, Philosophie des Probabilités, 1786

(no commitment on the nature of randomness, like Pascal)

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Physical Determination and Randomness

Laplace’s view:A) determination implies predictibilityB) determination ≠ randomness

[J. Monod, Le hasard et la nécessité, 1970]

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Physical Determination and Randomness

Laplace’s view:A) determination implies predictibilityB) determination ≠ randomness

[J. Monod, Le hasard et la nécessité, 1970]

Today’s consequences of the Laplacian view:A process is deterministic and predictable

if and only if it is programmable

Thus, the “DNA is a program” theory.

Moreover, both Turing-Kolmogorof and Shannon “information theories”, on discrete data, are explicitly Laplacian (Longo et al, 2012).

Randomness is noise, copy errors … no commitment on its nature

7The problem: Determination and Randomness

“The cell is … the molecular processes are a Cartesian Mechanism, autonomous, exact, independent from external influences …

Oriented transmission of information … (in the sense of Brillouin)

Necessarely stereospecific molecular interactions explain the structure of the code … a boolean algebra, like in computers.

Genes define completely the tridimensional folding of proteins, the epigenetic environment only excludes the other possible foldings.

Evolution originates in noise, imperfections …” [J. Monod, 1970]

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Physical Determination and Randomness (Classical)

Laplace’s view:A) determination implies predictibility (false: Poincaré, 1890)B) determination ≠ randomness (= determ. unpredictab.)

Poincaré analysis of the non-linear interactions of Three Bodies in their gravitational field (1892).

An understanding of randomness by a pure analysis of the equation: non analyticity, bifurcations, homoclinic trajectories … (sensitivity) + measurement

Epistemic randomness, but grounded on principles: Fluctuations: thermal, gravitational.

(cf. Spinoza)

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Physical Determination and Randomness (Classical)

Thus, Poincaré broadened determinism by including randomness (an analysis of its nature): a fluctuation/perturbation below measurement, may yield an observable effect, over time:

“et nous avons un phénomène aléatoire”, [Poincaré, 1902]

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Physical Determination and Randomness (Classical)

Thus, Poincaré broadened determinism by including randomness (an analysis of its nature): a fluctuation/perturbation below measurement, may yield an observable effect, over time:

“et nous avons un phénomène aléatoire”, [Poincaré, 1902]

Examples: dies, coin tossing, a double pendulum, the Planetary System (Poincaré, 1890; Laskar, 1992)…

finite (short and long) time unpredictability(the dies deterministically go along a unique geodetics, determined by Hamilton’s principle).

Note: Laplace: • « … prédire complètement tout fait de la mécanique … » False • Demon, perfect knowledge: OK (also over space-time continua)

Conservation properties and symmetries

The modern structure of determination as symmetries

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Conservation properties and symmetries

Noether's theorems [Noether, 1918] pull out of the equations the continuous transformation of symmetries which preserve the equations of movement.

Formally: “If a Lagrangian is invariant under an n-parameter continuous transformation (in the sense that the Lagrangian function is invariant), then the theory possesses n conserved quantities”

To each of these transformations correspond conserved physical quantities

(e.g. invariance w.r.t. translation in space ≈ conservation of the kinetic moment; invariance w.r.t. translation in time ≈ conservation of energy

[van Frassen, 1994; Bailly, Longo, 2011, ch. 4])

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Some consequences of conservation principles

The conceptual priority of the least (or stationary) action, a geodetic, in the intended space (also very abstract Hilbert…):

A radical change in the notion of “Law”:

A physical law is the expression of a geodetics

in an adequate space and with its metric.

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Some consequences of conservation principles

The conceptual priority of the least (or stationary) action, a geodetic, in the intended space (also very abstract Hilbert…):

A radical change in the notion of “Law”:

A physical law is the expression of a geodetics

in an adequate space and with its metric.

Conservation properties as symmetries

(Riemann-Einstein; Poincaré for classical dynamics).

Curie principle: the symmetries of causes are in effects;

Randomness in non-linear systems (sensitive): symmetries changes below observation ... 14

De Laplace au Code

Schrödinger, What is life? (1944), part I

Schrödinger’s remark on drosophila eye colour «We call … “locus”, or, if we think to the hypothetical material structure which serves as support of it, a “gene”. In my opinion, the fundamental concept is more the difference of properties than the property it-self »

The (great) physicist attitude: propose general principles (Galileo’s gravitation and inertia… geodetics principles).

Schrödinger, What is life? (1944), part I

Schrödinger’s remark on drosophila eye colour «We call … “locus”, or, if we think to the hypothetical material structure which serves as support of it, a “gene”. In my opinion, the fundamental concept is more the difference of properties than the property it-self »

The (great) physicist attitude: propose general principles (Galileo’s gravitation and inertia… geodetics principles).

Chromosomes: a code-script, for Forms (!)

Schrödinger, What is life? (1944), part I

Schrödinger’s remark on drosophila eye colour «We call … “locus”, or, if we think to the hypothetical material structure which serves as support of it, a “gene”. In my opinion, the fundamental concept is more the difference of properties than the property it-self »

The (great) physicist attitude: propose general principles (Galileo’s gravitation and inertia… geodetics principles).

Chromosomes: a code-script, for Forms (!)

« In calling the structure of the chromosomes a code-script, we mean that the all-penetrating mind, once conceived by Laplace… could tell from their structure how the egg would develop… . »

Schrödinger’s right consequences of his principles!

Today, the code-script has been fully decoded…

Turing on Laplace and the Discrete State Machine

[Turing, 1950; the “imitation” paper p. 47]:

“ In a Discrete State Machine (DSM)... it is always possible to predict all future state …. This is reminiscent of Laplace's view ... The prediction follows.”

[Turing, 1950]: “The displacement of an electron … an avalanche killing a man” … "It is an essential property of ...[DSMs] that this phenomenon does not occur. Even when we consider the actual physical machines instead of the idealized machines,..., prediction is possible”.

Reason: perfect knowledge is possible: discrete data types (exact access) imply perfect iteration (a time translation symmetry).

Summary (classical): State Determined Systems

A physical system/process is deterministic when we have or we believe that it is possible to have a set of equations or an evolution function ‘describing’ the process;

i.e. the evolution of the system is ‘fully’ determined

by its current states and by a ‘law’.

Classical/Relativistic systems are State Determined Systems:

randomness is an epistemic issue = unpredictability in the intended theory

Thus, randomness, is at the interface “(equational) determination

vs. (physical) process”, accessed by measurement (its principles)

Quantum unpredictability as intrinsic indetermination

Quantum Mechanics is not deterministic (not SDS):

intrinsic/objective role of probabilities in constituting the theory:

• measure of conjugated variables [pq – qp > h] ; • Entanglement of observables, a-causal events, no hidden variables.

Quantum unpredictability as intrinsic indetermination

Quantum Mechanics is not deterministic (not SDS):

intrinsic/objective role of probabilities in constituting the theory:

• measure of conjugated variables [pq – qp > h] ; • Entanglement of observables, a-causal events, no hidden variables.

Schrödinger’s idea: the equational determination of a “law of probability” in Hilbert sp. (thus the indeterministic nature of QM)

Quantum Mechanics: you can’t even think of an infinitary daimon. Key differences: measure of conjugate variables and, e.g.,

the “spin up – spin down” of an electron is pure contingency !

Against Descartes, Spinoza, Leibniz: “all events have a cause”

Recent survey/reflections: [Longo, Paul et al., 2008-09], [Bailly, Longo, 2011]

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Summary: Physical Randomness

1 - Classical randomness = deterministic unpredictability

Epistemic, e. g. since Poincaré (phase space: momentum x space)

non-linear dynamics and the interval of measure (dice)

2 - Quantum randomness (phase space: state function, Hilbert)

Objective or intrinsic (to the theory):

• indetermination (position/momentum or energy/time)

• entanglement (Bell inequalities: dice vs. entangled quanta)

Different probabilities, different theories of randomness…

Handled in different spaces over the same observables (energy …)

In search for a unified theory!

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Towards Biology

“Science has dealt poorly with the concept of contingency”

(S.J. Gould, Wonderful Life, 1989; p. 10)

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Hints to the Nature of Biological Randomness

Darwin (1875, The variation of animals and plants under domestication, p. 236): “Let an architect be compelled to build an edifice with uncut stones, fallen from a precipice. The shape of the fragments may be called accidental; yet the shape of each has been determined by the force of gravity, the nature of the rock, and the slope of the precipice, events and circumstances, all of which depend on natural laws”

Implicit non linearity of the dynamics; contingency; the activerole of the organism (Jacob’s bricolage, Gould’s exaptation …).

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Hints to the Nature of Biological Randomness

Darwin (1875, The variation of animals and plants under domestication, p. 236): “Let an architect be compelled to build an edifice with uncut stones, fallen from a precipice. The shape of the fragments may be called accidental; yet the shape of each has been determined by the force of gravity, the nature of the rock, and the slope of the precipice, events and circumstances, all of which depend on natural laws”

Implicit non linearity of the dynamics; contingency; the activerole of the organism (Jacob’s bricolage, Gould’s exaptation …)

Luisi (2006), “Contingency … for example, a tile falling on your head from a roof can be seen as a chance event … the concomitance of many independent factors”

Back to Spinoza.

Question: evolutionary contingency = “being there”; how random?

The constitutive role of randomness in Biology

One of the crucial « changes of perspective », in Biology:

Not noise, no “stochastic” stability (large numbers), but

Randomness implies variability implies diversity

An essential component of structural stability

Compare: Randomness as intrinsic to Quantum Mechanics:

it changes measurement and the “structure of determination” (Schrödinger equation).

Take an analogous, not homologous conceptual step …

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Biological relevance of randomness

Randomness in molecular activities …. more :

Each mitosis (elementary and fundamental):

Asymmetric partitions of proteomes; differences in DNA copies; changes in membranes …

In multicellular organisms: varying reconstruction of tissues’ matrix (collegen structure, cell-to-cell connections …), a symmetry breaking (a new coherence, a critical transition [Bailly, Longo, Montévil,

2006 – 12]).

Not “noise”, “mistakes” from DNA to Proteins, in a “program”,

but non-specificity and randomness is at the core not only of variability and diversity (the main biological invariants), but even of cell differentiation (in embryogenesis: sensitivity to a context in a critical transition).

More than one hundred years after Poincaré,some dynamics at the molecular level

Since • Alternative Splicing [Brett et al., 2001 ; Sammeth, 2008], • The new role of methylation and demethylation [Caroll, 2008]• Torsional constraints on chromosomes [Lesne, 2009]• Stochastic gene expression [Heams, 2013]• Level of nitrate in metabolism modifies plants genome, known since Durrant, 1962 [Buiatti, 2013]

New key words:“…it is not the static genome but rather the dynamic proteome that determines the phenotype of an organism…”

G. Ophanides, D. Reinberg, Cell, vol. 108, 439-451, Feb. 2002.

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Which form of randomness ?

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Quantum Randomness in Biology

Quantum tunneling: non-zero probability of passing any physical barrier (cell respiration, Gray, 2003; destabilizing tautomeric enol forms – migration of a proton: Perez, 2010)

Quantum coherence: electron transport (in photosynthesis and in many biogical processes: Winkler, 2005)

Proton transfer (quantum probability): RNA mutations (G-C pairs: Ceron-Carrasco, 2009)

REFERENCES IN:

Buiatti M., Longo G. Randomness and Multilevel Interactions in Biology, Downloadable

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Classical Randomness in Biology

Non linear affects (molecular level):

• Molecular enthalpic oscillations

• Turbulence in the cytoplasm of Eukaryote cells

• Empowered metabolic random activities by (water) “QED coherence” (Del Giudice, 2005; Plankar, 2011)

• Stochastic gene expression, (R. Arjun, R. van Oudenaarden, Stochastic gene expression and its consequences. Cell, 135(2): 216–226, 2008; Heams, 2013)

And … Hydrodynamics? Fluidity and incompressibility in continua (no quantum analysis: which role of permeability of membranes?)

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Classical and Quantum Randomness in Biology

Molecular level:

non linear dynamics (classical)

and quantum processes superpose

That is:

They happen simultaneously and interfere (not analyzed in Physics)

Morover:

a quantum effect may be amplified by a (classical non-linear) dynamics

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Proper (?) Biological Randomness 1

Randomness within other levels of organization in an organism:

• [Besides: Molecular activities (classical+quantum randomness)]

• Cellular dynamics and interactions in a tissue

• Developmental dynamics (contact inhibition between cells: Soto et al., 1999)

• Fractal bifurcations (mammary glands development, ongoing work)

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Proper Biological Randomness 2:

Recall: since Poincaré, randomness as “planetary resonance”

Extended to general non-linear dynamics at equilibrium:

at one level of (mathematical) determination

(far from equilibrium: Pollicott-Ruelle resonance, dynamical entropy in open systems (Gaspard, 2007))

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Proper Biological Randomness 2:

Recall: since Poincaré, randomness as “planetary resonance” …

Extended to general non-linear dynamics at equilibrium:

at one level of (mathematical) determination

(far from equilibrium: Pollicott-Ruelle resonance, dynamical entropy in open systems (Gaspard, 2007))

Bio-resonance (Buiatti, Longo, 2012):

Randomness between different levels of organization in an organism:

thus, resonance (as interference) between different levels of (mathematical) determination (aim: analyze randomness)

The mathematical challenge: the Mathematics (of Physics) does not deal with heterogeneous structures (of determination)

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Bio-resonance

Physical resonance (at equilibrium / far from equilibrium) is related to “destabilization” (growth of entropy or disorder)

Bio-resonance includes “integration and regulation”, thus

it stabilizes and destabilizes

Examples (networks and morphogenetic dynamics):

- The lungs, …

- In embryogenesis …

- In “colonies” of Myxococcus Xanthus, a prokaryote, and Dictyostelium discoideum, an eukaryote (Buiatti, Longo, 2012)

Aim: role of randomness in structural stability (organisms, niche, ecosystem …)

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Biological relevance of randomness

Randomness in molecular activities …. more :

Each mitosis (elementary and fundamental):

Asymmetric partitions of proteomes; differences in DNA copies; changes in membranes …

In multicellular organisms: varying reconstruction of tissues’ matrix (collegen structure, cell-to-cell connections …), a symmetry breaking (a new coherence, a critical transition [Bailly, Longo, Montévil,

2006 – 12]).

Not “noise”, “mistakes” from DNA to Proteins, in a “program”,

but non-specificity and randomness is at the core not only of variability and diversity (the main biological invariants), but even of cell differentiation (in embryogenesis: sensitivity to a context in a critical transition).

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Back to Darwin

Darwin’s Principles

“The Origin of Species”, Two Fundamental Principles:

1 – Descent with Modification

2 – Selection

The first as revolutionary as the second, which has no meaning without the first.

Recall: each mitosis is a symmetry breaking, it (randomly) engenders variability thus diversity thus,

jointly to reproduction (inheriting DNA, proteome, membrane …), by modification it contributes to structural stability

(adaptability of an organism, diversity of a population …)

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Onto-phylogenetic trajectories

Each bifurcation is a symmetry breaking

Being here is evolutionary contingency

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Onto-phylogenetic trajectories

Each bifurcation is a symmetry breaking

Being here is evolutionary contingency

Evolutionary contingency is the result of 1 - (physical and biological) randomness (symmetry breakings), 2 - under (historical and ecosystemic) constraints, and3 – crossing of different causal (physical and biological) dynamics

(“Spinoza’s contingency”)

Contingence, hasard, ergodicité, stochasticité, probabilité …

Biological contingency: “being there”1. Result of a history, as a “cascade of symmetry breakings”2. which are (highly) constraint random events

The path is not ergodic (physical meaning: asymptotic exploration of the entire space of possibilities; molecules of 200 amino acids by 1080 interacting atoms at Planck time, in 1030 lives of Universe).

Probabilities as for molecular events (stochastic gene expression, macromolecular interactions)

No probabilities outside molecular events (phenotypes dynamics)

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ENABLEMENT

Longo G., Montévil M., Kauffman S. No entailing laws, but enablement in the evolution of the biosphere. GECCO’12,

July 7-11, 2012, Philadelphia (PA, USA); proceedings, ACM 2012.

Longo G., Montévil M. Extended Criticality, Phase Spaces and Enablement in Biology. Invited Paper, Special Issue of

Chaos, Solitons and Fractals, 2013.

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RECALL FROM PHYSICS

“Causal” relations: e. g.

f = ma

Since Weyl, Noether … van Fraasen

Geodetics and symmetries

in the right phase spaces

A unifying (better) frame for intelligibility of “causes”.

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FROM PHYSICS TO BIOLOGY

Note: empirical evidence for causes:

differences causing differences

E. g. identical acceleration implies identical force (Galileo's gravitation); yet, the “general law” is not evident (Newton)

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FROM PHYSICS TO BIOLOGY: ENABLEMENT

Gravitation causes a body to fall

Gravitation is not a cause in biology: it is a constraint

It contributes to the niche/ecosystem.

Key reason:

The default state in physics is inertia

The default state in biology is “proliferation with variation” (Darwin's first principle)

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FROM PHYSICS TO BIOLOGY: ENABLEMENT

Gravitation causes a body to fall

Gravitation is not a cause in biology: it is a constraint

It contributes to the niche/ecosystem.

Key reason:

The default state in physics is inertia

The default state in biology is “proliferation with variation” (Darwin's first principle)

Changing constraints (the formation of a new niche)

Enables a variation to succeed

A omnipresent phenomenon in evolution: allopatric speciation (a species formed from a population in a different niche/ecosystem)

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ENABLEMENT and CAUSES

Claim: (evident) causes are differential in biology

A (a-causal/random) mutation (a difference) may cause a phenotypic difference.

Bacteria (a difference from normality) may cause a pneumonia.

Yet, this causal consequence may be enabled by the niche (a wounded lung, a weak immune system ..)

A different role of constraints, in physics vs. biology due to the difference in the default states:

inertia vs. proliferation (with variation)

Life does not need a “cause” to be active (to move and proliferate)4949

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ENABLEMENT and CAUSES

Different role of constraints, in physics vs. biology

Examples:

1 - A river at a bifurcation: fully deterministic analysis (possible highly non linear, thus unpredictable) of inert (gravitational) matter.

2 - A population proliferation facing a “niche multifurcation”: phenotypic variations are co-constitued with the possible enablement(s) by one or more possible evolutionary paths (a different default state)

In 1, the structure of determination describes causes;

in 2, it must include enablement.

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ENABLEMENT and CAUSES

Different role of constraints, in physics vs. biology

Examples:

1 - A river at a bifurcation: fully deterministic analysis (possible highly non linear, thus unpredictable) of inert (gravitational) matter.

2 - A population proliferation facing a “niche multifurcation”: phenotypic variations are co-constitued with the possible enablement(s) by one or more possible evolutionary paths (a different default state)

In 1, the structure of determination describes causes;

in 2, it must include enablement.

Physical objects never go wrong.

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Some references (downloadable: http://www.di.ens.fr/users/longo )

• Bailly F., Longo G. Mathematics and the Natural Sciences. The Physical Singularity of Life. Imperial College Press, London, 2011 (français: Hermann, 2006).

• Longo G., Palamidessi C., Paul T.. Some bridging results and challenges in classical, quantum and computational randomness. In "Randomness through Computation", H. Zenil (ed), pp. 73–92, World Scientific, 2010.

• Longo G., Montévil M. From Physics to Biology by Extending Criticality and Symmetry Breakings. Invited paper, special issue of Progress in Biophysics and Molecular Biology, 106(2):340 – 347, 2011.

• Longo G. The Inert vs. the Living State of Matter: Extended Criticality, Time Geometry, Anti-Entropy - an overview. Invited paper, a special issue of Frontiers in Physiology, n. 3, 39, 2012.

• Longo G., Montévil M., Kauffman S. No entailing laws, but enablement in the evolution of the biosphere. Invited Paper, Genetic and Evolutionary Computation Conference, GECCO’12, July 7-11, 2012, Philadelphia (PA, USA); proceedings, ACM 2012.