Longo - Presentation CMSG

7/31/2019 Longo - Presentation CMSG

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Philosophy and theories of the

living state of matter:

Biological Theories as extended PhysicalTheories

Giuseppe Longo

CNRS, Dpt. Informatique ENS,et CREA, Polytechnique, Paris

http://www.di.ens.fr/users/longo

F. Bailly, G. Longo Mathmatiques et sciences de la nature. Lasingularit physique du vivant. Hermann, Paris, 2006.

(in English, Imperial College Press / World Sci., 2011)


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Physical vs Biological Theories

The completeness of the Physical World:

OntologicalvsTheoretical issue

OK foressences (just molecules)

But completeness and reduction are theoreticalissues:

Reduction to the physical (sub-)theories? Why not To which Theory? Existing ones (Mayr) ? Galileo, Einstein


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The completeness of the Physical World:

OntologicalvsTheoretical issue

OK foressences (just molecules)

But completeness and reduction are theoreticalissues:

Reduction to the physical (sub-)theories? Why not To which Theory? Existing ones (Mayr) ? Galileo, Einstein Yet, inPhysics: the point isunification more than reduction:

1. Newton vs Galileo (the falling apple and the planets: a new theory)2.

Thermodynamics (Boltzmann: the thermodyn. integral, a limit);

3. Relativity/QM (newobjects- strings, a newspace - non-comm.Geometry): ongoing work (within incompatible theories)


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The despair of the physicist looking at biology:

in biology, whatever theory one proposes,

there is always a counterexample


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The despair of the physicist looking at biology:

in biology, whatever theory one proposes,

there is always a counterexample

Add the conceptual opposite


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Ever since DarwinBuffon: the Earth and Life have an history (1752)Lamarck: . a progress (an adaptive expansion of life)


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Ever since DarwinBuffon: the Earth and Life have an history (1752)Lamarck: . a progress (an adaptive expansion of life)Darwin: and also the opposite: death is essential to life evolution by (expansion and) selection.


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Complexity: lempilement du simple ?


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[Edelman, 2000]: "complex", at once: orderered anddesordered, regular andirregular, variant andinvariant, stable andinstable differentiated andintegrated


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[Edelman, 2000]: "complex", at once: orderered anddesordered, regular andirregular, variant andinvariant, stable andinstable differentiated andintegrated Add:bounded andopencritical andextendedlinear (time) andbifurcatingentropy and anti-entropy


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In Biology, organisms are "differenciatedandintegrated":(Note: regulation ; integration) living unit (metazoan)

organ (e. g. fractal structures)

cell (in a tissue: maths of networks)

but these levels of organization are already present in the cell (elementary and complex)Gould (1997): maximal objective complexity.


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Some Physics and Maths in Biology

.


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Some Physics and Maths in Biology

Remarkablephysico-mathematical work at

different levels of organization:

Organs:Morphogenesis, phyllotaxis since DArcy Thompson, Waddington,Turing, Thom : mostly organs (loci ofenergyexchange - e. g. geodetics:fractal structures )

Tissues:Networks (Von Neumann, Hopfield G. Parisi): neural, cellular(intercellular exchange -gradient of energy)

More (e.g. bio-informatics)

Different mathematical methods (mostly in continua) fordifferent levels oforganisation (no dialogue )

What about the resonance effects between different levels of organisation?


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The myth

the stability and the organisation of the DNA and the subsequentmolecular cascades completely determines the stability and theorganisation of the cell and the organism


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The myth

the stability and the organisation of the DNA and the subsequentmolecular cascades completely determines the stability and theorganisation of the cell and the organism

False! Since:

the stability and the organisation of the cell and the organismcausally contribute to the stability and the organisation of theDNA and the subsequent molecular cascades

(see, say, [Fox KellerThe century of the gene, 2000];

[Brett et al. 2001;Bartel, 2004; Longo, Tendero, 2007])

Yet, incompleteness of molecular analyses, does not mean useless!


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The paradigm of Incompleteness and

Molecular Biology

DNA: the main component of the cell!

Its analysis and those of the molecular cascades are

fundamental, yet

(causally) incomplete (=/= useless)

Formalism and molecules: the alphabetic myth

(incomplete w.r.t. structures and meaning)


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a matter ofTheories

The concern of many with vitalism

The confusion: the issue is theoreticalnot ontological

(monism of the matter)

The analogy: accusations ofvitalism in Biology parallel those of

non-realism in Quantum Physics:

Dont you see that matter/reality/objects are there?No entanglement, but locality, separability


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Our theoretical approach

Physical vs. Biological Theoriesin Bailly-Longo three (correlated) approaches:

Theoretical extensions (in the sense of Logic) ofphysical theories (thermodynamics)

Are these Physical theories?


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In Biology: extensions of Physical Theories byproper observables:

1 proper (irreversible) time (to be added to the thermodynamic

arrow of time) and two dimensional time (not linear time);

biological rhythms are pure numbers (i.e. total numbers of .heart beats, respirations, metabolic cycles) with M. Montvil

2 - extendedcriticality(in physics: pointwise critical transitions;

living objects are in a permanent critical transition - symmetry

changes), JBS, 16, 2, 2008.

3 -organization (a new observable) as anti-entropy,JBS, 17, 1, 2009.


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Physical vs. Biological Theoriesin Bailly-Longo three (correlated) approaches:

1 -proper (irreversible) time and two dimensional time (not linear

time), with M. Montvil

(2 - extendedcriticality(a physical oxymore), JBS, 16, 2, 2008. )

3 - organization (a new observable) as anti-entropy,JBS, 17, 1, 2009.)

Common point to the approaches in 1, 2 and 3:Strict Consistent extensions, in the sense of Logic,

compatible with current physical theories, but not necessarely

reducible:

1: collapse the extra dimension (a time bifurcation);

2: contract the extension of criticality (from interval to point);

3: = instead of in balance equations (anti-entropy goes to 0).

Question: are they strict, conservative?


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CONSERVATIVE (?) EXTENSIONS

Examples from Logic: T

T = T+NewAxiom (T extends T)

Formal Arithmetic (PA)

1. PA + Knigs Lemma (any infinite, finitely branching tree has an

infinite branch) is a strict, conservative extension: it proves more

on infinite trees, but no more arithmetic statements.

2. PA + Axiom of infinity = Set Theory (Set)

is a strict, non-conservativeextension of PA, since Gdel 31:

an axiom ofinfinity allows to prove Consistency of PA (Coher).

Hilberts wrong conjecture:

Set is conservative over PA (thus, PA Coher )


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1 - Biological extensions of physical time


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One dimension, three forms of time

Different observables

A. In thesame dimension; e.g. in Physics, Energy, kinetic vs.

potential

A.1. thermodynamical time(physical(ir-)reversibility)

A.2. time of the constitution of biological order

(Evolution, embryogenesis: properbiologicalirreversibility)

B. Add a new dimension for time in order to accommodate

biological rhythms.


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More on the first form of time (thermodynamics)

a debate: physics vs. biology

1. thermodynamical time(physicalirreversibility): entropy as1.1 energy dispersal (not necessarely disorder, inphysics)

1.2 energy dispersal implies disorder in biology


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More on the first form of time (thermodynamics)

a debate: physics vs. biology

1. thermodynamical time(physicalirreversibility): entropy as1.1 energy dispersal (not necessarely disorder, inphysics)

1.2 energy dispersal implies disorder in biology

inphysics, a lowered energy state is not necessarily disorder,

because it simply results in the identical molecule with a

lowered energy state. The fact that such a molecule might be

biologically inactive may not concern the physicist, but it

definitely does concern the biologist.

(Hayflick , 2007)

Note: in 1.1, entropy growth, in open systems, may be reversed


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More on the second form of time

(biology)

2. time of the constitution of biological order(Evolution, embryogenesis: properbiologicalirreversibility)

Moreover, mitosis,per se, increases order, yet:

- it is never an identical reproduction (at least non-identity of

proteomes and membranes);- it induces anunequaldiffusion of energy.

Thus, biological reproduction, as morphogenesis, is intrinsically

joint to variability and, thus, it produces entropy also by lack of

(perfect) symmetries. By this, it induces its properirreversibility, beyond (and in addition to) thermodynamics.

(cf. a computers production: reversibility and iteratability )

An ongoing project


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B. Biological Rhythmsadd a second time dimension

2.1 External-physicalrhythms (Ext: periods or physical

frequencies):

dimensional: s, Hz exp(it): daylight, seasons)

2.2 Internal rhythms (Int: physiological functions):

non-dimensional: heart beats, respiration, metabolicrhythms b 1.2x109 , r 0.8x109 in mammals;

pure numbers: theyproduce time scales as afunction of the mass, e.g. LifeTime W1/4


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Geometric scheme fortwo dimensional Biological

Time

1. Thermodynamical oriented time t: the horizontal

axis -------> t


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Time


axis -------> t

2. Compactified dimension R: the circleInternal rhythms (Int): physiological functions


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Time


axis -------> t

2. Compactified dimension R: the circleInternal rhythms (Int): physiological functions

Their product:

R


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Taking into account also External Rhythms

(Bailly F., Longo G., Montvil M.. A 2-dimensional Geometry for Biological Time. Toappear inProgress in Biophysics and Molecular Biology, 2011.)

2.1 Ext: Day/Night

2.2 Int: heart beats, respiratory (+ the internal trace of Day/Night)


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An application

Convention: enlarge at constant speed (and renormalize)


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Cardiac Rhythm: two daysSample s20011 from The Long-Term ST Database, [13]


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Cardiac Rhythm: dayvs. night(200beats per circle)


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Comparison (sudden cardiac death): (a) Healthy case,

(b) Female aged 67 with sinus rhythm and intermittent pacing.

(c) Female, 72, with atrial fibrillation.

(d) Male, 43, with sinus rhythm.Data from samples 51, 35 and 30, The Sudden Cardiac Death Holter Database, 2009 (200 beats).


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Some more philosophy

.


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Some more philosophy

On complexity:

Elementary Simple (the cartesian myth)

vs.

Elementary &Complex (todays challenge)

(strings (Physics); cells; cognitive units)

.


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Causality and complexity

(Classical) Physics:

Causal relations are local; global only in the sense of a field(by propagation oflocalinteractions; i. e. by transitivity) or ofthe global determination (by equations overlocalvariables; cf.Quantum Physics: entanglementor non-local variables).

Biology:

local causality may differradically from global correlations, yetit cannot be isolated from the latter: integration andregulation, typically, causally affectlocal interactions(e.g. local bio-chemical exchanges may be regulated by cascades of hormones orneural signals of an entirely different theoreticalnature).

Possible connection, since the 80s (Bak, Kauffman ):

The Physics ofCriticality: the formation of global Structuresof Coherence in critical transitions (singularities).


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Bailly, Longo Extended Critical Situations JBS 2008

Our proposal: Life phenomena as an extended critical transitions:

1. continual phase transitions (over an interval)2. global unity of new entity (causal entanglement)3. infinite (physical) measure of complexityBiological units live in a state ofmaximal (infinitary),

physically unstable (even:physically unsuitable), state ofcomplexity:

an extended critical transition

(a dynamical interference of global and local causality)

The physical paradigms helped us to formulate this notion, which isnot internal to physical theories

Longo, Montvil From Physics to Biology by Extending Criticality


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From Physics to Biology by

Conceptual Dualities

(or: changingprinciples by dualities)


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Dualities in Physics vs Biology

1. Physics: Specific trajectoires (geodetics) and generic objects

Biology:generictrajectories(compatible) andspecific objects


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Dualities in Physics vs Biology

1. Physics: Specific trajectoires (geodetics) and generic objects


2. Physics:energy as operatorHf, time as parameterf(t,x) ;

Biology: energy as parameter, time as operator (entropy

associated to all irreversible processes) [Bailly, Longo, 2009]


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An application to

Biological Evolution and Complexity


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Evolution and Complexity

The wrongimage (progress?):


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Growing complexity in Evolution?

Which complexity?

Evolutionary complexity?A possible representation of phylogenesis

(Bacteria; Archea; Eucaryota):


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An analysis in terms ofObjective vs. Phenotypic complexity


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Objective complexity

A. Objective Complexity:

1. Metabolic processes,2. Production of energy(3. Existence of different levels of organisation)

S. J. Gould: equivalent in the Eukaryotic Cell and the Elephant


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Objective vs. Phenotypic complexity




B. Phenotypic(Morphological/Epistemic)complexity:

F. Bailly, G. Longo. Objective and Phenotypic Complexity in Biology. 2003


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Objective vs. Phenotypic complexity




B. Phenotypic(Morphological/Epistemic)complexity:

1. cellular combinatorics as differentiations between cellularlineages (different tissues)

2. topological forms and structures (e.g., connexity and fractalstructures)

3. networks: neuronal and cellular (interactions)F. Bailly, G. Longo.Biological organization and anti-entropy. 2009


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However: Goulds growth of morphological complexity

[Full House, 1989]


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However: Goulds growth of morphological complexity

[Full House, 1989]


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Random increase of complexity [Gould, 1989]

Asymmetric Diffusion Biased Increase


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How to understand increasing complexity?

No way to explain this in terms of random mutations (only):

1. DNAs (genotype) random mutations statistically haveprobability 0 to cause globally increasing complexity ofphenotype (examples: mayfly (ephemeral); equus[Longo,Tendero, 2007])

2. Darwins evolution is selection of the incompatible(the bestmakes no general sense)

3. Greater probabilities ofsurvival and reproduction do not implygreatercomplexity (bacteria, lizard)

[Maynard-Smith, 1969]

Gould's idea: symmetry breaking in a diffusion


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Mathematical analysis as a distribution of

Biomass (density) over Complexity (bio-organization)

Derive Goulds empirical curb from

general (mathematical) principles, specify the phase space explicit (and correct) the time dependenceWrite a suitable diffusion equation inspired by Schrdinger

operatorial approach

Note: any diffusion is based on random paths!

F. Bailly, G. Longo.Biological organization and anti-entropy. IBS, 17-1, 2009


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Morphological Complexity along

phylogenesis and embryogenesis

Specify (quantify) Goulds informal complexity as morphologicalcomplexity K

K= Kc + Km + Kf( + + = 1)

Kc

(combinatorial complexity) = cellular combinatorics asdifferentiations between cellular lineages (tissues)

Km (phenotipic complexity) = topological forms and structures(e.g., connexity and fractal structures)

Kf (functional complexity) = metabolic relations, neuronal andcellular (interaction) networks


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Recall: Dualities in Physics vs Biology

Physics:energy as operatorHf, time as parameterf(t,x)(Schrdingers approach);

Biology: energy as parameter, time as operator

(= entropy associated to all irreversible processes: the two

observable forms of time irreversibility[Bailly, Longo, 2009])

Main idea: define biological complexity Kas anti-entropy

( negentropy -S, since S + -S = 0 andKsensitive to coding)

(Caenorhabditis Elegans, see [Bailly, Longo, 2009])


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The theoretical frame: analogies

.... by a conceptual analogy with Quantum Physics:

In Quantum Physics (a wave diffusion in Hilbert Spaces):

The determination is a dynamics of a law of probability:ih /t = h22 /x2 + v (Schrdinger Eq.)

In our approach to Complexity inBiological Evolution:

The determination is a dynamics of apotential of variability:f /t = Db

2f/K2 + bf

A diffusion equation, in which spaces? What is f?

Random walks


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The theoretical frame: dualities

.... by conceptual dualities with Quantum Physics:

In Quantum Physics (Schrdinger equation):

Energy is an operator,H(f), the main physical observable. Time is aparameter,f(x, t),

In our approach to Complexity inBiological Evolution:

Time is an operator, identified with entropy production Energy is aparameter,f(x, e) (e.g. energy as bio-mass in

scaling-allometric equations: Q = kM1/n)

Ourf is the density of bio-mass over complexity K (and time t ):

m(t, K)


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Some technicalities: how to derive the diffusion equation

Schrdingers operatorialapproach:

from total energy E = p2/2m + V(x) (1)with V(x) potential

(e.g. E = p2/2m + kx2/2, the harmonic oscillator)

associate E ih/t and p ih/x (operators)andobtain:

ih /t = h22 /x2 + v (Schrdinger Eq.)

Our operatorial approach applies to T, apower:

thus T is a product of forces by fluxes ( ~ the square of a mass)

T = bM2 + T0b (2) (the analog of (1))

61


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A diffusion equation:

m/t = Db2m/K2 + bm(t,K) (3)

A solution

m(t,K) = (A/t) exp(at)exp(-K2/4Dt)

models Goulds asymmetric diagram for Complexity in

Evolution (diffusion random paths), also along time :(biomass and the left wall for complexity, archeobacteria original formation)

F. Bailly, G. Longo.Biological Organization and Anti-Entropy

Next picture by Mal Montevil:62


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(Implementation by Mal Montevil; ponctuated equilibria smoothed out)


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LogicalSummary of our viewPhysical vs. Biological Theories

in Bailly-Longo three (correlated) approaches:

1 - a two dimensional time (not linear time), with M. Montevil, to appear.

2 - extendedcriticality(a physical oxymore), JBS, 16, 2, 2008.

3 - organization or complexity as anti-entropy,JBS, 17, 1, 2009.

Common point to the approaches in 1, 2 and 3:

Strict Consistent extensions, in the sense of Logic, not

incompatible with current physical theories, but not reducible

(conservative?):

1: collapse the extra dimension (a time bifurcation);2: contract the extension of criticality (from interval to point);

3:= instead of (anti-entropy goes to 0)


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More methodological lessons from Physics

H. Weyl on the epistemological lesson of Relativity Theory:Objective knowledge begins when the subject explicitly lays the

reference system and the measure

(and theirrelations by Gauge Theory)

Quantum Physics relativizes even further the subject-object relation

(a polarity or entanglement): base or reference system constitutedin measure

In Biology:

is it a matter of the choice even of the observables andparameters? (complexity, time as a 2-dimensional operator)

within changing phase spaces? Randomness? Paulis theorem and the lower bound of time


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More on:

From Physics to Biology by

Conceptual Dualities

(or: changingprinciples by dualities)


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SUMMARY

Physical variation vs. biologicalvariability (individuation)

Physics: generic (invariant) objects andspecific trajectoires (geodetics)


Physics: energy as operator, time as parameter;

Biology: time as operator(Prigogine),energy asparameter

Physics: critical transitions are singularities (a point);

Biology: : Extended critical situations w.r. to control parameters

Physics: determistic impredictibility or quantum indetermination within a givenphase space (entangled probabilities)

Biology:Intrinsicindetermination due to change of the phase space

Bailly F., Longo G. Mathematics and Natural Sciences. The physical singularity of Life. ImperialColl. Press/World Sci., 2011 (in French:Hermann, Paris, 2006)

Some references


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Some references

http://www.di.ens.fr/users/longo orGoogle: Giuseppe Longo

Bailly F., Longo G. Mathematics and Natural Sciences. The physicalsingularity of Life. Imperial Coll. Press/World Sci., 2011 (in French:Hermann, Paris, 2006).

Bailly F., Longo G., M. Montevil. 2-dimensional geometry for biological time.To appear inProgress in Biophysics and Molecular Biology, 2011.

Bailly F., Longo G. Extended Critical Situations, in J. of Biological Systems,Vol. 16, No. 2, 1-28, 2008.

Bailly F., Longo G.Biological Organization and Anti-Entropy, in J. ofBiological Systems, Vol. 17, n. 1, pp. 63-96, 2009.

Longo G. Quest-ce que ltat vivant de la matire? Criticit tendue,gomtrie du temps, anti-entropie.

Confrence invit

, Seoul, (South Korea), November, 2010.

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