# A Deep unity between scientific disciplines

Cedric Gaucherel

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Cedric Gaucherel. A Deep unity between scientific disciplines. Open Journal of Philosophy, 2013, 3 (3), pp.413-421. 10.4236/ojpp.2013.33061. hal-01837350

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# A Deep Unity between Scientific Disciplines

Cédric Gaucherel¹,²

¹French Institute of Pondicherry, IFP-CNRS, Pondicherry, India

²UMR AMAP-INRA, Montpellier, France

Email: cedric.gaucherel@ifpindia.org

Received March 21st, 2013; revised April 21st, 2013; accepted May 1st, 2013

Copyright © 2013 Cédric Gaucherel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Are scientific disciplines really different? This question often crystallizes into the old debate: Are Physics and Biology different? If Physics and Biology worked on highly different entities (objects), or if they had highly different methods, it would be straightforward to close the debate by a negative answer. However, if we cannot identify any differences, we should explore more deeply the status of the laws found in Physics and questioned in Biology. By slightly modifying the definition of what is a law, I argue here that both disciplines possess some laws exhibiting various “degrees of confirmation”. I finally propose explanations for why P and B give the illusion differing radically, although they both belong to the same continuum of a unified scientific domain.

**Keywords:** Scientific Law; Unicity; Contingency; Universality; Neutral Model; Evolution; Gravitation.

## Introduction

The old debate on whether Physics (P) and Biology (B) belong to the same culture has recently been reactivated. Here by culture, we are not thinking to the social part of the scientific activity, rather than to the deep nature of their studied objects. Some scientists claim that physicists seek simplicity in universal laws, while biologists revel in complex interdependencies and specific processes (Keller, 2007). Still others admit these differences in method, but claim that they hold for both physical and biological studies (Harte, 2002). In this paper, I argue that P and B do not differ, that, in particular, physical and biological entities are not different in nature, and that physical and biological disciplines use a similar method (Pombo et al., 2012). P and B both build some laws to interpret their observations. The central argument of this paper proposes a slightly modified definition of what is a law to accommodate their possible differences. I finally propose an explanation of why P and B often give the illusion differing radically between themselves.

There is no doubt that P searches for laws, a law being viewed in the broad sense as a statement expressing an observed regularity. I will not debate the relevance of laws (Cartwright, 1983), but instead treat them as useful models of reality to explore possible differences between P and B. According to Carnap, in particular, a scientific law is said to be “universal” if it is a principle that is observed to operate at all times and all places, without exception (Carnap, 1974). Particle collisions conserve the total energy of the system. This is always observed, and there are no exceptions to it. It is a universal law. It is less clear that B possesses such universal laws.

When subjected to careful scrutiny, it seems that P does not have universal laws either. Quantum theory indeed highlights processes that are intrinsically probabilistic, meaning thereby that we cannot formulate a deterministic statement based on observations. This limitation is not a result of our ignorance, as

was shown by W. Heisenberg, but rather a result of the intrinsic structure of our world. This view suggested a need to define what has been called “statistical” laws, which assert that regularity occurs only in a certain percentage of cases instead of in all cases. Even with this less constraining definition, are we allowed to assert that B has any laws at all that are applicable? This is the main question addressed in this paper, the central idea being that any differences in (or in the use of) laws in B and P would definitively discriminate these two disciplines.

For this reason, this paper proceeds in three successive stages. In the first part, it examines, with examples, whether physical and biological entities are similar in nature. Living systems are often perceived as unique, contingent (i.e. dependent) on events, and ultimately irreversible entities. Such a view can lead to a feeling that the functioning of living systems is less universal (i.e. less systematic) than is that of inert systems. If true, either of these properties would be sufficient to attest to a radical difference between P and B. Another way P and B might differ relates to the specific methods they use. One of the most commonly used scientific methods today is the hypothetico-deductive model, formulating a hypothesis and validating (or invalidating) it on the basis of experiments. Practically, physicists and other scientists often use “neutral models” to verify whether their models (intentionally forgetting the process being studied) correctly represent observations or not. The steadily growing use of neutral models in B will help us to study hypothetico-deductive methods common to P and B. The type of method used in each discipline, and the related considerations, make up the substance of the second part.

In the third and last stage, I will discuss the two previous arguments (namely, whether physical and biological entities and methods are similar) in order to better identify the remaining specificities of P and B. In particular, it will be necessary here to explore the perceptions we have of P and B processes. The
arguments presented in the previous stage highlight the crucial
difference between the probability of a process to occur, and
the probability of its associated law to exist. Following Carnap
(1974), I suggest here a resort to the concept of a "probabilis-
tic" law, rather than a "universal" law, to analyze the "degree of
confirmation" we have from the laws being applied. Such a
probabilistic view of P and B suggests moving the qualitative
differences often be perceived between the two disciplines into
the quantitative continuum of a unique scientific domain. More-
over, this conceptual continuum may be explained and justified
by the remaining differences in nature as discussed above.

Are P and B Different in Their Nature?

At first sight, the inert entities and the living entities studied
by P and B respectively seem to differ highly in their nature. If
true, this assertion would support acceptance of different scien-
tific disciplines for their respective studies. Yet, what do we
mean when we talk about the nature of entities? P and B are
wide domains of research, studying entities as varied as miner-
als or stones on the one hand, and cells or individuals on the
other hand. I will not address the Holism-Reductionism debate
here, which is out of the scope of this paper and would bring a
sterile view of P and B differences (Trepl & Voigt, 2011). We
need to list some of the most important properties defining
these entities and their natures in order to examine whether they
are found to be similar in P and B.

One of the most important properties of B objects that has
been cited in the past is their unicity (Pesic, 2002). A cell or an
individual always exhibits sharp differences from its neighbor,
although a star or a particle is supposedly similar to its neighbor.
I will show in the next sub-section that this somewhat simplis-
tic view of unicity is not a systematic rule. A second important
property that apparently differs between physical entities and
biological entities is the contingency involved in their construc-
tion (Gould, 1989). Contingency is the fact that we observe an
entity as it is, mainly (or only) because of a succession of
events that may not have occurred. We often have the feeling,
although not yet demonstrated, that most living entities are the
result of a combination of singular events. These events, and no
other events, have occurred. I will show that this is true in some
cases, and false in others.

Furthermore, unicity and contingency may be two facets of
the same important property. An object that is contingent, such
as the brain of an individual, is also unique, in that it would
certainly be necessary to replicate rigorously the same sequence
of events as must have been followed in the original if one were
to wish to re-construct the same brain. Could we imagine dif-
ferent events sometimes leading to exactly the same entity? On
the other hand, it is highly probable for a unique entity to be the
result of contingent events, as the events of its construction
would inevitably lead to the same entity. These events, if it
should ever be possible to make them occur again, would lead
to an entity not unique any more. So, unicity and contingency
are not identical concepts, but they remain closely linked due to
a third hidden property: irreversibility. Indeed, specific events
are determinant in some entity construction, especially in case
of irreversible events (Nicolis & Prigogine, 1977). In the case
of reversible events, the entity depending on them can system-
atically come back to its previous state, and is therefore no
more either contingent or unique.

B and P: Unicity

First, the fact that Life is unique (we know only one single
sample of it!) suggested to some biologists to highlight the
specificity of B, and to reject the Popperian view of scientific
research in evolutionary B (Mayr, 2004). Indeed, if we knew of
a second sample of Life, we would start to be able to refute
some hypotheses based on the Life we know. In astrophysics,
scientists similarly handle a unique entity: the Universe. This
remark is true at finer scales too, as Earth (or at least the geo-
sphere component of it) is a unique entity studied by geophysi-
cists.

Yet, we all know that these assertions are frequently debated. For example, it has been argued that each trait convergence (similar traits observed between different species) is another confirmation that Evolution acts in a reproducible manner in similar conditions (Morris, 2010). While we are on the way to discovering planets similar to Earth, we are not sure how similar they will be. Furthermore, there are active discussions on about multiverses, challenging the usual limited definition of the universe (Tegmark, 2003). On the other hand, the unicity that may be true for evolutionary B is basically false in molecular or cell B. There exist as many molecules and as many cells as necessary to test biological hypotheses. This observation is very similar to the one that there exist plenty of rigorously similar particles and nuclear entities to be studied in high-energy P.

Regardless of what elements might be true, and what might
not, what is important for our discussion are the similarities be-
tween physical and biological entities. For the sake of the dis-
cussion, I question here whether this dichotomy between unic-
ity and multiplicity of entities is partly related to scale or not.
At scales larger than our human scale (e.g. meters to kilometers
and seconds to years), Life and the Universe appear unique. At
least, this seems to be the case to our knowledge, and our
knowledge is strongly limited at higher scales. Entities at lower
scales can be found in many samples, down to cells and parti-
cles. At intermediate human scales, geophysics and ecology
offer interesting similarities too. They possess an intermediate
status ranging from unique Earth geosphere and biosphere
(Lovelock, 2003), through a few plates and continents, down to
a multiplicity of geophysical systems and ecosystems.

Finally, entities with inert properties and those with living
properties appear to exhibit very similar natures, both covering
the whole range of diversity, from a unique entity to high num-
bers of replicates (of events). Therefore, it seems that the com-
monly observed acceptance of unicity of physical and biologi-
cal entities is more closely linked to their associated scales than
to their domains.

B and P Contingency

Secondly, the life sciences often present contingency as a
property responsible for the specificities of biological entities
(Gould, 1989). Hence, we may observe living entities as they
are only due to a combination of isolated and improbable events
(sometimes called "accidents"). These events may be random
or not. Most biological entities are supposed to be contingent.
A cell or an individual is highly dependent upon events and
environmental states leading to its construction. At the same
time, many physical entities may be contingent too. Plate tec-
tonics leads to a contingent geology on earth, precisely the one
we observe today. Planetary astrophysics, studying how the so-
lar system has formed, is also a clear example of contingent
physical entities. These systems would not have been the same
with a poorer composition of the surrounding environment or,
on a longer time scale, with another date of the Universe's for-
mation.

Here again, there is a debate about these possible contingent
entities. For example, it has been recently suggested that evolu-
tionary trait convergences are confirmations that Evolution acts
in a similar manner when exposed to similar conditions (Morris,
2010). The recent discoveries of extrasolar planets in distant
planetary systems also highlight the possibility that a different
set of astrophysical events may lead to approximately similar
entities, thus being less and less contingent (Beaulieu et al.,
2006).

Whatever the degree of contingency in physical and biologi-
cal entities, the property appears to be present in these domains.
Finally, P and B both study entities and events that have similar
properties and similar requirements of universality. These enti-
ties may sometimes be unique, sometimes not; they may some-
times be contingent, sometimes not. Contingency and unicity
could be two facets of the same property: systems symbolizing
unicity, such as Life or the Universe, are clearly a result of a
succession of highly improbable events. It must also be re-
membered that events exhibiting these properties are usually
irreversible events. The next subsection explores this critical
property of irreversibility to show up possible differences be-
tween P and B.

Irreversibility

Most physical events appear to be reversible. In interactions
among particles and those among stars, the equations governing
their movements keep the same shape when time is reversed.
Yet, our experience with everyday physical events tells us that
these macroscale events are irreversible. The decay of a fruit
and the mixing of milk in a cup of coffee are typical and famil-
iar examples. It is even easier to find irreversible events in B,
such as cell mitosis or the birth of an individual. Is such simi-
larity between P and B real or only apparent? And in the case of
an apparent similarity, why is there a difference?

Irreversibility is not a property of time: it is rather a property
of the objects and the events studied. A wide range of physical
processes have been discovered to be irreversible, since New-
ton's pioneering work on viscosity. We might also mention
Coulomb's law, the Navier-Stokes equations, the laws of ther-
modynamics, Fick's laws of diffusion, the Joule effect, etc.
Scientists waited for the thermodynamic synthesis, in the early
19th century, by S. Carnot and R. Clausius, to understand this
observation as a natural tendency for closed systems to go to-
wards disorder (i.e. the second law of thermodynamics). So,
although many physical processes appear to be reversible, ire-
versible processes at macroscale are common too. More re-
cently, in the second half of the 20th century, physical ire-
versible processes have also been observed at microscale, in
particle physics experiments on matter's symmetry. Time's
symmetry, as also the parity and charge symmetries, have been
violated in the now famous CP (charge-parity) violation ex-
periment by J. Cronin and V. Fitch in 1964.

So, are physical events reversible or not? L. Boltzmann al-
ready suggested a century ago how to explain this apparent
paradox. Considering that a macroscale entity or event implies
a huge number of constitutive entities, it would seem sensible

to adopt a probabilistic view to understand the entities' dynam-
ics. A reversible process is in theory always possible, whatever
its scale. Yet, this large number of constitutive macroscale enti-
ties is the only reason why such a reversible change is highly
improbable (Balian, 1991). One liter of water contains at least
1025 molecules, a far higher count than physics experiments
yield for a comparable measure of particles. The probability for
a system to go back to its previous state is infinitesimal in case
of macroscale systems, varying inversely as the number of its
components. In another context, H. Poincaré had quite graphi-
cally suggested that we might have to wait far longer than the
age of the Universe for a chance to be able to observe such a
reversible change at macroscale.

Finally, B processes often appear irreversible mainly due to
their high number of interacting components. They possess a
very low and even negligible probability to revert to their pre-
vious state (Nicolis & Prigogine, 1977). In this context, each
event plays an important role in the entity's construction and
fate. Such entities are unique and are contingent. Some physical
processes are irreversible too. For example, Earth's components
are far more numerous than those encountered in reversible
microscale experiments. Irreversibility is found in both P and B.
This appears obvious as both domains study entities that have
variously a high number or a low number of components, thus
variously exhibiting unique, contingent and irreversible charac-
teristics, whatever their scale.

The Scale Issue

Microscale events are reversible. At the same time, we have
seen that irreversible events are frequently found at intermedi-
ate scales, e.g. at human scales. Hence, we may wonder in par-
ticular why stars, spanning very large spatial and temporal
scales and with an enormous number of particle components,
should again behave in a reversible way. Their growth and
movement equations are indeed symmetrical with respect to
time. To understand this, it is necessary to analyze the four fun-
damental interactions found in P. Strong and weak nuclear
forces only concern very fine scales due to their very short
interaction ranges (between 10 - 18 m and 10 - 15 m). Despite
this, they are much stronger than the gravity (1025 to 1038
times more) governing the movements of stars and galaxies.
Gravity has an infinite range of influence. The electromagnetic
force, also having an infinite range of influence, does not play a
role at such large scales (planetary systems range in scale from
1012 m to 1014 m). Unlike the gravitational force, the electro-
magnetic force can be absorbed, transformed, or deflected.
Ratios of the measures of the strength of the forces to the sizes
of the associated entities for gravitation are very similar to the
corresponding ratios for nuclear forces (both strong and weak).
A planetary system is approximately 1022 to 1026 times larger
than an atomic system, while its associated fundamental forces
are approximately 1025 to 1038 times stronger.

This scaling ratio partly explains why planetary systems be-
have similarly to atomic systems, although both act under dif-
ferent fundamental forces. The ranges of their interaction com-
bined to their relative strengths are probably responsible for
their similarity. The gravitation force has the effect of reducing
the interactions among the large and massive entities under its
influence by separating those entities in such a way that they
behave as if they were new, coherent and independent or unre-
lated entities. In a sense, a star behaves under gravitation much
as a particle would behave under nuclear forces. The electro-
magnetic force may have a similar effect, but as it can be de-
flected, it loses its influence at larger scales. Indeed, entities
located between two other entities hide their respective influ-
ences, and indirectly reduce the force range. Hence, gravitation
affects matter at large scales, and ceases to be perceptible at
finer scales and on entities at such scales. This is not the case
with entities found at intermediate scales, such as our close en-
vironment, which is governed by the fundamental force of elec-
tromagnetism and, in a reduced measure, by the other forces. I
suggest that these differences could partly explain why the elec-
tromagnetic force increases entity interactions and favors irre-
versible events and entities.

Finally, it is worth observing that both P and B cover almost
all scales. Hence, we can now assert that both exhibit in their
own individual manner the complementary faces of the nature
of entities.

Are P and B Different in Their Methods?

If physical and biological entities are similar in nature, do
their associated disciplines also work in similar ways? We need
to scrutinize the specific methods or approaches of these do-
mains before we are able to answer this question. Now, how do
scientists usually go about achieving an understanding of an
event, and providing a demonstration that there is a process that
drives the functioning of physical and biological entities? When
we talk of a process, we mean something that is happening on
its own, by chance as it were. Although chance itself might be
considered a process (called random), this process possesses a
nature very different from that of non-random processes. Fur-
thermore, the inherent stochasticity of our world adds varying
amounts of noise to every process, thus blurring it. Only an un-
covering of such a veil will allow us to see the process at work
behind the noise.

A simple and easy-to-manage method for this purpose would
be to formulate a hypothesis stating that the supposed process
in question is present, and that it could be differentiated from a
purely random process, under certain conditions. We would, of
course, identify the conditions necessary to succeed in control-
ling (i.e. reducing) the inherent stochasticity of the process. We
would know when such conditions occur, and when they do not
occur, and we would know their nature. Such a method of
searching for a hidden process is the familiar process of choos-
ing a null hypothesis. A Neutral Model (NM) is a model that
deliberately avoids a process of the studied entity or event, with
the idea that it actually drives it (Nitecki & Hoffman, 1987).
When not invalidated, the NM suggests that chance may be a
"process" sufficient to drive and to explain the observed entity.
Conversely, when the NM is invalidated (i.e. rejected or falsi-
fied), it reinforces our belief that the process being studied is at
work. Ultimately, the NM helps to define new alternative hy-
potheses, foundations of a new class of processes.

P has been using NM for a long time (Fisher, 1966). Chance
being ubiquitous in physical processes, and because of the huge
amounts of data provided by instruments and sensors in P, it
has become common, and meaningful, to use NM to test hy-
potheses. The recent appearance of powerful computers capable
of analyzing the very large volumes of data generated has also
contributed to enhancing the use of NM. As far back as thirty
years ago, B's efforts to develop NM were documented
(Nitecki & Hoffman, 1987), and the progressive increase in

collected data in the biological sciences, as well as the recog-
nized influence of stochasticity, together present a strong ar-
gument in favor of NM use in this domain. These two factors
may not explain, by themselves, the recent spread of NM in B.
Still, that fact provides a strong clue, in my opinion, that P and
B adopt a similar scientific method.

Neutral Models in Biology

The growing recourse to NM in the life sciences in recent
decades is a clear departure from past practice. The variability
of neutrality possible in a neutral model enables one to develop
increasingly chance-driven models, and choose from among
them the most parsimonious model, ensuring, of course, that it
has not been invalidated. The importance given to chance be-
comes obvious in this approach. Compared to P, B today has
many NM that have not yet been rejected, thus underlining the
dominant role of chance in biological and ecological processes,
as illustrated below.

The neutral-community theory proposes that species of the
same community are not distributed according to their niche
requirements (i.e. the habitat and ability to use resources), but
according to random processes of dispersal limitation and game
theory interactions (Hubbell, 2001). Species might all be ecol-
ogically equivalent in terms of migration and extinction proc-
esses. Although still debated, this hypothesis has not been
completely rejected to date (Chase, 2005). Interestingly, spe-
cialists have started to believe that this view may be true at
some scales (functional groups and biogeographic regions), but
false at others (for example, at landscape scales). This anomaly
may be due to habitat heterogeneities or to other spatial proper-
ties at intermediate scales.

Landscape-neutral models have been developed to simulate
landscape structures and landscape functioning without explic-
itly using the processes and rules usually favored to generate
these landscapes (Gardner et al., 1987). Landscape-neutral mo-
dels attempt to generate natural as well as anthropogenic land-
scapes, and grid-based or vector-based landscapes (Gaucherel
et al., 2006). But how far are observed landscapes from a neu-
trally-generated landscape? It seems today that almost-random
statistical rules are often capable of building a high diversity of
relatively realistic landscapes.

Correlated random walks appear to be the best strategy to use
in searching for a particular resource when its distribution is
unknown. In a similar spirit, indeed, several NM have been
developed to improve our understanding of animal movements
(i.e. trajectories). It has been proposed that most animal move-
ments are equivalent to some weighted random walks called
Lévy flights and Lévy walks (Viswanathan et al., 1999). This
observation starts to be wrong when resources are aggregated in
patches, suggesting that animals move more straightforwardly
between resource patches and more erratically inside patches
(Benhamou, 2007). Here again, we quantify with the help of
this NM how far from random walks animals move. Such es-
timation between various NM appears to help in quantifying the
role of stochasticity in these processes.

The neutral genetic theory proposes that Life experiences a
genetic drift when some neutral genes (i.e. genes without phe-
notypic expression) are fixed by chance in a genome (Kimura,
1983). We know that evolution of Life is a complex combina-
tion of various forces among which some are neutral. Hence,
these genes are not fixed by a natural selection process, but
rather by a neutral process. Stochasticity appears here to be
systematically associated with evolutionary processes.

Neutral Models: On the Way to Build a Law

Finally, NM are not restricted to specific scales. NM in the
life sciences range from broad scales to fine scales over a wide
sweep of living entities, often crossing many scales simultane-
ously. Furthermore, self-similar NM, characterized by scale-
invariant (also called fractal) properties of the studied entity,
are surprisingly ubiquitous in the life sciences. For example, the
lungs, most tree and phytoplankton species and some vegeta-
tion or land cover patterns have been discovered to be self-
similar (Scanlon et al., 2007; Gaucherel, 2011). Self-similar
patterns highlight processes that are uniform across scales, over
several magnitudes of orders. They are linear in a logarithmic
plot, the so-called power laws, indicating that these patterns
have no peculiar scale. Such perfect NM are always false, in a
sense, as are all models, but they carry part of the real nature of
the entities studied.

Which part of it? Self-similar NM capture a kind of system
self-organization that is not yet understood. They tell almost
nothing about the entities' functioning and are not able to ex-
plain processes generating the observed scaling pattern (Halley
et al., 2004). Yet, many scientists think that ubiquitous self-
similar patterns pave the way to a more universal self-organi-
zation principle of living entities (Kauffman, 1993). The self-
organization principle hypothesizes that many processes may
be interpreted through a kind of optimizing principle, some-
times called preferential attachment (D'Souza et al., 2007;
Barabasi & Albert, 1999).

This attempt too is a good example of what could one day
become a law, or at least a principle, in B. NM are not laws but,
when not rejected, they help us to understand by the neutral
hypothesis the widest range of observations in a specific field.
In this case, chance is sufficient to explain the observation.
When NM are rejected, they help to define a new alternative
hypothesis, new processes potentially serving as foundations of
a natural law. Such a new hypothesis may progressively be-
come a law, in the sense that every single observation in the
discipline could then be interpreted in the context of this law.
The following part of this paper intends to explore in more
detail what a law is and which differences may exist between
physical and biological natural laws. Finally, it appears that
both P and B are largely using NM to test their hypotheses.
This is a strong clue that they appear to have a similar way of
working. They are very similar, and this similarity is becoming
increasingly apparent in their methods and in relation to their
construction of laws.

Differences between B and P: Universality

We have so far not identified in the course of our arguments
any significant differences between P and B, either in the nature
of their entities, or in their scientific methods. Yet, we all have
the feeling that P and B differ. For example, we have the intuit-
tive impression that P encounters more “universal” processes
and events than B does. Would there be a realistic basis for
such an impression?

For the purpose of dealing with questions such as this, we
need to have more accurate definitions and to determine whe-
ther they are appropriate or not. A process is an outcome of

chance. When a (possibly unknown) process is recurrent and
never fails, we usually call it a principle or a law. Newton's law
of universal gravitation and the laws of thermodynamics are
familiar examples of physical laws. Laws differ from theories
in that they do not give any process and they do not formalize
this process of their associated events. As laws are based on
empirical constructions, i.e. observations, they are often found
to be false when extrapolated. Newton's law of gravitation only
applies in weak gravitational fields, and the second law of
thermodynamics appears to be violated by random fluctuations
of the system close to equilibrium (Evans et al., 1993). At the
same time, I also have the feeling that theoretical entities are
more valid than laws (Cartwright, 1983), as they persist over a
longer span of time, but I still maintain that laws remain useful
tools with which to understand the scientific representations of
reality that we build.

Does this definition help us to understand what a universal
law is? When all observations of a field are explained by a par-
ticular law, it may be called a “universal law” (Carnap, 1974).
A universal law suffers no exception; never. Yet, some princi-
ples may be valid in most cases (i.e. in a certain percentage of
observations), but not in all. They may not be called universal
laws, but then do we have a term for such almost-always-valid
principles? We must be careful here: what is usually called a
“statistical law” concerns the probability of the event or the
process involved, and not the confidence we have in the related
principle or law (Carnap, 1974). This subjective feeling we
have about universal laws is the main reason behind the inher-
ent and definitive differences between the spirit, and thus in the
nature, of P and those of B. We may be tempted to imagine that
because physical laws are universal, we can search for some
universal explanation of physical processes or events. We may
similarly tend to believe that because biological laws are not
universal, we do not need to search for some universal explana-
tion, but instead to study processes and events case by case. I
intend to show in the following discussion that such differences
in the spirit are illusory.

Are P and B Different at All?

Do universal laws exist in B? The process of natural selec-
tion or, more generally, the forces of evolution, appear to be a
universal explanation of Life, as every living organism is sub-
ject to this “law”. Indeed, although C. Darwin never called the
principle he discovered a “law”, the description would fit
snugly into our previous definition of the term, as it drives
every living entity. G. Mendel’s genetic inheritance law also is
a simple and generic principle of living entities, all of them
carrying genetic information. Yet, these laws are not universal.
The genetic inheritance law is a statistical law, because it ex-
presses that sexual individuals depend on their parents’ charac-
teristics. Also, epigenetic and other Lamarckian-like processes
are found to blur the clear view of a universal natural-selection
law by adding to reproduction and evolution some processes
that do not fit perfectly the variation-selection principle (Gau-
cherel & Jensen, 2012; Por, 2006). Further, we admit that the
processes and the laws we are talking about are the founda-
tions of the observed events or entities, and cannot be deduced
from some simpler processes or laws.

A careful scrutiny of the related facts tells us that both the
biological laws mentioned show exceptions. Gene expressions
sometimes depend on their environment (and not only on natu-
ral selection) when epigenetic processes occur, and may possi-
bly be fixed across generations. Such exceptions to the initial
biological laws seem very similar in nature to those of anoma-
lies in the precession of the perihelion of Mercury first ex-
plained by A. Einstein in 1915 and later confirmed by Edding-
ton's observations in 1919. These observations highlight the
limits of the Newtonian law of gravitation, and encouraged
some scientists to develop the general relativity theory. They
demonstrate that B adopts similar ways of thinking to those that
P does. Yet again, it seems intuitive that finding universal prin-
ciples in B is harder and needs longer time than is the case in P
(Keller, 2007).

Symmetrically, P is also experiencing studies on specific
processes without seeking universality. Indeed, we saw that P is
using methods that are focusing on a specific process and a
specific site when necessary. Geophysical processes, for exam-
ple, when interpreting a specific tsunami or eruption, adopt
very similar methods of study to those in a study of a specific
cell division or protein production. However, these methods are
hypothetico-deductive. Such examples are local and statistical,
not universal. Yet, instead of biological examples, they may
serve as bases on which to build inferences on more general
principles. For example, the non-linear dynamic involved in the
physical examples mentioned is a more generic principle that
may be studied and developed for its possible universality.

Finally, these observations highlight the unclear definition
we have of what is a law. They also illustrate the fact that a law
is valid for a specific domain and at a specific date, and may be
later replaced by a more accurate and more universal principle.
As for theories explored by T. Kuhn, laws seem to carry for a
while some paradigms that ultimately shift when the initial law
is updated. Why should it be different in B from what it is in P?
Natural selection, for example, might be a powerful law for a
long time, then be modified and improved when we observe
anomalies difficult to explain with its former version. This is
exactly what Neo-Darwinism (with genetics and then epige-
netic) brought to the pioneering work of Darwin.

Redefinition of a Process

In order to bring to light possible differences between P and B processes, or between P and B laws, we need today to revisit their insufficient definitions. Let's explore again what is a process and in which cases it progressively leads to a law. We have explained how a recurrent process starts defining a principle (or a law), and how a law without any exception defines a universal law. Neutral models are often of great help when they differentiate a process from a chance occurrence, i.e. when they detect any departures from neutrality.

Neutrality exhibits a wide range of facets. The first evidence
of this fact appears in the observation that macroscale neutrality
occurs with a purely neutral process, or arises as a limiting
distribution by the aggregation of small-scale, non-random pro-
cesses. In this case, non-neutral fluctuations tend to cancel each
other out in the aggregate. S. A. Frank has clearly explained
how neutral patterns describe patterns of nature that follow
from simple constraints on information (Frank, 2009). Utilizing
the powerful method of maximum entropy, he shows that each
neutral generative model (Gaussian, exponential or geometric
patterns) is a special case of a wider domain of the same neutral
pattern. For example, any aggregation of processes that pre-
serves information only about the mean and the variance tends

to the Gaussian pattern.

Many patterns and processes in nature arise from limiting
distributions. These neutral generative models form what are
usually called probabilistic laws, for the reason that for a purely
random process and a great number of events, the related dis-
tributions suffer almost no departure; the related laws suffer
almost no exception. We should be careful here: these probabil-
ity distributions are completely different from the natural laws
previously discussed. Probabilistic laws concern chance (random
processes); natural laws concern what is all but chance! In
a sense, natural laws arise from neutral laws, as a clear depart-
ure from them: they are not random any more. Despite this
difference, the basic concept behind a law, a pattern into which
every process fits, is present in both cases.

Natural and probabilistic laws have another critical differ-
ence: only probabilistic laws exhibit a distance to the idealistic
and pure (i.e. without departure) law. Testing a law indeed is
rather a discrete task. In the case of a probabilistic law, the
confidence level computed regarding to the known idealistic
law quantifies this "distance" to it, i.e. how far from the pure
(theoretical) law the observation is. In contrast, a natural law
either exists or does not exist; it cannot be "in between". This
definition of a law is appropriate for a universal law. But why
should we not propose another definition inspired by probabil-
istic laws of what is a non-universal law? Why should we not
interpret the rare failures of a universal law as a distance to the
(supposed) universal law itself?

Redefinition of a Law

Suppose now we have correctly identified a non-random pro-
cess at work. If such a process occurs recurrently under similar
conditions, we may start to believe that an invariant principle is
taking place here. We may observe some exceptions to this
principle, say, with a random process occasionally taking the
place of this non-random process. For example, the off-spring's
gender is defined on the basis of their parents' genders, but this
gender may occasionally change during the fetus' development,
due to external factors. This is the case of reptile sex, when
eggs are developing under various environmental temperatures.
Finally, when the principle is systematic, we call it a law. With
such a definition, Mendel's genetic inheritance law is no more a
universal law, because it does not take into account environ-
mental factors that can perturb it, because it is "almost" always
true for sexual reproduction.

When we have in mind a biological law, such as the so-called
Mendel's law, we do not think about a universal law, but rather
a law against which some processes might be found. This ex-
ample highlights a critical difference between variations found
in processes and variations found in laws. Carnap is a pioneer
philosopher having insisted on this difference, although not in
modern terms (Carnap, 1974). A process is always observed to
possess some stochasticity, either because of inherent stochas-
ticity, or because of sampling stochasticity. In other words, a
noise process is detectable in so far as it is possible to reduce
enough noise around it. But the process is always present. This
analysis is related to probabilistic laws, as the experimenter has
to manage the chance superimposed on the present process. In
other cases, the process might be present or not, depending on
the various internal and external factors of the entity involved.
The consequent analysis is here related to the universality of the
law, rather than to the chance element present in the process.
Therefore, the associated law is universal or not, according as the process has a systematic presence or not. However, when the process is systematically present except in one isolated case, could we not say that it is “almost” universal?

Two types of failure of a process can be found in nature. A non-random process might be more or less visible, emerging from a noisy background, and leading to the illusion that the principle is not a strong principle. Also, such a process is occasionally replaced by, and not just hidden by, a random process (or another process). It may have a certain probability to occur and to be observed. I propose here that it is possible to interpret the latter type of failure with a probabilistic view similar to the former type of failure, but at the law level instead of at the process level. Laws are universal when they suffer absolutely no exception, but none of them are truly universal. Most of them are only rarely violated by the absence of their related process, and the replacement of it by another process. Hence, they have a probability of validity of less than unity. I suggest that every law possesses a probabilistic nature, with a probability to be valid that could be defined as equal to unity in the case of universal laws.

Carnap (1974) uses the notion of logical probability (also called inductive probability), which he borrowed from John Maynard Keynes, to handle the statement that a law could be probabilistic instead of universal. Carnap asks: “How well established is the law?” He then provides a possible answer: “This hypothesis is confirmed to degree .8 on the basis of the available evidence”, which thus “expresses a logical relation between a sentence that states the evidence and a sentence that states the hypothesis”. This form of probability is quite different from the previously mentioned statistical probabilities used to control the stochasticity of a process. With logical probability, we are no longer talking about its related process, but rather about its law and the confidence (called “degree of confirmation” by Carnap) we have in it. Such logical probability is “especially useful in meta-scientific statements” and could, similarly to usual probabilities, be interpreted by a frequency meaning. Logical probabilities offer the opportunity to make (logical and) quantitative judgments on laws, on the basis of experience.

## Differences between P and B Laws: Number of Events

We often have the feeling that we are less confident with respect to biological laws than we are to physical laws. This would have been so if biological laws were more uncertain than physical ones. Following the previous definition of a law, all goes as if biological laws had lower logical probabilities than physical ones. In a sense, this logical probability quantifies how far removed a particular law is from the universal law it could be associated with. Whatever the probability of a stochastic process, we may be more or less confident about the law with which it is associated.

I propose here the thesis that physical and biological disciplines exhibit different logical probabilities. Moreover, I will try to explain why I think physical and biological laws have differing logical probabilities. We did not find any difference in nature between B and P, although we collected in the previous sections several (dependent) clues that sometimes differ among themselves, namely scale, irreversibility, or number of events.

The number of events, or of interactions of entity components, is a fruitful property to explore in this context. P usually

handles a larger number of events or of components than B, as living entities are built on bricks of inert entities, and not the other way around. To illustrate this assertion, just think about the Avogadro number, which is defined as the ratio of the number of constitutive atoms (or molecules) in a sample to the amount of any substance (a mole). The Avogadro constant (6.02 × 10²³) is a kind of scaling factor between macroscopic and microscopic scales, or, more precisely, between the scale of an entity and the scale of its components. The assertion on the number of components is not about the scale per se of a particular P or B process, but intends instead to point attention to the ratio of the scales. Conceivably, this scaling ratio is not always higher in P than in B. We saw counter-examples at the beginning of this text, which might even be another reason that blurs the frontiers between P and B. At least, this is a difference that common sense can accept: events and constitutive entities in these two disciplines differ in number in general.

So, P usually appears to have highly stable and reproducible processes, often due to the higher number of components present in it. This partly explains why physical observations converge to neutral statistical laws, due to the “law of large numbers” (Frank, 2009). This law states that the average of the results obtained from a large number of trials should be close to their expected value, and will tend to become closer as more trials are performed. Statistical laws appear to be limiting distributions reached with confidence if a sufficiently large number of entities interact to produce the observed process. With lower numbers of components, it is more difficult and less frequent to observe with confidence the limiting distribution.

Similarly, I hypothesize that this number of events is directly related to the fact that natural laws are either valid or invalid, and more or less certain (i.e. valid or invalid), depending on the discipline being considered. We could say too: With lower numbers of events, we are more likely to observe departures from the universal law, i.e. a case where the process fails to occur. I suggest labeling as a robust law a probabilistic law which is close to its associated universal law. Hence, a robust law has a logical probability close to unity. With such a definition, we can say that B's laws are less robust than P's laws, as they are pushed away from their universal laws by the relatively low number of events and entities they involve.

## Discussion and Synthesis

It has been illustrated that P often searches for universal laws to explain physical events, while B usually focuses on specific processes, without a search for universality. Of course, this dichotomy is probably less sharp than it appears at first sight. Some authors explain how these methods may be merged into a common, more powerful and more complete scientific method (Harte, 2002). Some others insist on the fact that these P and B cultures are and should remain separated (Keller, 2007). A natural question follows: Are the P and B cultures so different?

The feeling that P and B represent a “clash of two cultures” is, in my opinion, partly related to the other feeling that inert entities and living entities are different. This point has never been demonstrated up to now, as we do not have today a clear definition of what is Life and how Life appeared (Schrödinger, 1945). In agreement with other writers (Pombo et al., 2012), I have tried to explain with examples why unicity, contingency and irreversibility, the three properties sometimes proposed to differentiate living entities from inert entities, are not relevant
or, at least, not sufficient in themselves to split the scientific culture into P and B cultures.

This feeling about P and B cultures probably also comes from the weak knowledge we have of what our scientist neighbor is doing, as only very few physicists and biologists shift to (and stay in) each other's disciplines. This remark does not mean that physicists and biologists are not collaborating, but that to switch disciplines involves each recognizing the other's entity and event specificities, the other's ontology. It may also involve adopting another scientific method, although, as I have also explained, the rise of NM in both B and P should illustrate a shared approach to the two domains practice in their respective research work.

With a persistent feeling that B and P may indeed be different in nature, I have tried to explore the complex role of the concepts of scale and number of events in the two domains to interpret possible intrinsic differences. It appeared that it is always possible to identify processes and entities involving similar scales and numbers of entities between B and P. Yet, in general, physical entities (and events) involve a higher number of entities than do biological entities. In P, this greater number of events usually leads physical processes to more easily converge towards the ideal limiting distribution. P, with its highly stable and reproducible events, therefore justifies a higher level of confidence with regard to the processes observed.

The multiplicity of the components in a physical system tends to average its behavior more than would be the case in B. Following Carnap, I am proposing here the first thesis that a law might occasionally be violated, rather than saying that the law is wrong and should be replaced. Such occasional violation could be interpreted as a logical probability of the law, based on a meta-scientific judgment. Whatever the probability of the process being studied, we may still be more or less confident about the law it is associated with.

The variations inherent in biological entities suggest recourse to small samples with high heterogeneity among them. This is tantamount to implying low confidence in the laws. Based on the new definition of a law that we have referred to, I propose here the second thesis that physical and biological disciplines exhibit different “logical probabilities”. We therefore have differing degrees of confidence in their laws. Another way of expressing this view would be to say that it is as if living entities would require “relaxed” confidence levels for their laws compared to physical laws. Say, for example, that we only have a 99% chance that Natural Selection would apply to Life, whereas the second law of thermodynamics has a 99.9% chance to apply to a system. In some cases further away, found on Earth or on the planet Pandora for example, we may find living entities based on other evolution rules (Gaucherel & Jensen, 2012). Could it be that biological laws are less robust than physical laws?

This proposition does not suggest that all physical laws are robust. We have seen non-universal laws in P that are nevertheless relatively robust. Let's go back to the two previously mentioned laws in P: the second law of thermodynamics and the law of universal gravitation. The “fluctuations theorem” in thermodynamics states that out-of-equilibrium systems behave similarly to small fluctuations of systems at equilibrium (Evans et al., 1993), with a non-zero statistical probability to reduce the system entropy. Therefore, such situations momentarily violate the second law of thermodynamics, which states that systems never decrease their entropy. This violation is due to random

fluctuations in the process itself, reminding us that the second law is a statistical law.

On the other hand, Newton's law of gravitation has been invalidated for strong gravitational fields, such as the ones encountered in the famous 1919 Eddington experiment on the anomalous precession of the perihelion of Mercury. Thanks to that experiment, the domain of the validity of the Newtonian law of gravity has been redefined, thus losing its “universal” attribute. It is not that the process behind gravitation was not clearly measured (due to chance or noise), but rather that the process itself was no more the same between weak and strong gravitational fields. We are here in the presence of a probabilistic law, as it remains valid in a relative proportion of cases. The Newtonian law of gravity is relatively robust, and is today less robust than the general theory of relativity.

In these physical examples, old and strict laws (i.e. suffering no exception) were modified into new statistical or probabilistic laws (with rare but acceptable exceptions). Yet these exceptions have completely different origins: they arise in the processes associated with the older statistical laws, and in the confidence we have in the later probabilistic laws.

If this concept turns out to be true, laws may be found both in P and B disciplines, but with a kind of “conceptual continuum” between very robust laws in P (i.e. with a very low probability of being refuted by a single event or entity) and less robust laws in B (with a probability of temporary or local exceptions being found).

To extrapolate this definition, I would like to suggest that laws in economics (or probably in most human-related sciences) are even less robust than they are in B. The numbers of humans or of events in human society are lower than the numbers involved in B, and this may also explain why their associated laws show so little robustness. Conversely, we may extrapolate this definition into other directions of the robustness. Mathematics, daily handling infinite quantities of data, could have the most robust laws, despite the fact that it is not an empirical discipline. Hence, differences between physical and biological laws could be quantitative (linked to the laws' probabilities) instead of qualitative (either universal or not), as common sense would first suggest.

## Conclusion

P and B do not present a sharp “epistemic rupture” (Keller, 2007), but rather a conceptual continuum of scientific disciplines. P and B both search for some universal laws, but these laws may exhibit different degrees of robustness relative to the probability that they encounter an exception. The laws' robustness could be measured on the basis of logical probabilities. If this concept is revealed to be true, laws may be found both in B and in P disciplines, but with a continuum between very robust laws (often found in P, with a very low probability of refutation by an observed event) and less robust laws in B (with a non-null probability of occasional violation or refutation by locally found exceptions).

So, why not search for universal laws in the life sciences, bearing in mind that they may occasionally be violated, although with a low probability? In a second stage, we would try to minimize our probabilistic view of the living entities studied, by increasing our confidence in their associated laws (i.e. by reducing the uncertainty we have regarded the laws and the explanation of observations). It is possible that we may not be
able to increase our confidence in B's laws. This confidence is
sometimes linked to the relatively low number of entities and/or
interactions involved. In this case, a universal law, playing the
role of a theoretical and limiting law, may never be reached,
and we would need to radically change the law studied, as we
have usually done up to now. To sum up, P and B do not differ;
rather they represent the two poles of a unique scientific culture.
This scientific culture may just be modulated by a probabilistic
understanding of the world.

Acknowledgements

I would like to express my warm thanks to P. Huneman and
F. Munoz for their patient reading of the earlier versions of this
paper, and Allan Bailur for English editing.

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