Individuality and Collectivity

Jordana Cepelewicz of Quanta Magazine wrote an article titled “What is an Individual? Biology Seeks Clues in Information Theory” [1] where she summarized the work of David Krakauer, Jessica Flack, Nils Bertschinger, Eckehard Olbrich and Nihat Ay. The scientific paper was published in “Theory in Biosciences” with the title “The information theory of individuality” [2]. These researchers are associated with the Santa Fe Institute. In the text below I refer to them as the “Santa Fe team”.

The Quanta article [1] as well as the scientific paper [2] resonated strongly with me and inspired me to say few words.

Central theme of the paper:

“At the core of that working definition was the idea that an individual should not be considered in spatial terms but in temporal ones: as something that persists stably but dynamically through time.” [1]

I agree. In my 2013 post titled “New Perspective on Unification” [3] I introduced the concepts of ‘horizontal attributes’ and ‘vertical attributes’. Horizontal attributes are associated with collectivity and multiplicity. Vertical attributes are about individuality, individual histories and individual characteristics. In [3] “time” is classified as a vertical attribute. Since “individual” is also classified as a vertical attribute it was clear in [3] that individuality is a temporal expression.

horizontal and vertical attributes as shown in my 2013 blog post

The Santa Fe team based their work on 3 axioms:

  1. Individuality can exist at any level of biological organization.
  2. Individuality can be nested — one individual can exist inside another.
  3. Individuality exists on a continuum, and entities can have quantifiable degrees of it.

Axiom #3 is interesting. There is a similar idea in [3].

Back to the work of the Santa Fe team:

“One way in which we might identify individuals is to check to see whether we are dealing with the same aggregation at time t and t + 1 . If the information transmitted forward in time is close to maximal, we take that as evidence for individuality.” [2]

“Within this theory, individuals can be cells, tissues, organisms, colonies, companies, political institutions, online groups, artificial intelligence or cities — even ideas or theories, according to Krakauer. “What we’re trying to do is discover a whole zoo of life forms that extend far beyond what we have conventionally called living,” he said.” [1]

The last point is important. The definition of “life” should not be restricted to organic/biological life.

Axiom #3

I claimed in [3] that all entities are mixtures of individuality and collectivity. This is very similar to their axiom #3. I do not think, however, that the mixture can be realized on a continuous scale.

What is the difference between individuality and ‘cognitive core’?

I am still working on the formulation of ‘cognitive core’ concept. I made an introduction in this post. My concept of ‘cognitive core’ does not depend on time. Santa Fe team’s concept of individuality on the other hand is a temporal expression.

Conceptual refinement

Let’s assume simplistically that the ‘cognitive core’ of an electron is [charge, spin, mass]. This information bundle gives electron it’s character but is it enough to assign “individuality” to an electron? All electrons are identical after all.

My proposal is to consider ‘cognitive core’ as the minimum degree of individuality. If the entity demonstrates integrity with distinguishable history over time then it assumes more individuality.

I suppose the degree of individuality depends on the complexity and the compositeness of the entity as well.

Uniqueness and maximum individuality

An entity can be unique (distinguishable from all other entities) yet it may exhibit a degree of individuality less than the maximum. Theoretically there is no end to complexity. There may be a limit to the level of complexity a physical structure can reach but there is no limit for the sophistication (complexity) of the mind-body combination. Therefore, there is no maximum for the degree of individuality.

Integrity over time, compositeness, complexity

I propose that the time-independent ‘cognitive core’ of an entity is the minimum degree of individuality.

I also propose that the compositeness/complexity of an entity is part of the individuality measure of that entity.

These are to be added to the Santa Fe team’s definition of individuality as a measure of organizational integrity over time.


Some entities have memories. If the information content of the memory is influencing the future behavior of the entity then those pieces of information should be included in the ‘cognitive core’. I still insist on ‘cognitive core’ being time-independent but I also recognize that there might be quantum jumps in the information content of the ‘cognitive core’. So, in effect, I am saying that ‘cognitive core’ may transition into a different ‘cognitive core’. Yes, this is a change in time but after the transition it is a different ‘cognitive core’. Between the jumps the ‘cognitive core’ remains time-independent.

Elaboration on the definition of ‘cognitive core’

The full set of explanatory factors describing the behavior of an entity may be changing in time but we can always pick the subset from it that is not changing in time and call that subset ‘cognitive core’.

Should physics laws be part of the definition of ‘cognitive core’?

Dynamical laws of physics use a parameter we call “physical time”. The second category of physics – conservation laws – do not depend on “physical time”. Therefore, I propose that we include the conservations laws in the definition of ‘cognitive core’.

Should external fields be part of the definition of cognitive core?

By “external fields” I mean the environment. The “external fields” can be any field mentioned in physics such as the magnetic field, electric field, gravitational field or it can be any chemical, biological environment or even any social environment.

If we agree on the definition of ‘cognitive core’ as the set of time-independent explanatory factors, we can refer to all other explanatory factors collectively as ‘interaction’. So, in terms of terminology, “external fields” or “environment” or ‘interaction’ refer to the time-dependent category of explanatory factors.

The ‘interaction’ category includes the dynamical laws of physics. All explanatory factors in the ‘interaction’ category use the “physical time” as a parameter.

Therefore, by definition, “external fields” cannot be part of the ‘cognitive core’. Environment (external fields) is part of the ‘interaction’ category.

Case study: electron

Cognitive core of electron: [charge, spin, mass, conservation laws]. Electron has a specific charge (-1 unit), specific spin (1/2 unit) and specific invariant mass (~0.511 MeV).

Individuality of electron: Electron is the most stable elementary particle in the universe. A free electron maintains integrity of its ‘cognitive core’ for practically an infinite duration. This fits the definition of “individuality” described by the Santa Fe team.

Collectivity of electron: Electron belongs to the group of elementary particles known as fermions. Electron belongs to the first generation of fermions (electron, electron type neutrino, d-quark, u-quark). Electron also belongs to the lepton category (electron, muon, tau and their neutrinos). Leptons are fermions other than quarks. These group memberships are expression of collectivity.

Another aspect of the collectivity is the fact that electron is a quantum of the “electron field” theorized in the Quantum Field Theory. The “electron field” is an expression of collectivity.

Yet another aspect of collectivity is the fact that electron exhibits quantum mechanical effects when confined to small volumes. Quantum mechanical effects are expressions of collectivity. In various condensed matter phenomena electrons form (quasi-particle) pairs. These are even more interesting expressions of collectivity.

Can we claim continuous degrees of individuality for electron?

From the categorization perspective, no. By the nature of categorization, we put the entity in various conceptual boxes. This is necessarily a discrete (not continuous) mental operation. If we look at the electron from the quantum mechanics perspective we can then perhaps assign smaller degrees of of individuality. But, I am not sure that this happens on a continuous scale.

I propose that the minimum measure of individuality is the cognitive core. Through quantum mechanical effects such as the fractional spin (as discussed by Frank Wilczek) the individuality of electrons can be further reduced. This, in effect, means that we are dealing with another entity with a different ‘cognitive core’. But again, this is not happening on a continuous scale, in my opinion.

Same story with electrons in quasi-particle formations (superconductivity). So, it seems to me that the “continuous degrees of individuality” claim of axiom #3 of the Santa Fe team does not cover elementary particles and quasi-particles.

Case study: photon

Can we say that a photon exhibits less individuality therefore more collectivity than an electron?

In terms of behavior, yes. Photon belongs to the category known as gauge bosons which are identified with their spin=1 characteristic. Electrons belong to the category known as fermions (spin=1/2). Fermions are the constituents of matter, gauge bosons are the carriers of force. No two fermions can occupy the same quantum mechanical state (Pauli exclusion principle). Multiple bosons on the other hand, can occupy the same quantum mechanical state. Bosons certainly exhibit more collective behavior.

Case study: neutrino

Neutrinos can change their flavor (fermion generation) spontaneously (unpredictively). Is this a counter-example to my claim that ‘cognitive core’ is time-independent?

As I mentioned above, I pick the time-independent explanatory factors and call that subset ‘cognitive core’. Therefore, the ‘cognitive core’ of neutrino does not include “flavor”.

Possible set of explanatory factors for neutrino: [spin=1/2, chirality=left-handed, conservation laws, flavor, 4-momentum, energy, dynamical laws of physics]

Cognitive core of neutrino: [spin=1/2, chirality=left-handed, conservation laws]

Neutrinos of all flavors are left-handed (anti-neutrinos are right-handed). Even when the flavor changes unpredictively the left-handedness of neutrino does not change.

Similarly, the spin=1/2 (fermion-ness) characteristic of a neutrino does not change when its flavor changes.


[1] Jordana Cepelewicz, “What is an Individual? Biology Seeks Clues in Information Theory”

[2] David Krakauer, Nils Bertschinger, Eckehard Olbrich, Jessica C. Flack, Nihat Ay, “The information theory of individuality“.

[3] Suresh Emre, “New Perspective on Unification

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