Towards a Dynamics of Emergence

                                               Rating = (∑∞≈∩♥…what the Schmuck is going on here ?)

This post and the scientific work associated to it,  is dedicated to Spiritual Teacher Andrew Cohen for being a formidable, yet mysterious, source of Inspiration.

In this post we will push forward  our contemplation of the Infinite as multiplicity. It is a continuation of  the previous post, remember … the exponentials… and how they  saturate !

Pierre Teilhard de Chardin, a philosopher who ...

1) The context

There have been a few spiritual teachers, in all times, who have addressed the issue of Evolution. Evolution of  matter, of spirit, of  culture, of consciousness… Theilhard de Chardin is one of them. He was a scientist, an anthropologist. For him,  matter and spirit were incarnate together , and are evolving together at this very moment, hand in hand, one influencing the other. This hypothesis of Theilhard, of simultaneous incarnation of matter and spirit,  although is at the moment ( and some people say always will be ) un-testable, remains nevertheless the simplest hypothesis which reconciles  the purely Scientific and Spiritual  viewpoints on Evolution.   Teilhard vision from then on is  very broad and gets a huge “directionality”, a Telos shall we say. It points out towards the ultimate stage of development of the universe,  that Teilhard doesn’t specify but calls the “Omega Point”.    This fixed point assumes nonetheless that  Spirit and Matter, at the ultimate stage, will have formed a new phase, and emergent new state of evolution, in which they will be re-united.  Recently  I was listening to Andrew Cohen, who exposes a very intriguing, and   new idea that  Enlightenment, the traditional non dual Enlightenment  celebrated in the  East, and Evolution, one the most revered  ideas of the West, have something in common. Something forgotten for a long time, something deep, powerful, mysterious… Andrew’s idea is that the same flow of the  Infinite, the same  force of Absolute is  going through those two  phenomena. Infinite is the Ground of Being, the sum total of all Emptiness, that is found beyond thought in the traditional Enlightenment. Infinite as well is the force of Evolution,  eternal becoming forever…

So… with this preamble, let’s be now very simple scientific and matter of fact.    Having listened  to those very appealing ideas, we can now let the scientific mind ask a few questions.  Let’s suppose that  the spiritual teachers are right. Suppose that they have seen  with their Intuition, through some very deep Truth of the Fabrics of our universe. Then what would be the simplest possible physics theory which encapsulates those Intuitions ?

In the  Intuition  of Andrew Cohen, the main drive for the Evolution of the Universe is what he calls the Evolutionary Impulse. This impulse, or the Creative Force, can simply be equated with Eros ( it is a simplification of his teachings, my apologies for this. The motivation behind such a  simplification is to satisfy the criterium of a physics model). Eros  is seen as the force driving procreation, but also as the force of creativity, and ultimately as the Force  behind the evolutive spiritual drive. In simple terms, everything that is New and that enters this world of form as New, is due to Eros.

Here, we want to  assume that Andrew got it right and that all the Evolutive Forces of the Universe are indeed due to Eros. Now within a physics theory, Eros is described precisely by an exponential growth. Think of it.  One can get an easy picture of an exponential growth simply by looking how sexual desire arises in the psyche. But let’s contemplate instantiation of  strong emergence, any instance where  new state has suddenly appeared and supplanted the old one. In cases of strong emergence, the characteristics of the  parts, even added up together, are not enough to  describe the New state as a whole.  It is a reasonable hypothesis to assume that strong emergence requires, at some point in evolution, an exponential  growth   in time, an very rapid and sudden evolutionary phase, which is so quick that is can almost appear as discontinuous.   Simply stated, our first hypothesis is then :

Eros  IS the Evolutionary Force. As such,  it always expresses itself  as an Exponential Law.

Then let’s constrain the future theory a bit further and make the reciprocal statement.

Anything else than an  Exponential Law ( for example a linear law or power law of development)  is not an Evolutionary Force.

What is it then ?    we will call it, for reasons just explained below, and evolutionary velocity

2) The Newtonian analogy

In order to understand why we call anything else than an exponential law, a “velocity”, a small retrospective is maybe necessary. Back to  Galileo and Newton. One of the first principles of classical mechanics was enunciated by Galileo as the Inertia Principle.  It states that a body on which no force is exerted is moving at constant speed. Not zero speed, but constant speed.  Constant speed is precisely equivalent to saying that no Force is exerted on a physical body. This principle, one of the most important of  physics, which will be foundational for the development of special and general relativity,  is often used to  define  galilean reference frames, or Galilean invariance. A Galilean reference frame is then simply a reference frame on which a body moving at constant speed  receives the influence of  no external Force.  A simple example of such reference frame  is  a train moving at constant speed with respect to an observer at rest.

A reference frame in motion at constant speed

In our investigation, we  hence call evolutionary speed any law of evolution which is  not driven by an exponential. We infer here a kind of Galilean invariance, for evolutionary processes.   Our main insight is that the only existing Forces of Evolution are the one which produce exponential behavior. All the rest is thus “not a Force” and hence, within the viewpoint of classical mechanics can only be a velocity.

We now ask the question:

What is the simplest physical  equation which satisfies the two following requirements : 

1. the only existing Forces of Evolution are leading to exponential growth

2. all the other types of growth,  being linear or power law,  are described by velocities ?

It is time to introduce  the next hero of our story… for the sake of this post, let’s call him Kandidus.

2) An Equation of the Dynamics for Emerging Processes

Kandidus was born in Westphalia, you know…“Over There”… behind the blue line of the Vosgian mountains, close to the “Chateau de Thunder-Ten-Tronckh”. Like the hero of Voltaire,  he was born with a good and solid brain and a good an solid heart.  Kandidus is a young physicist spending six month in Paris at the end of his PhD program, and will be carried away in our adventure. Last week, Kandidus’ PhD advisor was absent for a scientific visit back to Germany, so Kandidus and I got four full working days to go in-depth into  getting an equation for the  evolutionary Forces.  What follows is our derivation.

We start with our two constraints, this time  expressed with  Maths ; let’s a call  y the variable which is evolving. In physics such a variable is viewed as a field. It could characterize for example, the  growth of a natural species, of life, or even the evolution of consciousness. y is the entity which  is growing under  the emergent phenomenon that we are considering.  t is the time. We define the evolutionary velocity as follows

3) Quantization



  1. Alvaro

    Very interesting, Catherine. However I still don’t follow your for your definition of evolutionary velocity. As it stands it is simply a ratio of two independent dimensionless scales. It doesn’t seem connected to Newtonian physics. Can you comment on that?

  2. Dear Alvaro, it is very nice to have your attention on that matter. You are right, the definition of the evolutionary velocity is not standard, and is not used later on to write the equations of hamilton in order to quantize the system. For quantization we are doing it the standard way by defining

    v_standard= d log y / d t

    and then as usual, P = d L/d v

    We find the following Hamiltonian :

    H= P^2/( 4t) + U

    with thus the momentum

    P= 2 t dlog (y) / dt

    P and log y are now conjugate variables, their Poisson bracket is 1 and we can proceed with quantization.
    That’s pretty nice, don’t you think ? we can from there on build a full theory out of it.

    Not that the momentum P, which is defined above is still dimensionless… a nice feature of the theory…

    The definition of evolutionary velocity given, directly Inspired by the Spiritual Teacher is thus corresponding with the momentum…

  3. Bob

    We have organic chemistry; do we have an “organic physics”? that elucidates the thermodynamics of emergent order? If so, we might better understand the tensions and conflicts that plague us.

  4. Ah ! Bob, I see that you found the most interesting post … ! I was just speaking about this new idea with a colleague to day and this little post is still at the Edge; I feel that the methods of biologists for studying evolution are completely far behind the methods used by the physicist to study emergent phenomena. If you are interested I can send you by e-mail two paper by Goldenfeld explaining this. So yes, this preliminary work is indeed very promising. I will find the time to push it somehow.

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