Thanks Ken.  The effort to define and explain complexity is at the heart of our new field.  Your point about complexity being made possible by energy flows that permit increasingly complex relationships among units understood as the exchange of information merits attention.

Jack and I agree on the fundamentals here. First, as I will discuss below, we need to better come to agreement as to what "information" and its variations are before positing it as being the core constituent that gives rise to and defines "complexity." After all, Dr. Chaisson does make a good case in regards to its vagueness.

Second, I agree with Jack and others I've heard, that increasing complexity is due the "nesting" of subsystems upon subsystems to create a greater complex system like a Matryoshka doll, i.e. quarks beget hadrons, begets nuclei, begets atoms, begets stars . . .   Melanie Mitchell's book, "Complexity - a Guided Tour," offers 9 different analyses of what defines complexity.  The last one she describes is "degree of hierarchy" and is essentially the same as what we are proposing. 

I would like to back up at this point, however, and see if we agree that "information" is equivalent to "relationships," which is essentially the same as Jack's "correlations."  This makes sense if we agree that Shannon et al demonstrated that information is the flip side of entropy (disorder). Information or order seems contingent on their being relationships between entities. My justification for also stipulating information = relationships of entities in space-time is because it isn’t certain as to what happens when information is absorbed into a black hole – which arguably resides outside of known space-time. Other people who have studied information including Benjamin Schumacher (John Wheeler’s last grad student and an expert in quantum information at Kenyon College), and Terrence Deacon (neuro-anthropologist at Berkley) have also stated that they believe that information is fundamentally concerned with relationships – so, we have good company here.

As a helpful exercise, it is good to see if the definition holds in different situations, especially at the extremes.  For example, before the Big Bang, we could assert that in terms of Shannon bits, there was no information or just a “0.”  At the Big Bang and during the intense radiation phase, we can add a “1” because now there is something, even it was just an amorphous soup of radiation without discernible relationships, (okay, there might have been other universes, but we’ll keep the model simple). As the universe expanded and cooled relationships between entities began to form.  The very simplest relationship, which might not ever have existed, would be the appearance and location of the first hadron which we can designate as being at (x,y,z,t) with appropriate conversions of each axis to 1’s and 0’s if you prefer, plus a bit for its existence. (note, in a universe with no boundries, we might need to posit the existence of a second particle so that a location is relative to something). At the opposite end of the cosmic historical timeline, we have the possibility of “heat death.” If thermal equilibrium occurs, there would be no available energy differentials for new relationships or processes to occur. Instead, whatever cold structures remain, held together by the residual forces of nature, would be static and even locational relationships would not change, i.e. “11010010101101110000000000111” would remain “11010010101101110000000000111. ” (Note: I am not a cosmologist and I might have the details of “heat death” wrong.) Other mental exercises are possible as well to try and test the proposed definition.

It’s also critically important to make the distinction between syntactical information and semantical information.  A distinction also echoed by Terrence Deacon, but missed or ignored by Dr. Chaisson. I will leave the discussion at this time with these thoughts: Syntactical information is about relational forms and processes that can often be described and even predicted by science and mathematics. For example, particle physicists like Paul Dirac and Peter Higgs mathematically predicted the existence and properties of anti-matter and the Higgs Boson, respectively, before they were even experimentally confirmed to exist.   In astronomy, Robert Oppenheimer predicted the existence of “black holes” from the mathematics of Einstein’s theory of general relativity.  Shannon was also concerned about syntactical information when asked to calculate how much data could be transmitted over a phone line. He determined that bits are the basic currency of syntactical information. Semantics was not relevant to his assigned task.

Ironically, we have the least math and physics to describe and predict that with which we are closest and most familiar: “life.”   Life begins to worry about semantical information, or information with “purpose” (e.g. bacteria senses environment with a pH that is too low for its persistence, so moves away) and at some point in the evolution of a nervous system, “meaning.”  It seems that semantic information can eventually emerge from syntactical information. How this can happen remains a deep mystery.

A review of the variety of treatments of ‘information’, in wikipedia, leads me to understand better why some have felt the concept of ‘information’ is too ill defined and multifarious to be treated with productively, but also to have more persuasion that Ken and I are on the right track, so to speak, in equating, or relating, information to relationships. Credit to Ken for the boldness to make the suggestion. 

Of course, humans are notorious for confirmation bias, and mutually reaffirming fantasies. But some simple and I hope elegant logic points in this direction.

Let us take randomness as a starting point. ( I will shortly give a little word picture to illustrate what that ‘means’).  In a completely random situation (could such a situation have what we see as ‘existence’), one could not associate  anything with anything, or for that matter nothing with nothing. 

But let us now introduce a correlation between elements. Now if you encounter element A, you have a better probability of encountering B. 

This correlation is a relationship. “Order ‘ is made up of relationships. Order is made up of realized probabilities. 

So when we encounter A and B, we are ‘informed’. We can assign a probability other than randomness. 

At the same time, when A and B are correlated, they are informed’ by that act of correlation. When A encounters anything other than randomly, it encounters B, and vica versa. 

And so up to a crystalline lattice, and many other things. 

This is why I like to keep focus on BGS math, or analysis. Because it is an elegant way of conceptualizing states of randomness, the mathematical possibilities of correlation or non correlation, and the amount of correlation, or order, or probability assignment, in a given state set.

And by the way, that is why the ‘power law’ distributions are ubiquitous in the U: they arise from the characteristics of correlational processes.

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A brief digression. The quantum physical acts humans engage in can make easier to understand why subjective, or encounter,  approaches to probability assignment often get related to info theory, in a Bayesian oriented discussion. 

Such a discussion may presume that an entity makes probability assignments, and alters them in an encounter based process. 

So we can say that S1 can encounter S2 only probabilistically and often partially. So S1 can attempt a probability assignment as to S2, and to characteristics of S2, and the correlations of S2 with S….

And so we have Bayesian probability assignments

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Now to the little thought experiment/illustration.

Suppose there is a totally random universe. (RU) 

There cannot be an RU. There would be no universe as we understand the universe, as the ‘tangible’ universe is made up of correlations, and thus information. But let us make this supposition.

We try to interject Oscarina the Observer into RU. (We have to interject Oscarina, because Oscarina is an intricate set of relational structures, and that cannot exist in RU. But Oscarina is willful, and insists on doing this. )

What does Oscarina observe?  

Nothing. The atoms are too small to be seen by a huge correlation of atoms, and they have no regularity between themselves in their various  impingement on Oscarina. 

There are no suns, no planets, no galaxies, no ‘voids’. 

There is no ‘information’ given Oscarina, other than perhaps temperature from the atoms encountering the correlated atoms which make up Oscarina’s integument. 

And that, we might note, is an observation made by Oscarina as to Oscarina, in Oscarina’s terms, who cannot be there in the first place. 

A little Saturday night fun. 

Jack 

Apparently complexity begets complexity!! I’m doing my best to keep up!! It's hard!! But I largely have two points of connection to this discussion, the first lies in the opening offering; the endorsement of Eric Chaison’s suggestion that the cosmos is progressing to greater degrees of complexity. The second involves those two, so far characterless charmers, S1 and S2 and their antics (well worthy of Dr Zeus)

As to the first point, there is no doubt that, looked at in one way, the cosmos is progressing towards a greater degree of complexity, but what is its most complex offering to date? I would venture to suggest that the human is the most complex offering of which we know. But the question arrises; is progress to complexity the fundamental narrative of the cosmos (if such a notion has any currency)? Or is it an actual consequence of another narrative? What else is there to see? What else is there to consider? It is no surprise that a scientist would see complexity. That is to a large extent what scientist are inclined to do, but what else is there to see? Is science the only valid modality by which we engage these questions?

The fundamental questions that underscore such discussions in a big history context are: what is the cosmic narrative that gave rise to us? How will the cosmic narrative that gave rise to us progress from here (if it is to progress at all)? and thirdly, in what way or ways will we the humans actively (or otherwise) participate in that progress? Is the process of our becoming aware of big history an essential prerequisite to our continued participation in its unfolding narrative?? Is the concept of narrative applicable at all?

In this context it is interesting that we can choose perspectives and choose disciplines within which to accommodate those perspectives. The very discussion that we are having here could be seen in terms of the cosmic narrative that gave rise to us in the first place (and by extension “it”)

Jack, you talk about S1 looking at S2 and seeing just a unity of presentation (as opposed to the complex “manyness” of composition)  This is very interesting and may point to another possible cosmic narrative of which the imperative towards increased complexity is part (if that is what we choose to see).  The fundamental narrative of science has involved to a large extent a process of trying to identify the entities of which things are composed and how they relate to one another. This has lead to the search for fundamental entities which can not be further dismantled. Bigger and bigger experiments to find smaller and smaller things. It is interesting to think of the opposite to this. To consider an entity that is such that it will not constitute an operational entity in respect of something else. We may look to S1 and we can ask two things; firstly, what is S1 composed of and secondly, what kind of a “Thing” will S1be a compositional element of? We know that we are composed of cells and unless the cosmic narrative that has given rise to us, the humans has come to a conclusion in us, we may well be cell-like to future entities, if cosmic precedent is anything to go by. We can consider that this is already happening.  You suggest Ken that there is no mathematics to address the living reality. There is actually a very simple one. 

We casually use these terms, like “entity”, “thing”,  “element”,  “unit” etc. We could categorise them under the tag “Unit” and we can say that one of the things that gives rise to a distinction in humanity (with respect to other living things) is a capacity to realise the “One”. This has an odd biblical ring to it which is not altogether out of place, but for now I literally mean the number “one”, the unit. This involves the ability to perceive boundaries; firstly in two dimensions; to conceive of them in three dimensions and to attribute a nomenclature accordingly. We can not actually see the entire physical unity of anything. In any given situation we only have a concept of such based  on a conceptual assembly of experiences. 

We know that this capacity to perceive well defined unity has a limited applicability in the cosmos at large, but the cosmic narrative that gave rise to us has produced that capacity in us and may actually be progressing through that capacity.

 The essence of this system of nomenclature involves the attribution of collective terms; hydrogen atom, atom, molecule, cell, multi celled organism, human etc. these are the entities that stock the narrative that gave rise to us over a 14.5 billion period of cosmic evolution. If we apply a collective term to all these entities, and the one I have coined is the term “priunit” we notice a very simple but inescapable fact. As the cosmos progresses, the total number of priunits in it is decreasing. This imperative (the one that has given rise to us) must in time lead to a count of “one”. The cosmic narrative that has given rise to us is progressing, perhaps through our capacity to both realise and articulate it, to a state of “oneness”. (the correlation with some religious narratives might be interesting if not contentious!!) If we consider our old friend S1 retrospectively in terms of that narrative we encounter complexity. If we consider he/she prospectively we see that the cosmic narrative that gave rise to us is progressing to simplicity. Read more at www.priunit.ie.

Jack H, or S3, I did not mean to dismiss or demean your perceptions by  referring to them as merely intuitions -- though much of 'science' is prompted and guided by intuitions.  I have looked into your website, and have spent a more time on the questions you present in your post. 

I will not attempt to address all your copious observations and suggestions -- just a couple.

At present, it would seem all the U's probabilistic realizations of complex states are done in its vast, decentralized set of local evolutions. So if we ask ourselves, with good reason, what unification may we humans identify with, now, here, in our lovely island of complexity in the great cold space surrounding us, beyond tribe, nation and even global humanity, it would be the realization of the wonderful, non equilibrium thermodynamic ordering process on this solitary, unitary  Earth.

In a manuscript which I am in the process of assembling for a publisher (wish me luck, please) I suggest that the better to avoid our own civilizational collapse, or withering, or stunting, we need to stop asking so narrowly what Earth will do for us today, and ask how we best fit into the realization of the potentials of Earthlife. If we make our global niche into the entrainment of life's energy and ordering potentials -- and by the way its information embodiment potentials -- we may better serve our own survival and efflorescence. 

Enough for now. On to Holiday. 

Jack P