What else do you expect if you take the attitude that we are free to construct metrics which are valid in terms of our own particular interests?
A point of confusion between H and S should be dealt with here. That is that one must keep in mind the scalar level where the H is imputed to be located. So, if we refer to the biological diversity of an ecosystems as entropic, with an H of a certain value, we are not dealing with the fact that the units used to calculate the entropy— populations of organisms—are themselves quite negentropic when viewed from a different level and/or perspective. More classically, the molecules of a gas dispersing as described by Boltzmann are themselves quite orderly, and that order is not supposed to break down as the collection moves toward equilibrium (of course, this might occur as well in some kinds of more interesting systems). — Salthe
I agree we can do just that. We can describe the world in terms that pick up on some characteristic of interest. I just say that is not a deep approach. What we really want is to discover the patterns by which nature organises itself. And to do that, we need some notion about what nature actually desires.
So you are down among the weeds. I'm talking about the big picture. Again, it is fine if your own interests are narrow. But I've made different choices.
So "disorder" is just an application of the principle of indifference. A messy system is one in which the details don't matter. Gone to equilibrium, the system will be generic or typical.
It is pretty clear that I’m talking about dissipative structure. And so is ascendency. So is Salthe, Kay and Schneider, Bejan and the many other cites I offered. But your critique amounts to me failing to relate dissipative structure theory to some mundane measure of species diversity.
The process of eutrophication for example is characterised by a rise in ascendency which is due to an overt increase in the activity of the system which more than compensates for its concomitant decrease in in its developmental status. — Ulanowicz
I think you usually handwave this by calling it 'coupling', too (forgetting that coupled systems have shared parameter spaces). Lo and behold, when you put a bit of work in, you can see literal coupling when your figurative sense of coupling was implicated and it looks like there's some way to take the intersection of parameter spaces such that each individual system's has a non-empty intersection with enough of the rest to make a connected network of flows. — fdrake
The principle of indifference cannot be extended as equiprobability to countable or continuous state spaces - this is because a uniform distribution cannot exist on infinite sets of outcomes. — fdrake
Without lingering too long on that fact that that isn't actually correct, there's an observed upside down U shape in ascendency (increase then decrease) over an eutrophication gradient, though since the paper detailing that doesn't do an error analysis it's still up for debate - he has to at least engage with the relative strengths of the terms in the formula. He does. — fdrake
The yin and yang of ecology
By now the reader may have noticed that two countervailing tendencies are at play in the development of any dissipative structure. In one direction a continuous stream of perturbations works to erode any existing structure and coherence. Meanwhile, this drift is opposed by the workings of autocatalytic configurations, which drive growth and development and provide repair to the system.
This tension has been noted since Antiquity. Diogenes related that Heraclitus saw the world as a continuous tearing down and building up. With the Enlightenment, however, science opted for a more Platonic view of nature as monistic equilibrium.
Outside of science, Hegel retained Heraclitus’ view of the fundamental tension, but with significant amendment. He noted that, although the two tendencies may be antagonistic at the level of observation, they may become mutually obligatory at the next higher level. Hegel’s view is resonant with the picture of ecosystem dynamics portrayed here.
Indeed, the second law does dissipate what autocatalysis has built up, but it has been noted that singular chance is also necessary if systems are truly to evolve over time and develop novel emergent characteristics. Looking in the other direction, complex, evolved systems can be sustained only through copious dissipation.
The problem with this agonistic view of the natural world is that, unlike the mechanistic (Platonic) convention, dialectic like dynamics cannot be adequately represented as algorithms.
To repeat again, mechanistic simulation models are inadequate to the task of describing ecosystems over the longer run, because the selfsame selection exhibited by autocatalysis can unpredictably replace not only components, but their accompanying mechanisms as well. Not only does the notion of mechanism defy logic, it seems also to poorly match the dynamics that actually are at play.
The chief advantage of using information theory to describe organization is that it allows one also to quantify the opposite (or complement) to information in similar fashion. Whence everything
that is disordered, incoherent and dissipative in the same network can be captured by a related, non-negative variable called the system’s overhead...Furthermore, a system’s ascendency and overhead sum to yield its overall capacity for development.
The actual pattern of order is the result of two opposing tendencies: In an inchoate system (one with low a), there are manifold opportunities for autocatalytic cycles to form, and those that arise create internal constraints that increase A (and thereby abet a). This tendency for a to grow via autocatalysis exists at all values of a. The role of overhead however, changes as the system progresses toward higher
a.
In inchoate systems (low a), it is ˚ that provides the opportunities for new cycles to form. In doing so it abets the tendency to increase autocatalysis. However, in systems that are already highly developed
(a ≈ 1), the dominant effect of ˚ becomes the disruption of established feedback loops, resulting in a sudden loss of organized performance. (The system resets to much a lower a.)
So at high a, ˚ strongly opposes further increase in a. Presumably, a critical balance between the countervailing roles of ˚ exists near the value of a at which the qualitative role of ˚ reverses.
Originally, it was thought that ecosystems increase uniformly in ascendency as they developed, but subsequent empirical observation has suggested that all sustainable ecosystems are confined to a narrow "window of vitality" (Ulanowicz 2002).
Systems with relative values of ascendency plotting below the window tend to fall apart due to lack of significant internal constraints, whereas systems above the window tend to be so "brittle" that they become vulnerable to external perturbations.
Digging in the weeds — fdrake
Elsasser argued that nature is replete with one-time events - events that happen once and never occur again. Accustomed as most investigators are to regarding chance as simplistic, Elsasser's claim sounds absurd. That chance is always simple, generic, and repeatable is, after all, the foundation of probability theory.
Elsasser, however, used combinatorics to demonstrate the overwhelming likelihood of singular events. He reckoned that the known universe consists of somewhere on the order of 10^85 simple particles. Furthermore, that universe is about 10^25 nanoseconds in age. So at the outside, a maximum of 10^110 simple events could possibly have transpired since the Big Bang.
Any random event with a probability of less than 1 in 10^110 of recurring simply won't happen. Its chances of happening again are not simply infinitesimally small; they are hyper-infinitesimally small. They are physically unreal.
That is all well and good, one might respond, but where is one going to find such complex chance? Those familiar with combinatorics are aware, however, that it doesn't take an enormous number of distinguishable components before the number of combinations among them grows hyper-astronomically.
As for Elsasser's threshold, it is reached somewhere in the neighborhood of seventy-five distinct components. Chance constellations of eighty or more distinct members will not recur in thousands of lifetimes of the universe.
Now it happens that ecologists routinely deal with ecosystems that contain well over eighty distinct populations, each of which may consist of hundreds or thousands of identifiable individual organisms. One might say, therefore, that ecology is awash in singular events, They occur everywhere, all the time, and at all scales.
None of which is to imply that each singular event is significant. Most simply do not affect dynamics in any measurable way; otherwise, conventional science would have been impossible. A few might impact the system negatively, forcing the system to respond in some homeostatic fashion.
A very rare few, however, might accord with the prevailing dynamics in just such a way as to prompt the system to behave very differently. These become incorporated into the material workings of the system as part of its history. The new behavior can be said to "emerge" in a radical but wholly natural way that defies explanation under conventional assumption.
To get political: isn't not too closed, not too open, being self-regulating while allowing lines of flight - i mean isn't that, in a perfect nutshell, neoliberalism? — csalisbury
So all that being said, acknowledging I can't keep up with the math, I'm still confident enough to engage the OP on its own terms which are, I believe, metaphorical. Which isn't to say I think you think that self isn't literally an ecosystem - I believe you do, and I probably agree - but that I think the significance of this way of looking at the self ultimately relies on - and is motivated by- what can be drawn from it conceptually. It's about drawing on empirically-sourced models to the extent that they facilitate conceptual considerations. It's metaphorical in the literal sense that we're transporting some way of thinking from one level to another. — csalisbury
Succession does not always lead to more complexity. It depends on the specific case of the environment.
For example in the post ice age landscape of the South Downs of England the tundra led to a range of scrub, bushes, heathland and trees. The species diversity increases in some instances, but can as easily become less complex by bearing fewer species.
Ash, elm, beach, hazel, will eventually succumb to the climax vegetation which in this case is oak woodland so dense as to make many larger herbivores seek life elsewhere; all the scrubs and less long lived trees will have to give way to the oak. — charleton
I didn't get a chance to read everything, but in the case of thermodynamic systems, the evolution of any given system is determined toward a state of equilibrium, and ergodicity attempts to ascertain the averages of behaviour within a system (transformations, arbitrary convergence, irreducibility etc) and political systems are an attempt to order the nature of Hobbesian chaos. I really like this: — TimeLine
This is an example of our different interests. You presume parameter spaces can be glued together. I'm concerned with the emergent nature of parameters themselves. You have your idea of how to make workable models. I'm interested in the metaphysics used to justify the basis of the model.
So it just gets tiresome when your criticism amounts to the fact I'm not bothered about the details of model building for various applications. I've already said my focus is on paradigm shifts within modelling. And core is the difference between mechanical and organic, or reductionist and holist, understandings of causality.
Canopy succession is an example. Once a mighty oak has grown to fill a gap, it shades out the competition. So possibilities get removed. The mighty oak then itself becomes a stable context for a host of smaller stable niches. The crumbs off its feeding table are a rain of degrees of freedom that can be spent by the fleas that live on the fleas.
I like two key points. Natural systems are irreducibly complex because they feed off their own accidents. The traditional mechanical view wants to separate the formal laws constraining systems from the material accidents composing systems. But nature includes the accidental or spontaneous in the very thing of forming its laws, or constraining regularities.
So good luck to any science based on a mechanistic metaphysics that presumes accidents are simply uncontrolled exceptions that can be hidden behind a principle of indifference. Yet also the universe does have lawful regularity. It incorporates its accidents into the habits it then forms.
Canopy succession is an example. Once a mighty oak has grown to fill a gap, it shades out the competition. So possibilities get removed. The mighty oak then itself becomes a stable context for a host of smaller stable niches. The crumbs off its feeding table are a rain of degrees of freedom that can be spent by the fleas that live on the fleas.
Which possibilities are closed? — fdrake
What degrees of freedom does this create? — fdrake
What degrees of freedom does this create? How does it create rather than destroy them? How do those degrees of freedom get turned into degrees of freedom for certain organisms? Which organisms? What properties do those recipient organisms have? How do the 'degrees of freedom' in the 'crumbs' relate to the 'smaller stable niches', in what manner do they 'rain'? In what manner are they 'spent'? How does one set of degrees of freedom in the canopy become externalised as a potential for the ecosystem by its deconstruction and then re-internalised in terms of a flow diversification? — fdrake
Now back to your tedious demand that I explain ecology 101 trophic networks with sufficient technical precision to be the exact kind of description that you would choose to use - one that would pass peer review in your line of work.
I'm sure you will have a bunch of nit-picking pedantry welling up inside of you so I will leave off there.
I wanted you to be technically precise with your use of terms - good that you did this. — fdrake
(Empiricism and Subjectivity); I think this is exactly the model that ought to be adopted. — StreetlightX
Is that a zizek sweater from 2006? — csalisbury
Ed Gein was (literally) a bricoleur — csalisbury
The possibility of something else having happened. The existence of the oak is a constraint on the existence of other trees, shrubs, weeds, that might have been the case without its shade. Without the oak, those other entropifiers were possible.
So excuse me for being baffled at your professed bafflements in this discussion. I mean, really?
Again, you claim that I'm hand-waving and opaque, but just read the damn words and understand them in a normal fashion.
So the oak becomes the dominant organism. And as such, it itself can be host to an ecology of species dependent on its existence. Like squirrels and jackdaws that depend on its falling acorns. Or the various specialists pests, and their own specialist parasites, that depend on the sap or tissue. Like all the leaf litter organisms that are adapted to whatever is particular to an annual rain of oak leaves.
The oak trophic network is the primary school level example. You can pick away at its legitimacy with your pedantry all you like, but pay attention to the context here. This is a forum where even primary school science is a stretch for many. I'm involved in enough academic-strength discussion boards to satisfy any urge for a highly technical discussion. But the prime reason for sticking around here is to practice breaking down some really difficult ideas to the level of easy popularisation.
It's fun, it's professionally useful, I enjoy it. I agree that mostly it fails. But again that seems more a function of context. PF is just that kind of place where there is an irrational hostility to any actual attempt to "tell it right".
So bear in mind that I use the most simplified descriptions to get across some of the most subtle known ideas. This is not an accident or a sign of stupidity. And an expectation of failure is built in. This is just an anonymous sandbox of no account. My posts don't actually have to pass peer review. I don't have to worry about getting every tiny fact right because there are thousands ready to pounce on faint errors of emphasis as I do in my everyday working life.
So it is fine that you want that more technical discussion. But the details of your concerns don't particularly light my fire. If you are talking about ecologies as dissipative structures, then I'm interested.
For me. diversity just falls out of a higher level understanding of statistical attractors - https://arxiv.org/abs/0906.3507
While actually measuring network flows is a vain dream from a metaphysical viewpoint. Of course, we might well achieve pragmatic approximations - enough for some ecological scientist to file an environmental report that ticks the legal requirement on some planning consent. But my interest is in the metaphysical arguments over why ecology is one of the "dismal sciences" - not as dismal as economics or political science, but plagued by the same inflated claims of mathematical exactness.
OK. Degrees of freedom is a tricky concept as it just is abstract and ambiguous. However I did try to define it metaphysically for you. As usual, you just ignore my explanations and plough on.
But anyway, the standard mechanical definition is that it is the number of independent parameters that define a (mechanical) configuration. So it is a count of the number of possibilities for an action in a direction. A zero-d particle in 3-space obviously has its three orthogonal or independent translational degrees of freedom, and three rotational ones. There are six directions of symmetry that could be considered energetically broken. The state of the particle can be completely specified by a constraining measurement that places it to a position in this coordinate system.
So how do degrees of freedom relate to Shannon or Gibbs entropy, let alone exergy or non-equilibrium structure? The mechanical view just treats them as absolute boundary conditions. They are the fixed furniture of any further play of energetics or probabilities.
The parameters may as well be the work of the hand of God from the mechanical point of view.
So I say degrees of freedom are emergent from the development of global constraints. And to allow that, you need the further ontic category or distinction of the vague~crisp. In the beginning, there is Peircean vagueness, firstness or indeterminism. Then ontic structure emerges as a way to dissipate ... vagueness. (So beyond the mechanical notion of entropy dissipation, I am edging towards an organic model of vagueness dissipation - ie: pansemiosis, a way off the chart speculative venture of course. :) )
Anyhow, fill in the blanks yourself. When I talk of a rain of degrees of freedom, as I clarified previously, I'm talking of the exergy that other entropy degraders can learn how to mine in all the material that the oak so heedlessly discards or can afford to be diverted.
The oak needs to produce sap for its own reasons. That highly exergetic matter - a concentrated goodness - then can act as a steep entropy gradient for any critters nimble enough to colonise it. Likewise, the oak produces many more acorns than required to replicate, it drops its leaves every years, it sheds the occasional limb due to inevitable accidents. It rains various forms of concentrated goodness on the fauna and flora below.
Anyway, when I talk about degrees of freedom, my own interests are always at the back of my mind. I am having to balance the everyday mechanical usage with the more liberal organic sense that I also want to convey. I agree this is likely confusing. But hey, its only the PF sandbox. No-one else takes actual metaphysics seriously.
So an ontology of constraints - like for instance the many "flow network" approaches of loop quantum gravity - says that constraints encounter their own limits. Freedoms (like the Newtonian inertias) are irreducible because contraints can make reality only so simple - or only so mechanically and atomistically determined. This is in fact a theorem of network theory. All more complicated networks can be reduced to a 3-connection, but no simpler.
So in the background of my organic metaphysics is this critical fact. Reality hovers just above nothingness with an irreducible 3D structure that represents the point where constraints can achieve no further constraint and so absolute freedoms then emerge. This is nature's most general principle. Yes, we might then cash it out with all kinds of more specific "entropy" models. But forgive me if I have little interest in the many piffling applications. My eyes are focused on the deep metaphysical generality. Why settle for anything less?
Surely by now you can work out that a degree of freedom is just the claim to be able to measure an action with a direction that is of some theoretical interest. The generality is the metaphysical claim to be able to count "something" that is a definite and atomistic action with a direction in terms of some measurement context. We then have a variety of such contexts that seem to have enough of your "validity" to be grouped under notions like "work", or "disorder", or "uncertainty".
So "degree of freedom" is a placeholder for all atomistic measurements. I employ it to point to the very fact that this epistemic claim is being made - that the world can be measured with sufficient exactness (an exactness that can only be the case if bolstered by an equally presumptuous use of the principle of indifference).
Then degree of freedom, in the context of ecological accounts of nature, does get particularised in its various ways. Some somewhat deluded folk might treat species counts or other superficialities as "fundamental" things to measure. But even when founding ecology more securely in a thermodynamical science, the acts of measurement that "degrees of freedoms" represent could be metaphysically understood as talking about notions of work, of disorder, of uncertainty. Ordinary language descriptions that suddenly make these different metrics seem much less formally related perhaps.
That is the reason I also seek to bring in semiosis to fix the situation. You complain I always assimilate every discussion to semiotics. But that is just because it is the metaphysical answer to everything. It is the totalising discourse. Get used to it.
You keep demanding that I cash out concepts in your deeply entrenched notions of reality. I keep replying that it is entrenched notions of reality that I seek to expose. We really are at odds. But then look around. This is a philosophy forum. Or a "philosophy" forum at least. Or a philosophy sandbox even. What it ain't is a peer review biometrics journal.
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