What's your single sentence definition then? I mean, just for fun. — apokrisis
In the light of these results, the network defi-nition of eutrophication (Ulanowicz, 1986) does not appear to accord with the gradient in eutrophicationin the Mondego estuarine ecosystem. Rather, it would seem more accurate to describe the effects of eutrophication process in this ecosystem in terms of a disturbance to system ascendency caused by an intermittent supply of excess nutrients that, when coupled with a combination of physical factors (e.g. salinity, precipitation, etc), causes both a decrease in system activity and a drop in the mutual information of the flow structure. Even though a significant rise in the total system throughput does occur during the period of the algal bloom and does at that time give rise to a strong increase of the system ascendency, the longer-term, annual picture suggests instead that the non-bloom components of the intermediate and strongly eutrophic communities were unable to accommodate the pulse in production. The overall result was a decrease in the annual value of the system TST and, as a consequence, of the annual ascendency as well.
If instead you really want to say that entropy is simply whatever act of measurement we care to construct as its instrumental definition - that there is no common thread of thought which justifies the construct - then how could you even begin to have an intelligent discussion with me here?
So the normal reductionist metaphysical position is that degrees of freedom are just brute atomistic facts of some kind. But I seek to explain their existence. They are the definite possibilities for "actions in directions" that are left after constraints have had their effect. So degrees of freedom are local elements shaped by some global context, some backdrop history of a system's development.
So evolution drives an ecology to produce the most entropy possible. A senescent ecology is the fittest as it has built up so much internal complexity. It is a story of fleas, upon fleas, upon fleas. There are a hosts of specialists so that entropification is complete. Every crumb falling off the table is feeding someone. As an ecology, it is an intricate hierarchy of accumulated habit, interlocking negentropic structure. And then in being so wedded to its life, it becomes brittle. It loses the capacity to respond to the unpredictable - like those either very fine-grain progressive parameter changes or the out of the blue epic events
Then switching to that informational or negentropic side of the deal - the tale of life's dissipative structure - the degrees of freedom become the energy available to divert into orderly growth. It is the work that can be done to make adaptive changes if circumstances change.
Life is spending nature's degrees of freedom in entropifying ambient energy gradients. And it spends its own degrees of freedom in terms of the work it can extract from that entropification - the growth choices that it can make in its ongoing efforts to optimise this entropy flow.
So the degrees of freedom are the system's entropy. It is the through-put spinning the wheels.
That blog post was fascinating! I keep wandering back to psychoanalytic point where the cheating husband's relationship with his lover only 'works' insofar as he is married: were he to leave his wife for the sake of his lover, the lover would no longer be desirable... Of course the psychoanalytic lesson is that our very 'subjective POV' is itself written into the 'objective structure' of things: it's not just window dressing, and if you attempt to discard it, you change the nature of the thing itself.
And I think this slipperiness is what makes it so hard to fix the status of a 'parameter': if you want to make a parameter 'work' (i.e. if you intervene in a system on that basis), you will cause changes - but that doesn't mean the system is 'in-itself' sensitive to such parameters: only that, through your intervention you've made it so. — StreetlightX
We're basically a series of loops, some only residing 'inside' us, some extending far beyond our skin. — StreetlightX
A baby girl is mysteriously dropped off at an orphanage in Cleveland in 1945. “Jane” grows up lonely and dejected, not knowing who her parents are, until one day in 1963 she is strangely attracted to a drifter. She falls in love with him. But just when things are finally looking up for Jane, a series of disasters strike. First, she becomes pregnant by the drifter, who then disappears. Second, during the complicated delivery, doctors find that Jane has both sets of sex organs, and to save her life, they are forced to surgically convert “her” to a “him.” Finally, a mysterious stranger kidnaps her baby from the delivery room.
Reeling from these disasters, rejected by society, scorned by fate, “he” becomes a drunkard and drifter. Not only has Jane lost her parents and her lover, but he has lost his only child as well. Years later, in 1970, he stumbles into a lonely bar, called Pop’s Place, and spills out his pathetic story to an elderly bartender. The sympathetic bartender offers the drifter the chance to avenge the stranger who left her pregnant and abandoned, on the condition that he join the “time travelers corps.” Both of them enter a time machine, and the bartender drops off the drifter in 1963. The drifter is strangely attracted to a young orphan woman, who subsequently becomes pregnant.
The bartender then goes forward 9 months, kidnaps the baby girl from the hospital, and drops off the baby in an orphanage back in 1945. Then the bartender drops off the thoroughly confused drifter in 1985, to enlist in the time travelers corps. The drifter eventually gets his life together, becomes a respected and elderly member of the time travelers corps, and then disguises himself as a bartender and has his most difficult mission: a date with destiny, meeting a certain drifter at Pop’s Place in 1970.
The question is: Who is Jane’s mother, father, grandfather, grand mother, son, daughter, granddaughter, and grandson? The girl, the drifter, and the bartender, of course, are all the same person. These paradoxes can made your head spin, especially if you try to untangle Jane’s twisted parentage. If we draw Jane’s family tree, we find that all the branches are curled inward back on themselves, as in a circle. We come to the astonishing conclusion that she is her own mother and father! She is an entire family tree unto herself.
What does 'dichotomous to constraints' mean?
There are lots of different manifestations of the degrees of freedom concept. I generally think of it as the dimension of a vector space - maybe calling a vector space an 'array of states' is enough to suggest the right meaning. If you take all the vectors in the plane, you have a 2 dimensional vector space. If you constrain the vectors to be such that their sum is specified, you lose a degree of freedom, and you have a 1 dimensional vector space. This also applies without much modification to random variables and random vectors, only the vector spaces are defined in terms of random variables instead of numbers. — fdrake
So I suppose I should talk about configurational entropy. — fdrake
The Shannon Entropy is related to the Boltzmann entropy in thermodynamics in a few ways I don't understand very well. — fdrake
The theoretical links between Shannon's original entropy, thermodynamical entropy, representational complexity can promote a vast deluge of 'i can see through time' like moments when you discover or grok things about their relation. BUT, and this is the major point of my post:
Playing fast and loose with what goes into each of the entropies and their context makes you lose a lot. They only mean the same things when they're indexed to the same context. The same applies for degrees of freedom.
I think this is why most of the discussions I've read including you as a major contributor are attempts to square things with your metaphysical system, but described in abstract rather than instantiated terms. — fdrake
Shannon's strictly broader than Boltzmann since it allows for non-equidistribution. — fdrake
I'm baffled that you say Shannon entropy came before Boltzmann's entropy.
It is fine that science does create simpler indexes. I've no problem with that as a natural pragmatic strategy. But also, with Shannon and Boltzmann, it became clear that informational uncertainty (or configurational degrees of freedom) and entropic material degrees of freedom (or countable microstates) are two sides of the same coin. The mathematics does unite them in a general way at a more abstract level.
You can keep re-stating that a proper scientist would use the proper tools. You can reel off the many kinds of metrics that reflect the simpler ontology of the reductionist. You can continue to imply that I am somehow being unscholarly in seeking to consider the whole issue at a more holistic level - one that can encompass physicalist phenomena like life and mind. And indeed, even culture, politics, economics, morality and aesthetics.
Then from an infodynamic or pansemiotic point of view, constraints become the informational part of the equation, degrees of freedom are the dynamics. In the real material world, the configuration can be treated as the knowledge, the structure, that the organismic system seeks to impose on its world. The constraints are imposed by a mind with a purpose and a design. The degrees of freedom are then the entropy, the dynamics, that flow through the organism.
But I know what I'm about so I'm only going to respond to your critique to the degree it throws light on the connecting commonality, the linkages to that more holistic worldview.
Does that remain the case now that information theory has been tied to the actual world via holographic theory?
Going from ATP being used to fuel an organism straight to a 'global' sense of infodynamics and signals/signs in pansemiosis. It works only when you wave your hands and don't focus on the specifics. When what before was concrete becomes metaphorical, then what was metaphorical becomes concrete. — fdrake
This is why what we're talking about has almost no relation to the OP. — fdrake
What does this measure? The diversity of flows within a network. How? It looks at the proportion of each flow in the total, then computes a quantification of how that particular flow incorporates information from other flows - then scales back to the total flow in the system. It means that the diversity is influenced not just by the number of flows, but their relative strength. For example, having a network that consisted of 1 huge flow and the rest are negligible would give an ascendency much closer to a single flow network than another measure - incorporating an idea of functional diversity as well as numerical biodiversity. Having 1 incredibly dominating flow means 0 functional diversity. — fdrake
Where every pipi is the proportion of the i-th species of the total. This is a numerical comparison of the relative abundance of each species present in the ecosystem. This obtains a maximum value when each species has equal relative abundance, and is then equal to the number of species in the ecosystem. Look at the case with 2 species each having 2 animals. p is constant along i, being 0.5, then the Shannon Biodiversity is -2*0.5*log(0.5) = log2, so its exponential is 2. — fdrake
Of course, if you've read this far, you will say 'the middle state is the one furthest from order so of course it has the highest degrees of freedom', which suggests the opposite intuition from removal of dominant energy flows 'raining degrees of freedom' down onto the system. This just supports the idea that your notion of entropy has poor construct validity. — fdrake
Its not metaphorical if infodynamics/semiosis is generalisable to the material dissipative structures in general.
So it is not me waving my hands. It is you demonstrating a deaf ear to context. I am careful to distinguish between the part of what I say which is "normal science" and the part that is "speculative metaphysics". And the speculative part is not merely metaphor because the project would be to cash it out as concrete theory, capable of prediction and measurement.
I agree that may also be a tall order. But still, it is the metaphysical project that interests me. The fact that you repeatedly make these ad hom criticisms shows that you simply wish not to be moved out of your own particular comfort zone. You don't want to be forced to actually have to think.
A lot of your focus seems to be on how to we specify richness or complexity or healthy biodiversity. And you instinctively think in terms of counting niches or something else "structually concrete".
A lot of your focus seems to be on how to we specify richness or complexity or healthy biodiversity. And you instinctively think in terms of counting niches or something else "structually concrete".
So here, aren't you assuming that we can just count species and have no need to consider the scale of action they might represent? One might be a bacterium, the other an elephant. Both might be matched in overall trophic throughput. We would expect their relative abundance to directly reflect that fact rather than a species count having much useful to say about an ecosystem's healthy biodiversity or state of entropic balance.
Organisms lay
Jumbled up yet striving for
Their own mouths to feed
Each cell binds a gap
Consuming a gradient
Where to find new food?
Digging in the weeds
An old domain of feasting
For new specialists
Symmetry broken
Entropy from exergy
Degrees of freedom — fdrake
I'm not suggesting you 'look at the formulas and find a master one', the thing I cared about was that the measures of entropy in terms of ascendency and relative abundance meant different things - they summarise different aspects of the behaviour of the ecosystem. — fdrake
So a commonality is that they are mappings from some space to the real line. But what matters - what determines the meaning of the entropy is both what the inputs to the entropy function are and how they are combined to produce a number. To speak of entropy in general is to let the what and the how vary with the implicit context of the conversation; it destroys the meaning of individual entropies by attempting to unify them, the unification has poor construct validity precisely because it doesn't allow the what and the how of the mapping to influence the meaning. — fdrake
I love this so much though. — StreetlightX
I see you jiggling with joy on the sidelines. SX and his man-crushes — apokrisis
It would be interesting if Shannon biodiversity was related to ascendency — fdrake
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