@apokrisis, incidentally, I think the peculiar fractal'ish thing applies to self-knowledge in particular.
(This coincides with documented (evident) introspection illusions, an illusory information horizon necessitated by a finite self-model.)

Instead, the simplest map just tells you where are the obstacles, where are the paths. That is, where are the constraints, where are the degrees of freedom.
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The kind of tool we are talking about here is a map. And maps are interested in the global structure of an environment, not its inessential details. — apokrisis

Right.

If we abandon the peculiar fractal'ish structure, then it seems that the only exhaustive map is the territory.
It's just that, by that line of thinking, the term "map" is then implicitly bent around instead (or "territory" is).
Where maps (models, understandings, idealized abstracts, information, memories, etc) are epistemic - they're ours - territories are ontological.
But then, by collapsing maps and territories, we sort of populate it all with us (like a self-externalizing hypostatization), if you will.

Maybe omniscience-granting maps, or otherwise entirely accurate maps, are a pipedream.
Still useful (cf your pragmatism), if not required, just in a domain of excluding particulars, or flattened as you put it (if I'm reading your comments right).

A bit fractal'ish I suppose, infinite in depth where the map maps itself. — jorndoe

When you say fractal, you could mean holographic or scalefree. So like a hologram, every bit of the reality provides a map of its whole.

And this would be the way I see it. It is what the cosmological principle of fundamental physics presumes. The Universe is homogenous and isotopic. It should look essentially the same, in terms of its basic structuring laws, over all observable scales.

And that would be like a 4D fractal. Zoom in or zoom out and the view remains the same.

So that is what I am describing. It is why from the inside, the complementary limits of the structure and the chance are flattened so that they appear to be at the beginning and end.

Like being inside a fractal, a perfect hierarchy of scales, look down towards the smallest grain and it becomes eventual a continuous blur. Look up towards the largest fractals and eventually they becomes so large that one eventually fills your whole view. The entire world is now inside a single instant of the complete design.

So the larger story is indeed fractal. And our best cosmological theories, or maps, of reality do elevate that fact to the status of a meta-principle. Homogeneity and isotropy are presumed. The laws of physics have to look the same from any possible physical point of view. That’s how the really key maps, like relativity, were derived.

Sorry -- this just seems like the worst analogy for what you're after. — Srap Tasmaner

So not just a weak analogy, or a bad analogy, but the very worst analogy that could be imagined?

Sounds legit. I mean you made such a stellar argument for that conclusion. ;)

In fact I can't think of any kind of map that isn't based on selecting certain accidental states of affairs to mark and the rest to ignore. There's never any essential/accidental distinguishing such as you describe. — Srap Tasmaner

So I said maps would boil down to a picture of the essential constraints and their resulting degrees of freedom. Obstacles and paths.

Can you present a map which doesnt simplify in just that fashion?

Indeed, if the paths are a mechanical level constraint, like a motorway network or an underground line, you don’t even need to show the hills they skirt, the suburbs they must connect.

And what exactly is accidental about a road or rail line? It is essential that you use them if you are using a car or carriage. The only accidents now are you making wrong turns or getting on the tube heading the wrong way.

My thought here was that the usefulness of a map is showing you what roads happen actually to exist connecting features you're interested in that also happen to exist, and it shows where the features and roads actually happen to be. You could abstract away location, distance, and so on, and just show the connections -- but this town and that city and the road that connects them are still matters of accidental history.

Constraints would only show you what connections could exist, where they could be, etc. We need to know which ones actually obtain.

Granted some features are considered essential to a map, in the sense that they're included when others aren't or needn't be, but it seemed to me those included features are still historical and accidental -- this town might not exist, there might not be a road between these two, etc.

So do maps need to map the essential or the incidental? What do you think abstraction is apart from the shedding of the inessential particulars to arrive at the structural generalities?

My thought here was that the usefulness of a map is showing you what roads happen actually to exist connecting features you're interested in that also happen to exist, and it shows where the features and roads actually happen to be. You could abstract away location, distance, and so on, and just show the connections -- but this town and that city and the road that connects them are still matters of accidental history. — Srap Tasmaner

So the maps have to have enough essential information. And - for the sake of optimality - they would thus leave out all information that is inessential? Do you agree here or not?

If you are mapping the geography of a planet's surface, then sure, all sorts of accidents of time will have become today's dominating constraints. A mountain range is - in plate tectonic terms - just an accident. But for an army, a tourist, or some other relevant expression of a human interest, it is an obstacle, a constraint on our free and easy motion. So that doesn't change the principle of what I said.

A map is an umwelt - the world experienced in terms of some set of signs, some collection of affordances. We take note of all that is fixed so as to see the opportunities that are thus, dichotomously, created.

Constraints would only show you what connections could exist, where they could be, etc. We need to know which ones actually obtain. — Srap Tasmaner

They are only constraints if they obtain. If they are accidents, then they are accidents. Like it says on the label.

As individuated events, fluctuations are unpredictable. You can't draw a map of them. Even if you can record a history of them. Or draw a map of a field of probabilities - a map of the constraining context, the obstacle course, that gives a predictable shape to fluctuation now viewed as the generalised thing of a process. A structure in motion.

Granted some features are considered essential to a map, in the sense that they're included when others aren't or needn't be, but it seemed to me those included features are still historical and accidental -- this town might not exist, there might not be a road between these two, etc. — Srap Tasmaner

You are trying too hard to manufacture problems. Sure history is full of accidents. But if these accidents can accumulate, then they become the constraints that act in the present to limit the accidents of the future.

They are no longer accidents once they become part of the constraints that prevail. So you are simply attempting to make an analogy the worst possible by abusing it in the worst way you can imagine.

Sure history is full of accidents. But if these accidents can accumulate, then they become the constraints that act in the present to limit the accidents of the future.

They are no longer accidents once they become part of the constraints that prevail — apokrisis

That makes nice sense. Yesterday's chance is today's necessity. I understood your project to be pushing back or outward to ever greater generality, to the "purely" necessary. I guess if that's only an ideal, you'll be mapping the ossified accidental just like the rest of us. I suppose that's the sense of mapping "from the inside", as you put it.

So you are simply attempting to make an analogy the worst possible by abusing it in the worst way you can imagine. — apokrisis

Really not. Since what is essential depends on the purpose of the map, I couldn't see what a truly generic map could be. Since what today is a constraint might not have been, I couldn't see what a map of only the necessary would be. Your response helps. I still don't quite get the big picture, but I'm good for now.

Carry on.

That makes nice sense. Yesterday's chance is today's necessity. I understood your project to be pushing back or outward to ever greater generality, to the "purely" necessary. I guess if that's only an ideal, you'll be mapping the ossified accidental just like the rest of us. I suppose that's the sense of mapping "from the inside", as you put it. — Srap Tasmaner

The "map" is of the very fact that accidents accumulate to form the regularity of habits. That is the Peircean ontological story of the Cosmos.

And then the Platonic part of that is that there are structural attractors. Given the accumulation of accidents, certain flow patterns must be expressed. The latent structure will be what emerges by the end.

This was highly speculative metaphysics in Peirce's day. It is now routine scientific modelling - dissipative structure theory, hierarchy theory, chaos theory, constructal theory, self-organising criticality, far from equilibrium thermodynamics. There are a ton of labels for the current mathematical variants of the basic metaphysical model.

Your response helps. I still don't quite get the big picture, but I'm good for now. — Srap Tasmaner

Great. I appreciate that.

The "map" is of the very fact that accidents accumulate to form the regularity of habits — apokrisis

This pattern I like very much, and I'm totally on board there.

But since we're talking metaphysics, do you have any qualms about the word "fact" here? What kind of fact? Are we forced to call such accumulation itself either accidental or necessary?

I would like to think this is where pragmatism slots into the story, but I don't quite get it. (Metaphysics just not my thing, as you know all too well.)

But since we're talking metaphysics, do you have any qualms about the word "fact" here? What kind of fact? Are we forced to call such accumulation itself either accidental or necessary? — Srap Tasmaner

The fact is a fact about the metaphysical process. It is its distinctive structural feature. Out of individual accidents, collective order arises.

So the story is of this duality. The accumulation is not a case of either accidental or necessary. As said, it is about both. Both the chance and the necessity, the accidents and the habits, the tychism and the synechism. Each are fundamental in being the limits that sandwich the actuality of being.

So history, the passage of time, fuses together the material and the formal causes to produce the hylomorphic whole, the thing in itself. You have a past of congealed accidents that are steadily expressing the necessity of some global structure or order. And then the world as actual substantial reality - the richly varied thing - is the bit in the middle, the present moment in which much is constrained and yet much is still open and free.

That's a nice summary. Chance and necessity make a nice pair of terms in which to explain everything, but I would imagine you could tell a similar story with other pairs (or mores) of fundamental somethings. They all make me uncomfortable, but that's my problem.

Pierce is interesting, on the one hand, for giving Chance a seat on the dais, right? And then you realize that if we are honest, and serious, about our model-building, it too will have a place for chance, at least as whatever it is our theory doesn't account for, the noise accompanying the precious signal. Now we get to match up the epistemic and ontological, as you've noted, and we can be indifferent to questions like, "Is chance real?" We can posit it, or not, but it will always be in the model either way. And this would be Peirce's pragmatism, yes?

Oddly, this matching up makes me even more uncomfortable than the Big Theories do on their own. If the big theories already seem to hang in the air (the way a brick doesn't) on the buoyancy of their own internal coherence, this version seems more like jumping and forgetting to hit the ground.

Again, my problem. If I've understood, what most convinces you you're on the right track is what gives me the willies, which is curious. As always, I appreciate your patience with my questions.

Chance and necessity make a nice pair of terms in which to explain everything, but I would imagine you could tell a similar story with other pairs (or mores) of fundamental somethings. They all make me uncomfortable, but that's my problem. — Srap Tasmaner

Of course you need many dichotomies here. There isn't just a single dialectic. Discrete~continuous, flux~stasis, one~many, matter~form - we are talking about the deeper thing of the metaphysical mechanism that is dialectical opposition itself.

It would be nice to boil down the list to a single over-arching dichotomy. For me, I think it comes down to a pair of them - a dichotomy of dichotomies.

I would defend local~global and vague~crisp as the two key ones. One talks of the hierarchical structure that is what you have when you have something definitely developed. Then the other talks about the fact of development - the move from a monadic potential through a dichotomous symmetry breaking that gets you to a final equilbrium stability which is the triadic thing of a hierarchy.

But why so many metaphysical oppositions to describe the one nature? It is because you are trying to fold all the rich variety of an emergent cosmos back into the barest metaphysical scheme. It is not about which single dichotomy covers every angle that has emerged. It is about how every possible angle will emerge once you have the singular mechanism which generates that kind of variety.

Is chance real?" We can posit it, or not, but it will always be in the model either way. And this would be Peirce's pragmatism, yes? — Srap Tasmaner

Well reductionism wants to reduce all forms of chance to some kind of hidden determinism. Nothing could be actually just spontaneous.

So that is the bold move. To actually accept absolute chance as being as real as determinism (or absolute constraint). But then, it is only accepting either being absolute in terms of being the bounding limits of the actual.

So it is a more subtle, or sly, story. Chance and necessity are only absolute and actually existent in terms of each other. They are as real as each other. Which on some views - with them being flattened limits - makes them not really real at all. They are just co-dependently real. One exists to the degree the other is lacking. And neither can be completely lacking for either to actually exist.

Oddly, this matching up makes me even more uncomfortable than the Big Theories do on their own. If the big theories already seem to hang in the air (the way a brick doesn't) on the buoyancy of their own internal coherence, this version seems more like jumping and forgetting to hit the ground. — Srap Tasmaner

Surely it is the opposite. A dichotomy is the organisation that could bootstrap itself as it depends only on that which it bootstraps. Continuity exists only as an exclusion of the discrete. And vice versa. So each is what makes the other. They have a formally inverse or reciprocal relationship.

The internal coherence of a dichotomy is complete. By definition, a dichotomy is that which is mutually exclusive and jointly exhaustive. It only needs itself to make sense.