Don’t forget dark energy. You haven’t budgeted for that. — apokrisis
I should have written 'the map = territory fallacy" by which I mean idealists tendency for confusing – conflating – epistemology (i.e. what I/we know) & ontology (i.e. what there is), that is, there is not anything more than what I/we can 'experience'.
it is just that there are maps all the way down. There is no territory.
Always the Hegelian. That's the fallacy / incoherence of idealism I mean. — 180 Proof
The Lorentz strange attractor caused excitement as a model for that reason. — apokrisis
On the other hand assuming there is a territory requires a leap of faith and the assumption of an archimedic point which ultimately leads to some sort of foundationalism. Every foundation leads to problems because there is no way it reveals itself. — Tobias
Most of those systems iterate a single complex function. — jgill
You have mentioned symmetry breaking several times in posts. I know practically nothing of it, but it seems to somewhat parallel the fundamental notion of chaos theory, sensitive dependence on initial conditions. How do you perceive it? Does it resonate in metaphysics? — jgill
So metaphysically, this is quite complex. Some history of constraints has to drive the system to the point that it is in a state of poised perfection — apokrisis
As with cellular automata, the mathematician sees a pattern emerge from the algorithm and finds it striking because it is a pretty pattern. Maybe even a suggestive pattern. Possibly even what looks like a pair of butterfly wings that might seem to stand as a good model of bistability in a natural system. It all gets very exciting - a la Wolfram — apokrisis
But it is then so easy to skip over the many steps needed to start using these sparkling new toys as actual scientific models — apokrisis
You do write the most interesting posts. This is related to catastrophe theory as well. — jgill
I've wondered whether fixed points (attracting, repelling, indifferent) have any metaphysical properties. Stanislaw lem's ergodic theory of history presents a counterpoint to the butterfly effect in Chaos theory: certain social movements are so strong that minor fluctuations have little to no effect on large scale outcomes. — jgill
:fire: :up:My systems science approach is predicated on global constraints that produce local stability. [ ... ] So fixed points are important as the emergently stable invariances of a physical system. The symmetries that anchor the structure of the self-reconstituting whole.
This is the guts of physical theory. — apokrisis
Take the usual examples of a pencil balanced on its point, or Newton's dome with a ball perfectly balanced on the apex of a frictionless hemisphere. The pencil and ball are objects in a state of symmetry, being at rest with no net force acting on them, so they should never move. But then we also know that the slightest fluctuation - a waft of air, the thermal jiggle of their own vibration, even some kind of quantum tunnelling – will be enough to start to tip them. The symmetry will be broken and gravity will start to accelerate them in some "randomly chosen" direction. — apokrisis
So metaphysically, this is quite complex. Some history of constraints has to drive the system to the point that it is in a state of poised perfection. The symmetry has to be created. And that then puts it in a position where it is vulnerable to the least push, that might come from anywhere. The sensitivity is created too. The poised system is both perfectly balanced and perfectly tippable as a result. The situation has been engineered so randomness at the smallest scale - an infinitesimal scale - is still enough to do the necessary.
All this is relevant to the OP - as the Big Bang is explained in terms of spontaneous symmetry breaking. And thus the conventional models have exactly this flaw where the existence of the "perfect balance" - a state of poised nothingness - is just conjured up in hand-waving fashion. And then a "first cause" is also conjured up in the form of "a quantum fluctuation". Some material act - an "environmental push" - tips the balance, as it inevitably must, as even the most infinitesimal and unintentional fluctuation is going to be enough to do the job of "spontaneous" symmetry breaking. — apokrisis
My systems science approach is predicated on global constraints that produce local stability. So fixed points emerge due to top-down acting constraints on possibility. — apokrisis
My systems science approach is predicated on global constraints that produce local stability. So fixed points emerge due to top-down acting constraints on possibility.
The tricky bit is then that the local degrees of freedom thus created have to be of the right kind to rebuild the whole that is creating them. It is a cybernetic loop where the system maintains its structure in a positive feedback fashion.
So fixed points are important as the emergently stable invariances of a physical system. The symmetries that anchor the structure of the self-reconstituting whole. — apokrisis
My mammalian brain still asks where did it come from ? And from this I just realise that this question will never really have a satisfactory answer.
Thoughts ? — Deus
4. {{ }, 0}. This set is a valid set. — Agent Smith
Perhaps you could explain but do keep it simple, I no mathematician. — Agent Smith
How can nothing be something?! — Greeks
I recall, vaguely, that it all begins with ϕ. — Agent Smith
What sayest thou? — Agent Smith
Barring infinity, what's the solution set to the equation x = x + 1? — Agent Smith
Mathematics, though proven as a tool for uncovering truths, is itself not/only partially about truths (truths to be understood in the conventional sense). — Agent Smith
I recall, vaguely, that it all begins with ϕϕ.
Ex nihilo nihil fit Creatio ex nihilo
How can nothing be something?!
— Greeks — Agent Smith
Zero, or empty set. is nothing, but it is a type of nothing, or nothing of a specific type of thing. If we proceed to say that the specified type is every type, so that it is nothing of any type of thing, then "every type" is a type. And if types are things, (Platonism), then nothing is something. — Metaphysician Undercover
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.