Feigenbaum's constant is an eternal object

A.N Whitehead defines an eternal object[EO] as any entity whose conceptual recognition does not involve a necessary reference to any definite actual entity of the temporal world. Squareness or roundness are eternal objects according to Whitehead’s theory. The Feigenbaum constant[FC] is a ratio of distances between successive bifurcations which converges rapidly to a constant of 4.669201660910.

This number is independent of the system studied. It has be verified independently in multiple labs. The constant results in a periodic doubling cascade. It appears in physical systems as diverse as dripping faucets and acoustic feedback {Jimi Hendrix was an earlier master of the latter phenomenon who influenced subsequent electronic musical applications. } The F constant is as constant as Pi. What is exciting about it to me is that it’s new. Of course, the concept of eternity is problematic in itself. Eternity is not empirically observable but may be inferable by extrapolating from duration in our experience of time. Eternal objects are purely conceptual, but are instantiated in every actual entity. This proposition could have been posted in the Math Forum, but I am more interested in considering the religious/spiritual implications.

Why don’t you start. I wouldn’t know where to begin.

Rather than an “object” the eternal is an abstraction.
One is invited to think about God (Einstein, newton) when thinking of these “eternal”, what? Consistencies? But the eternal is never lived, never actually encountered, nor can it ever be. The object, the concept, is a judgment on the collection of moments.
Mathematics in theoretical physics are important. But one should beware of the nature implied by its application upon what is? If all you have is a hammer then everything starts to look like a nail. So, while I believe that science and math can be as communicative to the soul as prayer, I believe that they remain, like prayer, dependent on the strenght of someone’s confidence. What these mathematical formulas end up telling us about God, about the eternal, or even their capacity to serve as “eternals”, will continue to be more a reflection of the observer than of the observed.
Note that I don’t mean this as a “put down”, but more as a reminder of what our role is in the exchange with reality.

OK. I begin with the discovery of mathematical order in apparently chaotic phenomenon. Contemporary postmodern thinkers often speak of truth and values and even of our most basic perceptions as social constructs. They tend to emphasize the disconnectedness of these social constructs from the alleged world “out there,” almost as if there were no world at all but only the worlds we construct. The F constant is an instance of discovery of order deeper than our social practices, languages, and concepts.

I’m keeping to the philosophical distinction between what is actual and what is possible or potential. The qualities “squareness” and “redness” are general possibilities that are actualized in a particular square or red thing. They are universals. Many different particular things may be square or red. Following Plato, we recognize that these possibilities are themselves never changing. But, the term “idea” has a long complex philosophical history. To free the concept from this history, Whitehead called them “eternal objects.” Instead of "eternal"we could say they are non-temporal. By themselves they are not actual. They depend upon actualization by particular actual entities. An “eternal object” is a “pure potential”. The F constant is a striking instance of an eternal object because despite its ubiquity, it has only been recently discovered [@ 40 years ago].

Yes, I’ll agree with that. Just the fact that there are verifiable laws of nature attests to the fact that there is a pattern or order to the universe. Now, I’m not one for the design argument for God, but I must say this pattern/order indicates that the universe is not just chaotic and random.

Hello Felix,
I guess my point is that calling “ideas” by something else does not address or solve the philosophical objections to Plato’s idealism.
For many decades the speed of light was pretty much “set”. Now some believe that light may behave differently now than it did in the early universe. I just mention this to illustrate how a “eternal object” might become temporalized. So what was so eternal about it? Maybe the universality of objects can be known only to the Eternal. To us temporal beings things suggest universal ratios, laws, values but we only assume, they are as eternal as it seems to us, they are “eternal” as judged by us, the finite and fallible observer.

I don’t really see any significant difference in Feigenbaum’s constant and the speed of radiant energy, “light”, as far as eternalness. Neither can ever be any different than it is and neither, propagation or mathematical representation of chaos can ever change, never has, never will.

Perhaps to those who never understood the whole God issue, this might seem relevant or significant. But to me, it isn’t anything extraordinary. There are other constants that can never be anything different than they are such as the universal maximum rate of change (which causes that propagation of light speed). The shape of a sphere is eternal in that the universe can never be without one somewhere, thus all of its mathematical representations are also eternal and “physical”.

They found yet something else eternal, well okay. No big surprise to me.

I think we have to be careful about what “eternal” means in this case. Does it mean “continuing forever”? Does it mean “at” eternity (as in, the end of time)? Or does it simply mean atemporal. My bets are on the latter. Pi, for instance, doesn’t “last forever” or exist “at the end of time,” it is something that doesn’t depend on time. It isn’t 3.14 at 2:35 AM but then become 3.15 at 4:46 PM the next day. It remains constant, not as a function of time, but as a function of being outside time.

Oh for God’s sake no, Rumplestiltskins constant?

Please don’t use maths in philosophy like that it kills all reason.

Feigenbaum’s constant my ass. :slight_smile:

Horrible thread i don’t know where to begin either, but I know that maths is not exactly equal to something that is conceptual, it’s close to something that is not at the best of times! I mean for Odin’s sake. What?

It’s only a constant because we’re making a repeating 2-d object behave like three-d. I’ve written on this before.

Anyway… this is one of the reasons why we can’t calculate Mersenne’s Primes, people don’t grasp that polynomals- which fractals have to behave the rules of progressive series of- from the highest to the lowest (literally in that order)- WITHIN, are a series parallel to our number theory. If you start big, and work down… these things don’t go on for infinity, they break down into angles relative to their square root, in relationship to the shape squared above it. You can find all the primes patterened off of that. All fractals behave to these rules that are based on polynomal successive series. It’s remarkably simple- retardedly simple, and early mathematics in the west were built on this very assumption, but the stoics and aristelians butchered this system of numerics early on. And we’ve suffered for it ever sense. In our current system, we’re aware that spirals dominate these series, but don’t officially know why. We also know that the patterns seem to be finite, but when applied geometrically, goes on forever… but no one quite explained why other than numbers such as 1 2 3 4 5 go on forever.

At bottom, I’ve found it to be a simple cognitive glitch. Classical systems of Abacus using different base numbers, such as Chinese versions, are better at navigating fractal distributions via multiple root systems.

We need to note the obvious about these… it’s the formulas we have that are failing us… they ‘appear’ to go on forever, but don’t actually go on forever. It’s because they simulate depth… but the formulas lack expressions of depth in and of themselves. Hence the need for polar and grid mapping of position when you focus in on any given point. That picture above you present doesn’t go on forever… 0.5 picoliters is the max for the average high end computer you would expect to find in a math institute… then it becomes meaningless. The formula is devlivered visual, and it stops at that size. It tells us more about how our brain processes information, than how infinity works. We didn’t evolve to comprehend visual infinities, just to accept things go on for a very long ass time, and that such journeys are likely not worth the energy expended. What is important about such fractals is the way prime numbers play out in them. Fractals give us the advantage that most series play by polynomal rules, outside of rules of progressive succession. You can get all sort of weird bifurications resulting. rDNA seems to encode on this basis, as many plants and cellular organizations play by this rule. Life doesn’t stretch out for infinity… there isn’t a cell the size of a planet that kept growing forever… like fractals, size and logistics limits it’s rules… something a limited mathematical model doesn’t compensate for. However… for the size and chemistry of life on earth… these bootleg eternal objects are dead on in terms of importance. They might not be eternal, but they are the building blocks that ceelular intelligence builds larger lifeforms out of. Hence the importants, and my focus. It goes well beyond mathematical curiosity, it’s a fundamental question of philosophy. Just no good to get stuck in the cognitive glitch of assuming they go on forever when… well, they never do. Just we such at math so bad we don’t have a native way in our mathematics to close open ended math problems realistically.

That cognitive glitch is mystical though admittedly, from a biological perspective. Just doesn’t give you the full picture. But the best mathematicians historical have also been mystics, working with the paradoxes of the systems they are presented with. We gotta remember the mystical, cultic roots of mathematics, from egyptian and babylonian temples to Pythagorians and Perganum Stoics. So… it’s not unhealthy to assume this has religious roots. Religion always has had this element… just some fairly secular people can also think it once it’s formalized without the need for further mysticism. They are call scientists, and they tend to be remarkably stagnant and uninventive. And their always amazed that religious people can be good scientists too. Absolutely blows their mind… but takes massive ignorance on their part to not look into the origins of how the systems they used came into existence.

Hence, kudos to this thread- your carrying on a beautiful and most ancient tradition. Just don’t annoy me by saying the son of god talks through the fractals to you. Just appreciate God exists, and he knows why your interpreting such things so wrongly, and loves you for seeing beauty in such misunderstandings. Means at the very least your exploring your own potentiality and nature through them, which is quite worthy.

We live in a universe that is a rare bubble of space-time in the infinite, seething cauldron of the eternal meta-universe. Outside our absolutely unique and isolated bubble, which we call the Big Bang, there is neither space nor time as we know it. Eternal objects “exist” non-temporarily as pure potentials outside space and time. So Feigenbaum discovered something that was there potentially all along.

Arrogance or ignorance?

Not true, btw.
And don’t even think that Science has in any way proven or seen the slightest evidence of it.

This, this whole quote is a good example of what I am saying. You define what is, “where” etc, and yet all of it is an interpretation, a theoretical construct, mathematically valid but not necessarily factual, actual.
Eternal objects are useful in the pursuit of an atemporal perspective, to provide a structuring to what exists. We do need that, but it isn’t necessary also to believe our own hype and treat abstractions as objects. They are not pulled from thin air but they are not independent of peer review and acceptance.

Guys–I’m well aware that I am speculating.

Anyone have any idea why there is such a big Whoo-haa about Platonic existence?

“…philosophy is explanatory of abstraction, and not of concreteness. It is by reason of their instinctive grasp of this ultimate truth that, in spite of much association with arbitrary fancifulness and atavistic mysticism, types of Platonic philosophy retain their abiding appeal; they seek the forms in the facts. Each fact is more than its forms, and each form ‘participates’ throughout the world of facts. The definiteness of fact is due to its forms; but the individual fact is a creature, and creativity is the ultimate behind all forms, inexplicable by forms, and conditioned by its creatures.”

A. N. Whitehead, Process and Reality (Gifford Lectures Delivered in the University of Edinburgh During the Session 1927-28) (p. 20).

Okay…
…now could you perhaps address the question…? :-s

Why do people care if Platonic forms “exist” (especially since they have no notion of what “to exist” even means).

As far as I can tell, it seems to be merely an issue of dogmatic religious propaganda - from the anti-religion religion; the worship of the Hindu Shiva, the Christian Devil, and the Judist Yetser HaRa - the “Destroyer”.

I thought I did.

Because when something exists it has affects.

An issue for whom?