Thanks for your comment @GraveItty

Update

I haven't the slightest clue about musical theory but Pythagoras around 2 millennia ago deduced that for harmony of notes, they lengths of the string had to be in whole number ratios.

1. Physical constants are irrational. The universe is, in that sense, discordant. Something's off. No wonder Hippasus of Metapontum was killed - he upended the Pythagorean theory that the universe was harmonious.

However,

2. If we use the rational approximations for physical constants, e.g. $\pi = \frac{22}{7}$ and fine-structure constant $= \frac{1}{137}$, the universe might turn out to be one grand, melodious composition.

---

3. Is there something geometric about the universe? I'll leave the reader to interpret this question as s/he pleases.

All physical constants are irrational numbers — TheMadFool

That strange fact does suggest something mysterious about a Real world with transcendental numbers. They do imply, not just the logical-geometric foundations of the physical world, but that abstract (metaphysical) geometry is not limited to the space-time boundaries that we take for granted. For example, the transcendental numbers, such as "Pi" and "e" are never-ending, Such fractured integers just keep on going long after our finite minds give up.

The ancient mathematicians were so baffled by the notion of infinity, that they labeled such numbers "irrational". Which they are literally, since human reason is only capable of dealing with fractions of whole numbers. But, now that we have tireless computers to calculate those amaranthine digits, the mystery goes beyond just human limitations, to suggest that even the material world, that we assume is a stable comprehensible reality, is somehow transcendental. Leading some to imagine things that never were, and cannot be . . . in reality.

Personally, I don't normally take such anomalies too seriously, since I'm not a professional mathematician. So I can usually just ignore anything that points beyond space-time. But as an amateur philosopher, I do find that inherent irrationality to be somewhat spooky. I just posted a new blog essay, which reviews a science-based book that reaches some transcendental conclusions, which seem to point beyond the limits of empirical science into the Great Transcendental Beyond. Since I remain somewhat agnostic about such ideas, I'd appreciate your comments. It's only three pages. :nerd:

Information-Consciousness-Reality :
http://bothandblog7.enformationism.info/page18.html

Amaranthine : ceaseless, eternal, never-ending, . . . immortal ???

All this math stuff exists in the mind only. All math stuff has acounterpart in physical reality — GraveItty

Yes. I typically refer to Mathematics as Meta-Physical, because it is not physically real, but a logical abstraction from Reality. So, since this is a philosophical forum, you'd think Metaphysical topics would be routine. But I get a lot of negative feedback whenever my arguments veer from Empirical Physics into Non-empirical, hence debatable topics. That's why I thought the notion of Irrational and Transcendental mathematics would encounter some friction from those insecure posters with Physics Envy. :smile:

PS___Of course, I understand their uneasiness with fringe ideas and pseudoscience. But, I have learned to deal with the uncertainties of the borderlands. So, I like to discuss edgey ideas, but prefer open-minded Skepticism to encapsulated Cynicism. :smile:

Physics Envy :
https://en.wikipedia.org/wiki/Physics_envy

Personally, I don't normally take such anomalies too seriously, since I'm not a professional mathematician — Gnomon

Most of us don't either.

Most of us don't either. — jgill

When I said I don't take irrational & infinite concepts in Mathematics "too seriously", I meant they don't bother me, as they did the ancient Greeks. But, they do intrigue me, in the sense that many scientific & mathematical discoveries have resulted from anomalies that evoked a "huh? that's strange" response.

I'm aware that Pseudo-scientists tend to cut themselves loose from Physical grounding when they explore the open-ended possibilities of ethereal Meta-physical implications. But, although my personal experience is the touchstone for my belief-system, I am painfully aware of how biased misinterpretations of observed "facts" can lead us astray. Anyway, I find the metaphor of the physical world as a manifestation of its mathematical/logical structure to be useful for my personal worldview. :nerd:

I didn't realize this until now of course but I think we need to dig deeper into irrational numbers. What are they? Does it have to do with the continuous as opposed to discrete nature of reality? Geometry seems, in a certain sense, more physical than arithmetic. I'm not as certain about this as I'd like to be.

They are the cutting points of a continuum, the irrational lies in the point where you tear it up. Tearing up is irrational. Unless you apply the scissor to a well rationally determined way. Which is impossible. You can't hit the continuum at a rational point. Eventhough it contains an infinity of them. You will always be slightly irrational. Rational are an idealization. Though for buying 3/2 kilograms of ice-cream they suffice. The dark torn apart. Amaranthine, as I learned above! The are the consequence of irrationally tearing apart. — GraveItty

So, it's not possible to tear at a rational point. I suppose there's no point in asking why?

"You will always be slightly irrational". You as in me? Why?

To suggest that the universe is geometric would assume that there are geometries outside of our universe?

Otherwise where does this geometry fit?

Can something be discordant without some sort of nominal instrument?

Ramification, a branching, an offshoot of geometry, can we sense it in the universe? Perhaps this is a sign that the universe is geometric. The space - the gaps - are not necessarily ending here. Maybe, this will support a view that there are external geometries.

I would seem petty and unwise to presume life ends in the universe. The only way this could be geometric without external geometries would be to say that this was so...

You've lost me but that's the point I susppose.

To suggest that the universe is geometric would assume that there are geometries outside of our universe?

Otherwise where does this geometry fit?

Can something be discordant without some sort of nominal instrument? — Varde

Kindly elaborate on the topics these questions touch upon.

Update

There seems something physical (messy) about geometry and something nonphysical (crystal clear) about arithmetic.

Immanuel Kant, likely for profound reasons, associated space with geometry and time with arithmetic.

Update

There seems something physical (messy) about geometry and something nonphysical (crystal clear) about arithmetic.

Immanuel Kant, likely for profound reasons, associated space with geometry and time with arithmetic. — TheMadFool

Platonic Forms? @Wayfarer

Geometry seems, in a certain sense, more physical than arithmetic. I'm not as certain about this as I'd like to be. — TheMadFool

In my personal Information thesis, Geometry is indeed more "physical" than abstract math, in the sense that it measures relationships between real things, instead of relationships between abstract concepts. But, it's still the metaphysical (mental) relationship (inter-connection) that makes the meaningful difference (qualia), not the physical object (quanta) itself. :nerd:

Immanuel Kant, likely for profound reasons, associated space with geometry and time with arithmetic. — TheMadFool

Perhaps, for similar profound reasons, Einstein associated Space with physical Matter (Objects), and Time with metaphysical Energy (Change). Maybe not in so many words, but implicitly in his Relativity theory. :smile:

I didn't realize this until now of course but I think we need to dig deeper into irrational numbers. What are they? Does it have to do with the continuous as opposed to discrete nature of reality? Geometry seems, in a certain sense, more physical than arithmetic. I'm not as certain about this as I'd like to be. — TheMadFool

I believe that what is the case is that there is always an incommensurability between two dimensions. This is demonstrated by the irrationality of the square root of two, and of pi. What it indicates, is that as dimensions, is a faulty way of representing space. Space being represented by distinct dimensions is a convenient fiction.

There is no clear question in the OP, but I'm happy to speculate. :grin:

As a minor point, geometry and algebra are dual descriptions of nature as Michael Atiyah argues across a number of addresses.

So yes, geometry seems spatial, and algebra seems temporal (or about the sequential order of operations). But in the end, they are mirrored descriptions of the same deeper thing. Just as Einstein had to unite spacetime, so physics generally has developed algebraic geometry as a way to unify a dichotomous description of nature.

Descartes started it by showing curves were algebraic functions in a coordinate space. It continues right up to the central place that permutation symmetry has in particle physics. If it can be said one way in geometry, it can be said the other way in algebra. And Atiyah was the one to really hammer this home.

Then the issue of constants - and why they may or may not be irrational values.

Again, dualities or dichotomies rule. And symmetry principles.

A constant speaks to a lack of change. Change can be lacking either because the world is frozen, static, inert. Or because further change can no longer make a measurable difference. And the world being a dynamic and change-filled place - not the kind of timeless realm of the Block Universe or Many Worlds Interpretation – would have to be defined by constants of the second kind.

So imagine a disk of paper, perfectly circular and unmarked. By virtue of its symmetry, you can't tell if it is spinning or still, let alone if it is spinning and how fast/in which direction. As with quantum spin, you are dealing in whole numbers because the symmetry is such that every change maps the circle back on to itself. Any amount of change winds up as no meaningful change. Until you break the symmetry by marking the perimeter of the circle with a dot, motion if the disk makes no difference.

So one way to arrive at a constant in a dynamic world is perfect symmetry. And that will produce a simple rational value. With quantum spin, the values are 1, 0 or -1. Or when it comes to the electromagnetic charge of quarks with their more complex rotational symmetry, rational fractions like 1/3 and 2/3.

It is also why you get the inertial constants of motion. Newton's law/Noether's theorem telling us that rotation and translation are both costless actions. A rolling ball would roll forever in a frictionless world.

And it is why in mathematics you have identity elements. Zero is the identity element of addition/subtraction operations, one is the identity element of multiplication and division. These particular numbers are the only numbers that make no difference, and so serve as the conceptual anchor for all numbers that then could make for a difference.

One times anything leaves that anything unchanged. Anything divided by one is likewise left unchanged. Zero added or subtracted to anything again leaves it unchanged. Apply the same identity element as often as you like, and like a spinning circle, nothing will be measurably different. The identity element underwrites the mathematical closure of the system.

Then there is the other way to arrive at an unchanging constant in a dynamic world - the path that is open-endedly infinite, yet also an asymptotic approach to a fixed value. This arises in maths, and also likely in physics, because it is the extremisation of an asymmetry rather than the extremetisation of a symmetry.

So pi and e are efforts to relate opposing kinds of things. They produce irrational values as they are imagined as the final convergence of the discrete and the continuous - that ambiguous place where a line becomes an infinitesimally separated pair of points. A Dedekind cut.

Pi is what you get from trying to map lines on to curves. A radius is a line. The circumference is a curve. The ratio of the line to the curve is then the attempt to map two incommensurate things. You can approximate the (straight line) length of the circumference by laying an infinite number of tiniest lengths around it - ie: an infinity of points. But in the end, you are trying to bridge a category difference, an asymmetry. The discrete and the continuous, the straight and the curved, are dichotomous concepts. Ratios of two things metaphysically defined in terms of not actually being the other,

To be discrete is to lack all discernible trace of continuity, and vice versa. To be straight is to lack curvature. To be in inertial motion is to lack acceleration. Etc.

Likewise e does the same trick, except it contrasts geometric growth with its antithesis. That which is growing has to grow from whatever exact value it had at some point of time. But it was growing then as well, so had no exact value.

However in all these cases you can integrate. You can asymptotically approach a fixed and stable value that has an irrational value. The answer will converge towards the same place, even if it does so in a never-arriving and open-ended fashion ... and thus the resulting constant represents a fundamental, locked down, degree of asymmetry which can be used as an identity element.

The famous arbitrary constants of the Standard Model look to be fundamental in this second sense. They arise because the couplings giving rise to mass and energy values for particles are quantum sums over histories. Each is an open-ended sum of all the possible contributions from interactions - as in the most famous case of the QED calculation of the magnetic dipole moment. But also, the convergent sum because as the interactions become more complex and rare, they rapidly contribute less and less.

So somehow - and this is at the speculative edge now – nature sums over every possible asymmetry of a particle's symmetry breaking and winds up converging on a value. This reflects the fact that we are trying to force a metaphysics on the world - the particle as the discrete point, the quantum vacuum as the continuous whole. The incommensurability of these two categories then leads to an irrationally-valued constant for the same reason even the number line ends up suspended between the notions of discreteness and continuity. Even the number line can only converge on the fictitious place where one category - the continuity of a line - becomes its other of the zero dimensionality of a disconnected point.

Anyway, constants can emerge either because of a symmetry that is unbreakable by change - like an unmarked disk, or any kind of relativistic coordinate change - or because of an asymmetry that is asymptotically convergent, locked in on a fixed value to be found at an infinitely distant horizon.

Geometry doesn't have anything special to do with it, except that it too illustrates the general duality of nature. And the importance of algebraic geometry to modern physics shows how a convergence from all directions on symmetry and its asymmetric breaking is also only to be expected.

Duality is everwhere. But then final theories are where it seems to get blushingly hidden from sight, safely wrapped up either as an emergent symmetry constant, or convergent asymmetry constant. Or - whoops - a combination of the two. The combination of fundamental laws and fundamental constants.

As a minor point, geometry and algebra are dual descriptions of nature as Michael Atiyah argues across a number of addresses. — apokrisis

Yes, it in't clear to me too what I'm trying to ask. It's just a vague notion. If the ancient Greeks were left doing only arithmetic they would've never encounterd irrationals - ($\sqrt2$,the length of the diagonal of a square & $\pi$, the ratio of a circle's circumference to its diameter). From this I thought that irrational numbers are closely linkes to geometry.

The rationale behind, the logic to, that is rather simple: Helium, the noble gas, was first discovered in the sun and not on planet earth. Scientists soon found out why - thermonuclear fusion in the sun. That is to say there's something sunny/sunnish/solar about Helium.

It isn't too much of a stretch then to posit there's something geometric about the irrationals. Helium - Sunnish; Irrationals - Geometric.

As a minor point, geometry and algebra are dual descriptions of nature as Michael Atiyah argues across a number of addresses. — apokrisis

The article in that link is above my paygrade. However, I do know some coordinate geometry (Descartes) but that, I soon realized, doesn't cut it because irrationals are incommensurable and some are transcendental. Take the equation of a straight line (y = 2x). No matter what you plug into that equation as the value of x, you will always miss out some points (incommensurable/noncomputable/transcendental numbers) i.e. the line will actually be discontinuous.

Therefore, though geometry and arithemtic are brought together using algebra on the Cartesian plane, it's not a perfect match.

So one way to arrive at a constant in a dynamic world is perfect symmetry. And that will produce a simple rational value. With quantum spin, the values are 1, 0 or -1. Or when it comes to the electromagnetic charge of quarks with their more complex rotational symmetry, rational fractions like 1/3 and 2/3. — apokrisis

Didn't know that! :up:

So symmetry produces neat rational constants in your opinion? However, I maybe wrong of course, these values (spin and the other one whatever it is) don't show up as physical constants in Wikipedia. :chin:


The rest of your post went over my head I'm afraid.

I believe that what is the case is that there is always an incommensurability between two dimensions. This is demonstrated by the irrationality of the square root of two, and of pi. What it indicates, is that as dimensions, is a faulty way of representing space. Space being represented by distinct dimensions is a convenient fiction. — Metaphysician Undercover

Nec caput nec pedes.

So one way to arrive at a constant in a dynamic world is perfect symmetry. — apokrisis

Does that relationship between Symmetry and physical Constants, imply that the Big Bang Singularity was also perfectly symmetrical and unchanging (e.g. eternal), until some perturbation (outside force) broke the symmetry, resulting in our dynamic and evolving world? I ask that strange question because I just wrote a review of a book that reaches Anthropic conclusions from the : "unique “initial conditions” and “fine-tuned constants” that seemed arbitrarily selected to produce a world with living & thinking creatures."
http://bothandblog7.enformationism.info/page10.html

If the ancient Greeks were left doing only arithmetic they would've never encounterd irrationals — TheMadFool

So geometry then injects just enough physical reality into the mathematical abstraction to raise the problem?

Zeno's paradoxes were another route into the same issue. As an object of the mathematical imagination, the number line claims to be both continuous yet also infinitely divided. That is a useful quality for modelling/measuring the world, but what way is it realistic?

I'm with Peirce and those who argue that reality is at root vague, and then this vagueness can be organised towards opposing dichotomous limits of being. So reality is organic rather than mechanical. It has to develop the counterfactuality attributed to rational structure.

When it comes to the number line, this means that it is neither continuous nor discrete in the absolute sense usually claimed. Instead, it is only relatively connected or divided. It can approach either of these claimed states "in the limit". But the limits are themselves unreached in actuality. It is only in the mathematical model that it is useful to think this way.

So mathematicians tend to want to treat the closest approach to these paired limits on possibility as being true actualities. The infinite and the infinitesimal are both real objects in the mathematical imagination. They stand for the concepts of the continuous and the discrete, the line and the point, being extremetised - boundaries states which can actually exist in categorical fashion.

But the alternative view - based on Peirce's organic logic of vagueness - is that the infinite and the infinitesimal are the two ends of a process of dichotomising. Each is yoked to the other in a reciprocal relation. Infinity = 1/infinitesimal, and infinitesimal = 1/infinity. So as quantities, each is formally quantified not in terms of what it is, but in terms of how little of its other it contains.

The rational numbers stand far enough back from the fray that it seems quite easy to treat a continuous line as an ordered series of points. As an object, it can paradoxically be the two things at once. But then as mathematicians go deeper, they have to keep expanding the notion of continuity to come up with a transcendent hierarchy of infinities. Likewise, the ability to cut the number line ever finer leads to a hierarchy of divisions. We encounter the infinite decimal expansions of the irrationals.

This maths is useful, so people believe in it. People get used to "taking the limit" and that allows them to knit together models of reality that marry dichotomies like lines vs curves. We can do calculus and other tricks. We can employ constants like pi, e and phi that are treated as exact values - even though they are at root vague values, being irrational numbers.

So there is no dispute the maths works. But the point is that it works by simplifying reality. It models the fact that reality arises in this symmetry-breaking, dichotomous fashion - the good old unity of opposites - but instead of treating the two halves of the deal as co-defining limits, it treats them as two categorical states of being.

A Peircean approach adds a further dimension to the picture - the organic and developmental one. It says at root is the vague. And so the infinite decimal expansion of an irrational value is another way of accepting this, without openly admitting it. We are happy to have the first four or five digits of pi. That is enough for almost all our practical purposes. The rest of the long line of digits can be allowed to disappear into the mists of the unknowable. We don't have to make a big metaphysical deal out of the fact we can never actually arrive at a final number. Instead, we create a metaphysics which claims that the infinite expansion actually exists ... in some Platonia.

But I am coming at this from the side of physics where vagueness might be a useful thing to be able to model and measure. And where the difference between a constant being produced by a closed symmetry operation, vs a constant reflecting an endlessly convergent series, seems like an important dichotomy to understand.

It isn't too much of a stretch then to posit there's something geometric about the irrationals. Helium - Sunnish; Irrationals - Geometric. — TheMadFool

I have no idea how you make that connection. Was that some other post?

No matter what you plug into that equation as the value of x, you will always miss out some points (incommensurable/noncomputable/transcendental numbers) i.e. the line will actually be discontinuous. — TheMadFool

Well, the more points you plot, the smoother the line will become. So as a construction, you are progressively limiting the possibility of the line turning rough, jagged or fractal inbetween the points you have so far plotted.

It depends which way round you want to view the situation. But the mathematical object appearing on the page is becoming both more a collection of points and more a continuous line at the same time.

So symmetry produces neat rational constants in your opinion? However, I maybe wrong of course, these values (spin and the other one whatever it is) don't show up as physical constants in Wikipedia. — TheMadFool

That is the idea I would explore.

The dimensionless physical constants of the Standard Model are made a fuss of because they seem to be arbitrary values. They are numbers that could have been anything as they don't seem to follow from some fundamental symmetry that would have to be enforce on any form of material being. They are irritatingly patternless as well as irrational as actual numbers.

On the other hand, values like quantum spin are well behaved because they fall directly out of symmetry principles. There is an exactness imposed on them in the way that resonances in a cavity must fall into countable whole numbers - the Pythagorean discovery of harmonics, the music of the spheres, which was the pleasant metaphysical surprise the ancient Greeks celebrated, alongside their disgust at finding numbers could also be irrational or matchingly discordant.

So if we really dig into the issue from the side of fundamental physics, I see three classes of constants.

There are the arbitrary numbers (dimensionless ratios of measured values) that give us things like the odd difference in mass between an up and down quark. Why does one weighs 2.01 megaelectron-volts, the other 4.79 (give or take current measurement error)? A theory of everything would want to find a way to calculate such values from first principles rather than have no good explanation at all.

Then there are the properties of particles that follow directly from closure of symmetry relations - things like the Lie groups or permutation symmetries that underpin gauge symmetry breaking. It is quite natural to see why these are rational numbers, being counts of transformations that leave things unchanged. A perfect triangle maps onto itself three times with every rotation. We are counting its resonant states. In the same way, quarks and leptons - as products of Platonic-strength symmetries, and indeed quantum harmonic oscillators - have no other choices, no possible intermediate states, as they are metaphorically, but effectively, like reverberations in fixed cavities.

The third class of constants are the magic triad of the Planck constants - c, G and h. Okun's cube shows how they anchor all of physical theory, and a theory of quantum gravity will finally unite all three values in the one fully relativised quantum field theory. As constants, these have measured values. But really, it makes just as much sense to set all their values to 1 as they are arranged to create a set of reciprocal equations. Each represents a different kind of physical limit - a limit on connection, curvature and certainty - and so are just absolutes. We can presume that like the gauge symmetries written into the Standard Model, they have no specific material value as they are just pure forms - the expression of pure relations, an ontological structure that would have to be the same for any universe with a self-organisingly "resonant" geometry.

So my overview is that the notion of a physical constant refers to that which is fundamental because of closed symmetry principles - change that doesn't make a change, then that which is fundamental as an measured and apparently arbitrary ratio (why should up and down quarks lack symmetry in their relative coupling strengths?), and finally, underpinning everything is the Planck triad that is itself a kind of decomposed ultimate constant in breaking reality in three absolute ways.

G defines flatness (in terms of a lack of curvature). h defines uncertainty or vagueness (in terms of a lack of counterfactual definiteness). And c defines the rate at which a thermalising coherence of the two is achieved - the universe arriving at a state that is as flat and decohered as it can get at any particular moment in its thermodynamic trajectory.

Again I stress this is my speculative understanding and not even my final opinion. It is how the current physics looks once you see its maths as a reductionist mask and you start to interpret things instead from the point of view of a holistic systems science, or Peircean metaphysics, approach.

The rational numbers stand far enough back from the fray that it seems quite easy to treat a continuous line as an ordered series of points. As an object, it can paradoxically be the two things at once. But then as mathematicians go deeper, they have to keep expanding the notion of continuity to come up with a transcendent hierarchy of infinities. Likewise, the ability to cut the number line ever finer leads to a hierarchy of divisions. We encounter the infinite decimal expansions of the irrationals. — apokrisis

Well, 1/3 is rational and has an infinite decimal expansion. Thinking about it, it is questionable if the idea of the number line is even justified: A line is a spatial object as opposed to a number (i.e. a "count of things"). Writing the "1" somewhere on the line tries to synthesize two very different things and "flaws" the pure space with the pitfalls of "counting".

Well, 1/3 is rational and has an infinite decimal expansion. Thinking about it, it is questionable if the idea of the number line is even justified: A line is a spatial object as opposed to a number (i.e. a "count of things"). Writing the "1" somewhere on the line tries to synthesize two very different things and "flaws" the pure space with the pitfalls of "counting". — Heiko

Every rational number has a decimal expansion that's fully predictable. I know that 1/3 contains 3's only behind the comma. Irrationals are unpredictable until infinity. Hence the amount of rational inumbers between two infinitely close rational is infinite. Between two infinitely close points lies infinity. Rational numbers have no place in Nature. The exist in the mind only, as do so-called natural numbers, the integers. But if integers exist in the mind only, don't irrationals too? Yes. But they refer to a real aspect of Nature. Rationals don't. Nature is irrational.

But they refer to a real aspect of Nature. — GraveItty

But one point of quantum mechanics is that nature does not seem to be that continuous.
Perfect space is still an idea.

But one point of quantum mechanics is that nature does not seem to be that continuous. — Heiko

The wavefunction and its evolution are continuous. Except on interaction, where a strange collapse happens. In the light of QFT, there is a continuous distribution of co-existing paths. Collapsing to a smaller bundle when interaction. Hence the difficulty to describe bound states in that "field".

Does that relationship between Symmetry and physical Constants, imply that the Big Bang Singularity was also perfectly symmetrical and unchanging (e.g. eternal), until some perturbation (outside force) broke the symmetry, resulting in our dynamic and evolving world? I ask that strange question because I just wrote a review of a book that reaches Anthropic conclusions from the : "unique “initial conditions” and “fine-tuned constants” that seemed arbitrarily selected to produce a world with living & thinking creatures." — Gnomon

I really like Wheeler as a bold and holistic thinker. The anthropic principle is also an obviously powerful argument when it comes to the cosmological problem. And I even agree - as Peirce argued - that the cosmos arose from unbound possibility as the inevitable growth of a rationalising structure. Wheeler also got that right with his geometrodynamics.

But the issue is where do you insert some cut-off point between what is truly a product of Platonic-strength inevitability and that which is just some kind of residual chance, spontaneity or indeterminism.

The Peircean view is that arbitrariness, or vagueness, must always exist in the system as Platonic order exists only to suppress or constrain it to the degree it matters pragmatically. Existence is statistical and so based on the stability that arises once a state of affairs can become indifferent to further change - an equilibrium condition in other words.

So anthropic thinking doesn't have to squeeze all the arbitrariness out of cosmic history so that it is seen to arrive at the singular conclusion that is a "self-aware human", let alone carbon-based life. These can be left as local meaningless accidents of history - especially as the basic state of Universe seems to have been fully locked in at the Big Bang, and the long-run destiny is for it to become a generalised Heat Death - a void with a temperature of absolute zero and the only material action being the black body radiation emitted by the holographic boundaries of an anti-de Sitter spacetime metric. That is, the faintest possible sizzle of photons with wavelengths that are redshifted to the size of the visible event horizon itself.

So sure, the Big Bang baked in this story of an eternally cooling~expanding dissipative structure - a cosmos developing in the form of its own heat sink. And then more complex dissipative structures can live for a time on top of that, so as to break down particular accidental entropic blockages.

It was inevitable the Higgs field would get tangled up in the gauge particles and create a degree of gravitating crud that needed to be returned back to the general spreading CMB radiation bath somehow. Stars collected the hydrogen and helium into burning balls of fusion to start that process, but then blew up in supernova, that left behind new levels of crud - all the complex atomic elements. That in turn led to tectonic planets and eventually life as new levels of dissipative structure.

Anthropically, if these higher levels of dissipative structure could happen, they had to happen. The initial conditions of the Big Bang already mandated that. And given that carbon and water are materials that had to emerge if every combination of atomic matter was going to be tried out, then life was going to happen as these materials came with such rich possibilities.

Peirce gives the argument for why semiotics is then itself an inevitable organising informational arrangement. We get to the point where information (as genes, neurons, words, numbers) must become a thing ... because there is a sufficiently rich stock of local negentropy to be dissipated. The heat of a sea floor thermal vent, the radiation of the sun, petawatts of fossil fuel trapped in underground deposits.

So the fact of a hierarchy of dissipative structure was foreshadowed by the very fact the cosmos was based on dissipation as its fundamental principle. Everything is constrained by the laws of thermodynamics. But the same laws only work because of the way they can gloss over the detail.

That is why we can model reality using statistical patterns. Every mountain range on every planet will look fractal - a tectonic flow caught at some snapshot moment between its negentropic building up and its entropic erosion. Humans might want to celebrate any peak which seems especially high, or unusually pointy. But for nature, these are the predictable accidents. Local spontaneity is built into the model along with the global necessity. There is a cut-off - and it is what the maths of chaos and criticality make measureable in terms of things like fractal dimensions and Lyapunov exponents.

To bring it back to your particular concerns, this view does see information as the structure of constraints that limit the arbitrary. So holography has become a big deal as light cones bound the degrees of freedom available to some defined region of spacetime. Information thinking is just a better description of nature as it captures the physicality of a constraining context. You can talk about the material world in terms of a relational structure. And you can add measurement to such a conception by using information entropy as the fundamental unit. You can imagine the dialectical extremes of absolute order and absolute disorder - information vs entropy - and measure the one in terms of the absence of its other. The reciprocal relation of a dichotomy, as I have earlier said.

So there is good reason for science to be shifting generally towards a metaphysics of order out of chaos - an information theoretic framework. But entropy descriptions are still ones that presume an essential meaningless of reality, so we need the next level of information theory - the Peircean semiotic one – to begin to talk about dissipative structure with the extra machinery that makes it alive and mindful.

Then on your first question - was the Big Bang Singularity perfectly symmetrical and unchanging - that is another long answer.

But in brief, it does all come back to symmetry and asymmetry principles – and how these themselves might be the two complementary faces of an even deeper, hence triadic, story of developing structure.

So there just is no singularity, as there is instead just a vagueness that becomes a somethingness as soon as it starts to become a structure of relations. The Big Bang would have arisen from an Apeiron - an unbounded and formless "sea" of fluctuation. A chaos of impulse. A fundamental incoherence that could thus start to become something by becoming structurally constrained in some developing fashion.

In a sense, a chaos of dimensional fluctuations is a perfect symmetry. Any and everything can be happening. It is also the definition of unchanging as even its ceaseless change is no change. Everything remains as confused as before, which is confused as possible.

But the anthropic principle tells us that something had to happen, something had to change. The Apeiron's very lack of any limits or character would be the grounds from which limitation and charactersation must have been able to arise.

So the breaking of the "Big Bang singularity" would be like a phase change where disorder learns to constrain itself. But all this would be in the form of an internally caused shift. We have to note that the Big Bang described in its purest sense would be just an adiabatically spreading and cooling radiation bath. There would be nothing really happening except an expansion making more spacetime, driven by a cooling which made the general energy density ever more spread out.

The universe is a hot point tumbling into the vastness of its own heat sink. And it is a closed system from start to finish (once we clean up details like dark energy - the true source of the cosmological constant). So it is both a pair of extreme changes - a plunge from the Planck Heat to Absolute Zero, an expansion from the Planck Length to the de Sitter holographic solution that spells the practical end of time. But also, all this is just a swapping of the tiniest/hottest radiation bath for the coldest/largest radiation bath.

If we count the total number of degrees of freedom - the total entropy or information - the same number at there at the Big Bang as they are at the Heat Death.

This again is where we seem to need a deeper level of description to measure what seems to us some real physical event - namely the birth and eternalised death of a Cosmos. And that is where being able to measure this tricky thing of Peircean vagueness, or Anaximander's apeiron, would look to have a role to play in fundamental theory.

Information is the brave new metric. But an even more general metric looks called for.

Well, 1/3 is rational and has an infinite decimal expansion. — Heiko

And even 1 is 1.00000.... (and claimed to be indistinguishable from 0.9999....) :smile:

Thinking about it, it is questionable if the idea of the number line is even justified: A line is a spatial object as opposed to a number (i.e. a "count of things"). Writing the "1" somewhere on the line tries to synthesize two very different things and "flaws" the pure space with the pitfalls of "counting". — Heiko

All modelling is questionable. But the main question that needs to asked is: "Does it work, is it useful?".

Obviously, I want to ask the metaphysical question of what reality actually is. But I also accept the epistemic constraint that all our accounts of that are going to be constructed models.

So it is not a problem that maths might use a rather paradoxical construct like an unbroken line that is also an infinity of broken points. That construct doesn't have to be the truth of the reality it models.

The problem only arises when the maths starts to be read as what is the indubitably real, and that is used to either make obviously silly claims about reality (such as the Block Universe) or to close of metaphysical inquiry as to other reality models.

I really like Wheeler as a bold and holistic thinker. The anthropic principle is also an obviously powerful argument when it comes to the cosmological problem. And I even agree - as Peirce argued - that the cosmos arose from unbound possibility as the inevitable growth of a rationalising structure. Wheeler also got that right with his geometrodynamics. — apokrisis

Wow!! I didn't expect such an expanded & erudite response to my open-ended question. Since my brain is also a "dissipative structure", it may take me a while to digest all that "Piercean vagueness". A lot of it goes right over my pointy little head. So, I'll have to get back to you. :wink:


In theoretical physics, geometrodynamics is an attempt to describe spacetime and associated phenomena completely in terms of geometry. Technically, its goal is to unify the fundamental forces and reformulate general relativity as a configuration space of three-metrics, modulo three-dimensional diffeomorphisms. ___Wikipedia

PS__My own attempt to make sense of Big Bang & space-time may be labeled "geo-info-metro-dynamics". But, at the moment, I'm not sure what that means. :cool:

I thought I would have to think about your "erudite" post over the weekend. I'm only vaguely familiar with Semiology. But, I couldn't resist digging into the Piercean vagueness right away. So here goes :

First, I'll have to translate some of that apokrisean semiology into terms that I am more familiar with.

- that the cosmos arose from unbound possibility as the inevitable growth of a rationalising structure

Unbound = eternal?? . . . . rationalizing structure = Logos??

arbitrariness, or vagueness, must always exist in the system as Platonic order exists only to suppress or constrain it . . .

Arbitrary = Random Chance? Order & Constrain = Natural Selection? Natural laws?

been fully locked in at the Big Bang, and the long-run destiny is for it to become a generalised Heat Death

locked-in = natural laws? . . . . Heat Death = born to die?

this story of an eternally cooling~expanding dissipative structure

Dissipation & Entropy seem to be necessary adjuncts to Integration & Energy in the program of Evolution.

Adjunct : "a thing added to something else as a supplementary rather than an essential part."

"Dissipative structures are nonequilibrium thermodynamic systems that generate order spontaneously by exchanging energy with their external environments."
https://www.encyclopedia.com/education/encyclopedias-almanacs-transcripts-and-maps/dissipative-structures

"Dissipative systems have a tendency to become more “complicated” while dissipating energy. That is, they develop patterns, structures, or behaviors that they did not have when first formed"
https://gmwgroup.harvard.edu/dissipative-systems

Anthropically, if these higher levels of dissipative structure could happen, they had to happen.

Necessity = esssential to the design or program?

why semiotics is then itself an inevitable organising informational arrangement. . . . negentropy to be dissipated

Semiotics seems to imply that Meaning is inherent to the system of evolution. The question is : meaningful to whom?

"Semiotics is the study of sign processes, which are any activity, conduct, or process that involves signs, where a sign is defined as anything that communicates a meaning that is not the sign itself to the sign's interpreter". Wikipedia

Negentropy is what Aristotle called "entelechy" and what I call "enformy" in my Enformationsim thesis.

laws only work because of the way they can gloss over the detail.

By "gloss over" you mean "allow" or "permit" such details as the temporary exceptions to thermodynamics that we call living organisms?

Local spontaneity is built into the model along with the global necessity.

That's what I call "freedom within determinism"

information as the structure of constraints that limit the arbitrary. . . . information vs entropy

That "structure" may be what I call the constructive power of EnFormAction.
Information vs Entropy = Enformy

a metaphysics of order out of chaos - an information theoretic framework. But entropy descriptions are still ones that presume an essential meaningless of reality,

But "order" is the essence of "meaning". So the fact that Reality contains creatures capable of semiotics and extraction of meaning would seem to deny the "essential meaningless of reality"

So there just is no singularity, as there is instead just a vagueness that becomes a somethingness as soon as it starts to become a structure of relations. . . . Apeiron - an unbounded and formless "sea"

The un-formed "vagueness" of the Singularity may be comparable to a seed that doesn't resemble the tree.
What you call "Apeiron" is similar to what I call "Enfernity" : the unbounded realm of Eternity and Infinity, which is an unformed ocean of Possibility. Which I also call BEING, the eternal power to be, the essence of existence. The "seed" contains a tiny bit of Potential (genes, programs) that gradually Becomes (come into being) a Real World.

is a perfect symmetry. Any and everything can be happening. It is also the definition of unchanging

Perfect Symmetry = eternal & infinite, but still, pool of Potential

"Tyger, tyger, burning bright / In the forests of the night, / What immortal hand or eye / Could frame thy fearful symmetry?" ___William Blake

something had to happen

So, that infinite Potential couldn't be bottled-up forever? Something Actual must come out of it. But what Cause triggered that phase change from Voltage to Amperage, from Ideal to Real?

where disorder learns to constrain itself.

That's what Design does : it constrains disorder into order; it organizes (pattern) that which is disorganized (randomness).

same number at there at the Big Bang as they are at the Heat Death.

The evolutionary process comes full-circle from the nothingness of Potential, to fullness of Actual, and back to zero again. From Eternity to Timelessness.

But an even more general metric looks called for.

I propose that the emptiness of Shannon's Information as container, be supplanted by []Enformation[/i] as carrier of content.

Whew! I'm exhausted from writing all those big words. I'll have to take the weekend off to recuperate. :nerd: :yawn:

EnFormAction :
Ententional Causation. A proposed metaphysical law of the universe that causes random interactions between forces and particles to produce novel & stable arrangements of matter & energy. It’s the creative force (aka : Divine Will) of the axiomatic eternal deity that, for unknown reasons, programmed a Singularity to suddenly burst into our reality from an infinite source of possibility. AKA : The creative power of Evolution; the power to enform; Logos; Change.
http://blog-glossary.enformationism.info/page8.html

So geometry then injects just enough physical reality into the mathematical abstraction to raise the problem? — apokrisis

There's something physical about irrationals in the sense that there's measurement (geometry) involved: length of a square's diagonal ($\sqrt 2$), length of a circle's circumference and diameter ($\pi$). However, I don't know how it works for physical constants though - are they too measured like we would a line or a curve on a piece of paper?

Zeno's paradoxes were another route into the same issue. As an object of the mathematical imagination, the number line claims to be both continuous yet also infinitely divided. That is a useful quality for modelling/measuring the world, but what way is it realistic? — apokrisis

Zeno's paradoxes of motion uses ratios. The method of reiterated halving would mean both Achilles and the tortoise would've never ever found themselves on an irrational point along the track. Infinity though has something to do with irrational numbers - most formulae for irrational constants (e and $\pi$ are infinite series).

I'm with Peirce and those who argue that reality is at root vague — apokrisis

What's vague about irrational numbers? I thought they were distinct points on the number line (geometry). Now that reminds me of representing numbers using, as the authors in a book posited, 1. the set method and 2. the number line method.

1. The set method: {€} is 1, {?, q} is 2, so and so forth
2. The number line: Google

The set method is not is not amenable to irrationals while the number line (geometry) is.

Ah! I get why you brought up vagueness. The Greek method of computing $\pi$ was by approximating it, the final value being given as a range the lower and upper limits being rational numbers. Archimedes in fact proved that $\frac{223}{71} \lt \pi \lt \frac{22}{7}$

Unbound = eternal?? . . . . — Gnomon

It is unbound possibility. So not about an actualised duration.

Vagueness is defined as that to which the principle of noncontradiction fails to apply. There just is no fact to the matter. Anything might be the case when nothing has yet concretely happened.

rationalizing structure = Logos?? — Gnomon

Yep. Heraclitus spoke about the dichotomy of logos and flux. The Pythagoreans framed it as apeiron ("Unlimited") and peras ("Limit"). Peirce as tychism and synechism.

Everyone uses a different jargon to say essentially the same thing.

Dissipation & Entropy seem to be necessary adjuncts to Integration & Energy in the program of Evolution. — Gnomon

A vortex is a dissipative structure - the emergence of order in the service of disordering.

What would be a big conceptual shift is to see dissipative structure (a "far from equilibrium" system) as not secondary to the ordinary Second Law definition of an equilibrium system, but instead the more generic case.

So instead of nature being already dead - entropically closed - and so make it a mystery why anything ever happens at all, nature is seen as a self-organising vortex (metaphorically). It organises the deeper thing of a vague potential into an entropic gradient. It creates the heat sink which is what then also creates the heat that fills it.

The Big Bang was a symmetry breaking which gave action a direction. Action became something countable - as information/entropy, or local degrees of freedom. And the expanding and cooling also became countable as the density of the action became as spaced out as possible.

So you are always dealing with duality. And dissipative structure is the order out of chaos story. Organisation develops to maximise the production of entropy.

We don't generally see that because we enter the story at the point in the Universe's history where it is only a few degrees from its Heat Death and it is full of material crud that is going to take forever to round up in black holes and radiate away.

Semiotics seems to imply that Meaning is inherent to the system of evolution. The question is : meaningful to whom? — Gnomon

Semiotics is indeed the science of meaning. But having a strong definition of meaning is also what allows you to define the meaningless.

So sure, any complex dissipative structure that also has a coding mechanism and can thus implement an epistemic cut, or have a modelling relation with its world, is all about truly meaningful action. Even a bacterium is semiotic as it has genes to run the show and model its world in useful fashion.

But a tornado lacks a model of its world. It has no code to support a selfish point of view. It is a dissipative structure, but now the information informing its behaviour is spread out in its environment. It moves across the landscape in pursuit of gradients of hot air to feed its upward spiralling existence. But we wouldn't credit it with any actual capacity to store a purpose and pursue an outcome.

Information theory lacks a division - an epistemic cut - between a-biotic and biotic dissipative structures. Semiotics can speak to both the continuity of the mental and physical "realms", as well as put a precise finger on the difference between the two.

Negentropy is what Aristotle called "entelechy" and what I call "enformy" in my Enformationsim thesis. — Gnomon

Negentropy is materialised constraint, entelechy is the potentiality of having a purpose. So one looks to the structured future, the other is that structured future embodied.

So the fact that Reality contains creatures capable of semiotics and extraction of meaning would seem to deny the "essential meaningless of reality" — Gnomon

Semiotic systems construct meaning. A code-based modelling relation with the environment - such as the ones supported by genes, neurons, words, numbers - is how a first person point of view arises within a "third person" physical world.

So sure, information theory is now dual with statistical mechanics. The same maths underpins both. But that glosses over the semiotic story. Information loses its everyday meaning and becomes simply a count of symbols or marks. I can count how many bits a channel can reliably transmit. That doesn't mean the pattern of marks is a language in which something is trying to be said. It could be just random noise.

What you call "Apeiron" is similar to what I call "Enfernity" : the unbounded realm of Eternity and Infinity, which is an unformed ocean of Possibility. Which I also call BEING, the eternal power to be, the essence of existence. — Gnomon

Why invent another jargon to describe something that already has so many names?

The Tao, Brahman, Apeiron, Hyle, Quintessence, Bosenazelo, Hunabku, Manitu, Orenda, Wakonda, Wakan, Mana. Peirce called it both Firstness and Vagueness. The Kaballah calls it Tohu wa-bohu.

All cultures have some version of it as the way a cosmos could arise organically as order triumphing over raw chaotic possibility. The more advanced versions, like Ying-Yang, Buddhist dependent co-arising, or the Greek Unity of Opposites, also get the duality that breaks the symmetry of the unformed potential. But the next step has to be to develop a fully logical, mathematical, model of what everyone can understand intuitively.

Peirce is certainly important on that score. As is modern hierarchy theory and dissipative structure science.

So do we need yet further jargon like Enfernity? And in fact, it seems wrong because the vagueness of a pure potentiality is that which lies beyond the concreteness of time and space. It is where time and space would arise as complementary limits on being. The birth of an organised cosmos is a structure that becomes a measure of properties like duration and extent. The extremetisation of those properties as eternity and infinity are then to take these physical directions and point to a future (but not a past!) that is unlimited, yet definite.

So infinity and eternity are a pair of concepts that come from a quite different metaphysics - one based on a mechanical understanding of the world. It leads to an Atomist conception of a Cosmos that simply exists forever and has an unending extent.

The organic metaphysics I'm talking about is all about the self-organising creation of the Cosmos as the growth of focusing limits on unconstrained "everythingness". So the Cosmos is not eternal. It has a birth and death of time, space and material content. The Heat Death may last "forever", but that is essentially a state of ultimate void. It may always have a matter content, but it will be just that of a quantum vacuum - a featureless rustle of virtual particle excitations.

So I would say your thinking goes in the wrong direction here. It re-embraces the mechanical model of reality that an organic conception is intent on rejecting. :chin:

"Unbound = eternal?? . . . ."

It is unbound possibility. So not about an actualised duration. — apokrisis

Agreed.
Potential :
Unrealized or unmanifest creative power. For example the Voltage of an electric battery is its potential for future current flow measured in Amps. Potential is inert until actualized by some trigger. In the Enformationism metaphor, the real world was originally an idea in the Mind of G*D, with the infinite possibilities of Omniscience, that was realized by an act of Will.
http://blog-glossary.enformationism.info/page16.html

A vortex is a dissipative structure - the emergence of order in the service of disordering. — apokrisis

Yes. Ironically, in thermodynamics, far-from-equilibrium is not necessarily disorder, but can be self-organizing.

And dissipative structure is the order out of chaos story. — apokrisis

Reductionism tends to focus on the local chaos, and to ignore the stable global order.

Why invent another jargon to describe something that already has so many names? — apokrisis

In my Enformationism thesis, I was repeatedly linking Eternity & Infinity, so for brevity I simply coined a contraction to "Enfernity" to describe the opposite concept from Einstein's "Space-Time".
Enfernity, Enfernal :
A contraction of “Eternity & Infinity” to indicate the irrelevance of those dualistic terms in the holistic state prior to the emergence of space & time from the Big Bang Singularity. Eternity is not a long time, it's the absence of space-time.
http://blog-glossary.enformationism.info/page8.html

So I would say your thinking goes in the wrong direction here. It re-embraces the mechanical model of reality that an organic conception is intent on rejecting. — apokrisis

I think your thinking is seeing only one side of a two-sided coin. My model is both Mechanical (scientific) and Organic (philosophical). :cool: