Math? pffft.


The philosophy of informative connections
(a dissertation)

Potentials are things we use to establish a baseline or first point of informative connection, to plot a graph of some evolution, in terms of "work".
How the system works, compared to 'requirements' any output has, in thermodynamic terms. (How much fuel produces how much output).

A potential (as unused fuel for the engine), forms a 'non-moving' reference for a moving one. A potential is only possible because of movement.
Any object is 'stationary' only in any sense that other objects are not. All motions and so all potentials, are relative (A. Einstein).

The universe is discrete (there's only one, that we can see), and continuous - because the single universe is in constant (continuous) motion; it's expanding, more or less continuously, though there is no reason for the expansion to be a "single-movement", and there is some evidence it is at least two kinds of expansionary motion.

Continuity and elasticity are invariants; discrete or algebraic relations with continuous elastic connectivity, evolve dimensionally.
Heat and convection are limited, by geometric continuity, and elasticity. Discrete states as modes, evolve algebraically; information is discrete and continuous.
The universe is information, potentially and in 'working' form.

'Particles' in motion are the equivalent of work and information content.
Content is a volume, which is in relative motion across a surface area. Any discrete state with algebraic content (potential) evolves by diverging around a center, which is an informational 'zero-point'. This reference is another potential, moved or scaled to be motionless relative to the 'working system'.

Informational divergence or dissipation, scales as \,k_B ln(2) \, algebraically (discretely).
Heat is continuous (but also evolves as discrete particles of 'energy'), a volume of heat has an equivalent volume of information. A glass of (continuous) water has an equivalent discrete content of 'drops of water'. A 'bit' in your computer is a quite large number of these individual particles (electrons), that we say represents a single potential, a glass of water is a 'bit', of information (an empty glass is too).
When we can scale information content as single atoms, then as single 'fractions' of atoms, we'll be near the 'informational limit', although black holes are at this limit, which is elastic, and thermodynamic.

Just as a discrete universe implies the existence of a medium, the existence of a discrete medium implies its own non-existence. "The universe exists", conveys the information that the universe didn't exist (or another one still doesn't).

Information has to have a phase, it has to 'flow' or change from one discrete state to another, or a continuous flow has to be of discrete states, or algebraic modes. An elastic medium implies modes, of vibration or oscillation. Discrete states imply a difference in phase in the oscillations, including the polarity of the same 'discrete' oscillations.
That is, an oscillation goes 'up and down', or 'forward and back', by definition, an external frame 'sees' a center move away and return, or rotate around a central equilibrium, a reference point.

Phase changes evolve around a critical point, near which either of two discrete modes are 'mixed' so that they are equivalent (indistinguishable). When the critical point moves (the system moves, equivalently), discrete modes appear.
In a liquid, with continuous translational symmetry, the disorder is equivalent to a lattice with indistinguishable points (each vertex, or molecule, has an equal translation parameter or vector, no position is unique).

A transition to a solid phase breaks this symmetry. Now there's a regular lattice (no disorder or translational equality, every molecule has to 'report' a unique position). A chemical way to say this, is the more symmetric phase is seen above the critical point which is thermodynamic (elastic).

The Hamiltonian (transition function) of a system 'exhibits' all possible symmetries, and higher temperatures mean that more states are available. The Hamiltonian (the algorithm), finds more 'solutions' as modes - thermal symmetries - across a broader spectrum.
This broadening of available states, is not seen at low temperatures; near absolute zero the potential of thermodynamic 'informative connections' is attenuated, or confined. A certain continuity is lost.

Energy 'drives' the transition function, or the Hamiltonian processes the available states as energy allows it to find them.

Consider a curved surface. Curvature in 2 dimensions can be 'convex', or the opposite: 'concave'. Positive and negative curvatures are the only possible 'states' available to a surface.
A bowl is a curved surface. A bowl is symmetrical (it has a center at which curvature is locally flat; there's a horizontal neighbourhood near the central point of the bowl). It has a symmetrically located 'rim' or edge, at a constant radius from the central point.

If a 'particle' (a marble, say), is positioned 'on' the edge, (the edge has a 'width' that's sufficient so the marble finds a static position on it), at a constant radius.
Then assume this marble is given just enough momentum to leave the edge and roll towards the center - it will continue past the center point and towards a point on the opposite edge, but it won't get there.

It won't because gravity and friction mean energy will be lost (as sound, and heat), from the marble to the surface it's moving along.
The opposite edge is 'unreachable'; it expands away from the marble's potential to reach it.
If the marble and the surface were frictionless, it would have enough energy to potentially reach the other edge.

Instead it's 'forced' to reflect or invert from a point which is short of the outer diameter - it scatters back from the opposite side of the bowl towards the center again. This repeats until sufficient momentum is absorbed from the marble that it finds a static position near the center (in the flat neighbourhood of it).

This models what photons scattering from the last visible surface, at the edge of visibility of the universe do. Well, they don't 'bounce' back and forth between edges like a marble in a bowl, but they do most certainly get halfway - to the central neighbourhood, where we are.

We seem to be lacking a thesis and some foundationa definitions.

Also the foundational claims don't seem well established and there seems a fair amount of seemingly irrelevant information, but I'm willing to consider that I'm missing a point here.

Are you using "informative connections" in the same sense as these fellows?
Discovering Informative Connection Subgraphs in Multi-relational Graphs
http://lsdis.cs.uga.edu/library/download/SIGKDD-FinalCameraBWLatest.pdf

Why is it a "philosophy?" It would seem you are striving more for a "physics" of informative connections.

Galileo was a philosopher. He did several thought experiments - so did Archimedes.

If the universe has a geometry and a photon looks like a particle, then it's like something that's a message from the void. If Galileo had been able to see that the universe was expanding or figure out a bit more about geometry (that wasn't figured out back then), he could have beaten Einstein, maybe not Maxwell, though.

The idea is that any connection is like a process that delivers something (a "channel"), a photon has a certain frequency, you can measure this by interacting with it, or capturing it. A connection means there are two ends, in the case of a distant galaxy or star, we can see it because it can see us. So the edge of the universe that we can see, must be able to see us.

Information is a connection. If we did reflect a beam of light from the most distant object back towards it, it wouldn't be able to get back because the object will have accelerated to beyond the limit, the velocity the beam can have.

What we know about the geometry of marbles, and the geometry of bowls, means we know a marble will accelerate from the edge of a symmetrically curved surface, which is convex (negatively curved) and has a locally flat center. It will decelerate correspondingly as it moves away from the center.

Its movement is confined; the geometry of this cavity will 'process' the marble's momentum symmetrically, it will oscillate in a damped way and lose momentum, decaying to a minimum potential (static position).

When it has momentum, it has velocity at every point on the surface it interacts with; it accelerates toward the center then decelerates away, so logically it has an acceleration of zero at the center. A 'free' particle can move from one edge to the midpoint to the other edge, but will not evolve 'at' the midpoint, only beyond it. Curvature is locally flat, any accelerations toward the midpoint are countered by equivalent decelerations away from it. At the midpoint, acceleration is zero (velocity is constant). A surface can accelerate a particle to a constant velocity, QED.
The bowl and marble can be described by an equivalent constant velocity from one edge to the other of a surface that 'admits' constant velocity marbles.

One that looks like the marble in a convex cavity looks like, in the central neighbourhood where it has a constant velocity.
Marbles arrive (from infinity) and pass through the centrally flat neighbourhood, on to infinity. The curvature has to be different; instead of being locally flat, maybe it looks locally curved, and the 'cavity' has zero curvature. The surface could be described as having a tension, which the marble deforms somehow, or the marble is deformed - the tension 'squeezes' on the marble somehow, on its surface, and it gets pushed along.

What sort of transforms are needed to retain the geometric picture?

One other thing about a real marble (a really nice spherically symmetrical one. an 'ideal marble'), and the mechanics or dynamics of rolling, which means friction and sound are 'lost energy': the motion is non-adiabatic. If the marble could accelerate slowly enough, it would make a minimum level of noise, although friction is an inevitable outcome of being against a surface, so can only be minimised by making the surfaces as smooth as possible (there's a big marble that got made out of a single crystal of Si, as a standard, with a surface that is supposed to vary overall by no more than 3 atoms).

Non-adiabatic changes are what happens when two phases mix too quickly, a discontinuity occurs or a symmetry "breaks" (diabatically); if two phases mix slowly enough, or the discontinuity is smoothed, or a symmetry-point is "maintained" (equilibrium, and reversibility) so the system doesn't condense into one or the other (or the phase-difference doesn't appear suddenly, like a bump in the road), the phase-change is adiabatic.

Photons are adiabatic, and incompressible, they aren't multi-body systems but look more like 'traveling bumps', for them. Heat is a vibration of atomic lattices (a crystal is a lattice with discrete positional information for each vertex, a liquid or a gas is a lattice with no discrete positional information); heat is also photons with a certain range of energies.

Any 'substance', such as water for example, can be in different states which depend fundamentally on the 'energy' available. At high energies, molecules of water are separated, they're individual particles that bounce around in a space, average distance is because of the average energy a molecule has.

A single molecule of water can't "be" a gas or a solid molecule - it needs other molecules to interact with. The level of interaction or communication is determined by thermodynamics.
A gas is compressible, because of intermolecular distances. A liquid is not compressible because these distances are minimised - liquid molecules are 'close together', but retain translational freedom.

You can't compress a liquid because the molecules are free to translate away from any local pressure on them (a gas has to 'surrender' some of its intermolecular space to an applied pressure). Liquid molecules are already at a distance limit, determined by electrostatic repulsion, a gas has more space to 'explore' than a liquid does. A gas condenses into a liquid when all the 'free space' of intermolecular distance is absorbed, by lowering temperature or increasing pressure.
This means that temperature is what processes these average distances between molecules in a gas - a gas absorbs thermodynamic energy as intermolecular distances increase.

Water molecules condense into a solid when the molecules stop 'moving around' and energy is absorbed by electrons when they bond with neighbour atoms - a regular lattice of stationary molecules appears with energies determined by vibrational modes which are structural - bond lengths and angles.
Nuclear vibrational modes are 'stationary' in a solid; in a liquid or a gas, nuclei are 'free' to move around a space.

So the state, or phase of a substance - solid, liquid or gas - such as water, depends on the kinds of interactions molecules have with each other. A molecule is a nucleus surrounded by electrons. Nuclei interact through vibrational and translational states, so do electrons, which are usually 'bound' to the nuclei and constrained to behave in certain ways. In a gas, nuclear modes have the greatest freedom, electrons repel each other - they look like an electrostatic envelope around the nuclei; there's a thermodynamic gap between molecules.

In a solid, nuclei are bound in a lattice, electrons form an extended structure by interacting with neighbouring nuclei, rather than looking like an envelope for individual 'free' nuclei, electron interaction forms an extended envelope for all of them which confers structure and 'long-range' order.

A liquid is like a mixture of these two extreme 'end-states', liquids retain the ability to flow like a gas, but they preserve their volume (it's at a limit already), and don't expand to fill a container like a gas does. Thermal expansion is the same kind of order as in solids, which is why bulb thermometers use liquids with high expansion 'coefficients', instead of solids or gases, generally.

P.S. the word 'adiabatic' is a compound (ex latina) of 'diabatic', which starts out as 'abatic'. From the L. abatus meaning "to the beat/rhythm".
A diabatic change is literally: "half to the beat", so adiabatic means "as half to the beat". Asymmetrical means "not symmetrical", except it really means "like/as (a) symmetrical, nearly symmetrical", etc. This is so we can horribly confuse all those Romans.

If you're still here, then the universe is expanding (if it wasn't, would you be able to tell if you were still here?).

The surface of the universal bowl looks flat locally, except it does have a 'local' curvature after all - it deforms, and deformations affect particles that 'interact' with any such local deformities. We can presume that the surface looks like this at the edge too (as far away as we can see).

This is uncle Albert's primary postulate, that the laws of physics we can observe affecting the evolution of 'particles' is universal. A photon or an atom, or any group of them will behave at the edge of visibility, like they do right next to us. The nature of spacetime is invariant over the entire surface.

The speed of light is determined by the curvature of spacetime, but this means a global curve (like a bowl) and a local curve (like the central neighbourhood of a bowl).
A local plus a global curvature, which is determined by singularities (masses), which are themselves groups of particles. These have a more-or-less spherical symmetry, and angular momentum, but spacetime has a global symmetry which is more-or-less hyperbolic.

There's a connection between a local 'spherically symmetrical' potential (the gravity well we're in), the shape an object with mass assumes (a hanging cable is a good example), and the edge of the visible universe (including all the universe in between).

You can connect a sphere or a circle, to a curve like this by constructing a circle with a constant radius (i.e. \, x^2\, +\, y^2\, =\, (2r)^2\, ) and plotting the curve \, x^2\, -\, y^2\, =\, r\, (it helps to assume r = 1).

It shows that the area of a right triangle in a single quadrant of the circle, is equal to the area of a hyperbolic right triangle with its apex on the latter curve. I'm working my way through this 'proof from first principles', that relates ordinary circular geometry to hyperbolic geometry (in 2 dimensions). How you can induce the existence of transcendental numbers like e, with trigonometry. And the imaginary roots of "1". It also demonstrates that gravity has a hyberbolic/spherical structure to it, to do with distance and potentials.

You still seem to lack a thesis and are still not making much sense.

"Sense"? What's that?

Can you supply a definitive meaning for that term? How about "lack a thesis"? Can you supply some indication of what you are saying with that?
Or can you indicate why you feel the need to mention either of these?

Does the universe make "much sense"? Does it have a "thesis", or would you say it "lacks a thesis"? Is the statement: "gravity has a hyperbolic/spherical structure", one of these "thesis" thingamys?

Has the possibility occured to you, that none of the previous posts are in any way related to yourself, but to myself (I'm talking to the latter, not the former?)

It's occured to me that your previous post mentioned "foundations" that aren't "well-defined" or something. What does that mean? What's a "foundation"? Is it like the big tortoise that supports the four elephants holding up the planet?

Similar is my thread "No" which seems to explain

anyway all good philosophies about the world, what we do need as he stated is some general foundation, some general statement. Like commenting "reword that to 3 sentences or one paragraph" or something ...

Nope, still not very clear on the "foundation" thing. It's "general" then?
Can someone at least comment on why a "foundation" is a requirement, or why anyone would comment that there is none?

It's just that I don't seem to be able to make an informative connection to this, whatever it is...

General may be a good word, ...... idk I suppose hard to finda central theme, I have looked at it and it appears to be very good but lacking a clear progress (like i said, idk)

What's a "clear progress"??

Does the thread title: "Information AND potential", suggest a connection? I think it does.

A dissertation requires a thesis aka a proposition stated or put forward for consideration.

In otherwords, when you said it was dissertation that implied there was actually some point being made.

But it seems to just be random psuedo scientific ramblings without real rhyme or reason.

Rant on McDuff. Rant on.

A dissertation requires a thesis aka a proposition stated or put forward for consideration.Not at all.
There is no "requirement" in any dissertation, that's what a dissertation is: something that "disserts".

You seem to be labouring under some sort of illusion? Can you point out any "ramblings" that are pseudo-scientific? Can you offer anything, at all? Can you make a point of some kind?
(Other than bland, dismissive comments, I mean)

Or better, fuck the fuck off. Go and post vague, somewhat meaningless comments some other place?

OK, for those who are otherwise too mentally challenged, this is the guts of all the above:

1) we live in a continuous universe - it expands continuously

2) we live in a discrete universe - it has singular objects in it; there is a single, discrete universe

3) the universe has curvature - you can see this by simply standing in a potential well (in an inertial field, that extends from a local singularity - the planet we happen to be on)

4) you can construct a logical 'map' of the universe, and see that it extends like a surface with hyperbolic and spherical distances and 'paths' in it. A sphere can fit inside a cone, an hyperbola (and a parabola) are conic sections

5) the universe has discrete particles in it that represent the singular spherical geometry of the surface, which is because of mass potential

6) these particles are in various 'phases' between themselves, three 'major' states of matter exist in relation to a local thermodynamic level or background - another potential

7) a surface can accelerate a particle to a constant velocity, which is then a constant potential

8) the particles can interact with each other's spherical potentials, by 'relaxing' their hyperbolic shapes into elliptical shapes or curves - they orbit each other
(and yes, an ellipse is also a conic section)

9) these symmetries, and how they evolve 'potentially', depend on the discrete conic sections, of each potential (mass, charge, and so on)

While its vaguely interesting that you think these things. So what?

At the moment they are vaguely contradictory mismash of some what sciency some what mathy sounding statements which make no points and from which you draw no conclutions.

Unless you are seeking the write dadaist poetry you should give all this direction with your thesis and then show how these points come together to support your conclution.

So, there are no "conclusions"? Isn't "the universe has a curvature" a conclusion?

Isn't "potentials evolve continuously, and have a spherical/hyperbolic geometry" a conclusion?

They might not be conclusions that I've suddenly come to all by myself, though. unlike yourself, who seems to be able to jump to conclusions for lack of anything less boring to do.

I bet you've managed to form some kind of a thesis, despite the overwhelming pointlessness of it all? I mean, so fucking what??

You should try to give your comments some direction, then show how you've managed to say anything that's remotely meaningful.

If there is any thesis, it's implicit in the title, information and potential are equivalent.

So information is geometrical, and algebraic - continuous and discrete, and has topological invariance. Its geometry and algebra conserve phases. Information is a conserved phase-difference. A particle with charge has a potential phase difference (because it has mass and charge, which is two different things). I thought it was fairly bloody obvious.

And there's a mathematical slip-up with the eqn for a circle, back there. It's scaled by a factor of two relative to the other curve.
The circumference is a factor of two relative to the radius, and pi. Whoops.
The hypotenuse of a right triangle with sides that are equal to the radius (=1), is the sq. root of 2. A circumscribed square has an area equal to twice the radius. A circle (pi) contains a square (2). The ratio of the circle to it's inner square is pi/2, which is the angle subtended by a quadrant.

You only have to rewrite this in terms of the x and y on a line from the origin, tangent to the hyperbola which is focused at y=0.

(just thought I'd clear that up)

Maybe everything we see is because of differences. Mass might be just a fundamental kind of phase difference that is conserved, when masses have a distance between them, there's a potential. Charge is like that too.
The forces that have a finite range or extent, inform the ones that have an infinite extent. The surface has a local 'fine structure', and a general curvature. We can only see anything because of distance (mass and charge), and because of the wavelike nature of anything that exists - since waves can add together but are still separable.

Exploring the idea of a thermal symmetry, like, what does it mean?
Again, with a gas which is generally a highly symmetrical, but also highly disordered state, their thermal background controls the symmetries. A gas in a container is controlled by temperature or the heat content. Scale it and the volume scales as a pressure.
A gas is elastic, the density of particles in a gas depends on the inverse of heat density. Up to some heat content or entropy, the electrons are localised around the massive nuclei, electrostatic repulsion keeps the density/elasticity of the gas at a symmetry point [( \rho(\nu,T);\;\frac V T =k :bugeye:)]. A free or unconstrained gas will expand as a pressure 'wave'; its density gradient will decay exponentially, it 'bounces' apart elastically.

[This is tied to a frequency; the time domain expands the frequency domain. A transition is a commutation of phase (individual wavenumbers and angles) that have greater symmetries at higher temperatures and frequencies. The fact that time is linear means frequencies and wavenumbers add together that way, :shrug:. Chaos is when this linearity 'breaks' somewhere and a system finds another centre. These symmetry-points must therefore be available, like two surfaces, one smooth, the other non-smooth, or two horizons of a surface, to a thermodynamic mass-energy sum-of-products. That is, chaotic and linear modes are conserved by thermodynamic exchanges.]

The universe is like a free gas of particles (which are singularities), but it contains large collections of gases (mostly hydrogen and helium) that appear to 'bounce together', and form the singularities. This process is driven by compression, which is only possible because of relative motion between different parts of these 'nebulae'; the part that minute particles of dust plays in the compression and eventual collapse is still being explored.

So while this universal gas expands elastically, parts of it cycle through phases of compression and expansion, or pass 'through' critical points or phase changes. There is a high probability that gravitational singularities will form in an expanding universe of matter.

It DOES Suggest a connection but that connection still is kinda broad or somethin imo.
But I will contribute.

I think that physics and some things you're saying share their "potential" with the human being. I think that information shares this relation in a very profound way. That perhaps the universe has a great ability to share its wealth with an individual human being....

If you consider the simple act of drawing something, or even what I'm doing right now, which is the same thing really as drawing a figure of some kind.

Why can we 'construct' something like a circle? It's pretty straightforward - you need a 'divider', something with two 'fixed' points that are connected, like a straight line with a variable angle at the midpoint (you can think of a clock this way). Why do we know we can do this?

And why, since we know we can, is it related to 'connecting' things; it's a communication, circles we can draw communicate something that's 'in our minds' already.
A 2-year old can do this, but needs to get a bit older so their brain can abstract the thing that circles communicate back to us, when we 'play' with them.

I've seen comments elsewhere about the mathematical nature of reality, how the logic of math seems to be "unreasonably effective" at explaining it. How some abstract logic is connected, irrevocably, to physicality, we 'discover' or uncover the connections - learning the mathematical, logical nature of reality is, in a sense, just cataloging and correlating these connections.

Thinking about how or why it shouldn't be "reasonably effective", when it is, leads me to think, there is no reason it shouldn't be as effective as it is. In fact it should be effective, it's as effective as we make it.

These days it is fairly effective, we seem to have pared back the layers as it were - taken the gadget apart and figured how it goes back together to a large extent. And we're poised to take the fabric, the stuff the gadget's bits are made 'out' of, to bits and figure how that goes back together (a seriously non-trivial process for our logic, a major undertaking requiring much use of the logic parameter).

Because of course the universe is mathematical, we are too.

The unreasonableness, is really just not seeing that we develop logical, mathematical symbologies (our lexicon's information entropy expands), since we are made the same way as the universe.

It evolves mathematically because we do too, of course. Everything we learn increases the probability that we will learn more - a convergence which is like an infinite series, we keep adding and canceling terms to it, rewriting (encoding) the message. How much is this a function of our own biology? It's an absolute.

And following from that connection, we find that there are absolutely no 'individual' things anywhere (except perhaps the universe itself). Any thing we can think of or represent or measure, has another thing that must exist for the first thing to also exist, this appears to be another kind of fundamental: everything is a duality.

A simple divider can create a circle, which is a symbol, a representation. It's a logical thing then, and a physical thing. One requires the other, we wouldn't 'know' what one is if we didn't have the logical symbol somewhere, and the real physical 'shape' somewhere.
By convention, the logical representation is an abstraction, but the constructed one is a real, physical thing. Actually both are physical things, because the logic requires a physical brain, it isn't a totally abstract structure, it must have a representation in the mind that 'uses' it. Brain information is just as physical and subject to the same communication and dissipation rules as electronic pulses in a wire.

What is the radius of a circle? Drawing one, you figure that the constant 'distance' from the first fixed point varies the circumference, as a constant distance from the central fixed one. The center mediates the circumference, according to a constant (mathematical or logical) relation.

The radius can be whatever you say it is: "one" of something, or "many" of something. A dimension is just a logical sort of label for anything at all.

Say you make the radius equivalent to some constant, then you can see how the dimension of a 'flat' constant derives other relations, like between the speed of waves in a medium (a constant determined by the tension of the medium), and the amplitudes, angles, etc, of discrete waves in or on some medium, even how the medium itself deforms. If a central fixed reference can have a radius, then that radius distributes or disperses that fixed reference, with a constant curvature which is the relation between a square inside a circle and its circumference.

Every circle has a diameter, so every circle has another perpendicular diameter. This just says you can 'fold' a circle in two, and you still have a circle, if you fold it again, into four, it's still a circle. An arc of a circle represents enough of the whole thing that it 'induces' it, IOW.

The fundamental structure of our universe is matter and energy, which we know are equivalent representations. Information is both - it's matter 'with' energy, or it's energy that 'informs' matter. These dualities are equivalent.

Energy is equivalent to mass, distributed as a product which is of the maximum velocity that energy can distribute itself. So if you make this maximum velocity the radius of a circle (c is constant in an ideal medium, like the relation between volume and temperature is constant in an ideal gas), you are representing how 'energy' is distributed over an area. What's the area, and what does the circumference represent?

In geometry a circle \, S = \pi r^2;\,C_{s} = 2\pi r;\, S \in \mathbb {S}^1 .

In physics, \, E = m c^2;\, C_{\varepsilon} = 2\pi c;\, E \in [?]

So mass is then a ratio like pi, since energy is a product (an area); the ratio is energy distributed as the square of the 'radius' = the constant velocity of light (energy).
Velocity distributes energy (as mass).

What happens if you introduce another dimension, another kind of 'charge' or ratio (with a constant distribution over some area)?

To accomodate charge, just add another perpendicular radius. Since the mass 'dimension' occupies the 2 in the area of a circle, another radius (call it 'positive' charge), extending from this 2-dimensional area, could be imagined or constructed, from this surface.

You could imagine 'cutting' along the circumference, halfway around the circle and folding half of the 'real' area up from the surface, et voila, another dimension. This projection preserves the original shape, and constructs the same areal/radial relations along another radius, wrt the 'real' radius/diameter.

The 'positive' charge dimension creates a hemisphere, on a 2-d surface. There's an angle along 2 'dimensional' distributions, or directions, for every point 'along' a hemispherical surface - the frame shifts to 3 dimensions, like an upside-down bowl.

An electron or a proton has a polarized kind of charge, and a non-polarized kind (its mass), though because of a significant distance between their individual, fixed masses, their polarized charges distribute at significantly different velocities in any medium. Both kinds of 'particle' can have localised/delocalised angles and directions (velocities and positions), because they have a fundamental phase wrt each other - a mass phase which distributes another kind of phase. Phases and potentials are equivalent.

To get a 'volume' from an angle, you integrate a path along a surface, which 'closes'. Then there's a solid angle, since the surface is curved (all surfaces are, though), which represents the content of the surface area; the solid angle subtends an area. Phase angles are also phase differences, you see these terms being used interchangeably, quite a lot.

We have to have containers, to be able to imagine we can 'put' things in them. A container and its contents aren't "the same thing", but we can abstract either of them "out of the frame", and so derive or figure the remainder; either see what an 'empty' container is like, or what the contents are like, when they're "out" of the container.

An optical fibre is a container, for signals made out of 'pulses' of light. Information content is then the number of pulses of light (transitions in polarity), per volume of fibre.

These dimensions are physical, kilometers per second and pulses per kilometer, expressed as a product (like any volume). If velocity is an area, acceleration, which is a product of velocity and time, must be a volume wrt velocity. Momentum is a product of velocity (= derivative of acceleration), and mass. Momentum can be a volume wrt position and mass, since position is derived from velocity.

A pulse is a phase change. A wave, when you 'chop' it into parts, looks like a series. A part-wave, unlike a part-circle, doesn't represent enough of the whole wave to be able to construct the original, extended waveform - waves are 'unbounded' by time and distance, they depend only on a medium. You could 'chop' the waveform up into 'transitions', which transforms a continuity into discontinuities; an 'up' transition is '1', and a 'down' transition is '0' - you digitize it.

Wave-particle duality, is the same thing as the duality between a container and its contents.

So, there are no "conclusions"? Isn't "the universe has a curvature" a conclusion?

No, its just a statement as you currently have it.

What did you just contribute, then?

It looks like "a statement". ??

But you haven't backed it up with anything; and why the need to trawl up a post that was made a week ago? Does your ego take that long to bounce?

You see (or even if you don't see), saying nothing in particular, leads to nothing in particular.
Do you have anything to say, or can you only manage inanity and inaccuracy? Do you know what a question is, say? Are you aware that some questions have answers?:spank:

How about this one:

do you see a problem at all, with giving a circle a radius of c which is the speed of light in a medium, which is maximal for a medium of 'zero', i.e. the vacuum? Seeing how mass can't have a velocity of c?

Or, if you have a philosophical bent, do you know what a fluence is? Why it can have dimensions?

Ok so this philosophy is 'founded' if you insist, on something quite rigid, or dense at least. Which means it has a high potential, compared to the other which, although it has an equivalent kind of potential (one informs the other, in our dualistic universe) it spreads it around.

There are two kinds of potential, one is like a regular (also compact or dense) surface, the other is conversely irregular, not compact or dense sort of surface. Volume 'scales', which means 'distributes itself', as or through an area.
This is just like what happens when water flows across the rim of a glass - too many drops and the surface tension can't 'hold' the excess back. Chaos and nonlinear flow, at the moment the '1 too many' drop perturbs that surface so it breaks, mean that more than 1 drop will flow out; or the volume first 'overfills' to a critical value and has to restore itself.

This is driven by elastic surface tension between the circumference, which is glass, and the surface area, which is water. With a denser liquid like mercury, the nonlinear flow is damped; it 'loses' less overflow than water does.

Water, and glass and mercury, are all examples of particulate matter. This is made out of quarks (that make nucleons) and leptons, and the force particles that they exchange, the bosons. We can look at the "contents" of the first family because we know enough about the container(s) that they're in so we can abstract just the particles, that have mass.

There are four fundamental kinds of mass particle in the 1st family that together constitute ordinary matter, which is the lowest energy level of the 'mass spectrum' for our environment, such as it is.

The quarks in protons and neutrons are the bulk of an atom's overall mass, the electron in say, a hydrogen atom, is a small but significant factor in how mass interacts over an infinite range, via the derived 'forces', gravity and electromagnetism. Distance and relativity are seen as extended (hyperbolic/spherical) surfaces that deform an extended 'spacetime'.

Chaos is an elastic limit, beyond which momentum evolves non-linearly in the time and frequency domains. One surface is invariant, the other varies; nonlinear chaos is 'freely bounded', linear elasticity is 'tightly bounded', by the connections.

These connections are 'fuzzy' at the mass limit of leptons; an electron has 'just enough' mass to perturb the much denser surface of proton/neutron mass; a single drop of water has just enough mass to 'break' the much greater volume by interacting across its surface.
A single drop can cause more than one drop to flow out of the glass in a nonlinear way, but nucleons preserve their (phase) volumes, and exchange angular momentum with each other, and with charged leptons.

The free momentum of unbound particles has a chaotic and a linear path integral - which is bounded by 'uncertainty' of its potential('s) phase relation. Informational uncertainty is the equivalent of quantum uncertainty, and at its classical limit where we live. [This looks like it might be because of the chaotic way electrons interact via the charge and mass (and spin) they have. Spin is invariant, mass and charge 'diverge' over a regular volume in a chaotic way. Chaos has a regular way it can and does evolve, which is tied to the uncertainty of lepton mass and charge. Neutrinos only have 'mass' or a certain resonance as matter-waves, close to their critical points; they can't evolve over the same surfaces, but conserve angular momentum by orbiting the largest radius they are allowed along the local gradient.

They find a maximum velocity by finding a minimum in the surface, whereas their partner has to orbit at a closer radius, or in a potential well. Electron neutrinos 'allow' the (electromagnetic) polarity of electrons to relate their masses over a 'tenser' kind of surface, with extra potential in it, than neutrinos can see. Neutrinos are the analog of massless bosons, as 'chargeless', so are unpolarizable; no spin-orbit coupling except to a general 'centre-of-the-universe', for the mass term.

Electrons couple to protons' mass+charge term, as a regular shaped volume - a mode which is vibrational/oscillatory distributing or 'delocalizing' the mass+charge (reflecting it, in a sense). Proton/electron modes are coupled oscillations with 'chaotic' distributions which conserve angular momentum. Where nucleons are a 'liquid surface', the leptons are a 'gas surface' and evolve in elastic/inelastic ways because of charge.

What did you just contribute, then?

Its called a "critique."

But you haven't backed it up with anything; and why the need to trawl up a post that was made a week ago? Does your ego take that long to bounce?

I do occasionally have other things to do. Also, I'm not claiming that I'm presenting a dissertation on anything.

I can see by your thrashing around you are aware of the inadequacy of your offering. There is no need to be defensive. Learning to express yourself clearly is difficult.

You should also consider what a difference of kind is and why randomly mixing pure mathematical concepts with formulas which describe aspects of physical reality results in erroneous conclusions.

and why randomly mixing pure mathematical concepts with formulas which describe aspects of physical reality results in erroneous conclusions.Which 'conclusions' are you ranting about?

You aren't going to say are you, because you haven't got a clue what it's about, right? It just looks like a big jumble of random ideas, like the ones in your head?

How did you get from "pure mathematical concepts", to "physical reality"? Can you dissert this at all?

FYI, I'm abstracting, as you do.
I don't have to follow any advice, OK, smart guy?

Where's your answer to that question then, if you're such a good critic, or do you have other things to do, you thought you might just occasion a little bit?

Here's one for Ron: how are those equations for density, as a function of temperature, and the constant ratio of volume and temperature related? Any ideas, or you've "got other things to do"?
You went to the extent of reading, I assume, some of the 'dissertation'? But it's only worth a little criticism, you'd say?
You really need to learn about something called 'vapidity'.

I'll do my own critique, since I've either been left to it, or haven't posed any questions for the thinkers.

Start with the 'topic', which I think is really about what we do when we abstract; which means what our brains do when we see or hear anything, or 'feel' or 'taste'.

Every 'sense' we have, biologically, is a set of two kinds of 'input' to a neurobiological machine that 'computes' reality, for itself.

Abstracting a simple shape and looking at how its parts relate to a lot of what we see, how the 'shape communicates with' reality, how we usually measure, with instruments, things like pressure and density, the practical result of abstraction, the applied science, as technology.
A circle is a 'static' shape, but you can easily imagine a rotating radius, that 'sweeps out' a circumference, we measure the passage of time that way, f'rinstance.

What if this radius 'sweeps' another way, around another 'radius'?
What if you have an 'imaginary' radius that rotates circularly, as \mathtt {\,x^2+y^2}\,, but 'expands' and 'contracts' as it does, in a periodic way, or a 'non-periodic' way? Why does an abstraction like that, look so much like reality does?

Why does having a 'shape' that projects, say a sundial projecting from a flat or inclined surface, expand something along a surface, the shadow made by light from a big shiny circle, the sun, as it 'rotates' across an axis, a specific direction?

Why does that 'direction' have a slow rate of change that we can see, and have seen, also has a period of tens of K.yr? There is a 'circle' in this rate of change of the sun's axis, that it follows across the 'heavens'; we've been keeping track of it for a while now.
The Egyptians, and the early Picts and Celts in pre-Roman Britannia, knew about it. The periods we can see everywhere, and the cycles in climate, are related.

Our immediate 'sense' of the world, arrives via the kinds of interaction we make with it, obviously; each kind of interaction, is essentially a comparison, between two 'sensory' inputs - light and sound have an 'audiovisual' process, pressure and density are measured by a somatosensory process, our skin is a pressure transducer, and a thermometer; there are two 'inputs' for this comparator, one for our 'sense' of locality, our own 'density', and how our physical self moves and extends (parts of it rotate differentially, against an inertial gradient); the other for our sense of 'warmth/comfort' - we have to be able to 'rotate against' the inertial surface in case the comfort level is exceeded - we have to maintain a narrow 'width'.
Our 'niche' in the local background, radiation-wise, there's a local minimum and a local maximum for the audiovisual/somatosensory 'shapes', the geometry and algebra.
The other sense, which is actual 'sampling' of chemicals, is an interaction with discrete shapes (that rotate chemically/thermodynamically) from the 'continuum' of the environment.

So relating frequency and pressure - the latest question for the day.
Pressure and density are related. Pressure is expansive, and compressive. A gas will expand freely, but apply a pressure and it gets compressed - its volume changes elastically. We know elastic 'behaviour' is because of an elastic constant, that every solid object has; elasticity implies plasticity, which implies viscosity. Density is 'invariant' in the sense all matter has a density, a plasma or a beam of protons, superfluid He or a cloud of Ce atoms at << 1K, all have a density.

Measuring the density of matter, is like relating the idea of a continuum, to a discrete state; the simplest 'shape' we can abstract, a line, relates the idea of something constant to a continuous set of points, a period or a set of radii, distributed as an area when it's rotated, by being 'fixed' at one end, while the other 'completes' a single (discrete) rotation.

There is a finite 'set' of points, in each structure, each part of a circle - the centre, the radius, the circumference, the area bounded by it, the number 2 and its root, the roots of 'numbers' in the square 'inside' a circle. Discrete numbers with continuously variable 'angles' or phases. We try to 'compress' most of the measurements we make into simple shapes like this, or make the data 'fit' a curve which we know is ubiquitous, there's more to a simple circular shape than meets the eye.

p.s. symbols inside '', are implied as abstractions (these are ideas we have, in our minds which we perhaps imagine because our brain 'invents' itself, or it invents an "elf", maybe, like a sprite.)

p.p.s. has anyone else here, ever played marbles? Did you keep your marbles in a bag?

A linguistic side-tour: the word "adiabatic" again. I said before it meant: as half to/at the beat.
The numbers we use today are based on the Roman numbers, their numeration/denomination gave us the nominative ordinal and cardinal numbers (for counting or sharing out stuff) and versions for associating and distributing the nominative versions.

A cardinal number names the value, or quantity of some thing/things. One apple is less than two apples etc. If you eat one of two apples, you are giving the two (otherwise identical) objects an order - you eat one first; ordinal and cardinal numbers can look the same in English, but they aren't in Latin, we still retain the idea of an 'independent' number, and an 'ordered' number, ordinality is the place in line, the location. Cardinal numbers are for value, ordinals are for position.

From a L. dictionary:

# | Card | Ord. | Distr. | Assoc.
-------------------------------------------------
1 | unus | primus | singuli | semel
|'one' |'first' |'single' |'once'
2 | duo |secundus | bini | bis
|'two' | 'second'| 'double'| 'twice'
3 | tres | tertius | terni | ter
...
The 'di' affix, from the ordinal/cardinal forms of 'two', can mean "twice", or "as two", or it can mean "from two"; you have apples "as two", or you eat apples "from two" (by eating the first). So, diabatic means: "as/from two at the beat". Adiabatic implies "away" from the twin-beat, or half-beat, then.

Adiabatic changes/cycles, are the same idea as small displacements (over time, a number of small changes in position or energy for a component in a larger system, add up to a large change, but the system doesn't 'see' the change).
SHM is the same thing as, say a simple pendulum 'swinging adiabatically'; give it a large displacement, and it swings chaotically; the string might jerk around and the weight won't have a 'smooth' path through space.

And once again, the inertia of a simple weight, attached to a spring illustrates this "nominative form".
Suspended (from - a surface); you give the weight a bit of forward + sideways ("two for the beat"), it should move in a curvilinear orbit, around the fixed end of the spring. If instead you just give it a one-directional push or pull (and release), it moves by extending and contracting the spring ("twice to the beat"); it moves diabatically. The first way, the spring movement is adiabatic, "away from" how it moves when it has to rotate in a plane.

Quod erat, et alia.

And the connection or the connection machine, is 'us' and how we use these 'forms', simple numbers are just simple 'containers' for us to carry around things (like marbles), to 'translate' or 'transduce' or to amplify and (natch) to 'de-amplify' or suppress.

Chaotic motion is, of course, motion that 'obeys' mechanics, is subject to the same conditions, initial, and consequent, what 'follows' is caused, by what precedes it. We don't or can't build many things that do use chaotic motion in a 'useful' way; it turns out that not only many kinds of regular motion or progression are chaotic as well, they would not be regular or periodic unless they were chaotic, that is.

Like our brains for example, our neural 'circuitry' needs to 'communicate' with chaos, with 'disorder and randomness', because that's the way it goes. Regularity, or order, and chaos or disorder are apparently a part of the whole 'linearity vs nonlinearity' thing.

The connection to information theory and content of a channel, like an optical fibre say, is that 'noise' is suppressed, the content is generally a 'forced' kind of resonance, induced by a carrier, that we arrange so it 'responds' by amplifying the signal we want it to carry - we move the part we want to 'see' away from the part in the 'channel' we don't want, we use a gap or a difference, or we 'make' one.

A [metallic] conductor, [a telegraph line, say] is a channel made of something along these lines. We take the unwanted stuff 'away' from the stuff we want to use - a purified, or 'refracted' metal, we know we can make it vibrate or 'ring' a certain way, because that's what they do.

Electronics, communication, optics and lasers are all connected, there's a straightforward path from Maxwell, to Einstein and nowadays, the whole mysterious idea of quantum communication.
This is the utilisation of the smallest, simplest particles we can, they don't get any smaller than this, so now it's about separating a signal that's a kind of fundamental excitation, in a lattice that looks like a complex network.
A solid interface, a surface, interacts with a 'liquid' phase, which might be a fundamental kind of potential that then 'moves' in a diabatic sense, across a more complex kind of surface, with a helicity in it. The dimension of invariant fermionic spin. To 'see' this liquid, we have to take it away from something we 'don't', which is heat; we have to run this machine at the thermodynamic limit, the left-hand end that is. We have to scale back the thermal background, which is chaotic.

A lattice is ordered by 1, 2, and 3-dimensional 'connections' between N particles, a liquid has N particles and NxN degrees of freedom.
A 'particle' is a nucleus of an atom in these lattices, and the lattice connections are electron orbitals, the liquid/solid interface is ordered by the geometry - 'particles' of potential exist because there's a regularity in it that we 'put' there, by arranging for the surface to be flat, i.e. have zero curvature - the 'particles' have to move in a planar way. [This resembles the way a torsion pendulum moves when it rotates in 2 instead of 3 dimensions ( - a spring is helical). Pendular motion can 'reflect' quite complex kinds of momentum, you can arrange a 'chaotic' pendulum setup quite easily. But then, things behave that way because of a potential or two.]
This is the fractional/integer Hall effect, and it has a more complex kind of algebra (way more squiggles) in it.

Mythology and symbology:

Getting back onto the merry-go-round, the circular argument - the geometry with numbers thing.

A circle is a simple shape, like a number - it implies "going around", so you can go around once, or more than once, or an indefinite number of 'cycles'.
We get the words 'rotate' and 'revolve', from Latin (via Greek, natch), 'cycle' is Greek-Latin; "kyklos" were/are cycles in Nature and also referred to epic poetry - poets told and re-told tales, usually involving some journey, as in a people or their hero representative (whom the story 'revolved' around), what they encountered and resolved, generally such tales, epic poems, were/are full of metaphor and parable.

They were generally moralistic/heroic in form, and of course involved interactions with 'gods' who generally brought chaos and disorder to the scene - a storm and shipwreck; fantastic creatures who needed to be 'conquered' to make progress (towards some 'promise' or treasure).

These themes are found scattered throughout many cultures - tied perhaps to the notion of struggling and prevailing against a world that is hospitable, but only when it 'feels' like it, for us mortals. "Life is struggle", is the overarching theme, and our history and imagination take it from there.

Stretching things:

Back to the practical shape of something entirely prosaic (these days), a hanging weight.

So looking at this 'device', what sort of instrument is it? What are the components?

You need: some 'string' or something that connects the weight to a dependable surface; because of gravity and the local curvature, you have to find an 'inverted' kind of surface; i.e., you can't 'hang' a weight from the floor - it has to 'go' on a ceiling.
If you 'fold' up the surface you want to hang the weight on, like say, into a cylindrical 'bar', you can use it as the dependable surface (from which the weight 'depends', on its string).

A string has 'width', which is negligible but sufficient for the weight to 'swing' freely, which it does in generally curvilinear 'revolutions'; it orbits the centre, which is the fixed end of the string, elliptically - it has two superposed linear motions in general, a forwards/backwards motion on top of a sideways one. How do you fit something like this into an 'ordinary' circle? What sort of approximations should be made about the shape of the orbits of a string pendulum, and the geometry/algebra of a string pendulum?

What if instead of a '1-dimensional' string as an ideal 'connection' (the radius of curvature, for revolutions or cycles), you use something stretchy? A coiled spring or a length of rubber strip, say? How to accomodate the added 'rotations' as the weight 'rotates' along another axis - the 'free' end of its connection?

The initial condition in each case is similar - you displace the weight, by 'holding' it away from its central relaxed state, (when it's motionless and depending vertically). Horizontal displacement should mean the weight will accelerate directly toward the central position, and swing linearly. You can, however introduce a bit of 'english', by pushing the weight sideways slightly as you release it, or 'launch' the weight by moving your arm a certain way (two ways in fact, like 'drawing' a circumference of sorts); the pendulum's weight 'processes' the potential you introduce by moving (or not), your arm, and it will swing according to a well-understood 'algorithm' as soon as you 'free' it from your hand. The motion is formulaic.

The 'problem' is how accurate a particular logical representation, of the physical device, can be, and so understanding what these are is kind of important if you want to use a swinging pendulum of some kind to 'measure' inertial changes (accelerations). Gyroscopes are 'flatter', or less prone to the chaotic kinds of motion a simple string (or spring) pendulum can sometimes see, we use gyroscopic motion as an inertial reference, in fact. Gyroscopes are 'fitted' to a circular kind of geometry, so are constrained that way - by the distribution of their potential (mass as matter) over two kinds of surface, again this is the surface of the earth, and their own surface - the 2 sides of a 'disc'. The 'sides' of a string pendulum have a different kind of relation to the surfaces it is 'between'.

A string pendulum and a gyroscope have their potentials distributed by different geometries or shapes, which are 'seen' evolving as momentum between, or against, inertial 'surfaces'.
Their radii 'interact as'/'intersect with' different kinds of cyclic patterns - they have different 'resonance' when they oscillate in a cavity made out of potential (as a bowl is made out of matter which is 'fixed', so has a static potential - so something has to be 'free' to move against its surface, and complete the circle). When instead of a 'rigid' connection like a 'taut' thread (with it's 'width') you use something more elastic, you get a stretchy kind of distribution, you add a way or 'amplify' a way the pendulum can now move, so it goes ahead and computes it, right on cue.

OK, so this 'dissertation' has gone from the idea of a potential, to the idea of a moving potential; swinging, or 'dangling' weights; through pressure and density and what connections these have to elastic behaviour; and a bit of linguistics (which ties to meaning and so "information in a message").
So what is an 'informative connection'?

We know we're made out of 'matter' like everything else. The ancient Greeks thought there were 4 fundamental kinds of substance or material - "earth, air, fire, and water". They saw 3 'phases' of matter, and fire or combustion as the 4 'quadrants' of the universal circle. We know that they got this fundamentally wrong, but really only in the way the components go together, or 'work'.

Work is like a gauge of information - no information (i.e. energy/mass transfer) is possible unless more than zero work is done. Energy or mass has to 'flow', or move across something. Any 'working' system has a thermodynamic limit, beyond which chaotic 'amplification' essentially expands the potential of the system to 'infinity'; it 'breaks' or melts down (think Chernobyl).
A photon with '1-dimensional' spin can 'divide' into 2 photons, still with 1-dimension of spin, as two halves of the original potential. It can't expand its spin potential, so can't do work in that dimension - which is why entanglement which is a kind of interference, can't 'do work'.

We have uncovered something quite fundamental about ourselves and the universe since the days of Archimedes and Aristotle (also Ptolemy and Galen), so we're a lot more sure that matter comes in 'twos'.

There are 3 'fundamental potentials', which are: mass, charge, and spin.

Mass is really a kind of charge, but then, so is spin. Spin however, is 'conserved', it's a kind of 'universal systolic flow'.
The other kind(s), which are diastolic, wrt spin, are what happens when charge and mass are separated.

When we expand or compress something, or a 'singular' large collection of mass+charge+spin (say some hydrogen gas), 'relaxes', you get systolic flow of 3 potentials; when it compresses or 'undergoes' systole as a pump does, you get diastolic flow.
The 'flow' in a pumping action, IOW, has a 'constant' background which is systolic, and a varied diastolic type of flow - the inverse of what the pump does to the flow, type of thing. A systole, or 'pump contraction', causes a 'pulse' in the background 'relaxed' form of fluid (or gas) convection (like in a diabatically moving weight on a spring), a diastole, or relaxation in the pump , produces a systolic flow of/in the fluid. Fluids can flow linearly/laminally, or chaotically/turbulently; this is tied to viscosity.

Separated charge is a phase(-difference) between potentials, which will expand (if they're opposed or 'pushing against' each other), or compress.
Expansion is (potentially) limitless with gravity or EM, but is actually bounded by an expansive/compressive potential 'elsewhere' in the general system, i.e. the universe. Compression is bounded by the 'limits' of mass and charge and spin, which are constants, i.e. Planck's, Boltzmann's, Faraday's, Kelvin's etc.

That is, fermionic/bosonic spin is bounded by Planck's 'spin constant', and by 'mass'; massless spin-1 bosons have no (i.e. zero) diabaticity, since they evolve as a tangent. but fermionic (electron/proton - and neutron) spin is 'halved', or has directionality.
Spin has an extra phase, which 'distributes' itself twice around the same circle that mass does. The universe of matter has an equivalent universe (an imaginary one, in our case) with 'antimatter' in it, which 'spins' the opposite way - antimatter like the leptons seen in neutron decays (a diastolic kind of pump with a systole that implies an electron/electron-antineutrino 'pendulum'), balances the 'creation' of charged protons and electrons.

The proton 'keeps' the massive quark fermions, and the leptons and massless bosons they then exchange, are also seen in pair production, and in neutron star compression (diabatic relaxation due to a mass limit, which is gravitational).

Blackbody radiation has a peak intensity, characteristic (across a spectrum of frequencies) of the body.
Black holes must conserve the systolic flow of invariant spin, and suppress the diastolic (thermodynamic) modes; when matter is compressed, something else must expand away.
Mass becomes the pump (limited by a gravitational constant, not thermodynamics) that acts to (systolically) compress the matter to the Planck limit of diastole - 'binary' fermionic spin. A black hole's potential (which looks like an 'infinite cavity' for particles) conserves mass and general angular momentum, but must conserve spin and charge too, which are thermodynamic in a 'free' space.

Magnetic 'vector' potential can condense into fractional particles (a kind of adiabatic or 'static' flow, connected to electron spin and bounded by linear charge). This is because the EM field is fundamentally a kind of pump, where charge is linear, magnetism is curvilinear.
A moving charge potential means a curving magnetic (vector) potential. The vector potential of the EM field is a surface across which 'charge information' expands, or charge is a surface against which magnetic potential flows, or compresses (condenses) into particles.

The way these small, helical bits of potential move when external fields are varied or rotated, is connected (in perhaps a deeper way than we understand fully yet), to vorticity and curvature - i.e. a surface can exist which has a helical kind of geometry in it, so that 'particles' appear which are effective 'systolic/diastolic' modes, of the field itself.
Electrons pair up and 'compress themselves' against an electric potential, into helical wave-numbers, they 'spin' in place, in a kind of reflection of the spin of individual leptons. The quarks in nucleons provide the background surface - which we make nice and flat, so that the electron pendulum has to rotate in a plane.

P.S. expanding on what a tangent to a sphere has to do with photon spin should not be tricky (if you know about tangent spaces, and polarisation, optical kinds, say, or if you get the hang of "a tangent makes the hypotenuse vanish..."), when you know that the kinds of movement you can see in a weight hanging on a spring (diabatic compressive/expansive movement where an elastic spring 'works', and the other kind where it doesn't) are related to the same kind of things photons do when you polarise (polarize) them.

Which is what you do when you put a pair of polaroid lenses in front of your eyeballs.
Because the lenses have stretched chains with delocalised electrons in them, because the chains are doped with certain elemental substances - long-chain molecules with a 'valence' atom, distributed periodically along their length, and linearly stretched out so they present a gridlike mesh (a kind of graph) with gaps between the chains.
These chains are like a molecular lattice of vibrating 'strings', through which photons pass, and exactly half (to a good approximation) are 'absorbed' by the motion their electric field induces in these molecules, and half are 'scattered' through the (biological, yet plastic) lenses in your eyes; you put a filter in the circuit, or flip a switch, too.

Forgot to mention that there are electromechanical examples of 'pumps' all around these days, that work like a big sort of 'rubber band' being wound up so they have enough spare potential for "demand use".

The power transmission/distribution systems everywhere (the 'grid') is a network that is pumped continuously, and drained at individual household/commercial/industrial outlets. The 'capacity' of a national or citywide electrical grid is elastic.

Just like pumping a torsion pendulum by say, moving it with your hand, or equivalently moving the base (or the room). A pendulum in SHM will expand into a linear mode, or 'find' a direction for any accelerations in its inertial frame.

Copper wires are a metallic lattice; a lattice is a 'solid graph'. Take a metal (or a dielectric solid) away from the thermodynamic 'ambient' realm (with an expensive cryogenic system, possibly a vacuum pump or two, some lasers to pump certain modes, and/or a way to generate strong magnetic potentials), the universe gets a bit stranger.

Maybe it will always be stranger than we can know; maybe the strangeness, and the unreasonable nature of logic to open up the containers (to find there are more containers), are some kind of a signal. Maybe the place will get even stranger, if we manage to stay around to find out.

And about those containers; the universe we can see has less and less 'stuff' in it as we watch it expand in a systolic way with perhaps a bit of a diabatic pulse on the boil, we are on the edge of a shift up the curve - or given what we understand about how the light we can see from distant objects arrives, the tension in space and the approximate densities of the potentials in space (how they evolve in an extended spacetime).

The expansion appears to be a 'central' or therefore generally elastic expansion of space - a relaxation. If it isn't and something is pushing harder than something else is pulling (the tension in free space isn't as 'relaxed' as we thought), then there is something seriously wrong with our view, because our view up close does not connect up well with the long-range one - the wide-angle view is skewed somehow, or there is something about mass we don't know yet. We know we've answered some 'big' questions but the ones we haven't yet really are big. We may not understand something about the view yet that explains why it looks like it does in the large.

Another special thing about Einstein's first big theory is that a hyperbolic curve is special; other conic sections aren't bounded the same way - an hyperbola, as the math and the physics books will tell you, is a curve bounded asymptotically, it's a quadratic curve which corresponds to a positive potential (inertially) but is open or extends to infinity. It seems to be related to the frequency domain - the time independence of oscillatory 'stationary states', as well, which implies inertial motion is a case of oscillatory motion.

Special relativity relates the geometry of spacetime to the special limit of its tension or ability to 'transmit' any sort of energy, which is a hyperbolic surface with covariant 'tensors' in it - these are what we label the operators or the 'actions' in it. What "the gauge of the field is the photon" means, say. Gauge theories are about how frequency and energy - momentum, are measured against a potential -the one we set to 'zero' which in fact is us, or if its an instrument like the Hubble scope or a thermometer - we have to 'measure' what they do. A track in a bubble chamber has to be 'looked at' - it's known to be against a significant magnetic potential, so the curl in its field is then reflected in the spirals - the helical paths they take through the chamber.

The other special thing about conic sections is there are 4, two closed and two open curves - the first 2 can represent 'bound' kinds of behaviours generally, and the 2nd can represent 'free' kinds, but every kind of motion or potential motion is really a mixture of each, divided in a 'universal' way; the poles around which each kind evolves are generally resonant and 'expansive but condensing', zeros are absorbent and 'compressive but extending'; it's a complexed frequency domain that we compress into the time domain (because we have to expend energy to measure any of it - i.e. we have to do work too). Measurement is a kind of compression, IOW, and something 'expands' to compensate - which is what we call 'entropy'.

Which 'conclusions' are you ranting about?

I think the main conclusion which I must reevaluate is that anything here is going to be of any interest or that you will be fun to have a discussion with.

My mistake.

Tighten your foil and carry on. I shan't disturb you further with suggestions of coherence.

OK, so no more vapidity then?
I would have thought, at least a little, or inanity, perhaps?

You realise, it's all bullshit anyway? As if it's meant to make sense or some completely pointless thing like that?

I suppose we'll just let that expand into infinity then, say, the apex of the next conic section?

More doodles:

for some reason I've been drawing and making cones. You can deform a sheet into a Mobius strip (a non-orientable surface), a sheet has to have at least 3 'edges' or 3 'vertices' to make one, though.

You can deform a sheet into a cylinder, and join the inside surface of one end to the outside surface of the other (or the same) end, by cutting along the cylinder in two places, from either end, or you could just cut two rectangles from either edge of a sheet before the step of rolling it up.

A Mobius strip can have 'bumps' in it - you can make a paper cone, and cut sections out of the sides so you can join the inner surface of one 'leg' to the outer surface of its opposite. A mobius 'surface' with a regular cone in it. You can have an infinite number of cones, in fact. You could also have an infinite number of open cylinders instead.

A bicone is a deformed sphere, if you 'puncture' it along the greatest diameter - assume it's the original diameter of an undeformed sphere, say - and puncture it again - that's twice, can you deform it into a Mobius strip?

P.S. this is a kind of stab at the relationship between intensity (of radiation) and my statements about massless photons - how a photon is adiabatic; photons have no 'diabaticity', etc; why their spin and polarisation angle are "a tangent" to something and why that means photon spin can't 'do' any work (although when we polarise photons they do work on electrons, in the waveguides they propagate through).
What Galileo and Archimedes and co thought about ocean waves, or waves in rivers, and so on.
I mean, we persist in insisting that 'solid' objects like wooden and metal boats aren't at all like the waves that they plow through, but this may be a kind of illusion

Feynman diagrams - what sort of 'informative connection' do they make?

These are graphical representations of "fundamental exchanges", generally there are 2 edges entering and 2 (or more) leaving the graph. A single diagram of say, 2 electrons exchanging a photon, is a vertex of a much larger graph. Feynman diagrams are bounded - the axes are time (which is linear) and distance. They're directed graphs, the edges represent 'particles' with a definite worldline through a SMALL region of space and time.

2 electrons with 'vertical' worldlines (if the time axis is in the 'up' direction), reach a vertex which is the exchange of a photon, then have 'bent' or angled worldlines.
The angles represent momentum or energy changes. The vertices are 'time and distance' symmetry points, in a calculation (a process), which is reversible.

Neutrons decay into protons and electrons, by exchanging a particle called a vector boson, a W particle. Neutron decay and electron scattering are then equivalent kinds of space and time graph.
A neutron can 'decay' into a proton by scattering with a neutrino (which becomes an electron), or by 'producing' the exchange boson, the W, which then becomes an electron + antineutrino.
The symmetry in neutron-decay Feynman diagrams, is that an incoming neutrino (which interacts with a neutron, by 'absorbing' a W), can be replaced with an outgoing antineutrino. Mass as particle 'resonance' is conserved, and 'energy' is exchanged at the vertex; a neutron decays by emitting a W which then decays into an electron + antineutrino.

Bingo, we get "positive" protons and "negative" electrons, and the whole polarisation thing. Neutron decay is an example of a kind of expansion+compression, and a kind of polarisation (which is 'hidden' in the neutron). We assign labels like 'decay', and 'mediation' (to a vector boson with mass, or to a massless boson).
Feynman diagrams are graphs (with a set of 'computation rules') of contributions to a ratio or rate of change which is statistical; it puts different processes into the same frame.

They're a 'simple' shape that has general applicability. The shape relates the geometry and algebra of fundamental processes, as a kind of vertex-with-edges in a directed graph - the diagrams can be as simple or complex as needed.

And as a kind of summary; the OP was about how we 'get' information, what it is, and what it does.
Also about the connectivity of everything. Everything is connected or related somehow.

You can't, however, substitute mass for spin, or equate km/s with squiggles on paper (except logically).
Things are separated, logically and physically; it's the connections between that matter.

There are those who maintain that mathematics is about compartmenting things (even go out of their way to pursue a kind of 'closed logic') - that you can't say one thing is connected to another thing, unless math says you can.
But this is just formality, because everything, including math (a symbology, an approximation for reality), is connected.

We are connected to the 'light' from distant objects, for example, even though the objects have (potentially) 'vanished' when we see them.
This is universal or general, because of motion - of physical objects and of the 'light' we intersect (here at our central location), motion is "just" another kind of phase-difference though.