Aerodynamic gravity meter

Ok, so say "we" decide that a device or computational machine can be constructed, there is available technology that can record, as accurately - though not precisely, since recording itself will lose some information about the positions of the wire, the weight, and the frame itself - as needed.
Then a general model can be built or designed on paper, or the algorithm can also be written down and a real computer language, or a real computer will be able to "handle" and process - i.e. compress into "results" - all observations and measurements that in principle can be made.

To make it just a little more interesting, and since you know that the air damps the wobbles and the swinging because the weight in motion causes frictional interactions wih the air around it, you decide the weight is also a bell, B. In fact it's a flat piece of steel, galvanized and shaped into an 'n' or inverted 'u', open at 2 sides.

It has a small section of pipe welded to it's midsection through which a braid extends, through the small cylindrical pipe, along the inside of the bell and from one 'short' side to the braid where it's interwoven again. It connects to the wire, which has an eyelet about 1/2 way along it. The eyelet is the attachment point for the sail, which is a grinding disk made from another compressed solid, a matrix of material which has a low flexure. It rotates around the wire alternately occluding and revealing the wire across its diameter vertcally. Since the sail can flap freely, because the central hole has a short, rigid wire hook through it, the other end of this is also looped through the eyelet and the entire sail area can be held outward or rest against the T1 steel (guitar) wire. The T1 connection is actually 2 different gauge strings, steel wound, with one through the other's brass eyelet at its end, so one is free for the sail's 'boom' or attachment.

[ed. the "braid of polymer" is plaited into three lengths, one length is longer and extends through the bell and back into the weave, making a 4-braided weave; the lower guitar wire is plaited or woven into the upper part, but is essentially connected at a single point to the lower knotted braid - this is only a tensional arrangement, there are three tensions in the T1 connection that depend on their individual structure, and each has different torsion but contributes to the rotation around T1 of the weight equally, over T).]
The braid is made of a polymer (weed-whacker string). The bell will strike the upright of F, the vertically aligned cylindrical pipe, if the weight is held outward at an angle away from that normal to the cylinder's 'roll' or circumference - i.e across it - the bell will precess as it swings back and forth towards the upright.

If the length of the pendulum P, is within a range that sufficient angles from the horizontal, will mean the precession will take the bell's outer diameter of rotation and swing, to a "strike".
Energy will be restored to the surrounding air medium as sound, and the upright will absorb the bell's swinging motion, but may increase or decrease its torsional motion.

The frame damps the transverse swinging so eventually sufficient inward motion remains that the bell will strike the upright. The frame vibrates as the weight swings, storing and restoring momentum to it, and capturing its outward (transverse-to-frame) motion.

All the materials and the system, such as it is, represent controlled motion since, I did all the building, searching for parts, assembly, application of knowledge - a set of instructions that realize a physical model, complete with states that I can, or the wind can, induce by doing work.

Hamilton was a dude who realized one day that, the best time to know or understand something is when you need to. He was struck by the simplicity of something about physicality one day and formulas, decided it was best to record it somewhere, a quite general extension of the idea of an imaginary number.
It's still there, updated to a stone plaque in the side of some wooden bridge,

A general form of any physical system is called a transfer function or system response. Usually the letter H, for Hamiltonian is used, and the formula (equation) is a set of polynomials in time expressed as a ratio. Each term has a root which for the upper terms are zeros, for the denominator they're poles which can't be "zero" or the response is infinite. The denominator is where the 'start' term goes; when T or t is zero this term is too. IOW, the base of the steel upright is the "start function" for the frame. The weight has a different or independent Hamiltonian, for which an action exists - the weather.

The single (steel)-pole system for the wind-activated torsion pendulum is "at zero". It has a point of reference - the ground state - where it doesn't bend. The upper arm does all the work as the weight swings. If you install a keeper or torsion arm on the vertical upper pipe, and move the wire support for the weight to the end of it (attach a pipe wrench and hang the weight from its handle), it will capture axial motion along the pipe, keeping the swinging along its axis, which is perpendicular to the T-bar construction.

Another upgrade possibility is strengthening, by using three or more angled sections of pipe to make an open pyramid, starting with a tetragonal shape, it can have a base that supports each upright and a three-way connection at each vertex. There are several options here, the pipes could also be a mixture of steel tubing and some kind of piston, so the upper connection for the weight is damped. Pressure in a closed gas cylinder can be a measurement of the damping of modes in the weight so that a record of pressure changes is a log of wind movement.
So you can see that extending the model is also like algorithmically finding Tn, so then finding Tn-1 and then Tn+1 as well. Hamilton did much the same with Ti, Tj Tk and quaternionic algebra. As you can see, if ijk are a triple of imaginary T1 dimensions (+ -),(- +) then you get squares and cubes of them. These are logarithms of real things like pressure and volume, periodic motion, vibration, tension and stress.

Next step: having introduced a real structure which is a steel pole upright with a t extension or a T-bar, and a weight attached or hung (suspended) from the extended vertical bar, and some algebra I'd like to go abstract and use some symbology - invent a programming language.

Turing thought about what picking up a sheet of paper and writing on it meant one day, and decided that the paper was really a tape with symbols on it, read by a machine (the writer). So that a page with text on it is also a Turing tape, the machine is the person reading it, or these days is the character-recognition software trying to read it. Languages, written and spoken are complex so we use simplified or compact symbologies to describe algebraic states, in some machine or engine, or weather-driven torsion pendulum.

So, applying a basic OO (object-oriented) analysis, the first 'priority' is defining the objects "in-frame" where the OO frame is the problem domain, i.e. P=NP?
Polynomials in P are not in NP, for a torsion pendulum. NP is the wind strength since, this cannot be predicted by the model, only responded to (recorded on a tape or on a 'sheet' of some kind).

So a constructional type of analytic approach might start with "what is a pole of steel?". Since I know what this is, I simply state pole = steel tube.
Now to construct an upright pole, it needs length and has to be plumb, a T-bar construction means welding or bolting together two sections, etc. A general 'joining' algorithm. So that:

join(pole1,pole2,i,j,k) welds pole1 at point i, section j, height k of pole2, for instance. If pole2 is "the ground", you join pole1 to the ground at point i, section zero, height zero. Since a steel tube = a pole and is already a cylinder of metal it retains the tensile properties over i,j,k and interconnections or joins, over the structure. the ijk index of each join and the points of intersection are "meets and joins" of stress energy, torsion and rotation in frame

frame(i,j,k) = sum(pole({p1,p2,...,pn},i,j,k)) = pole({sum(i,j,k)},n) "for n poles in the frame"
pole = join(i,-j,k) "a cylinder is an outer i, minus an inner j radius, with a length k"
...

Since the poles are all in the denominator for the overall transfer function in the frame (F), a zero function is required for the numerator:

zero({},,,.) "assign the empty set to empty i,j,k (i.e. do nothing)"
zero({},i,,) "assign {} to i, leave j,k alone"
zero({},,j,k) "erase j,k"
...

Then for poles Pn, over polynomial time Tn, the transfer looks like:

transfer(Zn,Pn,Tn) " Zn/Pn is transfer polynomial for Tn sections of time"

Great going, skipper! I'm surprised there are no comments here yet!

A corollary or correspondence with all T, P and Z in the frame is that i,j,k and ijk represent the meets and joins in the "triangulation" of frame F.
That is, the upright pole and its join, the vertical pole are Tz-join-Txy products in ijk over i,j,k meetings.
Or, IOW, (the standard mnemonic for alternation of the algebra) the Tz "up" pole meets the vertical "in-plane" xy pole, so that a single section along Tz, length k, from i(p0,p1) points "in i" is the vertical side of the triangle, y is either the cross-sectional area of the vertical tube of steel with an x = the axis, or these can alternate. Meet and join are what the Tn sections (poles made of steel) do or not, since join means "weld together", meet means "put together", i.e. lift vertical pole Px (with section y, s.t Txy = Px(y)) to height k of pole Pz = Tz(zero({},i,,,)). The y-section = zero({},,,k) will move (after the weld is made) as the weight swings, the diametric measure = 2y, will change over time.
So that, positions and momentums will change as Tq,p and Zpq over i,j,k, for poles Pn = P|(x,y,z) or *P, over XX', YY', ZZ', for all T.

P.S Ahoy there cap'n K! This is a general (ala Einstein) look at model-building and explaining how things work, why we build stuff, etc.

Ok I'll skipper past the induction of Z, the integer group of numbers. I and i are inertial and imaginary, or "identity" numbers.
Math being symbolic, and languages as well means Boole's logic is also a decomposition of English written/spoken language. There is a correspondence between a constant and the phoneme "k". And you cannot decompose an argument into less than a single proposition, Turing added that we cannot propose that building a machine is guaranteed to do anything, we can't write a program after designing an algorithm that won't 'lose' information either as abstract bits - unless the program copies all register states, i.e. debugs itself - or as heat. We cannot say if a given algorithm will halt, only that it computes a given problem using less time as heat or computational "power" or efficiency.

The system I've set up with readily available components, for general observation of wind energy in local conditions - given what I know about them - is efficient at storing this weather information, I just have to "collect" the stored energy somehow and analyse it - Fourier and Gauss, Poisson etc are useful with that. I could build an electromagnetic ring (metal detector) and install it under the weight and log the fluctuations in AC sinewave signals as a carrier,
So that the vector space of electromagnetic interaction can be X,Y, and Z.

It is a bit long. Will need to take out time to read it thoroughly. Will catch this thread later in the day.

Actually it's a bit short, on definitions.
And it's a model I hope will explain GR and not require SR as a precondition, or, if I can construct a symmetric "information collector" for all the energy in the system, that corresponds to the one Einstein used for spacetime, then connect it to the signals in a metal detector coil from the motion of the suspended metal weight, see how it goes.

GR is a bit long too, like 3 years of undergrad then some more grad study. Even postgrad and doctorate level doesn't cover the whole thing. Einstein didn't cover much ground with it either but a lot of others have since it was published. Hamilton's problems and some of Hilbert's remain to be resolved either completely in some sense (as of being able to build something) or at all, in Hilbert's case for certain mathematical examples in his list.

The word "manifold" might induce a picture of something attached to a combustion engine, an electronic circuit is a manifold too, it exchanges electrical energy with the environment as heat. The environment is the air or an insulating medium, since metals are where charge can travel or flow smoothly. A simple model for a manifold is a sheel of paper folded against itself. The manifold meets two surfaces, and joins a 'crease' or diameter = distance between them.

A folded sheet is a join if both sheets are 'glued' or connected in a fixed, immovable (irrotational) frame. Otherwise they can slide across each other (you can slide two halves of a folded sheet). This is a simple doubled surface, the distance between two sheets that meet is imaginary, if they're joined so no sliding distance is allowed (available), then it's always at Z(0).

Ed: the thing about staying with the 19th century classical approach, bending, tension and torsion, but updated to the 20th-21st is because physicists have assumed gravity needs to "go back to Einstein", i.e. if you don't get past Lorentz and proper units of time your boat sinks straight away. The goal is to connect gravity,inertia and mass to quantum energy levels. These have a tensile structure which can, in fact, be related to a pendulum in motion. Introducing a wound coil which will induct a magnetic field around itself is introducing Maxwell's quaternionic 'insight' all over again.
There are algebraic extensions, but I would like to stick with a basically object-in-parts idiom, with P/NP. P is, for instance the first letter of certain "p-words", such as "position, particle, prime, pump, problem, polynomial, pole". The language toolkit has parts as well, that the spec for the proposed (i.e propositional) machine is used to construct the plans, the design for hte machine itself.
This is the domain of the algorithmic, i.e. Turing sense, of halting or the inverse, starting a process. Extended to that is the question can an algorithm solve a problem, in P? Exponential time is "the problem" in that, the "T=sense" which is strongly-connected. T-words are "total, tangent, tension, triangle, triangular, tile, trisect, triple", also "two. totient, trihedral". And of course, Time.

Also assume someone's been given some homework about GL(2,n) and SO(3), rotational symmetry in space and time -> rotational axis of spacetime symmetry.

Ed2: The philosophical angle or the history of the study of motion and gravity goes back past the likes of t'Hooft, Penrose, Hawking, Einstein and Maxwell's daemon. We use the last in that list today in a certain derivative of a system I've followed since not too long after it "came out" which was initially (i managed to inherit an original set of AT&T manuals from '78) in the minicomputer domain and now on clusters of them, and boosted by the ubiquity of a design (the PC) which we might rename the polynomial computer. "Nomial" here means "nominative, instantive"; these machines assert things. We still don't know what gravity is, but we see it "all around". It's the most obvious thing about being on the surface of a planet, the next most is sound, and light, two more things. Taste, smell, sense of warmth relate to the first two of sound and light, in a fundamental way. Our monomial selves are "in" a time that is along a T-axis, like the upright pole is, since it also bends slightly if the weight rotates aound it, from the end of the vertical extension, or X'. In fact the entire surface the pole is embedded in could be sliding along a frictionless subsurface that we can't see. The planet might only look like a slightly out of shape sphere.

Another interesting historical fact is what early surveyors used (and navigators) to build straight edges for things, upright and along the ground, i.e. roads.
The Romans were the first to build in straight lines for large distances. They used a plumb rod, and a balanced twin-bob plumb at the end of a vertical, slightly angled support beam, which they sighted along to eyeball an assistant holding another pole and would signal to them where to place their surveying stick. With a plumb weight + pole and a balancing arm, the addition of a remote observer (of the signal) straight roads were constructed across the Empire.



As you can see from the picture [??] the upper arm rotates around the upright pole. This means the vertical can be checked by swinging the sighting arm around the pole and sighting along the central plumb bob string (a second string bob behind the pole was included in some of these "gromas". From the "agri" root for farmland etc and Greek "gnomon".

So if I decide to build a coil and use an electrical signal to capture the metal weight's position and rotational information, since I know what shape it is and since it's insulated by the polymer plaited rope I made, it's an aerial that will generate an electric field, since it's moving through the earth's magnetic field. Here I might improve the efficiency of the detector in several ways.

1) by adding a local circuit, a transformer that captures the magnetic potential in the core of the metal weight. That is, use the metal bell as a core. There is probably a better design for a core than a single metal plate bent at both ends into a u shape. (actually there's a good reason I know about that transformers have metal plates stacked together).
2) substitute a decent size transformer, prewound. Keep one winding energized and use this known magnetic inductive potential to measure the potential flux in the other, longer winding as it responds to the alternating (rotating) field in the core of the planet.

3) since differential rotation of the planet's iron core is believed to be the cause of the magnetic field the device will respond to, the moving coil (swinging because the wind drags the sail around) is a galvanometer of the planetary magnetic field, relative to wind strength which is the time-dependent part of the excitation. Alternatively I could make the transformer move by suspending the wire from a ballbearing race and motor that turns the wire at a fixed (DC motor) rate.

Using the statndard Zn, Tn, Pn notation, the x,y,x 'spatial' index and i,j,k to count 'states', or "meets nd joins" in x,y,z, so that p or q can assume mixtures of these indices, i.e. (p,q) | {x,y,z},{i,j,k}, where the upright "|" means a pole. This pole could be vertical, horzontal or in-between. I need to associate a metal, steel pole with an approximately constant inner width (of steel) to a resistance a capacitance and inductance.

Since a pole is straight and each section through it - if I cut it into sections, will be the same width, but not necessarily the same length. I can cut the pole into arbitrary lengths but the w = w' along it. The length is equivalent to a resistance (to bending); the width which is circular is the amount of Fe alloy in the pipe section s. Then this measure w(C) is the capacitance, or capacity of the metal to store energy or electric charge.

In fact a pole of steel, galvanized is an aerial too. It is receiving radio signals but because it's joind to the ground, the signal is lost as soon as the tube responds to it. I could make a pole-aerial by connecting several sections end-to-end, and insulating hte ground before lifting the structure - a mast - so it has better "headroom", but the signal detection will depend on how the aerial reacts to incoming signals, in- or out-of-plane.

Inductance due to gravity is the bending moment (slight for small displacements of the weight) of the torsion bar when two poles are welded so one extends vertically.
This joining, of ends of sections together (to build an arbitrary length) and at cross sections represents a resisitive ladder either upright or on its side, as a supporting frame for the current flowing across or through it.

So if I decide to build a coil and use an electrical signal to capture the metal weight's position and rotational information, since I know what shape it is and since it's insulated by the polymer plaited rope I made, it's an aerial that will generate an electric field, since it's moving through the earth's magnetic field. Here I might improve the efficiency of the detector in several ways.

1) by adding a local circuit, a transformer that captures the magnetic potential in the core of the metal weight. That is, use the metal bell as a core. There is probably a better design for a core than a single metal plate bent at both ends into a u shape. (actually there's a good reason I know about that transformers have metal plates stacked together).
2) substitute a decent size transformer, prewound. Keep one winding energized and use this known magnetic inductive potential to measure the potential flux in the other, longer winding as it responds to the alternating (rotating) field in the core of the planet.

3) since differential rotation of the planet's iron core is believed to be the cause of the magnetic field the device will respond to, the moving coil (swinging because the wind drags the sail around) is a galvanometer of the planetary magnetic field, relative to wind strength which is the time-dependent part of the excitation. Alternatively I could make the transformer move by suspending the wire from a ballbearing race and motor that turns the wire at a fixed (DC motor) rate.

Using the standard Zn, Tn, Pn notation, the x,y,z 'spatial' index and i,j,k to count 'states', or "meets and joins" in x,y,z, so that p or q can assume mixtures of these indices, i.e. (p,q) | {x,y,z},{i,j,k}, where the upright "|" means a pole. This pole could be vertical, horizontal or in-between. I need to associate a metal, steel pole with an approximately constant inner width (of steel) to a resistance a capacitance and inductance.

Since a pole is straight and each section through it - if I cut it into sections, will be the same width, but not necessarily the same length. I can cut the pole into arbitrary lengths but the w = w' along it. The length is equivalent to a resistance (to bending); the width which is circular is the amount of Fe alloy in the pipe section s. Then this measure w(C) is the capacitance, or capacity of the metal to store energy or electric charge.

In fact a pole of steel, galvanized is an aerial too. It is receiving radio signals but because it's joined to the ground, the signal is lost as soon as the tube responds to it. I could make a pole-aerial by connecting several sections end-to-end, and insulating the ground before lifting the structure - a mast - so it has better "headroom", but the signal detection will depend on how the aerial reacts to incoming signals, in- or out-of-plane.

Inductance due to gravity is the bending moment (slight for small displacements of the weight) of the torsion bar when two poles are welded so one extends vertically.
This joining, of ends of sections together (to build an arbitrary length) and at cross sections represents a resistive ladder either upright or on its side, as a supporting frame for the current flowing across or through it.

😁

So reviewing where the scenario, the wind and the mast is bending, I now have the Coriolis effect, Focault and the climate to explain. The problem domain can be restricted nonetheless to the known magnetic field of E.g the planet (E for Earth, g for gravity) exemplum gratis. This is the inductive step: the planet is a given.

The model already looks like it has the makings of a stack architecture. X,Y and Z are the values and i,j,k are addresses on the stack or heap, operators are sums of addresses, like ij, or i+(-j) to get relative addressing over n the stack depth. If n is the address counter, V is the size of the register set, for all i,j,k and extensions over values x,y,z, where the latter are real lengths and widths of tubing, one of which is at Z(0). However, this is actually below-ground, in that case the embedded pole of steel (let's say it's anchored in compacted soil packed with stones) is only partially fixed, it must bend or change its angle wrt to central force acting to keep it "stationary" in the ground.

What can be measured is the "free" rotations in the weight and the sail as they turn, one in a regular but alternate way (there are torsion pendulum clocks that were popular because they ony needed winding once every 400 days or so) the other in a quasiperiodic way, it depends on the torsion in the eyelet, which rotates with the weight, and how much of it is "at" the sail's boom - it's tied to the mast, but the wind is "free" to blow it randomly except, it tends in the direction it's already turning, although it reverses as often as it turns the same way, behind (out-of-phase) with the regular, ponderous weight in the bell, at B. At B(0), the weight is activated by wind alone, but I'm free to investigate what large swings, etc mean in terms of bending, rotating in and out of plane, line of sight and so on result from such "imputs". Sine waves abound, and responses at various levels are seen.

I could expand these general observations into the Maxwellian domain easily, as above. Without actually losing much generality, since "we" know that gravity and electromagnetic charge behave with an inverse-square "law" in terms of area and distance from center of mass or charge.

The recording device, needs some stack registers for all the bits of info, angles, inversions of swing, rotations, bending moments, the list is quite long potentially. But say I attach a pre-recorded device, an image that has a known 'signal' which is very long and densely encoded. If I mount it on the 'sail' so it's flat unless the wind lifts it, I have a known 'program' I can try to read and copy.
So there's an n-bit register, on the sail with information I in it and the sail has an identity n bits long.
The sail has a CDROM on it.

Right now I have the sail collecting wind information, and sun position and intensity information to an in-principle laser interferometer setup with the CD as one of the mirrors. There's a way to send signals down a fibre-optic cable using a kind of beam-splitting mirror.

But to seriously invest in a real gadget I would need a serious machine. I could do a modest run prototype with some sort of polarized light, an LED high-intensity lamp, a plasma tube etc, and see what A/D can do in terms of looking for a trend. The signal would have information on several levels. A way to process it in parallel would be nice.

I blew that last series of posts because of a lack of response from the "net", I'll try to put stuff together before posting it.
Then think about drawing a right triangle with one side twice the length of the other. You have to then do two things, find the circumcircle around Tn, Where T1,T2, and T3 (the last is numeric root of three) and the circle arc from A to B.
T1, or A.B is the line, T2 or B.C is the plane (rational quadratic of root(3)) and T3 is the cube. T is a pseudo-triangle or tile = [root(5) + 1]/2

The next thing you do with a 2:1 triangle is finish building the square and circumscribe it. The inscribed circle in the completed square represents the quadratic area of x,y. The outer circle represents the diagonal product or 11, when y 'takes x to 1' or the line y = 1 - x. The ring between the inner and outer circles is the rational bound for x,y. If there is a T3 on the triangle, it's the root of a cubic polynomial in T.
T1,T2 appear together, T3 is the horizon (hypotenuse) of T2 or the limit of T1.

Another filler on algorithms and design. I learned "in school" that the best approach is to prototype a system, then build a beta version. So that, the question "can it be done" is like: "we have the beta release".

Turing, again, decided that a Boolean proposition is like asking "is there an answer, and how is the answer like building a device of some kind as a way to test the answer? How is asking a question the answer to the question, that is?
To decode an unknown message you look for a pattern, a background 'carrier' in the data. With large prime factors which by the laws of large numbers and arithmetic, are hard to compute in P. So the "can we decode it" questions are in the P=NP domain of P.

Parallel computation is a way to process several contexts (processes) at once, so you can consider a process as a sheet of computational 'material' which is a switching network. The signal are all gated in pairs in digital logic so you fundamentally have 2 bits, or a bipartite graph. Crossings are when signals change as in, x,X <- x',X, and y,Y <- y',Y. Each switch either reduces or sums the inputs there are only 3 inputs needed to build a "universal" logical net.
You can stack sheets, and have data barriers between each, or have interconnects that are a 4th switching dimension, and so on. The most efficient way to transmit a signal is at the resonant frequency of the carrier or at a harmonic in the low k-numbers, for k the wave number.

So that a universal, switchable net can in principle connect any 3 dimensions along XY, using Z to switch (add or sum) and so invert X or Y, by removing one or both, either producing -(X,Y), or X'+Y = X+Y', and X'Y = XY'.

Retaining either X,Y or Z the actual switch function or state at time t, requires a stack of sheets that retain their state or a way to copy them somewhere; It turns out you need 6 switches to control 4 inputs, two switches at a time by either routing them - inverting them - or sending them on, or by adding them or producing a third (y') signal, summation is easier to recover the signal from if you have a copy of it (x), this number of gates, 6, scales as the powers of 2 in number of switch inputs and outputs does.

The reason I'm doing the 'project' is, I thought about how difficult it would be to set up a system "in-house" (actually in-backyard) that could do some serious gravity monitoring. Connecting this to some kind of observational data-logger running automatically took a little more thought. Building the model physically was the easy part.

Measuring the changes in position and angle for the surface of the suspended CD is a bit like trying to look down a telescope for evidence of the Apollo missions. However, NASA does astronomy with lasers at lunar distances. They don't read a string of bits to check it is the right mirror though; this is the essence of what the physical system I have, will need.

Rather than a lunar gap I have a "motion gap" since I can set up a fixed range laser beam, but only expect it will see any part of the CD surface at any sample time. Also the disks are meant to be read by lasers with focusing lenses and at small distances, at a known rate of travel for the spiral of the track, reading this from a distance is a challenge. But it's also a diffractive surface, I can ignore the code and just assume the pits are spread, on average, evenly over the spiral track, so that the diffraction will be equal at any given angle. If I set up two fixed lasers and a beam splitter I should be able to recover information about the orientation and rate of travel or rotation, if I also assume the local conditions will mean low-energy states, so mostly torsional rather than tensional rotations in-frame.

I've generalized the idea of constructing a frame to building a circuit which is resistive, and reactive. I can use damping in several ways, by installing air-filled shocks in the 'T-frame', or by using additional torsion bars as keepers. Or I could damp the bell's swinging magnetically, by counter-rotating a magnet's field around the one induced in a swinging transformer with a plated core.

The kit for pole-joining needs general "brackets" for up to three or more joins. If the joins are restricted to two pipes you can still make a stand of sorts. Join 2 pipes at 60 deg,, and repeat so there are 2 T2 sections. Lift two sides together and rest them so they meet at an upright Z position, over XY the plane of the ground, you can use 2 more brackets to join the ends. On the ground there will be a T1 meeting a T2 but not joined to it. Two T2 sections joined at 60 degs, + 1 more join = T3 a tetrahedral frame. The second bracket goes on the end of the other T1 lying along XY, adding an extra pipe section also meets a T2 but isn't joined. Thats T1+T1 = T2; T2+T2 = T3 = T2+T2+T1, with four 60-deg brackets, so all ends either meet or join all other ends. The frame is 'closed' but not joined except from T2 to T2 subframes, over 5 T1 sections.

It has a complex structure, since an upright or vertical T1 is resistive (can be loaded without bending), when they aren't plumb, loading will bend them more. The damping shocks represent absorbers for this reactive behaviour, like having resistors in series with capacitors, to smooth a waveform or 'absorb' it.
Pipes can be bent, instead of straight, so you can easily make things like inverted catenaries.

Frames and the astronomical angle aren't hard to connect, I could be building a telescope mount, or a large inverted geodesic structure as a radio dish.

Here then, you can (I can) construct a general "gravitational" model, with a simple hanging weight. A hanging weight is free to move around, but unless it's hanging from a truly fixed location, the surface it depends from will also move. In fact we know the surface, and my backyard - which I could go to the trouble of looking for on wikimap, is moving around a gravitational center.

So, the rule is, whatever I build or anyone else does, it isn't motionless, a fortiori. Newton dealt with planetary motion by assuming the sun was fixed in place, and all the other distant stars. This is known to be incorrect: the stars are all in motion 'independently' like molecules of gas. The 'molecules' are made of metals, like Lithium, Carbon and on up to Iron, the stuff my model uses for pipes, with a 'fixed' or manufactured circumference, C(pipe). I've assumed - though I know it's false - that I can only use pipes with circumference C, so that the thickness is preserved regardless of where I section or join two or more lengths.

If you look at the local arm of the galaxy - what we call the Milky Way, all the luminescence is a field of gazillions (a number that is larger than any worth bothering to contemplate) of individual 'star parts', or metallic lumps of hot gas, in fusion of hydrogen to produce the metals > He in the table. Each star is (looks like) a molecule in a long tube or rod, extended along the arm, A, which is the Sagittarius-Carinae.

So that, the idea of using a general construction of 'resistive, capacitive, inductive' metal pipes, has to necessarily connect to Maxwell and EM, and to the structures I can see beyond the horizon of planet earth. In fact, the tetrahedron I can build with 2 meets and 2 joins = 4xT1 sections and brackets at 60 + 60, so all angles are equal, implies a bracket can be made. I can extend this T[sub]2 [/sub] connector to T[sub]3 [/sub], T[sub]4 [/sub] etc. The first step is to make a T[sub]1 [/sub] "collar" and make a T[sub]2 [/sub] or trivial "T-bar".

I have this with the T[sub]1[/sub] xT[sub]1[/sub] construction, where R, the rigidity - resistance to torsional bending, collapse due to overstressing, heat buildup because of these continued motions in the pipe, C(i,j,k) - with inner thickness or metal width (mass distance, density of Fe etc), is i -j, if i is any point on C and j is any point on the corresponding inner 'void'.

Now of course, j is only a measure of a void space if the pipe is in vacuo. A gas isn't metal but a pipe can transport gas, or liquid. It can transport particulate solids like sand or ballbearings too, or billiard balls (if it happens to have about a 3in diameter = about 7.5cm), We use pipes to carry along various forms of matter, energy (as electric current). Since a steel pipe is also resistive I can at least connect Ohm's law to the rigidity or stress-energy in an upright, along i.k a point from "G" to Z1, where the vertical pole is balanced on the upright R1, at 1/2 its length, i.e. R2/2. The R1 pole divides R2 in two halves like a parallel resistance. Then R2/2 (+R1) is the rigidity available for bending (inductive modes) that store-and-forward momentum changes pB in the bell's weight, over T.

"T" is a catch-all for "tube of steel with rigidity" (since C is a cross-sectional capacity), time-domain response in |H|, the transfer function (input, output and system responses, between two abstract poles or surfaces or somewhere between horizon 1 and 2), or torsion and tension in T[sup]1 [/sup] T[sup]2 [/sup] , T[sup]3 [/sup] products for T[sup]* [/sup], as abstract arithmetic that is based on algebraic states (left/right angular momentum, swinging, wobbling, vibrating, sound waves, etc), and geometry - spatial extent and angles between "straight" lengths and bent ones. Arithmetic must appear for the formulation to be consistent with the geometry and its algebra. There are 3 mathematical "maps" to be determined or derived. This is much the same as the idea of a spectral triple: an algebra: A, a transfer function: |H|, and a structure (causal): G[sup]*[/sup](V,E). V is the vector subspace for G(E), E is "energy in system G, or entropy measure". Entropy as all engineers know is the stuff that disappears when work gets done.

The "triple language" will need an object&class library that corresponds to:

1) physical, static elements (tubes Tn)

2) joining and meeting elements that do "work" connecting Ta to Tb, lifting T(a+b) etc, consistent with geometry, in T; this means a space S will be needed (this is trivially true, but it needs defining as at least "a plane, XY, with individual x,y elements = positions in plane XY"

3) a way to build the graph (V,E) with v,e elements = vertex,edge pairs.

So a tube T has as we know, various representations. T can be "a pipe", "a hose" or even "a nanotube of C(12) isotope". A tube is a cylinder with a central part removed, the class&object needs strict definitions for how this is done = a tube-making procedure. I could (I need to) define a "pipe-filling" where a hollow tube is filled with some resistive material, bingo, one large electrical resistance R(Tijk), where j is the inner diameter of the material. The ij part is circular - it circulates around a center of mass- equal to a product of C the fixed tube diameter (which is only true in the backyard model).

So a tube T, needs a circular measure function, and a way to complete a circle (of steel, plastic, C(12)), by rolling a sheet and gluing or welding it, or by drawing (moulding) the tube mechanically.

The circle isn't "free", it has to be complete to close the pipe diametrically; the ends are open but can be closed by either bracketing them (with universal pipe-connectors) or filling the pipe (or just the ends). A sealed tube is also a container for gas, liquid, sand, etc so also measures gas pressure, liquid and solid volumes. An airshock element in each bracket, or as part of a pipe-length represents a capacity which changes (pressure in the air bounded by the container and a release valve or gauge) as the pipe tries to maintain its structural integrity.

This integrity is because of tension and stress, deformation (bending, flanging) and momentum. Inertia comes along for the ride.

Say I decide that lunar cycles are actually "me" looking down a tube, at the sunlight that shines at an angle through the tube, to reach the end I get to see. The sunlight in the Tube T, is only "full" when the tube is straight. When it's dark = no sunlight coming down tube T, the other end is bent too far out of alignment., In between I see the curve along the inner face of T, which is made of a material I can't see (I can see a "moon", and light), but I know there must be a tube of some kind, or how else does the image look nice and round?
How come I can see the curve of light, along the outer radius of T, and along the inner cylindrical surface as it "bends" and distorts the sun's image?

Hmm, no problems with viewing phases of the moon as light shining down a tube of some kind?
I'd have thought that one would raise an objection or three; since at two times during a cycle the image has a straight line across it - the lunar curve is straight for first and last quarters...

Well, surprise, surprise, you can explain this with a tube-model, and lensing. This implies the moon and the sun (and the earth) are a 'kind-of' telescope. One with a lensing property, and you can divide the 'full, empty' lemniscence (lunation or waxing + waning of the "yellow" color) into quarters, thirds, etc.

If you start with an assumption, the usual approach is to try to show the assumption is invalid, so that if you can't show this, then the assumption, no matter how strange or off-axis, stands (since you can't prove it's an incorrect one). If I assume the full moon is exactly "one circle" on or in the tube I can't see the circumference of except as the lunar surface, then I can divide the circle up into 2 halves, that represent the first and last quarters as they're labeled by astronomers. Then I can try to find the sides of the distorted tube of whatever-it-is in the assumption to see if that makes sense geometrically. The arithmetic is then the intervals of time that correspond to lunar phases, of which the full/empty state is two diametrical opposites. The quarters are not in 'halves' of these two extremal states (nodes in graph G), so that I need to find at least two other poles, to align against the lunar disc + solar bending, over the surface of the earth or the moon (the sun doesn't wax or wane so is always at an extreme, in G).

That is, I need to triangulate the surfaces, using geometry over the sphere to note the arithmetic 'time-intervals' between lunations on the remote 'lens'. I need an algebra of the circle that fits on the sphere, in corresponding sections. If I start with F0,F1 to represent the new and full lunar states (no color, full color Y) then I need to construct an algebra that corresponds in time, to all lunations which I or anyone can observe, from any three points (triangulation) on the surface of the earth = lunar astronomical observations over time. I need to be able to 'plug in' the quarter-cycles at appropriate points, in the triangles on the sphere.

Alrighty, so hopefully most other observers can also measure the area of Y, at any time, a series t,t' for observers at o,o' on the sphere of the earth, which is E the flat plane, in very small sections that we build this 'flattened' way = bridges, tall buildings that sway in the wind, rigging or scaffolding to make a "work shell" around a structure - sections of standard width steel tubing and connectors that can rotate, fixed u-collars at either end of a tube = T2 possible interconnections at inner sections over the length k.l, if k is the fixed length, then l is the unit length. In engineering they are understood to be equivalent; in astronomy they're determined by observation and individual location of tubular structures = radio dishes, telescopes (Hubble & helioscopy) things we build and launch after a lot of engineering.

If I 'pick up' my model of an area, C that is the capacity of lunar 'distortion' over time of L, the lenticular curve which vanishes, for F0, and is at full capacity at F1 = Y, It has 4 quarters to explain.
Ok, that fits easily into a circle, obviously whatever the curve in the tube I'm looking down is, at these points it's like a fixed connection between T1xT1. When Y (= F1 => Fx4) then we have Y/4.
There are 8 curves left to find a solution for, at separate points on E, or "me" and any T we can construct, in T* the logic or engineering.

So that, B/4 and 4/B* must exist as exponentials in time, since the capacitance over time, has two straight solutions, two poles at 1/4 and 3/4 or "first, and last" quarters in the cycle, it must have quadratic solutions at F0, and F1 respectively. The roots will look like y = 1-x, and its reciprocal. These have a solution corresponding to y = 1/x on B, the bending moment.

Several things are in play here. because I've noticed in my pursuit of answers, as it were, that can be encoded in some kind of device or computer
that like the CD is "the answer" to a Turing question, as in "can a program be written that solves a problem, and halts?", is equivalent to "can a computer
be built?" so, necessarily the two questions recur. Also, I intend to show that Rubik's cube is like a pole of steel, sectioned but still torsionally connected,
and, this maps directly to a 4-color problem on the sphere. Archimedes shows up since, he proposed building a lever (out of steel scaffolding) in principle,
and so on.

The cylinder, and something like a steel cylinder or even a paper one, can be used in the same forwards and backwards sense. as I've tried to show with
the aspect of lensing or the quartering of the moon's occluded surface. Tidal forces can be related to the same thing happening in the simple pendulum,
the wobbles that the torsion "in system" will try to convert into torsional motion in the wire and the eyelet the weight controls.

Because the T-bar is least deformed when the weight isn't swinging or wobbling. the grounded part of the pole absorbs this bending, the single pole pulls
along the x direction, to the point of suspension at right angles, or along Y in the XY ground plane. The weight, is able to capture its share of this, because
it's the other end or the 'needle' in my compass, or alternately it's the coil that drives a meter, keeps the CD spinning.

The angle of the CD as a refractive surface determines the visible color projected from the disk in any direction. The sun's image will reflect on a flat mirror
along the same z coordinate as the T1 pole, as a switch in an optical circuit, and a color-sampling device that simply records a strip across the spinning CD
when it sees the maximum intensity - the sun's image - reflected from the mirror, a 2-level switching circuit that stores a color-stripe and the time it was stored.

It would only record at a certain interval of each day, it would have to rotate with the sun otherwise, as well as having a line of sight to the mirror, and a light
intesity switch. You're looking at building a robotic device of some kind, that follows the sun, and also it's a reflection from a fixed and a moving surface, to
compare results with astronomical records, or, you could build in a lunar-imaging part as well, since the moon appears during the day sometimes.

You could look into a machine that can extend parts of itself to learn how to do this, or preconstruct most of the basics and use a heuristic/neural net approach,
since there will be several ways to switch two signals with access to a general computational device. Again, an initial prototype can be modest since CCDs are
about as cheap as steel tubing.

The colors from the CD because there are runs of small pits, in an overall statistically flat distribution across it are the equivalent of a set of tracks that have a width
that scatters visible light. However if the tracks are followed there's a code specific to the entire recording across any section or 'slit' unless the width is 1 bit wide.
If you could read in parallel in both directions you would have a chain of bit-values, side to side across the CD from edge to center to edge. This will also have a color
index.

We conventionally divide the 29 and some days of a lunar cycle, as seen from the earth into eight phases; I can call these 4 forward, and 4 backward phases of the
bending of the equivalent 'fixed' connection as the pendulum has. This will be directly observable when there is no wind and both the sun and moon appear, and the
pendulum is moving torsionally, directly across the XY plane, with T1 parallel to G. Its motion spirals left to right in time as the wire winds and unwinds alternately.
The wire's overall tension differentiates the momentum in the weight, and the winding or spring tension absorbs any vibration in the wire by converting it into torsion
and rotating the weight, which is a zero for the vibrational modes in S, the total space of all motion in Z, across XY.

Day n:
This all started about 2 years ago when I read something online which I can reiterate as two statements about physics - QM to be exact - and symmetries
in space and time.

This led me to the OO approach I know about, and the topological version or "tube model" I'm trying to develop; I'm free to adopt any reasonable geometry,
in-plane that represents what I have in-principle in my backyard. If Einstein was introduced to tensor calculus with a simpler approach rather than struggling
, as his teacher commented with multivariate calculus, or "the calculus of variations", or if his teacher had simply handed him a number-squares puzzle
(where you have to fill a hole in a recursive way to solve the puzzle and correct a scrambled number sequence) and said: "this is a numeric tensor, it has slots
for values and any given permutation is a tensor sum-of products, see if you can figure out which is which", he might have clicked on a little sooner.

But he obviously figured out a few things about gravity and bendy stuff. Sectioning solids, like steel tubes derives a number of possible shapes -> rings, tubular
bells or organ pipes, a pipe with a single slot cut along T1, or around the i circumference -> (pi)i ,and so you induce e, the natural log of numbers either with tubes
or with number puzzles in a square, if the statement I read, "tensors are components with slots" is correct.

If you then look at the benzene ring and consider how two rings join together, how a nanotube forms, and so on, the vibrational and structural modes and angles,
or a vertex-edge map of benzene as a 'component, with slots', how chemistry and tensor arithmetic/calculus have an obvious spectroscopic connection (IR, MR,
NMR, flame photometry, polarity of liquids in solution, in gels gravitic or centrifugal separation, spin moulding in metal fabrication tech, etc, etc).

So that the symmetries are actually constraints - we have exactly 3 dimensions to build in, the 4th is time which implies T4, or 4n. If T4 and T3 imply T7, then T4 -> T2+T2,
you have two 2,3,7 groups of symmetry; T7 is the hidden customer, possiby.

All the Tn 'tubes' can live in a general computational device that has register components, T0 - T1, and T1 goes up to say, T10, or n is > 0 and < 10, for register word
lengths, i,j,k. You need X and Y 'working storage' and a trace of all the storing/forwarding is a register-dump, over the space S = a CD recorded spirally, with
fixed-dimension pits or 'small cylindrical holes in alumina foil', each up to k bits long. The Z-register has i,j,k components and ancillaries Rn, that store values for x,y,z.

You need a sectional function, for windings on T1, that generate torsion, or w over a vertex along T1 = ijk the width times the height k, along each T1 tube; the pullback
or bending when the weight swings or wobbles, is T1' = 1/T1, etc. You need universal brackets that can 'bolt' T1's together. To make an equilateral triangle with tubes,
use 3xT1 and a single bracket, with a slot in it that allows each T1 to 'find' an angle (which will be (pi)/3) before bolting the T2 together, and so on.

The slots represent fixed angle brackets or (pi)R/3, which I'm free to label either "{" and "}", or "<" and ">" or even "||" for a T2 parallel to 2xT1 tubes; then the system I have
looks like:

<ij|T2|k>. Because - the left angle is perpendicular or 'at horizon G-zero'; the right angle is the bracket that holds the T1xT1 together, there are two poles "|"; it just encodes
the T-bar I'm using, if the angles in the section are (pi)/2 instead.

I've also decided I need to connect my model (such as it is) to a more general design that includes things like cathode ray tubes (TV devices) and generally the frequency domain
which is asymptotic analysis.

This is what the transfer Hamiltonian deals against, in terms of the probability a CD reader will be able to detect any color-stripe across the CD, and any code words; since the CD
is encoded in a constant run-length the 'bits' are all equidistant; I have a faithful bit-length copy of the CD run-length (n-bits long) to compare any I can read with some device (made
with lasers, mirrors, CCDs, etc).

Then the 'sail' part of my device that the weather operates, is like a croupier at a roullette wheel, the code words are a sectional 'probability distribution' that I can gamble I will be
able to read, over the surface area of the CD, at any time. Time is ruled by the torsional pendular motion the device tends to relax into after the "croupier" has spun the "wire wheel";
I have to wait for a result, or tell the logic to capture a slice "when" the torsion pendulum is stable, when wobbles and swings are near zero, or absorbed (by the T[sup]2[/sup]
tensional triangulation, over G the scalar constant value that accelerates the earth towards the bell, or the other way around - it's the tension in the wire that counts, or 'goes in the slice'
at times Tn, Tn+1 for the Turing-graph in polynomial time = the e[sup]st[/sup] domain, for s a complex frequency (one with a FFT transform, for instance).

I thought about how the cylinder model has an obvious place in combustion engines. I've pulled a few engines apart, though I haven't made a career out of it;
one of the things about engines, cars, lawnmowers etc is that the larger they are, the dirtier you get; you have to spend time 'under' the vehicle getting drips of oil
in your eyes, skinning your knuckles trying to turn a wrench, etc. Lawnmowers and small engines - motorbikes say - are more accessible.

I can still recall the first combustion engine I took apart, it was an old "Iron Horse" 4-stroke, single-banger with a standard float-carb. My father let me "work" on it,
in that cheerful way fathers have. He let me strip it down and leave a big pile of parts lying around the backyard, some soaking in kero to degrease; then he pulled
rank on me and announced it was heading for the tip if it stayed where it was.

So began my first real rebuilding of an engine (yes, I got it working). So I can say that, after working on a few more engines, some with multiple cylinders, I have a
somewhat 'deep' understanding of how they work, it didn't come from a book or a lecture, but from hands-on, up close and personal investigation. I had to figure out
by myself how to reassemble all the parts - taking an engine apart is a lot easier than figuring out how to put it back together.

Persistence and sufficient time let me do this - the customer had no expectations than having to dump another failed project (I can still remember my father's reaction
when I pulled the start rope to test the re-assembly, to my surprise and his it started first pull - yay for 4-stroke single bangers that a kid can put together in their backyard!).
The success of my first rebuild was 'satisfying', I thought at the time I'd only really done a kind of jigsaw puzzle, since it was kind of obvious what went where - the
carburettor was tricky and took me several attempts, I had to figure out that it was meant to float freely, I knew very little about the principles but I can still remember most
of the details - the jets have to be set properly,
I recognised that two of the adjustments were to set the amount of fuel flowing into the float chamber, and into the intake manifold, they had to be set within some value of
each other. I tested the settings by flooding the chamber a few times, I knew it was crucial that the flow be correct, and the throttle would alter the flow exponentially
(though I hadn't heard of logarithms or exponentiation at that age, which was about 8).

So a single-cylinder engine is a tube, with a piston in it that compresses and expands a gas. At the 'top' of a cycle of compression the sparkplug ignites a mixture of fuel
and air (vapor) which expands thermodynamically, driving the piston to the 'bottom' of the cylinder. Each cycle in a 4-stroke is identical except for which valves open and
close. The crank rotates twice, each rotation is either an exhaust of spent fuel followed by an intake, or a compression followed by an ignition.

In multiple-cylinder engines, you go from one cylinder to two, and keep adding, usually in pairs after you have two -> 2,4,6,8, ...
We also have engines with odd numbers of cylinders = 3 or 5.
V6 engines are two ranks of 3 cylinders. With a single-banger, you usually have 4 engine-bolts. I put the old lawnmower's cylinder and head back together with an ordinary
wrench, torquing it to "about there should do", which I assume worked because the engine's cylinder is isolated and any differences in torsion over the 4 bolts didn't make any
significant difference - the head was too small to deform over the area and the applied torque.

Torquing a cylinder head on a V6 or V8 means doing it in a cycle. You are NOT supposed to just start at one end and tighten all the bolts, one after the other. This can lead to
a cylinder head that is warped out of shape - you really need to apply the torque gradually (adiabatically, or as evenly as possible). Most manuals for cars and other vehicles
with combustion engines have instructions for this tightening down of the head against a gasket that seals all the cylinders externally. The valves then represent a way for the
inwards and outwards flow of pressure to control the 'power' transferred to the crankshaft.

The void-space in each cylinder is filled once per cycle, by the piston. Each piston is the 'J-space' or inner section of the engine overall. The cycles are equivalent to swinging
in the inertial pendulum model; torsional modes in the 'clock' I've built are equivalent to the torquing bolts, 4 per cylinder, but 6 per 2 cylinders, and 8 per 3 cylinders = 16 for a V6.
I don't know that this is standard, but my experience tells me engine designers tend to use a minimum of parts and weight is important, since it 'absorbs' momentum a heavy vehicle
will require more energy to stop and start moving.

The vibrational modes in the wire of my pendulum are equivalent to vibration in the engine - say when a car goes over a bumpy, uneven surface, and various parts move around
inside and outside the engine's constrained space. The pendulum absorbs this string movement and it eventually resolves into torsion in the wire = torsion in the head bolts of a
set of combustion cylinders. The swinging is then equivalent to forward motion or 'horses' in terms of power-to-weight ratio.

Tensors sure are fun. You can divide an ordinary circle into a tensor space, by quadrature. For a 4-cylinder engine, each piston is in 1/4 of this quadratic space
= {{+ +}, {+ -}, {- +}, {- -}}; add the inner angles each piston's crank makes with the axis of the driveshaft and you have a product of 4 'tensors' over the dynamics. 4 tubes,
each with an inner radius (void = -j) and an inner piston = j.

Then i is the radius of curvature for each cylinder in terms of the 'power' output, and the energy absorbed by moving the valves, drawing in fresh vapor and expelling it etc.
The power output along the driveshaft is = 4xTij, over the Tijk of the shaft, which has j = inner radius of steel, i = outer circumference of shaft, k = shaft length. The rest is details.

I've made a connection between the weather vane plus a 'cube of T' (since, I have T2 ,and T3 is the edge the wire makes with 'gravity' in 3 directions)
so that, T4 is the true "axis" that states have in the frame, stretching and bending relaxes over time into a precession toward the weight rotating - the wire
has an efficiency in this direction around the axis, which is parallel to T and perpendicular to G.

In fact the color spectrum across the diffracting light is the same thing as two plastic puzzles I also have which are maps of each other. Both are also
torsional with an 'about there' sort of feel. Twanging a string means if it's taut it will expand into all three spatial dimensions. The connection to that, and to
the puzzles I have is that high tensile steel guitar strings are different gauges, and the puzzles have different colors, one has "number" symbols on it = T5,
or a 5-dimensional kind of logic.

If i build a 'log' machine that can use these symbols in base 5, then use smaller 4,3,2 and base 1 type symbols (actually any state I can represent, with
another state like a capacitor charged to capacity etc, is itself, so I really only need to make this the 'clock' and test if it's "itself" by inverting it, copying it
and erasing the copy, which is "making sure zero and one exist", like a guarantee that the machine can at least do a self-test, by generating a single clock
cycle, copying it and testing it "against itself", so that you need a 2-bit register, with either {0,1), or {1,0] in it after the self-test, so the machine "knows" it can
clock itself and at least get to binary for a basis of computation - recording and reading some code.)
get to base 5; but I need a lower-dimensional way to store things, I mean binary logic is nice but it has a thermodynamic dimension. Maybe I'll just
have to do it logically. A 5-dimensional logic can be simulated, is it possible to build a 5, or higher dimensional machine? We can use any base except zero,
for numbers. What happens when we do use zero?

The fact is, anything we or I can try to actually construct will have this dimension, this principle appears to extend to living creatures, or evolution and its
principles (one of which I've learned a little about the dynamics of). I have an example of what this results in, which is a large clam shell, I can still see the
place the critter would have been at about 2-3 years old, with a jeweller's lens. The folding up of minerals, by proteins over time is the same domain as the
CD, but reading the latter is comparatively easy, just use the right logarithms. The domain of folding proteins and the spirals in seashells are much harder
dynamics to follow but, there are logarithmic spirals.

Imagine building a puzzle like this:
Slice through a nautilus shell along the spiral and separate two exact halves (search for a nice, exact nautilus shell,
or make do with a 'good approximation'; here you might make one on say, a computer screen with 'colors' that appear
because of collective electron motion, Coulomb scattering, and complex interactions that result in visible light "on screen").

Place one half on a flat surface and draw a straight line across the shell "from directly above", that intersects the
outside 'lip' and the outer radius of the shell on the other side = a greatest diameter. The smaller distance from the
shell to the central point of the spiral is the radius of curvature for the inner 'loop', this should reach to about 1/2 the
distance across the opening or the 'mouth' of the nautilus.

Then draw three straight lines across the shell, one is the same radius, extended to the beginning or inner lip of the
opening, and two others that form a right triangle, and the "Y" axis, if the hypotenuse = radius of curvature, is the "X" axis.

The straight lines projected onto the nautilus shell are projected by the shape of the half-shell into the 3rd dimension.
The two 'sides' of the right triangulation are single arcs, the hypotenuse has three arcs and two cusps. The 'pole' is the
centroid in the spiral, that the creature builds in an Archimedean, logarithmic way, over time.

Here's a piccy (sorry, it's a bit large, but it's a good plot)

p.s. dang, the puzzle, it's : "figure out how this plot relates to creatures evolving in the deep pelagic regions
of the ocean, and why the logarithmic spiral or log_e(X) appears so consistently, why it looks fractal and
suggests a creature that lived long enough would develop extremely complex shapes; explain what the
values along the axes in the plot mean, in terms of logarithmic values and different bases of numbers,
up to [ T[sup]3[/sup] ] on the chart."

Stefanides Panagiotis is a Greek mathematician/engineer/astronomer who has revisited the Platonic 'ideal forms' the tetrahedron, the icosahedron, etc.
Water, Fire, Air and Earth were connected to 4 fundamental shapes. The classical approach led Panagiotis to analyse the logarithms in these regular solids.

The "most beautiful triangle" mentioned above is one with sides of the golden ratio, expressed as a sq. root, a root and a cube root of it (Phi).
He compares his mathematical result (pure or ideal form) with a natural example, a nautilus shell. The approximation appears to be fundamental (or that's
my conjecture), since if you do the math, this method of triangulation (T, T[sup]2[/sup], T[sup]3[/sup]) using semicircles yields a result which is always approximate
(within about 0.001 of a measurement) and never exact.

If you assume the nautilus has an 'exact' ratio to correspond to (the golden ratio) but is forced by its environment to adapt to an approximation, it exponentiates
its 'shell' over time according to the formula Panagiotis has uncovered (or rediscovered) in Platonic solids. This approximate curve-fitting is the "freedom" evolution
gives to creatures; or to their adaptation to the environment.

Since the astronomy (helioscopy) finds the same ratio as Panagiotis found in the logarithmic spiral (up to 0.001 of a circular measure, over any diameter), then
it would seem the golden ratio, Kepler problems, gravity, seashells, etc, are also regulated by the same approximate curve-fitting.

Which I think is interesting, since there are the Voyager anomalies to explain. The spiral here is the one both missions had to follow to first encounter [Saturn],
after spiralling around the earth's orbit in the ecliptic plane. Now one of them is well beyond the 'curve' in the plane of the ecliptic and the anomaly shows up...?

p.s. whoops corrected - Venus is the wrong direction...
The Venus 'direction' I may have been thinking about is the one in the half-shell

The "anomalies" are reported in the Pioneer craft, or one of them. But, in my crazy-engineer opinion, we have 4 long-distance programmed machines,
communicating their observations, like 4 CDs out in space, orbiting something that we want to locate. We transmit the right codes (directionally) and
the CDs transmit back, so more like a CD-reader with a remote connection (bluetooth comes to mind).
But the model is applicable, since, my adaptation is also a device that transmits diffraction information - if I know what's on the CD I can pattern-match this
and try to recover polarization signals, it's a mere problem of sensitivity and filtering out the colors, etc.

So that, my non-anomalous gravity-meter is a reference for the solar inertial moment, that these system "explorers" are moving around, their direction and
velocity is also a code. The signal pattern overall, appears to be distorted when it's mixed with my one - or anyone else's here on a surface where mg is the
direction bells hang, and against which the pyramids at Giza (another valid reference point for astronomy) were constructed logarithmically.

Fitting a solar system inside numbers and also inside rotatable plastic "toys" which are also algebraic manifolds (cycle groups, symmetries and "volumes",
both of the solids which are sectioned and of the colors as they get permuted) isn't all that hard, you just have to remember the ecliptic plane is inside a spherical
shape, the Oort cloud. This is also surrounded by a double shell of solar wind particles, the heliosphere. The solar system is traveling through the intergalactic
sheath, and a bowshock wave exists, much as a boat forms a bow wave, or a river pylon has a wave against it.

The intergalactic space is like a vast sea of mostly hydrogen gas; the sun and planets revolve torsionally around an axis, embedded inside the heliosphere,
which has a sheath like all plasmas. In that sense it also resembles a plasma ball, where the glass sphere is the intergalactic space, and the plasma strreams are the heliosphere.
The sun is the central cathode and electric charge is the solar wind, in that case. Planetary bodies are the filamentary 'tubes' of flux, except they divide and merge.
When you place a finger or two or more on the outside of the glass you create stable planetary configurations.

Physics is nuts.

Hi skipper,

Amazing article though almost going over my head.😔 I have few basic questions
a) Are you sharing information about how an aerodynamic gravity meter should be made?
b) Are you asking us for contributing in this?

PS: Grant excuse if any silly questions are asked.

Actually, I confess my m.o. was to expose my own ignorance of a certain 10-dimensional problem, connected to, as I mentioned earlier in this
effective monologue, or blog, the symmetry of spacetime one.

After doing an online course which was remarkably easy, and getting "the hang" of tensors and since I know calculus I reviewed my grasp of
undergrad physics (I did electronics, did I mention?) and writing down a few basics about Rubik's cubes and the like, here I R.

The exercise has been a mixed bag, some sites you find yourself wrestling with people who just don't see your argument. So the idea was to
start simple and hopefully post the 'review' sans algebra or calculus, which these types insist you don't understand usually, and see where
I could take it. I also realized something about 'color' along the way: color is an abstract value or symbol even. A graph can have colored
edges or areas, or vertices, color is "free", and it also can be numbered, or be a number, so it's "itself" as well as having an index = "pullback operator".

This is reflected in Turing machines and the so-called "Universal Turing Machine", of which the latest, and conjecturally smallest, is 3-colored with 2 states,
and doesn't halt. The pullback is the output, since it's a tree-walk of the states for the 6 possible things it can do sequentially. It's equivalent to a 2-bit
register machine with 6 instructions, or ways to test and set the 2 bits.

I wanted to veer off again and have another look at a tube of steel, and engineering. Say I know how to build a cutting device that I can section a tube of galvanized steel with,
a laser cutter or a high pressure hydraulic cutter.

If I make a deep cut, across the tube I get two lengths. If the cut is at an angle, the angles add up to zero if I make the ends meet but not join. If the cut is straight across the angles
are equal. If I make a shallow cut, only marking the outside or 'burning' a track, if I rotate the tube and shift it along its length I can carve a track around and along the tube in a spiral.
I can arrange easily if I calibrate this machine to slice only through one, rather than 'deeply' across both surfaces, and remove a minimum of material as I do this (i.e. slice the tube
precisely). Then I have a spring constant, k = the tension in the remaining metal.

After n windings around the tube, the track has 'penetrated' the structure and transformed it. Leaving only a shallow track implies a low-energy application - a miminal pressure or
time-of-contact for the cutting head.
The thinner the coils in the result, the greater stretch, in k the tension or elastic constant, and g the gravitational constant accelerating all the motion toward G.

Since the tangent in the cutting angle, during the spring making process determines how deformed each slice around the cylinder is (how far off the axis, as the length
travels under the cutting head axially), the "pre-image" or manufactured angle in the coils; smaller angles mean a looser spring.

This is because, around the cylinder "about to be cut" the torsion is minimal, the bending moment is mostly around the k-axis or along the steel tube. It doesn't twist much,
or is 'rigid' around a circumference: then the spring's deformation is also "more available" when the number of sections per length of unit tube, is greatest. So k, is now k/n,
plus an angle. I, the outer circumference, is restored when the spring is either compressed and vertical or horizontal against G, or 'against' XY, the ground-plane.

J is what's left, it's where the mass "goes" in the Tij and k/n registers.

Another thing I have to account for is what if I slice or cut open the cylinder of steel (or paper) without rotating it.
I can bend a tube of steel with a pipe bending machine, up to making the ends meet if I use the right equipment. If I want to use a pipe like a gravitational channel for a fluid or for some kind of particulate matter, even say, ironsand I have to allow for the rate of flow and friction; there will be points of failure to allow for and how long I can expect the structure to function without breakdown (halting). Mean time to failure is a back-of-the-envelope case, for my string-model is how long the lower string will withstand being 'bowed or struck' by the edge of the grinding disk - built in obsolescence, and rusting (G+B Martins for a Yamaha acoustic or D+G for an electric, wound with two extra gauges of wire, G' and B').

Note: the wound strings have outer windings, each touching the inner string like a cutter can make a track, a sort-of tangent space that doesn't cut or slice the material, only 'marking or drawing' the surface at a tangent, which if the cutter is at lowest energy means only a shallow track is made.
If a spring is made by cutting open a steel tube it will deform along its axis if you hang a weight against gravity - i.e. pull the end of a spring vertically or horizontally, using your weight.
The pullback is the tension in the metal, and a torsion spring pendulum bobs up and down periodically, as the weight and the end of the spring rotate, around the barycenter which the axis of the spring is 'aimed' at.

Tension and torsion are usually explained as two aspects of shear and stress. Stress is easy, it's what you do to a guitar string when you stretch it to tune it to a predetermined tone or 'note'. If you remove strings after tensioning like this, the ends are deformed, by the way they were torsioned, or torqued around the posts. The metal preserves this 'work function' by curling up. Shear is probably easy to explain as what's happening to the string at the point of it eventually breaking (and restoring T-zero). Then the string will recover all it's shape, and some of the stress it's had up to the point the lower string separates (probably near the point of contact of the disk).

P.S. I've also decided that since I can build a model of tension and torsion (a tensile structure which is geodesic, and "center-seeking"), I need to explain, how come I can do this everyday thing (which Romans, Archimedes and even Newton would have had to do a lot of work to accomplish) and slice up a tube - even a tube of paper which I can assume represents an abstract volume or surface (I can abstract volume, and pressure of imaginary fluids and gases, or density measurements) with geometry, invent a 'cutter' and so on. So where did the steel tube come from? I 'located' it in my back-yard.

It was manufactured, by an extrusion process, or a rolling mill that 'squeezed' enough steel together that the tube can be expected to withstand certain accelerations, to its center of mass, and it will have 'metallic' qualities such as ringing, if struck at a point on its outer or inner surface. I could, for instance, try to damp the rotation in the wire support for the weight, by setting up a pulley that releases a swinging clapper either inside the open bell, or inside the frame of the tubular sections of steel (I can make either structure ring, by striking it with the edge of a flat or squared stick of wood). Iron is a last-stage element formed in stellar fusion; I learned about the main sequence a while ago, so I have to incorporate the evolution of Fe, which is later in the table of elements than carbon. This appears to be either a coincidence of cosmic proportions, or just our dumb luck, we ended up in a universe that uses carbon to build lifeforms.

I was reading this thread since starting; Very very informative thread.

Just a suggestion skipper ... Slightly slow down your speed. Actually in general it takes a bit time to grasp the fundamental of the technical topics (mechanism) such as Aerodynamics gravity meter.

Again super work buddy !!!

Folks - pour in your comments/questions in this thread.

-CB

Just a comment on the aerodynamics: this is part of the physical system, and as I've commented I can do stuff with mirrors and CD-roms (even if I cut a CD into parts, since if I have a copy of the CD the parts can be identified, if I can read the code); I can ignore the coding in the CD (I can ignore dust on a mirror too) and use the color spectrum from diffraction angles to measure rotation of the weight at the end of the wire support.

The wind 'action' is just a way to perturb the string so the weight moves, and the torsion in the string (stretching from the weight wobbling or swinging) is 'captured' by the wire rotating like a spring torsion pendulum. The tension and stress, drives all the movement to precess into torsional motion = diabatic rotation around the "Z-axis" of energy in the system.

I just found the issue of SciAm I had stashed away, that discusses the 'meet-join' relations in classical logic, and in quantum (spin) logic, or orthocomplemented lattice theory. Meet is equivalent to AND, join is equivalent to OR, since, if you join two steel tubes in a 'T' the join is the union (which can be disjoint) of two tubes/poles. I have to lift both poles, before or after the join, from "zero" to "one pole high". This is equivalent to 0+1; if I use 0x1 I get "0", so in a logical sense the join is an exclusive selection (XOR), and meet is intersection, like in set theory.

With the quantum spin-lattice you also have disjunction, but at a completely different (physical) level, since you can determine all the x,y,z dimensions in a physical setup made of metal pipes, but you cannot determine spin along x,y,z; you have 3 disjoint states (complementarity), if you measure 'z-spin', then x,y are indeterminate...

[p.s. ok, I'll have a rest now.]

Next instalment: I had a think about how I need a device as mentioned in the start of this discourse; it has to be able to start and stop 'recording' when motion in the pendulum/bell device starts and stops. Or it has to be able to record the time-intervals that certain classes of motion (rotation, swinging, ringing after a 'strike', vibration in the wire, movement in the sail in 3 directions - up, down, left-to-right occultation of the wire support, its inverse) and other observables that 'evolve' in the system.

I need to assume things about being able to measure all these things; that A) I will be able to specify a class, in abstract and "most general" form (such as, "gravity acts centrally in the frame"; "all forces are conservative, and inertia is distributed according to moments, of inertia corresponding to centrally acting masses or centres of mass", etc). B) I have to assume that not all information is "captured" as is; I need to extend the device to measure "temperature" although there's a general notion of "energetic wind strength", and "intensity" from reflections to gauge this.

But a more accurate way to measure the ambient conditions will be required, independently and in conjunction with temperature, ambient wind-strength and direction over large intervals, unless I ignore "heat" as such and just stay with a simple wind-operated weight.
Since I know the pendulum swings according to the fact it's suspended above a gravitational surface, and according to how it's attached (at a single point, which is along the same "tangent space" as the upright pole), and the bending moments in the T of steel tubes which 'act' along the edge facing the pendulum; that is to say, the tension in the wire is supported by the compacted steel 'width' of the tubular sections. The tangent along the upright connects (via the 'meet-join' relation) to the vertically extended pole and the point of contact for the wire is "at k.xy/2 " for T2, using the standard index. I know how to measure a tube using the i,j,k indices so I get either a closed or open tube (open/closed inner volume = -j.+j or -j[sup]2[/sup] as it "divides the length of tube Tk", i.e. -j[sup]2[/sup]|kT,i). The outer surface, described by index "i" is the "face" of the cylinder. Here if I imagine I'm a small observer on the surface of a steel tube, I'm either on the outer convex one or the inner concave one. Any view along the cylinder is "flat" only if I look "from i to i" along the "k-direction"; so that distance inside or outside the tube is "straightest" when I draw a tangent along the tube, from point a(i) to point b(i).

Using just 3 indices gives me a metric of 3 dimensions, for metal tubes and a geometry which is analytical. If I want to have a general logical machine that "calculates" dimensions I need, as mentioned, a general object-oriented model, that in a sense asks questions by answering them, or it answers questions with answers which imply further questions. The first question I have to get it to ask is "can I generate a clock signal or pulse, and measure it, i.e. perform a clock-test by setting it = ask:
"does time exist" -> answer:
"the system clock is functional"
-> ?

...and, it needs a "lexicon" that defines groups and sets of words or lexemes like "start, stop, copy, erase," etc, to function as a recording device - it needs a tape it can read and a tape it can write, or equivalently a Turing machine which is "universally general", or a Von Neumann machine which is a dual of such a UTM.

EIther machine will have to be able to run "programs" that are essentially copies of each other (up to some limit of exactness, precision, and repeatability). It will need to be able to handle "error-conditions" which I will need another algebra for - coded in a TM or VN algebra such as a stack or list language (Prolog, LISP, RPL, etc) which are all in the domain of "lambda-complete", by which I mean any reasonable "measuring program" I might write for it will have a default lambda-condition or fall-through in any state transition, which has a halt instruction attached if there is no input.

That is, the machine can switch parts of its recording capability on and off, and learn when to do this, as the system under observation changes in steps of time, Tn, Tn+1, ... Tm-n+1, Tm-n, ...; so that n,m intervals are "on,off" states in any measurement space.

And, it will need to be able to answer the question: "what is the smallest unit, apart from a section of tubing, or wire, that corresponds to tension or stress?". IOW, what do "atoms" of Fe do apart from occupy a place in a metal pipe, and the Periodic Table of elements (where the element has a number of neighbours that are also found in many 'organic' systems, in complexes with carbon chains and rings, amino acids, polymers that form around Co, Mo, Zn, and many other "minority metals" that are part of biochemistry and enzymatics, proteins, DNA/RNA molecular dynamics); how do I model protons and neutrons as a 'kind-of' tube?

Note: the abstract machine I'm trying to describe is equivalent to an "intelligent" observer. That is, I'm considering "copying myself" in machine form, as an independent system which can observe as I do, but also make precise kinds of measurement, or produce a run-length code corresponding to all measurements of the system (a subset of all the measurements which I or another observer can make universally).

I want a specialized but intelligent device which can encode all the information it collects, properly so that any analysis "program" I can reasonably consider for the data, will yield results that describe all the motion, what gravity is "doing" etc.

I will need to revise my "pole model" or look more closely down the tube. For instance, quaternions are a group (under multiplication) which describe a 3-dimensional symmetry. The group has indices i,j,k but includes "-1" as well, or "-1 commutes with i,j and k" so that there are -i,-j,-k in the symmetries. Now I know I can't use or build a tube with a negative length; the only negative is any missing material. So my tube will need to have dimensions that correspond to Q[sub]8[/sub], Hamilton's quaternion group.

This means i[sup]2[/sup] = j[sup]2[/sup] = k[sup]2[/sup] = 1; and that relation means that ( -i)[sup]2[/sup] = i[sup]2[/sup]. This is the commutator that "takes -1 to i,j,k" in the quaternions. The rest of the relations are:

ij = k; ji = -k; jk = i; kj = -i; ki = j; ik = -j;

which is the rest of the symmetry, for i,j,k and the commutators. This means the "tube" has an outer i circumference = inner j circumference (there is a width of metal = 0) and the height is also k = ij.

The negative values, or -i,-j,-k represent 'vectors' along the surfaces; k is still a length, i and j are still outer and inner measures; the metric is {-1, +1}. This implies -1 +1 = 0.
The 'sum' or exclusive "meet" of -1 and +1 is zero. I can consider that the "0" means an open tube, aligned so ij appears, k disappears; such a tube is "empty" or has no "lift".

A "1" is an upright tube, which contains something or is not "empty" (ik or ki appears, j disappears). This is a general interpretation, of course; an upright tube can be as empty as a [horizontal] one. But "empty" = 0, "full" = 1, this is a reasonable assumption to make, that "zero" is actually something (it's what I want to find, or rather, I want to find "k" for a tube which I can see ij and ji for, and "j" for a tube I can see ik and ki for). I need to set all distance measures for i,j,k to "1".

Then "1 neutron" can have the same metric (cylindrical, spherical, etc) as an ordinary steel tube. The i represents the outer "radius", j is the inner one, and k is the "height" of a neutron (in mass terms). These will have complex coefficients that correspond to all of the external behaviour of neutrons, and inner "states" that may exchange something with the outside, I will need to know about the density of the "material" etc.

Dang, looks like I got vertical confused with horizontal; maybe I should use "parallel or perpendicular to Z", instead, since the direction is arbitrary.

More precisely I should say that an empty tube (0) is what you get when k = 0 (ij = -ji); and a full tube is when j = 0 (ki = -ik). So if "k = 1" the tube is "full"; if "k = 0" it isn't. Then I can use "k or not k" and "k and not k", for different poles/zeros.

If anyone is interested in quaternion algebra Wikipedia responds to a search on such terms. also some programmers here may know that the quaternion group is a big deal in 3d rotations, in animation engines and graphics.

Note: I made a deliberate mistake with the ijk thing, this is actually equal to -1 to close the group "algebraically" (if we assume an algebraic space can be closed, for the meantime and just write programs). It doesn't matter since you represent complex numbers as real, floating point values, so it's just math and arithmetic, and the laws of commutativity, associativity and distributivity (as actually commuted, distributed and associated electric charges, or abstract "signals", i.e. a computer with digital logic).

So I can hand over to a tutorial about programming with quaternions, with a link to: <a href="https://www.cprogramming.com/tutorial/3d/quaternions.html" target="_blank" rel="nofollow noopener noreferrer">Quaternions and 3D Rotations - Cprogramming.com</a>

Then, "it's all about geometry", in the case of tubes made of steel; what about the wires, and the disk of grinding-material, and the CD? I can stay with some form of i,j,k for three dimensions, as long as I 'find' a x,y and z in each case which correspond to 1,2 and 3 spatial directions (so I stay in SO(3), the rotation group in "space, as we know it captain").

With a disk, you always have two faces, like a coin. In fact coins are an ideal classical version of the abstract tensor spaces in QM, where quantum spin behaves much like coin spin does (a coin always lands with one face up, a quantum measurement is always polarized). With x,y and z in fermion/boson spin states, there is exactly one measurement, which is time-dependent. Quantum coins can spin in all 3 directions at once (around 3 axes, like a Rubik's cube) but when you measure one of the axes, that means the coin is either face-up, OR face down along that axis "forever". Changing a spin state by measuring it is equivalent to spinning a coin that you can't spin again, it "sticks" to the table you spun it on (or to the floor or your hand, if you spun it through the air), and shows heads, or tails every time you look.

So, a classical coin (or two) spinning on a flat table are interacting over their edges (between heads and tails) which, for the xy of the table meets the xy of each face of the coin, i.e. ({x,x'},{y,y'}) with the "z" of the width of metal of the coin or it's "thickness", or density of mass (say it's made of iron). Then any marks the coin makes (say it has a considerable content of lead, and it marks the table) are a direct product of the momentum the coin has as it rotates and translates over the table. You could perhaps abstract this to a coin made of chalk, spinning on a level blackboard.

A coin made of electrons, spinning on a level "DC flat" electrical metal surface = a loop of metal rotating and translating over an insulated metal sheet, which is charged with a Hall voltage so the spinning loop has a current induced by the local field strength and the rate of rotation, and translation over the voltage gradient, if g the acceleration from gravity is assumed "flat" as is the insulated metal sheet. The only other problem is measuring the current in the loop, attaching wires from a spinning open loop of metal (possibly bridged with an insulator) to an ammeter/voltmeter, or a 'scope.

Maybe you could build a loop of metal, with an insulated section that contains enough circuitry to measure vi characteristics and transmit them - the loop would be free to rotate and translate along any part, including the 'command module' part. This would mean miniaturized parts and some design steps (but sounds do-able these days; transmitter-receiver components are getting quite small). So the "path writing" by the loop which is acting like a coin will be of linear momentum, the writing will be a signal "from g" encoded in vi, the metallic-conductive character of the loop. The weight or density due to "G" means g is a derivative, which the loop "uses" to find a line-integral (of the elements l(i) across the edge from face to face) of all rotations r(j), along the path. The constant or "k-part" is G, the universal gravitational (inertial/"accelerational") constant, for Newtonian frames.

Reference in such frames is between the inertial frames of "you" and the irrotational table, and moving coin.

Now suppose I have exactly two coins, which I abstract to the spin-states of an electron and a proton (i.e. a Hydrogen atom). Each 'coin' has two faces, so there are the following metrics: {00, 01, 10, 11} that correspond to the 4 possible outcomes of spin (a coin toss x2).

Say I want to track which of the 4 states corresponds to a set of results; over time the set of all results will approach a balance between those "available" from tossing or spinning 2 coins. If I also adopt the convention that for a 2-level state, the left digit is an electron, the right digit is a proton (since I'm only concerned with the order of states); so each "throw" will be like having two distinct places or tables to spin the different coins.

Since protons are about 2000 times heavier than electrons (give or take), then mass is already a differentiator I can use to mark each coin first, with a "mass value". I'll need either a table that can discriminate the mass-difference, or two separate tables, one sensitive to proton mass, the other to electron mass, then all I have to do is separate the "coins".

If I assign an abstract color-index (since I can, for no good reason) to each state, and keep track of the states with a "flag register" 4 bits wide, then assign the values 0001, 0010, 0100, 1000 to the four quadrants of a circle (actually a disk). Then a 4-color map can be constructed, starting with no color for each quadrant and ending with 4 distinct colors = 16 possible colorings for the disk.

Each of the 16 maps represents "mixtures" of the states {00, 01, 10, 11}, encoded in the 4-bits each quadrant has. In classical space, you can't have more than one color on the disk, in quantum space, you can. A null-colored map (no heads or tails for either coin = coins are still spinning) has the same probability as a 4-colored map (all states are seen at once = large number of "atoms" in a distribution of states). This disk with 4 quadrants is a map of the vector space. I can construct a lattice with 5 levels, where the highest corresponds to "all quadrants colored", the lowest to "no quadrants colored", and the 3 intervening levels correspond to logical "meet-join" relations, or binary logic. I just need to install an inclusion relation that maps electrons to protons, via their spin-states. That is, show how subset relations map to logical predicates like "the electron is spin up and spin down in exactly 1/2 of the disk".

The lattice and coloring go straight to Rubik's cube and complementary puzzles. A 3-slice group (Rubik's original puzzle) is a lattice. These puzzles directly model the symmetries of rotational states in 3 dimensions. The time factor, and the puzzles being freely rotatable means scrambled permutations of colored pieces, algebra, prime knots in space and time, all that stuff. In fact, the 3x3x3 cube is an algebraic rep of a large symmetry group, the M[sub]12[/sub].

Now to try tying all this together, since I've done a bit of a tour. My backyard device generates "inertial motion", under the general or local influence of gravity. Wind strength is 'captured and stored' by tensional and torsional modes in the system.

The "gravity meter" is a simple pendulum - Romans used simple plumbing devices to build roads in straight lines (over hills) for centuries - it's a "simple phase-space"; all the motions are in or out of phase, and are all responses to perturbations induced by a "Gaussian" function - the wind, which is random, but smoothed over large intervals of time - and which responses are all absorbed, by the ground(ed metal pipe) and by "ringing" in the bell section, and the wire. I can hear the noise either the wire or the bell makes when the weight is swinging, and if I arrange for precessional motion to "take the bell to the surface of the upright".

The whole phase-space including the ground (which is at zero-phase where g is 'pointing') tries to "find" a relaxed state. The most relaxed is zero wind strength, zero swinging or rotating. I should use a shorter word for "rotating" like "spin", since I can relate spin to a solid rubber ball. A rubber ball can have backspin, etc. The bell "spins back and forth"; I can apply a rule-of-thumb which conventionally means I align my left or right thumb "upwards" along the wire or axis of rotation, and then the orientation of my fingers is "curled" the same way the spin of the bell is.

This is a general mnemonic way to consider or "orient" a general flow. My undergrad physics is a little thin, but I still have the textbook. The intro talks about using a new approach which instead of treating various physical phenomena separately, tries to tie them together and show how the concept of "flow" applies equally to heat, electric current, water, sound, light, even to abstract "numeric" quantities (see Rubik's cube group for details). Waves and the flow of "energy", the mechanics and dynamics involved, the geometries used (which for QM are entirely imaginary "orbital configurations", with a probability density), is the thrust of the text.

I'm actually trying to put together something called "fibered space" and tangents to a surface, "tangent and cotangent bundles", etc. This is topology of a phase-space. You generally consider the phase-space itself (the physical x,y and z dimensions) are the cotangent-space (bundle map), so that all the tangents you get from i,j,k (j "hides" when a pipe has "lift") are an external "base" which the whole frame plus the suspended weight map to, as real tangible solid surfaces. The wire in effect is the 'slice function', since it has the smallest cross section in the space.

I don't want to get into discussing either what a phase space is, mathematically (since there are plenty of textbooks, and good intros, if a little abstract, on Wikipedia), or what a fiber bundle is.
However, the sail part of the wire-frame, rotates or spins at a different phase than the bell. The bell has a 'smooth' left-to-right turning mode, the sail is a 'follower' but is always behind the constant "spin-gradient' of the bell's inertia, the sail spins or "wags" both ways as the bell moves in one spin-direction. Hence, a phase-relation; the wire has differential tension along its length (it's a composite steel wire); the point of contact for the sail (the "boom" or linkage) rotates at a rate determined by the stress-energy in the wire at that point. It's at an "antinode" of torsion, set by the position of the eyelet and the tension in the wire. Hence, stress (from the wind) becomes differential torsional rotation, or a spin-follower; the sail "ratchets" as the bell forces it to rotate.

An ideal torsion balance (Etvos') can discriminate local differences in gravity, mineral deposits etc. An ideal "fibered space" is a mathematical (and physical) model of something like the "machine" I've built, with local parts, according to a well-understood formula. Fiber bundles map to quantum space, since they are entirely general phase space representations/models.

I still haven't done a lot with the abstract spaces represented by Rubik's cubes and the "Brain Racker" which is an interesting map of the icosahedron. In fact I'm also trying (since 2 years ago I looked at a curriculum and tried to plan out which courses I needed to take to get a real handle on QM and QIS) to understand topology and "advanced theories" which are pretty abstract.

But abstraction is just the use of language - it's like learning to read music - you know you only really need to learn the symbology, which parts are "verbs" etc (as notes in a stave are instructions to play notes on a keyboard or a set of strings) which are nouns (the key signature is instantive and instructs changes in signature, where these occur in the musical flow, or harmonic structure).

You can apply the "science" of musical algebra to the spherical 4-color puzzle, since there is a set of 4 circles of color, and each circle is 1/4 the area of the surface, then each circle has 5 equal triangular sections.
Going backwards, each triangle (which is a spherical cap or shell, with 3 straightened sides) is a major (or minor) third = 3 'tones' in the algebra. The removable red triangle is the "free" or principle note (since, it can be replaced in any orientation = all 3 sides are equivalent). Each circle is a "perfect 5th" of color, and the 4 colors are a "perfect 4th" of a circle of 5ths = 5 triads.

Sharps and flats are the orientation 'algebra' for each restricted piece. The red "1" section which is removable, is "natural" when the 1 is oriented pointing upwards, like a normally written numeral. It's "flat" when pointing to the left, and "sharp" when pointing to the right. If the 1 is inverted that means the sphere is, or, the red "1" orients the entire sphere; the red_1 is the "free Hamiltonian" for such cycles in the "choral structure", i.e the graph G.

The algebra has several "chords" in it, there are 19 "notes" left on the sphere, and the "conductor" is free to orient the staves at will (change the signature from sharp to flat or invert the staves completely). The indices i,j and k map to whichever geometry you like; x,y and z can be the sides, and the thickness of each section, k is the fixed width of the red_1 piece, i,j are the orientations of each side (as x,y coordinates), since the "hole" is free to translate over the sphere, each of its 3 sides will have 1,2 or 3 colors to "choose", and each adjacent color will be 1 of 5 numerals (intervals in a perfect 5th). The harmonic structure is definitely musical, patterns over the sphere (an icosahedron with a missing section) are the "tunes", made by flattening and sharpening (extending) the "tones" in a 4 dimensional space of 4 colors/5 sections per color.

So that, the ansatz for the disk here is 5p|4q, for q colors, p numbers, or "5 numbers divides 4 colors". The colors map directly to 4 quadrants (by flattening a circle into 1/4), each color is one of the 4-bit values {0001, 0010, 0100, 1000}. Again, combining these via logical binary relations (meet-join graphs) means "ancillary register" values from "0000" to "1111" in terms of 4 colors "q".

Since Each 4q(5p) section has 3 sides (trivially the red_1 has 3 equal sides) there are 4 ways to "mix" each of 20 sides, with each of 4 colors (ignoring the numbers).

The 4ths are only "perfect" if you're a red piece on the sphere; this is because a 5th in the diatonic scale is a maj 3rd + a min 3rd, if you sound the 3rd note it's a maj triad. If you invert this and play a min 3rd instead (by flattening it with the "flat function") it's a min triad. The triads are formed by mixing colors, maj or min intervals depend on the orientation of the numerals (in the 5th diatonic interval).

To get this to the Rubik's cube you have to swap the 3 colors on each corner section (1/2 a cube, or a cube with 3 hidden colors) for the 3 sides of each triangular section from the sphere; each corner "sub-space" can be -1/3 or +1/3 oriented wrt to fixed central face color. Or if the corner is "sane" it has the same color as the fixed center. Orientation is number-independent, but face-dependent for the 3-slice group. The intervals in the cube's geometry that map to the icosahedron are because you can swap the meaning of color around, from the idea of a curved shape, to the idea of a rotated shape (swap corners for edges, swap face colors for "orientations" etc).

Ok, so I have my collection of "devices", including a computer that can solve arbitrary algebraic equations (across an extended alphabet of symbols and associated functions, a stack register and counter, etc), then what I've actually been up to here is really just reviewing, in public (such as it is) what "I think I know" about QM, and larger physical systems.

What I think I really need is a general model of "flow", for which the logarithmic structure can be derived, either in the sense of building something which has an algorithmic, instructional kind of flow to it, or in the sense of a general fluid motion along a channel (i.e. a tube or pipe). For instance, with my "industrial" metric or basis-space for steel as tubes with a standard length and gauge, k is the "flow relation" of the material to the inner and outer width ij of the same material; then k becomes the unit length of "an industrial unit of steel tubing". So extruding a steel tube is "shifting" ij along k, i.e "place the unit width ij, in register Rk".

Then flow in Rubiks cubes and derived "platonic" shaped, and sliced-up solid puzzles is "algebraic", there are "chords', triads and harmonic structure because of how many ways you can slice a solid. All the "well-formed" puzzles are internally symmetric to a sphere. So, the constraints in the mechanisms that the puzzles "inherit" from design rules (which follow Platonic axioms) have an equivalent set of constraints in the rules for their design.

In QM, you have to suspend ideas (intuitive though they are) of how fluids behave, waves on liquid surfaces and in springs and wires. Flow is "counter-intuitive" in the quantum domain. For instance, superfluid helium has a well-formed model as two counter-moving flows, one of normal fluid, the other of superfluid. The 2-fluid model explains the mechanism by which vortical motion "captures" this flow.

How can I relate this idea of general, fluid flow (which can be particulate matter in the solid, liquid or gas phases), to the pendulum I made? In what sense is anything flowing, apart from air around the "collector" at the point of contact for airflow?

p.s. like to thank CE for letting me post my thoughts, and now open to suggestions.
I've found wikipedia commons is quite informative in updating to "modern form" the stuff I learned about circulation and integrals, What "doing a Laplacian" or a Z-transform is. Here are some of the relevant links I've found to be helpful:

<a href="https://en.wikipedia.org/wiki/Scalar_curvature" target="_blank" rel="nofollow noopener noreferrer">Scalar Curvature</a>
<a href="https://en.wikipedia.org/wiki/Vector_bundle" target="_blank" rel="nofollow noopener noreferrer">Vector Bundle</a>
<a href="https://en.wikipedia.org/wiki/Distributive_lattice" target="_blank" rel="nofollow noopener noreferrer">Distributive Lattice</a>

This thread makes for a good read!

Alright, I'm going to try modeling a flow-relation of some kind for the "toy" devices I have. Now I know I can buy kitset versions of Rubik's cube and construct my own hack, even join cubes together (I've seen a few mods). I know that the 3-slice cube is a multiple of the 2-slice, I can disassemble a standard 3x3x3 puzzle and build a 2x2x2 sub-cube representation, equivalent to removing the central fixed axis and all the edge pieces.

Cubes with higher numbers of slices, 4,5,6 etc are projections of the simplest 2x2x2 subcube (the 3-slice group has 2-slice subgroups in each corner). Solving a 5-slice say, is like solving a 3-slice with extra inner edges, which you can treat as being the "same" edge; solve the inner puzzle edge-wise and then solve the 8 corners = 2-slice subgroup.

The icosahedral puzzles like the MegaMinx and the Brain Racker, have a different rotational symmetry, depending on how deep the slices go. A deep-sliced puzzle means the colors diverge over all 6 sides; the shallow slices in the Brain Racker means colors diverge only on a single side at a time. A cube has 6 faces, the sphere with icosahedral sections has 6 edges around its perimeter. Each triangular section divides a diameter (geodesic circle) by 6, each face of the cube divides the volume by 6.

With diatonic scales you have 12 notes, equally tempered or each note in a 12-note scale divides an octave (a sound area or volume element) by 12; there are 6 sets of "double notes" in a scale or 6 major 2nd intervals. A third is either maj or min; a 4th is perfect and spans 5/12 of the octave. On a guitar fretboard the 5th fret is where all the 4ths are for each string; the 7th fret is 2 notes along and is where all the 5ths are which are perfect (= maj+min 3rd); 7/12 of the octave corresponds to the 2nd perfect interval in a scale.

This suggests that perfect 5ths as 7/12ths of an octave (a doubled frequency), and perfect 4ths can describe a cube or sphere "doubling" kind of algebra.

If you map an octave to either "puzzle", which is a representation of a rotation group, in 3 spatial dimensions, you get: each triangle on the sphere has 1 edge on a geodesic circle, which edge is 1/6 of the geodesic "great circle" around the sphere; you get each face on the cube has 4 edges.

On the sphere a geodesic path that starts and ends on the same edge of a triangle, is a scale of 2nds, each "note" corresponds to the corners of each triangle meeting (disjoint union) along 6 edges; the edges are the maj 2nd intervals (generally there is no min 2nd, this corresponds to a single 1/12th of an octave). The edges are 2/12ths of each octave, so that 1/2 this interval is the "minor 2nd" = 1/2 maj tone, or semitone. 2nds construct diminished and augmented intervals, since 2+2 = 4 semitones = diminished 4th, 2+2+2 semitones = 6 semitones = dim 5th; 8 semitones is an augmented 5th; 10 semitones is a flat 7th.

Musical tones and equal tempering suggests that the decimal numbers (as far as tempered sound is concerned) have 7 parts; it also suggests that a perfect 4th has 5 parts, and a 5th has 7 (a maj 7th is an augmented interval or 11/12ths of an octave.
An "octave" suggests 8 parts, from 12 equal tempered notes or integral sounds. It also suggests an algebra with 8 dimensions, 7 of which "appear" as algebraic modes in the "musical surface".

I need to relate a real piece of music to rotations on the cube and the sphere, of colors (with numbers attached). Music is rotations in a volume with "notes" attached.

I'm running out of steam a little here; I'd like to point out that 2 years ago I had an encounter of the science forum kind, with someone who dissed my opinion of music being a complex space, a vector field. After I read something about a mathematician who embedded two discs (circles of fifths) into a torus, and turned the construction into a Mobius strip.

I don't know the details but I have an idea how it was done (it's tricky to visualize, you need to think in lots of 5 circles), and if any of this has piqued any interest, I can assure those sufficiently piqued that the Rubik puzzles are a hot topic, they "contain" absolute universities full of science from QM and quarks to models of gravity and spacetime. The Brain Racker is tectonic, the pieces slide past each other and the tension 'lifts' some of the other pieces in the vicinity. I have a copy of a special issue of SciAm about the most important scientific discoveries of the 20th - plate tectonics, electronics and QM figure quite large; a deep-slice group as a colored cube, and a shallow-slice group as a colored sphere can represent each of these disciplines in some way.

What I now think I want to look at (but perhaps not here) is the quaternion and octonion algebras and the various disciplines they attach to; computer graphics for instance (and the involutional JPEG/MPEG image compression, which the cube represents since solving a scrambled cube is an involute algorithmic process), the Fano plane and some axioms so I can do some "Fano on the piano".

That is, if music really is 7-dimensional and the triangles, with curvature (unlike flat triangles on the plane) have 7 'points': 3 at the vertices, 3 at halfway along each edge, and 1 central point which is collinear with 2 others. 3+3+1 as a triad (maj/min) which is 1/5 of a circle (of triads with 7 dimensions), so that 7x1/2 tones is a natural 5th (which is perfect by construction, in the algebra).

The 5th in a scale of 8 notes can be diminished or augmented; any interval can be sharp or flat; maj or min intervals depend on the fundamental 1st or root note of the scale.

Ok here goes: if I stay with tectonics, then I can model earthquakes as the edges (on the Brain Racker) sliding past each other and locking into place, which is piecewise.
The hole is 1/20 of the surface, a single move has a boundary of 1/10 the surface, since halfway there are 2 points at about 1/2 the distance along 2 edges; the number of edges (of the hole) effectively expands and collapses, 1n -> 2n -> 1n, as a single 1n 'volume' (the shell) rotates; at halfway the single apex which is 'joined' during and after the move to (or it meets with) [3] others = the center of rotation [is 4], there is maximum stress in the outer layers, which lift slightly at the halfway point.

Now say I want to relate this to gravity, starting with lunar phases = the moon's orbit. The two states on the sphere are a volume change, that lifts a surface mechanically. The two states = full and new (or "empty") are a volume change that lifts a surface (the lighted part of the moon) gravitationally.

thought for the day: the logic of refutation should be irrefutable

I think physics teachers and lecturers should talk more about how the idea of a force is tied to the idea of a flow, or a pressure. I mean, when are these two words equivalent? I can think of one obvious example - place your hand in a stream of water, flowing from a tap. You feel something, we call it the force of water falling, or the pressure from the flow. So that's when they equal, even when you slow the flow-rate to drops you still feel water pressure.

All you need to do with lunar phases algebraically is use the existing "basis", or say that 0 is an empty or new, state F and 1 is its opposite - a binary object. It has a diameter d. The lighted area goes in and out of phase, call these a and b, the divisors of F(0), and F(1). If a is large, b is "at unity" and it's a full phase or maximum; if b is large and a is 1, it's a minimum.

There are 6 conventional phases left, 2 are "quadratic, linear" solutions, equal to d, as roots of the remaining "area" relation F(a,b), as polynomials (the phases with linear solutions are when Fa = Fb. If you assume that F(1) = -F(0) you can use roots of unity, in the lattice algebra. When does a 'meet' b, etc? Use the disk again to quarter the phases.

Interesting thread !Will post a detailed comment once I'm done with going through what is posted. 😉

Note that, numbers are dimensionless, but also "dimension-ful", in the sense they are "capacitive".
The reflection of this capacity is obvious when we construct mathematical puzzles (sudoku, chess problems, coloring a map, etc).
The abstraction of a 'metric' or measure to these kinds of mathematical spaces is also fairly obvious, or mnemonic - the cube is colored and "sliced up", the sphere is colored and numbered as well. The latter has a mechanical "solution" so that the missing piece (the freedom to rotate the others) has at least 3 possible new positions to migrate to in a "haptic, tensional" feedback kind of way, the hole moves over 3 potential directions, along a path p = x1, x2, x3 where "x" is the t+1th step in p. This is an isometry of the path a corner or an edge makes on the cube (just number or mark a single corner as a "hole"). Then the algebra maps directly to Euclidean plane geometry, where the flat plane of the side of a cube (face) is the curved surface (a wrapping) of the sphere.

This "transform" is realized as the mechanical puzzle, with tracks for the pieces that are fixed or "embedded" by the mechanism. The surface pieces 'cut' across the tracks, the hole has a central "void space", which is what 1 of 3 mechanisms has to rotate through.
The substructure is "wheels in tracks" and the surface structure is mapped over this, so that 5 vertices meet or join (during rotations) over a single supporting structure, which must have 5 voids around it and 5 tracks. This maps the icosahedron as a substructure to the circumscribed sphere.

These concepts are related to algebraic manifolds, space and time (since the puzzles exist in space, and change over time, their inner geometry is preserved, etc) and of course permutations and combinations. Just the two I have imply a whole lot of things, about colors and dimensionless numbers, what happens when you give either a dimension and what "flow" along a dimension can mean in a "dimensionless" way.

Too long and geeky for me mate...

Well, it's really about a way to connect certain concepts together, and understand tensor calculus at the same time.

What does an "ideal" mean? Why do we have ideal solids, ideal gases or ideal fibers? Where does QM enter the picture? I've been trying to answer these questions, mate.

We use flat surfaces all the time to prove that a right triangle has exactly 180 degrees in it, that we can circumscribe such a triangle and so on. But there are no "flat" surfaces, this is an illusion, gravity looks one-dimensional standing on the surface of the earth, but it can't be because the earth has a center so gravity is "spherical" at least, and a sphere is not one-dimensional.

Then the lunar angle comes into it, since in order to predict the phases, you need to triangulate over the same sphere and find the plane of the ecliptic crossing point, for the lunar angle.