Thunderbolts Forum v3.0

by **d3x0r** » Sun Jan 02, 2022 10:27 am

paladin17 wrote: ↑Wed Oct 14, 2020 10:41 am
d3x0r wrote: ↑Tue Oct 06, 2020 11:45 am
paladin17 wrote: ↑Sat Sep 19, 2020 6:07 pm You have to keep in mind though that 3D rotations (e.g. Lie group SO(3) - rotations around 3 orthonormal vectors) are non-Abelian. I.e. the order of the application of rotations matter. Rotate around X to x degrees and then rotate around Y to y degrees is not the same as in the reverse (in the general case anyways).
But these additions are not rotations applied to rotations... they are the sum of impulses that result in an acceleration or velocity (or accumulate into a position)
I don't quite get what you mean by "rotations applied to rotations". You mean the situation when the second rotation happens around a new Y axis (as if it was "locked" to the rotating body)?

A rotation vector represents a rotating thing, it's spinning around an axis indicated by the direction of the vector, and the magnitude of the spin is represented with its length. This is representing a spinning thing, not a thing that is at an orientation, but a thing that is in the act of spinning, this is the sort of thing I'm also calling 'rotation'. Applying the rotation to another 'rotation'.

But you can also have rotation vectors representing angular accelerations, and a rocket with various engines at various points from its center of mass has a torque that can be represented as a rotation vector; these vectors add together, and the order doesn't matter, because they are all applied simultaneously for any combination of thrusters the rocket should turn on. The net sum of the vectors is a rotation vector that is the resulting velocity...

Then, that sort of rotation vector would be applied with the rockets own rotation vector representing its spin, and because the rocket is spinning, and the acceleration happens over time, it's a more complex calculation than just addition; this is also what I would mean with 'a rotation applied to a rotation'.

paladin17 wrote: ↑Wed Oct 14, 2020 10:41 am
d3x0r wrote: ↑Tue Oct 06, 2020 11:45 am
paladin17 wrote: ↑Sat Sep 19, 2020 6:07 pm This actually is very important in quantum field theory, where the fundamental interactions are represented by abstract rotations in the abstract space (see principle of local gauge invariance) and some of these rotational groups are Abelian (e.g. U(1) which represents electromagnetism) while others aren't (e.g. SU(3) which represents the strong nuclear interaction), which leads to radically different properties of the resulting theories.
I would like to know more about these assignments, and why they think that that actually works... I can certainty generate the result of a rotation with 2 more rotations applied to it (and yes the order matters, A then B then C is not the same when 'applying' when 'adding' a+b+c IS actually the same).
Which assignments do you mean? SU nomenclature? Or the [gauge] field theory in general? There is quite a lot of literature on both topics.
Long story short: somebody has found certain symmetries in electromagnetic field wave function, so they expressed these symmetries in the language of the group theory, and then were able to find similar symmetries for other two interactions (so in the end we have U(1) group "generating" electromagnetism, SU(2) "generating" weak nuclear interaction and SU(3) "generating" strong nuclear interaction - all through this local gauge invariance formalism).

So as I understand it then, it's just a composite of three spins, which is what this Hopf Fibration stuff is a representation of, (and some of that looks worm-hole-ish) which is a 1 dimensional cycling between electro static and electro magnetic states? .... I dunno
There's 3 quarks that make up a proton, sort makes more sense to have a rotation, rotating around 2 other rotations like such, which would end up being the same sum of the products, 1 quark rotating is U(1) 2 is 1 rotating around another, and SU(3) is the combination of them rotating around each other; if they behave like their other dipole like cousins the electron, their motion based on the influence of other things will move towards the cross product of the rotations; similar to how gyroscopes precess... so I already have that; but that doesn't really explain what charge is, or how those numbers would manifest in likes repelling likes; other than there are two distinct always-positive spin directions; it sort of turns out all operations on a rotation will keep its same spin direction; so you can have a duality of a positive and negative spin that will never change from what they are to something else (without first being emitted as a photon).

paladin17 wrote: ↑Wed Oct 14, 2020 10:41 am
I can see that. So we're talking about physical systems that have certain limitations. If I understand you correctly, you're trying to work with what may be formally called nonholonomic constraints on rotations.

That might apply...

I did move on to tackle relativity and curved space- instead of just rotating around a single curved surface... https://thunderbolts.info/wp/forum3/phpBB3 ... f=11&t=663

by **A Gnostic Agnostic** » Sat Oct 24, 2020 10:36 am

Short 8-page paper:

'On How to (Properly) Measure a Circle
(Without the Need/Inclining for Approximation)'

https://vixra.org/abs/2010.0100

Addresses:
i. Methodology to measure a circle without the need/inclining for "approximation" (using the golden ratio).
ii. Outstanding Riemann Hypothesis Millennium Problem: the barrier of a deficient π of 3.14159... ("blunder of millennia").
iii. Rational Precedent to e = MC² as 16 = Φπ² implying corollary rational unity as 1 = Φ(π/4)² wherein Φ and π are one (via.)
v. Reciprocity, the latter resolutely being the nature of the relation between space and time:

1 = Φ(π/4)²
s/t = v, motion (measured in/as a speed or velocity)
t/s = e, energy (measured in discrete units using ordinary mathematics)
s/t x t/s = 1
∴ all universal motion has a corresponding t/s energy constituency proportional to the reciprocal of its own s/t velocity.

by **paladin17** » Wed Oct 14, 2020 10:41 am

d3x0r wrote: ↑Tue Oct 06, 2020 11:45 am
paladin17 wrote: ↑Sat Sep 19, 2020 6:07 pm You have to keep in mind though that 3D rotations (e.g. Lie group SO(3) - rotations around 3 orthonormal vectors) are non-Abelian. I.e. the order of the application of rotations matter. Rotate around X to x degrees and then rotate around Y to y degrees is not the same as in the reverse (in the general case anyways).
But these additions are not rotations applied to rotations... they are the sum of impulses that result in an acceleration or velocity (or accumulate into a position)

I don't quite get what you mean by "rotations applied to rotations". You mean the situation when the second rotation happens around a new Y axis (as if it was "locked" to the rotating body)?

d3x0r wrote: ↑Tue Oct 06, 2020 11:45 am
paladin17 wrote: ↑Sat Sep 19, 2020 6:07 pm This actually is very important in quantum field theory, where the fundamental interactions are represented by abstract rotations in the abstract space (see principle of local gauge invariance) and some of these rotational groups are Abelian (e.g. U(1) which represents electromagnetism) while others aren't (e.g. SU(3) which represents the strong nuclear interaction), which leads to radically different properties of the resulting theories.
I would like to know more about these assignments, and why they think that that actually works... I can certainty generate the result of a rotation with 2 more rotations applied to it (and yes the order matters, A then B then C is not the same when 'applying' when 'adding' a+b+c IS actually the same).

Which assignments do you mean? SU nomenclature? Or the [gauge] field theory in general? There is quite a lot of literature on both topics.
Long story short: somebody has found certain symmetries in electromagnetic field wave function, so they expressed these symmetries in the language of the group theory, and then were able to find similar symmetries for other two interactions (so in the end we have U(1) group "generating" electromagnetism, SU(2) "generating" weak nuclear interaction and SU(3) "generating" strong nuclear interaction - all through this local gauge invariance formalism).

d3x0r wrote: ↑Tue Oct 06, 2020 11:45 am Spatial position can be measured absolutely from one point to another, pick one on the floor, and one on the roof across the street, changes are high that most of those direct paths are not actually paths you can take to get to (x,y,z) target... it's the same with rotations;

Yes, of course. Any rotation around 3 axes, strictly speaking, can be expressed as a single rotation around a single axis (which, of course, except trivial cases would not coincide with any of the 3) - see Euler's rotation theorem. And curiously enough the same idea was used by F. I. Fedorov in the realm of particle physics (see his book "Lorentz group" and related works of other people, such as this one).

d3x0r wrote: ↑Tue Oct 06, 2020 11:45 am But absolutely, if you have two positions, you can immediately identify an axis of rotation and amount of rotation around that axis to get to that target point. (and compose a matrix to apply to get there even)
A physical system though has limitations, and a robot arm has 'yaw/pitch and roll' settings that are fix - and usually fixed as a result of each other... so a specific mounting order of 3 motors on a robot arm segment have to be applied separately - and that becomes a complex system of 3 equations that mutually affect each other.

I can see that. So we're talking about physical systems that have certain limitations. If I understand you correctly, you're trying to work with what may be formally called nonholonomic constraints on rotations.

by **A Gnostic Agnostic** » Sun Oct 11, 2020 6:45 pm

d3x0r wrote: ↑Sat Oct 10, 2020 6:08 am at 3 thousandths of a unit, such an error would be obviously wrong in many circumstances. While on the scale of an inch, it's not notable, in a circle the size of ... (looks for an example round Greek building, and fails) 1000 inches is some 83 feet, not even 1/3 of a football field, but then I couldn't find an equivalent circle of known measure that an equivalent size - at 1000 inches there'd be a 3 inch gap somewhere...

Such an error *is* obviously wrong, as the "missing" "dark" matter/energy is contained in/of (as) the incorrect value of π. If one measures a 1000mm diameter circle, one will find that 3141.6mm is too short. A real physical measurement of a real symmetrical circle of diameter 1000mm will measure no less than 3144.6mm if the measurement/instruments are sufficiently precise. The problem with the "approximated" π is it does not represent a real, physical circle, hence appears "transcendental". π can not be "transcendental" as all real circles minimally have a scalar radius of 1/2 such to scale with the golden ratio 1/2 + √5/2 whose reciprocal is discretely one less than itself (1/Φ = Φ-1) and whose square is discretely one greater than itself (Φ*Φ = Φ+1). This golden ratio is the only number in the universe with these unique properties, hence it must be contained in any real solution to unity, as it is: 1 = Φ(π/4)².

d3x0r wrote: ↑Sat Oct 10, 2020 6:08 am Honestly I've never needed PI, other than sin and cos functions are in units of PI; and I don't see that changing in hardware any time soon. It would be just as accurate if the scalar were 'OneOverSqrtPhi' or, in my preference 1.

Well the physical universe needs π just as it does Φ. The sin and cos functions are based on an unreal π, so you are not missing out on anything there. What you may be missing out on is the natural reciprocal relation between line and curve (space and time). This follows as a natural consequence according to the real geometry that underlies π = 4/√Φ, the latter being a real root of f(x) = x⁴ - 16x² + 256. The roots of the latter function create a real/imaginary axis (symmetrical), the same the physical universe adheres to.

d3x0r wrote: ↑Sat Oct 10, 2020 6:08 am Most machining of round things is just 'shave it down until it's round enough' or until 'this diameter matches this other diameter' and doesn't worry about the circumference anyway; so in math using the pi character is usually sufficient.

The circumference of a circle is fixed to the radius of the circle. The ratio c/d is fixed, and this ratio scales by way of the golden ratio. However note: a diameter is composed of 2r, thus c/2r discriminates against 2r/c/4=8r/c implying the 2r is a right angle instead of a flat diameter.

d3x0r wrote: ↑Sat Oct 10, 2020 6:08 am Having a larger value for the circumference vs radius one would end up with a spiral and not a circle.

ie. it would not be a circle anymore because the scalar nature of the golden ratio would be broken.

d3x0r wrote: ↑Sat Oct 10, 2020 6:08 am https://youtu.be/gj-u8qXdmJA - using an inscribed and circumscribed polygon, and increasing the number of sides seems like a reasonable method to get to the ratio of radius to circumference... and it's not even very many required to get under 3.144 (/4)

No, it will miss an entire constituency of the circle. The portion that is missed is recursively redistributed via the deficiency of the methodology. There is only one polygon that one must inscribe into an r = 1/2 circle, that is the square of the same area s = 1/√2. This square correlates the four axial points where both the circle and the square join/meet.

d3x0r wrote: ↑Sat Oct 10, 2020 6:08 am I maybe missed it- but what is the reasoning that arrives that the value is also equivalent to 1/sqrt(phi) *4?

If you inscribe an r = 1/2 circle in a unit square s = 1, you will find the circle and the square meet at four symmetrically equidistant points. Both the circle and the square are composed of four right angles: the square via the four corners (out-in) and the circle via the axial radii (in-out). This is the geometric reason π must be in some relation to '4'. The circumference of the r = 1/2 circle is a consequence of the golden ratio, thus by taking the square it correlates these same four points.

Here is an image showing the underlying geometric relation:
https://i.postimg.cc/15gS29s1/Circle-Pi7.jpg

by **d3x0r** » Sat Oct 10, 2020 6:08 am

A Gnostic Agnostic wrote: ↑Tue Oct 06, 2020 12:33 pm Nobody claimed it was - the "approximated" π of 3.14159... is deficient at the thousandth decimal place.
The "approximation" methodology (of exhaustion) recursively misses an entire constituency of the circle.

If ones actually measures a circle without "approximating" it, it can be seen that the reciprocal of √2
viz. 1/√2 = √2/2 captures the square of the golden ratio such that the reciprocal yields the arc
associated with π/4. This is a natural property/consequence of ordinary mathematics.

Western science is not going anywhere until they learn how to measure a circle.
The correct value of π as 3.1446055... is in relation to the golden ratio (and light).

at 3 thousandths of a unit, such an error would be obviously wrong in many circumstances. While on the scale of an inch, it's not notable, in a circle the size of ... (looks for an example round Greek building, and fails) 1000 inches is some 83 feet, not even 1/3 of a football field, but then I couldn't find an equivalent circle of known measure that an equivalent size - at 1000 inches there'd be a 3 inch gap somewhere...

Honestly I've never needed PI, other than sin and cos functions are in units of PI; and I don't see that changing in hardware any time soon. It would be just as accurate if the scalar were 'OneOverSqrtPhi' or, in my preference 1.

Most machining of round things is just 'shave it down until it's round enough' or until 'this diameter matches this other diameter' and doesn't worry about the circumference anyway; so in math using the pi character is usually sufficient.

Having a larger value for the circumference vs radius one would end up with a spiral and not a circle.

https://youtu.be/gj-u8qXdmJA - using an inscribed and circumscribed polygon, and increasing the number of sides seems like a reasonable method to get to the ratio of radius to circumference... and it's not even very many required to get under 3.144 (/4)

I maybe missed it- but what is the reasoning that arrives that the value is also equivalent to 1/sqrt(phi) *4?

by **A Gnostic Agnostic** » Tue Oct 06, 2020 12:33 pm

d3x0r wrote: ↑Tue Oct 06, 2020 11:42 am by the above there's also no approximation when using Π/3 or any other Π based number, it's still a perfect ratio.

Correct, but this has nothing to do with the correct value of π as a discrete ratio.

The reciprocal of √Φ viz 1/√Φ = π/4. This is whence the "from Adam's own rib is derived Eve" analogy,
the real underlying relation being from √Φ's own reciprocal comes π/4. Adam and Eve aka. space and time
(line and curve) are reciprocally related. Mainstream science incl. EU does not know this (yet).

The above is why the Giza pyramid was constructed with a height of √Φ and 4x axial radii of unit length, hence 4/√Φ.

d3x0r wrote: ↑Tue Oct 06, 2020 11:42 am 4/√Φ (3.14460551103....) is NOT equivalent to 3.1415926
(or do some alegebra and move the /4)

Nobody claimed it was - the "approximated" π of 3.14159... is deficient at the thousandth decimal place.
The "approximation" methodology (of exhaustion) recursively misses an entire constituency of the circle.

If ones actually measures a circle without "approximating" it, it can be seen that the reciprocal of √2
viz. 1/√2 = √2/2 captures the square of the golden ratio such that the reciprocal yields the arc
associated with π/4. This is a natural property/consequence of ordinary mathematics.

Western science is not going anywhere until they learn how to measure a circle.
The correct value of π as 3.1446055... is in relation to the golden ratio (and light).

by **d3x0r** » Tue Oct 06, 2020 11:45 am

paladin17 wrote: ↑Sat Sep 19, 2020 6:07 pm You have to keep in mind though that 3D rotations (e.g. Lie group SO(3) - rotations around 3 orthonormal vectors) are non-Abelian. I.e. the order of the application of rotations matter. Rotate around X to x degrees and then rotate around Y to y degrees is not the same as in the reverse (in the general case anyways).

But these additions are not rotations applied to rotations... they are the sum of impulses that result in an acceleration or velocity (or accumulate into a position)

This actually is very important in quantum field theory, where the fundamental interactions are represented by abstract rotations in the abstract space (see principle of local gauge invariance) and some of these rotational groups are Abelian (e.g. U(1) which represents electromagnetism) while others aren't (e.g. SU(3) which represents the strong nuclear interaction), which leads to radically different properties of the resulting theories.

I would like to know more about these assignments, and why they think that that actually works... I can certainty generate the result of a rotation with 2 more rotations applied to it (and yes the order matters, A then B then C is not the same when 'applying' when 'adding' a+b+c IS actually the same).

There are a few places where additive rotations are better 1) it's an accurate SLERP operation that's cheaper...(these days) it's the pure rotation axis between one rotation frame and another... the vector between them is the rotation axis also.. the distance between them is how much around that axis the space is rotated.... and again, there is a place and time where X+Y+Z is the same no matter the order; however, due to physical limitations, the ability to USE that is limited.

Spatial position can be measured absolutely from one point to another, pick one on the floor, and one on the roof across the street, changes are high that most of those direct paths are not actually paths you can take to get to (x,y,z) target... it's the same with rotations;

If you're in a rocket with fixed point engines, the rotation of that body affects the directions it can apply thrust to change its axis of rotation; but all the thrusters at once, simply composite with addition.

Through experimentation and stubborn pursuit of 'what exactly ARE addable rotations' I can identify where they do work, but that's a very limited circumstance.... and unfortunately it's still a complex system of transformations to values that have to happen to rotate axis-angle around axis-angle .

(axis-angle is just angle-angle-angle separated ) like linear velocity can be speed*(x,y,z) or (speedX,speedY,speedZ) and the angles just add like normal linear x/y/z points (in some cases)

But absolutely, if you have two positions, you can immediately identify an axis of rotation and amount of rotation around that axis to get to that target point. (and compose a matrix to apply to get there even)
A physical system though has limitations, and a robot arm has 'yaw/pitch and roll' settings that are fix - and usually fixed as a result of each other... so a specific mounting order of 3 motors on a robot arm segment have to be applied separately - and that becomes a complex system of 3 equations that mutually affect each other.

---

And let me finish with reiterating

I would like to know more about these assignments, and why they think that that actually works... (how it's mapped) And I'm not certain WHY or the mechanism for it, but I suspect gravity is actually a spin axis; but rotates x/y/z at once - so it's more of a rotation around 'w'? but barring that I'd like to know what the SO(1) things actually imply, since I can directly visualize such things now.

by **d3x0r** » Tue Oct 06, 2020 11:42 am

A Gnostic Agnostic wrote: ↑Sun Sep 20, 2020 4:13 am
d3x0r wrote: ↑Sat Sep 19, 2020 8:14 am 3.1415926blah is a lot closer to accurate than 3.14460551103....
False - 3.14159... is an "approximation" which misses an entire constituency of the circle.
In doing so, it is impossible to sync/normalize to the scalar rate associated with Φ.

4/√Φ
8/√ˉ2(1+√5)ˉ
-2√ˉ2(1+√5)ˉ + √ˉ10(1+√5)
√(8√5-8)
etc.

are not approximations. These are all discrete ratios/relations of the same underlying relation
whose numerical output is 3.1446055... wherein 3.141.... is an "approximation" of the former, and
not the other way around (there is a lot of upside-down in Western academia).

...1/√Φ is equivalent to π/4.

[/quote]

by the above there's also no approximation when using Π/3 or any other Π based number, it's still a perfect ratio.

4/√Φ (3.14460551103....) is NOT equivalent to 3.1415926
(or do some alegebra and move the /4)

by **A Gnostic Agnostic** » Sun Sep 20, 2020 4:13 am

d3x0r wrote: ↑Sat Sep 19, 2020 8:14 am all that is needed in what way? Since it's already established that they can't rotate say 367 degrees; or recover that it is at 367 degrees....

A 367 degree rotation is the same result as a 7 degree rotation.
The difference would be merely the velocity (v = s/t) such to arrive at.
(If I spin a radial arm 367 degrees, then do the same only 7 degrees,
the outcomes are equivalent, though the means are not).

d3x0r wrote: ↑Sat Sep 19, 2020 8:14 am For an example a 5 segment arm with 5 motors that can go +/- 90 degrees, if they are all set at 60 degrees, the total is 300 degrees, which the quaternion only represents at -60.... so computing a minor change from the current position, ends up distributing -9 degrees and all the motors go from +60 to -9... all bad; This could be maintained in entire accuracy with simple additions.

I don't know what a 5 segment arm with 5 motors whose range of freedom is (restricted to) +/- 90 degrees
all (somehow) situated about the same 60 degree orientation... is meant to describe as (if) something "real".

To be real, one would have to begin with a quaternion of a photon.
This is why the "speed of light" (s/t = 1) should serves as a unit datum.
The axis for this photon is contained in/as the roots of the function
to which π as 4/√Φ is one-of-four roots, that f being f(x) = x⁴ + 16x² - 256:

±√9.88854381999... (beg/end location)
±i√25.88854381999... (Α/Ω direction)

These four roots compose a real/imaginary axis that couples rational/irrational
number relations (all of them), as Φ and π are the "scalar" relations associated:

Φ = (1+√5)/2 viz. couples irrational/rational
π = 4/√Φ viz. couples rational/irrational

π = 4/√Φ = √(8√5-8)
π² = 16/Φ = (8√5-8)
16 = Φπ²
(e = MC²)
1 = Φπ²/16
= Φ(π/4)²
...ad infinitum ...

Do you see the integer difference of '16' in the four roots?
This is how rational/irrational are in relation to one another.

Einstein's e = MC² is composed of a mass-electric scalar constant M
(whose properties resolutely reflect the same scalar nature of the golden proportion)
and a velocity-magnetic scalar constant C whose product is energy.

How this relates to how to measure a circle: these four roots reflect the four
equidistant points that relate a unit square (space and time are discrete units)
to the associated 2r = 1 circle. Further: measuring the circle properly without
approximation shows that line and curve (implies: space and time relations)
are reciprocally related. Reciprocity will be the key to future physics
because the physical universe is based on a bed of (incessant) reciprocity.

EU has a chance to push this forward, but so far, no dice.
Again: the barrier is in the "approximation" of π rather than
leaving it as a discrete ratio of the (root of the) golden proportion.

The golden proportion gives rise to the perfect circle.
In other words: if you treat Φ as Adam and π as Eve,
from Adam comes Eve, thus from Φ comes π.

The re-coupling of these will spark a progression to a golden age.
This can not happen until reciprocity is consciously acknowledged
as principally underlying the laws which govern the physical universe,
as evidenced upon properly measuring a circle without "approximation".

d3x0r wrote: ↑Sat Sep 19, 2020 8:14 am 3.1415926blah is a lot closer to accurate than 3.14460551103....

False - 3.14159... is an "approximation" which misses an entire constituency of the circle.
In doing so, it is impossible to sync/normalize to the scalar rate associated with Φ.

I know humanity has had this "approximated" value of π for ~2000+ years, thus is "believed" to be correct,
but this is the same problem I am highlighting: if there is no challenging of basic underlying assumptions,
there is no progress and human beings continue to circle/cycle through periods of prolonged ignorance/suffering.

d3x0r wrote: ↑Sat Sep 19, 2020 8:14 am And by that you're replacing one approximation with another; thought you'd at least have converted to a 1-norm arclength and have integral circumference.

4/√Φ
8/√ˉ2(1+√5)ˉ
-2√ˉ2(1+√5)ˉ + √ˉ10(1+√5)
√(8√5-8)
etc.

are not approximations. These are all discrete ratios/relations of the same underlying relation
whose numerical output is 3.1446055... wherein 3.141.... is an "approximation" of the former, and
not the other way around (there is a lot of upside-down in Western academia).

Arc lengths are naturally quarters:
1/√Φ = π/4 viz.
1/√Φ + 1/√Φ + 1/√Φ + 1/√Φ =
π/4 + π/4 + π/4 + π/4 =
4/√Φ (and/or all above equivalent expression)

Let √(8√5-8) be C in/of e = MC²:

e = M(8√5-8)
e = 8M√5 - 8M
M = e(√5+1) / 32

Mass becomes Φ if/when e = 16.

d3x0r wrote: ↑Sat Sep 19, 2020 8:14 am I'm curious how you can apply 1/√Φ in any way to get an meaningful circularity

...1/√Φ is equivalent to π/4.

d3x0r wrote: ↑Sat Sep 19, 2020 8:14 am And you again forgot rotations... which are a dimensions of objects in space regardless of linear position or velocity. Every Game/physics engine has a position and an orientation, velocity and angular velocity, accerelation of of course angular accelerations. While it is possible to describe the rotations using sets of coordinates for bivectors and matrices; but can more simply just use X/Y/Z coordinates that are the angles of rotation. Any vector of rotation describes an axse

No, I did not forget rotations (?) - that is what the photon does, it rotates
and does not move relative to itself and/or other photons.

It actually has a birotation which incessantly allows a "choice-between-two"
as divided into yang-and-yin-like ± wholly dependent on the "charge" of the body
interacting with.

In this way, light is the conduit through which positive and negative charges
(equivalent: any dichotomy such as rational/irrational, real/imaginary etc.) transit,
the charge(s) itself being a property of the subject/object, not of the photon/light.

All a photon can do is (bi)-rotate, it can not accelerate/decelerate
unless apparently as a consequence of being introduced into a medium,
such as water slowing down light such to speed up again upon exit.
The underlying "rate" is fixed, hence it speeds back up again.

720° or 4π steradians is normalized to unity time: one single rotation from our perspective.
Note: rotations are non-commutative because order of operations MATTERS.

d3x0r wrote: ↑Sat Sep 19, 2020 8:14 am You say there is no time...

No, I do not say this anywhere. I said time is not a 4th dimension.

d3x0r wrote: ↑Sat Sep 19, 2020 8:14 am and then you define a bunch of terms with time. If time isn't a dimension, what is it? And what makes it not exactly like any other dimension with a measure?

Time and space are not two separate things - they are merely reciprocal aspects of motion.
They have no further significance than a numerator and a denominator:

s/t = v (speed)
t/s = e (energy)
___________________
space and time are reciprocally related viz.
s/t x t/s = 1 wherein '1' is normalized to unity.

s³/t relates 3D of space on a base of normalized (to light/unity) time viz. s³/1.
t³/s relates 3D of time on a base of normalized (to light unity) space viz. t³/1.

2º = 1
2¹ = 2
2² = 4
2³ = 16 = Φπ²

Time is not a dimension - it has the same dimensions as space does.
Novae are explosions in 3D space, whereas things like
quasars are explosions in 3D time. There is no such thing as
"infinite mass" and/or "singularities" - there is a discrete threshold.

d3x0r wrote: ↑Sat Sep 19, 2020 8:14 am Dimensions can also be say... PVT (pressure,volume,temperature) ... or LC, EI (inductance,capacitance, volts, amps) and combinations thereof to get power, work, etc... but all of those are emergent properties from the base rotation and linear motion dimensions.

The only real constituency of the physical universe is motion.
All particles/molecules/atoms are particular configurations
of motion(s) of increasing complexity.

All particles can be described by some discrete displacement(s) from unity datum 1/1 = light.
If s/t = 1, it is a photon being described.
If s/t ≠ 1, it is "something else" being described as a displacement(s) from (in relation to) light.

d3x0r wrote: ↑Sat Sep 19, 2020 8:14 am There really isn't counter-space... other than (to programmers) a space containing scratch variables and counters; which none of which have any units or metrics.

All motion in time is counter-spatial. The underlying geometry is the inverse of space wherein
less space means more energy, hence recti- and polar-Euclidean such to describe the relation.

Implosion technology (rather than explosion technology) will be the future of energy generation.

d3x0r wrote: ↑Sat Sep 19, 2020 8:14 am Pi is as good of a bit pattern as any; I'm not so bothered by having to multiply turns times 2pi... have to anyway when a force is applied at a radius of 1, for 1m/s then the circle only gets a arc-length/angular speed of 1/2pi m/s ...
(and I don't see how replacing 3.1415 with 3.1446 is going to make that any more correct...)

A circle with a radius of 1 is not a normalized circle - you need a circle with a diameter of 1 viz. 2r = 1 or r = 1/2.
It is also necessary to understand that π is not a circumference/diameter relation (another false assumption),
all diameters are resolutely a product of a doubling (2) of the real radius, thus a diameter is fixed as 2r.

Because 2r is what is needed to compose a right-angle and corresponding π/4,
2r/c/4 = 8r/c is the correct way to understand the underlying relation, and not
a "circumference to diameter" as "defined" by presumptuous mathematicians.

The golden ratio is practically in/of/as light (itself), thus
if not reflected in/as π, there is no scalar synchronization.
This is why the "approximated" π of 3.141... is "transcendental":
it has nothing to do with reality. The correct 4/√Φ is not "transcendental"
as π is describing a REAL radius in relation to four really equidistant axial points.
Such a relation can not be "transcendental" unless one has the wrong answer
due to wrong conception/methodology (this being the case for the "approximation" of π).

The correction to π will invariably spark tremendous scientific reformation, however
as we know, there are men on this planet that want all control and all power over all people.
The solving of e = MC² can be (has been) used to solve the biggest problem(s) on this planet
to no degree(s) of error(s).

by **paladin17** » Sat Sep 19, 2020 6:07 pm

d3x0r wrote: ↑Sat Sep 19, 2020 8:14 am So buried in some abstract math concept there actually is something that says rotations just add; after I spent all that time trying to prove that they actually do... it's definatly needlessly complicated... https://en.wikipedia.org/wiki/Lie_product_formula basically A+B is the same as applying A and B at the same time, or, by iterating small steps of A and B continuously to get the result... So for some axis*angle + another axis*angle is just a third which is the effective rotation as if both of the individual rotations happened simultaneously. (makes adding multiple torque sources quite easy) But anyway I was converting everything to a 1-norm and doing the math, because the numbers looked better; but turns out it's really just a toString() sort of phenomenon to make the values human-readable as opposed to math-readable (typically the phrase is machine-readable). But a rotation of (90,0,0) and (0,90,0) to (90,90,0) looks a lot better as (90,90,0) than (127.6,127.6,0) IMO (which is what it would be to get to show as 90,90, or in total flipped over 180 degrees from the start).

You have to keep in mind though that 3D rotations (e.g. Lie group SO(3) - rotations around 3 orthonormal vectors) are non-Abelian. I.e. the order of the application of rotations matter. Rotate around X to x degrees and then rotate around Y to y degrees is not the same as in the reverse (in the general case anyways).
This actually is very important in quantum field theory, where the fundamental interactions are represented by abstract rotations in the abstract space (see principle of local gauge invariance) and some of these rotational groups are Abelian (e.g. U(1) which represents electromagnetism) while others aren't (e.g. SU(3) which represents the strong nuclear interaction), which leads to radically different properties of the resulting theories.

by **d3x0r** » Sat Sep 19, 2020 8:14 am

A Gnostic Agnostic wrote: ↑Thu Sep 17, 2020 5:59 am
This is not necessarily true. Quaternions may represent any/all possible rotation coordinates.
It is important to understand the geometry must be understood as projective following affine.
180-degrees is all that is needed to represent conjugation viz. ±180 degrees = 360.

all that is needed in what way? Since it's already established that they can't rotate say 367 degrees; or recover that it is at 367 degrees....

For an example a 5 segment arm with 5 motors that can go +/- 90 degrees, if they are all set at 60 degrees, the total is 300 degrees, which the quaternion only represents at -60.... so computing a minor change from the current position, ends up distributing -9 degrees and all the motors go from +60 to -9... all bad; This could be maintained in entire accuracy with simple additions.

A Gnostic Agnostic wrote: ↑Thu Sep 17, 2020 5:59 am
and reciprocity as the fulcrum, hence 1/√Φ = π/4 wherein from Φ (line) is derived π (curve).

3.1415926blah is a lot closer to accurate than 3.14460551103....
And by that you're replacing one approximation with another; thought you'd at least have converted to a 1-norm arclength and have integral circumference.

I'm curious how you can apply 1/√Φ in any way to get an meaningful circularity

A Gnostic Agnostic wrote: ↑Thu Sep 17, 2020 5:59 am
The 3D that are normally associated with space actually precedes all considerations of space and time entirely.
This means that whereas space has 3 dimensions, time has the same 3 dimensions despite our own being
bound to experience time as a linear progression.

And you again forgot rotations... which are a dimensions of objects in space regardless of linear position or velocity. Every Game/physics engine has a position and an orientation, velocity and angular velocity, accerelation of of course angular accelerations. While it is possible to describe the rotations using sets of coordinates for bivectors and matrices; but can more simply just use X/Y/Z coordinates that are the angles of rotation. Any vector of rotation describes an axse

A Gnostic Agnostic wrote: ↑Thu Sep 17, 2020 5:59 am

"Adding" in time as a 4th dimension is a big mistake. There is no 4th dimension of time, only 3D:

s³/t = motion (3D physical)
t³/s = energy (3D metaphysical)
s³/t x t³/s = (st)²

s³/t³ = gravity
t³/s³ = mass
s³/t³ x t³/s³ = 1 = Φ(π/4)²

You say there is no time... and then you define a bunch of terms with time. If time isn't a dimension, what is it? And what makes it not exactly like any other dimension with a measure?

Dimensions can also be say... PVT (pressure,volume,temperature) ... or LC, EI (inductance,capacitance, volts, amps) and combinations thereof to get power, work, etc... but all of those are emergent properties from the base rotation and linear motion dimensions.

A Gnostic Agnostic wrote: ↑Thu Sep 17, 2020 5:59 am
G is not a constant, this is another false underlying assumption Western science has (there are a lot).

Radial length vs. arc length is already reconciled by the correct value of π viz. 1/√Φ = π/4.

The key is reciprocity. The link between space and counter-space is natural logarithmic
viz. a transform from recti-Euclidean to reciprocal polar-Euclidean which effectively
turns everything inside-out in 3D (see mass and gravity above).

There really isn't counter-space... other than (to programmers) a space containing scratch variables and counters; which none of which have any units or metrics.

Pi is as good of a bit pattern as any; I'm not so bothered by having to multiply turns times 2pi... have to anyway when a force is applied at a radius of 1, for 1m/s then the circle only gets a arc-length/angular speed of 1/2pi m/s ...
(and I don't see how replacing 3.1415 with 3.1446 is going to make that any more correct...)

---
I have to make a bunch of changes to undo some of the calculations i made for additive rotations.

So buried in some abstract math concept there actually is something that says rotations just add; after I spent all that time trying to prove that they actually do... it's definatly needlessly complicated... https://en.wikipedia.org/wiki/Lie_product_formula basically A+B is the same as applying A and B at the same time, or, by iterating small steps of A and B continuously to get the result... So for some axis*angle + another axis*angle is just a third which is the effective rotation as if both of the individual rotations happened simultaneously. (makes adding multiple torque sources quite easy) But anyway I was converting everything to a 1-norm and doing the math, because the numbers looked better; but turns out it's really just a toString() sort of phenomenon to make the values human-readable as opposed to math-readable (typically the phrase is machine-readable). But a rotation of (90,0,0) and (0,90,0) to (90,90,0) looks a lot better as (90,90,0) than (127.6,127.6,0) IMO (which is what it would be to get to show as 90,90, or in total flipped over 180 degrees from the start).

by **A Gnostic Agnostic** » Thu Sep 17, 2020 5:59 am

d3x0r wrote: ↑Thu Sep 17, 2020 1:41 am It is... when evaluated the angles get converted through sin/cos to periodic functions... and doe fold at 2pi.... but can also represent rotations within 2pi to 6pi... -2pi to 6pi... 6pi to 10pi,. .. and periouds of 4pi after that... so saying that 2pi is the limit is quite wrong.... the real rotation period of rotating a rotation around another rotation is 4pi, and not 2 or 3 pi.

If it folds at 2π, then 2π precedes expressions requiring conversions.

2π is not the limit, it is the minimum which defines a beg/end circle/cycle.
I will elaborate shortly.

d3x0r wrote: ↑Thu Sep 17, 2020 1:41 am Quaternions only represent 1/2 of the possible rotation coordinates... since the Theta angle put in is cos(theta/2) even when you get out is only +/- pi or +/- 180 degrees, and fails to represent any rotations with degrees beyond that. And also fails to represent any single rotation of 181 degrees... which is probably why spins re only in +/- 1/2 because that's the maximum extend of the rotation expressible with hamiltonians.

This is not necessarily true. Quaternions may represent any/all possible rotation coordinates.
It is important to understand the geometry must be understood as projective following affine.
180-degrees is all that is needed to represent conjugation viz. ±180 degrees = 360.

The universe is a binary system: presence/absence (of) with 180 degrees of freedom for each.

d3x0r wrote: ↑Thu Sep 17, 2020 1:41 am We don't know how light works - it relies on stretching space, which isn't a thing.

I admit GR and/or EU do not know how light works. When I said "we" I was loosely referencing others.
There are other theories of the physical universe that know how light works (albeit suppressed).
The "stretching space" phenomena is an artifact due to the misunderstanding of space and time.
Space and time are not two separate things (or "things" at all). They are nothing but multiplicative
reciprocal aspects of motion. One may imagine a see-saw with space and time on either end
and reciprocity as the fulcrum, hence 1/√Φ = π/4 wherein from Φ (line) is derived π (curve).

d3x0r wrote: ↑Thu Sep 17, 2020 1:41 am Don't really get where you're going with sqrt of 5... that looks like trying to force rotation coordinates back into 2-normal somehow... which is just going to be self defeating.

√5 is the key to any/all kinematics (motion) both physical and metaphysical.
It is required to relate rational and irrational numbers (as) incessantly normalized to unity.
It also constructs the pentagram (underlying the human body) which allows for the following:

Apex: local ± binary discretion (to be (+), or not to be (-): that is the ± discretion)
Arms: null ± binary operators viz. Α∞Ω (particular orientation/direction)
Legs: null ± binary roots viz. beg∞end (particular location)

From the apex down, there are two possible routes towards two possible roots:
Apex → R1 → Α∞Ω → R2
Apex → R2 → Α∞Ω → R1
wherein both may happen at the same time such to grant variable discretion (consciousness).

The three powers of Φ viz. Φ, Φ², Φ³ composes the full pentagram normalized to 1/unity
as the symmetry can be seen by looking at any golden ratio pentagram: each of the powers
construct a portion of the pentagram.

d3x0r wrote: ↑Thu Sep 17, 2020 1:41 am Edit2: Quaternions also don't allow you to add rotations or compare them deferentially or relatively. So why even mention that as an altenrative when the system I presented already does work? Even Log(Quaternion) which is supposed to represent the angles of the rotation, doesn't, and doesn't provide additive rotations; if they did, I wouldn't have had to continue to work on them... but once I did figure out the error fractor between log-quaternions and actual additive rotations, it all became quite clear why a lot of other math ended up the way it did.

I am not sure where that deduction is coming from, but it is certainly possible to add rotations (?).
Perhaps the problem is how you are treating time? (No fault of yours, Western science is clueless on time).

The 3D that are normally associated with space actually precedes all considerations of space and time entirely.
This means that whereas space has 3 dimensions, time has the same 3 dimensions despite our own being
bound to experience time as a linear progression.

"Adding" in time as a 4th dimension is a big mistake. There is no 4th dimension of time, only 3D:

s³/t = motion (3D physical)
t³/s = energy (3D metaphysical)
s³/t x t³/s = (st)²

s³/t³ = gravity
t³/s³ = mass
s³/t³ x t³/s³ = 1 = Φ(π/4)²

d3x0r wrote: ↑Thu Sep 17, 2020 1:41 am I apologize I'm stealing your thread a bit, and really if you want to talk about rotations and challenge the system I have; I've yet to be defeated by any challenges And SLERP as a smooth rotation function is fairly bizaare in natural rotation coodinates.

I'm not challenging your system, it is not in my interest to challenge anything except basic underlying assumptions that underlie Western science as a whole - in particular, how to measure a circle.

I otherwise appreciate any/all dialogue absent polemics.

d3x0r wrote: ↑Thu Sep 17, 2020 1:41 am On topic - Circles
If you standardize a unit measure on the circumference/perimeter of a circle, that's a great, but then to construct that circle you need another distance, either in some other unit entirely (inches and centimeters for instance... but radial length vs arc length) so that it can remain in 'natural' units, but then the conversion will have a n/pi or n*pi scalar builtin ... kinda like that pesky 'G' constant. I'm not sure what you are arguing in favor of or against. Yes, we can only hope to approximate it, like Phi (golden ratio); e (as in the base of ln() ) ; sqrt(2); 1/3 in base 2....

The unit measure is standardized to units of motion viz. s/t = 1 or the "speed" of light (photons).
The circle 2r = 1 (all circular motion) is a natural product of the square (root) of the golden ratio.
The "speed" of light is not (only) a speed, it is a scalar "rate".
The rate is scalar because it is based on the same scalar relation in/of the golden ratio.
One unit of motion has an energy constituency of 16 units of energy capturing
binary information re: alpha/omega/beg/end (photon) wherein 1 unit of energy is
incessantly bound to unity (thus only 15 of 16 are degrees of freedom).

G is not a constant, this is another false underlying assumption Western science has (there are a lot).

Radial length vs. arc length is already reconciled by the correct value of π viz. 1/√Φ = π/4.
This relation scales from the unit of motion (unity/light) onward.

The key is reciprocity. The link between space and counter-space is natural logarithmic
viz. a transform from recti-Euclidean to reciprocal polar-Euclidean which effectively
turns everything inside-out in 3D (see mass and gravity above).

by **d3x0r** » Thu Sep 17, 2020 3:11 am

I apologize I'm stealing your thread a bit, and really if you want to talk about rotations and challenge the system I have; I've yet to be defeated by any challenges

And SLERP as a smooth rotation function is fairly bizaare in natural rotation coodinates.

On topic - Circles
If you standardize a unit measure on the circumference/perimeter of a circle, that's a great, but then to construct that circle you need another distance, either in some other unit entirely (inches and centimeters for instance... but radial length vs arc length) so that it can remain in 'natural' units, but then the conversion will have a n/pi or n*pi scalar builtin ... kinda like that pesky 'G' constant. I'm not sure what you are arguing in favor of or against. Yes, we can only hope to approximate it, like Phi (golden ratio); e (as in the base of ln() ) ; sqrt(2); 1/3 in base 2....

by **d3x0r** » Thu Sep 17, 2020 1:41 am

P=1/2at^2+vt+m may attempt to describe a kinematic situation(s) in a limited context, but is itself not kinematic.
A kinematic geometry must have a periodic (rotational) base (of 2π) that grounds/normalizes all motion indiscriminately.

It is... when evaluated the angles get converted through sin/cos to periodic functions... and doe fold at 2pi.... but can also represent rotations within 2pi to 6pi... -2pi to 6pi... 6pi to 10pi,. .. and periouds of 4pi after that... so saying that 2pi is the limit is quite wrong.... the real rotation period of rotating a rotation around another rotation is 4pi, and not 2 or 3 pi.

Quaternions only represent 1/2 of the possible rotation coordinates... since the Theta angle put in is cos(theta/2) even when you get out is only +/- pi or +/- 180 degrees, and fails to represent any rotations with degrees beyond that. And also fails to represent any single rotation of 181 degrees... which is probably why spins re only in +/- 1/2 because that's the maximum extend of the rotation expressible with hamiltonians.

We don't know how light works - it relies on stretching space, which isn't a thing.

Don't really get where you're going with sqrt of 5... that looks like trying to force rotation coordinates back into 2-normal somehow... which is just going to be self defeating.

Even if pi is an approximation, as soon as you want 2/5'ths of an arc you get an infinite, non precisice value that's just as far off as PI in base 2 calculations....

Edit2: Quaternions also don't allow you to add rotations or compare them deferentially or relatively. So why even mention that as an altenrative when the system I presented already does work? Even Log(Quaternion) which is supposed to represent the angles of the rotation, doesn't, and doesn't provide additive rotations; if they did, I wouldn't have had to continue to work on them... but once I did figure out the error fractor between log-quaternions and actual additive rotations, it all became quite clear why a lot of other math ended up the way it did.

by **A Gnostic Agnostic** » Wed Sep 16, 2020 11:12 pm

antosarai wrote: ↑Wed Sep 16, 2020 4:55 pm
A Gnostic Agnostic wrote: ↑Wed Sep 16, 2020 12:30 pmThat is all that has and would happen should I not have chosen to disengage.
...
Isn't it a pity?

But then perhaps you'd engage Mr. d3x0r and Additive Rotations - P=1/2at^2+vt+m for rotations?

Or isn't that kinematic geometry either

It is a pity because over 2000 years of human ignorance is contained in/as the "approximation" of π.
The magnitude of the error is, in my experience, wholly incomprehensible to most, thus we will have
people who do not pay the attention merited by the magnitude of the error. It is immense.

P=1/2at^2+vt+m may attempt to describe a kinematic situation(s) in a limited context, but is itself not kinematic.
A kinematic geometry must have a periodic (rotational) base (of 2π) that grounds/normalizes all motion indiscriminately.

The photon (and physical universe) can be represented as a quaternion(s) 1, i, j, k

q = a + bi + cj + dk

wherein ±π forms a dual conjugate quaternion(s) that give rise to recti-Euclidean and polar-Euclidean geometries (within which kinematics may be expressed).

I will address this in my reply to d3x0r.

d3x0r wrote: ↑Wed Sep 16, 2020 6:50 pm Edit: I guess a full circle is actually 8 in natural rotation coordiantes 2+2+2+2 ... with a radius of 1... so really 8r or 4*diameter
I'll have to revisit the area and volume too

Yes, this is correct. I encourage the following thought experiment (for others):

1. Imagine two 2x1 rectangles perpendicularly (axially) situation about an origin.
2. Use the vertices to compose a circle with diameter √5.
3. Travel back-and-forth along each of the 4x √5 diagonals.

This is whence we get our symmetrical '8' that captures the circle, hence:

2r/c/4 = 8r/c or c = 8r
viz.
π = √(8√5-8) = 4/√Φ

There is no such thing as a perfect circle that is not in golden ratio proportion.
In fact, the quaternion can be used to describe the photon and/or physical universe:

MATRIX.jpg

https://i.postimg.cc/bJxF8KzY/MATRIX.jpg

wherein e^πi + e^-πi = 2cos(x) re: (2D→1D) motion
(this is with the correct value of π as 4/√Φ).

We already have the photon/physical universe modeled as a (dual) quaternion(s) and understand what light is and how it works. This is not the issue, the issue is humanity does not know how to measure a circle, and instead approximates it with straight lines that completely ignore the need to measure the √5 diameter circle (this circle normalizes all motion to the unit square and/or 2r = 1 circle).

The incorrect "approximated" value of π is the obstacle. If EU can pick up on this problem/solution, they will be able to show that Einstein's e = MC² invalidates Einstein's own theory. The universe is not gravity-centric, as:

π = 4/√Φ
π² = 16/Φ
16 = Φπ²

...is the real relation underlying e = MC², wherein Φ is a scalar 1D mass-electric constant and π² is a scalar 2D velocity-magnetic constant (gravity is an inward motion / acceleration). The real/imaginary numbers become linked/coupled to the physical universe by way of the equality above.

This union of real/imaginary happens at f(x) = x⁴ + 16x² -256 which is the "junction function" through which all such relations immutably transit. π is a root of this function (along with its own conjugate) and relates to imaginary counter-parts that are off-set by a factor of 16, hence 16 = Φπ².

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