Title: The space time manifold tensor candidates
Post by: jehovajah on May 04, 2010, 07:42:27 AM
So, not complete but accessible and any of you are welcome to use them. The fabric of my thought turns out into these statements, and i frankly do not comprehend them.
I have not decided what is the best format for them or whether they need to be in all formats: these being iterated function systems, ordinary formulaic fractal generation, 3d graphing programme format or anything else.
So this is a work in progress,
I have not even checked the excellent QuaSZ (http://www.mysticfractal.com/QuaSZ.html) Mac to see if Terry has not done this stuff already! :embarrass:
I have not decided what is the best format for them or whether they need to be in all formats: these being iterated function systems, ordinary formulaic fractal generation, 3d graphing programme format or anything else.
So this is a work in progress,
I have not even checked the excellent QuaSZ (http://www.mysticfractal.com/QuaSZ.html) Mac to see if Terry has not done this stuff already! :embarrass:
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on May 04, 2010, 07:50:45 AM
Conical and Cylindrical Helix
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on May 04, 2010, 08:15:01 AM
So my first interesting candidate and truly fractal as I will show in developmental posts.
z=e^z+z*j+c+z
This moment at iteration 5 is where the underlying vortices are revealed for the first time:
(http://www.fractalforums.com/gallery/2/410_04_05_10_8_01_06_0.png)
A post in the Mystic Fractal Gallery (http://www.fractalforums.com/mystic-fractal-programs-gallery-b167/) details the creation of an atom from vortices interacting, so I look closer to see if one pops out here:
(http://www.fractalforums.com/gallery/2/410_04_05_10_8_01_06_1.png)
A closer look at the tip shows no atom,but reveals the complex motion that is being shaped here by |z|<20
(http://www.fractalforums.com/gallery/2/410_04_05_10_8_01_06_2.png)
z=e^z+z*j+c+z
This moment at iteration 5 is where the underlying vortices are revealed for the first time:
(http://www.fractalforums.com/gallery/2/410_04_05_10_8_01_06_0.png)
A post in the Mystic Fractal Gallery (http://www.fractalforums.com/mystic-fractal-programs-gallery-b167/) details the creation of an atom from vortices interacting, so I look closer to see if one pops out here:
(http://www.fractalforums.com/gallery/2/410_04_05_10_8_01_06_1.png)
A closer look at the tip shows no atom,but reveals the complex motion that is being shaped here by |z|<20
(http://www.fractalforums.com/gallery/2/410_04_05_10_8_01_06_2.png)
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on May 14, 2010, 10:25:19 AM
I have updated the text file with a major addition, in particular Terry Gintz correspondence with math doctor re quaternion hyperbolic and trig formulae. This is of significance to quasz mac users as the e^z formulae are quad formulae. Quasz sculpts in the quad block although it visualises in the tri block. The images above are so complex because of these additional factors and certain shapes that are intuitively expected do not arise as expected through these factors also.
The extension of hyperbolic formulae to quaternions leads to the speculation
e^q= e^(x+i*y+s*j+w*k)≈e^x*e^(i*y)*e(j*s)*e^(k*w)≈e^x*y^3*(cosy+i*siny)*s^3*(cos(s)+j*sin(s))*w^3*(cosw+k*sinw)/[sqrt(y^2+s^2+w^2)]^3
or some variation.
In any case the conditions for equality are clearly laid out in the reply.
The extension of hyperbolic formulae to quaternions leads to the speculation
e^q= e^(x+i*y+s*j+w*k)≈e^x*e^(i*y)*e(j*s)*e^(k*w)≈e^x*y^3*(cosy+i*siny)*s^3*(cos(s)+j*sin(s))*w^3*(cosw+k*sinw)/[sqrt(y^2+s^2+w^2)]^3
or some variation.
In any case the conditions for equality are clearly laid out in the reply.
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on May 17, 2010, 02:37:53 PM
For example, exp (i + j) = cos sqrt 2 + (i + j)(sin sqrt 2)/sqrt 2,
while exp i * exp j = (cos 1)^2 + (i + j)(sin 2)/2 + k(sin 1)^2, and
exp j * exp i = (cos 1)^2 + (i + j)(sin 2)/2 - k(sin 1)^2. However,
whenever ab = ba (for example, whenever a is real), then
exp (a + b) = exp a * exp b does hold in the quaternions
That fact is the secret to calculating exp (a + ib + jc + kd). Since
a commutes with ib + jc + kd (when a, b, c, and d are real),
exp (a + ib + jc + kd) = exp a * exp (ib + jc + kd). Now, you can't
break exp (ib + jc + kd) into exp ib * exp jc * exp kd, but you don't
need to. Simply divide this vector by its magnitude. The quantity
L = (ib + jc + kd)/sqrt (b^2 + c^2 + d^2) satisfies L^2 = -1 (check it
for yourself). And you can go back to the infinite series to see that
exp Lx = cos x + L sin x, whenever L^2 = -1 and x is real. So let
M = sqrt (b^2 + c^2 + d^2), so ib + jc + kd = LM. Then
exp (a + ib + jc + kd) = exp(a)*(cos M + L sin M)=exp(a)*(cos M + {ib+jc+kd}*sin M/M)
=exp(a)*(cos M + {i*bsin M + j*csin M + k*dsin M } /M)
So the speculation will be way off base but some weird conection may show up in the sculptures :embarrass:
while exp i * exp j = (cos 1)^2 + (i + j)(sin 2)/2 + k(sin 1)^2, and
exp j * exp i = (cos 1)^2 + (i + j)(sin 2)/2 - k(sin 1)^2. However,
whenever ab = ba (for example, whenever a is real), then
exp (a + b) = exp a * exp b does hold in the quaternions
That fact is the secret to calculating exp (a + ib + jc + kd). Since
a commutes with ib + jc + kd (when a, b, c, and d are real),
exp (a + ib + jc + kd) = exp a * exp (ib + jc + kd). Now, you can't
break exp (ib + jc + kd) into exp ib * exp jc * exp kd, but you don't
need to. Simply divide this vector by its magnitude. The quantity
L = (ib + jc + kd)/sqrt (b^2 + c^2 + d^2) satisfies L^2 = -1 (check it
for yourself). And you can go back to the infinite series to see that
exp Lx = cos x + L sin x, whenever L^2 = -1 and x is real. So let
M = sqrt (b^2 + c^2 + d^2), so ib + jc + kd = LM. Then
exp (a + ib + jc + kd) = exp(a)*(cos M + L sin M)=exp(a)*(cos M + {ib+jc+kd}*sin M/M)
=exp(a)*(cos M + {i*bsin M + j*csin M + k*dsin M } /M)
So the speculation will be way off base but some weird conection may show up in the sculptures :embarrass:
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on June 04, 2010, 08:02:28 AM
Further study and a confluence of ideas leads me to the following set of motion statements for the spacetime manifold. This time reflecting Classical Newtonian conceptions
z=z^(-2)+n*Z+c^(-1)
Where n is some real constant.
http://csep10.phys.utk.edu/astr161/lect/history/newtonkepler.html (http://csep10.phys.utk.edu/astr161/lect/history/newtonkepler.html)
Although not properly worked out i note
)
is analogous to
z^2 -2*(x#*y#*i-y#^2)+c =z which is analagous to
z^2 -2*y#*e^(i*ø)+c =z where ø is a real radian measure and z is the polynomial numeral x+iy
Using z=r*e^(i*ø) as a general form i posit
z^2 -n*z+c =z
And because i am interested in an inverse square law i suggest
z=z^(-2)+n*Z+c^(-1) as a protoform.
Alternatively
z^2 +2*y#*(flip(conj(z)))+c =z
suggesting again
z=z^(-2)+n*flip(Z)+c^(-1) as a protoform.
Of course for Quasz the z is a quad which is a polynomial numeral z= x+iy+zj+wk.
These kind of analogous manipulations are not rigorous but creative. the rigour comes later if anything interesting pops out! ;D
One of the straight jackets of classical maths was the emphasis on finding a solution, that is... an arithmetic driven scheme! From this we derived cartesian geometrical forms which gave solutions but did not explore the form of the statement in any other way. This gave a solution form in which the functions in more than one variable were inexorably plotted against a "z" axis to give a 3d form. However this device is confusing the function statement with a geometrical surface. The function statement is describing a relationship between the parameters which is intuitive or derived. This relationship does not necessarily have a geometrical form. Iteration is a more general way to explore functions in many variables and the use of visualisations rather than only geometry can help to develop an intuition about the function statement . I mean in this instance the use of a colour scheme and or a sound scheme to represent the variable values as well as the extensions along orthogonal axes or the use of non orthogonal axes which we do every day in 2d diagrams! :-*
z=z^(-2)+n*Z+c^(-1)
Where n is some real constant.
http://csep10.phys.utk.edu/astr161/lect/history/newtonkepler.html (http://csep10.phys.utk.edu/astr161/lect/history/newtonkepler.html)
Although not properly worked out i note
z^2 -2*(x#*y#*i-y#^2)+c =z which is analagous to
z^2 -2*y#*e^(i*ø)+c =z where ø is a real radian measure and z is the polynomial numeral x+iy
Using z=r*e^(i*ø) as a general form i posit
z^2 -n*z+c =z
And because i am interested in an inverse square law i suggest
z=z^(-2)+n*Z+c^(-1) as a protoform.
Alternatively
z^2 +2*y#*(flip(conj(z)))+c =z
suggesting again
z=z^(-2)+n*flip(Z)+c^(-1) as a protoform.
Of course for Quasz the z is a quad which is a polynomial numeral z= x+iy+zj+wk.
These kind of analogous manipulations are not rigorous but creative. the rigour comes later if anything interesting pops out! ;D
One of the straight jackets of classical maths was the emphasis on finding a solution, that is... an arithmetic driven scheme! From this we derived cartesian geometrical forms which gave solutions but did not explore the form of the statement in any other way. This gave a solution form in which the functions in more than one variable were inexorably plotted against a "z" axis to give a 3d form. However this device is confusing the function statement with a geometrical surface. The function statement is describing a relationship between the parameters which is intuitive or derived. This relationship does not necessarily have a geometrical form. Iteration is a more general way to explore functions in many variables and the use of visualisations rather than only geometry can help to develop an intuition about the function statement . I mean in this instance the use of a colour scheme and or a sound scheme to represent the variable values as well as the extensions along orthogonal axes or the use of non orthogonal axes which we do every day in 2d diagrams! :-*
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on June 05, 2010, 09:37:38 AM
In quasz Terry has an in built function number 37 which corresponds to the second manifold tensor candidate with n set to 0 and c instead of 1/c.
1/z^2 + c
The first sculpture is an image of a Minkowski torus with a gravity well structure that is complex
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_37_08_0.png)
the second looks into the gravity well structure
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_37_08_1.png)
the third shows the torus shape followed by 2 other views
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_37_08_2.png)
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_37_08_3.png)
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_37_08_4.png)
I then take a look at the gravity well structure which passes completely through the torus but not symmetrically and the structure appears to be the result of antisymmetric action from the other side of the torus
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_48_18_0.png)
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_48_18_3.png)
I then show the spatial structure with the wells
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_48_18_1.png)
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_48_18_2.png)
The sculptures are sensitive to the seed points with the real coefficient of the seed determining the toroidal shape while the i and j coefficients seem to determine the well structure. The anti symmetry is due to rotation not reflection which is a translation in relativistic motion i am currently cogitating.
The mandelbrots are informative especially mandelbrotp but i have no cosmological referent for the mandelbrot boundary conditions yet in mind.
Each sculpture relies on the quad motion statement in quasz and the cutting boundary |z|≤4. This parameter has much to do with the eventual form and surface structures of the sculpture and i am exploring form and structures in spaciometry.
1/z^2 + c
The first sculpture is an image of a Minkowski torus with a gravity well structure that is complex
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_37_08_0.png)
the second looks into the gravity well structure
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_37_08_1.png)
the third shows the torus shape followed by 2 other views
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_37_08_2.png)
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_37_08_3.png)
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_37_08_4.png)
I then take a look at the gravity well structure which passes completely through the torus but not symmetrically and the structure appears to be the result of antisymmetric action from the other side of the torus
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_48_18_0.png)
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_48_18_3.png)
I then show the spatial structure with the wells
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_48_18_1.png)
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_48_18_2.png)
The sculptures are sensitive to the seed points with the real coefficient of the seed determining the toroidal shape while the i and j coefficients seem to determine the well structure. The anti symmetry is due to rotation not reflection which is a translation in relativistic motion i am currently cogitating.
The mandelbrots are informative especially mandelbrotp but i have no cosmological referent for the mandelbrot boundary conditions yet in mind.
Each sculpture relies on the quad motion statement in quasz and the cutting boundary |z|≤4. This parameter has much to do with the eventual form and surface structures of the sculpture and i am exploring form and structures in spaciometry.
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on June 15, 2010, 07:34:16 AM
i*h*d(z)/dt=(-h^2/m)*(d2(z)/dt+c*z :a working note on schroedinger's equation, not formulated yet. The time element for example is going to be replaced by an iteration counter, and the specific constants by some more general ones hopefully preserving the relationships
(b*m*c^2+(a1*p1+a2*p2+a3*p3)*c)*z=i*h*d(z)/dt : a working note on diracs equation.
(b*m*c^2+(a1*p1+a2*p2+a3*p3)*c)*z=i*h*d(z)/dt : a working note on diracs equation.
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on June 15, 2010, 08:59:08 AM
A couple of sculptures using the protoforms
z=z^(-2)+0.1*Z+c^(-1) (http://www.fractalforums.com/gallery/2/410_15_06_10_8_45_34_0.png)
z=z^(-2)+0.1*flip(Z)+c^(-1) (http://www.fractalforums.com/gallery/2/410_15_06_10_8_45_34_1.png)
These suggest the conjecture that black holes form in pairs linked by a gravitational wormhole. :embarrass:
And notice the black holes are not symmetric or equal in cross section, and can have a distorted event horizon.
I am just glad the form sculpts out elliptical shapes!
z=z^(-2)+0.1*Z+c^(-1) (http://www.fractalforums.com/gallery/2/410_15_06_10_8_45_34_0.png)
z=z^(-2)+0.1*flip(Z)+c^(-1) (http://www.fractalforums.com/gallery/2/410_15_06_10_8_45_34_1.png)
These suggest the conjecture that black holes form in pairs linked by a gravitational wormhole. :embarrass:
And notice the black holes are not symmetric or equal in cross section, and can have a distorted event horizon.
I am just glad the form sculpts out elliptical shapes!
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on July 05, 2010, 04:12:10 AM
Some sculpts from the schroedinger equation. Very rough translation to Quasz.
(http://www.fractalforums.com/gallery/2/410_05_07_10_3_56_22_4.png)
http://www.fractalforums.com/gallery/2/410_05_07_10_3_56_22_3.png (http://www.fractalforums.com/gallery/2/410_05_07_10_3_56_22_3.png) (http://www.fractalforums.com/gallery/2/410_05_07_10_3_56_22_2.png)(http://www.fractalforums.com/gallery/2/410_05_07_10_3_56_22_1.png)
And finally
(http://www.fractalforums.com/gallery/2/410_05_07_10_3_56_22_0.png)
(http://www.fractalforums.com/gallery/2/410_05_07_10_3_56_22_4.png)
http://www.fractalforums.com/gallery/2/410_05_07_10_3_56_22_3.png (http://www.fractalforums.com/gallery/2/410_05_07_10_3_56_22_3.png) (http://www.fractalforums.com/gallery/2/410_05_07_10_3_56_22_2.png)(http://www.fractalforums.com/gallery/2/410_05_07_10_3_56_22_1.png)
And finally
(http://www.fractalforums.com/gallery/2/410_05_07_10_3_56_22_0.png)
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on July 08, 2010, 10:23:21 AM
So i refine the laplace to reflect its operation better and i get this
(http://www.fractalforums.com/gallery/2/410_08_07_10_8_33_14_2.png)
This is a sculpture of the d shells possibly.
Then i get this as an initial iteration with baiout 4
(http://www.fractalforums.com/gallery/2/410_08_07_10_8_33_13_0.png)
Which turns out to be what is left of this which is bailout 1000 (http://www.fractalforums.com/gallery/2/410_09_07_10_2_31_03_0.png)
Which seen in context looks like this (http://www.fractalforums.com/gallery/2/410_09_07_10_2_31_06_1.png)
which on iteration begins to morph like this (http://www.fractalforums.com/gallery/2/410_09_07_10_2_52_04_0.png) (http://www.fractalforums.com/gallery/2/410_09_07_10_2_52_05_1.png) (http://www.fractalforums.com/gallery/2/410_09_07_10_2_52_05_2.png)
which when seen close looks like the bailout 4 sculpture .
Over time then the s shell fades to a weak p shell? Is the s shell correctly identified here or is it showing 2 strong p shells fading?
Is this fractal sculpture in any way near the Schroedinger equation outputs?
(http://www.fractalforums.com/gallery/2/410_08_07_10_8_33_14_2.png)
This is a sculpture of the d shells possibly.
Then i get this as an initial iteration with baiout 4
(http://www.fractalforums.com/gallery/2/410_08_07_10_8_33_13_0.png)
Which turns out to be what is left of this which is bailout 1000 (http://www.fractalforums.com/gallery/2/410_09_07_10_2_31_03_0.png)
Which seen in context looks like this (http://www.fractalforums.com/gallery/2/410_09_07_10_2_31_06_1.png)
which on iteration begins to morph like this (http://www.fractalforums.com/gallery/2/410_09_07_10_2_52_04_0.png) (http://www.fractalforums.com/gallery/2/410_09_07_10_2_52_05_1.png) (http://www.fractalforums.com/gallery/2/410_09_07_10_2_52_05_2.png)
which when seen close looks like the bailout 4 sculpture .
Over time then the s shell fades to a weak p shell? Is the s shell correctly identified here or is it showing 2 strong p shells fading?
Is this fractal sculpture in any way near the Schroedinger equation outputs?
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on September 19, 2010, 09:34:58 AM
(http://www.fractalforums.com/gallery/3/999_13_09_10_1_05_46.jpeg)
Nice molecular, crystal lattice, with possible s,p and d shells showing. Inspiring!
Nice molecular, crystal lattice, with possible s,p and d shells showing. Inspiring!
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on October 07, 2010, 01:35:02 PM
An archimedian spiral requires a logarithmic increase in radius per iteration, while a golden ratio type spiral requires an exponential increase.
So z= r*e^z+c and z= r*ln(z)+c should be interesting julias.
So z= r*e^z+c and z= r*ln(z)+c should be interesting julias.
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on January 19, 2011, 10:11:11 AM
I watched a programme called Beautiful Equations (http://www.bbc.co.uk/programmes/b00wltbm/buzz) today , and it gladdens my heart to see artists and mathematicians and scientists once more united, reunited after a centuries long process of abstraction and dissociation . As human animates we are connected more than we are distinguished, and although distinctions are important they are not barriers between us, but stepping stones to different vantage points from which to view our common experience.
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on January 19, 2011, 08:29:05 PM
In the beautiful equations Matthew Collings is given a glimpse of a positron in a cloud chamber!
the Dirac equation was presented as
being a "twistor".
I will have a go at sculpting this.
Interestingly the cloud chamber reminded me of the dynamic magnitudes around and in me, and was the first glimpse of a dynamic relativity measure. It showed me how measurement is dynamic instantaneous, vectored, and aggregations of plethorate units which are dynamic.The particles in the cloud chamber were illuminated, drifting in Brownian motion, and their geometric relation was what was altered vectorially to show the positron path. The slight change in aggregational density was visible vectorially, a tensor relationship made visible in the clouds for an instant.
the Dirac equation was presented as
I will have a go at sculpting this.
Interestingly the cloud chamber reminded me of the dynamic magnitudes around and in me, and was the first glimpse of a dynamic relativity measure. It showed me how measurement is dynamic instantaneous, vectored, and aggregations of plethorate units which are dynamic.The particles in the cloud chamber were illuminated, drifting in Brownian motion, and their geometric relation was what was altered vectorially to show the positron path. The slight change in aggregational density was visible vectorially, a tensor relationship made visible in the clouds for an instant.
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on January 26, 2011, 12:22:38 PM
Betchen sent me this.
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on April 21, 2011, 06:46:21 AM
I love digging around in the dark, and then blue-skying with what i find, just as i feel it!
However Doug (http://www.quaternions.com/) really knows what he is talking about.
Doug's metric i suddenly realised is a kind of Trochoidal matrix.
doug Explains it actually was discovered by Rosen.
Here is the metric in tensor form
,-\exp \left( \frac{2GM}{c^{2}R} \right),-\exp \left( \frac{2GM}{c^{2}R} \right),-\exp \left( \frac{2GM}{c^{2}R} \right) \right\})
in quaternion form
\hat{e}-\exp \left( \frac{2GM}{c^{2}R} \right)\hat{i}-\exp \left( \frac{2GM}{c^{2}R} \right)\hat{j}-\exp \left( \frac{2GM}{c^{2}R} \right)\hat{k} \right\})
.
I have to figure out how to Quasz this, but it does remind me of a whole load of trochoid experiments i did late last year.
Here's Doug explaining what it means.
http://www.youtube.com/watch?v=XW7CzyE6Fjc
However Doug (http://www.quaternions.com/) really knows what he is talking about.
Doug's metric i suddenly realised is a kind of Trochoidal matrix.
doug Explains it actually was discovered by Rosen.
Here is the metric in tensor form
in quaternion form
I have to figure out how to Quasz this, but it does remind me of a whole load of trochoid experiments i did late last year.
Here's Doug explaining what it means.
http://www.youtube.com/watch?v=XW7CzyE6Fjc
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on August 20, 2011, 01:07:06 PM
Quote
Description: This was made using the following operations: inversion+rotation+scaling+translation
No "mirroring" folds used
UF5 code (iteration part):
Code:
if |z|<1
z=z/|z|
endif
z=z*exp(1i*pi/180*@angle)*@scale+c
No "mirroring" folds used
UF5 code (iteration part):
Code:
if |z|<1
z=z/|z|
endif
z=z*exp(1i*pi/180*@angle)*@scale+c
Kali wrote this formula, in which the scale and angle are changed throughout the iterations. This is a 2d/3d formula and i will work on a 3d form of it.
(http://nocache-nocookies.digitalgott.com/gallery/8/3869_20_08_11_4_33_44.jpeg)
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on November 12, 2011, 09:52:04 AM
This is my gravito electromagnetic formula.
(http://nocache-nocookies.digitalgott.com/gallery/9/410_12_11_11_11_07_24.png)
It basically models the effect of inverse square laws and inverse laws on space. I like to toy with the idea that gravity is some fractal arrangement of electromagnetism and this is my thinking so far. This is for a 2 body system with some kind of rotational relativity, one body being 20 times as massive as the other. whatever that means! ;D
Enjoy.
If you use Quasz, you can change the surface noise settings to remove a lot of clean up placed there to give control over surface output. I like to think that the system in space does not really have this option! :embarrass:
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on November 20, 2011, 11:47:29 AM
I am exploring some formulae around gravity and electromagnetism using Quasz. Certain vectors and vector/tensor combinations are becoming familiar to me, and complex and quaternion vector algebras are providing models of space-time . Because the fractal generator is effectively a cutting tool the models produced are in "negative" in a sense, with surfaces and bound regions representing less volatile regions.
(http://nocache-nocookies.digitalgott.com/gallery/9/410_20_11_11_11_21_28.png)
The models so far exhibit a big rotational vortex precedes a calmer steady state-like phase. The rotational region continues out at the edge of the universe, clearly weaker.
(http://nocache-nocookies.digitalgott.com/gallery/9/410_20_11_11_11_30_12.png)
(http://nocache-nocookies.digitalgott.com/gallery/9/410_20_11_11_11_21_28.png)
The models so far exhibit a big rotational vortex precedes a calmer steady state-like phase. The rotational region continues out at the edge of the universe, clearly weaker.
(http://nocache-nocookies.digitalgott.com/gallery/9/410_20_11_11_11_30_12.png)
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on November 23, 2011, 08:19:37 PM
This is the quaternion base of the tensor used in producing the above images
G,M,c are constants, R is a vector with 3 components, but i used a quaternion with 4 components, the 4th being a sort of radius.
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on August 24, 2012, 12:30:56 PM
In quasz Terry has an in built function number 37 which corresponds to the second manifold tensor candidate with n set to 0 and c instead of 1/c.
1/z^2 + c
The first sculpture is an image of a Minkowski torus with a gravity well structure that is complex
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_37_08_0.png)
the second looks into the gravity well structure
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_37_08_1.png)
the third shows the torus shape followed by 2 other views
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_37_08_2.png)
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_37_08_3.png)
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_37_08_4.png)
I then take a look at the gravity well structure which passes completely through the torus but not symmetrically and the structure appears to be the result of antisymmetric action from the other side of the torus
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_48_18_0.png)
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_48_18_3.png)
I then show the spatial structure with the wells
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_48_18_1.png)
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_48_18_2.png)
The sculptures are sensitive to the seed points with the real coefficient of the seed determining the toroidal shape while the i and j coefficients seem to determine the well structure. The anti symmetry is due to rotation not reflection which is a translation in relativistic motion i am currently cogitating.
The mandelbrots are informative especially mandelbrotp but i have no cosmological referent for the mandelbrot boundary conditions yet in mind.
Each sculpture relies on the quad motion statement in quasz and the cutting boundary |z|≤4. This parameter has much to do with the eventual form and surface structures of the sculpture and i am exploring form and structures in spaciometry.
1/z^2 + c
The first sculpture is an image of a Minkowski torus with a gravity well structure that is complex
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_37_08_0.png)
the second looks into the gravity well structure
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_37_08_1.png)
the third shows the torus shape followed by 2 other views
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_37_08_2.png)
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_37_08_3.png)
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_37_08_4.png)
I then take a look at the gravity well structure which passes completely through the torus but not symmetrically and the structure appears to be the result of antisymmetric action from the other side of the torus
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_48_18_0.png)
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_48_18_3.png)
I then show the spatial structure with the wells
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_48_18_1.png)
(http://www.fractalforums.com/gallery/2/410_05_06_10_8_48_18_2.png)
The sculptures are sensitive to the seed points with the real coefficient of the seed determining the toroidal shape while the i and j coefficients seem to determine the well structure. The anti symmetry is due to rotation not reflection which is a translation in relativistic motion i am currently cogitating.
The mandelbrots are informative especially mandelbrotp but i have no cosmological referent for the mandelbrot boundary conditions yet in mind.
Each sculpture relies on the quad motion statement in quasz and the cutting boundary |z|≤4. This parameter has much to do with the eventual form and surface structures of the sculpture and i am exploring form and structures in spaciometry.
I now have a referent and that is the Van Allen radiation belts that surround the planet. The details of this model are crude, but then it is a crude inverse square law motion in a constant solar pressure field c. The two wells correspond well with the aurora borealis effects of the magnetic field effect. That electric and magnetic effects are not well differentiated is again due to the crudeness of the model.
In my blog I discuss the electromagnetic origin of gravity.
http://jehovajah.wordpress.com/jehovajah/blog/newtons-magnetic-gravity-6 (http://jehovajah.wordpress.com/jehovajah/blog/newtons-magnetic-gravity-6)
I also discuss the controversial origin of the manifold concept in Die Mannigfaeltigkeit in my blog post archives.
I am currently looking at quaternions in detail to understand better how to model these relations in sculptures by Quasz
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on July 17, 2013, 08:48:17 AM
http://jehovajah.wordpress.com/jehovajah/blog/2013/07/17/newtonian-fluid-motive-as-spacematter
(http://nocache-nocookies.digitalgott.com/gallery/14/410_17_07_13_8_35_41.png)
This is both Newton's and Maxwell"s conception of Spacematter or the Aether. It is a fluid that is fractal and forms these corpuscular vortices.
What are they?
Our perception of the dynamic metaphysical energy all around us, the Newtonian motive which Maxwell envisaged as vortices of electic and magnetic fluids, after Faraday.
However, read my research to distinguish carefully between motive as matter and the concept of matter.
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on April 25, 2014, 05:51:10 AM
Sometimes I frighten myself! When I look back over my blue skying and find I have written something I clearly did not understand at the time, and then when I come to note something I do understand I find I have already written it!
In this candidate post I write down basically a Fourier series type formulation, based on my current research into Grassmann's Vorrede to the 1844 Ausdehnungslehre.
This represents the Newtonian fluid motive ie the energy plasma motive of pure space and in pure space as the electro Thermo magneto fluid element complexes of our formal subjective processing.
(coshmx+ sinhnx)•exp( cospx+isinqx+jsinrx+ksinsx)
For m,n,p,q,r,s as independent frequencies from 1 to N and -
<x<
And can have as many terms as feasible or desired.
In fact I do not restrict the arguments of the trig functions to x in the quaternion iteration in Quasz. More interesting results are generated using x#,y#,imaj(z), imak(z) appropriately.
The sinhx + coshx *)represents the radial extension usually associated with electrostatic energy, but Ivor Catt has shown there is no electrostatic energy! Rather this energy he says is constantly dynamic. However I do not even regard it as electric or magnetic. It is the radial expansion component of a vortex spatial dynamic, the rotational component cospx+isinqx+jsinrx+ksinsx , usually considered as the Magnetostatic energy is in my view the rotational component of the vortices In space and of space.
Magnetism, as empirically evidenced in a wire or a lodestone is due to the organised structuring of these spatial vortices. In particular in a twisted copper wire, the induction process of the vast sea of vorticular motion rolling onto the wire organises and concentrates the vortices to stretch out along it's length. The twist is put into the wire in its manufacturing process as it is drawn.
The inductive action is by Maxwell defined as conduction, and thus conductivity and inductivity are the same measure.
Because the new science wanted to distinguish itself, and because of industrial and corporate concerns and patents we lost sight of the simple Gilbert plasma model for these Phenomena.
While this formula is just the description, I will use it to generate some sculptures of how this iterates through space in its manifold forms and constraints, both as a Julia type and as a Mandelbrot type
*) also I use coshx + i*sinhx as a direct vector form of the radius, as Grassmann derives his concept using a general trig line segment! It gives similar results but shaped differently.
In this candidate post I write down basically a Fourier series type formulation, based on my current research into Grassmann's Vorrede to the 1844 Ausdehnungslehre.
This represents the Newtonian fluid motive ie the energy plasma motive of pure space and in pure space as the electro Thermo magneto fluid element complexes of our formal subjective processing.
For m,n,p,q,r,s as independent frequencies from 1 to N and -
And
In fact I do not restrict the arguments of the trig functions to x in the quaternion iteration in Quasz. More interesting results are generated using x#,y#,imaj(z), imak(z) appropriately.
The sinhx + coshx *)represents the radial extension usually associated with electrostatic energy, but Ivor Catt has shown there is no electrostatic energy! Rather this energy he says is constantly dynamic. However I do not even regard it as electric or magnetic. It is the radial expansion component of a vortex spatial dynamic, the rotational component cospx+isinqx+jsinrx+ksinsx , usually considered as the Magnetostatic energy is in my view the rotational component of the vortices In space and of space.
Magnetism, as empirically evidenced in a wire or a lodestone is due to the organised structuring of these spatial vortices. In particular in a twisted copper wire, the induction process of the vast sea of vorticular motion rolling onto the wire organises and concentrates the vortices to stretch out along it's length. The twist is put into the wire in its manufacturing process as it is drawn.
The inductive action is by Maxwell defined as conduction, and thus conductivity and inductivity are the same measure.
Because the new science wanted to distinguish itself, and because of industrial and corporate concerns and patents we lost sight of the simple Gilbert plasma model for these Phenomena.
While this formula is just the description, I will use it to generate some sculptures of how this iterates through space in its manifold forms and constraints, both as a Julia type and as a Mandelbrot type
*) also I use coshx + i*sinhx as a direct vector form of the radius, as Grassmann derives his concept using a general trig line segment! It gives similar results but shaped differently.
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on April 26, 2014, 04:06:08 AM
The attachments show some initial research results with Quasz and variations of the above expressiion.While these do not look like "wave" patterns they are, and the scale at which that becomes viewable obscures these details, and the almost similarity of the large structure and some of the smaller structures in the second image.
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on April 26, 2014, 08:11:46 PM
The posted equation does not produce an interesting julia. It is in fact a blank space until bailout 22.03 , then it is a uniform density . It represents either a cloud or an intense density. however the mandy type produces the attached sculpture.
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on April 29, 2014, 04:11:47 AM
This incredible formulation already produces a rich variety of sculptures applicable to all scales from the quantum to the cosmological
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on April 29, 2014, 04:55:29 AM
To place this thread in its context view this general discussion.
http://youtube.com/watch?v=XDAJinQL2c0
While I do not hold the same opinion as the good professor, nevertheless the empirical data does require intuitive models based on geometry and a prior Mechsnics. The results obtained by using Grassmanns analytical concepts, even partially understood are very illuminating.. I claim that thermodynamics is an incomplete theory, completed only in electromagnetodynamics, which itself is inconsistent without thermodynamics.
Further more, this complex of principles has one simplifying notion : that of rotating space dynamically dilating at all scales.
My sculptures are an attempt to show this notion has merit as a formal model .
http://youtube.com/watch?v=XDAJinQL2c0
While I do not hold the same opinion as the good professor, nevertheless the empirical data does require intuitive models based on geometry and a prior Mechsnics. The results obtained by using Grassmanns analytical concepts, even partially understood are very illuminating.. I claim that thermodynamics is an incomplete theory, completed only in electromagnetodynamics, which itself is inconsistent without thermodynamics.
Further more, this complex of principles has one simplifying notion : that of rotating space dynamically dilating at all scales.
My sculptures are an attempt to show this notion has merit as a formal model .
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on April 24, 2015, 07:42:37 AM
I merely note a whimsical notion that derives from my research into Hermann and Justus Grassmanns work. It is that the fundamental line element of space is a trochoidal line element that spirals and twists! Fluttering and flitting away !
The Grassmanns give us a direct expressive way to describe such stringlike structures in a status matrix that can model local dynamics.
The methods give us a hands on way to study natural dynamics and set out an algebraic label that can be manipulated manually to mimic the behaviour. Then we can explore the product design of such labels to see if they provide useful calculations that capture the complexity of natural movements.
Only then can we design a computer algorithm that generates model behaviours by design.
In the past I was taught to get hot and excited by these "mathematical" algorithms, but now I realise that that is like getting excited by a sculpture of a tree and ignoring the living tree!
But, I have been searching for an explanatory label to describe fluid dynamics specifically as well as generally. Such labels can lead to a language that makes it easier to discuss fluid dynamic observations and data measurements, and thus to develop expertise.
What is a manifold? It is the span of such line element systems, however many we place in the basis structure.
String theory wants to put at mostt 11 creating elements in a trochoidal line element . 3 such trochoidal line segments should form a system that models our space from quantum o classical magnitudes?
The Grassmanns give us a direct expressive way to describe such stringlike structures in a status matrix that can model local dynamics.
The methods give us a hands on way to study natural dynamics and set out an algebraic label that can be manipulated manually to mimic the behaviour. Then we can explore the product design of such labels to see if they provide useful calculations that capture the complexity of natural movements.
Only then can we design a computer algorithm that generates model behaviours by design.
In the past I was taught to get hot and excited by these "mathematical" algorithms, but now I realise that that is like getting excited by a sculpture of a tree and ignoring the living tree!
But, I have been searching for an explanatory label to describe fluid dynamics specifically as well as generally. Such labels can lead to a language that makes it easier to discuss fluid dynamic observations and data measurements, and thus to develop expertise.
What is a manifold? It is the span of such line element systems, however many we place in the basis structure.
String theory wants to put at mostt 11 creating elements in a trochoidal line element . 3 such trochoidal line segments should form a system that models our space from quantum o classical magnitudes?
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on February 04, 2016, 06:18:53 PM
http://m.youtube.com/watch?v=35Y7u_VDrww
It has been a while since I posted an update, but it has taken until now to see images published that look like the sculptures of those motion equations i was experimenting with so long ago!
It really indicates to me that iteration, rotation and fractal geometry is the most fruitful process for modelling natural phenomrena at all scales !
It has been a while since I posted an update, but it has taken until now to see images published that look like the sculptures of those motion equations i was experimenting with so long ago!
It really indicates to me that iteration, rotation and fractal geometry is the most fruitful process for modelling natural phenomrena at all scales !
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on March 15, 2016, 02:38:34 AM
http://m.youtube.com/watch?v=bdHkgtLgcSY
Many images show the fractal patterning achieved by fractal apps . It suggests that iterative processes have fractal outcomes because rotation is involved at all levels
Many images show the fractal patterning achieved by fractal apps . It suggests that iterative processes have fractal outcomes because rotation is involved at all levels
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on March 25, 2016, 07:38:47 PM
It behoves me to talk a little bit about space-time, about manifolds( Mannigfähltigkeit) and about Tensors.
Firstly Tensors are exactly what Hermnn Grassmann describes as,
Ausdehnungs Größe. It is rather technical but basically they are descriptions of extensive or intenive magnitudes in space . Relative to a specified space/ spatial object they describe in a lineal combinatorial format any or all relevant extensive magnitudes associated to that region. Thus a tensor provides a full description of a region and an opportunity to model the full dynamic behaviour of said region under dynamic circumstances.
It is a very general view which only has purpose if the specific aspect of interest falls out of the more general procedural manipulations.
So now we take a tensor as specifying a region. A manifold therefore is a varied collection of such Tensors. Together they describe a much bigger region or more regions of space. The many "folded ness " of these tensor collections represent the vorticular/rotational dynamic of space. Consequently the best representation of a manifold will be a complex lineal combinatorial arrangment of twistors, or if you prefer a complex 3d analysis of space in the Fourier transform format.
There are 2 Grassmannn representations of this type of high level(Stüfe) or grade Ausdehnungs Größe: the line segment version and the arc segment version. The arc segment version correspond to what I named a twistor ( not claiming priority) and which correponds to a very general Fourier Transform or a system/ collection of such. As a system they may be considered as a reference frame or a basis.
So now we come to spacetime. In fact the notion goes back at least to Galileo and probably back to the Greek mechanics. You are not able to describe a dynamic without some reference to positions( space) and some regularly changing dynmic! Yes it is circular!
Our system of measurement is Fractal and ased on the topological and Dynamical distinctions we adopt as Metron. We then proceed by proportioning these Metrons . The process is idntical for all measures, thus we hardly can in general proceed differently with spatial magnitudes and dynamical ones.
Distance and time thus fall out as a particular interpretation of a more general n-level process.
The concept of space-time in its general sense is a mathmatical abstraction( that is a contentless label / topology) which holds the general direction we wish to go in in our development of a dynamic descriptive system.
So we describe an aether philosophically according to Grassmann in this way specifying the content in general form and developing specific interpretations of the general tensor formats.
Firstly Tensors are exactly what Hermnn Grassmann describes as,
Ausdehnungs Größe. It is rather technical but basically they are descriptions of extensive or intenive magnitudes in space . Relative to a specified space/ spatial object they describe in a lineal combinatorial format any or all relevant extensive magnitudes associated to that region. Thus a tensor provides a full description of a region and an opportunity to model the full dynamic behaviour of said region under dynamic circumstances.
It is a very general view which only has purpose if the specific aspect of interest falls out of the more general procedural manipulations.
So now we take a tensor as specifying a region. A manifold therefore is a varied collection of such Tensors. Together they describe a much bigger region or more regions of space. The many "folded ness " of these tensor collections represent the vorticular/rotational dynamic of space. Consequently the best representation of a manifold will be a complex lineal combinatorial arrangment of twistors, or if you prefer a complex 3d analysis of space in the Fourier transform format.
There are 2 Grassmannn representations of this type of high level(Stüfe) or grade Ausdehnungs Größe: the line segment version and the arc segment version. The arc segment version correspond to what I named a twistor ( not claiming priority) and which correponds to a very general Fourier Transform or a system/ collection of such. As a system they may be considered as a reference frame or a basis.
So now we come to spacetime. In fact the notion goes back at least to Galileo and probably back to the Greek mechanics. You are not able to describe a dynamic without some reference to positions( space) and some regularly changing dynmic! Yes it is circular!
Our system of measurement is Fractal and ased on the topological and Dynamical distinctions we adopt as Metron. We then proceed by proportioning these Metrons . The process is idntical for all measures, thus we hardly can in general proceed differently with spatial magnitudes and dynamical ones.
Distance and time thus fall out as a particular interpretation of a more general n-level process.
The concept of space-time in its general sense is a mathmatical abstraction( that is a contentless label / topology) which holds the general direction we wish to go in in our development of a dynamic descriptive system.
So we describe an aether philosophically according to Grassmann in this way specifying the content in general form and developing specific interpretations of the general tensor formats.
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on March 26, 2016, 09:06:04 AM
https://see.stanford.edu/materials/lsoftaee261/chap8.pdf
In this particular presentation, the Fourier is notated in vector form. This is a simplification that avoids a more compact quaternionic format, but one which is too unfamiliar for most scientists and engineers.
The quaternionic form is topologically describing arbitrary rotations in space about a point. Even Grassmann found this difficult to apprehend in 1844, but by the time 1877 came around he had written a paper called " w
Where Halmiltonian quaternions can be found in the Extensive Magnitude Doctrine". I am part way through translating this paper but have elected to do the background work on Justus seminal combinatorics which underpins all Hermann and Roberts thinking or thought forms.
Suffice it to say that Bill Clifford appreciated this and laid the foundation for the Grassmann Clifford Algbras elicitly for describing "undulatory" systems, that is to say Manifolds!
In this particular presentation, the Fourier is notated in vector form. This is a simplification that avoids a more compact quaternionic format, but one which is too unfamiliar for most scientists and engineers.
The quaternionic form is topologically describing arbitrary rotations in space about a point. Even Grassmann found this difficult to apprehend in 1844, but by the time 1877 came around he had written a paper called " w
Where Halmiltonian quaternions can be found in the Extensive Magnitude Doctrine". I am part way through translating this paper but have elected to do the background work on Justus seminal combinatorics which underpins all Hermann and Roberts thinking or thought forms.
Suffice it to say that Bill Clifford appreciated this and laid the foundation for the Grassmann Clifford Algbras elicitly for describing "undulatory" systems, that is to say Manifolds!
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on March 26, 2016, 09:38:31 AM
http://glow-wacky.com/2013/03/21/2d-and-3d-fourier-transforms/
Here you will see a simple manifold on the left and the " array" of amplitudes of the Fourier transform on the right.
We can represent the manifold by arrays of amplitude data in the traditional
Complex format . The quaternionic format or higher will thus be represent able as arrays of data.
The process of linear transformations therefore encapsulates at a general level how we process arrays of data sets. MRI scanning is perhaps the most heard of , but least understood commonly , application of this kind of processing. Without computational machines this representation would be completely useless to us even though conceived in principle by Grassmann in 1844.
Despite the greater acceptance of quaternions over the Lineal Algebra of Grassmann, Hamilton was generous enough to regard Hermann Grassmann as his Master! Of all the people who could appreciate the Ausdehnungslehre 1844 Hamilton was the best placed to appreciate its philosophical significance as well as its scientific one. He strove to generalise his work beyond quaternions both for personal and academic reasons but mainly because he believed he had the. Methid of describing the electrical aether!
Here you will see a simple manifold on the left and the " array" of amplitudes of the Fourier transform on the right.
We can represent the manifold by arrays of amplitude data in the traditional
Complex format . The quaternionic format or higher will thus be represent able as arrays of data.
The process of linear transformations therefore encapsulates at a general level how we process arrays of data sets. MRI scanning is perhaps the most heard of , but least understood commonly , application of this kind of processing. Without computational machines this representation would be completely useless to us even though conceived in principle by Grassmann in 1844.
Despite the greater acceptance of quaternions over the Lineal Algebra of Grassmann, Hamilton was generous enough to regard Hermann Grassmann as his Master! Of all the people who could appreciate the Ausdehnungslehre 1844 Hamilton was the best placed to appreciate its philosophical significance as well as its scientific one. He strove to generalise his work beyond quaternions both for personal and academic reasons but mainly because he believed he had the. Methid of describing the electrical aether!
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on April 21, 2016, 01:44:01 PM
My recent meditations lead me to concentrate on Sir Roger Coaes natural logarithmic form for arc segment identity, especially as it is expressed in quaternionic format?
If the twistor is a Fourier transform in general, the "function" the transform is modelling is a form in space.
Thus the twistor or quaternionic Fourier transform models a spatial region or trochoidal bubble form. This form is adequate as a space-time manifold but is generally too complex to visualise. The Quasz sculptures of twistors are more the results of QFTs of these manifolds.
Using that line of analysis, the natural logarithm of the twistor should return exponentialed manifold form . That is, the natural logarithm of a general twistor should sculpt a space-time manifold directly, consisting of frequency and amplitude data.
Quite apart from suggesting that the data array of a Fourier transform Is a logarithmic transformation, it also makes possible the concept that a logarithmic transformation of a twistor/ QFT will give back the appropriate space- time manifolds analysis( into frequencies and amplitudes) as plotable sculptures.
I have experimented blindly with this in a couple of Gallery posts called Coatesgravity etc.
The reason for that name is my belief, as yet unfounded on documentation, that Cotes in his Harmonium Mensuraram was about to suggest this idea to Newton as a formulation of Gravity equations , but far more as a description of any absolute space with the Newtonian 3 force characteristics. Thus a dynamic space encompassing magnetic, sonic, thermic and electric behaviours.
(http://nocache-nocookies.digitalgott.com/gallery/5/410_26_01_11_1_32_17_0.png)
If the twistor is a Fourier transform in general, the "function" the transform is modelling is a form in space.
Thus the twistor or quaternionic Fourier transform models a spatial region or trochoidal bubble form. This form is adequate as a space-time manifold but is generally too complex to visualise. The Quasz sculptures of twistors are more the results of QFTs of these manifolds.
Using that line of analysis, the natural logarithm of the twistor should return exponentialed manifold form . That is, the natural logarithm of a general twistor should sculpt a space-time manifold directly, consisting of frequency and amplitude data.
Quite apart from suggesting that the data array of a Fourier transform Is a logarithmic transformation, it also makes possible the concept that a logarithmic transformation of a twistor/ QFT will give back the appropriate space- time manifolds analysis( into frequencies and amplitudes) as plotable sculptures.
I have experimented blindly with this in a couple of Gallery posts called Coatesgravity etc.
The reason for that name is my belief, as yet unfounded on documentation, that Cotes in his Harmonium Mensuraram was about to suggest this idea to Newton as a formulation of Gravity equations , but far more as a description of any absolute space with the Newtonian 3 force characteristics. Thus a dynamic space encompassing magnetic, sonic, thermic and electric behaviours.
(http://nocache-nocookies.digitalgott.com/gallery/5/410_26_01_11_1_32_17_0.png)
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on April 23, 2016, 12:41:31 PM
http://m.youtube.com/watch?v=oNqSzzycRhw
It occurs that QFT might automatically by the process provide a Finite Element Grid for this method and thus provide a speedier analysis of complex dynamical situations
It occurs that QFT might automatically by the process provide a Finite Element Grid for this method and thus provide a speedier analysis of complex dynamical situations
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on April 23, 2016, 01:41:28 PM
http://m.youtube.com/watch?v=o2Vlt1avXCs
The theoretical method which Hermann Grassmann was conceiving to present by lineal Algebra. The classical problem was laid out by the French Mathematicians in a way difficult Tom"see" on the page . It was a clear as mud! Hermann claimed to offer shining clarity!
The theoretical method which Hermann Grassmann was conceiving to present by lineal Algebra. The classical problem was laid out by the French Mathematicians in a way difficult Tom"see" on the page . It was a clear as mud! Hermann claimed to offer shining clarity!
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on April 28, 2016, 02:27:12 AM
http://math.stackexchange.com/questions/2552/the-logarithm-of-quaternion
One of the major difficulties I faced was understanding logarithms. But my research into the history dispelled the myths I had been taught. Later I became aware of the role of identities, over equalities and the role of labels and product design, and it's attendant rigorous responsibilities.
Euler in expressing the exponential in an infinite series , that is a power series that evaluated to the exponential of a rational power , was able to show that the structure could bear an identity. Thus the same structure allowed any symbol to be replaced by any other symbol throughout. Thus he was able to found the Cotes Euler formula on an algebraic structure which encoded a process of calculation. That process resulted in a remarkable identy
Exp(ix) = cosx + isinx
This was later developed to express the quaternion and then to express Banach and Clifford algebras.
Cotes decades earlier had made the identity
ix= ln( cosx + isinx)
From which we can easily expect the logarithm of a quaternion to be the complex combinatorial part .
Exponents and logarithms are just another use of an Arithmos that is a mosaical structure which is countable as well as measurable and spatial. As the symbols are identities we do nothing really new by implementing them in our computer applications. They are all quaternions in this discussion and as such the same structure produces the same results regardless of the underlying elemental behaviour.
Therefore the fact that we can develop a Fourier quaternion Transform means that regardless of whether it is expressed in exponential combinatorial forms or logarithmic combinatorial forms the same out put should result for the same structural format. That is up to the variation in the way the exponential and the logarithmic functions increase toward infinity and decrease toward 0
One of the major difficulties I faced was understanding logarithms. But my research into the history dispelled the myths I had been taught. Later I became aware of the role of identities, over equalities and the role of labels and product design, and it's attendant rigorous responsibilities.
Euler in expressing the exponential in an infinite series , that is a power series that evaluated to the exponential of a rational power , was able to show that the structure could bear an identity. Thus the same structure allowed any symbol to be replaced by any other symbol throughout. Thus he was able to found the Cotes Euler formula on an algebraic structure which encoded a process of calculation. That process resulted in a remarkable identy
Exp(ix) = cosx + isinx
This was later developed to express the quaternion and then to express Banach and Clifford algebras.
Cotes decades earlier had made the identity
ix= ln( cosx + isinx)
From which we can easily expect the logarithm of a quaternion to be the complex combinatorial part .
Exponents and logarithms are just another use of an Arithmos that is a mosaical structure which is countable as well as measurable and spatial. As the symbols are identities we do nothing really new by implementing them in our computer applications. They are all quaternions in this discussion and as such the same structure produces the same results regardless of the underlying elemental behaviour.
Therefore the fact that we can develop a Fourier quaternion Transform means that regardless of whether it is expressed in exponential combinatorial forms or logarithmic combinatorial forms the same out put should result for the same structural format. That is up to the variation in the way the exponential and the logarithmic functions increase toward infinity and decrease toward 0
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on September 03, 2016, 10:25:34 AM
http://m.youtube.com/watch?v=lqkTcJH5Bw0
This is Jupiter imaged by the Juno satellite.
The fractal images and sounds have been naively explored in this forum by some of our most innovative explorers.
I will try to post links to where , but if you know post them here p,ease xxx
This is Jupiter imaged by the Juno satellite.
The fractal images and sounds have been naively explored in this forum by some of our most innovative explorers.
I will try to post links to where , but if you know post them here p,ease xxx
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on September 11, 2016, 06:43:08 AM
https://m.youtube.com/watch?v=zFMJaVCXXFo
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on October 06, 2016, 10:18:12 AM
One of the difficulties of understanding a fractal sculpture is the so called iterated function format.
The quaternion format is misrepresented at a fundamental level among physicists and astronomers and mathematicians. But amongst Fractalers we have an intuitive grasp of its dynamical applications.
http://m.youtube.com/watch?v=KiDwqnanAYA
Hermann Grassmann claimed that his Ausdehnungslehre could depict many physical dynamical and static situations as well as crystallography., Phorometry and fluid dynamics. Amongst those claims he mentioned magnetism.
Here Bill Gaede attempts to explain magnetism in a dynamical system. The ropes or threads are representative. His mechanical modelnraisescas many questions as it answers but at least does not fob the engineer off with nothing!
Of course the aether is back in vogue as the old guard die off and new technology substantiates plasma and a ethereal substance. The dark matter dark energy response is a breathtaking Mathemythical nonsense parading as physics. It is much simpler to replace it by aether, and to correct the irrational fallacies.
In this thread I have sculpted a quaternion output for Einsteins gravitational theory. The outcome is interesting but hard to interpret. Moreover it applies equally to magnetic as well as gravitational behaviours.
Black hole cosmology and dark matter and dark energy are farcical attempts to hold on to funding streams. At the same time the trochoidal dynamic of the current gravitational theory does create a surface distribution which highlights curvature and rotation in an evolving system at any scale.
Gravity fails at a radius depending on the mass distribution , and that is why Newton was only concerned with our solar system and bodies moving within it. Outside that he had no idea, data or even comprehension of the vast known universe!
But for sure he would not rely on occult theories to develop astrological principles. The new Newton, that is Sir William Rowan Hamilton was keen to move to an electromagnetic description of the known universe even perhaps ahead of Grassmann who was limited by his circumstances and yet cleared the ground for the modern astrological revolution.
The quaternion format is misrepresented at a fundamental level among physicists and astronomers and mathematicians. But amongst Fractalers we have an intuitive grasp of its dynamical applications.
http://m.youtube.com/watch?v=KiDwqnanAYA
Hermann Grassmann claimed that his Ausdehnungslehre could depict many physical dynamical and static situations as well as crystallography., Phorometry and fluid dynamics. Amongst those claims he mentioned magnetism.
Here Bill Gaede attempts to explain magnetism in a dynamical system. The ropes or threads are representative. His mechanical modelnraisescas many questions as it answers but at least does not fob the engineer off with nothing!
Of course the aether is back in vogue as the old guard die off and new technology substantiates plasma and a ethereal substance. The dark matter dark energy response is a breathtaking Mathemythical nonsense parading as physics. It is much simpler to replace it by aether, and to correct the irrational fallacies.
In this thread I have sculpted a quaternion output for Einsteins gravitational theory. The outcome is interesting but hard to interpret. Moreover it applies equally to magnetic as well as gravitational behaviours.
Black hole cosmology and dark matter and dark energy are farcical attempts to hold on to funding streams. At the same time the trochoidal dynamic of the current gravitational theory does create a surface distribution which highlights curvature and rotation in an evolving system at any scale.
Gravity fails at a radius depending on the mass distribution , and that is why Newton was only concerned with our solar system and bodies moving within it. Outside that he had no idea, data or even comprehension of the vast known universe!
But for sure he would not rely on occult theories to develop astrological principles. The new Newton, that is Sir William Rowan Hamilton was keen to move to an electromagnetic description of the known universe even perhaps ahead of Grassmann who was limited by his circumstances and yet cleared the ground for the modern astrological revolution.
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on October 06, 2016, 10:42:26 AM
I love digging around in the dark, and then blue-skying with what i find, just as i feel it!
However Doug (http://www.quaternions.com/) really knows what he is talking about.
Doug's metric i suddenly realised is a kind of Trochoidal matrix.
doug Explains it actually was discovered by Rosen.
Here is the metric in tensor form
in quaternion form
.
I have to figure out how to Quasz this, but it does remind me of a whole load of trochoid experiments i did late last year.
Here's Doug explaining what it means.
http://m.youtube.com/watch?v=XW7CzyE6Fjc
However Doug (http://www.quaternions.com/) really knows what he is talking about.
Doug's metric i suddenly realised is a kind of Trochoidal matrix.
doug Explains it actually was discovered by Rosen.
Here is the metric in tensor form
<Quoted Image Removed>
in quaternion form
I have to figure out how to Quasz this, but it does remind me of a whole load of trochoid experiments i did late last year.
Here's Doug explaining what it means.
http://m.youtube.com/watch?v=XW7CzyE6Fjc
And the sculpture I figured out.
The two versions show the output from the elements varying directly( as you move through the quaternion block from - through o to +, and secondarily as the inverse of the elements do the same.
The inverse elements give a positive sculpture to the "negative" sculpture of the basic elements .
What we see is a snapshot of how the force dynamics move quaternion points( as representing material points) in the quaternion aether. The spiral form near the origin is hidden in the simple elemental sculpture but revealed in the inverse.
This spiral is a characteristic of the inverse square law and reveals the so called black hole , in the first sculpture to be the entrance to a magnetic curling funnel dynamic.
This is true in the sculpture however the centre is approached so the form is only apparent to this snapshot view, it is a dynamic curvature in space however the centre is approached.
While this is claimed to be gravitational, the result is similar for magnetic dipole forces of rotation
I am exploring some formulae around gravity and electromagnetism using Quasz. Certain vectors and vector/tensor combinations are becoming familiar to me, and complex and quaternion vector algebras are providing models of space-time . Because the fractal generator is effectively a cutting tool the models produced are in "negative" in a sense, with surfaces and bound regions representing less volatile regions.
(http://nocache-nocookies.digitalgott.com/gallery/9/410_20_11_11_11_21_28.png)
The models so far exhibit a big rotational vortex precedes a calmer steady state-like phase. The rotational region continues out at the edge of the universe, clearly weaker.
(http://nocache-nocookies.digitalgott.com/gallery/9/410_20_11_11_11_30_12.png)
(http://nocache-nocookies.digitalgott.com/gallery/9/410_20_11_11_11_21_28.png)
The models so far exhibit a big rotational vortex precedes a calmer steady state-like phase. The rotational region continues out at the edge of the universe, clearly weaker.
(http://nocache-nocookies.digitalgott.com/gallery/9/410_20_11_11_11_30_12.png)
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on October 10, 2016, 09:30:05 AM
http://m.youtube.com/watch?v=2d0hoG67KZA
This derivation follows the vector Algebra of Gibbs and Heaviside supported by Kelvin ..
The products designed ( dot and cross products) have to be explained . Sir William Rowan Hamilton took the imaginary magnitude as founded by Newton DeMoivre and Cotes and Euler and argued over by the Benoullis.
The work of Bombelli created a fundamental basis to the mathesis of the imaginaries, named imaginary by DesCartes, but it is Newton who set out the mathesis in its practical use. It was the basis of Newtons " vector" algebra .
The Fluxion Theory of Hermann Grassmann( Ausdehnungs Größe) explicated the work of Newton to the nth degree, based on the induction process of Newtons fundamental principles.
Hermanns work was takn forward by many but particularly by Bill Clifford. .he made it clear that which Hamilton Acknowledged : The Fluxion theory of Grassmann is more generl, but the same corpus of ideas as Hamiltons. The product design allows many useful models to be constructed for complex lineal algebras, both arced and straight.
This Calculus derivation obscures the direct formulaic processes. The exponential formulaic presentation gives a direct set of applicable measurement schemes that can encode Fluxion and fluent changes . These changes enable engineers to design robust mechanisms or calculate complex trochoidal surface forces in fluid dynamic of rigid dynamical( high viscosity dynamics) consistently within the limits of agreed measurements of constant ratios.
The twistors, therefore are the general olution to all physical situations that are dynamic and measurable in terms of surface interactions.
The B field surfaces indicating dipole orientation in magnetism are therefore expressible in exponents form. The Equipotential electric surfaces have the same form the phase angle difference is indicative of the gyroscopic principles in arc rotation about a generated centre
This derivation follows the vector Algebra of Gibbs and Heaviside supported by Kelvin ..
The products designed ( dot and cross products) have to be explained . Sir William Rowan Hamilton took the imaginary magnitude as founded by Newton DeMoivre and Cotes and Euler and argued over by the Benoullis.
The work of Bombelli created a fundamental basis to the mathesis of the imaginaries, named imaginary by DesCartes, but it is Newton who set out the mathesis in its practical use. It was the basis of Newtons " vector" algebra .
The Fluxion Theory of Hermann Grassmann( Ausdehnungs Größe) explicated the work of Newton to the nth degree, based on the induction process of Newtons fundamental principles.
Hermanns work was takn forward by many but particularly by Bill Clifford. .he made it clear that which Hamilton Acknowledged : The Fluxion theory of Grassmann is more generl, but the same corpus of ideas as Hamiltons. The product design allows many useful models to be constructed for complex lineal algebras, both arced and straight.
This Calculus derivation obscures the direct formulaic processes. The exponential formulaic presentation gives a direct set of applicable measurement schemes that can encode Fluxion and fluent changes . These changes enable engineers to design robust mechanisms or calculate complex trochoidal surface forces in fluid dynamic of rigid dynamical( high viscosity dynamics) consistently within the limits of agreed measurements of constant ratios.
The twistors, therefore are the general olution to all physical situations that are dynamic and measurable in terms of surface interactions.
The B field surfaces indicating dipole orientation in magnetism are therefore expressible in exponents form. The Equipotential electric surfaces have the same form the phase angle difference is indicative of the gyroscopic principles in arc rotation about a generated centre
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on October 10, 2016, 09:05:25 PM
http://m.youtube.com/watch?v=r9EPdcL9oM0
http://m.youtube.com/watch?v=lMrz7ISoDGs
The design of all Arithmetics is founded on topological combinations as identified in Stoikeia book 7
Starting with book 7 we may analyse topology by proceeding toward book one and synthesise the topology of regular forms by proceeding through the later books .
The fundamental process of Arithmetic is factorising larger by smaller topology or more by less!!
This gives not only the basis for comparison or ratio but also the impetus to count, order arrange and sequence .
The misdirection to Number obscured this general approach. Hermanns Grassmann was the first to rediscover this general approach in the 1830's and to make sense of a Pythagorean system or method of expertise development or even an ancient Indian subcontinent system of rhythm patterning ..
Within the process of topological factoring addition as a sequential arrangement along with subtraction as
the reverse or analytical sequence arrangement informs the counting response , the ratio response and the proportion response,
These manipulations of topological forms inhere translation and rotation . The mirror reflection informed thinkers of the topological duality in reflection and its use in analysis and synthesis.
Thus factorisation is a complex process by which we measure topology .
Appended to this topology is direction, orientation and intensity and extensivity.
When we experience weight for example we
Say weights are equal by a visual measure!
This our subjective proprioception is laid against a visual Identifier
This visually cued measurement system fails to capture intensity and density directly but nevertheless we can interpret these kinaesthetic and olfactory responses by the standard topological pattern to which we can assent as analogising these sensations .
The matching of intensity to a topological pattern no matter how precise does not inform our senses of the actual process merely of the approximate outcome
The mosaics which form the basics of any factorising method allow calculus to be constructed in lieu of actually performing the modelled process , one can only have confidence in such calculations if they prove by rigorous comparison to represent actual outcpmes.
http://m.youtube.com/watch?v=lMrz7ISoDGs
The design of all Arithmetics is founded on topological combinations as identified in Stoikeia book 7
Starting with book 7 we may analyse topology by proceeding toward book one and synthesise the topology of regular forms by proceeding through the later books .
The fundamental process of Arithmetic is factorising larger by smaller topology or more by less!!
This gives not only the basis for comparison or ratio but also the impetus to count, order arrange and sequence .
The misdirection to Number obscured this general approach. Hermanns Grassmann was the first to rediscover this general approach in the 1830's and to make sense of a Pythagorean system or method of expertise development or even an ancient Indian subcontinent system of rhythm patterning ..
Within the process of topological factoring addition as a sequential arrangement along with subtraction as
the reverse or analytical sequence arrangement informs the counting response , the ratio response and the proportion response,
These manipulations of topological forms inhere translation and rotation . The mirror reflection informed thinkers of the topological duality in reflection and its use in analysis and synthesis.
Thus factorisation is a complex process by which we measure topology .
Appended to this topology is direction, orientation and intensity and extensivity.
When we experience weight for example we
Say weights are equal by a visual measure!
This our subjective proprioception is laid against a visual Identifier
This visually cued measurement system fails to capture intensity and density directly but nevertheless we can interpret these kinaesthetic and olfactory responses by the standard topological pattern to which we can assent as analogising these sensations .
The matching of intensity to a topological pattern no matter how precise does not inform our senses of the actual process merely of the approximate outcome
The mosaics which form the basics of any factorising method allow calculus to be constructed in lieu of actually performing the modelled process , one can only have confidence in such calculations if they prove by rigorous comparison to represent actual outcpmes.
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on October 12, 2016, 04:26:28 AM
In the thread " Twistors" I attempted to deal directly with rotation from first principles. I had no real clue how to go behind the A level Physics I had studied quickly , or how confused I was by the edifice of mathmatical Physics. I knew that Mathematics was fundamentally incoherent but not how, or where, or when.
Luckily my years at university were not entirely clueless. David Hilberts book on the foundations of mathematics was my prize find in the library there. I spent my time devouring that book, amongs other things.
I should have flunked Mathematics, but the university decided to give me a pass degree.
Why? Because I had been a thorn in the flesh of much of the faculty. I had managed to upset most of their lecturers and readers by questioning what they were teaching. I had suggested to my professor that space was a continuum of points, I had impeached Cantor and I had mastered computer programming in Algol60.
So I had potential, even though I was thoroughly disenchanted with the whole subject as taught, as promoted and as revered.
In the thread "Fractal Foundations" I set out like Norman Wildberger to set things straight. But I did not know what I did not know! So that thread records how I learned the truth about mathematics and mathematical physics in the context of the forum.
In the meantime I was encouraged by a misunderstanding to start blogging on Opera . There I could really go to town on my growing understanding.
Opera blogs no longer exist, but Wordpress took them on as an import.
Here, in the forum I have tried to focus on what might be relevant to Fractalers at the same time as learning from the masters here. But my research interest is mathematical physics, and the foundation of physics.
Again I did not know what I did not know.
So I have meditated on rotation as the fundamental physical dynamic for years . I wanted twistors to be a fundamental depiction of " Vortices" . I wanted mathematics to reveal the foundations of reality as vortices!
Again I did not know what it was I was hoping for.
Fundamentally I had to apprehend Shunya . When I did I started on a journey of clarifying natural philosophical foundations to all the sciences but particularly Astrology.
I found that Astrology is the foundation of Mathematical Physics, and that Astrology was taught in the west by the School of Pythagoras. The mystery of Pythagoras is most likely resolved in Tibetan and Indian subcontinental traditions, but Sumerian, Indian and Egyptian traditions play a vital part.
For all these cultures the sphere was the ultimate magical form closely followed by the cube and the cone. These perfect ideals represented and represent mans mental and thought form interaction with Shunya, that is "Everything" . Outside of these forms was the wild chaos form of the trochoidal surface, typified by the serpent.
What controlled and defined the trochoid was the sphere and the circle. Thus the magic circle was the great defense against spiralling chaos.
The cone revealed aspects of this chaos that were stable and enduring even if filled with destructive power! And the cuboid was mans approximation to perfect uniformity. All of these arose from the spheroidal forms found whole or shattered in Shunya .
These are the Mannigfähltigkeit of Shunya, the manifold folded properties of space-time or aether as a dynamic fluid entity .
I started withbTwistors and ended ith Grassman Fourier series forms or Grassman Twistors. In practice I have been restricted to Quaternion Fourier forms, and yet they have proved to be candidates for the iterated function that delimits how points move under iteration .
The bounding condition plus this delimiting function reveals how internal and external limitations have very important effect on outcomes.
The question of how did we get to this fortunate position of having an application that oes this omplexity iteration of our derived formulaic expressions is a story that reminds us that
On Oct 14 2010 Benoit Mandelbrot died trying to urge his colleagues to recognise the importance of his work on fractal topology .
It is this topology that takes the work of earlier experimental philosophers and makes it amenable to and contiribuive to combinatorial and computational science..
Luckily my years at university were not entirely clueless. David Hilberts book on the foundations of mathematics was my prize find in the library there. I spent my time devouring that book, amongs other things.
I should have flunked Mathematics, but the university decided to give me a pass degree.
Why? Because I had been a thorn in the flesh of much of the faculty. I had managed to upset most of their lecturers and readers by questioning what they were teaching. I had suggested to my professor that space was a continuum of points, I had impeached Cantor and I had mastered computer programming in Algol60.
So I had potential, even though I was thoroughly disenchanted with the whole subject as taught, as promoted and as revered.
In the thread "Fractal Foundations" I set out like Norman Wildberger to set things straight. But I did not know what I did not know! So that thread records how I learned the truth about mathematics and mathematical physics in the context of the forum.
In the meantime I was encouraged by a misunderstanding to start blogging on Opera . There I could really go to town on my growing understanding.
Opera blogs no longer exist, but Wordpress took them on as an import.
Here, in the forum I have tried to focus on what might be relevant to Fractalers at the same time as learning from the masters here. But my research interest is mathematical physics, and the foundation of physics.
Again I did not know what I did not know.
So I have meditated on rotation as the fundamental physical dynamic for years . I wanted twistors to be a fundamental depiction of " Vortices" . I wanted mathematics to reveal the foundations of reality as vortices!
Again I did not know what it was I was hoping for.
Fundamentally I had to apprehend Shunya . When I did I started on a journey of clarifying natural philosophical foundations to all the sciences but particularly Astrology.
I found that Astrology is the foundation of Mathematical Physics, and that Astrology was taught in the west by the School of Pythagoras. The mystery of Pythagoras is most likely resolved in Tibetan and Indian subcontinental traditions, but Sumerian, Indian and Egyptian traditions play a vital part.
For all these cultures the sphere was the ultimate magical form closely followed by the cube and the cone. These perfect ideals represented and represent mans mental and thought form interaction with Shunya, that is "Everything" . Outside of these forms was the wild chaos form of the trochoidal surface, typified by the serpent.
What controlled and defined the trochoid was the sphere and the circle. Thus the magic circle was the great defense against spiralling chaos.
The cone revealed aspects of this chaos that were stable and enduring even if filled with destructive power! And the cuboid was mans approximation to perfect uniformity. All of these arose from the spheroidal forms found whole or shattered in Shunya .
These are the Mannigfähltigkeit of Shunya, the manifold folded properties of space-time or aether as a dynamic fluid entity .
I started withbTwistors and ended ith Grassman Fourier series forms or Grassman Twistors. In practice I have been restricted to Quaternion Fourier forms, and yet they have proved to be candidates for the iterated function that delimits how points move under iteration .
The bounding condition plus this delimiting function reveals how internal and external limitations have very important effect on outcomes.
The question of how did we get to this fortunate position of having an application that oes this omplexity iteration of our derived formulaic expressions is a story that reminds us that
On Oct 14 2010 Benoit Mandelbrot died trying to urge his colleagues to recognise the importance of his work on fractal topology .
It is this topology that takes the work of earlier experimental philosophers and makes it amenable to and contiribuive to combinatorial and computational science..
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on October 12, 2016, 09:55:23 AM
The secret of rotation in a circle, and thus a sphere is the quarter circle that is defined by the semi circle! .
Once you grasp that mystery i, pi, and the radian measure become insuperable and the notation for expressing algebraic labelling of dynamic processes becomes clear, the lineal algebra, both quarter arc and radius , segment and chord semi circle and diameter become invariant magnitudes that have an invariant ratio . I mean to say the invariance is captured by the ratio.
Thus ratio is how we discriminate unchanging truths in a dynamic fluid space time that may seem chaotic..
Newton never excluded chaos. He focused on that still ratio that exists in our measurement schemes to control chaos. That magic unit circle tames the chaos monster only by keeping it at bay . Rotation and Logos Analogos are curious for that very reason: they constrain that which is older fully chaotically unpredictable within defined bounds, but they never change the nature of the beast, the natural dynamic curvature of space-time or the aether.
That is the true space- time manifold : a dynamic trochoidal backdrop to everything we perceive or establish. Measurement scheme for. And not just objectively but also subjectively. We are in and of this space- time manifold and fractally entrained .
Once you grasp that mystery i, pi, and the radian measure become insuperable and the notation for expressing algebraic labelling of dynamic processes becomes clear, the lineal algebra, both quarter arc and radius , segment and chord semi circle and diameter become invariant magnitudes that have an invariant ratio . I mean to say the invariance is captured by the ratio.
Thus ratio is how we discriminate unchanging truths in a dynamic fluid space time that may seem chaotic..
Newton never excluded chaos. He focused on that still ratio that exists in our measurement schemes to control chaos. That magic unit circle tames the chaos monster only by keeping it at bay . Rotation and Logos Analogos are curious for that very reason: they constrain that which is older fully chaotically unpredictable within defined bounds, but they never change the nature of the beast, the natural dynamic curvature of space-time or the aether.
That is the true space- time manifold : a dynamic trochoidal backdrop to everything we perceive or establish. Measurement scheme for. And not just objectively but also subjectively. We are in and of this space- time manifold and fractally entrained .
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on January 28, 2017, 08:03:42 PM
Recent brealthroughs in understanding have enabled me to Ezolire the oatterning in the Nucleus.so called.
http://nocache-nocookies.digitalgott.com/gallery/19/410_28_01_17_6_45_17_180582077.png
http://nocache-nocookies.digitalgott.com/gallery/19/410_28_01_17_7_06_49.png
http://nocache-nocookies.digitalgott.com/gallery/19/410_28_01_17_6_45_17_180582077.png
http://nocache-nocookies.digitalgott.com/gallery/19/410_28_01_17_7_06_49.png
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on February 02, 2017, 12:07:54 AM
https://en.wikipedia.org/wiki/Orders_of_magnitude_(length)#1E-15
Orders of magnitude basically best estimates
Electron scattering and other techniques
https://en.wikipedia.org/wiki/Proton
https://en.wikipedia.org/wiki/Electron
ratios
Orders of magnitude basically best estimates
Electron scattering and other techniques
https://en.wikipedia.org/wiki/Proton
https://en.wikipedia.org/wiki/Electron
ratios
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on February 09, 2017, 02:22:30 PM
http://magneticuniverse.com/discussion/364/a-sound-basis-to-rotational-dynamics#latest
Some recent breakthroughs on the Boscvich theory of force.
These are connected to fractal iteration rules I will develop later as fied force and field velocity laws
Some recent breakthroughs on the Boscvich theory of force.
These are connected to fractal iteration rules I will develop later as fied force and field velocity laws
Title: Re: The space time manifold tensor candidates
Post by: jehovajah on February 12, 2017, 11:41:52 AM
http://m.youtube.com/watch?v=J9zupDFlB0Y
The Boscovich Argon nucleus visualised in Bill Shanks Trochoid.
http://m.youtube.com/watch? V=U1dPGi7bxO8
The Boscovich carbon atom nucleus in Bill Shanks TroTorted .
This is a 3d visualisation but the app is a simple version Bill wrote as a test of some ideas. It has 4 circular vectors and thn 2 sine vectors. The 4 circles are probably oriented on the faces of a tetrahedron and the 2 sines move this tetrahedron through quarter turns rather than circles..
The path is highlighted, but the surface motion is not visible in this video
This dynamic model of carbon nucleus reflects JJ Thompsons sticky plum pudding model as relevant to the Boscovich theory of force and obviates the instability of radially repulsive "forces" .
The Boscovich Argon nucleus visualised in Bill Shanks Trochoid.
http://m.youtube.com/watch? V=U1dPGi7bxO8
The Boscovich carbon atom nucleus in Bill Shanks TroTorted .
This is a 3d visualisation but the app is a simple version Bill wrote as a test of some ideas. It has 4 circular vectors and thn 2 sine vectors. The 4 circles are probably oriented on the faces of a tetrahedron and the 2 sines move this tetrahedron through quarter turns rather than circles..
The path is highlighted, but the surface motion is not visible in this video
This dynamic model of carbon nucleus reflects JJ Thompsons sticky plum pudding model as relevant to the Boscovich theory of force and obviates the instability of radially repulsive "forces" .