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Author Topic: Twistor  (Read 8559 times)
Description: some notes on Hermann Grassmann's Ausdehnungslehre 1844
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Sockratease
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« Reply #30 on: January 26, 2014, 11:42:22 AM »

Yes. My computer is enough old.
You right . I must purchase a newer computer, but yet I don't have money, so must wait a few time.
If my computer go slow, normally that any page hard on my browser on any sites can stuck, and my browser perish.
My computer is ESPRIMO at FUJITSU SIEMENS with 15GB at partition (C:) and 22GB at partition (D:) memory, and not recognise DVD's and seem be from second hand.


You may want to consider a script blocking tool so that you can have all of these things blocked and unlock the ones you wish to see individually.  They wont even be able to load until you allow it, and this will solve the issues completely.

For Firefox there is NoScript - which I swear by - and also AdBlock.  I can't say what to use for other browsers, but I would think similar tools exist for them.

I can tell you for sure that using Firefox with NoScript and blocking Everything google speeds up the entire internet by a third or more. If using Chrome, reconsider.  That browser reports so much of what you are doing to google-analytics that it can really slow down an older machine  (I honestly have no idea why people tolerate google and their intrusive invasions of our computers!  I block everything google with every tool I can find).

Hope it helps, and good luck resolving this.
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jehovajah
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« Reply #31 on: January 26, 2014, 10:34:45 PM »

Thanks Sockratease.
I think google must use something like this on its own google+ software for mobiles! I see cracked video symbols every time I load that app. But one click and they spring to life!

This video details cracked science and its commercial and financial overlords.

<a href="http://www.youtube.com/v/1kb_T8sCWL8&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/1kb_T8sCWL8&rel=1&fs=1&hd=1</a>

The results can be explained in terms of twistors and Twistorque , which are abstract concepts I know, but they measure the chemico physical phenomena.

The concept of electro Thermo magneto complexes as vortices is relevant.
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
jehovajah
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« Reply #32 on: January 28, 2014, 09:41:32 AM »

This really cool video only partly explains the processes.
Electro Thermo magneto complexes are involved in the so called shear plane or slip plane forces! In simple terms gyrodynamics( I love that word ! ) or twistors and Twistorque are involved.

<a href="http://www.youtube.com/v/GX4_3cV_3Mw&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/GX4_3cV_3Mw&rel=1&fs=1&hd=1</a>
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
youhn
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« Reply #33 on: January 28, 2014, 09:48:18 PM »

I wonder if that is reproducible in a CFD simulation.
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jehovajah
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« Reply #34 on: January 29, 2014, 12:10:19 AM »

I wonder if that is reproducible in a CFD simulation.

I do not know, but Claes Johnson is probably the man go ask.
<a href="http://www.youtube.com/v/t7e_6bkUFzE&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/t7e_6bkUFzE&rel=1&fs=1&hd=1</a>
« Last Edit: January 31, 2014, 04:13:30 PM by jehovajah » Logged

May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
jehovajah
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« Reply #35 on: February 08, 2014, 07:36:26 PM »

The research on barycentres has an impact on the notion of a twistor.

It is clear that a "vector" or Strecken notion is associated with a complement in a Barycentric system. The moments in the system are usually considered as turning moments, and they are arrange to produce the null or zero vector, however, the non zero vector for a Barycentric system is usually defined as Torque.

When developing the notion of twistor I based it on the circular disc. In this case the Barycentric system is "uniform".  This gives a symmetric system and a Barycentric point coincident with the geometric centre of the disk.  The Barycentric system is usually in dynamic equilibrium. This is confusingly called static equilibrium because the system in balance has no autonomous movement.

Because the system is in dynamic equilibrium we tend not to realise the barycentre is itself dynamic !

In a torque system, the dynamic equilibrium is non zero, but it is a vector quantity. This means it has a direction, and that is a so called bivector or planar  entity.

Can this bivector move freely in space?

The answer seems to be dependent on the barycentre!

A spinning object with a rotation pivoted not on it's barycentre seemsbtonoscillate wildly. This indicates that the barycentre is dynamic in such a system, and there is only one point where the barycentre will remain in equilibrium during rotation. This dynamic barycentre may move outside the body of the rotating system creating the wild oscillations. It may move within the plane of rotation effectively providing a sliding rotation centre responsible for elliptical motion in orbits.

It is a question that needs to be asked, because the dynamic barycentre is clearly an instantaneous phenomenon in a torqued system.

The combination of vector sums both action and reaction in free space seem to be best modelled by a network of springs rather than rods. It is the stiffness of the springs and the transmission of strain forces that may determine the locally observed motion behaviours even in a torque system. This kind of complex barycentre of a much wider system deserves investigation.
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
jehovajah
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« Reply #36 on: February 08, 2014, 08:51:04 PM »

Precession in a near constant gravitational frce field with rotation at the Barycentre.

<a href="http://www.youtube.com/v/EJWIl4MYMbw&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/EJWIl4MYMbw&rel=1&fs=1&hd=1</a>
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
jehovajah
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« Reply #37 on: February 12, 2014, 10:42:24 AM »

The research on barycentres And tangential points of contact, means my concept of a twistor is changing.

When Maxwell created the distribution of particles in motion theory, based on Gauss and Boltzmann error distribution theory and associated probability theory he used the Barycentric ideas in a different way. The assumed point mass particles moved in a collision field. Depending on whether the collisions are elastic or inelastic the distribution of the particles will be wide or regionalised. The density of the particles in a given volume, that is how many in a given volume affects the number of collisions and thus the progress of any test particle. Consider Brownian motion.

Maxwell determined that this effect. Was best measured by the mean square averages of the Pythagorean description of a general translation, which would be directly proportional to the velocity of the test particle described as some combination of its orthogonal component velocities.

There was a lot of data collection required to establish the validity of this analysis, and I do not know how this was experimentally achieved, but the root mean square measure was used as a representation of the average collision free path!

The idea attracted Kelvin who developed his Kinetic theory of gases around these ideas and measurements.
Kelvin eventually made some breakthroughs in his theoretical model, which established his theory for gases and Maxwells reputation for analysis. The idea was also visually communicable, even if the math was not! The bell shaped curve symbolised the nature of some gas properties. . As the gas warmed, the prediction was a dhifting and flattening of the bell.shape. It was the fact that data when processed showed this flattening that justified the statistical analytical tool Maxwell developed.

Because as a rule it does your head in thinking about how these mathematical models and analogies are cobbled together it is easy to overlook things.

Number one: rotation and the barycentres of these dynamic particles were not physically considered. The mathmatical means provide a Barycentric tendency by default, but this is statistical not physical.

By this I mean, for every 2 or 3 particles( assumed as point masses) scattered in space a physical Barycentre is computable in the constant gravitational or hydrostatic pressure field. Thus over a volume a combination of these sub barycentres should give the Barycentre of the gas as a volume. The summation of these sub barycentres allows weights to be introduced to describe regional mass or density variations.

The motion and distribution of these point masses contribute to these dynamic sub barycentres moving as "particles" themselves, and contributing to a Barycentre of barycentres.

For each level of this fractal, the tangential contact points can be computed, and in this way a fractal measure for strain deformations put in place.

These barycentres and tangential points can now be treated as Maxwells original point masses and represented by components. The resultant probability distributions of the method can now be in a similar way related to physical properties of stress and strain within the body forces of the gas volume.

The mathematical means are now means of physical point masses or barycentres.

To these physical centres we can add the properties of rotation and rotating tangential points of contact.

It is assumed in the kinetic theory that point masses are not connected, and that they are free to ieave each other. But this is a non physical idea. Gases expand  before dissipating. During this process, hydrostatic pressure defines a boundary to the gas, by collisions according to the theory. However, I wonder if this is only partially the case? When one introduces gyroscopic or rotational dynamics, boundaries naturally form independently due to the gyroscopic dynamics.

Collisions in this gyroscopic model result in a boundary layer like a surface tension, with fragments tha break away following trochoidal paths, as well as fragments of the external medium dragged inside this surface tension boundary.

The variation in density associated with these poit masses, and the associated barycentres and tangential contact points , would lead to a distinct regional surface tension dynamic. As it stands, diffusion studies and hydrostatic studies indicate that denser regional masses would drag in lighter densities to a certain extent, bu overall the denser regional mass would move through the lighter density episodically, like a Brownian motion, but with the lighter density doing most of the observed jiggling!

Similar densities with the same rotational dynamics would merge by anti gyroscopic action. Thus the gyre of the regions is important in terms of merging behaviours. Those with the same observed gyre will tend to repel, while those with ant gyres or contra gyres will collect together. Merging would be a factor of external pressures on the gyre antigyre system. The emergence of a single larger gyroscopic rotation is also probable , but not necessarily inevitable.
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
jehovajah
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« Reply #38 on: February 13, 2014, 05:46:20 AM »

Mind the flashing images!

I just feel in my gut this has a lot of relevance to the ideas I am expressing abstractly!

<a href="http://www.youtube.com/v/QxaHNurYgSI&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/QxaHNurYgSI&rel=1&fs=1&hd=1</a>
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
jehovajah
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« Reply #39 on: February 13, 2014, 07:14:03 AM »

Short and long springs behave differently.

A short spring  applies rigidity to any network of springs joined to point mass. A long spring allows and models rotational behaviour about the point mass!

Thus, as observed, gases and fluids tend to allow vortex behaviours, with gases particularly forming rotating plumes of billows( local rotations) . The kinetic theory does not predict this behaviour.

However, by introducing lon range spring action between point masses, not only is surface tension a consequence, but also the long mushroom like billows.

The long springs model the electro Thermo magneto complex energies and behaviours in fluid dynamics, while short springs model them in crystalline structures.

Removing springs in body force models altogether is a modelling flaw I think.

However, the motion behaviour springs model I think are rotations and their dependent trochoidal locii. The rotations are not just circles but in fact conic sectional including trochoidal forms based on conic section curves and surfaces.

For example Lissajous curves are a complex rotational motion that body forces might generate under certain conditions.

The concept of rotation, limited to the circle restricts the conceivable motions. But once trochoids are allowed and also conic sectional curve and surface trochoids the more complex motions, undulations and vibrations and frequencies are an inherent part.

The Barycentric and tangential contact points allow us to build strain gauge tools from materials up to youngs Modulus collapse behaviours. Beyond that we will have to use theory or real planet sized dynamics as strain gauges!
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
youhn
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« Reply #40 on: February 13, 2014, 08:21:46 PM »

Removing springs in body force models altogether is a modelling flaw I think.

Do you have reason to believe that springs are removed from the body force models ... ? I think they are in use since the life of Robert Hooke in 16... something. Just replaced the spring constant with the Young's modulus.
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jehovajah
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« Reply #41 on: February 14, 2014, 05:46:16 AM »

Do you have reason to believe that springs are removed from the body force models ... ? I think they are in use since the life of Robert Hooke in 16... something. Just replaced the spring constant with the Young's modulus.

Yes you are right, but I am thinking in general. Thus most engineers see the value of springs, but mathematicians ignore them under certain conditions. In the kinetic theory, based on Maxwells analysis, springs do not figure. Generally in the kinetic theory springs do not figure. The gas, when it becomes cool enough is considered as vibrating molecules close together. It is chemists who put the springs back in, under the "electrostatic" theory they developed for electron proton interaction.

Body force interactions typically require several eclectic theoretical models to describe, and springs are perhaps the least favoured, although Susskind and others develop quantum manifolds on such spring models.

You would not believe how insular many subjects are, preferring their own language and models over ones they classify as " mechanical". Mechanics has always been disdained through intellectual snobbery and religious rationalism. Mechanics is man aping god! ( meaning man is the ape that copies the superior handiwork of god).

I think it is a flaw to leave springs out of any model of fluid body forces, even high energy plasmas! My underlying reason is that motion is not rectilinear, it is trochoidal, I believe.
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
jehovajah
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« Reply #42 on: February 15, 2014, 11:18:14 AM »

Twistors and Twistorque  rotational kinetic energy are new concept terms I am exploring to draw together our knowledge of rotation.

Rotation has always been associated with the sphere, but this is really the arbitrary paradigm model. Within it many forms may be specified, and their behaviours determined by empirical observations and hypothesis.

The main principle of rotation is that it is about a point. This point is special because it can have a direction line segment( vector) associated with the Barycentre of an object. This line segment is variously named a vector, a point vector an axis of rotation etc, but it is a point around which any spherical motion can occur at tHe same moment.

Thus combinations of rotations are normal and tHese would be labelled as combinations of point rotations . These are what I have labelled as twistors.

Rotation in space I have come to realise is not circular but trochoidal, especially space trochoids. Constraining rotation to a circle introduces forces that we have not fully taken into account generally. Trochoids or roullettes as they are now called can be visualised as 3d Lissajous curves of various frequency ratios.
<a href="http://www.youtube.com/v/SePFwkbhxdw&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/SePFwkbhxdw&rel=1&fs=1&hd=1</a>
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
jehovajah
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« Reply #43 on: February 21, 2014, 12:06:08 PM »

Bearing in mind Grassmanns dictum " L鄚ge mit der Richtung Festgehalten"

His development of the arc may have started in radian measure where arc length is given by r and the arc segment described by ABC say giving a combined product

R讎BC or r讎C if we drop the middle point for convenience, although of course this was what constrained M鐽ius Barycentric method.
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
jehovajah
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« Reply #44 on: February 22, 2014, 09:12:13 AM »

The retention of the 3 point description of an arc ABC immediately links it to the product of 3 points which is a triangle in Grassmanns method, and immediately the geometric fact of the exterior circle of a triangle!

Thus r becomes the radius of this exterior circle and the radian measure of the unit circle arc based at this circles centre.

r讎BC is a complete Grassmann inspired description of a circular arc segment!

By analogy, this work should develop on concentric circles as the analogue of parallel lines!

In the mean time

<a href="http://www.youtube.com/v/bIr66quAKkU&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/bIr66quAKkU&rel=1&fs=1&hd=1</a>

The light shows it's spherical fluid nature, with absorption, scattering, re radiation and diffraction, refraction and polarisation.
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
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