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 Author Topic: Twistor  (Read 8560 times) Description: some notes on Hermann Grassmann's Ausdehnungslehre 1844 0 Members and 1 Guest are viewing this topic.
jehovajah
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 « Reply #15 on: January 18, 2014, 10:45:23 AM »

Returning to the description of rotation
http://hyperphysics.phy-astr.gsu.edu/hbase/rotq.html#avel

We see the use of the statistical average based on the equating of geometrical measures.
The notions of velocit and indeed angular velocity are presented as closed systems, not dynamically changing ones. The systems have a start ad a final state, both of which are assumed to be constant!

Familiarity with these closed systems does not prepare you for the open dynamic systems in which we live. The wide scae availability of fractal apps helps to remedy this failing. In addition he trochoidal app by Laz Plath is the only one I know that gives you freedom of motion in an n dimensional vector or rather circle space of trochoids.

While these rotational formulae are interesting as initial models, they are inadequate as descriptions of our experience. For that you need a fractal generator app and a trochoid motion and surface generator.. With these tools you can do " rocket science" and even high energ particle physics!

Oh yes you can!

What is rotational kinetic energy?
I say we must equate it to the lineal keychain energy generated by the object rolling long a surface. If the object is not circular we can expect some variation in the formula process used, due to the object receiving varying impulse of tangential forge generation.
While this has the same formulary as torque I would apply the method of Fluxions or calculus to any descriptive determination.

For example the average angular velocity from stand still, contributes the 1/2 scalar to the kinetic energy formulas but this ison the assumption of a constant acceleration!

We have a lot to learn about "real physicl" rotational kinetic energy!
http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#mi
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jehovajah
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 « Reply #16 on: January 18, 2014, 11:16:28 PM »

Now, out of habit I guess, I have introduced the tangential force acting on a disc at a radius r .
Ft is the label for this tangential force

The problem starts with the radian angle ratio.
Ø = S/r

I know what S is, it is the arc length. It is also the distance travelled by the centre of the circle if it rolls on this arc perpendicularly to a plane surface.
The plane surface is a tangent surface and in it I can draw any tangent line. The surface and the line are not instantaneous! The point on  the disc which contacts them is only instantaneously in contact . In fact physically it is a line in a cylindrical surface that contacts the plane surface or line in the surface.

So, if I draw a tangent to a disc to represent the arc displacement it has to be of length S.

Now let's look at rotational velocity, at a constant velocity.
In time t that is S/t

Thus  ŵ = ø/t = S/rt

If we say S/r is the velocity , what velocity is it?
Well it certainly is not a tangential velocity! If that was the case then all velocities are tangential velocities!

It is the velocity of the disc as a whole as it moves over the surface!

I have discussed how that velocity, measured at the centre changes with surface geometry.

Well if the disc is fixed at the centre it has no tangential or bodily velocity, it has only rotational velocity. Tangential velocity is meaningless for a fixed rotating disc. All we can measure is rotational velocity and rotational acceleration.

So what is Ft ?

It is a constant frictional force applied tangentially as it must!

We can work out the moment of this frictional force but that is meaningless.
Now if I apply a force that decelerates a spinning wheel, I am not justified in using a constant frictional force to slow it down. The reason is the force is not slowing it down by deceleration but the kinetic energy is being drawn out of the system by conversion to heat nd kinetic energy of sparks etc!

The experiments have to be done more carefully than that. We have to stop a wheel spinning without friction and very quickly , within the distance of an 1/8 th turn, to avoid obvious frictional force contact. A negligible hook mass must be attached and a spring force measure applied through tht hook to stop the disc quickly..

However such an arrangement does not apply a tangential force over the whole stopping distance or arc length.

So the only course left is to see what force stops the wheel from starting to spin. This means we have to apply the moment to measure the stopping moment! The applied moment may be through some pulley system which transmits torque through a connecting axle..

Now we know the experimental set up one can reasonably ask, what has that got to do with planetary orbit!?

When we apply these concepts outside there empirical basis, we are asking an analogy. And when we derive certain formulae by analogy with geometrical form we may not actually have a physicl mandate to do so!

The early mechanistic philosophers really did think these wheelers and spheres existed in nature , maybe as spiritual echmical gears and levers. Newton showed his insight when he said I frame no hypothesis! , and elsewhere he allowed for forces to be impulsive instantaneously not as the models would suggest constant and mechanical.

The physical picture for rotation is therefore mre complex. We cannot presume ome tangential force or torque drives the orbits of planets or the motions of fluids., at least not without complicating the dynamics with energy transformations which will be electro Thermo magneto complexes.

No matter how rarefied a bubble of SpaceMatter contains and is this rotational kinetic energy for which moves restive to other such bubbles generating trochoidal motions nd transforming save into other bubbles of energy in rotation! It is ths transfer and turns flatiron of rotational energy that we experience as " force" or electro Thermo magneto complex behaviours.

When Newton looked at Hookes spring experiments he did not wait for the spring to reach equilibrium. In that case he would only have noted extension of the sping. Instead he noted the dynamics. He saw that the acceleration of the bouncing spring was proportional to the weight/ force on it. And he knew that the weight / force was proportional to the mass or bulk of the object. A little thought made him realise the force was proportional to a quadratic form. His own Fluxions method informed him that the finl length of the extension was a derivative of the acceleration , the second derivative. So he could see behind Hookes law to the dynamical world in which we live. But rotation was and is different. It is different because it is the only natural form of energy we can witness. It is a store of kinetic energy and a means of transfortion of energy into electro magneto and Thermo complexes in and of space.

If I set rotational kinetic energy to kinetic energy , by passing torque
I get 1/2 x m x (ŵr)2 = 1/2 x m x v2

Which implies that kinetic rotational energy is scaled up when it is turned into lineal motion! The energy densit in a rotating form measures less than its equivalent dynamic form when in contact with a flat surface.. If the surface undulates that lineal kinetic energy will vary with it. It is as if the rotating form pulls linelenergy out of the rotating space or compresses it back in.

There is much to learn about Twistorque and rotational force fields!
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jehovajah
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 « Reply #17 on: January 19, 2014, 12:10:15 AM »

Electro Thermo magneto complex
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 « Reply #18 on: January 19, 2014, 08:52:01 AM »

Rotation is not as simple as the circle or sphere!

In my early definition of Spaciometry I defined spaciometric rotation as traversing the boundary of a form. Not all forms are closed, so open and closed loops are fundamental to describing rotations. I also defined a vorticular wrap, for a crazy idea I had of spiral reference frames! Later I realised that reference frames can be curvilinear, and in fact they have to reference points in space uniquely to avoid confusion and mental meltdown!

However, the fundamental aspect of motion around curved open or closed loops was established.

Since then I have got a better handle on affine and projective geometries, and twistors , allowing for a projective interpretation of rotation from a fixed point  or an axis in 3 dimensions.

In general we talk about centres of curvature to define arbitrary rotations and these can involve normal,tangents and oscillating circles and parabolas.

Normans series on differential geometry goes into mathematical or algebraic detail

However I want to start with Newton, because the elliptic error is best explained by his work in Principia on orbits.

The elliptic error is the common view that gravity acts centripetally to the centre of mass. Few know that gravity acts or behaves like an ellipse. Those that do ignore the second focus generally and do introduce an error into our thinking! The second focus is often in Empty Space! Either empty space has a mass or we are mislead in our thinking! In fact it is both!

There is no empty space and Newton assumed an elliptical vortex ( keplers discovery) for his derivation!

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 « Reply #19 on: January 19, 2014, 08:20:42 PM »

The things we are asked to believe  become suspect as one becomes older and hopefully more experienced.

I do not recall doing any momentum experiments in my secondary level physic classes. I do remember doing a gravitational acceleration experiment. I am fairly sure we did mostly calculations of momentum after observing a demonstration.

So, what is momentum?

Well it certainly is not m x v!
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

I can remember not believing that even as a child, just as I did not believe force was m x a. It took me a long time to actually stir myself to look at newtons work, nd the philosophical arguments of his era. That is when it started to make sense. I knew momentum was a kind of force that would not allow me to stop dead as a crashed through the finish tape! What kept me going forward was called momentum . What it was no one could tell me. I found Descartes called it a force, and said it was of god and thus conserved. Later Leibniz took issue with that. He knew from experiments that Descartes momentum, if measurable by mass and velocity was not conserved., or preserved, it changed tempestuously! However he knew Huygens had demonstrated that mv2 was conserved by Pythagoras law! This was a living mathematical law given by god, as far as Leibniz was concerned and he argued that the measure of this living force was mv2. It was living, and that is why it persisted. Every other kind of force he considered as a dead force, because it did not move anything!

Finally Newton defined Descartes measure as what it is a quantity of motion! MV was a vector sum concept, only really understandable by Grassmanns Ausdehnungs Groesse. It was precisely what Newton had in mind. The density in a volume sloshed about like a quantity of an accelerant he called motive. Mv  was the measurement of the resulting celerity. It was a vector sum of all the implied internal motions, and thus a quantity of motion.
Why did it keep moving with celerity? Because the body contained motive, and this motive was the cause of acceleration.

Then why did the body not accelerate? Because the motive was opposed by an equal and opposite motive, dissipating the acceleration leaving only constant celerity or velocity.

Now I am not sure if Newton commented on Leibniz vis viva, but his work formula based on his measur of force F = ma certainly confirms Leibniz notion of mv2 being important and conserved, only the factor was different.

Well, as we know Newton's formulae won out even if his metaphysics did not. But , instead of giving us his heirs a better metaphysics we got fed on a diet of mathematical tripe! Only, we were not allowed to question the dry crumbs we were being given . We would have starved to death if we had not been given a hard dose of mathematical vitamins by Einstein! Most of us who have persevered in this dietary combination have ended up malnourished, gaunt and somewhat crazy. We can believe a few impossible things at the drop of a hat, now we are delirious on mathematics!

Is momentum conserved? Lol!
I doubt it.

So let's look at the mathematics and the toy.

Ok ok ! Do now you have to believe momentum is conserved , right?

Well not exactly. In all demonstrations nothing went exactly as we were told to believe or trained to look and ignore! The point is we want our Maths to be exact, which it can be, but the physics is not, because it can't be!.

You see, if you question hard enough the ground shifts!

But , hey , we can not live without conservation of momentum, so despite everything just said, let's put it back right in there!

It is unlikely that there are any isolated systems in our universe, so these riles are approximations only ad that is why they do not match the observations. So all collisions do not conserve lineal momentum, we just apply the concept to all systems, and get an answer.

Can we believe the answer? Not always! NASA and rocket science knows that they have yo adjust their long range trajectories constantly, and then at the last minute! The 7 minutes of terror is a case in point!

Newton, when calculating centripetal acceleration derives a formula by successive approximations called Fluxions or calculus. He iterates down to the best approximation.

Newton developed a metaphysical concept called motive. It is based on ancient ideas but particularly Aristotles analysis of the Prime Mover or first Cause. Motive cuts to the chase, and says all things accelerate but they accelerate in opposition. This is the fundamental basis from which he begs us to start.
My argument is similar: if rotational motion is not the first cause, then there can be no motion. If you say lineal motion is the first cause then there can be no rotational motion. If you say variation in lineal motion is such that velocity is in all directions thrn you imply rotation as a prior cause of this , and if you say that parallel lineal motion has a variety of velocities you ignore the perpendicular motions that must exist to hod a body together in order for it to rotate.

Starting with relative rotational motion avoids all these issues because it allows all motions to derive naturally from the interactions of such forces.

The nearest concept to motive is energy. And it is this energy concept that therefore underlies all other notions , and is a better explanation than momentum for observed behaviours.. Underpinning that is the geometrical notion of Grassmann's Strecken!

One can explain all behaviours in terms of motive and it's effect in doing work on and in a body or region. This is why rotational,motive is so crucial. We know from the venturri effect that work done inside a body reduces the work done by the body externally. Thus the creation of bubbles will reduce the pressure exerted by a fluid element and will be seen as turbulence!

The work done in a collision changes the kinetic energy in the particles and they fly off or roll away or both accordingly.work is a vector or Strecken concept!
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 « Reply #20 on: January 20, 2014, 03:20:21 PM »

r x F and r x p are vector cross products, properly associated with the moment of a force and the moment of a momentum.

While the formula is quite general it is most commonly applied to lineal force and lineal momentum. Moments are quite applicable in mechanical lever situations , but often they are applied to situations where they act as potential torque or potential angular momentum.. This is not taught or understood and so a lot of mathematical chicanery is done before your very eyes to get what they want or more easily can get by simple definition.

The potential angular momentum or the moment of momentum is not constant. It varies as r sinø usually. Similarly the potential torque is not constant.

The usual argument is to show that if you differentiate the potential angular momentum you get the potential torque.

Then the argument goes if the potential torque is 0 then the potential angular momentum must be constant
But we know the potential angular momentum is not constant so where do we go from there?

We actually have to go to instantaneous versions of these 2 vector forms, and the instance when the potential becomes actual angular momentum, and some thing or particle actually starts rotating. In that case p is no longer lineal momentum and its path actually has to be defined!

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 « Reply #21 on: January 21, 2014, 01:53:09 AM »

It seems to be worth investigating James MacCullagh, and Green
http://en.wikipedia.org/wiki/James_MacCullagh

http://en.wikipedia.org/wiki/George_Green

http://www-history.mcs.st-andrews.ac.uk/Biographies/MacCullagh.html
https://archive.org/details/collectedworks00maccuoft
It would seem that Stokes, Kelvin and Boole represent irelands finest mathematicians of wold renown nd influence. Yet a deeper grass root strin of Irish mathematical and physical thought is traceable by its influence on Geometry and Electromagnetic theory.

Hamilton, MacCullogh, Samon and Fitgerald and Lamor buried themselves in forming and maintaining an Irish tradition in these fields.

We see the influence in the rapid adoption nd development of the vector mathematics inspired but Hamilton in the late 1820's and the wildfire spread of Quaternions . MacCullogh was able to use these ideas to positor postulate a potential equation which Hamilton described as the Curl of the vector displacement field.

We find Maxwell making use of this Curl in his theory of electromagnetism, as a straight development of Quaternions as proposed by Hamilton. Thus MacCullogh's ingenious idea transmits to Maxwell through Hamilon.

However it is not deemed of natural importance by others , who seemed to have opted for a settled science.

It is noted in Lamor's assessment that H A Lorentz a Dutchman, Helmholtz a Prussian who guided Hertz's research topics and Fitzgerald in Ireland who directed Lamor's research topics were the only 3 centres in the world seeking to advance the physical sciences and that through a more mathematical methodology.

To this we must also add Heavisides considerable efforts, based in England close to Maxwell.

Both Lorentz and Lamor conceptualised the Aether as containing a dynamic array of electrons. But electrons were non physical. In one case they were vortices of the aether described by the curl concept in Quaternion math, in another, they were a slip knot of strain in the aether, again an idea inspired by quaternion curl descriptions and due to Tait.
Helmholtz had developed a notion of the perfect vortex , along with Kelvin and influenced Hertz in that direction, looking for and expecting each vortex to be balanced by a contra vortex. Both Maxwell and Heaviside relied on the mathematical curl more than a physicl model, but saw it as a non physical vortex in the aether

The discovery of the electron enters into this background. Why it should be thought of as a physicl quantity is not clear unless the deep and abiding resentment of settled science and Victorian sensibility is taken into account.

To the rest of society, these theoretical postulations were preposterous. Lewis Carroll lampooned the new imaginary mathesis in mathematics in his influential books Alice in Wonderland! Lorentz was always seen as a crazy chancer who always seemed to pull it off! But he was always being corrected by one mathematician or senior sinister or another. It was his careless regard for the conservative opinion that gave him his reputation, but he more often than not got something right!

Lamor's theory was lampooned as being a non material explanation of matter! Only Hertz it seemed enjoyed some quiet respectability in his directed research. However he was reluctant to do the research, having other interests. It was the influence of Helmholtz that kept him on track.

Maxwell was derided for his theory and completely ignored by the establishment. Had he not had such an illustrious career he would have been openly attacked. Instead, his end is reserved that bitterness for his self styled acolyte Heaviside.

In the face of this social and professional and in some cases commercial hostility, these men kept blue skying it and making slow progress refuted by their contemporaries.

JJ Thompson, therefore provided the perfect patsy or fall guy to save face for the establishment and to bury these wild fantastical ideas. The relationship between mass and charge Thompson found , and that is all it ever was: a ratio. Now that is what it was and that is what it still is!

Using this ratio Thompson studied and rewrote the corpscuar theory that Newton and all settled science accepted. In a stroke of clever communication he transformed a ratio into a region containing a smaller region of opposite charge! The large region he did not name but postulated a positive charge. The smaller regions which sat inside the larger region to comply with Earnshaws instability calculation he styled as negative, because it was these that flew out LIKE corpuscles of light toward the anode in the Crookes ray tube set up.

All he knew was these corpuscles had a charge to mass ratio as per his calculation. He did not know, and no one knows if they were matter . But he could model them using a supposed unit mass for them giving a supposed unit charge, which by mathmatical manipulation made the mass of the region where they were initially stored relatively huge!

A bit more manipulation and you get a relatively huge mass with the same charge as a miniscule particle.

Lamor suggested he call this " particle" the electron, and eventually Thompson conceded, justifying Lamor and Lorentz at a stroke!

This particle was of dubious constitution. Was it matter or was it these strange vortices and slip knots?

It was only really decided on the back of Einsteins 1905 explanation of the photoelectric effect. By then all  opposition to corpuscles as particles of matter became meaningless it was thought. Matter interacts with matter!

Or does it?

Einstein posited a massless electron he called a photon. The only " proof" was the mathematics! In addition Rutherford was not happy with Thomson's atom. He dud not question the constituents, that was a minefield he did not want to enter! Instead he reeified the electron and named the proton. And together with Bohr's work came up with the planetary metaphor for the atom.

He had learned from Thompson to give the public a metaphor they could accept! Calling Thompson's model a sticky plum pudding immediately endeared their version to the students and later the public. Scientific communication had entered the sound bite age!

However it was done , the establishment moved toward spin doctoring and public relations management. The war and the propaganda effort made this move almost imperative. From now on science would be done behind closed doors in secret on a need to know basis. Scientific advances would be published by the " committee ".

In America powerful commercial and governmental forces were conspiring against the aether concept for many reasons, not least the distinction between a progressive American science and a stultified European one, in addition, those trained in America had a particular core of concepts that were identifiably American. The European trained scientist and potential industrial or governmental espionage agent would not have these concepts ingrained and so would give themselves away!

We end the 19 th century with questions and avenues for research. By the beginning of the mid 20 th century everything is virtually settled!

It has taken some of us a while to realise we have had the wool pulled over our eyes.

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 « Reply #22 on: January 21, 2014, 11:00:11 AM »

you should be able to understand what they are talking about , now and give a better explanation of the phenomenon/
Moyive is not "lost" it is just opposed!
Energy transforms, and one of the phenomenoa it transforms into is called Force!
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 « Reply #23 on: January 22, 2014, 01:16:12 AM »

James MacCullogh's collected woks

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 « Reply #24 on: January 22, 2014, 02:50:53 AM »

The curl of a vector field has changed its meaning as Quaternions have been pushed out of the way by Gibbs vector concept..mhowever it is still the same calculation and it derives from the multiplication of imaginary or complex numbers.

Hamilton describes the curl as an elastic  rotation.mthis has not changed and if you have done any multiplication of complex numbers you soon have to get your head around the general rotation and stretching of the product. However in Hamilton's Quaternions the vectors are described by the Combination of complex products. The initial element or product is the scalar.

Producing 2 Quaternions gives a quaternion resultant whic is a scalar and a vector, but part of the vector has an additional term called a cross product. This is the origin of the curl.

Because uatenionic were designed to do rotations a special vector product is constructed o as to cancel the elastic part of the rotation and set the scalar to 1.

What MacCullagh proposed was to use the bare product in a differential quaternion . The differential would model the displacement vector field, the product would rotate and expand ot contract the field. This was essential for strain transmission, but equally Fresnel and Arago had argued convincingly that a transverse wave was the only wave that status fied the experimental results under polarization. Essentially this meant the waves were only oscillating in a plane orthogonal to the lights propagating I reaction.

Young argued for a small longitudinal oscillation, but at those speeds shock waves are more likely than compression waves, it was argued.

The curl or as it is now called the Nabla cross product seemed to be the answer to MacCullgh.

This was all new, nobody wanted to adopt Quaternions with its deeply lien imaginary mathesis, nor did they want to understand it. Stokes comment about a curl not complying with angular momentum conservation is one of those deliberate misunderstandings.!

If the potential field is rotating and expanding it must have a source! Conservation of angular momentum, such as it is deals only where there is no source.

The idea that a wave is generated and then it moves on its own is like a billiard ball, is so engrained thst they  could not envisage strain moving into each point to generate and further the wave,. The poorly understood wave mechanics was being trounced by the rigid engineering paradigms tht were. Felt to be understood.

Angular momentum is conserved as much as the system can be isolated . It is not an issue. The issue is the whole set of conservation laws and what they mean physically and how and when to apply them.

We also see the elastic rotation engenders sn expectation of waves in the aether. Thegrometry not the mathematics leads to that induction!

Having said all this, I see the curl now for what it is, a poor measure of rotational behaviours underpinning electro magnetic theory.
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 « Reply #25 on: January 22, 2014, 09:13:12 AM »

Oh my God!
The penny has dropped, the light bulb has switched on, I straighten out another wrinkle in my understanding.

When I learned mathematics I old not wait to do calculus. It was supposed to be hard and that made it cool! I could do the hard stuff!
Unfortunately, when I got to university level I found myself floundering in the deep nd, drowning literally in unfamiliar concepts!

What happened?

I had applied for Cambridge entrance, but chose Manchester instead. Half way through the first month Cambridge sent the entrance papers up  to Manchester to my surprise! One of my tutors suddenly appeared waving some papers. I quickly grasped he meant for me to sit the papers!
What?
I was not even prepared or forewarned. But I took them anyway. I had no intention of going to Cambridge so what did it matter!

I read the papers and was immedately aware that I had been taught a different mathematics to the examiners who set the papers! I had been taught traditional Math, and the papers were set in modern math style. In that instant I knew I was right to have chosen Manchester. The new Math was not my cup of tea!

In 1960's  the English education system went through a number of reforms with regard to Maths. Cambridge county schools and Scottish schools were in the pilot study project areas. I was not brought up in those areas.

So back to the deep nd. An,yhis threw me for 6 and I never recovered from it until I started blogging. The applied Maths were more familiar but the notation and lecture style was hard to digest. The algebra class bewildered me. Group theory? What in heavens name was that all about!
Number theory , where were the numbers?it was all algebraic set theory, or so it seemed.

I went underground to the computer studies department to learn algol 60. But what was FORTRAN?

After 6 months of the most disorienting presentations I was ready to quit, but then things started to turn around a bit. I actually started to understand computer language. My faith kept me going to social and religious gatherings that gave me a goal in life , and the library had a book by David Hilbertbcalled the foundations of mathematics that I never took out, but rather I sat in the library reading it with fascination!

That book helped me to make sense of one question I had repeatedly asked myself since age 12. What is Mathematics?

I learned there that Mathematics was not consistent or could not be proved to be. I read Polya, about heuristics in mathematics and hw solutions might be obtained or how research into a solution might progress. And I read a smll treatise by Popper who argued for falsifiability as a measure of truth.

One of my gols when I went up to Mnchester was to develop a theory of gravity based on magnetism and magnetic vortices. Of course I did not know how I was going to do it, but I started a notebook to sketch out ideas. One particular day I came up with the notion of a continuum of points! It was more of a visual miasma of shifting points of light which just kept spreading apart nd revealing more points the closer you get.!

I sat outside a professors office for hours hoping to discuss it with him. Instead I eventually got to speak to obe of his colleagues or researchers. He listened and was kind and that was that! Or so I thought.

Later I was introduced to Cantors set theory and the uncountable sets. I loved these sets obviously, because they were just like my continuum of points! But I could not accept the proof!

I was busy trying to learn bout polynomials on the unit interval, or rather to get though the class. But every time one of the tutors would come to my seat and show me another unconvincing proof of cntor's uncountable sets. Eventually they sent a visiting Irish "Reader" in mathematics to show me a functional proof of it, using mapping terminology I had only just learned.  You know what I lied the guy, and I could not see any fault in his explanation. I just thought: this is tautological! So I said yes! I said yes to get them off my back!

By then I was too tired to argue and heading for a meltdown.

I have copious notes, and I wrote copious notes during my 3 years at Manchester. I put them in a box and said one day I might understand what all this gobble de gook is all snout! What I learned was mathematics was in trouble and I did not know how or hy, and by the time I finished I did not care!

My mathmatical training however stood me in goid stead hen it cme to analysing problems nd situations. And I appreciated that. I found also that I had lacked social skills and conversational skills. I did not realise this until I was brought low by my experiences. Building those skills was my obvious priority. And eventually, many years later I achieved that and found that I was autistic!
I was now ready it seems. Suddenly I was gripped by an unstoppable low of mathematical nudity! I filled book after book ith notes. I found out about fractls, nd blogging and forums all at the same time. I had to write!

Fractal foundations using set terminology took me deeper into mathematics than I ever thought possible.. It reveled the human failings of the subject , the mythologies that it is shot through with. It opened my eyes to deep and long TEM goals and conspiracies. It also revealed implement failings in communication by pedagogues!

It revealed my own myopic bias and misunderstandings .

So, I was taught geometry fom primary age. In secondary I taught myself logs and elementary calculus. I read Lancelot Hogben Mathematics for the Millions. At A level I took Maths Ohysicsvand Chemistry.  The Maths and physics departments combined to teach Calculus. My O level trigonometry came in handy but thst was all the only geometry I ever used beyond O level. The rest was dynamics and kinematics in physics, backed up by mathematics treatment of the topic of calculus, Algebra etc.
Graphs and curves were employed for physical data.

I never heard of coordinate Geometry!

Transformational Gometry, a little bit. Graph work a lot. Equations even more, and algebra. Polar coordinates and complex numbers briefly. Mostly I learned trics, methods, techniques, and problem recognition and decoding. I was a trained automaton. No wonder I found it hard to think through my ubject!

Despite all the research and a course by nomn in universal hyperbolic geometry, I still did not get the connection!
Suddenly, after working on Grassmann last year and toward christnpmas, I fell out of love with algebra! The meaning of the Arabic hit home clearly. It was pure "mind fluff!" almost literally! It was screwing with my brain!

I then saw clearly that Arithmetic and symbolic arithmetic had been the ages long goal of Astrologers and the Pythagotreans. Then I heard it again and again in Normans expositions- arithmetic! Symbolic arithmetic all of it.

I then saw clearly how geometry was a precursor to the Arithmoi via the Logos Analogos method of Eudoxus, a master Pythgorean, a qualified Mathematikos or Astrologer of the first rank!

But only this morning have I recognised coordinate GEOMETRY as geometry! That then immediately makes sense of differential geometry. The calculus was not just about dynamics or even dynamic surfaces, it was also about describing curvilinear surfaces in geometrical terms!

The equations that Norman developed for 3 dimensional surfaces have differential nalogues for more curvilinear ones. Solving differential equations is also linked to finding an ration o describe the Gometry of a set of surfaces!

The distinction between geometry and Mechanics and dynamics is the concept of time.

In the Principia Newton revealed this methodically and in multiple ways by use of his Fluxions. Fluxions are dynamic generated surfaces, differential Grometry is a geometric description or equation for a surface!

Einstein by replacing time with a fourth displacement measure created spacetime, that is a 4 dimensional space for 4 dimensional surfaces. Few realise he dd this to preserve the aether concept mathematically.

In America the aether was dismissed completely after Michekon and Moreley. Bitter debates broke out and with war looming scientists were divided on national lines. Those who held to aether dynamics were at once suspected as Nazi sympathisers and industrial espionage agents!. Einstein fleeing Nazi domination in Europe was aware of these struct wartime assessment protocols. Most of the time he spoke in German to preserve his thought processes, but when he wrote in English his advisers were careful to translate his words in acceptable forms.

Despite his media association with the nuclear bomb effort, the reality was he was too much of a suspect to be allowed in on sensitive US secret operations! However, the administration relentlessly used him as a propaganda tool after worked war 2 and during the Japanese war, and the cold war.

Towards the end of his successful career in America Einstein came out strongly in favour of the aether. He judged the time was right to reassert the fundamental philosophical and mechanical necessity of it. This was partly to counteract the strange logic that was being promulgated as quantum mechanics. He felt there was a flaw in it somewhere, but of course the powers that be we're not going to allow tht to ever be found!

Today we believe just about anything because of quantum mechanics and the statistical probabilistic approach!

There I a backlash brewing so be aware! Also be aware that when it comes it is not likely to be free from its own errors!
 « Last Edit: January 22, 2014, 12:39:09 PM by jehovajah » Logged

May a trochoid of ¥h¶h 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!
hgjf2
Fractal Phenom

Posts: 456

 « Reply #26 on: January 25, 2014, 10:46:58 AM »

At you, your topic so working hard and using heavy your system resources?
At me , when open this page fully movies from your topic, my CHROME browser can stop working, other browser surely crash, or worse my computer can shut down with the error "System has recovered a serious error" so my browser perish.

 « Last Edit: January 25, 2014, 10:59:52 AM by hgjf2 » Logged
jehovajah
Global Moderator
Fractal Senior

Posts: 2749

May a trochoid in the void bring you peace

 « Reply #27 on: January 26, 2014, 12:37:44 AM »

At you, your topic so working hard and using heavy your system resources?
At me , when open this page fully movies from your topic, my CHROME browser can stop working, other browser surely crash, or worse my computer can shut down with the error "System has recovered a serious error" so my browser perish.

Sorry hgjf2, I don't mean to blow up your computer!
I write my posts on IPad first generation, now not updateable, but it copes with this page ok.
Do you use a broadband connection to the Internet ?
How much ram do you have? How much is shared graphics?
What version of Chrome do you have? I use chrome on my iPad and it works ok
I f I think of any suggestions I will post, but for now try ramming your computer in safe mode if it is a windows machine.
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May a trochoid of ¥h¶h 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!
hgjf2
Fractal Phenom

Posts: 456

 « Reply #28 on: January 26, 2014, 08:47:35 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.
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jehovajah
Global Moderator
Fractal Senior

Posts: 2749

May a trochoid in the void bring you peace

 « Reply #29 on: January 26, 2014, 09:57:02 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.

It is the ram that is more important for dealing with modern web browsers, although if your hardware is too old it won't swap memory efficiently even with more ram. ( RAM is random access memory).

If you have a word with your computer technician/ service person they can advise if a simple ram upgrade would do the trick. If it will it might be cheaper than buying a new computer, but I do not know what deals you can get in your area.

Sometimes it is better to archive your hard drive onto a terabyte drive and upgrade your machine, if you can afford it.
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May a trochoid of ¥h¶h 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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