I woke this morning and thought about laser light diffraction gratings which are variable and tuning. This often happens and i feel it is an effect of the computational nature of my experiential continuum. This manipulations at a so called quantum level will play out the same response in all systems tuned to that sympathetic resonance frequency. Some will get a clearer signal than others,and some will be able to act on it while others will assist the manipulations enabling them to persist and extend. If you want to call them ghosts in the machine you can, but essentially they form a kind of software encoding of a continuing distributed universal computation .

The http://en.wikipedia.org/wiki/Virtual_retinal_display and the basic hardware http://en.wikipedia.org/wiki/Grating_light_valve pretty much nail the concept that i had come up with, happily. The notion itself is …

I woke this morning and thought about laser light diffraction gratings which are variable and tuning. This often happens and i feel it is an effect of the computational nature of my experiential continuum. This manipulations at a so called quantum level will play out the same response in all systems tuned to that sympathetic resonance frequency. Some will get a clearer signal than others,and some will be able to act on it while others will assist the manipulations enabling them to persist and extend. If you want to call them ghosts in the machine you can, but essentially they form a kind of software encoding of a continuing distributed universal computation .

The http://en.wikipedia.org/wiki/Virtual_retinal_display and the basic hardware http://en.wikipedia.org/wiki/Grating_light_valve pretty much nail the concept that i had come up with, happily. The notion itself is therefore not originated by me which i do not at this stage in my apprehension of my experiential continuum expect to be the case. Rather i expect there t be some coexisting creative development of an idea that i am perceiving or formulating. This is because as we communicate many seeds are scattered which grow as weeds to some and as beautiful flowers to others, but they grow in a multitude, rather than in isolation. I see this pattern which i have used in the several metaphors and paradigms i have used so far in this post, in the bacterial growth behaviour or in mitosistical cell division.

Because the idea is well established with regard to laser light diffraction gratings i can now advance a "pixel" for the diffraction gratings. Physically this would look like a diffraction grating in which the diffraction slits are crossing each other, let us say initially orthogonally. The actual slits are what allow an interference pattern to emerge on the other side, showing the wave nature of light. In this case the light source(s) would be white laser light in the form of a beam. Now it occurs that if the beam is rastered then variations in the interference pattern will occur due to the solid angle from the point laser source, and this would have to be compensated for, but essentially a set of parallel slits should produce an interference pattern local to the slit. The emissive radiation would thus be modulated, and perceivable by the eye. I might then see the expected oil-film rainbow patterns. Now add the modulation of the laser beam as per a televisual signal, what would i see?

Now add to this the orthogonal diffraction grating arrangement or some similar arrangement of parallel diffraction gratings and what would i see?

I would expect the "square slit" to have a radially emerging interference pattern locally behind it. This interference hemisphere i would hope would behave like a "pixel", and would with a modulated laser beam raster produce distinguishable images in or local to the diffraction grating.

So now i am going to find out who has done this at any frequency level.This may then provide me with a robust model for quantum interactions at the planck distance, modeling the spaceometric structure as a diffraction grid.My ultimate goal however is to model a relativistc motion grid with diffraction grating properties.

Of course the 3d diffraction grid would have to be explored built up of elements of thin diffraction gratings. Already i can see that the signal attenuation would be marked as the diffracted light moves from layer to layer, but this is consistent with the darkness of the generally.

I also thought about ratio and proportion the day before in terms of the way my neural network of actual axonic nerve impulses records and manipulates my apprehension of the set not FS and the set FS, but i will detail that in another post. The central nervous sysytem i see as a distributed processing neural network with a central coordinating processor, running a base operating system at the nanozoe level with additional software installed by a mentoring process called parenting and socialisation.

Looking again at the foundation of tensor analysis and the work of Ricci-Cabastro and Levi-Civita i realised that Einstein like Newton stood on the shoulders of many giants, not to mention David Hilbert.

I have given a lot of thought to Ratio and Proportion in the development of the "logos" response and see the unifying nature of this impulse and in particular a qualitative difference in mathematical thinking before the modern period. I now suspect that many of the innovations in the development of maths derive from the ratio proportion type of response and thinking whereas mathematics today seems to be about remembering formulae and equations and how to manipulate them symbolically, developing axioms and so called proofs that lead to an internal consistency in mathematics but very few new conceptions because it has all become too damn abstract!

"Abstract" means looking at the essential transform, that is algorithm or operation,and working with that as if it were a real entity.

"And YH¶H spoke and it was so!". Our language system has a reification operation embedded within it. It can bring something into a kind of "existence" simply by naming it. The archetypical example is the word "quiz", but what the etymology of this word shows is a reification process for all languaged notions and concepts, which may not be based in a reciprocal apprehension of not FS, but rather a new reciprocal apprehension within the set FS .

The Tensor notion is unsatisfying in how it is communicated because it is couched in abstract language and not interms of everyday things.

However our world has changed by the introduction of cameras and LCD displays and VLSI circuit wafers etc which enable us to give a referent to a tensor which is concrete. In fact "concrete block" is a tensor model which can be effectively utilised to ground the notion, or even better a "lego brick" block. A matress is another good model of a tensor.

Any way let you know if an other things "spring" to mind!

So i am on the way to the dentist and i think: extend the tensor notion to include spaciometric forms which are structured including "arbitrarily" structured forms eventually, but think of a plants cell structure in cross section, to begin with.."

Of course the spaciometric form is invariant under basis transform, that is to say reference frame, and spaciometric mass and spaciometric density can be attributed to the tensor.

Then i heard that because England scored some goals and won a game the economy was estimated to respond in various sectors "memorabilia, electrical items,sports items, FMG… to the tune of about a billion pounds. I saw a "complicated" input oitput structure there which could be represented in a tensor.

Then my dentist actuall y drilled my tooth and i saw a tensor relationship there between the input drill speed and path and the spaciometric result due to chemical and physical bonding energies being exceeded and strain maxima being exceeded being representaable in a tensor which would amalgamate the physical and chemical effect of the action of the dentists drill. The information stored in the tensor being accessed in various ways specific to the required output information.

Tensors as you may be seeing, although a spaciomtric form, may hold relational information, that is relativstic information, in this structured form. The structure of the tensor itself can mimic the structure of the form that it holds the information for or it can just be the "block" form with the correct structural relations adhered.

The fundamental relationship of a tensor is that the form does not alter as the reference frame (basis) alters. Thus if i reflected the components of a tensor in a "mirror" i would fundamentally alter the form of the tensor without realising it as the form looks the same just reflected. This would not be a tensor transformation as currently defined and needs a development in tensor algebra to accommodate it.

I am used to reflections as mathematical transforms but physically they have no counterpart except in the notion of chirality(left and right handedness). Whereas i can relate a left handed version to a right handed version by a mirror reflection i cannot physically do the transformation in the "solid" phase. These transformations will typically be found in chemical reaction products in the liquid,gas or plasma phases.

This relates to a discussion i began with regard to unary operators defined as spaciometric rotations of orientations and how a reference frame with an additional rotational attribute to the axis vector transforms a referenced region on its transformation.

In fact i proposed a more comprehensive vector definition, but now think that a tensor form would more than cover it! ah well such is life!

iimagined that funny effect you can get in those halls of mirrors taking place physically: The left side of me would squeez into the middle and then "pop" out on the right side of me and vice versa, but it would be an anti me that results! Everything would work in the opposite way! Kind of weird science!!

Any way for that reason i say reflection is not a tensor transform even if it is by Ricci and Levi! Except as i noted in the area of reaction products. I suppose i ought to allow seeing what you look like in a mirror for those of us to whom it is a daily necessity. Go on then, put it in but don't say i did not warn you!

My current interest is in trying to define a ralativistic frame of reference, and when i do i will have to make it tensor invariant also.

A tensor is a quantitative model of a spaciometric form that is firstly relational and this enables it to be relativistic, secondly differential and this enables it to be mapped to a network of related reference frames and finally quantitative in each differential element of the model of the spaciometric form in a relational way.

Although this is a one line staged explanation it is still not a comprehensible denotation. It is however more apprehendable.

We utilise and view many possible candidates for a tensor in our modern computing environments: any spreadsheet aplication allows me to create a tensor as a spreadsheet for example, where the spreadsheet is the spaciometric form and each cells represents the differentials which are thusly relational and referenceable relative to a common origin and also relative to each other. Thus a network of reference frames can be created that enables the whole form to be referenced by the origin/common reference frame or by a relational reference frame. This allows for macro and micro relations to be "describable" and is why i thought that tensors might be a relativistic reference frame initially. They are not, but they possess a relativistic reference frame, which i have just described.

Finally each cell can contain quantitative data which is corresponding to its reference either relativistically or by common reference or both. And additionally the quantitative data may be related by function/formula to any number of cells within the spreadsheet. It is to be noted that the quantitative data may be measurements or ratios of any quantifiable property of the spaciometric form at that referenced region

Now spreadsheets are a specific instance of a much more general class of applications which are: relational databases. Thus any relational database can be constructed to form a tensor which will have the description already advanced. Some relational database apps do not have all the mathematical functionality of a spreadsheet but this is a design consideration not a fundamental distinction, as this can be easily added to any relational database.

It is of course possible to reference between spreadsheets collected into a book format and across books et al .

Thus a good example of a tensor is a quantitative relational database. Many scientific measurements of experimental results are held in such relational databases, which when constructed appropriately would be exact tensor candidates .

So iguess just to finish the thought, that 3d Fractal generators are some kind of Tensor sculptor and tensor manipulator algorithms with the formula being the relational link to all differential elements of the tensor. These differential elements at least in Quasz are related in the form of a quad block.

So what i am delving into now is a spaciometric understanding of rotation which is not based on the euclidian tool "angle" but rather on some more topological notions.

I am fairly certain that i can distinguish two types of rotation which are discontinuous to each other but linked by topologically based limit processes, In addition i want to begin the analysis based on the "logos" response to see how much easier that makes intuitive mathematical thinking. All sensors are involved but the two i think i have to use in a TOTE analysis of spaciometric rotation are a visual region or boundary as a mrker for axiomatic visual orientation and an auditory linked sonar map with the auditory canal orientation sensors switched on. A Test Operate Test Exit (TOTE) is a basic , the basic cybernetic algorithm for traversing a self regulating system. This also happens to be the most basic iterative process that can be devised. Thus iteration and comparison and distinction are at the foundational level of any self regulating conscious intelligent system.

Again if this means my apprehension of the fractal nature of everything is inevitable because of this or that this is evidence that the fractal nature of the iterative processes in the universe are universal and always acting at every scale i cannot possibly distiguish.

Hiya matt, got to run but great to have some input. I am hoping Charles Wehner will return and give his insight. Will read your post link later.

Just to note that if i use P(ø,r) where r= n*ø and ø is in radians i have a reference frame which i can apply to a plane using 1 parameter ø and scalars n which are elements of the hyperreals as another parameter.

So now i am waiting to see if i can intuit a frame that works spaciometrically like this. This is inspired by plant leafing patterning, how plant spatially organise their leaves. Yep, i have been in the garden again!

So i was going to write about the probabalistic nature of my experiential continuum, but aside from the fact that it is a personal response to the uncertainty of induction and prediction it was only to note that our culture has measured it by chance, luck, likelihood, and probability and gaming odds. This combinatorial and permutational ratio map has brought the binomial theorem and the binomial series(discovered by Newton) into an important juxtaposition with a more computational approach to probability and a wider application of the probability model to physical/motion events, that is relativistic events; provided they can be represented by a compound interest type formulation. Thus second order Taylor Expansion with all its conditions provides a basis for a probabilistic formulation of the event described by the initial formula .

any way i guess i should flat out just define a unch of terms related to the logos response. These tems are all based on the comparison of sensor signals as measured by a iteratively structured array system with massive parallel processing functionality, i.e. me!

So i am going to have i think visiometry, audiometry, gustatiometry,kinesiometry which has an important subdistinction proprioceptiometry. Some of these words are pretty ugly huh? I might come up with some cooler ones later.

So basically there is in each of the major sensory systems in the central nervous system/ central neural network a process of ratio distinction and storage, which constitutes the comparison or measurement response of that system to raw signal input. Thus an initial sensor array has its raw signals processed and stored as a ratio response: the signal at its sensor locations compared to all the sensor locations and their differing signals. Immediately the concepts of Area , Focus , and attention become nascent and emergent along with relativity in location. All these factors as well as the raw signal are stored or inherent in the structured array system, available for the system to utilise at different levels of processing and iteration.

This is the logos response technically desceibed an the above terms enable me to focus on describing the functioning of one of the systems or a synesthesia of the systems.

When i listen to music the fact that it is an experience of ratio variation is immediately apparent,but when i look at a visual scene the symphony of ratios in it are tuned out because that is a musical metaphor. a patchwork quilt of ratios comes to mind. And the sensations of texture and touch are a "thrill" of sensational ratios of hard, soft smooth; just as the gustatory responses produces a bouquet of flavours all ratioed to one another.

~It seems obvious to me that our logos response is ratioed response that is the source of all our language distinctions and grammars and syntax as well as our mathematics.

Originally posted by author:

A bit of fun which may help me to apprehend a relativistic reference frame.

And then

How to build a hanging binary tree mobile .

Some homework

Which leads to a computer storage and processing analogy.

Which almost gets to my idea of a binomial tree mobile with the notion of a binomial heap.

Here is an application of a binomial tree to stock price evaluation. Essentially it is a tensor for a stock market movement over a given time frame. It is a good example of a dynamic tensor which can map dynamically scale variations in the quantities of interest, and show that a tensor is a store of relationally linked differential quantities in a relational way and does not have to have a spaciomeric form linked to it. In fact the tensor "form" as an array is a convention or set of conventions because the form for an array is physically different as one moves through different ways of representing it; eg. on paper,as a solid object, as a computer memory allocation, as a mobile… :tease:

So finally a binomial tree mobile can be simply made by hanging two binary tree mobiles from the same yoke.

My question is do i make a trinomial tree mobile by hanging 3 binary trees from the same yoke?

Have a play and enjoy ;D