So i have been looking hard for some easy introduction to tensors and there is none.
So i guess i will have to take you through my ideas simply.
Shunya is full: replete with all possibilities,I instinctively want to measure shunya. I cannot help it. Being sensate is to measure shumya and the Logos Response is my conscious apprehension of Shunya.
I learn to go further and by iteration i develop perceptual models of shunya that gradually realise distinctions as fundamental as "space" and shunyasutras in "space".
Shunyasutras are part of the language response to the perceived distinctions in space and are everything that gives me a sensate signal response. A subset of shunyasutras consists in the Arithmoi.
The shunya sutrasare perceived "forms". They are also what are referred to as Tensors.
Thus a Tensor example would be a frog, lets say.
Shunya is a summetria, my perception of Shunya reveals a summetria. This means that my perception of Shunya is fractal at all scales and is characterised by reflection in "points"/through regions;rotations aroound multiple centres of rotation and rotational expansion/extension around multiple centres.
My Logos Response provides me with a built in reference framework consisting of multiple centres of reference with a minimum of 2, and through this set up a relativistic sense of measurement within the summetria.
The summetria as a result consists of all shunyasutras or tensors.
Now my built in reference framework enables me to devise multiple tools of measuring shunya as representations of this innate "ability", and as i adopt and utilise each tool i develop and conform my apprehension of Shunya accordingly.
Therefore my notion of shunyasutras is conformed to whichever tool of measurement i utilise, consequently so is the notion of Tensor.
From my measuring tool i can define the inate notion of magnitude in line with the tool i am utilising. If i am wise o these connections i will utilise a dynamic tool not a fixed one, although fixed tools have there place down the ranking!
The inbuilt reference framework of the Logos Response is the Basis and the Well spring of any notions of Spaciometry. Utilising my dynamic measuring tool i can apprehend and construct a dynamic spaciometry, which being a representation of my innate perceptions of Shunya will contain representations of shunyasutras and therefore tensors.
Any representation will be subject to the fractal and iterative nature of my perception of the summetria of Shunya, thus for every shunyasutra i will be able to perceive a scaled version within it ad infinitum. These therefore are nested shunyasutras/tensors.
Depending on which measuring tool i devise will be the nested shunyasutras i will perceive in any shunyasutra. In particular if i devise a rectangular,rectilinear "ordinate" measure i will not only be focusing on arithmoi,but also cartesian tensors.
Focussing on a cube, then shunya "demands" an anti cube to maintain summetria. We conveniently ignore the anticube(!) and focus on the cube. The cube has an innate orientation defined by it and the anti cube,it has an inate rotation again defined relative to the anti cube and an innate rotational expansion,again ultimately defined by it and the anti cube,but with the first two motions and orientations defined the 3rd can be defined relative to these, thus forming an "internal" definition.
It is the internal definitions of orientation,rotation and rotational expansion which the notion of Tensor relies on for its "mathematical"abstraction.
Within the cube are an infinite number of nested cubes at varying scales. If i choose an internal scale i can use that internal cube to compare with the original. This type of comparison is the essence of measuring. The finer the scale the more detail i can measure.
Thus back to my frog shunyasutra/tensor: using a small enough scale i can measure every structure within its form with my cube.Because my cube is a dynamic magnitude i can measure every motion of every part of my frog. Thus i can establish a detailed cartesian tensor description/representation of the frog.
The devil is in the detail, and how to record that detail. The straightforward answer is to record it holographically, which essentially is what my innate memory capabilities do. Representing that in a tool requires me to have a stereocopic recording device, a laser hologram and a computer processing facility. job done.
On a historical note: before we developed these devices and machines we were forced o record these measurements manually. Thus we came up with lists, tables, blocks etc all as ways of recording this information.
The task was mammoth, so no wonder it was simplified to the minimal. Thus static systems ,small data sets, infinitesimal calculus methods all were employed to give an instance of a shunyasutra, particularly arithmoi.
Historically the idea of a vector a determinant and a matrix surfaced in different contexts. The contexts however were mainly dynamical ones,but not always. The issues arose with the inadequate definition of a vector in opposition to a quaternion which was if anything a dynamical system of the first order. Thus when "vectors" proved inadequate, matrices were sufficiently developed to be drafted in to support, and when this system too proved inadequate Levi and Ricci had sufficently genaralised the construction ideas to provide tensors.
However Quaternions were suffiviently developed to do all these things more efficiently. The difficulty with quaternions was they were not understood, and later were not trusted. Vectors and matrices have always been a derived subset from quaternions, an "easy" introduction to quaternion manipulations. And because thry had widespread support in the scientific community, especially in America, they ousted Quaternions as the tool of choice.
There is still much research to be done on the applicability of Quaternions, but Doug Sweetster has already showed their sophistication and power.
The only things to remember are the anti quaternion and the minimum dual quaternion reference frame. This duality would enable quaternion tensors to be utilised effectively as measures of shunya.
The only other thing to explore at this stage is the fundamrental trig ratio base to i,j,k.