http://m.youtube.com/watch?v=r18Gi8lSkfMWhen considering trochoidal rotations be aware of the dynamic nature of rotation. Hence recognise the need for space-time .

Traditionally we are taught axes as orthogonal triplets. We do not question this presentation as we have no idea what axes are? We are then hoodwinked into some faux reverence of Rene Des Cartes "Coordinate" system. The truth is DesCartes did not establish such a system!

The Greeks already used and established several flexible reference systems for locating proportions in space . Apollonius in particular refined a system that was " shape" or fom concordant!

In all greek thinking the circle shape was fundamental. Similarly both in India And Egypt the Sphere was a fundamental form. Not neglecting the Sumerian/Akkadian contribution in which many wisdoms of the ancient world were collected by the Empire and cuneiformed.

So the line segment became a fantastic tool for recording ratios / proportions ( Logos Analogos ).

The hardest won ratios were the chord and later Sine ratios. These ratios were not tabulated until much later, instead an Egyptian practice of using the circle to freely construct any right angled Triangle was later ascribed to Thales .

Wallis after studying greek thought combined many ideas into the measuring line concept, and many circle properties into the orthogonal coordinate Ordinate system we attribute to DesCartes! Really DesCartes ideas survived as the Lagrangian Generalised Coordinate system.

So what is an axis? It is a Spindle around which a wheel spins . It is derived from the concept of an Axle. The same notion underlies the word "axiom".

Wallis is responsible for the Law of Cosines, through which he was able to write down a general expression for the conic section curves. Until his breakthrough revision, Conics were carefully carved out of blocks of wood shaped into cones!

These cones themselves could form a reference frame, but we are so indoctrinated into the measuring line concept that we do not find that a natural thought!

We have many coordinate systems all based on a Fractal measuring schemes, but we typically obscure their inhomogeneity . We replace it by some pseudo reverence of Pi ! Because of pi many have no understanding of i that is sqrt(-1). And yet t most profound transformation scheme was set down by Cotes, and Decades later by Euler in greater detail that expressed how to use i as an axial lable for circular arc "lengths " or more accurately magnitudes as Euler and all classically trained philosophers described extensive and intensive experience.

Thus Fourier reintroduced this freedom of coordinate reference frame at a time when many of the intelligent elite were adamantly stuck in the straight line mode of measurement, believing their own assumption of Newtonian principles for Astologers and ignoring his general rotational , vortex exploring dynamics.

The Fourier transform enable us to reference a point in space using curved planes not merely straight edged planes. Typically you will require at least 3 intersecting surfaces to identify a point in der Raum!

This video introduces the method in the most accessible way for Fourier Analysis along one axis of rotation. Using 3 or more axes of rotation means any spatial form can be represented by a data set of Fourier transform coefficients.

We can view space-time as this rich description of rotating axes for which we can measure a data set of coefficients unique to any particular form.

More than that: we can characterise not only form, but also haptic force, colour intensities , physical signal response characteristics especially magnetic resonance responses for specific space - time topology. That is, any object is a space-time object not a classical " geometric" on.

For space-time we may substitute a Fourier aether .