The very first thing i notice about a summetria is what is called "invariance".
Naurally, in a motile field theory you would expect everything to be i motion. therefore "invariamce" immediately stands out.
n a motion field, which is how i characterize my experiential continuum, every thing is in motion, but these sequences are not detectable without an observer who ohjectively/subjectively establishes a reference frame by acceptance or connecting to one specific "invariant"-like feature. of course whatever invariant may be defined to encapsulate, it is immediately rendered relativistic by thi fundamental set of constraints.
Therefore i should not be surprised to not find , nor indeed should i rely upon absolute "invariance", or "perfect invariance".
Invariance in a motion field is a relativistic sequential motion effect,due to sequential motions that are relative to each other and a common relation. Such a common relation is called a centre of symmetry. This is not the same as the summetria within which or amongst which we find these centres of symmetry. Thus symmetry is a related but distinct sub idea to summetria, and its specific attributes are pertinent to the notion of invariance only.
Thus when i look around me the invariant forms are really relativistic motion forms with a centre of symmetry and a relativistic motion relation on any region perceived as being in that summetria. Without the centre of symmetry i do not perceive an invariant form, but with a centre of symmetry i perceive an invariant-like form which i classify as dynamic equilibrium or static equilibrium according as the inter rellationshipps of the "parts" with each other and the centre of symmetry are variable or fixed, that is whether i perceive motion or on motion within the summetria using the centre of symmetry as a reference frame.
Clearly this is all affected by my own relative motion. And in relation to that the so called invariant form is clearly not invarian except in this symmetric sense just defined.
Therefor i learn to recognise these summetrias which have these centres of symmetry in all aspects that my experience allows, and internally i process and store hem under a storage/memory system hat marks out their similarites, congruencies, transformations distinctions etc. Therefore when i by this system perceive a summetria as being attached to a certain attribute that i have in memory, this perception itself is named as recognition; re- again cognizing- processing into memory formats.
It is clear then that a subjective recognition is unavoidable, and a objective recognition is hardly possible except in the ideal, and particularly in the subjective recognition of A.N.Other. All is therefore built on the experiential continuum of my progressive existence and the innate processing systems within my sensory meshes. My "world" is thereby unique., and all inter dependent action is by agreement and acceptance of "other" formulations.
The common consciousness that we experience is in the main communicated by a common language which enables not only immediate formulations to be transmitted and received, but also "past" formulations and "consciousnesses", which Jung recognised as our "collective Unconscious". As such our language forms a vast software library enabling an individual to be "programmed" to access the environment in many ways we call cultural, but which reflect ancient past, near past, and current consciousnesses, that is sequences of recognitions of "invariant", or summetria with symmetry centres in our "world".
Another important set of summetria are the orthogonal dimensions. These are a sequence of motions that rotationally are independent. They are fundamental, and in fact we have an orthogonality rotation sensor, which is "why" but really how we even perceive this summetria. There are only 3 independent rotations in any given orientaion, but of course here are infinitely many orientations. Orthoonality is such a unique sense that it may very well be the source of all notions of independence.
In leaving i note that i cannot measure without motion. However motion may measure itself against a stationary sensor array. To be effective as a conscious measure rhis state of affairs requires massive parallel processing systems.
Thus i have a qualitive difference between innate notions of measure which are produced by a massive prallel processing scheme, and my derived measures by action, which are produced by a focussed or single thread processing system.
Due to this difference i do not have to derive invariance by locating the centre of symmetry. If a form is boundaried then from the relativistic relations within the boundary i am able to "impute" if not directly compute the location of the centre of symmetry. This imputation or computation derives from the massively paralle processing system which is being impressed upon by the sequential motion of an external source, or by an imperceptible "scanning' of the "eye" or other sensors to provide motion for the measurement or comparison.
What is the "center" of symmetry of a sound or a smell?