I'm not sure what you mean. A photon is an idea of energy, nothing rotating as far as I know?

A wave-packet if you rather like to look at it that way is nicely described here: " It is true that one can construct a "localized" wavepacket out of single photon states. Because it is constructed of single photon states, it is an eigenstate of the number operator. However, it is not an eigenstate of the Hamiltonian so it doesn't represent a state of definite energy. Of course, the wavepacket can have a fairly well defined average momentum and average position consistent with Heisenberg. You might be tempted to associate the variance of your packet with some kind of "photon size", but its clear this size has nothing particular to do with any kind of inherent "photon size" and is most properly associated with how you prepare the system. In particular, such a wavepacket isn't exactly what people usually mean when they say photon. Such wavepackets are nevertheless useful for instance when one is talking about the continuous mode theory where it is difficult to give a precise definition of the photon. "

And seen as a wave it's something 'immaterial' reminding us of waves in the ocean, having a lot of the same properties too. To me the photon only exist in the instant it 'dies'. It's first and foremost an 'interaction' between the observer and what's observed.

As for how string theory treat it? Well, I'm sure you already have looked at it but, if not,

look here. for the definitions used. The explanations made have to become 'esoteric' as they use one dimension to create two, by using the idea of 'world sheets' and 'vibrations' aka motion to build 'dimensionalities'. What they do is not only to use a singular dimension, they also introduce 'motion/vibrations' on it and from that and some 'arrow of time' build the rest, what we call matter and 3D. Times arrow they already introduced as they expect a vibration.

A vector is a description of something having 'a direction and a speed' so when you write "random probabilities within vector mathematics would lead to the occurrence of repetitive cycles that would perpetuate by lowering the deflection or conflict among its constituents below that of the chaotic ambient." I'm not sure what you mean? How do you get repetitive cycles out of vectors?

Maybe you are thinking of it out of gravity, a straight line bent to space?