Eckard,
Does common sense fit well to my idea of ""past" time displayed as the inverse of future time"? Good question and thank you for asking. My short answer of course is yes, (if by "common sense" you mean "good sense" and not "common opinion") for the purpose of the STM (space-time-motion) model.
What does not make good sense is the idea of negative time. From reading your essay, you seem to know a lot more than me about the history of math, but as I see it, the use of numbers to represent time is the same as the use of numbers to represent objects. Objects are numbered for the purpose of counting them. The number we assign does not represent the object. It actually represents a quantity. Negative numbers don't even represent a quantity. They represent a deficit or removal. In fact, there is no such thing as a negative number because negative is not part of the number, it is a mathematical operation.
Time is not an object and it is not something that passes. It is the scale invented to compare one motion to another standard motion (a clock). So it makes sense to quantify time. But how can you have a deficit of time? You could say that one motion takes less time than another, but that does not mean "past" time. As you said in your essay, "Elapsed time is always positive". The concept of "the past" identifies the elapsed time after which an event happens. That is POSITIVE time following the event reference point. So for general discussion, there is nothing wrong with considering the past to be a quantity of positive time as compared to that event. But the negative operator doesn't apply. I think that your discussion about the problem with mirror symmetries is a good one. A mirror image looks like it has depth, just like the space it reflects, but building a model based on that would be a fundamental mistake.
The inverse is also an operation and I think it is more appropriate for the STM model for the following reasons. Imagine a pulse of light from a star traveling directly toward a quantum particle. Let's say it is 1 light-year away. Using our standard clock we say it will take 1 year to reach a point at which we stop the clock to define the interaction (event reference) with the particle. It makes perfect sense to use positive time and say that it is going to take 1 year (future tense) to travel the distance, but once it did, we now say that it travelled 1 light-year within that year. "Within that year" means per year and "per year" means inverse year, so it makes perfect sense to use the inverse when referring to the past. You might argue that this also applies when speaking of the future, by saying the next pulse is going to travel 1 light-year per year, but now you are referring to velocity - something that can happen in the future. Once it has happened, there in no more velocity, no more change as such. Now there is energy that can be quantified by frequency. As you said, "only the past is absolutely closed in the sense it cannot be changed".
Remember, the purpose of the STM model is to relate the quantum model with the relativistic model. They are just two models that use the same variables but they differ in that one uses motion through space (requiring time as a variable for velocity = dx/dt) and the other does not (it requires frequency for energy = hf). Superimposing the two coordinate systems just allowed me to show how the equations (kinetic energy and a particle's internal energy) from the two models are related.
In terms of consciousness, interaction means that one bit of information has been transferred from outside to inside of the particle. This is just another model. It considers physical matter to be a holographic pattern that takes on physical form by interacting with its surroundings. Since I want to use the same variables, time (T) and frequency (1/T), to describe the transfer of information to a particle then 1 unitless bit of information can be written as the product T x (1/T). I'm still working on that.
I like the ideas you brought out in your essay regarding cosine transformations used in audio technology. I am more familiar with Fourier transforms (which seems appropriate since my axis uses both time domain and frequency domain) and LaPlace transforms (which are used for image sharpening in medical imaging).
I have started considering how the STM may be a convolution of the two coordinate systems but I'm not sure where that will take me. One of my goals is to see if the information can be de-convolved and back-projected in order to determine if information is actually recorded and retrievable.
Ted