You do realize.
That if you believe that there is a truth that is ideal in any sense.
And you believe that there is a one to one to one correspondence with your thoughts and mind and brain(no information is lost in exchanging those terms)
Presumable a part of the meaning of ideal is the notion of better than. Else it would be the real. Such is the presumption of the existence of a known ordering on truth conditions of being ideally anything, including truth.
Then there is a better state of a brain than another. Namely if there is a true one to one correspondence, there is an ideal state. And I can state that if you additionally believe there is a definite state at any one time; that is, that there are coherent discrete ways of chunking time and that there is a coherent way of discretely chunking space, that you think there is a truely unique correspondence. Because if you cannot detect something incorrectly at every moment, then that means you are correct. If it were allowed to vary at the level below the smallest that could be detectable, then eventually there would be a better theory, meaning that what you thought was the best theory wasn't actually. Another way to interpret that is that for your measurement system, if there is going to be any variation, you aren't going to be able to detect it by going smaller because then you detect it, so if there is such a set, then let be the equivalence set for a moment called the ideal equivalent set for your measurement right now. Except we were assuming that there is a unique truth, and so I would say there is but only conditional on your measurement system including evaluation functions.
If you believe that something has causal force in the world, and you believe the world is in any sense static, then at least for whatever that static moment is. There is something to detect. I want to argue that static is a misnomer. If relativity means anything it means that. One way one can interpret squared numbers is as an additional dimension. That is the premise of polynomial curve fitting.
That is you fit a separate mean parameter theta1 and 2 for x and x^2 not to mention theta0 which accounts essentially for your measure's mean. Why don't you consider the sum of each of their random variables then when fitting a linear model. If you actually think they are independent dimensions then they should be treated as independent dimensions, and each should have its own error term.
And there is some relation that might exist between every point in the rationals such that it is the square rooted relation of two points that define the space time derivative known as the speed of light which since we know it exactly in terms of our local units right, so we can just define spatial distances in terms of that integral over space known as a light year or 1 absolute amount of distance that light can travel in a year. If light can transmit information, then that means that if there is a definite minimal size for time, then there is a definite size for the minimal space estimate, since we've established a definite size for minimal information transfer via definite time and speed of anything(since definite inside definite can fit snugly eventually, that is going be the 'ideal signal' for your measurement device, but what would the square of a binary variable be other than itself. Since there is a maximal truth to be approached either you are on it in one interpretation or you are not. Any squares are still going to be identical to the original if true equals one. Therefor measurement of the ideal will create an equivalence class if truth is obtained, meaning that there is no more measurable variance ever. At all.
That's a bit boring innit?
Why don't we calculate variance in a time delayed manner? Or at least had an additional term for the squared term and the first term, and the measure itself. one way you could interpret any causal effect whether that is on something you are able to measure or something that affects any of your known measures indirectly. Which could be thought of as a ratio of sorts. Well my suggestion is just that ratio changes over time.
There seems no reason why it shouldn't other than that we live in a Euclidian world and so we only ever need to worry about intersecting lines that never vary in scale over time.
Fine polynomial, but why don't we try a Fourier basis if nothing else. Or a wave.
I don't understand how you could have a transverse wave without being continuous yourself. It would only at best be a step function since if only one wqs continuous you could transform it into a longitudinal wave (i think) or at least a countable set of waves if neither was continuous then you'd get steps. To get transverse though, to really model water if its randomly distributed wouldn't it at the very least have some Gaussian noise in addition to the obvious signal that it carries, even if it is composed of a squared term as well.
Oh and you can't record Euclidean distance on a cross product of two rationals, since then at 1,1 the distance from origin would need to be square root of two.
And note that if a particular truth exists, it is