What's a pop tart and where are the modular forms?

Disclaimer ( I assume modular forms are functions that map something congruent to the integer set to a cyclical set but I might be wrong)

When you see a painting and know that it is pop art how do you know that it is pop art? A helpful tool is to compare the style in question to something very simple and familiar such as realism. Now you may have seen many works of pop art that are not depicting anything that isn't physically possible, and they may even feel as though they closely approximate reality because of the nature of the objects and scenery depicted. So what do you notice that's different? Another helpful concept in art is the way that light plays off the object. Imagine any object as a collection of discretized surfaces. The simplest surface is a triangle. Now think about impressionism. Impressionism is a type art that plays with light in a way that is very vibrant, but is somewhat near to realism. This is because the painting technique makes use of many small paint strokes, which create many possible surfaces for light to sum with, and those become projections in our eyes that let us see the painting in detail and the more surface the more apparent detail there is, which is why good impressionism approximates reality somewhat well because things like water just have a lot of randomly placed surfaces. Almost realistic, but not quite. Realism however makes use of gradient, which is essentially the highest definition version of those triangular surfaces because the gradient is the spectral version of that otherwise discretized image which we would see in any other form of art by definition, unless it is surreal or classified as something other than realism because of some other defining feature that does not simply speak of the way the art behaves in the presence of light as it pertains to reflection, which is a bit of a misconception, but I've been over that and it's safe to just say objects behave like they can reflect light anyway so it's fine. The gradient is the continuous version of that otherwise triangular net which probably is actually a triangular net in some regard even in the presence of what looks like a gradation, because of the speed of light being finite, but that's also a discussion I've already had, but if you want a reminder it's due to the finiteness of clock rate that follows from the finiteness of the speed of light, which means a finite resolution, and the simplest surfaces are triangular surfaces so it just follows that they would probably be triangular at their highest resolution. So what is different about pop art that depicts only realist scenarios? Well look at the boundaries. The boundaries are well defined to the point of using only contour and not gradation. At least in my personal experience, but I have seen a few examples that are apparently to the contrary, although I think it's probably necessary to define it as art that makes use only of contour to create boundaries on objects. Also color, but not variance of color across a space.

Before you continue reading try yourself to imagine an example of ways to make use of variance. What does this mean? What do variance and color have in common?

Okay so we're done. Maybe we could make more observations however. I've made a lot recently. What do grayscale images have in common with colored images? What is color? Color is spectral. Spectral geometries make use of variance, because color is frequency, and variance happens at a rate. So when you vary in terms of a gradation, which we always do, we can imagine that playing with the brightness and darkness of an image is like using frequency, because it is a display of variance.

Let's double back. What about impressionism again? A familiar scene in impressionism is that of water. Why might this be? Well it works very well, because water is often seen rippling vibrantly in the presence of the sun and this rippling is due to the summation of many many waves which tends to a summation that looks more discretized, and truly is, because summations at infinity of sinusoidal waves or the spherical variant of that I believe always create modular forms if it is the case that the phase space is finite or discretized I should say if that is a better way to phrase it because that's what I mean. If the phase space is discretized then the set to draw from is a pattern and that pattern that is cyclical because it is of a finite foliation which means it creates a modular cycle because the phase space having discrete states or discrete elements in a finite space which physical reality is because of the speed of light and consequentially the observable bubble of the universe it means it creates a mapping that is like that of the integers to a lattice variant of the complex plane which I've discussed before and proved is a mapping that generalizes to n-dimensional integers due to congruence of the planar integers to the integers on the real number line, and that congruence therefor shows congruence to the n-dimensional integers which means that if modular forms map to the lattice variant of the complex plane then they have this congruences so even in an infinite number of spatial dimensions in terms of the phase we still have this same mapping for discrete phase spaces which practically speaking all phase spaces technically are as I've already described and this means that the summations in nature of waves that make the interference patterns that describe any object are of a discrete phase space and that phase space would therefor behave like a modular form because it's cyclical and the result of a summation of clocks with finite bit depth which means it's essentially the same as having integer wavelengths since the step size of the wavelengths is of a set that maps to the integers automatically by being of a finite bit depth. Here's a reason this is true: f(n) = (a/b)*n where a and b are any integer constants maps integers to f(n) which is the same as having a finite bit depth. An analogy that is somewhat removed, but somehow probably illuminates a little more information would be that of clocks. Periodic things are like clocks. Clocks have rates. You might say modular forms are clocks, which I don't entirely disagree with, but you can add clocks to clocks to make modular forms which is the premise I believe and that means you have strange forms of precession that feel less like the clocks we traditionally use. The speed of light is finite, so the rate of clocks are finite fundamentally. This means that given a set of clocks we have a discrete series of rates to map inputs to for a function that the series of clocks creates as a Fourier series. I guess it's not that far removed, but it is a little bit different because if it's a finite space you might assume it behaves continuously and since it's discretized you might assume it's finite, but reality is fundamentally continuous, so we have what looks like a paradox, but it resolves I assure you, because the finiteness of clock rate means every one of those clocks has a bit depth or resolution that can't be tuned to a variance greater than a certain value because the variance is measured once again by a clock, and every object is an interference pattern, and object interactions are essentially measurement or observations so this can be understood. The clocks occupy a finite phase space then that is also a lattice phase space, so they form a modular cycle. There is however the case of noise, but that's not a problem because the noisiest objects in reality are still for the previously mentioned reason not truly noise at what we can say is essentially a summation at infinity, because of the finite phase space those systems must occupy and you can't use prime number wavelengths as a set of the wavelengths to create a modular form because it's just a different series that isn't in the class of modular forms. This is what Wolfram is talking about in his description of causal invariance, but don't feel worried about it. Your practical free will is not at stake, and it just doesn't matter because it's so many states of reality that you'd feel satisfied and I'll leave it at that. Reality is also fundamentally amorphous so randomness is still possible. Indeterminism totally a real aspect of reality. If it matters to you for some strange reason. You can have all the possible foliations is what I mean to say and those foliations can involve situations where one outcome is the result of a rule where a is sufficient but not necessary to cause b but it looks like it was supposed to be that way because it caused b and when we make predictions about reality they are informed by our observations so we talk about causality in terms of probability and we would still have an overlaying sense that things are strictly deterministically causal unless we're doing quantum physics, and then we just don't believe that it's truly indeterministic, but it probably just is because of the amorphous nature of reality and the fact that distance is discretized so we can see randomness as a projection onto a Planck sphere like some information or hidden variable is at work that we can never uncover because of the nature of observation at that resolution, so the projection can display random looking data, and because of the arity of rotation in a plane it is the case that when we measure spin for example which is well known to be quantized and random, which we can now all understand, it is the case that we see that at an angle of measurement between quantized states we see probabilistically correlated spins, which are the result of the amorphous nature of reality due to the fact that reality is constructed out of information and information is by definition generic so it occupies all possible states, which means it can be random and since clocks tick at finite rates it follows that distance is quantized and this means geometrically the Planck sphere produces projections which contain causal coherence which is by definition probabilistic, and when we look at an entangled systems the correlation is due to what I previously mentioned is the arity of rotation in a plane, and the less likely the spinning objects are to belong to the same plane the less likely the spins are to be correlated, and due to the finite resolution of distance we consequentially see that when the angle is varied even infinitesimally so it does so probabilistically. The angle allows us to look at a greater range of spaces, but we can't deterministically effect what spaces we look at so we don't see perfect anticorrelation, or perfect variance of correlation, we see variance that is probabilistic in outcome, because we don't actually have the ability to vary continuously the angle of measurement, which is what bell's inequality experiment showed, and this is why. The Planck sphere obscures the space within some range, and what we observe is a very real random outcome if we vary the angle of measurement between the entangled particles. It's randomness might also be understood as random because it's sinusoidal and the sinusoidal functions is not unlike the result of taking a random walk and creating more and more instances of the random walk and looking at the summed image of all the random walks where we see that the image approaches that of an n-sphere, and so we see that perfect indeterminism smoothly varies like a sinusoidal function as we change the angle of measurement, because the summed image is n-spherical so the it maps to an n-spherical wave which we can now connect to the lattice variant of the complex plane as the phase space is discretized and there we have the modular forms that make the clocks of reality in n-dimensions, and finally I'll end on one last point which is the simplest to understand that is the sine wave maps random distribution because of a property of randomness that is its uniformity as well as a property of points that is their uniformity and consequentially a property of n-spheres, because of smooth expansion from a point and the resultant inferred uniformity of those n-spheres, and this is why Bell knew that if the outcomes of measurement of an entangled system mapped to a sinusoidal function then the distribution is true random and this how we knew back then that reality is on some level indeterministic, but as I pointed out in this article it's because of the genericity of information and the ambiguity of angle of measurement created by the discretization of spacetime that is caused by the speed of light which results in the resolution of a Planck sphere that it is able to have this indeterministic property. We can't actually vary the angle with absolute precision so our observations and all physical interactions have at some level an element of randomness.