I still don't think you understand. What I'm saying is that you are using two methods by which to use mathematics. Let's call these Method I and Method II.
Method I: The world began with some uncertain fluctuations and the closer that we can pin down the initial conditions and boundary conditions, we can use differential equations, etc by which to determine what the universe will look like at some later time (t1, t2, t3, etc). Mathematics is used to predict, but it is very ineffective if the model is very complex given the uncertainty due to the UP, complexity of the problem, etc. Knowing the number of galaxies is extremely unlikely since the calculation is very complex and the initial conditions may be random so we can never accomplish this task.
Method II: The development of particles conforms to certain symmetry groups and the world had no choice but to conform to certain mathematical identities once the physical constants were determined (either by other required symmetries or by random settings caused by broken symmetries). However, once we know these fundamental constants we can demonstrate why certain particles must exist and conform to certain properties (e.g., baryon number, strangeness, etc). The properties and existence in these cases are determined by the 'first principles' of the symmetry groups themselves.
Now, Method I is the traditional means by which science developed. It includes the majority of physics up until the gradual introduction of symmetry into science (e.g., Lorentz equations, Yukawa's meson theory, Gell-Mann's eightfold way, etc). Method II is now much more popular - especially in cosmology and particle physics. These disciplines have conditions much too complicated to use Method I, so using Method II is the best way to know why the laws are the way they are and why particles show the properties they do.
What I'm asking you is whether Method II can be used to determine how many galaxies exist in the universe? If not, then why not? Why can Method II be used for the number of elementary particles having certain properties but not for the number of galaxies exhibiting certain properties?
Warm regards, Harv