Whether our concept of number happens to be an abstraction of mind or not, our concept is derived from the perception of our environment.
Number is analytic, the absolute properties of any one number mean that there is always a predictable outcome, e.g. 5*5 = 25.
It is in this sense that we use number to predict outcomes or or objectify our observations, i.e. calculate lengths or distances, & calculate speed and force.
From this it seems, rather than self-identification, number is used in the process of identifying our externals through an internal process (e.g. counting).
The accuracy of mathematics and physics to describe material things and their processes means that our concept of number is accurate, but only as accurate as our observations.
Observable 'physics' is thereby limited by our own effective capacity to perceive physical reality.
For example, it is becoming evermore apparent in the realm of quantum physics that the mechanics of the subatomic world is much different to that which we perceive/observe directly.
Physics in and of itself, however, must work using mathematics. It's as easy as 1 + 1 = 2... supposedly.
In the quantum realm, calculations get much more complex and in some cases it becomes impossible to predict outcomes as we would expect; for instance, Heisenberg's uncertainty principle.
Despite the seeming unpredictability, one thing that is inherent in seemingly all things is proportion.
Whether it be in the form of quantum probability or even mass or volume, I am defining proportion as the relationship of two numerical entities in equalling a singularity.
Simply, a + 2a = 3a.
This proportion is inherent within all things that physics currently understands and can reduce to simple formula. The real problem arises in relationships we do not understand, because things don't add up when we run the arithmetic.
While number is an effective means to understand the world as far as we can observe, there is no way
to determine whether our conception of number is purely a figment of our own perception or exists objectively within reality at large, but it seems that through the bridge of our perception number is an effective way to describe reality at large, but the further we delve, the less effective number becomes.
One thing is consistent, however - proportion, where proportion is a relationship between two entities/variables.
While the world is in perpetual flux, number is absolute.
It is the relationship between absolutes that excites the state of variability.
Until again, change (function) meets constant (number).
Besides, 'numbers' by themselves aren't worth talking about. What is a number without it's relationship to other numbers? Or without it's individual proportion to a larger whole?
Self-identity has nothing to do with it.
Numbers are used to identify individualistic variables among others, such as a cat predicting it's trajectory when jumping.
It's not number how we would understand it in our model of 123456... , but number as proportion between singular entities as is the relationship between two numbers or variables that truly of interest.
Thus is the cornerstone for maths, physics, chemistry, and too biology.
Proportion either describes number or number describes proportion, but this is missing the point.
So, for all you avid sceptics: Proportion is inherent in nature. Am I wrong?
Sorry for being long drawn out and painful but I needed to go into depth.
As for the topic of physicality, 'physicality' as we describe it is contingent upon the experience of 'physicality', and 'physical' experience is determined by sensory perception.
Therefore, our understanding of 'physicality' in an objective sense is meaningless because it is contingent upon our perception to be understood within the realm of, say, physics and maths.
What is physical must be that which is an entity that undergoes physical change. Entity being, for example, photon. Physical change being for example, linear movement.
Therefore, what is 'material' is problematic, but what is 'physical' is not.
A photon is hardly material, although it does have insignificant mass.
However, a photon is involved in physical change - movement.
Therefore, a photon can be considered physical.
I'm going to leave it at this because I'd like to see some responses before I continue.