[jpatte]

You seem to forget that maths and physics are meant to describe reality, not be reality. Any abstract concept (like numbers, forces, shapes, temperatures, energy levels, ...) we use to describe a real thing is different from that thing itself. If you think about it, even 2 isn't "more real" that Pi, because there are no 2 identical things in reality.

When we say "a human hand has 5 fingers", we use the abstract concept of "finger" to make that description. It is abstract because each "finger" is actually unique. It's just a handy approximation we use (pun intended) for descriptive goals.

Basic maths is not reality. Therefore no, irrational numbers do not "fall out of it".

Edit: format

[coldtea]

>You seem to forget that maths and physics are meant to describe reality, not be reality.

So why describe reality with an ideal and infinities and not based on fixed/arbitrary precision but limited math?

[brians]

Two is the number of electrons in He, and the number of slots in the lowest orbital. Two appears in nature.

Circles appear in the shape of that same s orbital, though, so I don't see how to avoid pi.

[pbhjpbhj]

There's no such thing as an S-orbital, there a probability distribution where a bounded probability produces an approximate sphere, in any universe with more than two charges that sphere is going to be 'irregular'.

The parent argument works here as much as for fingers though, those 2 electrons are identical but their spin differs. All electrons differ in the Standard Model by either spin or location.

[pbhjpbhj]

So you deny classification of similarity - fingers have structural similarities that allow them to form a class of object/item, this class and it's per-person sub-classes have a reality that to me is not entirely abstract.

Even without classification we can create arbitrary groupings of physical objects, those groups have cardinalities. (Unless your materialism denies the existence of more than one thing/substance; philosophy is fun, eh.)

I'm for pragmatism in such things however.