if you place an object (a) with an identical object (a), together they form a group (a+a)

the ratio of the quantity of a in (a) to the quantity of a in (a+a) is

a:a+a

the ratio of the mass of (a) to the mass of (a+a) is

a:a+a

the physical ratio

a:a+a

is precisely identical to the numerical ratio

1:1+1

the physical ratio

a:a+a

is precisely identical to the numerical ratio

1:2

so

a:a+a = 1:2

human number theory and natural physical laws are based on precisely identical principles