Abstract Objects in Mathematics

If I draw square on a piece of paper has a mathematical 2 dimensional object been created and if so can it be touched?
- Steve (age 52)
Canada

Most of the objects in mathematics or geometry do not exist in the physical space. Those abstract things are not observables, but some imaginary objects which you define by arbitrarily assigning some properties. A square is a 2D object that has 4 corners and equal perpendicular sides. When you drew a shape on the paper, you have actually created a representative figure of it, i.e. that is a part of a paper bounded by some graphite which you imagine that it has all the properties of the idealized square object. The same is also the case with the numbers: 5 does not exist anywhere in the observable universe by itself. But you can assign integers to objects in an order to count them.

Tunc

(published on 02/07/2015)