User blog comment:TheMostAwesomer/Some things/@comment-180.214.232.83-20141220181138/@comment-1605058-20141220210649

But note that when looking at your hands, you don't see number 10 per se, you just see some representation of it - in this case, you see its representation in amount of fingers you have. But it's not really the essence of "10-ness" you see here. In physical world you will never see pure "10-ness". You might see a collection of objects and say "there is 10 of these", but it would be too much to say "this is what 10 is". Same goes for symbols - when you see a vertical line with a little hook followed by an enlongated circle, which is a common representation of number ten, it's again too much to say that "this is how ten looks like", because what you are pointing at is just a, one of many, possible representations of an abstract object which this number is. Why would you say that "10" is what ten looks like, if you can also have, say, a Japanese numeral? In what way would it be worse?

As for exponentiation example, I think this is pushing it a bit beyond what one would call a physical interpretation. By the same line of reasoning I could say that, for example, Bowers' linear arrays have a physical interpretation, because I can simply give an iterative procedure of achieving this number.