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Bob: So you say there is no need for the non-physical, eh Fred?
Fred: Indeed, Bob. I have yet to see anything that cannot be accounted for as a physical thing, in this physical world.
Bob: Aha! I have got you now, my friend. What about number?
Bob: Yes, number - that abstract concept upon which mathematics and taxes and so many other things are built. I look around, high and low, left and right, ahead and behind, but I see no number. Show me number, Fred.
[Fred holds up three marbles]
Bob: No, no, don't be silly. I can see the marbles. But I see no number, just marbles. Show me number!
Fred: Odd requirements you place on this number. Tell me, Bob, before I show you number, will you show me a banana?
Bob [sputtering]: What?! A banana? What does that have to do with the conversation?
Fred: Just humor me. Show me banana Bob.
[Bob grabs a banana from the philosopher's food on the table next to them, and holds it up to Fred]
Fred: No, no, I said show me a banana. I see yellow, I see length and shape, yet I see no banana.
Bob: Its right here! Are you blind?! [shoves banana in Fred's face] The yellow, the length and shape, these things make up a banana - this my friend, is a banana!
[Fred snatches the banana out of Bob's hand and holds it out in front of Bob]
When I made this post, it obviously wasn't intended as a detailed exposition on the nature of number, or of abstracts. I was merely trying to make a point creatively, and that point was that those who put forth the idea of number as a non-physical thing seem to expect it, if physical, to be some sort of unique object they can hold in their hand, look at, weigh, and so forth.
I feel that that view is too limited, that one should not expect number to be a simple unique object. You could carve a block of wood into the shape of a 4 (or IV, etc.), but that block is not the number four - it is a block of wood. It is also a symbol, which represents the number four to us because we use Arabic numerals (or Roman as the case may be), but if we did not use that numeral system, the block of wood would be just another random shape. Expecting to find number in such a way through a block of wood is absurd; but that does not mean that number is thus left only to some non-physical realm (that there is, say, some Platonic universe where a thing exists much like a block of wood, which is the number three or the number four).
I think a better way of looking at numbers are as patterns - patterns in the world and patterns in the mind, with the connection between. The patterns in the world are what I was getting at with my dialogue above. We see three marbles - or it might be more accurate to say we see O O O - and we associate that with three. We see any single object (like a banana) and we associate that with one.
This association takes place in the mind as patterns in the neurons that make up our brains. We apply the system of math and number in our mind to the world and the things we observe. O O O represents three, it is a symbol for a part of that system in our mind. Yet it is hard to imagine developing such a system in the first place, without an initial a posteriori experience with real world 'numbers', such as O, O O or O O O.
Similarly, the properties of a banana are what we see, are sense data that we receive, and it is in our minds that this data is associated with the concept of 'a banana'.
In a sense O O O is three, not in that O O O is some unique object that is the number three, like the block of wood was expected to be, but in that the association takes place between the patterns in the real world and the systematic patterns in the mind. In this way, the banana is one.
Now the obvious question hanging over the whole thing, when applied to the whole physical/non-physical issue is whether these patterns in the mind (in other words, the mind) can be physical. For that I refer you to my article Physical Minds. Keep in mind I am not trying to present a for-sure view of the nature of number, just trying to look at the whole thing from a different perspective, and defend against the claim that numbers must be non-physical.