Symbols

Last night we had one last (belated) Passover, with friends who were in Europe for the last half of April.  Jordan was feeling scholarly and impressed everyone with his knowledge about the holiday.  I was especially entertained by his explaining that this and that item on the seder plate are symbols that represent other things; he was being very pointed about the vocabulary, suggesting that the whole concept of symbolic representation is interesting to him right now.  Then on the way to religious school this morning, we had this interchange:

J: Infinity is not a number.
R: I would agree with that.  What are you thinking it is?
J: Infinity means that numbers never end.
R: That's what I would say too.  I would say infinity is a symbol.  It reminds us of that idea, that numbers never end.
J: Right.
R (walking on a little): I was thinking about our late Passover last night, and how you said the shankbone is a symbol.  Funny to think of infinity as being sort of like a shankbone.
J: Infinity even looks a little like a shankbone.  They're both round on the ends and thin in the middle.
(This cracked me up - the physical resemblance is so not what I meant.  But I didn't say anything.)
J: A color can be a symbol, too.
R: Oh yeah?
J: Like the pH thing we do with the fish.  The color of the water in the little tube tells you how much acid there is in the fish tank.

The pH indicator thing seems to me to be a different kind of thing than infinity or a shankbone.  The colors on the test strip stand for numbers, and that's probably what Jordan was thinking about - one thing standing for another different kind of thing.  But the colors on the pH scale are an indicator of quantity (of acid), pretty much just like the numbers they are substituting for; whereas infinity and the shankbone both indicate abstract ideas (of the nature of numbers, or divine protection).

On the other hand, maybe we live in such a symbol-laden reality that there's no point in making such a distinction.  Written numerals are symbols of mathematical objects (numbers), which are used to represent quantity; all language is symbols; etc.  When we arrived at religious school the kids were making an Israeli flag, which Jordan and I identified as a symbol of a country.  The six-pointed star, in particular, Jordan identified as being not only a symbol of Jewishness but also a symbol of the shield carried by David.  So I think that I will not try to get him to differentiate different kinds of symbolism.