I teach a Theory of Knowledge course in the I.B. curriculum when I'm not teaching Algebra. I presented this thought experiment to a class: If God, or some supernatural entity, could tell you the exact weight of your school mathematics textbook, would the resulting value be rational or irrational?
Sifting through the written responses, one kid had a pretty sharp response:
"The weight of a book is most definitely rational because it is composed of a specific and finite number of atoms so its mass is non-moving. Those atoms are not leaving the textbook so it is staying a specific weight no matter what."
While I agree with the specific/finite language and can set aside concerns about the image of atoms not "moving," I directly question whether the weight of individual atoms can be treated as uniform, rational units. Yes, there are integer combinations of subatomic particles defining the weights but does not each atom (or subatomic particle for that matter) inspire its own rational/irrational debate?
Anyway, this is where the discussion moves out of mathematics and into quantum physics where I tread with caution. So I throw it out to the crowd...Are atomic weights best viewed as rational values determined by integer combinations of mass/energy or unique irrational values which we statistically approximate for utility sake?
[Question inspired by Tobias Dantzig's outstanding "Number: the Language of Science"]