Re:Roger Penrose – Is Mathematics Invented or Discovered? [v...
by t_von_doom on Friday April 17, 2020 @05:41AM
(#22897557)
While negatively charged particles are real, the 'negative' charge is a way to distinguish them from a 'positive' charge. It's a naming convention more than it is an actual negative value.
We could easily call them 'black' and 'white' particles and the system itself would stay the same
Re:Roger Penrose – Is Mathematics Invented or Discovered? [v...
by feanaro on Friday April 17, 2020 @06:15AM
(#22897689)
This is not true. You're losing a crucial property in your translation, namely that the negative numbers are the additive inverse of the positive numbers. In other words, it's essential for electrodynamics that a + (-a) = 0. You could add this requirement to you 'black' and 'white' terminology, but then you've just arrived at negative numbers under a different name.
Don't let the naming confuse you. The name "negative" might be a peculiar, human-specific thing, but the concepts of addition and additive inverses are not.
Are you sure negative numbers are not "real" in the same way natural numbers are?
That would mean particles like electrons with a negative charge are not "real", too. And someone can argue that his negative bank balance is not "real".
As for complex numbers, I fail to see how they are less real than real numbers. Real numbers are points on the real axis, while complex numbers are points in R^2 plane. If we question the reality of real numbers, we can also question the reality of the plane.
Mr Euclid would frown to hear that.