The concept or meaning of zero strikes me as having, in some sense a positivity or substantiveness that is empirically verifiable. For starters, zero is big enough to be divisible by any natural number A since A x 0 = 0, so it must have some substance or size.
When we say we have zero dollars in our pocket, we mean we have absolutely nothing in our pocket- but do we?
Zero is more than absolutely nothing, i.e, absolute nothingness.
If a young lad has five quizzes and gets the following grades: 80, 90, 100, 70 and 60, His average grade is (80 + 90 + 100 + 70 + 60) / 5 = 80,
If his five quiz grades are instead : 80, 90, 100, 70, and zero, his average grade is (80 + 90 + 100 + 70 + zero) / 5 = 68
If getting a zero meant getting absolutely nothing on a grade and 'absolute nothingness' is considered to be the deepest form of nothing which is
absolute nothingness = negative infinity
then his average grade would instead be (80 + 90 + 100 + 70 - infinity) / 5 = roughly negative
infinity. But of course he does not sink to a grade of roughly negative infinity after getting a zero on one of five quizzes.
In a similar way if you have a fuel
economy guage on the dashboard, and you idle at zero miles per hour, all the positivity of gas mileage you gained on the
highway does not just get swallowed up in the few moments of some infinite nothingness of speed. Instead the
decline in fuel economy is gradual as you sit there idling. You actually see this
behavior on the guage and this seems to be empirical
verification of a
substantiveness of zero that is greater than absolute nothingness equal to negative infinity.
In other words
zero is, in an
empirical, experiential and verifiable sense, something greater than an "absolutely nothing" equal to the our most extreme mathematical expression of nothingness (negative infinity). There are obviously
gradations of nothingness far more impressive than zero; and, if negative infinity is at the bottom of the
scale of gradations of nothingness then the negative numbers also have some empirical
substantiveness and are not just artifacts invented to keep track of debits and help balance checkbooks.
Why is this important? Because scientists are wondering where all the dark matter in the universe is hiding of course.