I once got into an small argument with someone who came up with the memorable phrase, "It's a logical absurdity to say you can believe that things don't exist. It's like trying to prove a negative; you can't distinguish between things which have no existence."
By that "logic", zero is the same as an imaginary hippo or a unicorn. People are indeed weird.
Our understanding of zero is profound when you consider this fact: we don’t often, or perhaps ever, encounter zero in nature. Numbers like one, two, and three have a counterpart. We can see one light flash on. We can hear two beeps from a car horn. But zero? It requires us to recognize that the absence of something is a thing in and of itself. “Zero is in the mind, but not in the sensory world,” Robert Kaplan, a Harvard math professor and an author of a book on zero, says.
Imagine a box with nothing in it. Mathematicians call this empty box “the empty set.” It’s a physical representation of zero. What’s inside the empty box? Nothing. Now take another empty box, and place it in the first one. How many things are in the first box now? There’s one object in it. Then, put another empty box inside the first two. How many objects does it contain now? Two. And that’s how “we derive all the counting numbers from zero … from nothing,” Kaplan says. This is the basis of our number system. Zero is an abstraction and a reality at the same time. “It’s the nothing that is,” as Kaplan said. (At this point in the story, you may want to take another hit on your bong.)
Elizabeth Brannon is a neuroscientist at Duke University who studies how both humans and animals represent numbers in their minds. She explains that even when kids younger than 6 understand that the word “zero” means “nothing,” they still have a hard time grasping the underlying math. “When you ask [a child] which number is smaller, zero or one, they often think of one as the smallest number,” Brannon says. “It’s hard to learn that zero is smaller than one.”
https://www.vox.com/science-and-health/2018/7/5/17500782/zero-number-math-explained
"You can't prove that you don't have a sister"
ReplyDeleteIf you compare the five non-existent elephants you have in your left hand with the zero apples you have in your right hand, you'll notice that they look the same. I.e., zero can represent any number of non-existent objects. You'd think "hey... zero is non-sense. It isn't that useful!". Of course there is the fact that "0's" appear in lots of numbers and without those "nothing" placeholders a decimal expansion of pi would be non-sense. And lots of other numbers as well.
ReplyDeleteFor me, its not the number that's important. It's the unit. It tells us what the number refers to.
I'm good with the concept of zero, but the way people talk about "infinities" can be concerning.
ReplyDelete