Infinity, just as hard, impossible to grasp as nothing. It's just a word for something no one knows anything about. Like nothing about which much is made infinity leaves nothing to the imagination and, unlike nothing, is ignored.Think of zero as the midpoint between + and - infinity
How about a googol? (1 followed by 100 zeroes)
There are other ways to think of zero; as a placeholder, for example...Infinity, just as hard, impossible to grasp as nothing. It's just a word for something no one knows anything about. Like nothing about which much is made infinity leaves nothing to the imagination and, unlike nothing, is ignored.
Of course, in mathematics, a very concentrated language. But the essence of zero, as nothing, remains incomprehensible applied to what is...
Alright, then let me take the abstractionist's viewpoint, which is where this all needs to be anyway.
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Oh, enjoyable, philosophy underscores everything. But the zero. Yes, an abstraction, imposed on reality. Not a word game but we are to believe from mathematical modeling that nothing can exist yet nothing produces everything. Compared to finding a genuinely, absolutely, random number, which is questionable, at best, is nothing compared to modeling nothing. An area where questions lead to more questions. At the cutting edge all this matters when thinking of nothing and eternity, there is nothing to be said beyond no body knows but the investigation is fascinating.Alright, then let me take the abstractionist's viewpoint, which is where this all needs to be anyway.
Mathematics helps us understand things that do not appear in nature; zero may be one of those, but I am not convinced of that. It is rather easy for me to look at a blank desktop and say that there is no pen there. Zero pens present.
Similarly- space. Though, on the average, there is matter occupying all of space, I can mind-experiment myself down to a small enough volume that contains no atom.
Zero requires us to recognize that the absence of something is a thing in and of itself. And there are plenty of abstractions that one deals with on a daily basis; one instance would be color. There is no such thing as color in the world- just wavelengths of light/photonic energy. We make an abstract interpretation in the mind about that (and people will not even agree on the interpretation of a particular wavelength).
Zero doesn’t have to exist to be useful and we can use the concept of zero to derive all the other numbers in the universe.
John von Neumann's thought was this:
Imagine a box with nothing in it. Mathematicians call this empty box “the empty set” and is a physical representation of zero. What objects are inside the empty box? None/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. That can be how we derive all the counting numbers from zero … from nothing. This is the basis of our number system. Zero is an abstraction and a reality at the same time.
Also, don't forget about the reality of "absence" in digital engineering!
(you triggered my mathematician and philosopher's proclivities, sorry
Yes. Zero beyond meaning we're out some thing is a luxury to contemplate. Most of humanity throughout history to now has concerned itself, individually, with surviving each day, food, protection, everything. In the luxury of contemplating what is zero, as nothing, zero, nothing, that is an abstraction. Theories arise.
It depends on what one needs to know.
I would think that you'd have a bigger problem over negative integers.
And should I get anyone onto the complex numbers?
Negative integers, imaginary numbers, nothing to do with any of that. Mathematical modeling is an abstraction, needs something to model. It can't model nothing anymore than it can model infinity. That is a different domain.
Well, I guess that I'll finish with writing to you that mathematical modeling has preceded physics, spaceflight, and astronomical discoveries on many occasions. It also provides other pieces of the whole scaffolding of mathematics and helps with understanding it along with opening other avenues.
Of course. It is a tool for discovery, no doubt.
Yes, I know that you know that but all of what we've been musing on about is foundational to all of it. Once I got beyond applied mathematics (Calc IV and Diff Eq were the last of that) and into Number Theory and above, this all made sense and mathematics became creative and poetic.
Yes. Years ago, before realization, heard math teachers tell of the beauty of mathematics and indeed, it is, and poetic.
