Watch these two videos, they are very interesting, then comment.
So where does the disconnect come between the real world and our number constructs?
Personally, i blame fermions and the pauli exclusion principle.
Re: What do you mean, "two comes after one"?
Posted: Sat Aug 03, 2013 10:01 am
by johnson1010
I'm no expert at this at all, but i do like to think about this stuff.
I don't think it's possible to remove 3.5 if your number line goes to 4.
When there is no correlation to things with physical dimensions, what could be meant by "remove" 3.5?
Doesn't 3.5 exist definitionally because you have created a space between 3 and 4 built of units of 1?
To remove 3.5 you would have to end your number line before 3.5.
Numbers can be completely dimensionless when talking about a mathematical number line, but the same could never be said of a ruler. Rulers are things that exist in space which we use to gauge distance in space between real things. We can call any single place in space a "point" but that is an approximation. There is a granularity to reality which we can't seem to get past. You can talk about dividing a wooden ruler and trying to get to the "point" at 3.5 centimeters, but if you do that you may eventually end up at the last molecule which resides at the distance 3.5, but that molecule is granular. It has dimensions associated with it which can't be reduced any further.
It can be broken into it's constituent atoms, and those atoms can be reduced to the nucleus and you could try to look at one particular quark, but there is still a volume associated with that structure because it's a fermion. The world we interact with is made of such fermions and they have sizes. Points have no size whatsoever. So lets get rid of the fermions and just talk about space! You still have apparent granularity all the way down to the plank length.
I think what this is indicating is that numbers are an idealized construct which approximate reality, but which are not reality.
Like saying 1 apple plus 1 apple is 2 apples. You are dealing in approximations. You've labeled two objects in space "apple" and in the context of 1+1=2, that means by definition that you've completely equated the two apples to be identical.
But if you label one apple 1, you will find after careful scrutiny that the second apple does not =1. It might only be 95% the mass of the first apple.
1 apple plus another "1" apple would actually be 1.95 by that measurement. But there are other comparisons you could make which would change that outcome!
So when you mentally label two objects in space as both being equivalent to "1 apple" you have made a very sloppy approximation (as far as math is concerned), but a necessary approximation to deal with reality as it is. You have built a concepts to represent the object and added the labels together, not the actual objects.
We can do this because our error margins are so large. That is to say, we don't readily appreciate that there's a difference between the two apples of 5% of mass. That difference is too small for us to change our assesment of the two objects. But if we were ants and found that missing 5% of apple mass lying around somewhere, that would be quite a score!
Everything in the real world is proportional, and we as real objects with senses make approximations that fit inside our sloppy error margins.