Yeah, but it would add up indefinitely, making it infinite. Not the nanosecond itself, but every subsequent nanosecond that followed would be endless, and once you enter a space in which will never reach an ending (cease to exist), then eternity once entered would be an infinite amount of time. You're taking the finite and placing it into the infinite, like God takes us mortal beings and will have us put on immortality. If you took a stop watch from Earth and hit "start", and never hit "stop" it would go on forever (granted the battery doesn't die, haha).
Zeno gives me an infinite headache
1. We know this isn't really how things work, it's only an "apparent" paradox, because... the real world simply doesn't work this way.
A.
According to Zeno's paradoxes you can never actually move from one second to the next , or move from one location to the next.
And yet we DO move from one second to the next, and we DO move from one location to the next.
Therefore, these paradoxes, must, by necessity, have some kind of logical flaw... they don't actually occur in the real world.
B.
No matter how many times you divide a second, the pieces can only add up to 1 second.
Infinite "measurements" of a slice of time DO NOT equal infinite time, and they CANNOT equal infinite time.
The simplest proof is to keep an eye on your watch... we DO move through time, therefore these paradoxes must have a flaw.
C.
Try this with a bit of string.
Keep chopping it in half and see if it looks longer.
The string never gets longer... so there has to be some kind of flaw in the paradox.
D. Try walking across the room.
According to Zeno's paradoxes, this is impossible, as the distance you walk would keep dividing down into smaller pieces, and you could never traverse the distance.
And yet... we can easily cross a room.
We know intuitively these paradoxes created by "infinite slices" don't really occur in the real world.
This means Zeno's paradoxes have some kind of flaw.
So what is the flaw?
2. The Flaw of the paradox
There are different solutions to Zeno's paradoxes.
We know, logically, there MUST BE some solution, because his paradoxes simply don't work in the actual world.
We QUITE EASILY traverse time and space in our normal daily lives, and under his paradoxes, this would be impossible.
There are a whole lot of things in life I'm overwhelmingly ignorant about, so I'll just give one solution to the paradox... one I find compelling.
I'm only going to give the Aristotelian solution.
A. When dealing with infinity, we first have to differentiate the "actual infinite" from the "potential infinite".
B. Next, if we take a look, we have to recognize that the "slices" proposed by the paradox are only "potential"
C. Next, we see that Zeno starts with a presumption, a presumption that distances (in time or space) are actually COMPOSED OF, MADE OF, an infinite number of slices.
D. Aristotle would claim (and our normal experience bears this out) that the WHOLE is LOGICALLY PRIOR to any divisions which are made in the whole.
E. Therefore, the slices are not an initial condition, they are something imposed upon the whole.. and if the slices are not the initial condition, and the whole is not COMPRISED of these slices, but merely CHOPPED INTO slices, then the paradox fails. (The means the slices don't exist until you go and make the slices, therefore, in normal daily life, you never have to traverse these slices because they don't actually exist.)
F. I think this seems reasonable, as it gives us a simple solution that also mirrors what we see in daily life.
*. If you want to go further, Aristotle has another problem with the paradox, saying that because Zeno's slices are "unequal", they don't hold up in the normal ways we describe the potentially infinite, and thus zeno's paradox fails on this count because "unequal" parts in a chain of the "potentially infinite" can only yield a FINITE measurement.
3. There are other solutions to Zeno, but I'll leave those to someone else.
4. Ultimately, regardless of the "fun" we can have with Zeno's paradoxes, we can confidently start with the assertion there MUST be a solution.
Why?
Because Zeno's paradoxes, if correct, would mean I cannot even walk across a room... and... I'm walking across the room right now... for more coffee... which I need after writing this post.
: )