Considering that it is an application that uses vectors which can scale to any size because they're mathematically calculated, why can I only zoom to a certain level and what is the deciding factor?
Is it based on my hardware?
Is it based on limitations of the software?
What can I do, if anything, to be able to zoom in further?
Infinite zoom is not possible in any [Adobe] app.
All apps have to cap the zoom somewhere. 6400% is a decent cap to use. I'd guess it was merely an arbitrary decision on the part of the developers/Adobe. I don't think there's any real reason why it's 6400% other than it's a nice round number.
When looking at the defaults, the percentages merely double - 100%, 200%, 400%, 800%, 1600%, 3200%, and finally 6400%. They probably could have gone to 12800% but that seems like a considerably big jump.
The problem is, when working on a
15px x 15px image 6400% may not be enough. But when working on a
36in x 36in poster, 6400% is plenty. So.. it's all relative.
To zoom further, you could increase the size of the art. IF that's not possible you can use third party apps which zoom the screen rather than relying on Illustrator to go beyond 6400%. For example, on the Macintosh you can turn on zoom in the system preferences (accessibility) and that allows you to zoom the screen. This in conjunction with Illustrator's zoom will let you go far beyond 6400%.
Some technical and social context on the issue:
Its not really true that vector art has infinite precision. Internally applications use floating point arithmetic and i guess adobe uses double precision floats. But this is a pure guess they might use single precision floats or even a fixed size mantissa (adobe is a big fixed point programming shop after all).
In any case there is really a limit to how much precision this model can give. Its not like computers work on symbolic mathematics. The problem is that while you would get a pretty good near infinite resolution with floating points near the origin it would downgrade as you move further. So by limiting the size you can avoid having to try to fix issues with the relative scale metric.
Scaling up is a sane solution.
On a related note: Having to deal with clients that hit this barrier is a real support nightmare. Sooner or later somebody tries to draw the solar system at scale, and as a result, start wondering when their graphics start to drift uncomfortably. Yes yes you might say that's absurd but Ive seen it happen now about 20 times, 4 times as the support person who had to make it work. Nothing good comes out of this, my clients were engineers and they didn't get it until after millions of explanations (yeah the trick is to move the world around your relative center). So while the value is arbitrary a limitation actually is not a bad idea at all.