An Eternal Golden Braid

Godel Escher Bach is my most favorite book. And I recommend this to all the aspiring programmers out there.
Through this book, Douglas Hofstadter, explains how self is evolved. This book contains a lot of recursive and self-referential patters. This book will throw your mind into a state of profound thinking. At some point, I thought my brain (or what is left of it) was going to melt as I read it. I am enjoying this book so much. I haven't completed the book, yet. I will give an update when I am done. But until then, here is an interesting thing happened because I happened to meet a friend who read this book. I ll try explaining as much short as possible.
I was speaking with one of my friend the other day, and he happens to state his hypothesis that time and space might not be continuous. This is just a fun conversation, which I found very interesting. For his justification, he used Zeno's paradox as tool to validate it. Space has a smallest unit below which it cannot be further divided. By this way, Achilles can take huge number of finite steps to win the tortoise in the race. Thereby proposing that space may be discreet.
I was thinking about that. And I think it is not possible for space to be discrete. Here is my justification. Let us assume smallest unit of matter to be mloop (Smaller than quarks or whatever is smaller than quarks). Consider point A and point B. Lets assume that smallest unit of space is sloop. Now A is away from B by 1 sloop. mloop cannot be smaller than sloop as sloop is smallest unit of space. Now, mloop needs to moved from A to B. But there is no transition from A to B as nothing can exists between them. So logically speaking, mloop has to disappear from A and reappear in B in order to move. To summarize, matter has to disappear from space and reappear elsewhere for it to move through space. And I think that this is ridiculous. So, I don't think that space might be discreet.
Of course, I was thought from a very small age that Space-Time is a continuum, but I was just analysing the information to myself rather than blindly believing it without any questions. This is just one small stuff that GEB helped me think. This is why I recommend this stuff to all the programmers out there. It helps you think greatly.