Actually, broadly speaking, I think math (think summation etc.) in general is usually 1-index based while programming is 0-index (due to memory locations so that the array index also points to the first element?).
At first we were going to use 0-based indexing, but it made porting any Matlab code over very hard, which defeats a large part of the purpose of having Matlab-like syntax in the first place — to leverage the large amount of Matlab code and expertise that exists out there.
However, as I've used it more and more, 1-based indexing has really grown on me. I feel like I make far fewer off-by-one errors and actually hardly ever have to think about them. This has led me to conclude that 1-based indexing is probably easier for humans while 0-based indexing is clearly easier for computers.
Many divide-and-conquer algorithms seem to be easier to express with 0 based indexing, whereas quite a few array operations seem to be better with 1 based indexing. I can certainly understand and appreciate the different points of view, I just personally always think about algorithms with 0-based arrays.
As does anyone trained in the C tradition, but it's annoying, too, to have to translate 1-based math formulas to the C convention. Having recently used Octave for the Stanford online ML class after a couple decades of C, C++ and Java, I doubt programmers will have trouble with the mental transition.
Well, for what it's worth, I certainly also "grew up" with 0-based indexing (actually, literally grew up since I was a kid when I learned Pascal). I'm just saying that 1-based has really grown on me and that I find myself thinking about avoiding off-by-one errors far less often when using 1-based indexing. There are other times when I really wish I was using 0-based indexing. However, I find that that latter are more often times when I'm doing libraryish internals code, whereas the former are more common when I'm doing high level userish code.
