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?).

Also see Dijkstra's take on the matter: http://www.cs.utexas.edu/users/EWD/ewd08xx/EWD831.PDF for

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.

We shape our tools and then our tools shape us.

Be careful when generalizing from your own personal preferences and cognitive biases to what is easier for humans in general.

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.

My experience is the exact opposite.

I find 1-based indexing to be weird/illogical and prone to off-by-1 errors.

Inclusive/exclusive ranges as in Python along with 0-based indexing means the likelihood of any off-by-1 is negligible...