Two studies are reported investigating children's conceptions of the number zero. The first, with 31/2–61/2‐year‐olds, charts preschoolers' understanding that zero is a number among other numbers with its own unique value, namely nothing. Children's achievement of this understanding occurred in three phases. At each phase understanding of zero lagged behind comparable understanding of other small numbers. The second study, with 51/2–10‐year‐olds, investigated children's developing conception of simple algebraic rules, such as a + 0 = a. Results showed that even the younger children had some understanding of several algebraic rules. The older children had acquired more such knowledge, but at all ages algebraic understanding was advanced for rules pertaining to zero, in comparison to those pertaining to other small numbers. These results suggest that zero plays a special role in children's increasingly algebraic knowledge of number. We conclude that since zero is difficult to conceive of and use originally (Expt 1) children develop special rules for its use, and that this provides a first step towards their formulation of more general algebraic rules (Expt 2) and towards an expanded conception of number and mathematics.
If you look at ranks for worldwide sporting events , you’ll note that approximately none of them indicates first (zeroth ?) place with a 0. Can you give an example of a place where education at early childhood level is carried out as you claim ?
You're right ... sporting events ... how could I have not included that very scholarly pursuit of engineers, scientists and programmers in my analysis.
I'm not trying to claim that 0-based is better than 1-based. I'm just trying to point out that outside of the fairly limited crowd who spend their workday in things like Matlab and R, the vast majority of coders in the world in 2018 are working in 0-based indices languages.
If Julia is a worthy language which aims to attract a crowd beyond the niche R/Matlab folks, then choosing 1-based indices is poor tactics.
Since you mentioned children learning to count, I tried to find a general, widely known case that would be as applicable around the world, and I provided a study examining why 0 can be a difficult concept (which humankind developed very recently). The number of toddlers who are engineers in the sense I think you’re talking about is approximately zero, too.
Furthermore, the widespread mathematical / scientific computing languages have used 1-based from FORTRAN through Matlab and Mathematica. Statistical papers are published with accompanying R code , very rarely with Python. If 1-based indexing is too hard to get used to, you may not be in the target audience. Anecdotally, I used C and Python well before started R, and I’m not really the smartest bulb in the box. I was annoyed for about a week. If you have the knowledge of what you will use Julia for, this hurdle seems very minor in my opinion.
I think that is the key. "1, 2, 3. There are 3 apples." is a little easier than "0, 1, 2. There are 3 apples."
Counting the first item as "1" total items leads to 1 being more natural in the same way that incrementing a pointer by 0 giving you the first element is more natural.
The former is the abstraction layer most people are more familiar with.
