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I come from a culture which uses left-to-right language. In my mind, the following is true:

  • On number line, negative numbers are to the left of 0, positive are to the right.
  • In Cartesian coordinate system, X axis points to the right (same as number line).
  • Limit from the left is '-' and limit from the right is '+'.

Does the same hold true for mathematicians who come from cultures using right-to-left languages?

Ivan Koshelev
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    Context matters. In the case of languages "as written" there is in most cases precedent going back hundreds of years. Likewise in mathematics there are conventions that have historical precedents. You mention Cartesian coordinates, so we can consider Descartes as creating a certain tradition for analytic geometry whose power subsumed a great deal of previous tradition. But in other parts of mathematics the conventions of left/right or up/down can be (and are) different, not so much as a matter of ethnic culture but because of traditions peculiar to mathematical developments. – hardmath Jan 24 '18 at 02:28
  • Numbers are written with the most significant digit on the left in Arabic. Make of that what you will. – amd Jan 24 '18 at 02:31
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    Given the influence of historical precedent, the speculative question is perhaps "If the number line had been developed and popularized by a culture with a right-to-left language, would the conventional number line also be reversed?" It's not an implausible conjecture, but I doubt there's any way to prove it. – Semiclassical Jan 24 '18 at 04:12
  • I like your question since it is imaginative. The simplest answer I think is that if native Arabic and other right to left reading cultures weren't capable of making the switch from right to left words, to left to right symbols immediately, without even needing to think about it, it would be difficult for anyone using such languages to learn Mathematics, since the rest of the world has long used the left to right convention and all textbooks employ such representations. But there are in fact many fine Arabic speaking and reading Mathematicians in the world today.. Q.E.D. No problem! – Wd Fusroy Oct 11 '19 at 16:00

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I think this may answer your question:

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Of course one example is not proof, but clearly the fact of writing right-to-left does not (even temporarily) cause people to see everything as the mirror image of the way left-to-right writers see it.

As comments have already touched upon, the best-known right-to-left writing systems are ancient (not just hundreds of years old, but based on thousands of years of tradition), whereas the mathematical conventions of number lines and Cartesian coordinates are much more recent inventions.

David K
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