I was asking because when I tried to research the history of this
issue, I found distinctions including:
quaternions vs. vectors
vectors vs. scalars
vector notation vs. index notation
roman numerals vs. arabic numerals (also the absence or presence of 0)
The distinction between vector notation and index notation seems
particularly relevant here: a point made in vector notation is that
the indices do not really matter. They can be replaced arbitrarily and
the math still works.
And that might have been a benefit of quadIO -- by requiring
initialization or some other measure on all index expressions, it
tended to encourage the use of vector expressions where ever possible.
Basically, though, I think a declaration claiming that "1 should be
the origin for indexing and 0 should not be the origin for indexing"
to be unconvincing from a math viewpoint. Mathematics notation tends
to be all over the map, with mathematicians routinely disagreeing with
just about anything. We eventually get a consensus (actually more of a
chain of narrow claims which allows one point of view to evade the
other point of view), after generations ("0 was a great innovation")
only to go through that all over again (because it was never really
much of a consensus).
I am also reminded of a book where every section introduced a new
system of notation. (titled Elementary Arithmetic - though I sadly do
not remember the authors - and it was arithmetic in the sense of the
peano postulates and similar constructs - sadly, academic works seem
to be extremely profuse in variety and diffuse in general use...) I
have never seen another book use so many different lettering systems
and fonts (well ... other than works on typography...) You don't
survive such a class without becoming a little distant from issues of
the specific choice of notation.
Generally speaking, though "Mathematics" is never a convincing
argument. When mathematics is relevant, it's always going to be a
specific branch of mathematics that had that relevance.
Or: that's my opinion and I'm sticking with it.
Thanks,
--
Raul
On Fri, May 18, 2018 at 11:17 AM, Don Guinn <[email protected]> wrote:
> The first one I looked at was "Handbook of Mathematical Functions"
> published in August, 1966. Also looked in several texts from college. I
> couldn't stand returning them to the bookstore for almost nothing. Then
> looked up vectors and matrices online. Whenever the index was not
> significant in the calculation other than to select an element the index
> origin was one.
>
> On Fri, May 18, 2018 at 9:12 AM, Don Guinn <[email protected]> wrote:
>
>> Agreed.
>>
>> On Fri, May 18, 2018 at 8:46 AM, Roger Hui <[email protected]>
>> wrote:
>>
>>> > The mistake in APL was to duck the issue by allowing both making
>>> generalized indexing difficult.
>>>
>>> That is why I say "⎕io *delenda est*" and not "1-origin *delenda est*",
>>> although I do have a preference.
>>>
>>> ⎕io *delenda est*!
>>>
>>>
>>>
>>>
>>> On Fri, May 18, 2018 at 7:40 AM, Don Guinn <[email protected]> wrote:
>>> ...
>>>
>>>
>>>
>>> > This may change as now that so many people program and are used to an
>>> index
>>> > origin of zero. My point was not what the index origin should be when
>>> it is
>>> > only used to locate a element. One works well as does zero. The mistake
>>> in
>>> > APL was to duck the issue by allowing both making generalized indexing
>>> > difficult.
>>> ----------------------------------------------------------------------
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>>>
>>
>>
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