"John Doty" <jpd@[EMAIL PROTECTED]
> wrote in message
news:bpSdnZU2Z7CTl9_anZ2dnUVZ_quhnZ2d@[EMAIL PROTECTED]
> Gary Coulbourne wrote:
>> Rod Pemberton wrote:
>>> I don't recall if they converted to the "new math" or not.
>>> Anyway, I think that learning math has much more to do with brain
>>> psychology
>>> than the "one size fits all" solution you've presented. For example,
we
>>> now
>>> know that females do better in math in a cooperative environment than
a
>>> competitive one that males prefer.
>>>
>>
>> I had to deal with "new math" as well, and had a terrible time of it.
I
>> felt that learning postfix notation actually helped me a great deal
with
>> understanding math generally -- in particular, learning to convert
infix
>> into a tree to convert it to pre- and post- script notations. That
was,
>> as my high school calculus teacher used to say, an "expando-head"
moment.
>>
>
> And that kind of thing connects the languages of math and programming
with
> the human instinct for language. Natural languages include prefix,
infix,
> and postfix elements, but their constructs can generally be diagrammed
as
> trees. So from that perspective, traditional math and classic RPN are
> equally "natural".
>
> One difficulty with Forth is it generalizes RPN in a way that is natural
> from an implementation viewpoint, but unnatural from a linguistic
> viewpoint. Even if we restrict our attention to purely numeric
expressions
> (no flow control or other fancy stuff), Forth expressions *cannot*
> generally be diagrammed as trees! The reason is that to make a tree,
each
> node must have at most one connection toward the root (root nodes have
> zero). Traditional mathematical notation, classic RPN, and natural
> languages all have this property.
>
> But Forth words often have more than one output, therefore may have more
> than one grammatical connection to the root of the expression. Forth
> expressions are networks, not trees. They therefore violate a common
human
> linguistic principle. While unfamiliarity may be some of the issue in
the
> frequent "Forth code is unreadable" complaint, I think Forth is also
> genuinely unnatural to a human reader in this sense.
>
> Now of course information flow in all but toy languages is more complex
> than trees, but all useful languages I know (both natural and
artificial)
> have explicit extragrammatical mechanisms for this (variables, pronouns,
> ...). Only Forth makes the reader track a network of implicit
grammatical
> relation****ps instead of a simpler tree.
>
yes, a very interesting assertion.
I would have just assumed it is how the language "looks", but a semantic
explanation is also worthwhile IMO...
> --
> John Doty, Noqsi Aerospace, Ltd.
> http://www.noqsi.com/
> --
> Specialization is for robots.
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