<div dir="ltr">Thanks for the thoughtful responses on this. Yeah, a distinction between
nouns and verbs can't be made too rigid, as, for one thing, some words, like 'shout', can serve as either nouns or verbs depending upon context, and in some languages, such as a designed language, such a distinction might not be necessary, but there is an interesting contrast that naturally
arises, similar to the one between 'things' and 'processes'. A related
question I had is whether nouns and verbs are processed differently in
the brain? From what I've found, the current
view is that, yes, there are differences, but there is of course lots
of debate about the details. The most recent views explain the
difference in terms of grammatical 'markers' associated with noun or verb
phrases, not the specific noun or verb itself. "nouns and verbs <span style="font-style: italic;">qua</span>
nouns and verbs are not represented in separate regions of the brain."
I'm completely unqualified to really say anything further about this, so see <a href="http://talkingbrains.blogspot.com/2008/08/representation-of-nouns-and-verbs-in.html" target="_blank">Talking Brains.</a><br><div>
<br>It makes me wonder about
how our brains process functions, as we can understand functions as either 'nouns' (values) or 'verbs' (processes acting on other values) or both. <br>
</div>
<br>Again, to summarize what prompted my original question, those high school math texts that do describe math as a
'language 'typically will call the comparison operators 'verbs', as they
contain 'is'. Expressions are not considered complete statements.
Equations or inequalities are defined as the only complete statements, and these
are built from expressions. Again - that's how the high school texts
typically present it. However, it is clearly the case from the
discussion here that computational expressions can indeed be interpreted as imperative
statements. And, as I mentioned, I bet that most
students and teachers automatically think of arithmetic expressions in
a computational or imperative way, especially in an age of calculators,
so it would seem that this could become part of the argument for
weaving computational thinking into the math curriculum? We would be
giving them a richer language for expressing the kind of thinking
they're already inclined to do. The block Parmenidean universe of
traditional high school math where nothing actually 'happens' is kind
of distant from how most kids naturally think.<br><br>
- Michel<br><br><br><div class="gmail_quote">On Sun, Aug 24, 2008 at 8:48 AM, kirby urner <span dir="ltr"><<a href="mailto:kirby.urner@gmail.com" target="_blank">kirby.urner@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
On Sun, Aug 24, 2008 at 1:30 AM, Edward Cherlin <<a href="mailto:echerlin@gmail.com" target="_blank">echerlin@gmail.com</a>> wrote:<br>
<br>
<< SNIP >><br>
<div><br>
> Actually, to the mathematician, programming is a fairly simple concept<br>
> that can be expressed in several different ways as the working out of<br>
> only two basic concepts, such as the S and K combinators (Unlambda or<br>
> J), or Lambda expressions and application (LISP and many related<br>
> languages). Most programming languages have a good deal of unneeded<br>
> and counterproductive complexity added on, like C++.<br>
<br>
</div>Mathematicians may boil it down to a few basic concepts (like a Turing<br>
Machine or whatever), but when push comes to shove they like their<br>
traditional notations and both MathCad and Mathematica have gone to<br>
some length to get those old pre-computer typographies on screen, so<br>
that math looks like it used to.<br>
<br>
Lots of mathy types didn't want to touch a mouse and keyboard as long<br>
as programming looked like FORTRAN (not saying I blame them). We've<br>
come a long way baby.<br>
<div><br>
> To the non-mathematician, these simpler solutions seem harder than<br>
> memorizing the complex syntax of conventional languages, as was often<br>
> borne in upon Computer Scientist Edsger Dijkstra. He spent much of his<br>
> career trying to make programming easier to do well, and was regularly<br>
> told by practitioners that he had made it harder instead.<br>
<br>
</div>Distilling to two concepts might be theoretically advantageous in some<br>
context, but trying to code anything sophisticated in such a primitive<br>
manner would be tedious to say the least, although I realize LISP is<br>
all S-expressions (exciting to purists in that way).<br>
<div><br>
> The same principle applies with even greater force in education.<br>
> "Don't do us no favors," teachers seem to say. "if you make it so that<br>
> we can really teach this stuff, then we will all have to go learn it<br>
> ourselves, and we can't." This is a delusion in a way, but not the<br>
> delusion of the teachersthemselves. It is a delusion enforced by the<br>
> social system they work in. Like Ethiopian teachers treating questions<br>
> from students as personal insults, until they get XOs. There<br>
> experience suggests that there is hope for the profession as a whole.<br>
<br>
</div>Yes, it's good to have languages so accessible that we don't really<br>
need teachers any more (just self teaching abilities), although if we<br>
have them that's cool (teach your peers!).<br>
<br>
The self-marginalizing of professional adults to where they're not<br>
relevant to passing on so many core aspects of the culture, because<br>
not venturing to keep up, even if called "teachers" originally, is<br>
certainly a social problem. akin to juvenile delinquency in some ways<br>
(i.e. whole groups of people feeling they have no accepted role in the<br>
ambient culture anymore).<br>
<font color="#888888"><br>
Kirby<br>
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