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Re: Show and 6.0
*To*: mathgroup at smc.vnet.net
*Subject*: [mg89444] Re: Show and 6.0
*From*: David Bailey <dave at Remove_Thisdbailey.co.uk>
*Date*: Mon, 9 Jun 2008 06:21:01 -0400 (EDT)
*References*: <g2ij15$rnk$1@smc.vnet.net>
AES wrote:
> I believe I've more or less fully grasped the explanation of what Show[]
> now does in 6.0 that's been repeatedly restated in all the recent and
> earlier responses to all the repeated plaintive posts about ""Why
> doesn't my plot appear?!?" --- and this explanation actually make
> reasonable sense to me.
>
> [It's less obvious, however, how someone is suppose to know that
> Print[]; _will_ print something on screen, but Show[]; _won't_ show
> anything on screen. Read the Helps for these two commands and see the
> help pages make this obvious to you)
>
> I'm less sure that these expert respondents -- and also WRI -- have
> grasped _why_ these recurrent queries keep recurring; so led me add a
> few (5 actually) responses myself on that point (though it will make for
> a long post):
>
> 1) I suggest the primary problem is a deeper, long-standing, and quite
> understandable misunderstanding of compound expressions, and especially
> the role of semicolons in compound expressions.
>
> To quote, for example, from one of the recent "Plot and Show[]"
> responses, posted by someone who's often on this group:
>
>> In general, a semi-colon is used to separate the parts of a compound
>> expression
>
> Well, the correct response to that response is "NOT!", right? Or at
> least, "not entirely".
>
> That is to say, is the primary function of a semicolon to separate the
> parts of compound expressions? -- or is it to suppress output from an
> expression? And is it always necessary between two expressions?
>
> I've thought for all my years with Mathematica that you _had_ to put
> semicolons between two successive expressions on the same line or in the
> same cell, except for the very last line in the cell. And, I guess I
> deduced that this made sense and was necessary because logically you
> always needed to be clear where one expression ended and the next one
> began.
>
> Given this, I would never have believed that giving as input, on a
> single line and in a single cell, the following
>
> a = Plot[x, {x, 0, 1}]; b = Plot[x^2, {x, 0, 1}]; a b
>
> would be a legal input -- until I tried it a couple of minutes ago.
>
> But wait a minute! Aren't a and b now expressions (separately)? So,
> don't they require a semicolon between them, to separate them?
>
> [In fact, I just tried the above input with a + b and then a * b at
> the end of the line -- and they all worked exactly the same as just
> a b . WOW!!!]
>
> Semicolons need explaining and understanding!
>
> 2) So, where would an innocent but intelligent Mathematica user go to
> unravel these mysteries. I'd issue a small challenge: Don't explain
> compound expressions and semicolons to me. Show us -- show me -- in
> detail how a novice could learn the at least the essential elementary
> rules of compound expressions and semicolons FROM THE CURRENTLY
> AVAILABLE MATHEMATICA 6.0 DOCUMENTATION.
>
> [And, see if the Help for ";" comports with the results I just
> experienced in the preceding.]
>
> 3) And then think a little deeper: Ask yourself, WHY do these
> recurrent queries about Show[]keep recurring so recurrently?
>
> Could it just be because the _documentation_ provided for 6.0's
> introduction, and for the massive changes it introduced, has not been
> adequate in explaining or warning about these sizable changes for a
> large class of users???
>
> Let's just leave that thought to simmer for a while . . .
>
> 4) OK, now having understood the new character of Show[], what should
> users do if they want to really show some graphics -- have them appear
> on screen -- in the middle of a long compound expression.
>
> Respondents keep suggesting that one should Print[] the graphics. OK,
> that works, of course -- but it's a poor solution, among other things
> because Print[] messes with the sizes at which the graphics are
> displayed, in a way that doesn't always match with what's expected.
> Something better is needed.
>
> 5) Finally, to respond on a quite different aspect of Show[] that's also
> been the subject of a thread recently:
>
> Go to the Help for Show[], where you'll read:
>
> Show[g1,g2] . . . concatenates the graphics primitives in the
> gi, effectively overlaying the graphics.
>
> and then try
>
> a = Plot3D[x y, {x, 0, 1}, {y, 0, 1}];
> b = Graphics3D[{Red, Thickness[0.01],
> Line[{{1/2, 1/2, 0}, {1/2, 1/2, 2}}]}];
>
> followed by Show[a, b] and then Show[b, a]. Evidently,
> Show[a,b] =|= Show[b,a].
>
> I guess I grasp what happens here, don't need an explanation, and can
> sort of understand, yeah, that's what "concatenate" gives you. But it's
> a lesson on how careful you have to be with these things.
>
> That's it for the 5.
>
I think your comments relate mainly to the documentation, and I think
they do highlight the need for conventional book-style documentation.
The problem is, that when you read a book, you trust that information is
being presented to you in a useful order, and well paced. Such a book
would have a general discussion about compound expressions, the result
of an expression, the meaning of Null, the fact that everything returns
a result, etc. Without a book structure to the documentation it is hard
to know where to place such information, so that (a) it is found, and
(b) the user is not overwhelmed by a mass of such information in a "read
this first" notebook!
The other issue is that certain functions - in particular Show - have
rather changed their purpose, and it might be helpful if WRI renamed
Show CombineGraphics (but leaving Show as a deprecated synonym).
David Bailey
http://www.dbaileyconsultancy.co.uk
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