Show and 6.0

• To: mathgroup at smc.vnet.net
• Subject: [mg89425] Show and 6.0
• From: AES <siegman at stanford.edu>
• Date: Mon, 9 Jun 2008 02:28:55 -0400 (EDT)
• Organization: Stanford University

```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
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.

```

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