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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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