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