The discussion has wandered off topic, but it seems to me that it is true that "You Usually Do Not to Know about Internals". Otherwise you would not be able to use a computer or for that matter, drive a car.
I do not find it insulting at all. If Wolfram said that he didn't show internal code because you were too stupid to do anything with it, that might be insulting. Even if it were true for the generic "you", it would be insulting for some people. If he said that he didn't show internal code because it would be (a) an added expense or (b) a loss of proprietary information, then that would be no more insulting than for most commercial programs. I don't know what would happen if you requested access to Mathematica source, with the stated intention of improving it through your research efforts. Perhaps you would be given such access, presumably with appropriate non-disclosure agreements. Have you ever tried? If your reason for requesting such access is to rewrite it in Python and give it away, I can understand that Wolfram might be reluctant. As for most people being "not so bright", I suppose it depends on how you define "not so bright". Presumably we don't even see "most" people, because they do not take courses beyond high school algebra. Unless we teach remedial math. If half (+epsilon) of the population scores 100+delta on some common IQ test, and bright="IQ of 100 +2*delta" (say), then most people are not bright :) As for sin(10^5), consider this calculation, in your chosen CAS, to high precision: sin(4*arctan(1.000......0)) the symbolic answer of sin(4*arctan(1)) is of course 0. Mathematica 6.0 gives an answer like this.. nz = Sin[4*ArcTan[SetPrecision[1,100]]] returns 0.*10^(-100) Is this zero? Numerically with simple comparison, yes. In other kinds of tests, it is distinguished from zero. You have more than one additive identity in the "field." As for finding bugs by reading code: How do you assure that your "verification" by reading code has found all the bugs? Discussants on this issue could probably benefit by reading about program verification, testing, debugging. These topics are covered in some computer science courses. RJF On Apr 30, 11:21 am, William Stein <wst...@gmail.com> wrote: > On Thu, Apr 30, 2009 at 11:06 AM, mark mcclure <mcmcc...@unca.edu> wrote: > > > On Apr 29, 1:37 pm, William Stein <wst...@gmail.com> wrote: > >> On Wed, Apr 29, 2009 at 9:51 AM, mark mcclure <mcmcc...@unca.edu> wrote: > > >> > I think, though, that the statement that you need open source in order > >> > to have verifiable results is not really true. The fact is that bugs are > >> > found via experimentation, not by reading source code. > > >> This is not a fact! I have a lot of experience finding and seeing > >> bugs found, and I can tell you in no uncertain terms that a huge > >> number of the bugs found in Sage are in fact found by reading source > >> code. > > > I too have founds bugs by reading code that I've written - usually, > > very > > early on in the development process. Note that I'm talking in the > > context > > of result verification, however. That is, when I publish a paper > > that > > depends on computations, it is incumbent upon me to verify those > > computations. I'm saying that I don't think that reading source code > > at that point is particularly necessary or useful. > > Thanks for the clarification. That also doesn't agree with my > experience, but perhaps things are different in your area of research > which is probably far from mine (elliptic curves and modular forms). > > William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
