[GAP Forum] I'd like to know something again.

[Lisette Brillemans]

Dear James (and Joachim),

Of course, I know, people working with GAP and so on are mainly
professors and dr.'s, and they are programming it. I am not a prof dr.
so I won't ever say that gap, sage, pari etc. etc. are not good.
What I meant is: Can't there be a danger in using these programs? If you
trust them so much (They are open source and programmed by the world's
finest professors etc.) there is always a chance of big accidents. I
don't want to fly in an airplane designed with possibly faulty software.
That's my point. I already see it happen on television: "Yes yes, we
designed our planes (of which on crashed that day) with the best
software available... So that cannot be the reason."
No, but very seriously speaking now: There is always a danger that we
trust software too much. If we do so there will always be security risks
that could have been avoided.

Lisette



> 
> GAP, Sage, and most of Magma include the source files to the software 
> which means that if you are interested you can read the way that 
> computations are performed.  That is hard to do if you don't have a 
> background in the details of these platforms.   But most of the authors 
> of these algorithms also publish academic papers describing their 
> algorithms.  These publications receive peer review and the most used 
> routines receive a lot of testing before they are distributed.   You can 
> see this in the documentation.   Most of the documentation include 
> references to published papers where you can read about the theorems 
> behind the algorithms, and examples that show you the correct behavior 
> is being produced on well-known examples.
> 
> Are their mistakes?  Of course, both in the programming and in the 
> design of some algorithms.  But this is likely to happen at least as 
> often when you do similar computations by hand.  Furthermore, many 
> computations just cannot be done by hand because of their size, e.g. 
> proof of the 4 color theorem.  Others could be done by hand but rather 
> inconsistently because of their complexity.
> 
> Some people think of these tools as the microscope for mathematics.  It 
> lets you see things you couldn't see before.  But you don't just except 
> the data, you need to go in to each experiment with a hypothesis of what 
> you expect and then process the results against what you understand.  So 
> if you get a result that doesn't make sense you should endeavor to 
> explain it, redo it, and try to discover if there is a problem with the 
> microscope.  Overtime we will build even better microscopes and others 
> will redo important computations with their own tools to see if they get 
> the same thing. 
> 
> For most things I trust these platforms.  It has been my (limited) 
> experience that most of the incorrect outputs are a result of my failure 
> to ask the question in the right way and not the result of the computer 
> doing something contrary to what it claims it would do.  
> 
> You are permitted and encouraged to doubt anything in these algorithms, 
> but hopefully that simply spurs you to get more information on what they 
> do rather than give up on them :)
> 
> 
> 
> -James
> 
> 
> 
> Lisette Brillemans wrote:
> > Dear forum,
> >
> > I'm exploring the exiting possibilities of the wonderful GAP and there
> > is quite a lot to explore there but...
> >
> > How can I trust that everything GAP calculates is correct? I'm sure I
> > can't.
> > And then we're only talking about GAP. GAP has also been added to
> > another, much bigger, software package calles SAGE, where many
> > opensource packages and libraries can be used in one interface. But so
> > many libraries, so many programs, so many packages, this cannot all be
> > correct. There must have been programming mistakes leading to wrong
> > calculations.
> >
> > But I would say that one cannot rely on it without recalculating
> > everyting, or is that preposterous? I hope that I may ask this here...
> >
> > I wish you a nice day and am continuing to learn to use gap (and sage
> > too).
> >
> > Lisette
> >
> >
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> >   
>