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On Jun 21, 12:11 am, Richard Fateman <fate... at cs.berkeley.edu> wrote: > Noqsi wrote: > > Approximation is often puzzling. The ideological war you wage against > > WRI is unhelpful here. The wise person understands that there are > > multiple points of view. > > If it is required to be wise in the ways of WRI's (unusual) arithmetic > to use WRI software, then that is more than a user interface problem. You must be wise in the ways of the tool to use it. That's always true. There's nothing wrong with being "unusual": Mathematica is unusual in quite a few ways, and that's key to its ability to quickly dispose of problems that are more difficult with other tools. When a different tool is better, just use that and quit carping. > > Your IEEE754-based ideology has its own > > > weaknesses: abuse of the concepts of "rational" and "finite", and weak > > connection to the real number system. Matthew 7:3 applies. > > I'm not sure what you mean by IEEE754-based ideology. The ideologue never understands his own ideology. > Probably the > whole community of numerical error analysts agrees on a model that is > different from WRI's. In other words, your fellow ideologues agree with you. Unanimity in an area as tricky as this is a sure symptom of groupthink: difficult problems demand *multiple* points of view for truly effective understanding. Even in physics, where we think we are all working with a common reality, we have multiple ways of looking at it. Numerical analysis lacks that common reality: it serves a diversity of applications, with a diversity of requirements. Where I fault Mathematica's design here is that "Real" wraps two rather different kinds of objects: fixed-precision machine numbers, and Mathematica's approximate reals. Both are useful, but understanding and controlling which kind you're using is a bit subtle. "Complex" is even more troublesome.