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Re: Replacement Rule with Sqrt in denominator

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  • Subject: [mg114557] Re: Replacement Rule with Sqrt in denominator
  • From: Andrzej Kozlowski <akoz at>
  • Date: Tue, 7 Dec 2010 06:49:14 -0500 (EST)

On 6 Dec 2010, at 12:14, Bill Rowe wrote:

>>> The fact replacement rules operate on the FullForm of an expression
>>> but what is displayed is not the FullForm does mean inexperienced
>>> users of Mathematica will encounter some difficulties with
>>> replacement rules. But, that simply doesn't equate to being a bug.
>> No, I think the error is that users need to have another kind of
>> pattern matching, and that when too many people stumble over the
>> same feature, the correct response is NOT, "the customer is wrong,
>> yet again."
>> It might be ,  Oh, you want the semantic pattern matcher.
>> Maybe, Here's how we can set it up to be your default command pattern
>> matcher...
> In another post Daniel Lichtblau described the issues with
> trying to make replacement rules work on what is displayed
> rather than full form.

Whether something is right or wrong, is a bug or a feature or whatever ultimately depends on consensus of "experts" or at least people who are sufficiently qualified to make an informed judgement.  This is just as much true of design of computer programs, "correct" use of language etc. as of mathematics. In mathematics, of course, in most cases consensus is easy to reach, as in the case of whether two plus two is four or seven. No amount of stubborn insisting on the latter answer will win over the consensus of people familiar with basic arithmetic - at least not without additional incentives of the kind "That's not true! It's seven! Say it's seven or I'll hit you!"
(see Lem's story "Trul's Machine" here <> ).

In more advanced mathematics we too get situations that "qualitatively" resemble this. Sometimes someone, occasionally even a very good mathematician keeps insisting that he had proved something (usually a famous unsolved problem) while the majority of experts reject the claim. One of several such examples is Wu-Yi Hsiang and his alleged proof of the Kepler conjecture (see the article by T.C. Hales in "The Mathematical Intelligencer" in 1994). More common are the cases of individuals claiming that some well established theorem of theory is wrong.  In all such situations the thing to remember that "consensus" is not a matter of numbers - it does not help to have on one's side any number of people who obviously do not understand what the whole thing is about. Expert's themselves are not equal - in many areas the judgement of a few  individuals carries more weight than that of practically everyone else together.

My point here is this. Richard Fateman has been insisting for over a decade that this particular behaviour of Mathematica pattern matcher is some sort of "bug". He has posted the same arguments many times over, often in response to the same counter arguments from the same opponents. And, as far as I can recall, he has never succeeded in winning over  to his side a single informed person. He does indeed receive some support but almost exclusively from people who are either Mathematica beginners or "perpetual beginners". He has certainly never got anything remotely resembling "the support of experts" on his side.

Most importantly, he has never managed to get Daniel to concede any ground at all on this point. Now, unless one assumes that Daniel is just plain stubborn, or unable to see the obvious, or just totally under the thumb of his "evil boss", this suggests that the case for a bug is a weak one, I would say rather weaker than Hsiang's claim to have proved the Kepler Conjecture (I am not even sure if it is much stronger than the claim of Trul's machine).

Andrzej Kozlowski

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