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MathGroup Archive 2004

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Re: how to explain this weird effect? Integrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46439] Re: how to explain this weird effect? Integrate
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Wed, 18 Feb 2004 00:37:07 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On 2/17/04 at 7:05 AM, nma124 at hotmail.com (steve_H) wrote:

>Bill Rowe <readnewsciv at earthlink.net> wrote in message
>news:<c0qjgq$ka6$1 at smc.vnet.net>...

>>But these effect you label "artificial side-effects", are no
>>different that what a human might achieve. That is if you don't
>>see a way to re-arrange things or do things in a different order
>>you likely to get the same results as Mathematica does.

>Correct. This is IF you (a human) do not see a way to re-arrange
>things.  But I expect a computer program to see a way to re-arrange
>things. After all, it is supposed to be much better at doing these
>things.

But Mathematica is not better at this task. Computers aren't yet intelligent. They can do nothing that has not already been programmed into them. Mathematica's advantage with regard to this task is it has a large number of rules built in that I don't have to remember. But it isn't intelligent. Mathematica cannot determine what I have in mind nor make intelligent decisions as to what transformations to apply.

This point is clearly demonstrated by many of the comments concerning Simplify and FullSimplify expressed here. Mathematica has built into it an arbitrary definition of "simple" as it applies to expressions. It applies transformations to expressions to make them "simpler" consistent with this definition. But the result is often quite different than a human would consider "simpler".

>>Take the example you used when you started this thread. If you
>>gave the results of the integral with the same denominator, m^2 -
>>n^2, a human, they either have the same problem with division by
>>zero when m = n or must take the appropriate limit. Taking the
>>appropriate limit is an additional step. It is no different when
>>using Mathematica.

>But that is exactly my point. I wanted Mathematica to act as if it
>was a human. (A very smart human at that).

But since no one I know has intelligent computers, this is asking too much from any computer algebra system at this point. Nor is it even clear this would be desireable even if it was achievable. 
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