Re: Re: Re: Mathematica can't win against Tiger Woods
- To: mathgroup at smc.vnet.net
- Subject: [mg19877] Re: [mg19811] Re: [mg19765] Re: [mg19677] Mathematica can't win against Tiger Woods
- From: Leszek Sczaniecki <leszek2 at home.com>
- Date: Sun, 19 Sep 1999 01:20:58 -0400
- Sender: owner-wri-mathgroup at wolfram.com
David Withoff wrote: > Leszek Sczaniecki <leszek2 at home.com> wrote: > > Here is my point. Mathematica can certainly do plenty of problems much > > better than human. But, it is very, very frustrating, that in trivial > > cases the system often produces results worse then those delivered by a > > human. I see this as the challenge for Mathematica developers. The system > > should always produce better results than human. Presently, Mathematica > > is a tool for some kind of "scientific lower middle class". It is way to > > weak for people, who do serious mathematics or theoretical physics, and > > way to complicated for pedestrians. If Wolfram Research Inc. truly intents > > to reach "masses", it has to be more sensitive to their needs. > > > > Think about the education which is precisely about solving again and > > again old problems. How you are going to justify the usefulness of > > Mathematica in education, if it can't easily replicate known results? > > These sentiments are variants of the same mistake: starting with a > common frustration -- difficulty coaxing a machine to do things that > can be done by hand -- and extrapolating to the incorrect conclusion > that the machine is therefore useless, or at least seriously diminished > (useful only to a "scientific lower middle class") because of it. > You are generously crediting me with statements, I never made. I just pointed out an area for improvement. I never said that the machine is useless. Perhaps, It would be more productive, if you could tell us a TECHNICAL or any reason explaining why mathematica cannot do better in the area of linear differential equations with constant coefficients. Or perhaps, for what technical reason it can do this simplification In[1]:= FullSimplify[(Sqrt[2] 1/2))^2 Sin[x/2]^2] Out[1]= 1/4 (1 - Cos[x]) but fails here In[2]:= FullSimplify[(Sqrt[2] x/2))^2 Sin[x/2]^2] Out[2]= 1/2 x^2 Sin[x/2]^2 ? > > No one ever claimed that being able to reproduce hand calculations on > a computer was a Bad Thing. In particular, Prof. MacDonald, in the > message that introduced this thread, is entirely justified in being > disappointed that DSolve sometimes returns results in an awkward form. > To the extent that there is a practical way to do it, it is obviously > desirable to address this concern. > > It is in extrapolating beyond this point that this sentiment becomes > a serious and self-defeating error. > > It is not realistic to expect a computer to always give better results > than a human, any more than it is realistic to expect any human to > always give better results than a computer. As Andrzej Kozlowski > pointed out, computers are not intelligent beings, and you should not > expect them to behave that way. > > And no, education is not about solving old problems again and again. > It is about preparing people to solve whatever problems come their way, > and about showing them how to choose the right tool for the right job. > Being able to reproduce hand calculations on a computer is not > essential to this task. > People are being prepared to solve whatever problems come their way by solving old problems with known solutions. They are learning the same Newton equations in physics, the same chain rule in calculus, the same Maxwell or Lagrange equations for many dozens of years. Lectures, textbooks, problems and examples have been fine-tuned for years. It is nothing wrong about repeating old good stuff. It would be silly to reject that valuable heritage. I will try to illustrate what consider the best approach to the education using the following example. When learning about matrices for the first time, people should do the first computations manually becuse they gain better insight to the subject this way. However, later, when they study, say, the relativistic quantum mechanics via Dirac equations, they should use computer for manipulating gamma matrices. I hope you see the difference. In the first case, they benefit intellectually by doing "manual" work, exercising their brains. In the second case, because they already know well how to manipulate matrices, they would not significantly benefit from doing that agaim. They should use computer algebra to eliminate the tedious, mechanical work, that does not enrich them intellectually. They can then use the saved time to get deeper inside into the main subject. I used to do computations involving quantum mechanics for more then fifteen year, but the illustrations of solutions of two dimensional Shroedinger equations prepared by TerryRobb helped me to gain new insight. On other hand, the overdose of computer algebrain education can have decremental influence on people, who use it as a magic blackbox to deliver solutions and an excuse for not thinking. > > For example: using a computer to demonstrate all of the algebra that > would be used to do partial fraction decomposition by hand would be > difficult. It would also be a waste of time. Just use Apart. > That's really funny. Apart is an excellent illustration of one of my points. It behaves exactly as defined the documentation, but it doesn't do what users expect. Brian Evans, the principal author of "Signals and Systems", had to write his own version of Apart named MyApart, that is available on MathSource http://www.mathsource.com/MathSource/Enhancements/Algebraic/0202-071/MyApart.m for many years. Here is an excerpt from the package header. -- (* From: Brian Evans <evans at gauss.eedsp.gatech.edu> To: mathgroup at smc.vnet.net Subject: [mg19877] Re: Partial Fraction Decomposition with imaginary coeff. Source-Info: From (or Sender) name not authenticated. You just don't know how difficult Apart has made my life. It is crucial to the implementation of inverse linear transforms. Under 1.2, it would not handle polynomials with rational coefficients expressed in decimal form. Under 1.2 and 2.0, Apart does not break up terms like 1 / (x^2 + 1). About two years ago, I had to write a general purpose routine to work around Apart's drawbacks. I call it MyApart. It is embedded in the signal processing packages for Mathematica and is used by the inverse z- and Laplace transforms when Apart doesn't complete the decomposition. MyApart is, of course, darn slow. Brian L. Evans Digital Signal Processing Laboratory School of Electrical Engineering Georgia Institute of Technology Atlanta, GA 30332-0250 e-mail: evans at eedsp.gatech.edu *) -- Look at the dates. Brian wrote his package in 1988. For eleven (sic!) years electric engineers have been using "home made", substandard extensions to Mathematica. This is precisely what I meant asking for more sensitivity to user's needs. I have been trying to promote Mathematica in my company. Mathematica has here reputation of being "to difficult". I am doing my best. I train my co-workers for free, I am writing notebooks to present the system in its best to some wider audience. I am trying to help you guys. I know that others, such as a long term mathematica proponent Prof.MacDonald, who started this thread, are doing the same. When I pointed out, what hurts your business, I got in return lectures about computers and software engineering in general, some philosophical opinions that I never expressed have been promptly straighten up, I was advised on my career, told a personal success story, send a quote of a big shot taken out of context, and my credibility has been questioned, but I heard very little technical information. I didn't hear: "Yes, FullSimplify needs improvement, we are going to work on it" or "Sorry, at this point we don't have human resources to spend of FullSimplify". > > Another example: using a computer to demonstrate all of the steps > for calculating a square root by hand would also be difficult, and > it would again be a waste of time. Just use Sqrt. > > The most brilliant uses of Mathematica in education involve carefully > identifying which topics are still best illustrated using hand > calculations, which topics are best illustrated using the computer, > which topics (such as calculating square roots by hand) are obsolete > because of computers, and which topics can now be added because computers > are available to handle the otherwise prohibitive calculations. > > And the poorest uses of computers in education involve using them to > solve the same old problems, using exactly the same calculations that > were done by hand before computers. > > And finally: > > > Here is an example of what I meant by insufficient sensitivity to > > user's needs. It is absolutely critical for finance applications to > > have fixed point display of numbers with trailing zeros and Round that > > rounds x.5 up and not toward the nearest even integer. They are easy to > > implement on the kernel level. In past Round was rounding x.5 up so the > > code should be somewhere. Why Round cannot have an option Method with > > values IEEE, Up, etc.? I brought these issues many times. The only > > answer was: "Write your own functions". I wrote the functions, but > > others just abandoned the system. Wolfram lost. > > this seems like nonsense to me. I happen to know quite a few people > in the financial industry, all of whom couldn't care less what Round > does with x.5. Perhaps we could test your credibility on this point > with an informal poll of mathgroup readership. Is there anyone reading > this message who seriously believes that this aspect of Round "is > absolutely critical for finance applications"? If there is any demand > I am sure this feature will be added. > Sadly you chose to question my credibility rather than address technical issues. I might have for you a better way to check my claims than organizing a public vote. I advise you to consult Operations Committee of SIA (Security Industry Association) ((212) 608-1500) regarding the standards for fixed income instruments. For mortgage backed securities you can contact PBS (Public Securities Associations)((212) 809-7000). For other instruments contact the appropriate association. They regulate how many digits you must retain for intermediate results, how many for the final result, when the result has to rounded, when truncated, etc. I am talking about official business, privately you can do whatever you want. Dave, if any one of these organizations happens to accept the rounding to the nearest even number, I will send you a bottle of good Bordeaux.:-) BTW, if you care about the finance community, where are filters for spreadsheets? Like it or not, THE most common tool in business is spreadsheet. If you would spend just a little time to look into this newsgroup archive, you would certainly notice postings from users surprised by the behavior of Round. There is a story, that I learned from Neil Soiffer. It is about NeWS (Network Window System) developed by Gosling, who became later famous for his work on Java. Thesystem was technologically very advanced, included number of leading edge technologies, but people didn't use it. Desperate Sun organized events for developers to promote NeWS. On one of such events, after couple hours of work with no apparent success, hopeless Sun's employee asked the audience: "This system has so many modern, exciting, great features. Why you don't use it?". One developer from back rows stood up and said: "If you really want us to use it, fix the shell first, so that it doesn't crash so often". We know the rest of NeWS story. Here is my advice to Wolfram's developers. If you really want to succeed, while chasing very advanced features don't forget about the fundamental ones. Remember that customers can easily survive without Wolfram Research, but Wolfram Research can hardly survive without customers. Now, because this thread has been loosing the technical focus and getting unnecessarily personal, I decided to terminate my participation in it. :-( -- Leszek Sczaniecki > > Dave Withoff > Wolfram Research