Something that I learned years ago (very likely from Feynman or quoted about him to me by someone else) is that, when looking at a dataset in a presentation and listening to the presenter's description of the meaning of the data, in your mind drop the data points from the graph at its extremes and decide if the conclusions make sense. Why? The data at the extremes are often there because the experiment stopped being trustworthy at roughly near those limits so the strength of those points often would be in question....

There was an article published recently, but I can't find it here. Someone in the social sciences at a university was accused of cooking his results. Both sides are now claiming that they are blameless and the other is at fault. Somehow a side effect of this was a substantial effort to carefully replicate a few dozen major long accepted classical results in the field. Approximately one third of the replications either failed to support the hypothesis or had sufficiently serious problems with the experiment that no claim could be made. In every case mentioned the original experimenter is furious that they have been targeted by a witch hunt, their reputation has been permanently damaged, they have no way of defending themselves and nothing can be done to make up for this. You should track down the original source of this before using it, just to make certain that I have not somehow skewed the claims. It might have been published in Science in 2013, but I can't be sure.

If the likes of Tufte's standards could begin to make it the norm that uncertainty be clearly shown with every claim and Mathematica could position itself as one of the leading tools to simply and easily produce graphics for claims then, as mentioned above, perhaps everyone might be in a slightly better position to see at a glance what has sufficiently small uncertainty to likely be accepted and what has so much uncertainty that it can be dismissed.

Bill, that seems a bit off topic of whether academics are missing out by not making greater use of Mathematica. But maybe not completely. Because of their active and dynamic character, Mathematica provides the opportunity of presenting higher quality results with higher integrity. One can include, in the document, raw data and procedures for analyzing and representing the results. Others can check if they actually work or have entry points for exposing problems. If people want to lie about data I suppose they can but it's not quite as easy to get by with just plain sloppiness.

I once worked as a computer consultant for a group of biochemists. At one point I was asked to look at an experiment one of them was doing to measure the rate of some biochemical reaction. The person was very nice and very meticulous in his biochemistry. But when I looked at the reaction system and what he was measuring I discovered to my horror that it had no relation at all to the reaction rate he was trying to measure. Needless to say, he was not pleased with this. I left the group but later learned from someone who replaced me that they continued the experiment and analyzed it with a statistical program. The result was something like 1.0 +/- 10^6 millimole/minute - and they published it!

Bill, your remarks are well put. I think that Tufte somewhere does have a maxim to Be Honest. And he does give several suggestions in Visual Explanations page 34. This might include multiple presentations based on different measures or viewpoints and textual explanation that might address various concerns. That's why I'm an advocate of literate notebooks that make a case and try to clarify and present a true picture. I would be very skeptical of any analysis summarized in a single presentation without extended discussion. In the final analysis it largely depends on the integrity of the person making or responsible for the analysis.

Mathematica probably has the tools to present uncertainty and risk. You just have to figure out how to put them together. With a dynamic presentation you can provide information in tooltips. You can provide information in numerical side reports, which may vary as you move a locator about the primary data representation. You might be able to toggle a presentation between various assumptions. And of course there are the old fashioned error bars and multiple presentations. Your suggestion of fuzzing the data representation might work very well. To go one step further, in a Mathematica notebook (or application) you can give the reader active tools for performing various types of data reduction and the actual data itself. I'm not knowledgeable about statistical analysis of data; I'm sure you can work out much better methods. The point is: Mathematica does give you better tools to present honest results.

I first used Macsyma over a 300 baud modem over the Arpanet from Caltech to MIT back in the mid 70s. And I found a bug. They had the general solution to the cubic entered incorrectly.

"All of the manuals on how to use Mathematica have been written by people who know too much. Their work should be edited by someone like me who is trying to learn what the developers already know."

Luther, I find your basic thesis here by and large accurate. Mathematica does have a steep learning curve and to directly use the more advanced features (particularly the various programming paradigms) one has to think like Mathematica, which for me has not come naturally.

Like others here, I started off with FORTRAN punch cards in college and was simply amazed at what could be done with the "simple" Do Loop. Ten or so years later I stumbled upon Macsyma, anybody remember that ? It was a command line math tool that claimed it could do symbolic math, maybe it could but I did not find it useful. Then I noticed that our Technical Librarian had a copy of Mathematica sitting on her shelf, version 2.2. After inquiring about it I learned that one of the Chief Engineers owned it originally but returned it to her because he couldn't figure out how to use it. I convinced my company to purchase the Premier Support package which offers supurb technical support and over the years would amaze him (and myself) of what could be done with this tool. I also read a few Mathematica books which I enjoyed at the time but that didn't boost my usability knowledge as I had hoped. During and prior to these years I became somewhat proficient with FORTRAN, MathCad, Excel, BASIC, Minitab and Matlab. And from my experience only Matlab comes close to the power of Mathematica if various toolboxes were acquired. Out of the box, Mathematica was a clear winner for my technical computing and data processing needs. And when serious statistics were added (ver 8 I think) there was no need for any other tool.

Fast forward to today, I am still a clunky Mathematica user and I still rely on the basic Do Loop from yesteryear even though much more efficient programming techniques have been available in Mathematica for years. But I've done some pretty neat stuff that no one else in the company has been able to do.

I share the learning curve frustration but I will take a hard to use yet capable tool over an easy to use limited tool any day. And for my technical computing needs, Mathematica has never let me down in the sense that if I could conceive it, Mathematica could be coaxed to solve it; that is powerful.

On a practical note, the approach I have found very useful is to create and maintain a private library of "How To Notebooks" that describe a narrow task that you know you will be facing again in the future. The source material for these may come from the hard slugging and self-learning that you have produced, a call to Tech Support , the online Help, books, or the Mathematica StackExchange site. If I look at my "How To" Folder I see file names like

How to align entries nicely using TableForm.nb How to compute running averages.nb How to conditionally extract values from a list.nb How to convert time formatted strings to numerical values.nb How to control minor ticks on a log axis.nb How to create a 3-D surface plot.nb How to extract algebraic solutions produced by the Solve command.nb etc.

I find this is far more useful that trying to rely on the built-in Help which, in general, offers a very simple example or two (material that you already know) and then jumps to examples so complex that [literally] some Tech Support Engineers at Wolfram have had some difficulty with, and these guys are good !

Kudos to Stephen Wolfram and his team for inventing, enhancing and maintaining what I think is the strongest technical computing environment on the planet. The professors mentioned at the beginning of this discussion don't know what they are missing.

For an example, that I have put to use in my own work, Google and download the Sandia report Sample Sizes for Confidence Limits and Reliability, by J. Darby.

I basically use Mathematica for all my work unless otherwise forced asunder. I write all my documents in it and have done since around version 3 (when the typesetting became publication class).

I think it was either Planck or Boltzmann who said that progress in Physics is made at funerals. You advance a new theory or process and wait for the old physicists to die. Having a Ph.D. in Physics myself, I'm allowed to say this. It's probably true for almost all fields of human endeavor.

Luther, why don't you write me at djmpark@comcast.net and tell me what your project is.

Dear Luther, I've been puzzling over your observation for nearly 15 years, and I also fail to understand why Mathematica/Wolfram Language gets dismissed by my colleagues so haphazardly. In discussions with my colleagues about this question, I tend to go in listening mode and don't advocate on one side or another. I'll try to summarize what they say below.

Some background:

I'm a professor at MIT in physical sciences and engineering. I've been teaching a course on mathematics and problem solving in materials science for about twelve years, and I use Mathematica extensively in my course. I can't judge the efficacy of my course objectively, but my students generally have very positive evaluations; I've been given MIT's highest institutional teaching awards, as well as the School of Engineering's. I believe that these awards reflect the quality of the Mathematica based course. I give nearly all of my research presentations using Mathematica and these are received well (however, such feedback tends to be biased towards positive)

The summary (I don't agree with many of these, and am still honing my counter arguments)

1) Mathematica is not as fast as X (X may or may not be a compiled language).

2) Mathematica's syntax creates too steep of a learning curve.

3) Our (particular) scientific community uses X; so there are many more routines and working examples in X

4) I am already using X, why should I change?

I believe most of the above are the result of "user inertia".

I don't hear the comment that Mathematica gives "bad results" so much now. I doubt if many faculty roll their own algorithms, but are probably thinking back to when they were postdocs or graduate students--however, there are happy exceptions to this

I believe that the best way forward is to offer students a choice; and hope that they will make an unfettered choice of a their preferred programming language. However, I am not so optimistic: a student who went to graduate school at a university down the street wrote to me saying, "I'm taking this class and they insist on using X and I asked if I could use Mathematica instead, and he said no. We were doing more advanced things in 3.016 ( the sophomore class I teach)."

Ah, memories!