Most users of phylogenetic software do not understand what it is actually doing, nor therefore the potential for inferential errors, let alone actual algorithmic or coding mistakes. Which is part of a larger discussion that goes well beyond phylogenetics. But how to solve the problem?

The "R" package contains both unsound individual modules plus procedures that combine otherwise valid modules into an erroneous computation chain. Somewhere along the line, biology professors started equating "knowing how to program" with "knowing what to program".

Gareth, such an effort would involve eliminating several existing functionalities - so potential users would have to be educated as to why that is the case.

In my perspective, this suite of functions would be invoked by WL and perhaps a WL GUI app for novices; i.e. the R scripting interface would be eliminated.

Further, I'm a fan of commercially supported scientific software so I'd like to see Wolfram involved. This would mean that some of the software development monies went Wolfram instead of graduate students. This would also ensure the package did not become another free-for-all collection of erroneous modules.

Just to be clear - I have no grievances with community-based "non-computational" software. For example: LaTeX.

For the immediate future I'm heavily invested in a genomic ID and ancestry project for fruiting perennials. I'm willing to consider your proposal though. For further discussions feel free to contact me via the email posted on the webpage on my Profile.

Mathematica supports LaTeX with TeXForm, and if you press Ctrl+4, you can type TeX into Mathematica. Stephen Wolfram describes in his blog post where he announces the release of Mathematica 12.2 how you can enter TeX into a notebook.

Hi Tom,

I think a technically educated person should be writing with a word processor, doing reports with a spreadsheet, and thinking with a technical computing language as an extension of their thought process.

This strikes me as too prescriptive. Fifty years ago you would have had to write, perhaps: "a technically educated person should be writing with a fountain pen, doing reports using a pocket calculator and hardly thinking at all about technical computing languages, unless they are computer scientists".

The point is: time moves on. If you work at Wolfram Research I imagine you (try to) do everything in WL, whether it be writing text, producing some analysis, or programming an application. Certainly that's my understanding of Stephen Wolfram's expectation, anyway. For myself I do a large proportion of my work in WL, including carrying out analysis, creating presentations, and programming applications. It's very convenient to use a common UI and tech stack for all these varied tasks: it save shifting from one application to another, having to be concerned about file format compatibility, etc.

A technical computing language is not the right tool for producing commercial computer applications.

I understand your point, but I expect that there are legions of Fortran programmers, to say nothing of the good people at WR and Mathworks who would heartily disagree with you. And indeed on the pages of this post several examples are given of commercial applications developed in WL (including one or two of my own).

To your point, however, it's obviously a significant challenge to develop a commercial application in WL, even though it can be and has been done. I certainly wouldn't regard the development of commercial applications as a forte of Mathematica, in they way that, for instance, symbolic programming clearly is. Which goes to the topic of this post - i.e. what is Mathematica for? And I would have to concur that the development of commercial applications is not one of those things - although I am quite sure that Stephen Wolfram and others at WR would strongly disagree.

My answer: “it’s an extension of one’s thought process.”

This is a bold claim for any programming language/technology platform, including Mathematica. Could one not make a similar claim about C++, Java, or Julia? I suspect that, unless you are a professional developer, probably not. Mathematica has certain unique features that make it a natural fit for the rapid exploration of ideas, in a way that certainly isn't true of most other computer languages that I am aware of.

I think that your description encapsulates what Stephen Wolfram may be aiming for: a kind of cognitive sand-pit offering a plethora of computational tools that provide a unique way to explore ideas, whether experimentally, graphically, or analytically, that will assist the process of developing them into functional algorithms.

You may want to revise your 'way-back' time. Lotus did not come out until 1983. The HP-35 debuted in 1972, but the programmable HP-65 came out in 1974 -- at a whopping $795 -- equivalent to $4k in today's dollars. HP portables no earlier than 1987.

I started coding in 1972, and it was on a timesharing PDP-5. No personal computers at all -- Altair 8800 debuted in 1974. I got an HP-35 shortly after it came out, which meant that I could ditch my slide rule and log/trig tables. Most of us who learned to code in those days didn't take CS, because most schools didn't offer them. (I was a maths major, so I did have numerical analysis.)

So, 50 years ago (1972), I was writing on a typewriter (an IBM Selectric if I did so at work), doing calculations with my slide rule or walking to the Medical School computer facility -- or by hand, and when I did learn to code, used Assembly and BASIC. C came out in 1972, but I did not have access to a computer the compiler (etc.) would run on until the late 1980s.

SO, no need to make the 1970s 'better' than it was. It was the wild frontier.

I think a technically educated person should be writing with a word processor, doing reports with a spreadsheet, and thinking with a technical computing language as an extension of their thought process.

I observe that people don’t think about things much. If they do, they use a spreadsheet. And that may be too complicated for some. The market for technical computing language may be limited to what I think of as “practicing PhD’s”. Mathematica makes it practical to think about a problem in terms of differential equations, for example, but one first needs some understanding of calculus and not everyone does.

I have recommended Mathematica to others but so far none have been able to use it well enough for it to be an extension of their thought process. It’s a steep learning curve. I have been using Mathematica since version 1.

A technical computing language is not the right tool for producing commercial computer applications. They are two very different things. This is not good or bad, just two different things. And tools for commercial computer applications are well developed. I had an application where I was writing c-code for a microcomputer. It needed a digital filter. I used Mathematica to simulate the data and to design a digital filter. Expressing the filter as c-code was trivial.

My typical Mathematica notebook often starts with some simple notes on a topic. It extends to some “proof of concept” analysis. Then expands from there. This was the development pattern in a recent activity where I extracted telemetry data from a GoPro MP4 file and used it to analyze sailing performance.

My answer: “it’s an extension of one’s though process.”

Years ago, we may have understood that an analysis might be theoretically doable, but we did not have tools to do it. Now with a technical computer language as an extension of one’s thought process we can. The possibilities for expanding understanding become endless. Perhaps we should put more emphasis on teaching a technical computing language. It might enable people to use, for example, calculus in a meaningful way.

Hi Wener,

I am not sure I agree, for two reasons.

Firstly, the question was "What is Mathematica for", not "What is the Wolfram programming language for". i.e the question was intended to be a little more general. Indeed, as you yourself have pointed out, there is an

impenetrable jumble of products and licenses

i.e it's getting harder to identify the precise boundary lines between each product offering. I believe this is termed "confusion marketing". i.e. it's a deliberate marketing tactic.

Secondly, a major thrust in recent years has been to embed computable data / entities and related functionality within the WL, for example in geographics. I believe Stephen's vision for "Mathematica" is as a blend of computable data and programming capability. Indeed, access to Wolfram Alpha is itself embedded in Mathematica, as you know.

I recently programmed a prototype of a game that makes extensive use of computational geographics data. It would have taken many times longer to program that in e.g. Python, as a great deal of time would have been expended in data retrieval and wrangling. In Mathematica, it was relatively easy. That's a good example of why it makes sense to include computable data in the technology stack.

I think Mathematica is good for writing computational essays. Stephen Wolfram has a blog post on this.

I agree that Wolfram Alpha is becoming indispensable. I think Wolfram Alpha is used by math students, math teachers, science students, and science teachers.

I am a Wikipedia editor and I think Wikipedia is a good reference.

Maybe it's different in your country. I am in Germany. And I am not only talking about students in maths or engineering, but social and many other sciences that have at least to do much with statistics and probabilities.

A Wolfram|One Personal licence for Student costs EUR 333/Year (!). This is for one user, two installations. Euros are about the same as US dollars. This is a price never acceptable for students. Unless they have rich parents.

The prices for student Mathematica desktop licenses in Germany:

I reviewed again the German prices for Student's Wolfram / Mathematica. I found three products/licenses for Students:

They range from 104 €/Y to 333 €/Y. The cheapest one does not include the cloud (which probably is not very important, since everybody stores and synchronizes their files within other clouds, namely OneDrive for Windows users).

I could not really tell the difference is between Mathematica Desktop (181€/Y) and Wolfram|One Personal (333 €/Y) (I have the latter, but - strange enough - for 271 €/Y).

I don't even know what the difference is between Mathematica and Wolfram Language. I look at "Mathematica" as just the former name of "Wolfram Language" and abbreviate it as "WL".

Putting it all together, possibly a student could live with Mathematica Desktop for 104 €/Y. "Possibly" because I assume that this does not include any product upgrades which would make it pretty useless. If that is true, he would have to pay at least 181 €/Y, possibly 333 €/Y.

I think the ability to do symbolic math is underrated. I'm a hobbyist programmer, and I once encountered a problem that really did require to do symbolic math. I really, really didn't want to do the calculations with pen and paper so I bought a Mathematica license. Since then, I've learned to appreciate the capabilities of the language and the elegance of its design.

Mathematica has been the platform of choice for sensors-to-animation production by the film industry for decades. A colleague of mine is a system administrator at one of the sites.

The famous example are the animations added to the actors in Pirates of the Caribbean.

Hi George,

as far as I know the Wolfram Engine is already ported to iOS for the App "Wolfram Player" but not embeddable in a custom application.

https://apps.apple.com/us/app/wolfram-player/id1059014516

I think the complaints about cost are misplaced. Wolfram products are in high demand and so I don't believe the price is going to come down.

My thoughts on this topic, besides that it should recieve more public discussion, are twofold.

First, I am not sure whether I will buy Mathematica once I exit academia. As long as I have a 'free' license though, I'm hooked. I think both mathematics and computer science students have a hard time approaching MMA even though it has tremendous potential to benefit both kinds of people†. I like to tell them that MMA is the worlds best software rapid prototyping tool; or when I'm being cynical, that MMA is both good for nothing and good at literally everything††. Frivolous yet powerful things are often the most compelling and fun...

Second, can MMA ever have a practical use†††? I think besides small niches, there is exactly one possibility. I haven't played with it's C code generation very much, but it seems like it's mainly limited to producing 'zombie routines' that must hook into a kernel. The symbolic nature of WL admits, for instance, a search over all possible algorithms to achieve a task. I think a richer library of code generation tools/examples plus an expanded code generation interface (i.e. x11 calls, various windows dlls; think of existing gpu and ffmpeg functionality) could start to make WL useful for 'actual code development'.

†In many lower division math classes, the entirety of homework can be automated in MMA. Document scanning, equation parsing, equation solving with steps, typesetting and printing. Literally the whole process: it's a thing of beauty. Applied computer science students, once relieved of worrying about the nontrivial trivialities of modern software, can appreciate the beauty of theory.

††Good for nothing in that it's useless for producing anything dynamic (i.e. production software), and good for everything in that it's capabilities are wiiiidespread and richly interconnected and as a result can produce amazing static visualizations, sounds, videos etc. Most academic publications are entirely static--most of scholarship is just prototyping ideas--such that MMA is the perfect scholarly workbench.

†††Again, practical in the sense of providing a directly valuable service--there's some economics word I'm looking for. One might say I'm asking for the well crafted code that goes into the kernel to be freely given up. Instead, I'm suggesting that the symbolic power of WL could be suited for automatedly writing lots of code--I would only be able to give examples if I were to embark on this as a project.

I recently spent almost two weeks to install keras(the most star count deep learning framework on github) to my gcp compute engine linux debian machine, keras now bundled with tensorflow2, only can run inside docker container, docker itself is cloud native technology, and I also spent great portion of time to install the gpu support in docker, now everything seems ok to go. The Capability to package app inside docker to run seems the way to go in cloud era.

Hi Kapio,

I know about redmine. Actually I am a heavy user :) and it is definitely a step in the right direction. Direct contact with QA and sometimes with the developers helps a lot. Still what I would really appreciate is that development cycles are dedicated for bug fix only releases like version 12.1.1. Just polishing the existing stuff. There are also a lot of things fixed in regular releases but because of the new features almost always some regressions end up in the release.

Wenguang,

I happen to agree with you. But what would you say are the specific data processing capabilities that Mathematica lacks, or is inferior to Python, from your experience? Can you give some examples?

I always enjoy using Mathematica for serious and less serious work. Don't want to spend all time on finding the right python libraries and check there vitality etc when most absolutely necessary. I think Mathematica is fantastic and thoroughly enjoy listening to Stephen wolfram's discussions with his outstanding team. I mean I don't know any other cto doing that. I also believe that Wolfram is really looking for "stuff" that is actually useful for his customers. Other languages have also great features and sometimes better syntax but that doesn't matter. The flexibility is incredible. I also enjoy the documentation and all the crosslink to other fields that might be useful. You always learn from it. No other languages has given me more pleasure programming than this Wolfram language. I once played with low code software mendix in combination with sap software. I didn't really like it. Low code for sure but many many many clicks and different windows.. Not for me.

Jonathan, the answer is very simple:

"Mathematica is for Stephen Wolfram to do his NKS-stuff on."

Other features are put in from time-to-time and as is deemed necessary to make Mathematica sufficiently saleable to support Stephen so he doesn't have to get some other less enjoyable occupation while he pursues NKS.

;-)

B

Hi Raspi, in some ways I think you are an ideal Mathematica user - a total convert: MMA with everything! And I get it - it's a wonderful sandpit environment for every kind of experimentation.

But in broad terms, my thinking is that this is what Mathematica really is: a means of doing fast research, experimentation and prototyping - but not necessarily for production systems.

If you are not a professional developer that probably doesn't matter at all - everything is an experiment, or recreation! But for a professional developer, getting systems into production and making sure they are battle-ready is a critical part of what you do for a living. And its in this context that I see the greatest challenge for Mathematica - making WL applications that are sufficiently bullet-proof to hand over to an end user (rather than, say, a research co-worker).

BTW what do you use Raspberry Pi for?

You mention using your RPi to access Mathematica remotely. But cant that be done just as easily and more effectively by accessing MMA on your PC via remote desktop when you are travelling)? Is there something specific about the RPi implementation of MMA that makes it more accessible for remote work?