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Launching Mathematica 10

blog.stephenwolfram.com

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Re: Launching Mathematica 10

#51

Post by taliesinb »

programnature wrote: post #48
reikonomusha wrote: post #40

I hate to be that guy, but I wish to share my opinion about closed source mathematical software. There is no doubt that what Wolfram Research has done with Mathematica is amazing and tempting. It is a very complete and uniform engine, and can be very useful for very different kinds of mathematics. However, Wolfram Research deliberately keeps their methods and source code closed. Note that this is more serious than ju…

While well-meaning, sentiments like these are part of the problem. The proposed frame is "mathematica is somewhat better in polish and functionality, but we should stick to OSS on principle." The problem is, by this argument, no will actually ever know what Mathematica is, what it does, and what cool ideas it had that could potentially inspire further work. All the examples of alternative software have lots to learn…

I think you put your finger on it... people talking about Mathematica/Wolfram Language as a CAS are really chasing an idea of what it was 10 or 15 years ago.

Maybe I'm naive but I think that we really can just "all get along" -- notebook-based programming is just one example of how ideas can incubate in closed-source projects, and end up benefiting open-source projects. I'm hoping knowledge-based computation ends up being another.

And the reverse happens too -- Light Table is tremendously exciting, and I hope WRI can learn from that as it develops.

Re: Launching Mathematica 10

#52

Post by reikonomusha »

programnature wrote: post #48
reikonomusha wrote: post #40

I hate to be that guy, but I wish to share my opinion about closed source mathematical software. There is no doubt that what Wolfram Research has done with Mathematica is amazing and tempting. It is a very complete and uniform engine, and can be very useful for very different kinds of mathematics. However, Wolfram Research deliberately keeps their methods and source code closed. Note that this is more serious than ju…

While well-meaning, sentiments like these are part of the problem. The proposed frame is "mathematica is somewhat better in polish and functionality, but we should stick to OSS on principle." The problem is, by this argument, no will actually ever know what Mathematica is, what it does, and what cool ideas it had that could potentially inspire further work. All the examples of alternative software have lots to learn…

I am not proposing that Mathematica is "somewhat better". Mathematica is vastly better for many things, especially visualization.

Other systems should "learn" from it, sure. It is hard to change Maxima, unfortunately, since it's entrenched in its roots from the 1960s. That's no excuse for making it difficult to use.

I think Sage's Python interface is doing better and better, learning what it needs to learn from Mathematica, including its documentation and interface.

I definitely don't agree with you that everyone should use or learn Mathematica though to learn it. As a student of computer algebra, I'd have to contend that Mathematica actually does computer algebra remotely correctly. A much more beautiful system for doing computer algebra was Axiom [0].

[0] http://www.axiom-developer.org/

Re: Launching Mathematica 10

#53

Post by omaranto »

szhorvat wrote: post #46
reikonomusha wrote: post #40

I hate to be that guy, but I wish to share my opinion about closed source mathematical software. There is no doubt that what Wolfram Research has done with Mathematica is amazing and tempting. It is a very complete and uniform engine, and can be very useful for very different kinds of mathematics. However, Wolfram Research deliberately keeps their methods and source code closed. Note that this is more serious than ju…

My impression is that you don't hate to be that guy, but actually love to express this opinion. Open source systems like Sage always look desirable, simply by virtue of being open source. But every time I look at it I'm left with a very bad taste in the mouth because of the constant badmouthing of non-open-source systems that is going on in that community. Companies do that sort of thing, and it doesn't inspire trust…

Results obtained with are better because Sage is open: in a mathematical research paper you can say:

"This reduces the problem to computing blah, which we did using the following Sage code. The function foo used here uses the algorithm of X and Y as described in their paper [XY2006]"

You can't say:

"This reduces the problem to calculating blah which the following Mathematica code computes using an unspecified algorithm for which there is no accompanying paper proving correctness."

Of course a paper proving that an algorithm is correct can contain errors, and also even if the proof of correctness is fine the actual implementation can contain bugs. But if you have no way of knowing how something is computed and whether anybody at any point in time even tried to prove mathematically that the method used is correct, you have no moral authority to rely on the result. That's just the standard adopted in mathematics: you can depend on results you have good reason to believe are true and are documented in the literature; you can't rely on stuff that's not written about. I don't know how citing results works in other areas, but that's how it is in mathematics (at least in the fields of mathematics I'm familiar with).

Re: Launching Mathematica 10

#54

Post by madengr »

reikonomusha wrote: post #40

I hate to be that guy, but I wish to share my opinion about closed source mathematical software. There is no doubt that what Wolfram Research has done with Mathematica is amazing and tempting. It is a very complete and uniform engine, and can be very useful for very different kinds of mathematics. However, Wolfram Research deliberately keeps their methods and source code closed. Note that this is more serious than ju…

Sometimes it's just a matter of signing an NDA to see the source code. I use a pretty expensive ($100k) EE simulation package and have questioned model implementations on a few occasions. The developers had no issues sending me the code in question for a simple 1 page NDA.

Re: Launching Mathematica 10

#55

Post by programnature »

reikonomusha wrote: post #52
programnature wrote: post #48

Earlier quoted context omitted.

While well-meaning, sentiments like these are part of the problem. The proposed frame is "mathematica is somewhat better in polish and functionality, but we should stick to OSS on principle." The problem is, by this argument, no will actually ever know what Mathematica is, what it does, and what cool ideas it had that could potentially inspire further work. All the examples of alternative software have lots to learn…

I am not proposing that Mathematica is "somewhat better". Mathematica is vastly better for many things, especially visualization. Other systems should "learn" from it, sure. It is hard to change Maxima, unfortunately, since it's entrenched in its roots from the 1960s. That's no excuse for making it difficult to use. I think Sage's Python interface is doing better and better, learning what it needs to learn from Mathe…

People into traditional programming languages look at Mathematica and see abstractions for which they see no purpose.

People into PL research look at Mathematica and scoff at its low-brow, for-the-masses term rewriting, lacking whatever theoretical property deemed "essential" that week.

Yet somehow the language has formalized and made more computable and consistent more domains of math, science, and increasingly data than any other.

There is no honor or glory in purposeful ignorance.

Re: Launching Mathematica 10

#56

Post by ihnorton »

szhorvat wrote: post #44
Schiphol wrote: post #19

Earlier quoted context omitted.

I once tried to do meaningful work and, while things such as the NDSolve[] function are positively amazing, programming in Mathematica (which means using its editor) is a huge pain when you are used, say, to vim. In the end I moved everything I had to the Python scientific stack and I'm very happy I did it.

You need to get used to the notebook concept. In the end you'll find that it's much more convenient for interactive work than a traditional command line. For non-interactive work you can still use Vim if you like. In fact Mathematica shows its advantages most when used interactively (compared to languages, like Python, which were not really designed for this).

Python and Julia have a nice interactive notebook: IPython/IJulia.

Re: Launching Mathematica 10

#57

Post by judk »

reikonomusha wrote: post #52
programnature wrote: post #48

Earlier quoted context omitted.

While well-meaning, sentiments like these are part of the problem. The proposed frame is "mathematica is somewhat better in polish and functionality, but we should stick to OSS on principle." The problem is, by this argument, no will actually ever know what Mathematica is, what it does, and what cool ideas it had that could potentially inspire further work. All the examples of alternative software have lots to learn…

I am not proposing that Mathematica is "somewhat better". Mathematica is vastly better for many things, especially visualization. Other systems should "learn" from it, sure. It is hard to change Maxima, unfortunately, since it's entrenched in its roots from the 1960s. That's no excuse for making it difficult to use. I think Sage's Python interface is doing better and better, learning what it needs to learn from Mathe…

I am worried that Sage will get stuck in the mud as its Python code base grows, without a powerful expressive functional core like Mathematica's Lisp-ish core language. For example, see the discussion in this page about simple association lists vs what Mathematica 10 just launched

Re: Launching Mathematica 10

#58

Post by reikonomusha »

programnature wrote: post #55
reikonomusha wrote: post #52

Earlier quoted context omitted.

I am not proposing that Mathematica is "somewhat better". Mathematica is vastly better for many things, especially visualization. Other systems should "learn" from it, sure. It is hard to change Maxima, unfortunately, since it's entrenched in its roots from the 1960s. That's no excuse for making it difficult to use. I think Sage's Python interface is doing better and better, learning what it needs to learn from Mathe…

People into traditional programming languages look at Mathematica and see abstractions for which they see no purpose. People into PL research look at Mathematica and scoff at its low-brow, for-the-masses term rewriting, lacking whatever theoretical property deemed "essential" that week. Yet somehow the language has formalized and made more computable and consistent more domains of math, science, and increasingly data…

I disagree that it has made more domains of math computable and consistent. It's syntax is consistent, but it's evaluation semantics is wildly inconsistent. This is noticeable when you use some of their internal simplification algorithms on non-trivial problem.

I think Axiom covered more surface area in terms of mathematics than Mathematica. Mathematica is mostly good at performing over reals and complexes and doing term-rewriting algebra. Axiom supported arbitrary algebraic structures.

Re: Launching Mathematica 10

#59

Post by judk »

taliesinb wrote: post #51
programnature wrote: post #48

Earlier quoted context omitted.

While well-meaning, sentiments like these are part of the problem. The proposed frame is "mathematica is somewhat better in polish and functionality, but we should stick to OSS on principle." The problem is, by this argument, no will actually ever know what Mathematica is, what it does, and what cool ideas it had that could potentially inspire further work. All the examples of alternative software have lots to learn…

I think you put your finger on it... people talking about Mathematica/Wolfram Language as a CAS are really chasing an idea of what it was 10 or 15 years ago. Maybe I'm naive but I think that we really can just "all get along" -- notebook-based programming is just one example of how ideas can incubate in closed-source projects, and end up benefiting open-source projects. I'm hoping knowledge-based computation ends up…

Mathematica is decades ahead of LightTable

Re: Launching Mathematica 10

#60

Post by reikonomusha »

judk wrote: post #57
reikonomusha wrote: post #52

Earlier quoted context omitted.

I am not proposing that Mathematica is "somewhat better". Mathematica is vastly better for many things, especially visualization. Other systems should "learn" from it, sure. It is hard to change Maxima, unfortunately, since it's entrenched in its roots from the 1960s. That's no excuse for making it difficult to use. I think Sage's Python interface is doing better and better, learning what it needs to learn from Mathe…

I am worried that Sage will get stuck in the mud as its Python code base grows, without a powerful expressive functional core like Mathematica's Lisp-ish core language. For example, see the discussion in this page about simple association lists vs what Mathematica 10 just launched

Have you noticed that in Mathematica you're not even able to make your own opaque data types? Only Wolfram has that ability.

Python is usable for actually writing software systems and algorithms. When a Mathematica code base grows over 10 lines, it becomes virtually unmaintainable in my experience.

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