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In my opinion, while Mathematica is the world’s best general purpose calculator, it does more harm than good in producing reproducible and explainable science a

In my opinion, while Mathematica is the world’s best general purpose calculator, it does more harm than good in producing reproducible and explainable science and math. The topic of math software being closed source has been beat to death (by me and others), so I’ll veer into a different path. As a tiny anecdote, a colleague of mine recently published a paper in quantum computation and computed a representation of some mathematical object, specifically the exact value of an angle which modulates a particular quantum gate. In the paper was this bizarre continued fraction along with arctans and pi’s that no experimental physicist in their right mind would have derived themselves. “Where in the world did this come from?” I asked, while reviewing the paper. “Oh, it’s just what Mathematica gives,” he responded. “I don’t even fully understand it. But I do use it as proof that the angle is an irrational number and thus breaks its inclusion in some known finite group.” You might call out this otherwise accomplished physicist for what appears to be misusing the tool—taking results at face value without understanding them—but I guarantee scientists and engineers are doing this stuff daily, in more consequential places than abstract quantum physics papers. Wolfram and his team have built something amazing, and built an incredibly successful business, but I hope he uses his business acumen to find a way to contribute to the “greater good” while he continues to enjoy running a company and making money.

davesque 7y ago
It seems like the result of the paper should then be conditioned on the correctness of the chain of re-writes that Mathematica used to arrive at the continued fraction. Isn't there a way to tell Mathematica to output all re-write rules used to form an expression? I seem to recall something like this is possible.
- reikonomusha 7y ago
  This is not possible in Mathematica, especially since it’s not all based off of rewrite rules. Wolfram even boasts the 100s of of pages of C and Mathematica code used to implement even individual algorithms. With regards to conditioning the result, it should be as such, but no researcher would ever smear their result like that. Research is cutthroat.
nikofeyn 7y ago
what is the alternative? using some open source project that has no clear steward and nearly zero incentive (financial or otherwise) for tracking down esoteric bugs? mathematica is built by a company that seems to take a lot of pride in quality. they are also clearly incentivized by keeping the company afloat and thus by addressing major issues. i hear people barking incessantly about open source software in mathematics and science, but i just don't see what would actually be successful. in most people's daily jobs in engineering and even in large science projects, proprietary code is used everywhere. it's the only way to get things done in many cases. in my experience, getting a bug acknowledged, prioritized, and then fixed in open source software is like pulling teeth. what are you going to do with open source mathematics or scientific software where only like a person or two understand the bug? your story could easily have replaced mathematica with sage, and the story wouldn't be changed at all. okay fine, sage is open source. but what's more likely to be successful: (1) you are going to look through the likely millions of lines of code that makes up sage and find what's happening, or (2) you call up wolfram and ask what's going on since you have support for a product that you paid for? how is open source software supposedly inherently better for math and science research?
- murukesh_s 7y ago
  Why can't companies provide paid support for open source software? I believe lot of open source products work on that model, including Linux. The bad thing with proprietary software is not many students and researchers from developing countries cannot afford it as the pricing is always based on developed economies scale. But if it's open source, every one can use it and more affluent researchers can get the paid support so they don't need to hunt through thousands of lines of code or fix bug themselves.
- reikonomusha 7y ago
  Open source software first and foremost means reproducibility. With open software, anybody on earth with the right equipment can easily and trivially reproduce a result at no additional cost or hindering contractual terms. Reproducibility is paramount, and sits at the very core of science. Results that cannot be reconstructed hardly count as new knowledge. (As a funny story, even Wolfram-the-company can’t run SMP, the predecessor of Mathematica. Why? They can’t decrypt it or unlock it, and can’t figure out how to work around it.) Every major tech company on earth uses open source software at the heart of their business. So we know something sustainable is possible. Open source, one-size-fits-all math software is a tough nut to crack. I think most people could get most of their algebra and calculus done with existing open packages like wxMaxima or Sage. Specialized computations, such as those in group theory, already have open source implementations that exceed any closed competitor. As for the construction of a competing CAS, some organization would have to employ a team. That costs money, and so far no company (that I know!) sees it as either a worthwhile investment or charitable cause. If folks do know of a company, I’d love to know.

davesque 7y ago

It seems like the result of the paper should then be conditioned on the correctness of the chain of re-writes that Mathematica used to arrive at the continued fraction. Isn't there a way to tell Mathematica to output all re-write rules used to form an expression? I seem to recall something like this is possible.

reikonomusha 7y ago
This is not possible in Mathematica, especially since it’s not all based off of rewrite rules. Wolfram even boasts the 100s of of pages of C and Mathematica code used to implement even individual algorithms. With regards to conditioning the result, it should be as such, but no researcher would ever smear their result like that. Research is cutthroat.

nikofeyn 7y ago

what is the alternative? using some open source project that has no clear steward and nearly zero incentive (financial or otherwise) for tracking down esoteric bugs? mathematica is built by a company that seems to take a lot of pride in quality. they are also clearly incentivized by keeping the company afloat and thus by addressing major issues. i hear people barking incessantly about open source software in mathematics and science, but i just don't see what would actually be successful. in most people's daily jobs in engineering and even in large science projects, proprietary code is used everywhere. it's the only way to get things done in many cases. in my experience, getting a bug acknowledged, prioritized, and then fixed in open source software is like pulling teeth. what are you going to do with open source mathematics or scientific software where only like a person or two understand the bug? your story could easily have replaced mathematica with sage, and the story wouldn't be changed at all. okay fine, sage is open source. but what's more likely to be successful: (1) you are going to look through the likely millions of lines of code that makes up sage and find what's happening, or (2) you call up wolfram and ask what's going on since you have support for a product that you paid for? how is open source software supposedly inherently better for math and science research?

murukesh_s 7y ago
Why can't companies provide paid support for open source software? I believe lot of open source products work on that model, including Linux. The bad thing with proprietary software is not many students and researchers from developing countries cannot afford it as the pricing is always based on developed economies scale. But if it's open source, every one can use it and more affluent researchers can get the paid support so they don't need to hunt through thousands of lines of code or fix bug themselves.
reikonomusha 7y ago
Open source software first and foremost means reproducibility. With open software, anybody on earth with the right equipment can easily and trivially reproduce a result at no additional cost or hindering contractual terms. Reproducibility is paramount, and sits at the very core of science. Results that cannot be reconstructed hardly count as new knowledge. (As a funny story, even Wolfram-the-company can’t run SMP, the predecessor of Mathematica. Why? They can’t decrypt it or unlock it, and can’t figure out how to work around it.) Every major tech company on earth uses open source software at the heart of their business. So we know something sustainable is possible. Open source, one-size-fits-all math software is a tough nut to crack. I think most people could get most of their algebra and calculus done with existing open packages like wxMaxima or Sage. Specialized computations, such as those in group theory, already have open source implementations that exceed any closed competitor. As for the construction of a competing CAS, some organization would have to employ a team. That costs money, and so far no company (that I know!) sees it as either a worthwhile investment or charitable cause. If folks do know of a company, I’d love to know.