5 ms·

> along comes you, acting like you have some God-given right to inspect its internals Well,it's mathematics software, so it's actually really not unreasonable.

> along comes you, acting like you have some God-given right to inspect its internals Well,it's mathematics software, so it's actually really not unreasonable. Fortunately, the rest of mathematics has moved past the seventeenth-century style of "Here's my result, the proof is secret". If Mathematica is intended to be suitable for mathematical research, then its source must be open so that the results are auditable. Other mathematics software like Sage doesn't have this problem, and is already available for the Raspberry Pi for free, obviating the need to use Mathematica.

tzs 13y ago
> If Mathematica is intended to be suitable for mathematical research, then its source must be open so that the results are auditable You don't need source to audit the results. It's a tool, just like a calculator or a table of logarithms or a table of integrals. If I use an HP calculator for a calculation, for instance, you don't audit my results by examining the source for the calculator's firmware and convincing yourself it is right and then accepting my results. No, you audit my results by doing the calculation on your Casio calculator and seeing if it comes out the same.
- lutusp 13y ago
  > You don't need source to audit the results. In fact, you do. Modern computer mathematical results require full exposure, nothing can be left to the imagination. This is true and understandable. Going back to the first important computer mathematical result (the solution to the four-color map conjecture¹ in 1976), to be taken seriously, computer math results have been required to be fully transparent. Imagine auditing a cancer cure without knowing anything about the methods or tools. Same idea. 1. http://en.wikipedia.org/wiki/Four_color_theorem http://en.wikipedia.org/wiki/Four_color_theorem
  - taliesinb 13y ago
    I actually somewhat sympathize with your view. But I think you overstate the problem: if someone discovers something with Mathematica, they can then formalize it with an open proof assistant like Coq before they publish, and modern journals in fact encourage this sort of thing. Really, it's not a zero-sum-game between open-source and commercial tools.
    - jordigh 13y ago
      "Open source" and "commercial" are not antonyms, but people working on proprietary software think they are.
      - Someone 13y ago
        Some people may think that, but I doubt that that applies here. Wolfram certainly knows that "proprietary" and "free" aren't antonyms. I do think there is a commercial side to this, too, however. This is a kind of a hook to catch future customers of the commercial package.
      - comex 13y ago
        Only if you use an overly literal interpretation of "commercial" yet don't use the literal interpretation of "open source" (since it's also possible to make source code visible to the public without using a license that would be considered "open source").
        jlgreco 13y ago
        You have just rediscovered the reason that some people talk about "free software", and some people talk about "open source". The sort of access to source code that is being expected here is really no more than the sort of access that you can get to Windows code. It really is not an unreasonable expectation.
        comex 13y ago
        No - when most people use the term "open source", they mean something along the lines of the Open Source Definition (http://opensource.org/definition http://opensource.org/definition), rather than the literal meaning; this is independent from the distinctions between open source and free software, which are mostly about philosophy rather than the set of applicable licenses (http://www.gnu.org/philosophy/free-software-for-freedom.html http://www.gnu.org/philosophy/free-software-for-freedom.html) I suppose that you, however, do not, which makes what I was trying to say irrelevant.
      - 13y ago
  - thinkpad20 13y ago
    If what one is publishing is an algorithm or formula or what-have-you, it's only required that the algorithm itself be fully exposed. It particular implementation, much less so the implementation of the particular software that implementation is written in, is only incidental. When you're giving a driving test, you don't need to know how a fuel-injection system works.
    - lutusp 13y ago
      > It particular implementation, much less so the implementation of the particular software that implementation is written in, is only incidental. Not at all. In computer programming, examples abound in which the gap between the formal algorithm and its practical embodiment led to catastrophe. One can scarcely count the number of times in which the specific manner by which a simply stated algorithm was implemented needed to be examined more closely: http://en.wikipedia.org/wiki/Ariane_5 http://en.wikipedia.org/wiki/Ariane_5 "Ariane 5's first test flight (Ariane 5 Flight 501) on 4 June 1996 failed, with the rocket self-destructing 37 seconds after launch because of a malfunction in the control software.[20] A data conversion from 64-bit floating point value to 16-bit signed integer value to be stored in a variable representing horizontal bias caused a processor trap (operand error) ..." > When you're giving a driving test, you don't need to know how a fuel-injection system works. No, but someone does. If the software is inaccessible, then no one can check it except its owners, who have an incentive not to check it thoroughly, or to conceal what they have discovered.
  - blhack 13y ago
    Out of curiosity: how deep does that need go? Low level hardware analysis? Chip manufacturing facility audits? How would you even approach this?
    - noonespecial 13y ago
      Recalling the The Pentium FDIV bug, I'd say yes. Chip level.
    - lutusp 13y ago
      > Out of curiosity: how deep does that need go? Deep enough that the meaning of the result cannot reasonably be called into question, just like in science. > How would you even approach this? As scientists. Someone once described science as ... not so much knowing as knowing that we know. Same idea. Many results that seemed certain when published, evaporated once the mathematics were examined closely. This happens even when the entire process -- data, equations, conclusions -- are all included in the publication. Given that history, imagine how much more cautious people want to be when part of the process of arriving at a critical conclusion is concealed perpetually.
      - mkingston 13y ago
        "Deep enough that the meaning of the result cannot reasonably be called into question, just like in science." I think what is really being asked is: "What level of confidence is required?". I would assume you trust the hardware and only scrutinise the software? In contrast: are results tested on a plurality of machines with intentionally, measurably different hardware and the absence of discrepancies implies that the hardware is not a factor with regard to the problem being solved? Presumedly you'd need some sort of standardised test suite to pass on your hardware to really confidently declare the hardware to not be a factor. I doubt this is the case, but like the previous poster, I'm quite curious as to the specific level of scrutiny applied here.
        lutusp 13y ago
        > I think what is really being asked is: "What level of confidence is required?". That's something that varies from field to field. In physics, a new discovery requires a five-sigma result, meaning a result that has a one in 3.5 million probability of arising by chance rather than the legitimate detection of a new particle or phenomenon. http://www.select-statistics.co.uk/blog/webmaster/one-sigma-or-five http://www.select-statistics.co.uk/blog/webmaster/one-sigma-... In psychology, by contrast, a p-value of 0.05 (i.e. 2 sigma) is accepted as statistically significant, which by itself may explain the sad state of the field. http://en.wikipedia.org/wiki/P-value http://en.wikipedia.org/wiki/P-value > I would assume you trust the hardware and only scrutinise the software? No, a scientist doesn't trust either hardware or software, but hardware can be checked and validated. In the case of Mathematica, the software cannot be checked and validated, it must be trusted. And for a scientist, trust cannot be distinguished from faith.
- throwaway2048 13y ago
  Your table of logarithms and integrals is exactly the perfect example of why you need the source to audit the results, those things were notoriously error prone.
Someone 13y ago
IMO, the existence of Sage obviates the need to use Mathematica in the same way as the existence of the Gimp obviates the need to use Photoshop. In both cases, the commercial package has many, many features that the free version barely implements or even completely lacks, and implements many of the shared features better. On top of that, the commercial software has the advantage of being market leader. That brings with it that it, in general, is easier to find a Mathematica package to do X that to find a Sage one.
- lttlrck 13y ago
  If Sage really is to Mathematica what Gimp is to Photoshop then IMO it definitely does not obviate using Mathematica. The Gimp/PS argument is well worn.

tzs 13y ago

> If Mathematica is intended to be suitable for mathematical research, then its source must be open so that the results are auditable You don't need source to audit the results. It's a tool, just like a calculator or a table of logarithms or a table of integrals. If I use an HP calculator for a calculation, for instance, you don't audit my results by examining the source for the calculator's firmware and convincing yourself it is right and then accepting my results. No, you audit my results by doing the calculation on your Casio calculator and seeing if it comes out the same.

lutusp 13y ago
> You don't need source to audit the results. In fact, you do. Modern computer mathematical results require full exposure, nothing can be left to the imagination. This is true and understandable. Going back to the first important computer mathematical result (the solution to the four-color map conjecture¹ in 1976), to be taken seriously, computer math results have been required to be fully transparent. Imagine auditing a cancer cure without knowing anything about the methods or tools. Same idea. 1. http://en.wikipedia.org/wiki/Four_color_theorem http://en.wikipedia.org/wiki/Four_color_theorem
- taliesinb 13y ago
  I actually somewhat sympathize with your view. But I think you overstate the problem: if someone discovers something with Mathematica, they can then formalize it with an open proof assistant like Coq before they publish, and modern journals in fact encourage this sort of thing. Really, it's not a zero-sum-game between open-source and commercial tools.
  - jordigh 13y ago
    "Open source" and "commercial" are not antonyms, but people working on proprietary software think they are.
    - Someone 13y ago
      Some people may think that, but I doubt that that applies here. Wolfram certainly knows that "proprietary" and "free" aren't antonyms. I do think there is a commercial side to this, too, however. This is a kind of a hook to catch future customers of the commercial package.
    - comex 13y ago
      Only if you use an overly literal interpretation of "commercial" yet don't use the literal interpretation of "open source" (since it's also possible to make source code visible to the public without using a license that would be considered "open source").
      - jlgreco 13y ago
        You have just rediscovered the reason that some people talk about "free software", and some people talk about "open source". The sort of access to source code that is being expected here is really no more than the sort of access that you can get to Windows code. It really is not an unreasonable expectation.
        comex 13y ago
        No - when most people use the term "open source", they mean something along the lines of the Open Source Definition (http://opensource.org/definition http://opensource.org/definition), rather than the literal meaning; this is independent from the distinctions between open source and free software, which are mostly about philosophy rather than the set of applicable licenses (http://www.gnu.org/philosophy/free-software-for-freedom.html http://www.gnu.org/philosophy/free-software-for-freedom.html) I suppose that you, however, do not, which makes what I was trying to say irrelevant.
    - 13y ago
- thinkpad20 13y ago
  If what one is publishing is an algorithm or formula or what-have-you, it's only required that the algorithm itself be fully exposed. It particular implementation, much less so the implementation of the particular software that implementation is written in, is only incidental. When you're giving a driving test, you don't need to know how a fuel-injection system works.
  - lutusp 13y ago
    > It particular implementation, much less so the implementation of the particular software that implementation is written in, is only incidental. Not at all. In computer programming, examples abound in which the gap between the formal algorithm and its practical embodiment led to catastrophe. One can scarcely count the number of times in which the specific manner by which a simply stated algorithm was implemented needed to be examined more closely: http://en.wikipedia.org/wiki/Ariane_5 http://en.wikipedia.org/wiki/Ariane_5 "Ariane 5's first test flight (Ariane 5 Flight 501) on 4 June 1996 failed, with the rocket self-destructing 37 seconds after launch because of a malfunction in the control software.[20] A data conversion from 64-bit floating point value to 16-bit signed integer value to be stored in a variable representing horizontal bias caused a processor trap (operand error) ..." > When you're giving a driving test, you don't need to know how a fuel-injection system works. No, but someone does. If the software is inaccessible, then no one can check it except its owners, who have an incentive not to check it thoroughly, or to conceal what they have discovered.
- blhack 13y ago
  Out of curiosity: how deep does that need go? Low level hardware analysis? Chip manufacturing facility audits? How would you even approach this?
  - noonespecial 13y ago
    Recalling the The Pentium FDIV bug, I'd say yes. Chip level.
  - lutusp 13y ago
    > Out of curiosity: how deep does that need go? Deep enough that the meaning of the result cannot reasonably be called into question, just like in science. > How would you even approach this? As scientists. Someone once described science as ... not so much knowing as knowing that we know. Same idea. Many results that seemed certain when published, evaporated once the mathematics were examined closely. This happens even when the entire process -- data, equations, conclusions -- are all included in the publication. Given that history, imagine how much more cautious people want to be when part of the process of arriving at a critical conclusion is concealed perpetually.
    - mkingston 13y ago
      "Deep enough that the meaning of the result cannot reasonably be called into question, just like in science." I think what is really being asked is: "What level of confidence is required?". I would assume you trust the hardware and only scrutinise the software? In contrast: are results tested on a plurality of machines with intentionally, measurably different hardware and the absence of discrepancies implies that the hardware is not a factor with regard to the problem being solved? Presumedly you'd need some sort of standardised test suite to pass on your hardware to really confidently declare the hardware to not be a factor. I doubt this is the case, but like the previous poster, I'm quite curious as to the specific level of scrutiny applied here.
      - lutusp 13y ago
        > I think what is really being asked is: "What level of confidence is required?". That's something that varies from field to field. In physics, a new discovery requires a five-sigma result, meaning a result that has a one in 3.5 million probability of arising by chance rather than the legitimate detection of a new particle or phenomenon. http://www.select-statistics.co.uk/blog/webmaster/one-sigma-or-five http://www.select-statistics.co.uk/blog/webmaster/one-sigma-... In psychology, by contrast, a p-value of 0.05 (i.e. 2 sigma) is accepted as statistically significant, which by itself may explain the sad state of the field. http://en.wikipedia.org/wiki/P-value http://en.wikipedia.org/wiki/P-value > I would assume you trust the hardware and only scrutinise the software? No, a scientist doesn't trust either hardware or software, but hardware can be checked and validated. In the case of Mathematica, the software cannot be checked and validated, it must be trusted. And for a scientist, trust cannot be distinguished from faith.
throwaway2048 13y ago
Your table of logarithms and integrals is exactly the perfect example of why you need the source to audit the results, those things were notoriously error prone.

Someone 13y ago

IMO, the existence of Sage obviates the need to use Mathematica in the same way as the existence of the Gimp obviates the need to use Photoshop. In both cases, the commercial package has many, many features that the free version barely implements or even completely lacks, and implements many of the shared features better. On top of that, the commercial software has the advantage of being market leader. That brings with it that it, in general, is easier to find a Mathematica package to do X that to find a Sage one.

lttlrck 13y ago
If Sage really is to Mathematica what Gimp is to Photoshop then IMO it definitely does not obviate using Mathematica. The Gimp/PS argument is well worn.