6 ms·

Have you used Mathematica yet? I linked further downthread but I think you should consider this argument (ignoring the stuff about violent video games): https:

by Jach 6y ago

Have you used Mathematica yet? I linked further downthread but I think you should consider this argument (ignoring the stuff about violent video games): https://theodoregray.com/BrainRot/ https://theodoregray.com/BrainRot/

chongli 6y ago
No, I haven't used Mathematica. It doesn't hold much use for me (yet) because it's not allowed on any of my exams. Being able to diagonalize a matrix by hand may not be a useful real world skill but the ability to do it on an exam demonstrates that you understand the process. On the other hand, typing the matrix into Mathematica and calling the diagonalize function demonstrates very little other than that you know how to command the magic box to give you the answer. Mathematics is a tower of abstractions. In the course of my education, I am learning how all of the layers fit together. Skipping all that and teaching people how to use Mathematica is not teaching mathematics, it's teaching dependence on a tool (and a proprietary one at that). It's like teaching people how to use Microsoft Word instead of how to write their own word processor. I'm very critical of the way technology has infiltrated the modern classroom. I think we're in danger of raising a generation of Eloi [1]. [1] https://en.wikipedia.org/wiki/Eloi https://en.wikipedia.org/wiki/Eloi
- Jach 6y ago
  Surely you're not in mathematics just to pass exams and absorb/explore at whatever rate teachers and classes set? You should really give such tools a try. If proprietary ones aren't your cup of tea, play with Octave (and its Octave Forge package collection), Maxima, and R, and if you want throw in Julia, SymPy, Axiom, or Metamath too. See what they offer and what people have done with them. Or what if you programmed your own diagonalize function and used it thereafter (knowing over time you'd forget how to do it by hand)? Or would you insist on going through something like nand2tetris before writing in a high level language like, say, C? I have more questions but they're mostly rhetorical at this point. Re my previous link, are you so smart that you can learn all that has been made known so far as a neat tower floor by floor (despite it not being discovered/invented that way), and still have room for anything new? Are you sure you haven't skipped anything? Are you sure there's a singular tower? So you know how to diagonalize a matrix, either by hand or by using a magic box, do you know why you'd want to diagonalize a matrix? As a final external recommendation, check out chapter 9, "Forget It!", in Asimov's book On Numbers: http://www.arvindguptatoys.com/arvindgupta/asimov-on-numbers.pdf http://www.arvindguptatoys.com/arvindgupta/asimov-on-numbers... (e-page 75) If you haven't studied and passed an exam on compound addition (and subtraction, multiplication, division) how can you live with yourself?
  - chongli 6y ago
    Right now I'm taking courses in computational mathematics and computer statistics. The former is taught in Matlab and the latter in R. I know why you'd diagonalize matrices. I've taken two courses in linear algebra and I'm interested in studying computer linear algebra. I've been watching some of Gilbert Strang's lectures on linear algebra methods in data analytics. I know that computer methods for approximating a singular value decomposition (which I've also learned to do by hand) can provide enormous speedups over manual methods. I have no problem with using these tools, I just don't think they should be given to children in lieu of a traditional mathematics education. Society exists because we pass on knowledge from one generation to the next. This means teaching young people how problems were solved, not just handing them the solution. Do we want a world where everyone is dependent on technology but nobody knows how it works? That sounds like a post-apocalyptic scenario to me. Fun and interesting to explore in Caves of Qud or Numenera. Not a great way to organize a stable society.
    - Jach 6y ago
      > Society exists because we pass on knowledge from one generation to the next. Yes, but not all the knowledge, for then there would be no time for anything new. > This means teaching young people how problems were solved, not just handing them the solution. No, because this robs them of the time to build on that solution and do something new. This extends to all domains -- and all the way down to our most primitive survival needs. Most people have no idea how to build a home, they instead are typically 'handed' one (usually in exchange for money). Few can farm, hunt, and process food to the degree needed to ensure their own survival, but we eat the outputs from those who do, who are anyway also skipping steps by not having to learn and perform a solution that was maybe required hundreds of years ago when technology was less powerful. And taking advantage of all this knowledge we don't have to work for, then we can work for other, new things. This is not only fine but necessary for society to advance. > Do we want a world where everyone is dependent on technology but nobody knows how it works? We already live in such a world. Or rather, there exist critical things that no single mind fully comprehends. So again, if you at least agree that not everything needs to be transmitted, then where are you going to draw the line? Do you think kids should learn to calculate cube roots by hand and prove that with a no-calculator exam? Why? How about logarithms by hand? (Though even before computers, pretty much no one did that either, instead they let a small number of people work really hard to produce many tables up to a few significant figures so they could use those results for bigger things.) Don't you think the insistence on learning (and testing to demonstrate something was learned) so much "circus math" (math done for show, because there's vanishingly little other reason to do it by hand in current year) might have something to do with how so few students ever even get a taste of real linear algebra, statistics, calculus, and let alone more advanced topics? I consider it a failure mostly of the education system that I didn't learn about rotation matrices until my first semester of college. They could have been introduced in 9th grade or perhaps earlier. But that would require cutting a lot of other stuff. (I'm still rather happy my 9th grade teacher taught us row reduction, made us do a few by hand and one big 3x4, but thereafter said "using rref() is fine". Meanwhile a Canadian friend reported to me that his "linear algebra" class in university consisted almost solely of doing row reductions of various dimensions by hand, all semester. Useless. But my same 9th grade teacher got very insulted when I wrote back some suggestions for topics he could introduce after taking my linear algebra class, even something as simple as the concept of the codomain, oh well.)

by Jach 6y ago

chongli 6y ago

No, I haven't used Mathematica. It doesn't hold much use for me (yet) because it's not allowed on any of my exams. Being able to diagonalize a matrix by hand may not be a useful real world skill but the ability to do it on an exam demonstrates that you understand the process. On the other hand, typing the matrix into Mathematica and calling the diagonalize function demonstrates very little other than that you know how to command the magic box to give you the answer. Mathematics is a tower of abstractions. In the course of my education, I am learning how all of the layers fit together. Skipping all that and teaching people how to use Mathematica is not teaching mathematics, it's teaching dependence on a tool (and a proprietary one at that). It's like teaching people how to use Microsoft Word instead of how to write their own word processor. I'm very critical of the way technology has infiltrated the modern classroom. I think we're in danger of raising a generation of Eloi [1]. [1] https://en.wikipedia.org/wiki/Eloi https://en.wikipedia.org/wiki/Eloi

Jach 6y ago
Surely you're not in mathematics just to pass exams and absorb/explore at whatever rate teachers and classes set? You should really give such tools a try. If proprietary ones aren't your cup of tea, play with Octave (and its Octave Forge package collection), Maxima, and R, and if you want throw in Julia, SymPy, Axiom, or Metamath too. See what they offer and what people have done with them. Or what if you programmed your own diagonalize function and used it thereafter (knowing over time you'd forget how to do it by hand)? Or would you insist on going through something like nand2tetris before writing in a high level language like, say, C? I have more questions but they're mostly rhetorical at this point. Re my previous link, are you so smart that you can learn all that has been made known so far as a neat tower floor by floor (despite it not being discovered/invented that way), and still have room for anything new? Are you sure you haven't skipped anything? Are you sure there's a singular tower? So you know how to diagonalize a matrix, either by hand or by using a magic box, do you know why you'd want to diagonalize a matrix? As a final external recommendation, check out chapter 9, "Forget It!", in Asimov's book On Numbers: http://www.arvindguptatoys.com/arvindgupta/asimov-on-numbers.pdf http://www.arvindguptatoys.com/arvindgupta/asimov-on-numbers... (e-page 75) If you haven't studied and passed an exam on compound addition (and subtraction, multiplication, division) how can you live with yourself?
- chongli 6y ago
  Right now I'm taking courses in computational mathematics and computer statistics. The former is taught in Matlab and the latter in R. I know why you'd diagonalize matrices. I've taken two courses in linear algebra and I'm interested in studying computer linear algebra. I've been watching some of Gilbert Strang's lectures on linear algebra methods in data analytics. I know that computer methods for approximating a singular value decomposition (which I've also learned to do by hand) can provide enormous speedups over manual methods. I have no problem with using these tools, I just don't think they should be given to children in lieu of a traditional mathematics education. Society exists because we pass on knowledge from one generation to the next. This means teaching young people how problems were solved, not just handing them the solution. Do we want a world where everyone is dependent on technology but nobody knows how it works? That sounds like a post-apocalyptic scenario to me. Fun and interesting to explore in Caves of Qud or Numenera. Not a great way to organize a stable society.
  - Jach 6y ago
    > Society exists because we pass on knowledge from one generation to the next. Yes, but not all the knowledge, for then there would be no time for anything new. > This means teaching young people how problems were solved, not just handing them the solution. No, because this robs them of the time to build on that solution and do something new. This extends to all domains -- and all the way down to our most primitive survival needs. Most people have no idea how to build a home, they instead are typically 'handed' one (usually in exchange for money). Few can farm, hunt, and process food to the degree needed to ensure their own survival, but we eat the outputs from those who do, who are anyway also skipping steps by not having to learn and perform a solution that was maybe required hundreds of years ago when technology was less powerful. And taking advantage of all this knowledge we don't have to work for, then we can work for other, new things. This is not only fine but necessary for society to advance. > Do we want a world where everyone is dependent on technology but nobody knows how it works? We already live in such a world. Or rather, there exist critical things that no single mind fully comprehends. So again, if you at least agree that not everything needs to be transmitted, then where are you going to draw the line? Do you think kids should learn to calculate cube roots by hand and prove that with a no-calculator exam? Why? How about logarithms by hand? (Though even before computers, pretty much no one did that either, instead they let a small number of people work really hard to produce many tables up to a few significant figures so they could use those results for bigger things.) Don't you think the insistence on learning (and testing to demonstrate something was learned) so much "circus math" (math done for show, because there's vanishingly little other reason to do it by hand in current year) might have something to do with how so few students ever even get a taste of real linear algebra, statistics, calculus, and let alone more advanced topics? I consider it a failure mostly of the education system that I didn't learn about rotation matrices until my first semester of college. They could have been introduced in 9th grade or perhaps earlier. But that would require cutting a lot of other stuff. (I'm still rather happy my 9th grade teacher taught us row reduction, made us do a few by hand and one big 3x4, but thereafter said "using rref() is fine". Meanwhile a Canadian friend reported to me that his "linear algebra" class in university consisted almost solely of doing row reductions of various dimensions by hand, all semester. Useless. But my same 9th grade teacher got very insulted when I wrote back some suggestions for topics he could introduce after taking my linear algebra class, even something as simple as the concept of the codomain, oh well.)