3 ms·

What's preventing from having the brains...?

by nelsonic 8y ago

maxxxxx 8y ago
Lack of intelligence? I simply can’t do math on a higher level.
- onemoresoop 8y ago
  To understand higher maths intelligence is not enough. It is necessary, but not sufficient. To understand mathematics, someone needs discipline and hard work. Years of preparation, years of study of topics you don’t know for what they can be useful. But, as far as you go deeper in maths, more you understand the meaning of the first steps and theirs contents. It is a BS opinion that one which says that maths is something got by putting bricks over bricks. By the contrary, it consists of an eternal returning to the same points, ever seeing them from a different perspective, with deeper understanding. Try to read again a book you had difficulties when in basic school. You will find it easy.
  - maxxxxx 8y ago
    I just remember that when we had three dimensional differential equations I kind of hit a wall. Until then I had a pretty good intuitive understanding of things but this requires a lot of work. Other people had no problems with this. On the other hand I don’t have to work much on understanding computers and software architecture so it seems this is a better area for me.
    - Jtsummers 8y ago
      Differential Equations is often called Difficult Equations for a reason. You may have some more success in other areas of advanced math, particularly abstract algebra, graph theory, and related fields. You'll find more connections between that and what we do as developers than between programming and differential equations. And not just in the sorts of problems we solve (routing, etc.), but also in mapping between the structure of programs/architectures and concepts in algebra and graph theory.
      - maxxxxx 8y ago
        True. When we did finite elements linear algebra seemed more accessible. But I still don't think I could be cutting edge in any area of math.
        Jtsummers 8y ago
        Fair. I have no anticipation of being at the cutting edge in math either. One thing that I have found, though, is that as I've explored (particularly in programming and CS) more areas, that reviewing the math I had trouble with in college it all seemed "easy", or at least easier. An advantage of age/experience is the ability to draw from our numerous experiences and produce better (for us, personally) analogies with the material. Another crucial thing for me (post-college) is the absence of grading or immediate external or internal pressure. If I have trouble with a math or CS concept, I just set it down. It has no impact on remaining employed or future job prospects (well, mostly, some geometry and trig refreshers were good when doing some geographic stuffs; learning some languages were critical to a job, but that's not theory). Additionally, I removed the pressure from myself. If I don't get something, I don't (as I did in college, which led to other problems) see it as a personal defect or deficiency. It's just a fact, I simply don't understand it. I re-read the same material over and over across a several year period (Knuth's Concrete Mathematics) before certain sections of it became accessible to me. I desired to understand it, so I returned to it. But despite the desire, I didn't feel any external or internal pressure to understand it at that precise moment. When understanding came, it was a good feeling. But when it didn't, it was just a thing.
        maxxxxx 8y ago
        Same here. I really wish I could go back to school and relearn some stuff I ignored back then. Back then I had to learn a lot of stuff just because but now I understand how they can be useful. same with history. In school it was boring but now I listen to historical audiobooks all the time and love it.
      - Koshkin 8y ago
        > Difficult Equations Well, they are indeed difficult if you want to develop a new method of solving an equation or if you have discovered a new type of equation (which does not happen a lot these days). Otherwise, solving a differential equation seems to be not much more than simply a matter of recognizing a pattern and choosing the corresponding method.
  - Jtsummers 8y ago
    I largely agree with this sentiment: > It is a BS opinion that one which says that maths is something got by putting bricks over bricks. By the contrary, it consists of an eternal returning to the same points, ever seeing them from a different perspective, with deeper understanding. But want to point out the same concept within programming. As a programmer most of us learned to get things done, but often poorly, when we started. Instead of an array, your early programs likely used A1, A2, A3, etc. Then you learn arrays and suddenly what seemed like a bear to maintain was made trivial, and the utility of for loops was made obvious. Dozens, hundreds, maybe even thousands of lines of code could be eliminated with simple patterns from these early programs. See things like The Evolution of a Haskell Programmer [0] for an entertaining take on this idea. When you start viewing mathematics in a similar light it can really help improve your level of math comprehension rapidly. Sure, you could do sums before you learned calculus. But it was tedious to sum up N values of a discrete function (without a computer, of course). Then you learn calculus and find out how to integrate that function and then the summation becomes as trivial as the integration (easy in some cases, hard in others). Instead of treating each new math concept as totally new or a level above the thing before, examine how prior problems can be solved in light of this new concept. And, like programming, there will be a hundred ways to solve a particular problem (different data representations, different techniques). Learn to see the same problem from multiple perspectives and see how that shifts the difficulty of solving it. [0] https://www.willamette.edu/~fruehr/haskell/evolution.html https://www.willamette.edu/~fruehr/haskell/evolution.html

What's preventing from having the brains...?

maxxxxx 8y ago

Lack of intelligence? I simply can’t do math on a higher level.

onemoresoop 8y ago
To understand higher maths intelligence is not enough. It is necessary, but not sufficient. To understand mathematics, someone needs discipline and hard work. Years of preparation, years of study of topics you don’t know for what they can be useful. But, as far as you go deeper in maths, more you understand the meaning of the first steps and theirs contents. It is a BS opinion that one which says that maths is something got by putting bricks over bricks. By the contrary, it consists of an eternal returning to the same points, ever seeing them from a different perspective, with deeper understanding. Try to read again a book you had difficulties when in basic school. You will find it easy.
- maxxxxx 8y ago
  I just remember that when we had three dimensional differential equations I kind of hit a wall. Until then I had a pretty good intuitive understanding of things but this requires a lot of work. Other people had no problems with this. On the other hand I don’t have to work much on understanding computers and software architecture so it seems this is a better area for me.
  - Jtsummers 8y ago
    Differential Equations is often called Difficult Equations for a reason. You may have some more success in other areas of advanced math, particularly abstract algebra, graph theory, and related fields. You'll find more connections between that and what we do as developers than between programming and differential equations. And not just in the sorts of problems we solve (routing, etc.), but also in mapping between the structure of programs/architectures and concepts in algebra and graph theory.
    - maxxxxx 8y ago
      True. When we did finite elements linear algebra seemed more accessible. But I still don't think I could be cutting edge in any area of math.
      - Jtsummers 8y ago
        Fair. I have no anticipation of being at the cutting edge in math either. One thing that I have found, though, is that as I've explored (particularly in programming and CS) more areas, that reviewing the math I had trouble with in college it all seemed "easy", or at least easier. An advantage of age/experience is the ability to draw from our numerous experiences and produce better (for us, personally) analogies with the material. Another crucial thing for me (post-college) is the absence of grading or immediate external or internal pressure. If I have trouble with a math or CS concept, I just set it down. It has no impact on remaining employed or future job prospects (well, mostly, some geometry and trig refreshers were good when doing some geographic stuffs; learning some languages were critical to a job, but that's not theory). Additionally, I removed the pressure from myself. If I don't get something, I don't (as I did in college, which led to other problems) see it as a personal defect or deficiency. It's just a fact, I simply don't understand it. I re-read the same material over and over across a several year period (Knuth's Concrete Mathematics) before certain sections of it became accessible to me. I desired to understand it, so I returned to it. But despite the desire, I didn't feel any external or internal pressure to understand it at that precise moment. When understanding came, it was a good feeling. But when it didn't, it was just a thing.
        maxxxxx 8y ago
        Same here. I really wish I could go back to school and relearn some stuff I ignored back then. Back then I had to learn a lot of stuff just because but now I understand how they can be useful. same with history. In school it was boring but now I listen to historical audiobooks all the time and love it.
    - Koshkin 8y ago
      > Difficult Equations Well, they are indeed difficult if you want to develop a new method of solving an equation or if you have discovered a new type of equation (which does not happen a lot these days). Otherwise, solving a differential equation seems to be not much more than simply a matter of recognizing a pattern and choosing the corresponding method.
- Jtsummers 8y ago
  I largely agree with this sentiment: > It is a BS opinion that one which says that maths is something got by putting bricks over bricks. By the contrary, it consists of an eternal returning to the same points, ever seeing them from a different perspective, with deeper understanding. But want to point out the same concept within programming. As a programmer most of us learned to get things done, but often poorly, when we started. Instead of an array, your early programs likely used A1, A2, A3, etc. Then you learn arrays and suddenly what seemed like a bear to maintain was made trivial, and the utility of for loops was made obvious. Dozens, hundreds, maybe even thousands of lines of code could be eliminated with simple patterns from these early programs. See things like The Evolution of a Haskell Programmer [0] for an entertaining take on this idea. When you start viewing mathematics in a similar light it can really help improve your level of math comprehension rapidly. Sure, you could do sums before you learned calculus. But it was tedious to sum up N values of a discrete function (without a computer, of course). Then you learn calculus and find out how to integrate that function and then the summation becomes as trivial as the integration (easy in some cases, hard in others). Instead of treating each new math concept as totally new or a level above the thing before, examine how prior problems can be solved in light of this new concept. And, like programming, there will be a hundred ways to solve a particular problem (different data representations, different techniques). Learn to see the same problem from multiple perspectives and see how that shifts the difficulty of solving it. [0] https://www.willamette.edu/~fruehr/haskell/evolution.html https://www.willamette.edu/~fruehr/haskell/evolution.html