4 ms·

I may be misunderstanding this, but isn't this only good for monotonic (whether increasing or decreasing) functions?

rwolf 15y ago
I wonder. Specifically, would you be able to "scrub" every number in the "equation" 1 beans / 1 buckets = 1 beans per bucket?
laughinghan 15y ago
Uh, what about this doesn't work for any solvable equation?
- Sniffnoy 15y ago
  How are you going to search the space of possible solutions? If it's monotonic, you can do binary search. If it's some crazy thing you don't know... well, you can't try all possible numbers!
  - laughinghan 15y ago
    Have you ever heard of a computer algebra system (CAS)? It's the generic name for software that performs symbolic mathematics, anything from the algebra that 8th graders are taught to differential equation solvers used in modern physics research. http://en.wikipedia.org/wiki/Computer_Algebra_System http://en.wikipedia.org/wiki/Computer_Algebra_System The specifics don't matter, the bottom line is, anything that Mathematica can solve, this can be useful for, simply by solving the equation for the chosen dependent variable (the red number) every time you adjust the value of an independent variable (any of the black numbers).
    - Sniffnoy 15y ago
      Firstly, if that's how this works -- rather than by allowing you to guess and check until things match up -- then I am very much misunderstanding it. Secondly, there's no way this thing is going to be as powerful as a CAS. Hell, from the description I seriously doubt it'll do so much as solve a system of linear equations for you, just let you explore the space until you find a solution.
      - laughinghan 15y ago
        One of us is misunderstanding something. What I'm imagining is, you adjust the value by dragging it, and then the CAS solves for the red value. There's no requirement for monotonicity or anything, if the CAS can solve for a unique red value to satisfy the equation, you're good.
abduhl 15y ago
It seems like the calculator is true to its name in that it only evaluates the given input function. Whether or not a function is monotonic should have no bearing on the calculator because it isn't actually solving anything, only evaluating. The solution method takes place in the user's mind and so the user would need to recognize that a given equality may be untrue (that is, the problem is unsolvable) but this would manifest in the user being unable to drive two equations to a single answer. For example, if the user had sin(x)+1=2 and x^2=4 (or, sin(x)+1=x^2-4 equivalently) then the lines would be set up as sin(3)+1 = eval 3^2 = eval and then the user would link the two 3s and proceed to "scrub" until a common answer for x was found. While this problem is unsolvable for x, each expression is valid and able to be evaluated. As somebody said below, this scrubbing amounts to nothing more than brute force guess and check of equations. No additional knowledge is gained through this type of approach and I would never recommend this for anything but the most trivial of problems and even then a standard approach would probably be faster. EDIT: Looking at the more advanced "locking" functionality, I think you are probably correct in that this functionality may be constrained to monotonic functions only.

rwolf 15y ago

I wonder. Specifically, would you be able to "scrub" every number in the "equation" 1 beans / 1 buckets = 1 beans per bucket?

laughinghan 15y ago

Uh, what about this doesn't work for any solvable equation?

Sniffnoy 15y ago
How are you going to search the space of possible solutions? If it's monotonic, you can do binary search. If it's some crazy thing you don't know... well, you can't try all possible numbers!
- laughinghan 15y ago
  Have you ever heard of a computer algebra system (CAS)? It's the generic name for software that performs symbolic mathematics, anything from the algebra that 8th graders are taught to differential equation solvers used in modern physics research. http://en.wikipedia.org/wiki/Computer_Algebra_System http://en.wikipedia.org/wiki/Computer_Algebra_System The specifics don't matter, the bottom line is, anything that Mathematica can solve, this can be useful for, simply by solving the equation for the chosen dependent variable (the red number) every time you adjust the value of an independent variable (any of the black numbers).
  - Sniffnoy 15y ago
    Firstly, if that's how this works -- rather than by allowing you to guess and check until things match up -- then I am very much misunderstanding it. Secondly, there's no way this thing is going to be as powerful as a CAS. Hell, from the description I seriously doubt it'll do so much as solve a system of linear equations for you, just let you explore the space until you find a solution.
    - laughinghan 15y ago
      One of us is misunderstanding something. What I'm imagining is, you adjust the value by dragging it, and then the CAS solves for the red value. There's no requirement for monotonicity or anything, if the CAS can solve for a unique red value to satisfy the equation, you're good.

abduhl 15y ago

It seems like the calculator is true to its name in that it only evaluates the given input function. Whether or not a function is monotonic should have no bearing on the calculator because it isn't actually solving anything, only evaluating. The solution method takes place in the user's mind and so the user would need to recognize that a given equality may be untrue (that is, the problem is unsolvable) but this would manifest in the user being unable to drive two equations to a single answer. For example, if the user had sin(x)+1=2 and x^2=4 (or, sin(x)+1=x^2-4 equivalently) then the lines would be set up as sin(3)+1 = eval 3^2 = eval and then the user would link the two 3s and proceed to "scrub" until a common answer for x was found. While this problem is unsolvable for x, each expression is valid and able to be evaluated. As somebody said below, this scrubbing amounts to nothing more than brute force guess and check of equations. No additional knowledge is gained through this type of approach and I would never recommend this for anything but the most trivial of problems and even then a standard approach would probably be faster. EDIT: Looking at the more advanced "locking" functionality, I think you are probably correct in that this functionality may be constrained to monotonic functions only.