Scrubbing Calculator (by Bret Victor, author of Kill Math)

http://worrydream.com/ScrubbingCalculator/

by tokenadult • 15 years ago

58 15 15 years ago

Sniffnoy3• 15 years ago

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

rwolf• 15 years ago

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

laughinghan4• 15 years ago

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

Sniffnoy3• 15 years 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!

abduhl• 15 years 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.

Birejji• 15 years ago

So it's guess and check on speed?

laughinghan4• 15 years ago

So here's something I've noticed about my own learning process: I can only learn by example. No matter how complete, precise and accurate an abstract description is, I don't understand something until I see examples. For example, when I try to understand some complicated code, I pick some representative example inputs and work out the corresponding output.

Am I alone in this?

enjalot• 15 years ago

I'm with you.

I'm very inspired by this scrubbing calculator because I think it is the perfect tool to introduce algebra. The abstract concept of a variable is not something that comes easy to everyone. This tool allows you to visualize the idea of a variable and play with it.

I think this would allow the introduction of algebra at an even earlier age for some, and make the transition much smoother for the rest.

gruseom• 15 years ago

No matter how complete, precise and accurate an abstract description is, I don't understand something until I see examples.

I believe this is why spreadsheets are so popular: you're never working with abstraction alone. It's always incarnated in an example. That seems to fit how most people's minds work. By contrast, tools that require users to specify their abstractions first and only then instantiate them with data have a much more limited appeal. It can be hard for programmers to appreciate this because we're on such familiar terms with abstraction.

sgentle• 15 years ago

That's exactly why I'm a programmer, and why I've always had trouble with math.

I won't say I only learn by example, but I need something tangible. Something I can pick up, squash, twist and break until I can feel what it's made of. Even if that manipulation occurs only in my head, and even if I've had to synthesise that tangibility from someone else's explanation.

For me, that's the way things really are, and anything else is an intermediate representation.

I never did learn the mathematical definition of bezier curves properly; I just looked at the animations on Wikipedia. This post kinda inspired me, so here's a scrubbing bezier curve: http://samgentle.com/playgrounds/bezier

abecedarius• 15 years ago

Bears some resemblance to the Thimbleby calculator:

http://www.cs.swan.ac.uk/calculators/how.html

Both have you write numeric expressions and then manipulate them while the calculator solves the constraints 'live'; how they developed that general idea differs.

mdonahoe• 15 years ago

I want this for the iPad

Scrubbing Calculator (by Bret Victor, author of Kill Math)

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