

Scrubbing Calculator (by Bret Victor, author of Kill Math) - tokenadult
http://worrydream.com/ScrubbingCalculator/

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abecedarius
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.

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mdonahoe
I want this for the iPad

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

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

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Sniffnoy
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!

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laughinghan
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>

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).

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Sniffnoy
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.

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laughinghan
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.

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Birejji
So it's guess and check on speed?

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laughinghan
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?

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sgentle
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>

