Re:Secret messages hidden inside equations
by pavel_lishin on Sunday June 19, 2011 @01:53PM
(#2671324)
I wonder how difficult it would be to write an equation generator for any given line of text.
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That's trivial. For example:
- pick any function P(x,y) whose graph looks like a pixel (close to one near the origin, drops off to zero quickly)
- to get A function with N pixels set in its graph, sum N translated versions of P.
Keeping the length of the equation low, however, will be a challenge.
It seems like what's wanted is something close to: the shortest equation that produces an output interpretable as the input text ("interpretable" at least by captcha standards, perhaps). To make that more formal, would require some model of the range of shapes that are interpretable as Latin letters by a typical reader.
> the shortest equation
That in itself is computationally impossible [1] but I guess "reasonably short" will do just fine.
I disagree; as I indicated, it is easy to find one equation. Once you have one, enumerate all possible equations up to the length of the equation you found, and check them. Assuming a finite alphabet, that set is finite, so if checking whether a function's plot resembles the target text is computable, finding the set of shortest solutions is.
If checking a candidate is not computable, Kolmogorov complexity would rear its head, but I do not think the problem of finding the shorter equation is well-defined in that case.
Re:Secret messages hidden inside equations
by wlievens on Wednesday June 22, 2011 @03:03AM
(#2682085)
That only holds if all your formula are guaranteed to halt. I guess that's true if they're limited to arithmetic functions, without looping or recursion of any kind.
Also do note that what you're saying is only easy in theory. In practice it could take years to find your shorter formula.
http://www.xamuel.com/inverse-graphing-calculator.php?phrase...
Found this link to just such a tool on a related comment thread. Pretty cool.
Re:Secret messages hidden inside equations
by afterstep13 on Monday June 20, 2011 @02:24AM
(#2673109)
seems like it has built-in equations for a-z and 0-9 which are translated appropriately, but very cool indeed.