Secret messages hidden inside equations | Hacker News Reader

Secret messages hidden inside equations

walkingrandomly.com

36 pointsColinWright18 comments

Here's something interesting: Tupper's self referential plot :-)

http://mathworld.wolfram.com/TuppersSelf-ReferentialFormula....

argh. i knew someone would post that.

it is not anything like as smart as it looks. the "formula" simply generates a bit-plot of whatever parameter is given. so the image is encoded in the bits of that particular value of n.

it's no more "self referential" than using some program that displays images to display a screenshot showing the program's source.

THANK YOU I've been mystified by that formula ever since I found it. I'll have to spend some time reverse engineering it tonight.

It's a funny one. It's not smart at all, but it is clever. It's one of those things that seem properly impressive up until you see how it was done.

When I met my girlfriend, I told her that her name was very mathematically pleasing. As a sign of my affection I figured out a formula that spells out her name from 1 to infinity. (Where A=1, B=2, ... Z=26)

f(x) = (13x+1)%26+((x+3)%4%3%2)*8

She said this was the most romantic thing a guy had ever done for her, but I think that says more about her ex-boyfriends than anything else. Anyway, it got me laid.

haha cool!:p these things I read on HN about girls are always genius :d

I wonder how difficult it would be to write an equation generator for any given line of text.

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.

[1] http://en.wikipedia.org/wiki/Kolmogorov_complexity

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.

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.

Given the finite number of shapes needed to create letters (a few lines, a few curves), it seems do-able.

http://www.xamuel.com/inverse-graphing-calculator.php?phrase...

Found this link to just such a tool on a related comment thread. Pretty cool.

seems like it has built-in equations for a-z and 0-9 which are translated appropriately, but very cool indeed.

wondering if some sort of encryption system is possible ...

nice to see I'm not the only one...

my first thought: ultimate captcha!

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