
Secret messages hidden inside equations - ColinWright
http://www.walkingrandomly.com/?p=19
======
xtacy
Here's something interesting: Tupper's self referential plot :-)

[http://mathworld.wolfram.com/TuppersSelf-
ReferentialFormula....](http://mathworld.wolfram.com/TuppersSelf-
ReferentialFormula.html)

~~~
andrewcooke
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.

~~~
szany
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.

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pittsburgh
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.

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

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

~~~
Someone
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.

~~~
_delirium
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.

~~~
wlievens
> 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>

~~~
Someone
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.

~~~
wlievens
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.

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

~~~
bugsbunnyak
my first thought: ultimate captcha!

