[odonnellryan]

Even with such a function, aren't there limits to how much sensible data can be stored? Something something Claude Shannon something something. I forget.

Otherwise you'd have infinite storage capacity, on any medium, which is very obviously impossible.

Why infinite? Well, there are infinite numbers. If your algorithm was just "keep applying f(i,j) by an increasing integer to get the next page of the data" then yeah you've actually just discovered infinite storage.

This is literally a compression problem, isn't it? :)

Edit: http://mathforum.org/library/drmath/view/65726.html

Something I came across a long time ago.

[_m8fo]

Indeed. However, the hard limit here is the number of "discernible" and distinct characters that can fit on the page. The whole second thing is really just a way of permuting the existing data. So I'd say there would be infinite data if the amount of characters that could fit on the page were also infinite. Applying the function really was just a way to represent the mechanism that gave you each combination. The whole seconds from midnight thing may have been needlessly convoluted.

Though, for that portion of my comment, it would've been easier to simply say the information is approximately equal to the amount of characters that fit on a page and all combinations of its arrangement.

Of course, if the actual "processing" of the information lies outside of the paper, I feel like that's kind of cheating. What do you think?

[odonnellryan]

I don't think it'd be cheating, just like using programs to compress files isn't cheating.

However, there's two ways to look at this.

1) designing "some kind of data" specifically for this problem.

2) a general-purpose solution, where you could could put any data on the paper.

You could hit some obscenely-high number for 1), using some tricks or whatever.

But 2 probably has some sensible solution on the order of MB.

Example: if our function is as simple as "raise each number in the sequence to the next" we'd get some obscenely-large number, and we can put that function right on the page.

But, finding an obscenely large number representing some kind of data that actually means something, then coming up with a rule like that to reduce it?

Anyway, my argument would be: no, having an external compression algorithm isn't cheating, but formulating your data to fit the problem is.

Anyway, there exists no general-purpose compression algorithm, so compression would largely be out of #2, unless we're taking a subset of the problem: "how many English words can fit..." which of course we can come up with a good compression algorithm for (I think!) which would make it work.