The Parable of the Mad Photocopier

(I came across this fragmentary blog post that I wrote sometime in December. It's a fine example of a failed allegory. To what, I'll let you determine for yourself. Anyway, in case anyone wants to know what dreck doesn't make it out of my computer onto the Intarweb, well, here's some. Which obviously made it out. Never mind... you get it...)

Once upon a time, there was a man named Mr. Darkena. He was more than a little nuts: his passtime was traveling to all the libraries in the world, and photocopying every book he could find. He didn't even use a normal photocopier; he use a special little instrument he'd made just for the purpose.

The instrument worked in a rather odd way. When Mr. Darkena (a.k.a. the Mad Photocopier) put a book in his instrument, it made many copies of the book -- but not complete copies. Rather, it made copies of partial sentences, chosen randomly from within the book. In order to make sure he had a copy of every sentence, the Mad Photocopier had to set his machine to make lots and lots of photocopies for each book.

The instrument had another problem: it wasn't terribly accurate. Each sentence it photocopied generally had a blotch on it that changed one or more of the letters in the sentence. (The Mad Photocopier either wasn't a great engineer, or he bought low-cost toner.)

Now, running this machine was the Mad Photocopier's hobby: he traveled around the world and fed books into his machine. And since he was independently wealthy, he did it a lot. In fact, by the time he turned 60 and was thinking about retiring, he'd actually copied every book from every library, in every language! All this was stored in a giant silo, in no particular order.

Coincidentally, the day after he turned 60, the Vogons came and demolished the Earth, to make way for a hyperspace bypass. The Mad Photocopier hitched a ride, and he brought along his private collection of book copies -- now the last and only remnant of humankind. Millions upon millions of copies of books, all in little fragmentary sentences, with lots of little toner blobs all over them.

---

Suppose you want to read one of these books in its entirety, from start to finish. Can you?

The first question is, is it likely that you have the information in the book in its entirety? If the Mad Photocopier didn't sample that particular book an awful lot, then you may be missing sentences, paragraphs, or even entire pages. But let's suppose that the Mad Photocopier really was just plain nuts, and you're pretty sure the book is in there. How do you put it together?

The basic problem is that you want to figure out which sentences go with which other sentences. Because the sentence fragments are chosen randomly, you have to check each sentence fragment against every other sentence fragment somehow to see if they overlap. This would be pretty easy, except that the sentence fragments aren't always correct copies: they may have blotches in the overlap. So you need to check for overlaps in some way that permits partial or fuzzy matches.

If you think this through, though, you may notice a few more challenges.

The first is that there are, literally, trillions or more of sentence fragments to check -- remember, millions of billions of books! That's going to take a while...

The second is that you've got to remember which fragments connect to which other fragments. That's a lot of stuff to remember...

A third thing is that any one fragment may be wrong at any one part of the sentence. If you want to make sure you have the correct sentence, you can line up all the fragments that contain that sentence and use the linup to correct for any mistakes.

A fourth issue is that books come in multiple editions and sometimes get combined into anthologies or put into Reader's Digest, so you will have to worry about sentences that look similar but actually come from (sometimes very) different texts.

A fifth issue is that some books are way more common or popular than others. For example, Huckleberry Finn has been assigned reading in junior high for 50 years or more -- you'd better bet that most libraries have a few copies of it. Same with the Encyclopedia Brittanica. But there will also be some rare books that aren't popular. So you'll have lots and lots of fragments from some books, and very few from others.

(There are lots more issues, but let's stick with these.)


Yep, I gave up here. It just wasn't working for me.

--titus


Legacy Comments

Posted by Jim Kreft on 2012-04-10 at 16:42.

This is almost exactly what metagenomic analyses are doing.  Grab
bunch of DNA (from the dirt, the ocean, guts, whatever) , fragment it,
amplify it, try to figure out what the heck is in there. Not easy.
Kinda doable, but not easy.

Posted by Titus Brown on 2012-04-11 at 09:39.

Yep, Jim -- metagenomics!

Posted by QP on 2012-04-11 at 15:27.

At least I have a interesting story to tell my parents to let them
know what I am working on.

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