I was thinking through my post last week about the Infinite Library and about all the stimulating comments from David Levine and others. I thought: let’s see if we cannot break the problem down a little. Instead of an Infinite library, which would be impossible, let’s accept a hybrid, but incredibly useful, library I choose to call the Answer Library.
Imagine a very short passage of text, say 100 words long only. In this short passage of text, the answer to life, the universe, and everything is embedded (the Answer Text). It might start off something like: “Love life, disdain money, embrace your fellow man, e=mc2, Lord Lucan stole Shergar…” etc. In this dense and beautifully worded text, mankind could finally all agree on something. The Answer Library is just the library of all conceivable 100 word long English texts, containing somewhere within it the Answer Text. How tantalising, that as one scanned the library and opened a random book, one could be looking at the answer to all our problems, the final say on all the big questions.
The Answer Library could be generated by computers. They could be asked to generate all random combinations of words that made text of roughly 100 words length. How many texts would that be? It is hard to tell, but one estimate might be that there are about 5,000 words used in the average vocabulary, so let’s say it is any random configuration of legitimate English words in a dictionary of only 5,000 words. That would be 100 to the power of 5000: a stupendous amount of texts!
Right, we need to winnow this amount down to a manageable amount. We can program the computers with an English library, advanced grammatical reasoning, and other forms of AI to force them to reject texts that are plainly illogical and not reasonable candidates for the real text (e.g. a text with just the word “aubergine” printed 100 times in a row). And they can group all texts that are closely related by choosing just one representative text to represent them all.
Let’s imagine (for this is a game) that this process cuts down the amount of texts by a factor of 100 to the power of 4900 say. That’s a gigantic leap of reasoning and doesn’t stand up to any scrutiny at all, but please bear with me. Even then, we are left with a library with 100 to the power of 100, or 10 to the power of 200, texts. The number of atoms in the universe is only 10 to the power of 80 or thereabouts!
I am reluctantly forced to conclude that any attempt to randomly produce any intelligible text of even such a short length as 100 words is doomed to failure. That’s even before we address the trickly questions of whether such a text could possibly exist in the first place, or whether we’d recognise it if we read it, or whether there wouldn’t be different texts for different circumstances.
My other conclusion is that there might be a simpler way to produce such a text: get the greatest minds of mankind into a room for a week say, and ask them to produce the text through the application of intelligence, reasoning, insight, and poetry. We could ask a physicist, a moral philosopher, an historian, a poet to write the text, and a couple of others.
Oh, wait. They’d never agree on anything. The physicist would want to concentrate on quantum statistics and the Grand Unified Theory, while the moral philosopher would want at least 90 of the 100 words to express the true foundations of moral conduct. The poet would want to squeeze in a particularly apt metaphor or two, comparing man’s quest for the answer to the soul of Confucious chatting to the soul of Buddha. Oh heck…let’s think again about this…