There's more to Life than Zeros and Ones

I recently heard from Göran on the Inclusive Church forum that the AND in (for example) "men AND women" is a kind of quantum disjunction. And what the blazes would one of those be? I quote:

I've always understood this AND to be a Hebrew "al kol", that is a manner of including both extremes (if be) and everything in between.

Well, that's what a "quantum disjunction" is. It's a way of modelling the phrase "A and/or B and everything in between them." If there is such a connective in Hebrew, this is very interesting, and if anyone can comment to confirm or deny this, that would be great ...

You get a similar usage in English with continuous quantities, e.g., if someone says "5 or 10 miles" they don't mean that 6 or 9 miles is not allowed, it's all part of the range between 5 and 10. This is deeply relevant to whether you can force things into a Boolean 0 vs 1 (us vs them, good vs evil) classification, or whether the universe has naturally in-between values that just can't be carved up into 0 and 1.

One obviously successful example of techonology breaking this 0 and 1 mould is the development of the search engine, from a computer program that divides a document collection into matching and non-matching collections, to a more flexible ranking program. This was forced by the amount of content (e.g., on the Web) becoming too rich to give a user all the keyword-matching documents and saying "these are what you want", because it would still take forever to wade through them. So for most decent search engines nowadays, you don't have relevant or non-relevant documents, you have varying
degrees of relevance.

The reason this discussion came about is the fact that the Anglican Church may be in the process of splitting up, honest, and though I'll certainly grant you that there are more relevant things you could read, believe it or not, an article about logical operators and the values they can take is not completely irrelevant. There are many in the Church who believe firmly that the world is divided into believers and unbelievers, people who are forgiven in God's eyes and people who aren't. God knows exactly who belongs to which category, and will judge accordingly. You see similar approaches to all sorts of things, a recent and obvious example being George Bush's version of "you're either with us or you're with the terrorists". Some choice! Other triumphs of over-simplistic classification include dividing the land area of the world into mutually exclusive "nation states" or "religions". When this mental straitjacket comes up against the patchwork of history, disasters result - the past century is full of simplistic attempts to draw boundaries on maps, and sooner or later the pot boils over.

Many of us in the Church believe that this is the wrong way to think about Jesus and what he wanted to bring into the world.

Binary classification is only one form of logic, and while it is useful for some things, it is way too simplistic for much of real life. The founder of binary logic in its modern form was George Boole, who based his argument on the fact that zero and one are the only solutions of the quadratic equation x²=x. You might argue that this is hardly a very good reason for dividing humanity into 'saved' and 'damned'. I would tend to agree.

Nonetheless, Boole's reasoning was very good, for many purposes. It enabled him to develop modern set theory, and a robust algebraic version of logic so that 100 years later, it became possible to program his system into machines, and the modern computer was invented. Those of us who program computers still talk about Boolean values every time we have a variable that is restricted to taking the values 0 and 1. It's good for many binary algorithms, though as seen above, you need more values nowadays just to make a decent search engine, because the range of information out there is too rich just to be partitioned into 1 for relevant and 0 for non-relevant.

To come in a full if brief circle, this more flexible "relevance ranking logic" relies on precisely the kind of "A or B or things in between" concept that Göran alludes to with the al kol conjunction. And it turns out that such a logic is not only a way of building a search engine, it is one of the key differences between classical physics and quantum mechanics. There is a lot about this in my book, Geometry and Meaning, the important chapter being this one.

So, for a combination of scientific, linguistic and theological reasons, I think that we should really explore the richer ways there are of approaching the questions "What is logic?" and "How should people and things be classified?" And if you look at our natural language, it's clear that we already do this in the vernacular. And search engines are pretty good at this, even if they're just computer programs. Humans, unfortunately, may have some catching up to do.