I get the idea, but I wish the blogger had explicitly defined the "'Babylonian’ approach".
I think he's saying that it's a mistake to take one theory, with one notation, and imagine that just because it is correct and covers all the cases, it is the one "truth". It sounds like solipsism: wanting a predicable and self-contained world that is safe and controlled.
But there are a few strange things about different notations that mean the same thing:<p>- notations have usability. Each one makes it easier or harder to do certain things. One notation might be good at one task, and poor at another; whereas another notation vice versa, even though both are equally "true". Notations also make it harder or easier to think/reason about certain things, in the way that language tends to shape our thoughts (not determine them, Dr. Whorf).<p>- notations are similar or different to related concepts and notations, making some connections easier to see, and some harder.<p>- notations generalize differently, having different suggestions for the "obvious" next step.<p>A particular notation is then just a shadow of the truth - a one dimensional projection, capturing only a plane of the unseen reality. It seems that mathematicians and scientists routinely invent new notations for new domains (not necessarily good ones). The advantages of different notations is what Alan Kay was talking about when he said that "point of view is worth 80 IQ points". Notation is a form of point of view.<p><i>It was based on a few things from the past like how smart you had to be in Roman times to multiply two numbers together; only geniuses did it. We haven't gotten any smarter, we've just changed our representation system. We think better generally by inventing better representations; that's something that we as computer scientists recognize as one of the main things that we try to do</i> <a href="http://ecotopia.com/webpress/futures.htm" rel="nofollow">http://ecotopia.com/webpress/futures.htm</a>