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## The correlation length of notation

Well, I’m buried up to my head in work trying to finish up a paper. I have been doing this for a while. A project that should have ended with a 20 page paper ballooned on me, and now I am writing a paper on the edge of 50 pages.

Which brings me to the title of the post. Fifty pages is a long paper. There is an additional problem in writing such a long paper. This is that by the time I’m writing the end, I’ve somewhat forgotten what I’ve written before. Mre specifically, not so much the content, but the way in which it was written. And even more specifically, what precise notation was used.

For example, just to give you a feel,  was it ${\mathbb C}$ or ${\bf C}$, or was it ${\cal C}$? Or was it $A,B$, rather than $W,Z$.

I’m writing stream of consciousness, so it can  be fixed later when I’m combing through the paper. Moreover, the longer the paper, the more symbols and fonts one needs, and they can  start overlapping. This means that notation degenerates as I’m writing a paper. It’s not consistent for more than I can work on in one day. About five pages that is. So that is what I will call the correlation length of notation: the amount of pages that one writes before the notation mutates and starts getting disordered.

So, on a 50 page paper, there are ten correlation lengths of notation, so the end looks nothing like the beginning in terms of notation. This gets worse with more authors. And don’t even get me started on writing books. To fix this, one has to ‘cool down the system’ so that it becomes ordered (I’m making an analogy with ferromagnetism here). This requires time and many passes. So a paper of length $m$ seems to take of order of $m^2$ time to write it down. Maybe that critical exponent is different.

There is always a plan B: give a guide to notation changes so that the work is piled on the reader. What do you think of this strategy? This seems to be the way for books, because there are many conventions that overlap: they come from different developments by different authors. Fortunately our brains seem to be able to read contextually, and $E$ can be energy, and electric field and $e$ can be the electric charge and the Euler constant all of them in the same equation, when it becomes obvious how to interpret it. Isn’t it?