My primary reason for writing the pages on this site is to help me to clarify and organise my thoughts: if I ever have a surfeit of leisure, I may do some thorough editing. I explain, below, the implications of that – which, please, read before suggesting changes. The interested reader is welcome, however, to what I have written.
Some folk might prefer the result of feeding this site to The Eater of Meaning; or you can read it in Cumbrian thanks to The Cumbrianator. Well, they amused me anyway ;^>
I have been quietly pouring various bits of my mind out into web pages. One day, I might get some of what I've written into a form in which I'd be happy to present them to the world as worthwhile discussions of the relevant topics, of value to any interested reader wishing to learn from them. Such well-written discourses, however, depend on the author's own clarity of understanding of the matter and how to express it. The first purpose of my pouring out my mind into web pages (not infrequently in the dead of night, writing an idea down to stop it rattling around my head and keeping me awake) is bluntly to employ the greater regularity of a computer's memory, when compared to my own, to help me keep track of the assorted pieces I do understand. By this road (greatly assisted by hyperlinks) I hope to clarify my own thoughts to a point where I may hope to write something whose value to others may approach its value to me.
Notwithstanding that my pages, as they currently stand, cannot pretend to be good teaching materials, I have no objection to other folk reading what I say and think on various matters. If you can learn anything by them, so much the better. If you can see some opportunity, that I've missed, for improving the clarity, I should be delighted to know it – it will probably teach me something.
Much of what I have written, especially under the banner of mathematics, is expressed both in terms of unorthodox definitions and in a plaintext notation which, though (defined and used with care, and) straightforward, will be unfamiliar to most – not wishing to resort to rather messy mechanisms involving highly complex XML, images or scripting, I do not have, at my disposal, the full expressive power of all the sundry squiggles that one can write on paper or a black-board, so I have devised (with some care) a straightforward idiom for expressing much that is normally expressed with squiggles.
This choice is motivated to varying degrees by: kindness to those reading the matter in text-only form; curiosity to know how well I can design a notation; the relative ease with which I can write and manipulate plaintext, as opposed to complex XML, images and scripts; the observation that truth remains true even if expressed in unfamiliar ways; and the plain fact that new perspectives on familiar truths can lead us both to a better understanding of the familiar and to the discovery of further truths. The result may fairly be accused of ediosyncrasy. I hope, in the fullness of time, folk will explore the neglected domain of notation-design well enough to improve on my notation: for now, it's the best at my disposal.
If you find errors in my pages, be not surprised. However, pause a while to consider whether the error is mine or in your own understanding, which the above-mentioned unorthodoxy may have confused. In either case, or if in doubt, do not be afraid to bring it to my attention: though you may be mistaken in the error you suppose you have found, the fact that the discourse lead you into that confusion is a matter I will wish to redress, if I can discover practical means to do so, for the sake of later readers. If you find something that even I can see to be an error, you will have enabled me to improve what I have written, and spared later readers from being mislead into my error.
If you have written up any of the material covered in these pages, or
matters closely related to them, as web pages, I shall be delighted to hear from
you – if only for the sake of reading another's exposition of the subject.
I shall not promise to insert links to all such sites: but I shall doubtless,
unless asked not to, use some such links – if only under the banner of