Paul Taylor's Web Pages - Technical Notes

www. Paul Taylor. EU
These Web pages are primarily about my research in the Foundations of Mathematics and Computation.
Please contact me by email at        pt 09 @ Paul Taylor. EU       I live and work in London.
I use LaTeX, DVI, PostScript (PS), booklets, PDF and HTML for these Web pages.
See below for why you see both www. Paul Taylor. EU and www.monad.me.uk in the Web addresses of these pages.
The photograph on the front page was cut down from one taken by Andrej Bauer at the Third Formal Topology Workshop in Padova on 9 May 2007. Behind me is the last slide of my talk. My T-shirt depicts African penguins near Cape Town.

1  Is my email address pt07, pt08 or pt09 @ PaulTaylor.EU?

Can you spot the pattern? This is just long-term spam control. As yet, the only address that I have blocked is binary-student @ PaulTaylor.EU, but I don't suppose that it occurred to you to use that anyway.
If you need to put my address in a database, please use your name (or that of the database) not mine before the @, for example bookshop @ PaulTaylor.EU.
Since most people just reply to the previous message, they do not even notice that I change my address periodically.

2  Software that is not used here

I have no MicroSoft software on my computers, and cannot read or generate Word documents. Therefore, please do not send such documents to me - use one of the non-proprietory or at least standard formats below instead.
Please send email to me in plain text. Here are instructions on how to turn off HTML and Rich Text in numerous mail programs.
Please avoid sending things to me as email attachments, particularly if they are confidential, as I archive multiple copies of my email on several computers.
Put your file on the Web instead, and send me the URL (Web address). So long as you don't link to it, only I will know about it, since the URL serves as a password. When I have read it, I will tell you, then you can delete it. This is how I give private or working documents to my colleagues - using the drafts directory on this Web site.

3  HTML (ordinary Web pages) for viewing

All of the HTML pages on this site are generated from LATEX (see below). This maintains compatibility with my mathematical work and allows me to generate parallel versions of pages in different formats.
The translation is done using either TTH or Hevea. These programs have the advantage of producing HTML with very few of the additional GIF files that their competitors use. I am gradually shifting from TTH to Hevea, since it is open source and it can be extended with LATEX-like packages or approximations to them.
They represent mathematical symbols using Unicode, which now seems to be recognised by most browsers. However, this is an exceedingly large code, only parts of which are configured on computers in the English-speaking world. I strongly disapprove of browser-specific websites, but my reference is FireFox version 3 (please note that Firefox 2 has quite a lot of mathematical symbols missing). If you find that symbols are missing or wrong in Firefox 3, please tell me.
Nevertheless. the HTML versions of my mathematical papers are still only intended for screen viewing. Please use the alternative PDF or PostScript versions to print them.
The HTML pages contain CSS commands for typographical style, which are interpreted on the client side, ie by your browser.
They may also contain embedded PHP commands. These are interpreted on the server side, ie my Web site, in order to provide a dynamic listing of the available file formats for each paper.
I plan to rebuild the HTML version of my book in due course.

4  LATEX source files and typesetting

I use LATEX to compose all of my documents, including these Web pages.
LATEX is nowadays the standard tool for typesetting documents (in particular books and journal papers) in the mathematical sciences. In practice, by "LATEX" people mean not just a single program but many contributions by a wide user community. At the root of this is the typesetting program TEX (the X is a gutteral sound like German "ich" and Scots "loch") that was written by Donald Knuth (in the 1980s, though it remains the most robust programming environment that I have ever used). You can obtain these things from the CTAN Website.
Besides the many programs and macros for LATEX that come from elsewhere, I use my own macros for category theory ("commutative") diagrams, proof trees and boxes, the right-justified end-of-proof mark and other things. If you have seen little squares that are placed reliably on the right hand side at the end of mathematical proofs in LATEX documents, they were probably produced using my code, albeit copied without acknowledgement.
LATEX documents are formatted or translated by programs into various other formats that you will find on these Web pages.
I have analysed the log files for my site from September 2007 to November 2009. For just those files that I offer in multiple formats, counting each ip address just once for each file even if it downloaded it repeatedly and excluding known robots, I found that the distribution of accesses was:
PDF: 74%       DVI: 13%       PS: 8%       Booklet: 5%

5  DVI for previewing

DVI is the principal output format of TEX.
You can view DVI files on your computer screen using the programs
DVI is a very simple and compact code, the bulk of which is the ASCII content of the document. Future digital archeologists would therefore have no difficulty in deciphering it when the existing browers or previewers have died from bit rot. Knuth designed TEX based on a lot of research into traditional typesetting methods, in particular Monotype, as a result of which it does certain things (such as breaking paragraphs into lines) far better than competing software.
But this also means that DVI's model is composition simply places characters from fonts at certain orthogonal coordinates on the page. It doesn't even provide the option of rotating them, which is an issue when drawing commutative diagrams. These shortcomings are overcome by embedding fragments of other languages as "\special" commands in DVI. Usually, this is PostScript.

6  PostScript for printing

PostScript, developed by Adobe, is nowadays the standard format in which documents are sent to printers. In other words, you can usually send it directly to your printer as it is.
DVI is usually converted into PostScript using the program dvips written by Tomas Rokicki.
You can also view PostScript files on your computer screen using the open source program Ghostview as well as Adobe's products.
PostScript has full graphics capabilities, and is indeed a Turing complete programming language, which occasionally causes printers to crash or hang like computers do.
Since PostScript files are rather larger than DVI, they are often compressed using programs such as gzip.

7  Booklets for printing on A4 (not American) paper

These are PostScript files that are indended to be sent to printers with duplex (two sided) facilities, using A4 paper. They are usually compressed.
The advantage of the international A paper size system is that folding an A4 sheet produces an A5 sheet, which has the same vertical/horizontal size ratio (of root 2:1). If you fold a sheet in American Letter size, you get something with a completely different ratio from the original.
Booklets are obtained by rearranging the pages of a PostScript file, using the psbook program by Angus Duggan, with a Perl wrapper written by Mark Dawson. It would be possible to produce booklets for American paper too, but I invite someone who actually uses this paper to work out the LATEX and Perl configurations.
Whereas the other formats are generated using (nominally) 10pt size type, the booklets are set at 12pt before being reduced, so the effective size of the type is about 9pt.

8  PDF for viewing and printing

PDF was also developed by Adobe and now seems to be the most popular document format. (Why do bus companies feel they need to use it instead of HTML for their timetables??)
There are numerous viewers for it.
I generate PDF using the program PDFTEX, which is a modified version of the original TEX program.

9  File compression

Some of the files (usually the PostScript ones) are compressed using gzip. After downloading, you will need to uncompress them using gunzip or a similar tool.

10  Hosting these Web pages

From February 2009, my website is hosted by PrimeXeon, which is a very small company in Cambridge that provides intelligent personal support at very low cost. I found them from their star reviews at FreeIndex.
There was a period of downtime 6-9 June when their data centre at VAServ had been hacked, bringing down over 100,000 websites in Britain. (Unfortunately, this led to the suicide in India of the author of the vulnerable software.) When this happenned, Ben Harris and Dan Smith at PrimeXeon did a magnificent job to bring their servers back up amazingly quickly.
However, for various reasons, both domain names www.PaulTaylor.EU and www.monad.me.uk are registered with another ISP called Daily.
Previously Freedom2Surf hosted my site and provided my ADSL (Broadband). In 2004 they too provided personal service, but they were bought by Pipex and then by Tiscali. Things went down hill, especially with their mail system and service.
See ISP Review for Broadband (ADSL) services.

This is www.PaulTaylor.EU/technote.html and it was derived from technote.tex which was last modified on 6 December 2009.