Paul Taylor

Independent research in categorical logic, constructive topology and a bit of history. Refuse to use American IT giants.

webpage: www.paultaylor.eu
location: Birmingham, UK

Last Notes

2026-08-28 16:03:50 UTC

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The "Lemma" wasn't Zorn's. Even in his paper it was an Axiom. The proof of the Lemma was by Kuratowski in 1922: see www.paultaylor.eu/trans/ which now finally has the whole of K's paper,

2026-05-26 10:04:39 UTC

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England's canals were also abandoned, particularly after they were frozen in the hard winter of 1962-3.
But they since been revived by the Canal and River Trust https://canalrivertrust.org.uk so that now there are more boats on the canals than there were in the industrial revolution.
The CRT also does far more for Birmingham (the centre of the network) than Birmingham City Council does.
(I hope that will change now that we have kicked out the arrogant incompetent Labour administration.)

2026-05-06 12:46:19 UTC

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ἑξακόσιχωρον --- or should it be ἑξακόσιτοπον (hexakositope)? --- except that I never got the hang of accents in Ancient or Modern Greek.
But more importantly, it's amazing that someone can have detailed geometric intuition in four dimension and come up with such results! I struggle in 3D.

2026-05-06 10:54:37 UTC

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If it's "Platonic", let's give it the glorious Greek name that it deserves: ἑξακόσιεδρον (hexacosihedron)!

2026-04-12 19:40:42 UTC

I have been using email for 40 years. It used to work.
As an (independent) academic researcher, I need to contact new people, primarily in universities, to ask questions.
I refuse to use Google, Microsoft or the other American IT giants.
But they are increasingly preventing refuseniks from sending email at all.
I know what RFC, DNS, MX, SPF and DMARC mean. My email goes through small British companies with intelligent, friendly and helpful staff.
mxtoolbox.com says that I must have DMARC to send email to M$. So I set it up. I now get a dozen copies of the same report from G or M$ for each email that I send out.
They show that my email gets to G and M$ sites, but then it is marked as spam.
The stupid senior management of numerous universities has surrendered their staff email to M$.
Web searches and AIs preach about spam. I don't send spam - I want to contact my colleagues.
Rumour has it that previously unknown senders are treated with suspicion and their emails are sent to spam. In other words, it is impossible to **initiate** communication with someone.
Let's be blunt about this. They are a mafia that is enforcing an **oligopoly**. It's got nothing to do with reducing spam --- I have no doubt that they let through emails from "trusted partners", ie companies that bribe them enough to send their spam.
The result of this is that it will only be possible to send emails by paying M$ to do it, and then it will only be allowed to express "approved" opinions.
What can we do about this?
At the very least, those of you with senior positions in universities can tell your management to revert to competent standards-based email systems hosted on Linux systems.