Many people have offered help and encouragement over the years. There have been far too many people to mention and far too many years to remember, but I am grateful to everyone. I would particularly like to thank the following.

Linda Anderson

To my wife, Linda, thank you.

Horace Barlow

Horace encouraged me to continue research on perspexes, especially because I was the only person willing to do it.

Vasil Corbas

Vasil patiently endured my questions on algebra and was not too upset when I computed the permutation set of order ten thousand using lazy evaluation. And not a boiled transistor in sight, eh, Vasil?

Steve Leach (Knight)

Steve engaged me in many interesting conversations about computer languages. On one memorable occasion, whilst attempting to test my program to destruction, but only just failing, he asked me where the number 3 was in my proof that the parametric perspex was correct. Minutes later it became the arbitrary dimensional parametric perspex and the code became another notch more reliable. Thanks, Steve.

Steve Maybank

Steve is a very good critic. He told me about the Pythagorean triples and, mostly inadvertently, sold me a very good book on computability.

John Ogden

John and I spent many happy coffee breaks discussing ethics and theology. It is good to consider these things, especially if one runs, even the remote risk, that one's research might, one millennium, produce a new form of super intelligent life.

Don't worry John. If we eat fish and chips and they eat silicon and electricity, everything will work out just fine.

If we arrange that they have feelings akin to ours, and free will, there are reasonable prospects of a fulfilling co-operation between humans and robots. But that is a more risky research goal, because it depends on future scientists, both human and robotic, behaving responsibly.

O.K. John. Now we can pray!

Aaron Sloman

Aaron and I engaged in a massive email correspondence about the programming language Pop-11 and cognitive aspects of computer languages. He encouraged me to continue research on the relationship between modal logic and vision, even when it seemed hopeless. It was hopeless, Aaron. It wasn't until I gave up hope that I succeeded, by relating vision to the Turing machine.

Geoff Sullivan

Geoff and I worked together for many years on human and computer vision. We had that rare, scientific gift for near total disagreement on everything - but we wrote some interesting programs.

Peter Sweby

Peter Sweby had the courage to back up my development of transrational arithmetic, even when it seemed absurd. I hope you like the perfectly orthogonal eigenvectors, Peter.

Anthony Worrall

Anthony and I spent many lunch times discussing the affine transformations and trigonometry. Anthony is one of the few people willing to consider a projection into dimension minus one.

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