Domain theory, a subject that arose as a response to natural concerns in the semantics of computation, studies ordered sets which possess an unusual amount of mathematical structure. This book explores its connection with quantum information science and the concept that relates them: disorder.
This is not a literary work. It can be argued that its subject, domain theory and quantum information science, does not even really exist, which makes the scope of this alleged 'work' irrelevant. BUT, it does have a purpose and to some extent, it can also be said to have a method. I leave the determination of both of those largely to you, the reader. Except to say, I am hoping to convince the uninitiated to take a look. A look at what?
Twenty years ago, I failed to satisfactorily prove a claim that I still believe: that there is substantial domain theoretic structure in quantum mechanics and that we can learn a lot from it. One day it will be proven to the point that people will be comfortable dismissing it as a 'well-known' idea that many (possibly including themselves) had long suspected but simply never bothered to write down. They may even call it "obvious!" I will not bore you with a brief history lesson on why it is not obvious, except to say that we have never been interested in the difficulty of proving the claim only in establishing its validity. This book then documents various attempts on my part to do just that.
After failing english in seventh grade, mathematics in eighth grade and being permanently expelled from school in the ninth grade, Keye Martin took some exams and enrolled at the University of New Orleans, eventually earning a degree in computer science while simultaneously leading a company that used to charge inflated prices for undisclosed services to some of the most corrupt organizations on the planet. He then used that money to live well above his means while earning a doctorate in mathematics from Tulane University. After that, he spent four years as a research fellow at Oxford University, pioneering the application of certain semantic techniques from computer science to information theory, quantum mechanics and general relativity. He is currently employed as a research mathematician at the Naval Research Laboratory in Washington DC, where he founded the section on informatic phenomena: a group of mathematicians, physicists and computer scientists interested in using natural systems to process information. He spends his spare time writing, proving theorems and playing music.
Table of Contents: Preface / Author biography / 1. Essentials / 2. Majorization / 3. The implicative order / 4. The Bayesian and spectral orders / 5. Open questions