Life Art and Mysticism

May 21st, 2010 • Uncategorized • No comments

Only he who recognizes that he has nothing, that he cannot possess anything, that absolute certainty is unattainable, who completely resigns himself and sacrifices all, who gives everything, who does not know anything, who abandons and neglacts everything, he will receive all; to him the world of freedom opens, the world of painless contemplation and of – nothing.

— L. E. J. Brouwer 1905

A Clockwise 45° embedding of Categories in Lattices

April 28th, 2010 • Uncategorized • No comments

It is generally believed that Categories constitute a unified foundation for modern constructive mathematics. However a simple observation is enough to refute this claim. It is possible to take a book on category theory and rotate the pages through 45° clockwise to transform commuting diagrams into lattices diagrams. Surprisingly, despite the generality of categories the converse is not possible. No degree of rotation of lattice diagrams results in commuting diagrams to appear.

The embedding, by rotation of paper, clearly refutes contemporary claims in the foundations of mathematics. There is however the concern that after rotation the theorems become more difficult to read, and when deciphered may not necessarily apply to lattices. This concern is overcome by the pragmatic observation that readers only look at the pictures scratch their beards and encode further theorems.

Embryonic Implants take Central Role in Proof Theory

March 16th, 2010 • Uncategorized • No comments

The department of Sémantique, Preuve et Implantation, at the University of Paris intend to emphasise further their role in Implantation. The Head of the SPI Group Prof Hardin says, “Ces Anglo Saxons consistently overlook la menstrual cycle pour dealing avec le explicit substituations.”

Accoding to wikipedia: Implantation is an event that occurs early in pregnancy in which the embryo adheres to the wall of uterus. At this stage of prenatal development, the embryo is a blastocyst. It is by this adhesion that the fetus receives the oxygen and the nutrients from the mother to be able to grow.

French is known to not always directly translate into English.

Idealised Conversations set to take Central Stage in Film

March 15th, 2010 • Uncategorized • No comments

The all time Best Selling Novel Surreal Numbers, by Donald Knuth, has been approved for the big screen. Director Woody Allen says, “People are still missing the point with my parodies of society. Donald Knuth has however provided me with the gripping story line to engage with the nincompoops who pay to watch my films.” The adventures in the theory of constructive logic are thought never to have taken a central role in a major film. On second thoughts, adventures in the theory of constructive logic have probably never even taken a side role in a small very bad film before. Bob, Mel Gibson, is rumoured to breach the axiom of choice and suffer for us all, so that we may stick to categories with finite support. In doing so he fills a crack in the tight protocol of Alice, Angelina Jolie.

The Fundamental Theorem of Categories disposes Programmers.

March 15th, 2010 • Uncategorized • No comments

The constructive proof of the Theorem, “The category of Profunctors over Bi-categories is a Bi-category”, provides an automatic means of generating compilers. Thus traditional tools such as C-programmers can be disposed of.

The Four Ages of Man.

March 15th, 2010 • Uncategorized • No comments

What follows Birth. What leads to Why. Why leads to How. How leads to When. When follows Death. Thus there is a bifunctor contravarient in the first argument which abstracts the category of Life homomorphisms from a category of a Foetus to a Corpse. Thus the interaction of What, Why, How and When functors provide operational semantics for Life.

Hopf Algebras occur by Accident

March 8th, 2010 • Uncategorized • No comments

You want a bibliography?

Y.-J. Ringard. MUSTARD WATCHES

March 5th, 2010 • illogic • No comments

An integrated approach to time and food

Abstract

L’article introduit le concept de montre à moutarde, qui généralise à la fois ceux de montre et de pot à moutarde. La propriété principale des montres à moutarde est qu’elles peuvent distribuer la moutarde selon les besoins (théorème 1) tout en conservant une potentialité d’affichage d’une précision de 30 secondes (théorème 2). Mais la supérioritéré elle des montres à moutarde sur les montres classiques est expriméepar notre théorème 3 : une montre à moutarde ne contenant pas demoutarde est au moins aussi précise qu’une montre ordinaire.

Process algebras crumble

September 15th, 2009 • review • No comments

Samson Abramsky states in “What are the fundamental structures of concurrency? We still don’t know!” what is obvious about what appears to be a fundamental subject. As Robin Milner points out, it is appears to be blindingly obvious that this is a world where concurrent processes in information systems are now unavoidable in our daily lives. The reality is that the languages and tools built to tackel this subject, which were in the 1980 buzzing with promise, have failed systematically, on every avenue, to take any realistic steps.

But from what appears lost there are messages to harvest. Concurrency models break from the world of Bertrand Russell, as demonstrated by the inadequacy of denotational models; a view is shared by the direction of abstract algebra. Concurrency models do not directly tackle concrete problems; there remains a gulf between the model and the implementation which is not systematically transcended. Such transcendence appears equally in logic, where often barely a cut elimination theorem can be achieved. Direct lifting into a field associated with higher levels of abstraction — categories of bigraphs, relative pushouts … — have added definitions but not insight.

The path is not staring us in our face. The path of elegance does not repeat the same questions over and over again. Not even for a handful of decades. Let us select a stronger branch but do not grapple it.