Over thousands of years remarkable people have been exchanging something of unestimated value, their ideas…
Manifesto
All natural phenomena can be explained as computations and seen as information exchange. We take that claim not as a mere metaphor but as an accurate description of our reality. What program is the universe running on? Science is the discipline for finding some of the shortcuts through compression for comprehension. Computer science is therefore the science of hacking the universe. Algorithmic information theory is the tool to test our claims that the universe produces and behaves in fact, in all or most regards, as a digital computer.
Motivation
This is a place where I can follow up with records for myself and share some thoughts with others about my experiences attending conferences, studying simple systems, and my fields on computability, algorithmic complexity and randomness, from my thoughts on symbols and languages, to computational linguistics. During the past year I have met -and exchanged some ideas with brilliant minds (a partial list of them can be found in the right column wiith links on my webpage including Stephen Wolfram with whom I work very closely as I am part of his Science Group at Wolfram Research in Boston, MA.
The space of all possibles
That is a place in which I will write about spaces of possibles, from axioms to algorithms, from theories to rules and systems such as tag-systems, substitution systems and in general rewriting systems, cellular automata, finite automata, Turing machines, register machines, lambda-calculus, graphs and networks, and as a consequence about related topics like functional programming, model theory and reverse mathematics.
Randomness and algorithmic complexity
Hermeneutics and early anticipations of scientific ideas
I used to make some hermeneutical research on ancient texts of Geometry from the Euclid’s axiomatization to Hilbert’s formal approach, through Saccheri’s unawareness discovery of non-Euclidian geometries. My main interest (not in my current field of research) is the emergency of the notions of space from plane geometry to generalizations to higher dimensions, specially involving the early study of the so-called platonic solids or regular polyhedra. These objects were the focus of my social service, from some stones found 3000 B.C. in Scotland and now in the Ashmolean museum in Oxford, UK, to the topological notion of dimension, and actually I wrote an interesting text as a result of two math courses on the topic and my 6-month social service spent at the National University of Mexico’s Museum of Science (Universum).I am also interested in ancient texts from Francisco Suarez and Robert Grosseteste upon the ancient study of the Infinity and ancient authors conceiving the human as a machine, like Julien Offray de la Mettrie. An early anticipation of automata research from von Kempelen.
Mathematical formalism and cognitive aspects
On the other hand, I am also interested on the process of mathematical proofs and the elements, in the cognitive sense, that play a role in math proofs. In the case of Fermat’s last theorem, the statement of the proposition can be made in pure arithmetical terms, however the proof relies in much stronger mathematical theories. So this is an example in which a proof uses alien concepts to the theory in which the original statement was made, so a purely arithmetic question required, in this case for Wiles’s proof, resources beyond number theory. Other examples are proofs in mathematical analysis in which it is necessary to make use of complex analysis even when the mathematical statement to proof has nothing to do with complex analysis. Many proofs rely on such uses of meta-theories. So questions about necessity and indispensability in this particular sense call my attention. Also, visual proofs are an interesting field in the cognitive and mathematical sense. The question about when a diagram is necessary to show, clarify or even proof a mathematical statement. When a diagram becomes necessary for the proof, explanatory or ornamental (this latter as it should be from an ortodoxal logical point of view). When visual representations induce mistakes when other logical possibilities are unawarely hidden. When and how such a visual representation can be translated into a formal language and be completely abstracted from the objects in faor of a purely algebraic manipulation between symbols. We can see such attempt and achievement in Hilbert’s work on re-founding geometry completely avoiding any geometrical object and diagram unlike Euclid’s style first approach in his Elements, in which diagrams play sometimes a fundamental role in the geometrical statements and their proofs, including the most important about triangle congruency for instance. So the question can be taken to the limit asking if such abstractions, without making reference to any concrete object or any representation, are possible even when completely abstract objects are used in mental representations when the lecture of those symbols happens. Becoming mental diagram-type representations of the abstract objects in question. In other words, the question on whether we are really able to think in triagles without realizing what a triangle really is. Formalization approaches always seem to come after some intuitively -diagrammaticaly- approach. The topic is of course deeply related to visual thinking.Some sources:- Nelsen, R. B. Proofs without Words, The Mathematical Association of America.- Marcus Giaquinto, Visual Thinking in Mathematics, Oxford University Press.
Minds and Machines
Regarding the theory of minds and machines I am interested in the explanation of neurophysiological concepts in terms of formal computation. The merge of disciplines in favor of interdisciplinary research for explaining cognitive phenomena. For example the so-called mirror neurons model explained in terms of universality, and more precisely concerning the possible computational power of the human mind.But this blog’s approach will not be traditional at all even when it will examine and discuss the relations between the computational and biological explanations of the mind. Topics include whether a machine could think, the arguments against AI based in meaning, whether thinking could be symbol generated, how complex or simple a system should be to reach intelligence. How intelligence could be related with the concept of computational universality, the Turing Test, mental representation and abstraction, the reduction of the mind to the brain to the computer, mirror neurons and neural networks, mental imagery, and consciousness.
Anima Ex Machina
The name makes reference to two interesting concepts, from one side the concept of a ghost in the machine, from where movies like Ghost in the Shell -that inspired The Matrix- took their ideas. The Ghost in the Machine was originaly a good book written by Arthur Koestler. The idea can be seen from two different points of view, either that machines can generate a ghost (which is used as a kind of synonym of soul) or that the soul is in fact nothing else but the product of the identity, the “I” of a machine (human or not). On the other hand, Deus Ex Machina describes a being, device or event that suddenly appears and solves a seemingly insoluble difficulty in a work of fiction or drama to resolve a situation or untangle a plot. Both sentences are in Latin.
The author
I graduated with a BS in math from the National University of Mexico (UNAM) and with a master’s degree in logic (LoPhiSS) from the University of Paris 1 Panthèon-Sorbonne. Currently I am a graduate student at Lille 1 University working toward a PhD in Computer Science and at Paris 1 University (IHPST) working toward a PhD in Philosophy, both on algorithmic complexity and randomness. My thesis advisors are Jean-Paul Delahaye from the University of Science and Technology of Lille, Cristian Calude from The University of Auckland and Jean Mosconi from the University of Paris 1 Panthéon-Sorbonne (IHPST). My former thesis advisors (B.S. and Master) were Francisco Hernandez-Quiroz from the National University of Mexico (UNAM) and Jacques Dubucs from the IHPST (Paris 1/ENS Ulm/CNRS). Since 2006 I am also an R&D fellow at Wolfram Research where I have been working on projects related to mathematical logic, automatic theorem proving, computational linguistics and data collections as part of the Stephen Wolfram’s Science Group. In 2005 I attended the NKS-SS at Brown University where I developed a research project under the guidance of Stephen Wolfram and the mentoring of Matthew Szudzik. In 2007 I was invited to join the faculty staff of the NKS-SS at the University of Vermont in Burlington, VT. During the Summer of 2007 I was an intern at the Massachusetts Institute of Technology (MIT) and I will be a research scholar at Carnegie Mellon University (CMU) during the spring semester of 2008.
My research interests include computability and logic, the relation between computation and physics, experimental algorithmic information theory and pure NKS research.For more information about the author of this blog click here.
The Matrix is going up now.
Hector Zenil
Images on this blog may have copyright either from their respective author or me.
