Picture taken by Hector Zenil, Berlin, Germany, November 2006
Short blog manifesto
Algorithmic information theory is the tool with which to test our claims that the universe in fact unveils itself, in all or most regards, as a digital computer. Science is the discipline for discovering shortcuts for comprehension through compression.
Holy Tech, by Alex Ostroy for God Is the Machine a Wired Magazine article on Digitalism.
This is a place where I can both share some thoughts with others and keep a record for myself of my experiences, working on my chosen fields, exploring and understanding a variety of subjects, from symbols to languages from rules to abstract machines.
Randomness and algorithmic complexity
Image created by Hector Zenil with Mathematica using a cellular automaton.
You are likely to find that topics related to my personal interests are frequently covered on this blog. Among my favorite books are:
- Richard Feynman, Lectures on Computation, Perseus Publishing, 2000.
- Gary William Flake, The computational Beauty of Nature, MIT Press, 2000.
- Andrew Ilachinsky, Cellular Automata, World Scientific, 2001.
- Marvin Minsky, Computation: Finite and Infinite Machines, Prentice Hall, 1967.
- Rudy Rucker, The Lifebox, the Seashell and the Soul, Thunder’s Mouth Press, 2005.
- Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002.
Hermeneutics and early anticipations of scientific ideas
I once did some hermeneutical research on pre-modern texts on Geometry, from Euclid’s axiomatization to Hilbert’s formal approach to Saccheri’s unwitting discovery of non-Euclidian geometries. My main interest (though it falls outside the ambit of my current field of research) is the emergence of the notion of space and dimension from plane geometry, with a particular emphasis on the early study of the so-called platonic solids or regular polyhedra. These were the focus of an internship I did several years ago at the Museum of Science of the National University of Mexico (Universum), where I worked on a number of things. From investigating some stones found in Scotland in 3000 B.C. that are now in the Ashmolean museum in Oxford, UK, to the topological notion of dimension. In fact, in the wake of two math courses on the topic and my 6-month service stint at the National University of Mexico’s Museum of Science (Universum). I’m also interested in the texts of Julien Offray de la Mettrie.
Mathematical formalism and cognitive aspects
On the other hand, I am also interested on the process of mathematical proof and the elements, in the cognitive sense, that play a role in achieving or deriving a proof. In the case of Fermat’s last theorem, for example, though the statement of the proposition can be made in purely arithmetical terms, the proof relies on much stronger mathematical theories. This is an example of a proof which uses concepts alien to the theory in which the original statement was made. Thus a purely arithmetical question required ( in this case for Wiles’ 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 be proven has nothing to do with complex analysis. Many proofs rely on meta-theories in this fashion, which raises questions about necessity and indispensability that interest me. Visual proofs are likewise an interesting field in the cognitive and mathematical sense, raising questions about when a diagram is necessary to show, clarify or even prove a mathematical statement;when a diagram becomes necessary for the proof, explanatory or ornamental (this latter as it should be from an orthodox logical point of view); when visual representations induce mistakes because other logical possibilities are unwittingly hidden; when and how such a visual representation can be translated into a formal language and be completely abstracted from objects in favor of a purely algebraic manipulation of symbols. We can see such an attempt in Hilbert’s work on re-casting geometry so as to completely avoid any geometrical objects or diagrams, a departure from Euclid’s approach in his Elements, in which diagrams sometimes play a fundamental role in the geometrical statements and their proofs, including the most important of them, triangle congruency for instance. The question can be taken to the limit by asking whether such abstractions that make no reference to any concrete object or 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. This amounts to asking whether we are in fact able to think in triangles without realizing what a triangle really is. Formalization approaches always seem to come after intuitive, diagrammatical- approaches. The topic is of course integrally 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.
Anima Ex Machina
The name of this blog makes reference to two interesting concepts. On the one hand there is the notion of the ghost in the machine, the premise behind movies like Ghost in the Shell, which in turn inspired The Matrix. The Ghost in the Machine was originally the title of a good book by Arthur Koestler. The idea can be approached from two different points of view– either that machines can generate a ghost (something equivalent to a soul) or that the soul is in fact nothing but the product of the identity, the “I” of a machine (human or otherwise). 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, thereby resolving a situation or untangling a plot.
The background image is one of my favorite elementary cellular automata rule 22, which is the rule that displays the largest transition phases according to my transition coefficient as proven in my paper Compression-based investigation of the dynamical properties of cellular automata and other systems published in the journal of Complex Systems in 2010.
The Matrix is going up now.
Images on this blog may have copyright either from their respective author or me.