Having quit his studies in physics, Theo Jansen became an artist. In this video he demonstrates his amazing life-like kinetic sculptures, built from plastic tubes and bottles. His Beach Creatures or Strandbeest are built to move and even survive on their own:

I’ve been in touch with Theo Jansen recently. For further details about his creations he referred me to his book (available at his web shop ) entitled The Great Pretender. Even more details are provided in Boris Ingram’s thesis on leg designs based on 12-bar linkages, in which he describes Jansen’s walker algorithm. Jansen’s designs are computer-generated using an evolutionary algorithm, and the animals, which are wind powered, are made out of PVC piping.

The valves essentially act like logic gates, allowing water to pass or not depending on the state of the other gates.

Jansen’s creations do not require engines, sensors or any other type of advanced technology in order to walk and react to the environment. As for Boris Ingram’s work, it would be greatly enriched if it were to incorporate a wider range of possible structures and algorithms.

More online references:

• Theo Jansen’s webpage.
• Theo Jansen’s Strandbeests, artfutura.
• Wild Things are on the Beach, Wired Magazine.
• Theo Jansen’s interview.

My paper On the possible Computational power of the Human Mind (co-authored with my BS thesis advisor Francisco Hernández-Quiroz of the Math Department of the National University of Mexico [UNAM], which I delivered as a lecture 2 years ago at the Complexity, Science & Society 2005 Conference at the University of Liverpool, U.K.) has been recently published by World Scientific as a book chapter. It is available from World Scientific at http://www.worldscibooks.com/chaos/6372.html ; also as a paper or from Amazon.
The book is edited by Carlos Gershenson, Diederik Aerts (Brussels Free University, Belgium) & Bruce Edmonds (Manchester Metropolitan University Business School, UK).

Introduction: Scientific, technological, and cultural changes have always had an impact upon philosophy. They can force a change in the way we perceive the world, reveal new kinds of phenomena to be understood, and provide new ways of understanding phenomena. Complexity science, immersed in a culture of information, is having a diverse but particularly significant impact upon philosophy. Previous ideas do not necessarily sit comfortably with the new paradigm, resulting in new ideas or new interpretations of old ideas.In this unprecedented interdisciplinary volume, researchers from different backgrounds join efforts to update thinking upon philosophical questions with developments in the scientific study of complex systems. The paper contributions cover a wide range of topics, but share the common goal of increasing our understanding and improving our descriptions of our complex world. This revolutionary debate includes contributions from leading experts, as well as young researchers proposing fresh ideas.Contents:* Restricted Complexity, General Complexity (E Morin)* Complexity Science as an Aspect of the Complexity of Science (D Mikulecky)* On the Importance of a Certain Slowness (P Cilliers)* Simplicity Is Not Truth-Indicative (B Edmonds)* Why Diachronically Emergent Properties Must Also Be Salient (C Imbert)* Some Problems for an Ontology of Complexity (M McGuire)* Physical Complexity and Cognitive Evolution (P Jedlicka)* Informational Dynamic Systems: Autonomy, Information, Function (W Riofrio)* The Complexity of Information-Processing Tasks in Vision (J Symons)* On the possible Computational Power of the Human Mind (H Zenil & F Hernandez-Quiroz)and other papers

An interesting thought experiment conceived by Daniel Dennet and recently published in the Time magazine.

New Steven Pinker article on Consciousness:
http://www.time.com/time/magazine/article/0,9171,1580394-1,00.html
with good links to related articles.

Steven Pinker recognizes in this article that the “I” problem has been over-estimated. However, despite a parenthetical moment of doubt, he does not recognize that the conscious/unconscious question is not a real problem. Science has long recognized that old problems can become meaningless over time. This is indeed the case with the Cartesian mind/body dichotomy, which for so long was the focus of  intense scholarly and scientific scrutiny. Nowadays no cognitive or neuroscientist will argue against the prevailing wisdom that every aspect of the  mind is nothing more than a consequence of brain activity.

Steven Pinker divides the problem of consciousness into two further problems –a first  ”easy” problem and a  second “hard” problem.  I don’t think there is a second problem, and the first is neither easy nor hard, it’s just the core of neuroscience–or should be. New developments in the field, such as the discovery of mirror neurons, have shed light on problems that we did not understand before. As Pinker points out, a neuroscientist is capable of reading the mind of a person just by observing the blood flow in their brain. And  this can be done with a  degree of precision so high that it is possible to distinguish between someone thinking they are driving a car, someone thinking they are seated watching TV at home and someone pretending he is talking.  There are many real problems in the field that remain to be investigated.  For instance, there is the question of the matching of mental and physical representations, whether inside a single brain or involving several individuals—what is traditionally referred to as the type/type or token/token problem. Manipulating consciousness is another immense–and delicate– field of research and Pinker mentions  it in his article. Surgeons are able to stimulate a brain in such a way that a patient is incapable of distinguishing  between these induced hallucinations and reality. Neuroscience is capable of creating a whole new kind of “virtual” experience,  and also of improving existing reality by attacking mental problems such as memory loss or depression. Better human-machine interfaces could be created, thereby improving the communcation channel between humans and computers, which at present consists of someone typing on a keyboard, touching a screen or moving a mouse. What of the claims made on behalf of newly released  Operating Systems, claims that they are much more sophisticated because they use “new” old-fashioned windows, which look better just because they are now transparent or simulate a 3D environment embedded in a flat screen? Software enginneering could also take advantage of a new kind of interaction between the brain and software through better interdisciplinary research.

When I realized that a dictionary, as a whole, could be viewed as a non -syntactical knowledge container, in other words, that there was  no new knowledge in it, I wondered how something that was such a perfect auto-referential source could actually be useful.  For since every word is defined by other words in the same language, looking up the meaning of a given word would lead you to other words and yet others and eventually back to the first word, the word whose meaning you set out to learn. This would be the case even if  the dictionary were bilingual, and the meaning of the word you wished to check was given in a second language. Thus all dictionaries are perfectly circular, closed, auto-referential sources. However, I discovered that the analytical knowledge in a dictionary comes from the net supporting words connected with each other. Thus  if “chair” is strongly connected with “table”, “office”, “dining room”, etc. it should be easy to map it to its equivalent in any other language. Of course this overlooks languages in which the word “chair” does not exist,  reflecting the lack of  a comparable object in the culture and thus the lack of a cognitive representation of it. But such instances are rare since most cultures share a basic physical reality and human experience.

Of course problems arise with  words like  “personne” in French, which  maps onto “persona” and “nadie” in Spanish,  a noun and an adjective respectively with completely different connections and different supporting nets. Or conversely, when the verb “gustar” from Spanish maps onto”gouter” and “plaire” in French.  So even when it seems that all words are surjective, the general case is not bijective, and that applies to homonyms too, which often creates ambiguities in translation. In other words, any word in any language has its equivalent in any other language, whether a single word in one langauge becomes two or more words in another, or whether two or more words become one after mapping– but one word could mean two completely different things in another language. However, the supporting network  would be able to uncover this fact and solve a possible ambuiguity based on  context by extending the word network to encompass the ambiguity. In other words, if a subnet cannot be uniquely mapped, extending it should eventually solve the ambiguity. What one would need  is a corpus big enough to build such a network once and for all and then simply make comparisons at the network level. This could work even for completely new or unknown languages, either dead or living, assuming that they share a part of our actual reality and hence some part of our mental representations  (In a sense this is what Champollion did when he deciphered the Rosetta stone– he discovered a partial mapping of a subnetwork of words from an unknown language - Egyptian - to a subnetwork of a known one - Greek ). In the final analysis, each language has a single unique network (changing slightly through time but remaining well connected and strong enough to make  it unique and recognizable while being isomorphic with that of any other language).  Thus an entire language could be identified by its fingerprint -its network.

Having  established that, what about mining the world of all possible meanings, the world of all possible translations, and the world of all possible ideas? We wouldn’t have the problem of distinguishing between a coherent idea and a non-coherent one since the network would provide some minimal coherence. Thus the net-into-the -net approach would give us a way of translating from word to word and from phrase to phrase and from idea to idea.

The above ideas would apply to unilingual dictionaries, lets say English-English. The analytical knowledge in them again comes from the net connecting the words, so even if someone does not know English at all I would say that he would be able, albeit with considerable difficulty, to learn English just by deducing the net connecting objects, in other words, by mapping his own mental  representations of objects onto words in the  English dictionary. In the process he could encounter some ambiguities, but the further he goes, the more of these he would be able to resolve. On the other hand,  speakers of those languages in which “chair” does not exist, both in the language itself and as a real object in the culture,   would be able to deduce what  a chair is by tracking its  relations with the objects they know and for which they do have mental representations and the phonemes to externalize them. So the problem of translation, which began with the mapping of word onto word and then phrase onto phrase  with statistical tools,  becomes with this approach a matter of  mapping net to net.  Indeed this seems to be the approach adopted  by Meaningful Machines http://www.meaningfulmachines.com/-.  Such ideas have been around for a while, for example at WordNet: wordnet.princeton.edu/, but they somehow remain old-fashioned even as they are shifting the paradigm.

These ideas could be carried to the limit by taking the sum total of human languages and enquiring into the mapping between such a network and our cognitive representations. Such a move would provide grounds  for rebutting the Chinese room argument, since in the end it does not matter whether someone inside the room has no knowledge at all of a language; he would be able to map what he is mechanically translating onto his own mental representations, generating what, according to the argument, could not be generated: understanding. Because Searle’s  idea was, as I recall, to build up a case against A.I. in terms of the Turing test.

My conclusion: Meaning resides in the net.

This post is  related to a previous post titled “Meaning against A.I.”: http://www.mathrix.org/liquid/?p=29

The original questions were posted here.

From Dr. Seth Lloyd’s answers it is clear that:
1) he is assuming the Deutsch quantum computing model, which is Turing reducible and
2) he is assuming that quantum particles encode a finite amount of information, so that they are completely discrete in every possible sense, including: space/time, mass, energy, momentum, and any other possible physical value.

1 and 2 are, by the way,  standard views in both fields, quantum computing (defined by David Deutsch) and quantum mechanics (as defined by several authors). From 1 and 2 it can be deduced that Seth Lloyd indirectly implies that the universe is Turing computable (since the only difference between a quantum computer and a Turing machine -disregarding the usual fact about the infinite tape- is the run time, a fact borne out by his answers). Regarding 2, most quantum quantities and solutions to equations suggest that there are minimum values, namely the Planck time and the Planck length, a fact which assorts well with a discrete scenario. However the issue is commonly bypassed by physicists and by the theory itself. In other words, quantum mechanics seems to be consistent with both a continuum and a  discrete universe and does not offer final evidence or an ultimate theoretical conclusion one way or the other. In fact it is usual among physicists to think of  superposition as an entanglement in a space continuum, which would allow  a particle to be in an infinite number of  states simultaneously.

From 1 and 2 we can conclude that Church’s thesis–in both its weak and strong non-physical and physical versions, which we will discuss in a separate post– remains intact  even when Dr. Lloyd’s approach is closer to a physical basis (an accepted modern model of the universe) and of course the empirical data (which supports quantum mechanics itself). His chain of reasoning is basicaly as follows:

a&b->c:

a) the universe is completely describable by quantum mechanics
b)  standard quantum computing completely captures quantum mechanics
c) therefore the universe is a quantum computer.

He proved a relation between a and b, which probably puts the standard (or some standard) theory of quantum mechanics and the standard quantum computing model in an isomorphic relation with each other. Here “standard” means that some assumptions were made.

Here is a literal transcription of the answers to my questions given by Dr. Seth Lloyd:
—–
A: A quantum computer differs from a Turing machine in that its bits are quantum bits, and so can exist in a superposition. In addition, it can be instructed to put those bits in superpositions. These two features make a quantum computer apparently much more powerful than an ordinary Turing machine. What a quantum computer does is still Turing computable, but a typical quantum computation of T steps on N qubits requires O(2^N) bits on a classical Turing machine, and O(T 2^2N )logical operations. That is, it takes a Turing machine exponential amounts of time and space to simulate a quantum computer or quantum Turing machine. (Compare the definition of universality: a universal Turing machine can simulate any other Turing machine in polynomial time.)
So a quantum computer is apparently more powerful than a classical computer.
There is a perfectly good definition of a quantum Turing machine (basically, a Turing machine with qubits and extra instructions to put those qubits in superposition, as above). A universal quantum computer is a physical system that can be programmed (i.e., whose state can be prepared) to simulate any quantum Turing machine. The laws of physics support universal quantum computation in a straightforward way, which is why my colleagues and I can build quantum computers. So the universe is at least as powerful as a universal quantum computer. Conversely, a number of years ago I proved that quantum computers could simulate any quantum system precisely, including one such as the universe that abides by the standard model. Accordingly, the universe is no more computationally powerful than a quantum computer.

A: As long as a quantum particle encodes 3, 4, or M states, where M is a finite number, then the computational picture remains the same (this is also true classically). Now, it is a fact that a physical
system with finite energy confined to a finite volume of space has only a finite number of discrete states. So we are OK.
——-
“Now, it is a fact that a physical system with finite energy confined to a finite volume of space has only a finite number of discrete states.”—I wish the obviousness of this final remark were readily apparent to me.

Dr. Seth Lloyd’s work is very compelling, and I am engaged in a project inspired by ideas related to those he expounds here—mining the computational universe to uncover Lloyd’s programmer monkeys. But I find that his theory of the universe– which by the way I agree with, though it may sometimes seem otherwise– assumes no less than any other conception of the universe, which leaves space for continued thinking on evocative hypotheses, including Church’s, even as we attempt to hack the universe.

Lloyd’s thesis adds to the conception of the Universe as a Turing computer an important and remarkable claim (albeit one that depends on the conception of the quantum computer), viz.  that the Universe is not only Turing computable, but because it is constituted by quantum particles which behave according to quantum mechanics, it is a quantum computer computing its future state from its current one. The better we understand and master such theories, the better prepared we would be to hack the universe in order to perform the kind of computations -quantum computations- we would like to perform.

I would agree with Rudy Rucker too as to why Seth Lloyd assigns such an important role to quantum mechanics in this story. Rudy Rucker basically says that being a subscriber to quantum mechanics, Lloyd doesn’t give enough consideration to the possibility of deterministic computations. Lloyd writes, “Without the laws of quantum mechanics, the universe would still be featureless and bare.” However, though I am one among many (including Stephen Wolfram) who agree  that it is unlikely that the universe is a cellular automaton, simply because cellular automata are unable to reproduce quantum behavior from empirical data (but note that Petri and Wolfram himself attempt explanations of quantum processes based on nets), there’s  absolutely no need to rush headlong into quantum mechanics. If you look at computer simulations of physical systems, they don’t use quantum mechanics as a randomizer, and they seem to be able to produce enough variations to feed a computational universe. Non-deterministic randomness is not neccesary; pseudorandomness or unpredictable computation seem to be enough.

Ist das Universum ein Computer?
http://www.dtmb.de/Aktuelles/Aktionen/Informatikjahr-Zuse/
Germany, November 2006, Informatik Jahr
Deutschen Technikmuseum Berlin
From Konrad Zuse’s Invention of the Computer to his “Calculating Space” to Quantum Computing.

Lesson One: For someone with a hammer in his hand the world seems to be a  nail. Joseph Weizenbaun.

Lesson Two: Knowing the input and the transition function of a Turing machine we know everything about it. Marvin Minsky.

Dr. Zuse’s futuristic drawing

- The first talk entitled  ”What Can We Calculate With?” by Prof. Dr. Bernd Mahr from the Technische Universitat of Berlin was a very good introduction to the standard theory of computation based on Turing’s model and classical mathematical logic. His remarks on the time when computing arose from math because the Greeks discovered they were unable to compute the square root of 2 were interesting. He pointed out some evident but not always explicit facts: Calculation has a subject (the individual who calculates), an object (what is calculated),  a medium (how it is calculated), and a symbolic representation (the language -binary, for instance). His use of the Leibniz medallion for explaining   starting points, ending points and transitions in a calculation was elementary but interesting (transitions: intermediate calculations). Further explanations of reversibility and non-linearity using transition nets were also illuminating. The context of a calculation (or computation) and the strong relation between the computation itself and its context is  such that it is sometimes difficult to distinguish them. Since any process can be seen as an object in itself, the context can become the calculation and the context of the context too. In some way, as we know, the concept of calculation is a constraint of a part of a calculation, and then it is defined in terms of an input, an ouput and a transition. He pointed out too that behind many of these complicated systems there is a Turing machine. It  is no longer visible from the top, but it is there.

Dr. Konrad Zuse

- Dr. Horst Zuse’s  talk titled “Konrad Zuse’s Calculating Space (Der Rechnende Raum)”:
Dr. Konrad Zuse’s son, Dr. Horst Zuse made some interesting remarks about his father’s book “Calcualting Space”,  in which  Dr. Zuse proposes studying  the universe as a digital system, specifically a cellular automaton. Dr. Horst Zuse is a professor at the Technische Universitat of Berlin and his personal webpage can be found at: www.cs-tu-berlin.de/~zuse and www.zuse.info

Dr. Konrad Zuse’s son, Dr. Horst Zuse

Dr. Zuse’s father’s main  question was: “Is Nature Digital, Analog or Hybrid?” It seems that he tended to answer “Digital,” proposing a No-Yes value language (binary). His thoughts were published in the Nova Acta Leopoldina. He evidently did acknowledge that there could be problems attempting to reconcile an explanation of the Universe in terms of Cellular Automata with Quantum Mechanics and General Relativity.

According to Konrad Zuse, laws of physics could be explained in terms of laws of switches (in the computational sense). Physical laws are computing approximations captured by the formulas in our models. He saw that differential equations could be solved by digital (hence discrete) systems.

Dr. Carl Adam Petri at the Berlin conference

- Dr. Carl Adam Petri (yes, the creator of the Petri nets!) on “Rechnender Netzraum” or “Computing Net Universe”:
According to Dr. Petri, at the Planck length quantum computing can be described by digital systems using combinatorial models (net models, kennings, combinat), and therefore the universe can be studied using discrete nets which are even capable of explaining quantum and relativistic fundamentals like Bell’s theorem and Heisenberg’s uncertainty principle. That would mean that discrete systems (for instance those proposed by Stephen Wolfram) would suffice to explain even quantum and relativistic phenomena.

According to Petri, measurement is equivalent to counting. For instance in S.I. one second is 9192631770 Cs periods. In fact Norbert Wiener proposed some axiomatics of measurement.

The correspondence of Petri nets with the Heisenberg uncertainty principle arises from the limitations of our observational capacities when carrying out measurements. When two different types of observations are performed, -for example momentum p and position q- we can only see p or q in a chain of succesive events related by a causality net. His nets as well as his explanations of such phenomena are very neat and elegant. The relevant slides  on causality and linear logic may be found  at:
http://www.informatik.uni-hamburg.de/TGI/mitarbeiter/profs/petri/slides/
He also distributed a CD with his slide presentation at the conference.

For Petri, the Universe is a Petri Net.

Dr. Seth Lloyd’s presentation at the conference in Berlin, Germany

- Dr. Seth Lloyd’s talk entitled “The Universe is a Quantum Computer”:
According to Dr. Seth Lloyd, professor at MIT, because quantum mechanics is the most fundamental and foundational theory of the universe,  assuming it would lead us to conclude that  the whole universe is a quantum computer computing itself. The input consists of basically random processes (which he characterizes using the metaphor of  programmer monkeys) and the outcome is all that we see around us. Because an elementary particle interacts with others and changes its state, he argues that each particle can be seen as information, as a qubit (for quantum binary digit), which unlike a bit  can be in 0,1 or both states at the same time according to the quantum property known as  entaglement or superposition. When a particle interacts with other particles they change their states according to a quantum logical gate.

Therefore, his conclusion is that the universe is not only a computer but a quantum computer. However some questions arise:

1. What does he mean by quantum computing? According to the standard model (by Deutsch) quantum computing is Turing computable (disregarding run time). If Lloyd is assuming the standard model then the universe is indeed a quantum computer, but even more remarkably (since we have scientific and philosophical hypotheses like the Turing thesis) it is Turing computable. However, if he is assuming the more general quantum mechanics model, let’s say the standard model in physics (which basically assumes the possibility of harmless continuity rather than inquiring into it) he is saying that the universe is not a computer (since the term derives  from what we mean by Turing computable and hence covers  digital computers too). So the assumptions made are significant and cannot be glossed over if one wishes  to argue convincingly that  the universe is  a computer in some standard sense. If what we  assume to be computing is something that seems to be deterministic or rule-based, the concept becomes fuzzy and  additional remarks need to be made.

2. What if a quantum particle encodes more information than just a 1 or 0 for the spin or any other quantum property? Let’s say a third value, or even worse, a non-computable number of values. In quantum mechanics for example, the superposition of a particle assumes an infinite and non-countable number of places since it is in all the spectra at the same time. If space/time is a continuum then it is evidently in a non -countable number of positions, which leaves us with  a non-computable model, or at least with something that’s neither a Turing-computable model nor a standard quantum-computable (namely Deutsch) model. And this is not a simple assumption since it requires anotherTuring-type thesis which in the final analysis does not answer the most fundamental  question, i.e. whether the universe is a computer or not and if it is, what kind of computer (in the computational power sense) it is.

I raised these questions with Seth Lloyd and I will be posting his answers soon.

Seth Lloyd at the conference in Berlin

A remarkable idea proposed by Seth Lloyd concerned “hacking the universe”. As Charles Bennett used to say, a computer is a handicapped quantum computer. So if Lloyd is right, a computer is not only a handicapped quantum computer but it is not taking advantage of the full computational power of the universe and it is just patching the universe instead of hacking it, as it would be in its power to do. By contrast, a quantum computer uses some particles that are already computing “something” (nothing less and nothing more than the processes in the universe ) to perform the computation that we want it to perform. It can be said to be  ”hacking the universe” in Lloyd’s terms.

On the other hand, if the notion of programmer monkeys is valid it should be possible to test it experimentally. Under the supervision of M. Jean-Paul Delahaye, computer science professor at the University of Lille I (http://www2.lifl.fr/~delahaye/) we are undertaking this task. We are exploring  Lloyd’s quantum computational universe (or at least a handicapped but representative part, the recursive computational universe), applying some complexity measures (universal distribution, average-case complexity or Levin’s measure) in order to uncover the monkeys behind the Universe, or in other terms, to analyse the average distribution of randomly discrete systems with random inputs.

Is Seth Lloyd falling into the carpenter’s problem of thinking that the universe is a nail and the moon made of wood?  Is it because he is a quantum computer scientist that he thinks the universe is a quantum computer? He argues of course that the charge is unfair, but then we have been told by Dr Petri  that the Universe is in fact a Petri Net which probably  needs neither strong randomness nor quantum mechanics!

Here  is a video online in which he explains much of this:
http://www.edge.org/video/dsl/EF02_Lloyd.html

Dr. Zuse’s futuristic drawing 2

- Jurgen Schmidhuber reprised his algorithmic approach to the theory of everything in his talk entitled   “The program that computes all computable universes”.
Jurgen Schmidhuber’s major contribution probably is his Speed Prior concept, a complexity measure similar to Algorithmic Information Complexity, except that it is based on computation speed and not program length. i.e. the fastest way of describing objects rather than the shortest.
There is more information on his website: http://www.idsia.ch/~juergen/ (where he includes an unfavorable review of  NKS) and in his slide presentation on the Speed Prior at: http://www.idsia.ch/~juergen/speedprior/sld001.htm
Of course Schmidhuber himself has identified a problem with the Prior measure: If every possible future exists, how can we predict anything?

Other interesting talks on philosophical issues: If the Universe is a computer, therefore the human mind should be a computer too.
Is “the Universe is a  computer” a metaphor?
My answer: The metaphor is “The Universe is not a Computer”

Lesson Three: Metaphors can be reversed.

Kovas Boguta’s  talk was titled ”Is the Computer a Universe?” In it he pointed out the richness of mining the computational universe of simple programs.

Because we were together during the gala dinner I had an interesting exchange with Dr. Konrad Zuse’s son, Dr. Horst Zuse (Also at our table were the Technikmuseum director Dr. Dirk Bondel and  my colleague Kovas Boguta from Wolfram Research, among others). He shed some light on his father’s interactions with Alan Turing ( none apparently),  with von Neumann (some interaction regarding the controversy over who first built a digital computer and concerning von Neumann’s architecture, which  our current digital computers do not conform to, the ALU being separated from the memory as it is in Zuse’s conception but not in  von Neumann’s original design).

Zuse’s Z1 first computer “the input device, something equivalent to the keyboard, at the Technikmuseum in Berlin”

Kurt Godel workshop for studying his legacy and writings. Lille, France, May 19-21, 2006

My thoughts, ideas, references, comments and informal notes:

- The wheel machine, a machine for real computation which I am proposing -as a thought experiment- in a forthcoming paper  on the Church-Turing thesis -Yes, one more paper on the CT thesis!- with comments on Wilfried Sieg’s paper entitled “Church Without Dogma: Axioms for Computability”

- “In case Cantor’s continuum problem should turn out to be undecidable from the accepted axioms of set theory, the question of its truth would loose its meaning, exactly as the question of the truth of Euclid’s fifth postulate in Euclidian geometry did”. Godel replies: “It has meaning anyway, as Euclid’s fifth postulate gave rise to other now accepted mathematical fields.”

- Godel Gibbs Lecture and his dicotomy on absolutely undecidable propositions and the computational power of the human mind (Turing did great work… but he was wrong when he proposed his formal theory as a model of human thought…)

- New contacts and references: Olivier Souan, Rudy Rucker, Karl Svozil

Mark van Atten’s “On Godel’s awareness of Skolem’s lecture”.
Rick Tieszen

- Herbrand on general recursive functions, letter to Godel.

- Leibniz’ influence on Godel’s arithmetization?

- Sources: Godel Editorial Project. Firestone Library, Princeton University. I.A.S. Marcia Tucker, librarian for Godel papers.

- Godel’s concept of finite procedure as the most satisfactory definition of computation. “A machine with a finite number of parts as Turing did” or “finite combinatorial procedure” as a definition of an algorithm, mechanical or computational procedure.

- Computation’s main constraints: boundness and locality (paper from Hernandez-Quiroz and Raymundo Morado).

- Aphorisms and autoreference (Gabriel Sandu and Hinttika)

- Feferman on Turing

- Is Sieg’s paper and the question of “finite machine=effective procedure” a tautology? In fact such an approach seems to be one of the most strict versions of the Turing Thesis, and even though both Church and Turing probably did propose it in such a strict sense, extensive versions of the thesis have traditionaly covered more content, but even when it is strictly stated that there is still space for a thesis, it is neither proved nor provable from my point of view, and most authors would concur, though some clearly would not. I will comment on this more extensively later, since this was one of my Master’s topics and merits a post by itself.

- Putnam’s thought experiment on cutting all sensorial inputs. Solution: It is impossible in practice. However, machines are an example in a sense, and that is why we do not recognize intelligence in them – they are deprived of  sensorial capabilities.

Yes, Godel found an inconsistency in the U.S. constitution. My answer: One? Certainly a bunch. That’s why we need lawyers, who make them even worse.

A significant number of researchers believe that there are sentences with semantic value that could never be understood by a machine. These researchers believe that the mind has a semantic component, unlike machines. Their’s is a  Chinese Room type argument a la Searle. Consider Chomsky’s example of two books in a library with the same title, and two readers, each taking out one of the books. Do they get the same book? These researchers argue that machines would be unable to answer correctly on the basis of context since the answer would depend on a cognitive understanding of the situation. My claim is that all  meaningful components of a situation are based on a hierarchy that can be artificially represented by categories capturing the essence and functionality of  human mental operations. The answer to Chomsky’s question would be “yes” if one is  referring to the information content of the books,  “no” if one is referring to the books as physical objects.