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Hypercomputation and Economics

2011-10-25T09:52:00.001-07:00

I have been thinking for many years why economists usually fail to make any reliable predictions. And when one does make some reliable predictions, then she is considered phenomenal! But if economics is to be considered a science, then it should be able to make reliable predictions, otherwise it is completely worthless. First of all economics is a social science. Thus, in order to make trustworthy predictions, one must ensure that an economic system is computable and, why not, deterministic. Economics systems consist of agents (ordinary people) that interact and create the world we see around us. But how can be so sure that the behavior of these agents is computable? In fact we are not and, furthermore, we shouldn't! One of the basic ideas of hypercomputation is that the human mind, ergo our agents, has capabilities computational, hypercomputational, and paracomputational (i.e., abilities that lie outside computation as we presently know it). In different words, economics is bound to fail unless economic theoreticians will not adopt a different way of thinking.

The universe as a quantum computer

2011-09-07T00:33:00.000-07:00

The other day I was skimming through Lee Smolin's The Trouble with Physics. On pages 317-138 one can read the following:

In the context of quantum gravity, it resulted in a new approach to quantum cosmology, made by Fotini Markopoulou and her collaborators. Markopoulou emphasized that describing the exchange of information between different subsystems is the same as describing the causal structure that limits which system can influence each other. She thus found that a universe can be described as a quantum computer, with a dynamically generated logic.

We all due respect, the idea that the universe is a computer was put forth by Konrad Zuse in his Rechnender Raum. Furthemore, Zuse's ideas form in a way the basis of digital philosophy. Whether the universe is a computer or not is another discussion that I have addressed briefly in an older post.

A brain simulator

2011-07-15T12:33:00.000-07:00

SpiNNaker is a project to create a simulator of the human brain, The computer will consist of up to a million ARM cores to host a brain simulator. But as Steve Furber of the University of Manchester has correctly noted "[t]here are about 100 billion neurons with 1,000 trillion connections in the human brain. Even a machine with one million of the specialized ARM processor cores developed at Manchester would only allow modeling of about 1 percent of the human brain." Nevertheless, I am sure such a project will provide some scientific knowledge.

New Worlds of Computation 2011

2011-05-29T06:33:00.000-07:00

The second workshop New Worlds of Computation, which was organized by the Laboratoire d'Informatique Fondamentale d'Orléans, took place in Orléans from May 23 till May 24. A number of researchers, mostly from France, gathered and presented their work and ideas regarding computation. Françoise Chatelin talked about the necessity to use mathematical tools in computability theory that have been largely ignored until now. Obviously, such a mathematical tools include fuzzy sets, quaternions, etc. Sama Goliaei talked about her work in optical computing. Mike Stannett talked about his joint-work in cosmological computation (i.e., the exploitation of the properties of the space-time to perform hard and "impossible" computations). Yaroslav D. Sergeyev presented his "numbering system of infinity" and its use in computation (a possibility that was mentioned in my book on hypercomputation). My talk was about vagueness and its use in computation. Unfortunately, some speakers were not talking loudly so I missed (most of ) their talks. Below is a picture that was taken just after the launch break:

Unfortunately, it was not possible to stay one more day, but my overall impression was more than positive! Jérôme Durand-Lose, our host and organizer of NWC 2011, talked about his plans to make NWC a biennial event with formal proceedings, etc. I believe this is wonderful idea and I wish him all the best in this endeavor.

Commercial Quantum Computer

2011-05-28T11:44:00.000-07:00

D-Wave, a Canadian technology company, has announced that they have sold their first commercial quantum computer to Lockheed Martin Corporation. The intriguing thing about D-Waves technology is that they were claiming to use the technology Tien D. Kieu has used in his adiabatic quantum computing method, which is a hypercomputational method.

Building a brain?

2011-05-13T10:00:00.000-07:00

Today Spiegel Online International posted an article entitled Researchers Hope to Build a Brain. The article discusses the efforts of the Blue Brain Project team (the article wrongly states that the team's name is Human Brain Project). The problem is that the article as well as the people involved with this project use the terms simulation and building almost interchangeably, which is wrong. To build a brain means to actually construct something that will function as a brain, while simulating means that the team will write software that will function similar to bran. I can imagine that such a simulation could be implemented in an object-oriented way, where each neuron will be simulated by a very complex object. Obviously, all these objects would form a network. Now, how will they respond to external stimuli? Moreover, what will count as an external stimulus? All in all, even the simulation of the brain is a very ambitious project and I don't think we are ready to implement it.

Technological singularity

2011-03-09T09:52:00.000-08:00

Technological singularity is described in a recent issue of Time magazine. I read the article because I was curious, but I was disappointed when I read the following paragraph:

Computers are getting faster. Everybody knows that. Also, computers are getting faster faster — that is, the rate at which they're getting faster is increasing.
True? True.
So if computers are getting so much faster, so incredibly fast, there might conceivably come a moment when they are capable of something comparable to human intelligence. Artificial intelligence. All that horsepower could be put in the service of emulating whatever it is our brains are doing when they create consciousness — not just doing arithmetic very quickly or composing piano music but also driving cars, writing books, making ethical decisions, appreciating fancy paintings, making witty observations at cocktail parties.

The problem here is that somehow intelligence is equated with processing speed, when, for example, it is common knowledge that people perform arithmetic operations very slowly. Obviously, a superfast machine might help us settle some problems like Goldbach's conjecturem, but that is all. Human intelligence is something different and we have absolutely no idea who matter can become conscious…

Does Nature Compute?

2011-01-25T08:19:00.000-08:00

Recently, I received an email about a new book entitled Randomness Through Computation: Some Answers, More Questions. Although, I fail to see how computation would create randomness, the title of one article seemed particularly… intriguing—"What is Computation? (How) Does Nature Compute?" I haven't read the article, so I do not know what it is about, but I can speculate that is advocates the idea that the Universe, Nature somehow computes. Well, to me the idea that Nature computes is pure Pythagorean mysticism (also known as Pythagoreanism). In different words, it is my opinion that a chair, a wall or even a black hole computes absolutely anything. I dare to say that people who believe such things are suffering from schizophrenia! But why is this idea of computing is everywhere so appealing to many thinkers and researchers? It seems to me this happens because it is so fascinating to say that my cup of tea computes the trajectory of a spacecraft that is located millions of light years away. Whether this has anything to do with reality or not is another story. Physics is one thing and computation is another. Clearly, computation is realized by machines that operate in our physical environment. Nevertheless, these machines have been constructed by conscious beings that what to calculate something. Nothing more, nothing less!

What is mathematics?

2010-06-04T11:20:00.000-07:00

Recently, I read in a certain forum the idea that mathematics should be identified with ZFS. Another idea discussed in the same forum is the idea that mathematics is a closed "thing". IMHO, both ideas are problematic. First of all, ZFS is one formalization of set theory, yet it is not sure whether sets are the most fundamental entity. Indeed, Mac Lane put forth the idea that categories are more fundamental than sets. Thus, it is not sure whether there is an "atom", in the sense of Democritus's atomic theory, in mathematics. The closeness of mathematics is one more absurd idea that seems to stem from finitism, which, in turn, has its root to intuitionism. Although, intuitionism was instrumental in development of certain ideas, especially in computer science, still I believe its ideas are not generally applicable. As a matter of fact, I am convinced that hypercomputation and intuitionism refute each other. Back to the closeness of mathematics. I had always the idea that, for example, complex numbers are a "proof" that mathematics is expandable. Are there any limits? No, of course not because if there are linits, then, in the end, mathematics is closed!

Can we debug the Universe?

2009-10-31T11:54:00.000-07:00

This was the title of a talk that I gave at the "Future Trends in Hypercomputation" Workshop
back in 2006. A revised version of the original paper has been posted to arXiv.org:

http://arxiv.org/abs/0910.2859

A correction

2009-10-12T09:55:00.001-07:00

Bruno Scarpellini was kind enough to point out to me a minor misprint that he discovered. In particular, on page 178 of line 11 froom above, that is, in clause (i) of definition 9.3.4, one has to replace

H(z(\lambda)) dy/d\lambda with H(z(\lambda)) dz/d\lambda,

that is, one has to replace dy with dz.

Some Thoughts on Hypercomputation

2009-10-12T05:50:00.000-07:00

Last year I wrote a "paper" on hypercomputation, but since it is not quite ready, I have posted it to the arXives. I believe the "paper" contains some interesting ideas. Anybody willing to have a look at it, can fetch an electronic copy from the following URL:

http://arxiv.org/abs/0910.1494

Impressions from SPUC09

2009-03-30T11:57:00.000-07:00

SPUC09 was an event that was organized by Mark Hogarth and Mike Stannett and it was founded by EPSRC . It attracted researchers from Computer Science, Mathematics, Physics, Biology, Artificial Intelligence, Economics, and Phylosophy. Delagates presented interesting ideas and the discussions that followed each presentation were very vivid. Personally, I had the chance to meet some new friends and to discuss with them some interesting ideas. Also, I had the chance to personally meet people with whom I had exchanged many e-mails in the past.

Black hole evaporation

2009-03-30T11:39:00.000-07:00

Recently, István Németi pointed out to me that there is an omission
in my book regarding the feasability of his relativistic hypercomputer.
In particular, the following passage

In 1974, Stephen William Hawking [80] proposed that black holes
emit thermal radiation, now known as Hawking radiation, due
to quantum effects. Thus, any black hole will vanish sometime
in the future. If Hawking radiation is indeed a real phenomenon,
then it is possible that a relativistic computer G will not be
able to finish a particular supertask it was assigned to finish.
The reason is that the black hole that the computer orbits
around might evaporate years before the computer completes its
task. Moreover, Hawking radiation should play a role in cases
in which the black hole has very small mass. For instance, a
black hole of one solar mass will evaporate in 10⁶⁷
years, while a black hole of 10¹⁶ kg will evaporate
in 3 billion years.

the word Morover should be replaced with However and the text should be augmented with a conclusion of the form

Since we are using extremelly large black holes, Hawking radiation
should not concern us, even if it is a real phenomon. In Section 5.4.1
of [140] there is a detailed discussion of Hawking radiation and
relativistic hypermachines.

Apostolos Syropoulos

"How to Program an Infinite Abacus"

2008-12-26T07:37:00.000-08:00

Joachim Lambek wrote an interesting paper entitled "How to Program an Infinite Abacus" which was published in the Canadian Mathematical Bulletin. Unfortunately, this paper is currently not available in any form. For the benefit of all those people who might like to have a look at this paper, I have prepared a transcription of this paper which is available here.

SPUC09 Conference

2008-12-10T08:21:00.000-08:00

The "Science and Philosophy of Unconventional Computing" (SPUC09) conference will take place in Cambridge,UK, March 23-25, 2009. People interested in either attending or presenting their own work should consult the conference's web page.

A comment on a comment

2008-12-01T05:14:00.000-08:00

Recently, "someone" posted a review of my book on hypercomputation on the Brains site. The reviewer argues that

This area is full of problems, some of which are physico/mathematical and some of which are conceptual. Unfortunately, from a quick sample, Syropolous's book does not avoid common mistakes and confusions—some of which I've been trying to correct in my own work.

First of all, I have to admit that back in 2004 I read a paper by this reviewer, but at that time I did not considered it interesting. However, after I read this review of my book, I read The Physical Church-Turing Thesis: Modest or Bold?, the reviewer's latest manuscript, in order to see what he meant by common mistakes and confusions and how he was trying to solve them. In this manuscript, the reviewer puts forth a number of criteria that every machine has to satisfy in order to be ``useful for physical computing.'' These criteria are:

Readable Inputs and Outputs
Process-Independent Rule
Repeatability
Resettability
Physical Constructability
Reliability

Obviously these criteria constitute a description of a feasible computing device. Unfortunately, it is obvious that these criteria are too restrictive or, to put it in another way, these criteria assume that only "modern" computers are useful physical computing devices. In particular, what for one person is readable for someone else is not readable at all (e.g., data on a computer screen are not readable by a blind person). As far it regards physical constructability, the reviewer talks about Malament-Hogarth spacetime computers and tries to prove that they are non-feasible while he ignores two important papers in the field: Non-Turing Computations Via Malament–Hogarth Space-Times and Relativistic computers and the Turing barrier.

All in all, I fail to see how he can correct the problems with such views. In addition, his view is deeply mechanistic and unfortunately too simplistic.

Hypercomputation and Physical Reality

2008-11-02T09:20:00.000-08:00

Konstantine Arkoudas argues in "Computation, hypercomputation, and physical science" why in his opinion

[T]he idea that physical science will be able to discover fundamental
computability limits is untenable.

A computation is carried out by concrete computational devices whose operation and capabilities are delimited by the laws of physics. It is one thing to argue that we have no idea what are the limits of computation and another to simple say that the limits of computation have nothing to do with physical reality. On the other hand, it is more than sure that there is a limit to what we can achieve with computing devices, but for the time being we simply do not know this limit. And this is exactly the essence of hypercomputation.

Landau levels and Riemann zeros

2008-10-01T12:19:00.000-07:00

German Sierra and Paul K. Townsend have recently presented an idea that may lead to the solution of the Riemann hypothesis. The Riemann hypothesis is a co-recursively enumerable problem (roughly, there is an algorithm that, when given an input number, eventually halts if and only if the input satisfies the problem, but no algorithm can decide if an arbitrary input satisfies the problem or not). The solution of this and other similar problems would falsify Church's Thesis. Interestingly, Fermat's last theorem and Poincaré's conjecture are co-recursively enumerable problems, nonetheless, these problems have been decided! A proof that Church's thesis is false...?

Hypercomputation Book

2008-09-23T05:20:00.000-07:00

I am really happy to announce that my book on Hypercomputation has been published by Springer. Hypercomputation is a new discipline that emerged from the ascertainment that the Church-Turing Thesis (CTT) cannot be possible true. Roughly, the CTT is about what can be computed with any real or conceptual computing device. In particular, if some function is computable, then it is definitely computable by a Turing mchine, that is, Turing's archetypal conceptual computing device. Hypercomputation, asserts that functions and numbers that cannot be computed by a Turing machine, can be computed by other more powerful computing devices. The description of such machines and their computational power is the subject of this book. In particular, the book describes the various approaches to hypercomputation in nine chapters

Introduction
On the Church–Turing Thesis
Early Hypercomputers
Infinite-Time Turing Machines
Interactive Computing
Hyperminds
Computing Real Numbers
Relativistic and Quantum Hypercomputation
Natural Computation and Hypercomputation

There are also three appendices that briefly describe some important issues:

The P = NP Hypothesis
Intractability and Hypercomputation
Socioeconomic Implications