tag:blogger.com,1999:blog-47171157209707747622018-08-30T14:38:16.712-07:00Hypercomputation.infoApostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.comBlogger63125tag:blogger.com,1999:blog-4717115720970774762.post-28586006227538822722018-08-07T07:58:00.003-07:002018-08-07T07:58:59.470-07:00 The Rolf Nevanlinna Prize<div dir="ltr" style="text-align: left;" trbidi="on">A few days ago I read that <a href="http://people.csail.mit.edu/costis/" target="_blank"> Constantinos Daskalakis</a> got the <a href="https://www.mathunion.org/imu-awards/rolf-nevanlinna-prize" target="_blank">Rolf Nevanlinna Prize</a> for<br /><blockquote class="tr_bq"> For transforming our understanding of the computational complexity of fundamental problems in markets, auctions, equilibria, and other economic structures. His work provides both efficient algorithms and limits on what can be performed efficiently in these domains.</blockquote>Thus, according to this, we now can somehow compute economies. However, even economists have started to realize that economies cannot be described with mathematics only. In fact, <a href="https://www.weforum.org/agenda/2017/08/why-economists-need-to-expand-their-knowledge-to-include-the-humanities" target="_blank">Why economists need to expand their knowledge to include the humanities</a> is a recent article that discusses exactly this problem. Daskalakis's approach is based on the assumption that humans are Turing machines. Unfortunately, they are not and this is the reason why economists fail so miserably in their predictions. Furthermore, there are some other things that people who work in computational economics "fail" to realize. For example, even if a human does not have capabilities that transcend the capabilities of the Turing machine, a human has a free will and this is definitely not computable. Yes, yes, there are physical theories that "prove" that there is no free will (in fact they prove nothing like that but somehow their assumptions lead to such a conclusion). But if we are Turing machines and there is no free will, then there is absolutely no reason to live! Our lives and our destines are known eons before our birth. Personally, I agree with Harry G. Frankfurt who wrote the following in his book entitled <a href="https://press.princeton.edu/titles/7929.html" target="_blank">On Bullshit</a>:<br /><br /><blockquote class="tr_bq">One of the most salient features of our culture is that there is so much bullshit. Everyone knows this. Each of us contributes his share. </blockquote></div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-45976886869262470822018-06-06T09:25:00.002-07:002018-07-06T03:40:24.010-07:00Everything is computable...<div dir="ltr" style="text-align: left;" trbidi="on">Recently I read an <a href="https://www.sciencenews.org/article/real-numbers-physics-free-will" target="_blank">article</a> that presented a <i>novel</i> idea by <a href="https://arxiv.org/abs/1803.06824" target="_blank">Nicolas Gisin</a>. In a nutshell, Gisin says that<br /><blockquote class="tr_bq"> only a certain number of digits of real numbers have physical meaning. After some number of digits, for example, the thousandth digit, or maybe even the billionth digit, their values are essentially random.</blockquote>This is very interesting because it means that there are no noncomputable numbers. Provided this idea is correct, we can easily decide if for example there are three 4s in the decimal expansion of π! The real problem of course is to agree on the number of significant digits. Once this problem is settled, then we can answer any question about physical real numbers. Another consequence of this idea would be that real numbers might be directly representable in even present computer hardware. What is left is to examine deeply this idea and see if it is actually valid.</div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-27081666239877637002017-04-11T13:53:00.002-07:002017-04-13T08:24:34.531-07:00A "Solution" to Riemann Hypothesis<div dir="ltr" style="text-align: left;" trbidi="on"><br /><a href="https://en.wikipedia.org/wiki/Riemann_hypothesis" target="_blank">Riemann hypothesi</a>s is "is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math>". The Riemann zeta function is conventionally represented as the sum: <br /><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><mi>ζ</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mo>∞</mo></munderover><mfrac><mn>1</mn><msup><mi>k</mi><mi>z</mi></msup></mfrac></math><br />Recently, I read in Peter Woit's <a href="https://www.math.columbia.edu/~woit/wordpress/?p=9197" target="_blank">blog</a> that some researchers have published a<a href="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.130201" target="_blank"> paper</a> that describes a Hamiltonian operator H that can be used to possibly solve this problem. This operator has the property that if the eigenfunctions obey a suitable boundary condition, then the associated eigenvalues correspond to the nontrivial zeros of the Riemann zeta function! The <a href="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.130201" target="_blank">paper</a> is also available as a <a href="https://arxiv.org/abs/1608.03679" target="_blank">preprint</a>. In a sense, this paper says that one can set up a quantum system whose evolution "solves" Riemann hypothesis. To me this is a reasonable approach to the solution of the problem. And it reminds me of the work of <a href="https://en.wikipedia.org/wiki/Leonard_Adleman" target="_blank">Leonard Adlemam</a>.</div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-29229312400628575522017-01-22T08:31:00.001-08:002017-01-22T08:31:13.963-08:00Multiverse and Computation<div dir="ltr" style="text-align: left;" trbidi="on">The idea that quantum computation is a manifestation of the multiverse is not new. For example, <a href="http://www.newyorker.com/magazine/2011/05/02/dream-machine" target="_blank">David Deutsch</a> believes that quantum computers can be used to test its existence. Personally I believe that the multiverse is good for scripts of scifi series (e.g., the <a href="https://en.wikipedia.org/wiki/Fringe_%28TV_series%29" target="_blank">Fringer</a>) but that's all. But I think that something is also logically wrong with this idea.<br /><br />Roughly, the multiverse is the idea that there many copies of our universe (or some universe) and each evolves differently, yet in each one of them there is a copy of me but all these copies are different pairwise. Obviously, at each moment many things happen that can have different outcomes so in one universe a spermatozoon fuses with an ovum while in another this never happens but in another universe a different spermatozoon fuses with it. Practically, this means that in the first universe person A will be born, in the second nothing will happen while in the third person B will be born. If all these things are quite possible (!), I wonder how and why a quantum computer would synchronize all these universes? In most of these universes there is no parallel of myself so who is going to participate in the computation that I just started?<br /><br />In my opinion, hypercomputation is the idea that we do not know enough physics to definitely say that the Turing machine dictates what can and what cannot be computed. On the other hand, the multiverse, in general, and Deutsch's ideas, are about the certitude that<br /><ul style="text-align: left;"><li>the multiverse exists</li><li>there are different forms of ourselves in parallel universes</li><li>quantum computation takes place simultaneously in a number of universes </li></ul>Some call this science but I call it pseudoscience!</div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-63839867779746682212016-02-19T12:05:00.000-08:002016-02-19T12:05:04.298-08:00Memcomputing<div dir="ltr" style="text-align: left;" trbidi="on"><a href="http://arxiv.org/abs/1405.0931" target="_blank">Memcomputing</a> is a new computing paradigm that is based on the idea that the memory can and should be used to compute. The idea is based on the functionality of the brain where neurons are used to both store information and process it. In particular the following drawing shows the way a memecomputer operates. The zigzag arrow specifies that a signal is sent. All other arrows designate flow of information.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-Txl3Pe5vtbM/VsdwSsbXhSI/AAAAAAAAA_w/_0BSrVn3HhM/s1600/memArchitecture.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="207" src="https://2.bp.blogspot.com/-Txl3Pe5vtbM/VsdwSsbXhSI/AAAAAAAAA_w/_0BSrVn3HhM/s320/memArchitecture.png" width="320" /></a></div><br />Now compare this architecture with the "traditional" von Neumann architecture:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-6svq_wx_TSU/Vsdw2LF5MEI/AAAAAAAAA_0/MkklJrwnJec/s1600/vonNeumann.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="181" src="https://1.bp.blogspot.com/-6svq_wx_TSU/Vsdw2LF5MEI/AAAAAAAAA_0/MkklJrwnJec/s320/vonNeumann.png" width="320" /></a></div>I think the difference is obvious. The interesting thing with me memcomputing is that the people who designed this computer architecture published a <a href="http://advances.sciencemag.org/content/1/6/e1500031.full" target="_blank">paper </a>where they claim that memcomputers can solve NP-complete problems. In particular, they claim that their machine can solve instances of the <i>subset sum </i>problem. This problem can be phrased as follows: Consider a finite set <i>G</i> of integers having <i>n</i> elements, is there a non-empty subset <i>K</i> of <i>G</i> whose elements sum up to<i> s</i>? As happens in this and other similar cases, a number of people com forward just to question the last claim without reconizing the general contribution of people. The <a href="http://www.scottaaronson.com/blog/?p=2212" target="_blank">Shtetl-Optimized</a> blog is such a medium. What is really annoying with such media is that their authors completely ingore Socrates's dictum: I know that I know nothing…<br /><br /><br /></div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-31219116168006820492016-02-19T06:21:00.000-08:002016-02-19T06:21:43.688-08:00Creator of EAC implementation passed away<div dir="ltr" style="text-align: left;" trbidi="on">Today I was informed that <a href="http://obits.mlive.com/obituaries/kalamazoo/obituary.aspx?page=lifestory&pid=177627505" target="_blank">Jonathan Wayne Mills</a>, the creator of an implementation of the <a href="http://www.sciencedirect.com/science/article/pii/S0167278908001231" target="_blank">Extended Analog Machine</a> passed away on January 27, 2016 at the age pf 64 after a six month fight against cancer. I am really saddened when I hear such tragic news.<br /><div id="stcpDiv" style="left: -1988px; position: absolute; top: -1999px;">on Wednesday, January 27, 2016 at the age of 64, after a six month fight against cancer. - See more at: http://obits.mlive.com/obituaries/kalamazoo/obituary.aspx?page=lifestory&pid=177627505#sthash.st1ONYH7.dpuf</div><div id="stcpDiv" style="left: -1988px; position: absolute; top: -1999px;">on Wednesday, January 27, 2016 at the age of 64, after a six month fight against cancer. - See more at: http://obits.mlive.com/obituaries/kalamazoo/obituary.aspx?page=lifestory&pid=177627505#sthash.st1ONYH7.dpuf</div><div id="stcpDiv" style="left: -1988px; position: absolute; top: -1999px;"> <hr class="NavigationDivisionLine" id="ctl00_ctl00_ContentPlaceHolder1_ContentTop_SiteNavLine" style="margin-bottom: 10px;" /> <div class="ObituaryHeader" id="ctl00_ctl00_ContentPlaceHolder1_ContentTop_obitHeader2"> <h1><span itemprop="name"><span itemprop="givenName">Jonathan</span> <span itemprop="additionalName">Wayne</span> <span itemprop="familyName">Mills</span></span></h1><div id="stcpDiv" style="left: -1988px; position: absolute; top: -1999px;"> <hr class="NavigationDivisionLine" id="ctl00_ctl00_ContentPlaceHolder1_ContentTop_SiteNavLine" style="margin-bottom: 10px;" /> <div class="ObituaryHeader" id="ctl00_ctl00_ContentPlaceHolder1_ContentTop_obitHeader2"> <h1><span itemprop="name"><span itemprop="givenName">Jonathan</span> <span itemprop="additionalName">Wayne</span> <span itemprop="familyName">Mills</span></span></h1></div></div></div></div><div id="stcpDiv" style="left: -1988px; position: absolute; top: -1999px;">Jonathan Wayne Mills</div><div id="stcpDiv" style="left: -1988px; position: absolute; top: -1999px;">Jonathan Wayne Mills</div></div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-23307192236634606132015-03-20T10:58:00.000-07:002015-03-20T10:58:14.115-07:00A solution to Thomson’s Lamp?<div dir="ltr" style="text-align: left;" trbidi="on">Today I discovered a paper that claims to offer a solution to Thomson’s Lamp.The paper is entitled <a href="http://arxiv.org/abs/1503.05847" target="_blank">Hypercomputation, Frege, Deleuze: Solving Thomson's Lamp</a>. Right now I have no time to read it and offer comments on it.</div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-8376724359275719152014-12-11T08:34:00.001-08:002014-12-11T08:35:52.591-08:00Deep Neural Networks are Easily Fooled!<div dir="ltr" style="text-align: left;" trbidi="on">In an article that was recently posted to the arXiv and is entitled <a href="http://arxiv.org/abs/1412.1897v1" target="_blank">Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images</a>, the authors discuss how Deep neural networks (DNNs) can be fooled when performing visual classification. In particular, the show how easy it is to produce images that are completely unrecognizable to humans yet that DNNs believe they are recognizable objects with 99.99% confidence...!</div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-32533544101740806992014-09-20T12:52:00.002-07:002014-09-20T12:52:56.872-07:00Transfinite Computational Conceptual Devices<div dir="ltr" style="text-align: left;" trbidi="on">A nice review of <a href="http://arxiv.org/abs/1409.5052" target="_blank">transfinite conceptual computing devices</a> by Philip Welch was posted to aRxin on September, 17. I think it would be interesting to readers to supplement the paper with a section on the (possible?) relation between these conceptual computing devices and physical reality.</div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-59947944682887000532014-08-25T13:28:00.001-07:002017-01-22T07:42:00.413-08:00Constructive Hypercomputation<div dir="ltr" style="text-align: left;" trbidi="on"><a href="http://en.wikipedia.org/wiki/Constructivism_%28mathematics%29" target="_blank">Constructivists</a> assert that one has to <b><i>construct</i></b> a mathematical object in order to show that it exists. And for some reasons they reject hypercomputation. In particular, Rasoul Ramezanian notes correctly in <a href="http://arxiv.org/abs/1408.2930" target="_blank">A Hypercomputation in Brouwer's Constructivism</a> that for Brouwer, who was the founder of the mathematical philosophy of intuitionism, something exists as long there is a <b><i>mental construction</i></b> for it and this is exactly the reason for the rejection. Some constructivists do not accept that there are infinite objects at all. In fact, some assert that there are 2<sup>1000</sup> elementary particles in the Universe and so they believe this is the largest number! To me such ideas are absurd. But Ramezanian concludes that intuitionism can co-exist with hypercomputation. Moreover, he presents his Persistent Evolutionary Turing Machines, which is a couple N = (⟨z<sub>0</sub>, z<sub>1</sub>,…, z<sub>i</sub>⟩, <i>f</i>) where z<sub>0</sub>, z<sub>1</sub>,…, z<sub>i</sub> is a growing sequence of codes of deterministic Turing machines, and <i>f </i>(called the persistently evolutionary function) is a computable partial function from Σ<sup>∗</sup>× Σ<sup>∗</sup> to Σ<sup>∗</sup>. Ramezanian demands that<i> f</i> has certain properties and from there he goes on to explore the hypercomputational capabilities of this machine.</div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-82259483383876471762014-08-25T11:49:00.001-07:002014-08-25T11:49:29.805-07:00Implementing an Analog Recurrent Neural Network<div dir="ltr" style="text-align: left;" trbidi="on">A. Steven Younger, Emmett Redd, and Hava Siegelmann published a paper entitled <a href="http://link.springer.com/chapter/10.1007%2F978-3-319-08123-6_31" target="_blank">Development of Physical Super-Turing Analog Hardware</a>, where they report their efforts to build a real hypercomputer. In particular, they present their work on the realization of Analog Recurrent Neural Networks (ARNN, for short). The theory of ARNNs is presented in <a href="http://link.springer.com/book/10.1007/978-1-4612-0707-8" target="_blank">Neural Networks and Analog Computation</a>.In a nutshel, the ARNNs are generally more powerful than Turing machines and so they are classified as hypecomputers. Younger et al. have designed and developed an OpticARNN which is depicted in the figure that follows:<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-rY3jhvzGohs/U_uD7dZ0tDI/AAAAAAAAA18/riXUCigXMFE/s1600/oARNN.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-rY3jhvzGohs/U_uD7dZ0tDI/AAAAAAAAA18/riXUCigXMFE/s1600/oARNN.jpg" height="276" width="320" /></a></div>Also, they have developed an electronic ARNN whose functional schematic follows:<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-3bE4M3Te8sg/U_uEVZ8gRLI/AAAAAAAAA2E/GgJ5nKGl-6Q/s1600/eARNN.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-3bE4M3Te8sg/U_uEVZ8gRLI/AAAAAAAAA2E/GgJ5nKGl-6Q/s1600/eARNN.jpg" height="320" width="308" /></a></div>These system have not been tested thoroughly and so one cannot draw definitive conclusions. The authors plan to build larger devices and continue their studies.<br /><br /></div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-2066643930056790702014-07-12T13:33:00.000-07:002014-07-12T13:33:09.573-07:00Hypercomputation and the Axiom of Choice<div dir="ltr" style="text-align: left;" trbidi="on">In the preface of my book on hypercomputation I have stated that all models of computation described in the book assume the axiom of choice. Instead of explaining explicitly why it is needed. I give an excerpt from Gregory H. Moore's prologue to <a href="http://store.doverpublications.com/0486488411.html" target="_blank">Zermelo's Axiom of Choice</a> in the hope that readers will understand why it is needed.<br /><blockquote class="tr_bq"> Yet without the Axiom, mathematics today would be quite different. The very nature of modern mathematics would be altered and, if the Axiom's most severe constructivist critics prevailed, mathematics would be reduced to a collection of algorithms. Indeed, the Axiom epitomizes the fundamental changes—mathematical, philosophical, and psycological—that took place when mathematicians seriously began to study infinite collections of sets.</blockquote></div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-25108099529871682072014-02-20T11:52:00.000-08:002014-02-20T11:52:15.645-08:00Is computation observer-relative?<div dir="ltr" style="text-align: left;" trbidi="on">The <a href="http://aisb50.org/the-7th-aisb-symposium-on-computing-and-philosophy-is-computation-observer-relative/" target="_blank">7th AISB Symposium on Computing and Philosophy</a> will examine whether computation is observer-related. In different words, participants will discuss whether computation is a sponteneous natural phenomenon or not. I think that computation, like art, is not a natural phenomenon. Nature is not a sculpturer or a painter, and for that matter not a programmer. To animals, a sculpture is just a stone or a piece of metal and that's all. Flowers are not beautiful or ugly: they just attract bees and other insects. Mountains are not fearsome and lakes are not picturesque. Only humans give this attributes to these physical entities. Similarly, no chair and no desk computes anything. In fact, even a computer does not compute anything unless someone would be able to interpret the result of the computation. I am sure that if one could present a computer to Aristotle he could not easily realize what kind of machine it is. </div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-14970365527142078212014-02-20T11:15:00.002-08:002014-02-20T11:15:49.585-08:00Quantum computing and mass media<div dir="ltr" style="text-align: left;" trbidi="on">In a recent issue of Time magazine there was an article about quantum computing entitled <a href="http://content.time.com/time/magazine/article/0,9171,2164806,00.html" target="_new">The Quantum Quest for a Revolutionary Computer</a>. The article describes <a href="http://www.dwavesys.com/" target="_blank">D-Wave's</a> machine and how quantum computing might affect our lives. </div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-6486315464255241192014-02-20T10:47:00.000-08:002014-02-20T10:53:28.940-08:00Superluminal Particles and Hypercomputation<div dir="ltr" style="text-align: left;" trbidi="on">Quite recently, Takaaki Musha published a book entitled <a href="https://www.lap-publishing.com/catalog/details//store/gb/book/978-3-659-51184-4/superluminal-particles-and-hypercomputation" target="_blank">Superluminal Particles and Hypercomputation</a>. I have not read the book but from the description I see that he proposes a new model of computation that is based on the existence of tachyons, that is, particles that travel faster than the light. I suppose that in <a href="http://www.uav.ro/stiinte_exacte/journal/index.php/TAMCS/article/view/87/66" target="_blank">Possibility of Hypercomputation from the Standpoint ofSuperluminal Particles</a> he presents an earlier version of his idea.</div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-70842660496440790732014-01-18T11:08:00.000-08:002014-01-18T11:08:18.580-08:00The Mathematical Universe<div dir="ltr" style="text-align: left;" trbidi="on">Today I read critical blog-post on the <a href="http://www.math.columbia.edu/~woit/wordpress/?p=6551&cpage=1" target="_blank">Mathematical Universe</a>, that is the idea that "physical reality is a mathematical structure". Of course, this idea is surprisingly similar to the idea that the universe is a computer. In a sense, one could argue that the two ideas are identical. What puzzles me the most is that both physics and computer science are following very dangerous paths… <br /> </div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-90925627136076150722013-12-13T09:40:00.002-08:002014-02-20T10:38:05.409-08:00On the Computing Spacetime<div dir="ltr" style="text-align: left;" trbidi="on"><a href="http://www.perimeterinstitute.ca/people/fotini-markopoulou-0" target="_blank">Fotini Markopoulou</a> has published a paper entitled <a href="http://arxiv.org/abs/1201.3398" target="_blank"><i>The Computing Spacetime</i></a>. The first sentence of this paper is: <i>That the Universe can be thought of as a giant computation is a straightforward corollary of the existence of a universal Turing machine</i>. This is a very bold statement, to say the least. We have absolutely no idea what are the (ultimate) laws of the universe and yet we can immediately prove that it is a gigantic computer! Now let's see the proof:<br /><blockquote>The laws of physics allow for a machine, the universal Turing machine, such that its possible motions correspond to all possible motions of all possible physical objects. That is, a universal quantum computer can simulate every physical entity and its behavior. This means that physics, the study of all possible physical systems, is isomorphic to the study of all programs that could run on a universal quantum computer. We can think of our universe as software running on a universal computer. </blockquote>First let me remark that Markopoulou confuses universal Turing machines with universal quantum computers, which means, I suppose, that she assumes that the Church-Turing thesis is valid. Second, it is known that the Turing machine operates in a Newtonian universe and naturally does not take under consideration any quantum phenomena. Third, to say that physics is essentially equivalent to the study of quantum programming is a fallacy because we have no idea what are the ultimate laws of universe. Unless, of course, we assume that <a href="http://hypercomputation.blogspot.gr/2013/12/fairytale-physics.html" target="_blank">fairytale physics</a> is real physics. In this case, it is crystal clear that we are talking nonsense.<br /><br />As with fairytale physics, the problem with the the-Universe-is-a-computer paradigm is that there is no experimental evidence that actually the universe computes something. In fact, I am pretty sure that this is something like an <a href="http://christianity.about.com/od/endtimestopicalstudy/a/JZ-Illuminati-Conspiracy.htm" target="_blank">Illuminati conspiracy theory</a> rather than a real scientific theory. Naturally, please bear on mind that the problem of quantifying gravity has not been solved yet.<br /><br />PS Today (20/02/2014) I discovered a preprint entitled <a href="http://arxiv.org/abs/1211.7081" target="_blank">The Universe is not a Computer</a>. In this paper the author puts forth an interesting argument against the validity of the idea that the universe is a computer.</div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-91788319783314751682013-12-10T09:57:00.001-08:002014-04-13T10:40:07.683-07:00Fairytale Physics<div dir="ltr" style="text-align: left;" trbidi="on">Jim Baggot in his recent book that is entitled <a href="http://www.amazon.co.uk/Farewell-Reality-Fairytale-Physics-Scientific/dp/1780334923" target="_blank"><i>Farewell to Reality: How Fairytale Physics Betrays the Search for Scientific Truth</i></a> advocates the idea that modern physics is going in the wrong direction. In particular, he critically examines superstring theory and concludes that this theory cannot explain the existence of many things we know they exist! Similar ideas have been presented in Peter Woit's <a href="http://www.amazon.co.uk/Not-Even-Wrong-Continuing-Challenge/dp/0099488647/ref=sr_1_1?s=books&ie=UTF8&qid=1386697384&sr=1-1&keywords=Not+even+wrong" target="_blank"><i>Not Even Wrong: The Failure of String Theory and the Continuing Challenge to Unify the Laws of Physics</i></a>. Recently, the British newspaper <a href="http://www.theguardian.com/" target="_blank">The Guardian</a> has published as <a href="http://www.guardian.co.uk/science/2013/jun/16/has-physics-gone-too-far" target="_blank">debate</a> between Baggot and string theorist Mike Duff. The later replied to Baggot's remark that "the positron was discovered in cosmic ray experiments just a couple of years after Dirac had agreed that this was what his theory predicted" as follows: <br /><blockquote>Dirac did not <i>assume</i> the positron; he <i>discovered</i> it to be a consequence of an equation that described the well-established electron. Similarly, string theorists did not assume supersymmetry, extra dimensions, the dualities of M-theory or the myriad possible universes; they discovered them to be consequences of a theory that subsumes empirically well-established features such as general relativity, gauge field theory and chiral quarks and leptons. Current research is devoted to finding out what else M-theory requires.</blockquote> The problem with Duff's argument is that none of the things superstring theory has been speculating about have been discovered! In fact, there are not even indirect evidence that might one lead to the conclusion that these bizarre things exist. (They do exist in <a href="http://en.wikipedia.org/wiki/Fringe_%28TV_series%29" target="_blank">Fringe's</a> universe…)<br /><br />One may wonder what all these have to do with computation. The answer, of course, is quite simple: when one proposes a bizarre model of computation she must make sure that the physics involved is valid beyond any doubt!<br /><br />PS On the 20th episode of season 7 of <a href="http://the-big-bang-theory.com/" target="_blank">The Big Bang Theory</a>, Sheldon wonders: <a href="http://bigbangtheory.wikia.com/wiki/The_Relationship_Diremption" target="_blank">"Am I wasting my life on a theory that can never be proven?"</a> and decides to stop his work on string theory... (I read about this in the <a href="http://www.math.columbia.edu/~woit/wordpress/?p=6832" target="_blank">Not Even Wrong</a> blog).</div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-2991365046830462132013-11-14T09:11:00.002-08:002013-11-14T09:13:04.145-08:00New book on the Theory of Fuzzy Computation<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: center;"><a href="http://link.springer.com/book/10.1007%2F978-1-4614-8379-3" target="_blank"><img alt="http://link.springer.com/book/10.1007%2F978-1-4614-8379-3" border="0" height="292" src="http://2.bp.blogspot.com/-glC4dqo7fI4/UoUDQ_EQxtI/AAAAAAAAAoI/k78pjkP8114/s400/TFC.png" width="400" /></a></div><br />I am really happy to announce the publication of my book on the theory of fuzzy computation. The book is available as an eBook and as a hardback. Readers can freely read <a href="http://link.springer.com/content/pdf/bfm%3A978-1-4614-8379-3%2F1.pdf" target="_blank">the preface and the book's table of contents</a>.</div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-9543722340265935092013-11-10T04:37:00.001-08:002013-11-10T04:37:53.718-08:00On Computation<div dir="ltr" style="text-align: left;" trbidi="on">In an old <a href="http://hypercomputation.blogspot.gr/2008/12/comment-on-comment.html" target="_blank">entry</a> of this blog, I had criticised a blog post who was a review of my book. The author of that review posted a new post entitled <a href="http://philosophyofbrains.com/2012/06/22/deflating-hypercomputation.aspx" target="_blank">Deflating Hypercomputation</a>, where he advertizes his paper <a href="http://bjps.oxfordjournals.org/content/62/4/733.abstract" target="_blank"><i>The Physical Church–Turing Thesis: Modest or Bold?</i></a> This paper is a defense of a "modest version of the Physical Church-Turing thesis":<br /><blockquote>Any function that is physically computable is Turing computable.</blockquote>The next question is, of course, what is meant by<i> physical computable</i>? Gualtiero Piccinini, that is, the author of this paper, proposes that "if a physical process is a computation, it can be used by a finite observer to obtain the desired values of a function". Now, finite observers are "human beings and any other intelligent beings of similarly bounded capacities". In an explanation of this description, he includes among observers beings that are located in spacetimes that are (currently?) inaccessible to humans (so hypercomputation near a black hole is not a fantasy!). Physical processes must be <i>executable</i>, <i>automatic</i>, <i>uniform</i>, and <i>reliable</i> in order to be usable. In particular, <br /><ul style="text-align: left;"><li><b>executable</b> means that the process can be started by the observer to generate results;</li><li><b>automatic</b> means that the process is mechanical;</li><li><b>uniform</b> means that the process is the same for different inputs; and</li><li>reliable means that it generates correct results in the course of execution. </li></ul>Then he proposes some other sub-criteria that should be used to define the notion of physical process. However, this definition is surprisingly similar to the definition of an algorithm that follows and which is borrowed from <a href="http://dl.acm.org/citation.cfm?id=2801" target="_blank">Fundamentals of data structures in PASCAL</a>: <br /><blockquote><b>Definition</b> An algorithm is a finite set of instructions that if followed, accomplish a particular task. In addition, every algorithm must satisfy the following criteria:<br /><ol><li><i>input</i>: there are zero or more quantities that are externally supplied;</li><li><i>output</i>: at least one quantity is produced;</li><li><i>definiteness</i>: each instruction must be clear and unambiguous;</li><li><i>finiteness</i>: if we trace out the instructions of an algorithm, then for all cases the algorithm will terminate after a finite number of steps;</li><li><i>effectiveness</i>: every instruction must be sufficiently basic that it can in principle be carried out by a person using only pencil and paper. It is not enough that each operation be <i>defined</i>, but it must also be feasible.</li></ol></blockquote>In different words, he is not proposing something entirely new. Now in my book I had used the following definition of computation, which I have borrowed from <a href="http://link.springer.com/article/10.1007/BF00974165" target="_blank">Computation is just interpretable symbol manipulation; cognition isn't</a>: <br /><blockquote><b>Definition</b> Computation is an implementation-independent, systematically interpretable, symbol manipulation process. </blockquote>Obviously, this definition is far more general and it can be applied in cases where Piccinini's formulation fails. Also, I have used this definition to rule out "computing" walls and stones as genuine computing devices. In conclusion, Piccinini "response" shows that he did not actually read the book. </div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-38048632363463951842013-09-07T08:41:00.002-07:002013-09-07T08:41:59.058-07:00A quantum computer for everyone!<div dir="ltr" style="text-align: left;" trbidi="on">People who would like to run programs for quantum computers have now the chance to use a real conventional quantum computer! Just point your browser to the <a href="http://www.bristol.ac.uk/physics/research/quantum/qcloud" target="_blank">Qcloud</a>! This is a service offered by the <a href="http://www.bristol.ac.uk/physics/" target="_blank">School of Physics of the University of Bristol, UK</a>. </div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-56421380237272990802013-07-04T14:13:00.006-07:002013-07-04T14:15:50.471-07:00 Infinite computations with random oracles<div dir="ltr" style="text-align: left;" trbidi="on">Merlin Carl and Philipp Schlicht have posted an article to the arXiv entitled <a href="http://arxiv.org/abs/1307.0160" target="_blank">infinite computations with random oracles</a>. A basic result of classical computability theory states that if a real x is Turing-computable relative to all oracles in a set of positive measure, then this real number is Turing-computable in the empty oracle. In different words, the use of random generators does not enrich the set of computable functions. The authors examine whether this is true for models of infinite computation. In particular, for Infinite Time Turing Machine, Infinite Time Register machines, α-Turing machines, and ordinal Turing/register machines, the authors ask whether there are noncomputable reals (in the sense of the machine type) that are reducible to all oracles in a set of positive measure. The authors show that the answer is negative for most models of infinite computation.</div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-47074400377282634152013-06-16T11:57:00.003-07:002013-06-16T11:57:51.312-07:00Quantum Computing and… Democritus<div dir="ltr" style="text-align: left;" trbidi="on">Yesterday I noticed that there is a new book entitled <a href="http://www.amazon.com/Quantum-Computing-since-Democritus-Aaronson/dp/0521199565/ref=sr_1_1?ie=UTF8&qid=1371406758&sr=8-1&keywords=Democritus" target="_blank">Quantum Computing since Democritus</a>. I haven't read the book but from what I have seen, it seems that it is a presentation of the field of quantum computing in a colloquial language (Democritus is called a <i>dude</i>!). What is really interesting is one of the <a href="http://www.amazon.com/review/R2NDP5WIYUVSUR/ref=cm_cd_pg_next?ie=UTF8&asin=B00B4V6IZK&cdForum=Fx20RU8CN5UFOLS&cdPage=3&cdThread=Tx2TUMV6VIUJK3&store=digital-text#wasThisHelpful" target="_blank">reviews</a> posted at amazon's web page. The review is by some one called Guy Wilson but it seems that Guy Wilson is actually <a href="http://www.amazon.com/Joy-Christian/e/B007T8VISY/ref=sr_tc_2_0?qid=1371407329&sr=1-2-ent" target="_blank">Joy Christian</a>. Christian does not really believe that it will possible to build scalable quantum computers.<br /><br />First of all, it is true that one cannot go to a computer shop and buy a quantum computer today, but this does not mean that there are no quantum computers. For example, Google <a href="http://bits.blogs.nytimes.com/2013/05/16/google-buys-a-quantum-computer/" target="_blank">bought</a> a quantum computer recently. But Christian argues that he has <a href="http://letterstonature.wordpress.com/2007/11/23/did-the-universe-just-get-less-wierd/" target="_blank">disproved</a> <a href="http://plato.stanford.edu/entries/bell-theorem/" target="_blank">Bell's theorem</a>, which, roughly speaking, implies that it is not possible to build scalable quantum computers.<br /><br />Unfortunately, in a way the situation looks familiar–just because someone has built a career on something, it doesn't mean quantum computing, or hypercomputation for that matter, is nonsense! And this is something the author of the book should not forget!<br /><br />PS Frankly, I don't understand what's the connection between quantum computing and Democritus, but then again I haven't read the book…</div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-58074423801114856262013-05-07T13:35:00.002-07:002013-09-23T10:13:57.984-07:00Creating a Mind<div dir="ltr" style="text-align: left;" trbidi="on">Recently, I read a <a href="http://www.nybooks.com/articles/archives/2013/mar/21/homunculism/?page=1" target="_blank">review</a> by Colin McGinn of <a href="http://en.wikipedia.org/wiki/Ray_Kurzweil" target="_blank">Ray Kurzweil's</a> <a href="http://www.amazon.com/gp/product/0670025291?ie=UTF8&tag=thneyoreofbo-20&linkCode=as2&camp=1789&creative=9325&creativeASIN=0670025291" target="_blank">How to Create a Mind: The Secret of Human Thought Revealed</a>. According to McGinn, the book reveals, at last, the secret of human thought which is pattern recognition! Kurzweil argues that one needs to build a machine that recognizes patterns in order to create a mind. Personally, I find this idea extremely naive because pattern recognition is just one of mind's many functions. On the other side, McGinn says that "the brain is causally connected to the mind and the mind contains and processes information", which seems bizarre. I always thought that the brain induces the mind but this statement implies that the brain and the mind are two separate entities. What is even more bizarre are reviews of the book like this:<br /><br /><blockquote>Ray Kurzweil's understanding of the brain and artificial intelligence will dramatically impact every aspect of our lives, every industry on Earth, and how we think about our future. If you care about any of these, read this book!</blockquote>So we are living in a new era where Kurzweil's theory will change our life. Are we serious? Scanners are going to profoundly change our life? One reader posted the following to amazon's site:<br /><blockquote>In "How To Create a Mind," Ray Kurzweil offers a fascinating and readable overview of his theory of how the human brain works, as well as a road map for the future of artificial intelligence.</blockquote>Really? Well, sometimes I wonder whether some people are getting paid to say such bullshit! All in all, I fully agree with McGinn's review and yes I do not believe there will be dramatic changes in our life because of Kurzweil's theory.<br /><br />PS In June 2012, the <a href="http://www.worldscientific.com/worldscinet/ijmc" target="_blank">International Journal of Machine Consciousness</a> published a <a href="http://www.worldscientific.com/doi/abs/10.1142/S1793843012020015" target="_blank">special issue</a> (Volume 04, Issue 01) on mind uploading. Currently, the contents of the issue are freely available.</div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0tag:blogger.com,1999:blog-4717115720970774762.post-16636798434772727872013-05-05T14:28:00.001-07:002013-05-05T14:28:07.403-07:00Oracle Machines and the Verification Problem<div dir="ltr" style="text-align: left;" trbidi="on">Florent Franchette presented an interesting problem in his "<a href="http://link.springer.com/chapter/10.1007%2F978-3-642-37225-4_13" target="_blank">Oracle Hypermachines Faced with the Verification Problem</a>". Franchette argues that a physical oracle machine cannot be used to prove that physical hypercomputers exist simply because we cannot verify the results computed by the machine. However, an answer to what can be computed by a form of oracle Turing machine is described in "<a href="http://rspa.royalsocietypublishing.org/content/464/2098/2777.full.pdf+html?sid=ebfa4bbc-8d16-499b-b7e0-37b8097cdae6" target="_blank">Computational complexity with experiments as oracles</a>" (see also "<a href="http://rspa.royalsocietypublishing.org/content/465/2105/1453.full.pdf+html?sid=ebfa4bbc-8d16-499b-b7e0-37b8097cdae6" target="_blank">Computational complexity with experiments as oracles. II. Upper bounds</a>"). Roughly, their oracle machine, which is called an analog-digital Turing machine, is an ordinary Turing machine coupled to an <i>abstract </i>physical experiment. The authors of these papers prove that this machines have computational power that goes beyond the Church-Turing barrier. Now, if one proves that a machine is actually a hypercomputer, then I think there is no need to verify results computed. After all, we trust the results computed by ordinary machines, so why shouldn't we trust the results computed by a hypercomputer?</div>Apostolos Syropouloshttp://www.blogger.com/profile/10707402947027857776noreply@blogger.com0