Dijkstra's Rallying Cry for Generalization - Research
https://dijkstrascry.com/taxonomy/term/6
enAn Exercise in Unplugging the Church-Turing Thesis [Part 1]
https://dijkstrascry.com/CTT
<div class="field field-name-body field-type-text-with-summary field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even" property="content:encoded"><p style="text-align: justify;">The year 2018 has been very productive: the attached pdf file contains my latest research findings, which pertain to the Church-Turing Thesis. The paper is under peer review. Its abstract follows.</p>
<h3>Abstract</h3>
<p style="text-indent: 0px; margin: 0px; text-align: justify;">Resorting solely to concepts from classical computability theory, I provide mathematical arguments to doubt — if not dismiss, on an objective basis — the Church-Turing Thesis. Defending the thesis amounts to believing that "any process which could naturally be called an effective procedure can be realized by a Turing machine'' (Minsky, 1967). Specifically, I present a natural modification of the "Turing machine'' model of computation, called the "Alternative Deterministic Machine'' model (or ADM for short). The relevance of this new model hinges on the following observation: Turing machines have a lower model fidelity than ADM's with regard to human (and electronic) computers. Both a Turing machine and an ADM model a human computer who contributes to her research community by publishing mathematical findings. But, in reality, humans publish in a piecemeal fashion, rather than all in one go. Turing machines, as formally defined by Hopcroft & Ullman (1979), do not capture this particular trait of human activity, while ADM's do. To recapitulate in technical terms: a Turing machine provides meaningful output (for the outside world to see) instantly, after having halted, while an ADM provides meaningful output (to its environment) incrementally, before possibly halting. This distinction will allow me to (i) prove that Turing machines partially compute less functions on the naturals than ADM's, and (ii) prescribe an ADM-based method to generate a subset of the naturals that is not computably enumerable. I shall furthermore discuss multiple ways to generalize the ADM model. This discussion will lead to a new incentive, based on a <em>mathematician-as-typewriter</em> metaphor, to embrace even more powerful models of computation — i.e., the so-called "eventually correct machines'' in the literature — as natural formalizations of algorithms.</p>
<p style="text-indent: 0px; margin: 0px; text-align: justify;"> </p>
<h3 style="text-indent: 0px; margin: 0px; text-align: justify;">Errata (since January 2019)</h3>
<ul><li>21 January 2019:<br /><ol><li>Bottom of page 2: "then M can print one more output symbol ..." --> "then V can print one more output symbol ..."</li>
<li>Page 8: Ignore the itemized statement "Knowledge of all (x,f(x)) pairs will still not suffice ...", for I have proved a stronger result in the paper. The same remark holds for the similar statement made on page 32.</li>
</ol></li>
<li>7 February 2019:
<ol><li>I often write <M_d, w_d> instead of <M_d, w_e>. This type of error is easy to correct, e.g. in the proofs of Theorems 25 and 59, and in the proof on page 39.</li>
</ol></li>
<li>21 February 2019:
<ol><li>In the proof of Th.25, I implicitly assume that strings 0, 00, and 01 represent unique naturals. The proof can be generalized so that this assumption need not be made.</li>
<li>The second clause of Def.4 on p.12 needs to be: "f(x) = undefined <em>otherwise</em>". As a result, some proofs need minor changes.</li>
<li>Most annoying is Def.17, which needs a drastic change. As a result, Lemma 21 needs to be weakened.</li>
</ol></li>
</ul></div></div></div><section class="field field-name-field-pdf field-type-file field-label-above view-mode-rss"><h2 class="field-label">PDF: </h2><div class="field-items"><div class="field-item even"><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="https://dijkstrascry.com/sites/default/files/papers/DaylightCTTsabamDec2018.pdf" type="application/pdf; length=699165">DaylightCTTsabamDec2018.pdf</a></span></div></div></section><section class="field field-name-field-tags field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">Tags: </h2><ul class="field-items"><li class="field-item even"><a href="/category-mistakes" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Category Mistakes</a></li><li class="field-item odd"><a href="/taxonomy/term/15" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Turing centenary</a></li><li class="field-item even"><a href="/taxonomy/term/3" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">paper</a></li><li class="field-item odd"><a href="/taxonomy/term/6" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Research</a></li></ul></section>Tue, 18 Dec 2018 08:45:38 +0000egdaylight168 at https://dijkstrascry.comhttps://dijkstrascry.com/CTT#commentsWhy Did Computer Science Make a Hero out of Turing?
https://dijkstrascry.com/Bullynck2015draft
<div class="field field-name-body field-type-text-with-summary field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even" property="content:encoded"><p>Draft version of a paper that will appear in March 2015 in the Communications of the ACM.</p>
<p>Authors: Bullynck, Daylight, De Mol.</p>
</div></div></div><section class="field field-name-field-pdf field-type-file field-label-above view-mode-rss"><h2 class="field-label">PDF: </h2><div class="field-items"><div class="field-item even"><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="https://dijkstrascry.com/sites/default/files/papers/BullynckDaylightDeMolCACM2015draft.pdf" type="application/pdf; length=155170">BullynckDaylightDeMolCACM2015draft.pdf</a></span></div></div></section><section class="field field-name-field-tags field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">Tags: </h2><ul class="field-items"><li class="field-item even"><a href="/taxonomy/term/15" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Turing centenary</a></li><li class="field-item odd"><a href="/taxonomy/term/3" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">paper</a></li><li class="field-item even"><a href="/taxonomy/term/6" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Research</a></li></ul></section>Tue, 13 Jan 2015 19:38:42 +0000egdaylight128 at https://dijkstrascry.comhttps://dijkstrascry.com/Bullynck2015draft#commentsTowards The Origins of Computational Complexity
https://dijkstrascry.com/essay2014
<div class="field field-name-body field-type-text-with-summary field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even" property="content:encoded"><p>One of my students at Utrecht University reflected during the spring of 2014 on the origins of computational complexity. She has given me permission to publish her beautiful essay here (anonymously).</p>
<p>Her chosen research topic is a difficult one to address. But, by presenting a pluralistic account in which she <a href="/DifficultTuringLegacy">lets her historical actors tell the story</a> (Cobham, Hartmanis, Rabin, Blum), she has succeeded in conveying technical information to an audience that need not be versed in complexity theory per se.</p>
</div></div></div><section class="field field-name-field-pdf field-type-file field-label-above view-mode-rss"><h2 class="field-label">PDF: </h2><div class="field-items"><div class="field-item even"><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="https://dijkstrascry.com/sites/default/files/papers/nEssay.pdf" type="application/pdf; length=718875">nEssay.pdf</a></span></div></div></section><section class="field field-name-field-tags field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">Tags: </h2><ul class="field-items"><li class="field-item even"><a href="/taxonomy/term/15" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Turing centenary</a></li><li class="field-item odd"><a href="/taxonomy/term/3" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">paper</a></li><li class="field-item even"><a href="/taxonomy/term/6" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Research</a></li></ul></section>Mon, 30 Jun 2014 13:49:35 +0000egdaylight124 at https://dijkstrascry.comhttps://dijkstrascry.com/essay2014#commentsTuring — the Father of Computer Science
https://dijkstrascry.com/TuringPaper
<div class="field field-name-body field-type-text-with-summary field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even" property="content:encoded"><p><em>Towards a Historical Notion of "Turing </em><em>— the Father of Computer Science"</em> is Edgar Daylight's Original Manuscript of an article submitted for consideration in the journal <a href="http://www.tandfonline.com/toc/thpl20/current#.UhOGjCD8I2w"><em>History and Philosophy of Logic</em></a>, copyright protected by <em>E.G. Daylight</em>.</p>
<p>A preprint of the article is available <a href="http://www.dijkstrascry.com/sites/default/files/papers/Daylightpaper91.pdf">via this pdf link</a>. The official publication <a href="http://www.tandfonline.com/doi/full/10.1080/01445340.2015.1082050#.Vj-wlr-yJME">is available here</a>.</p>
<p><strong>From the abstract:</strong></p>
<p>In the popular imagination, the relevance of Turing's theoretical ideas to people producing actual machines was significant and appreciated by everybody involved in computing from the moment he published his 1936 paper `On Computable Numbers'.</p>
<p>Careful historians are aware that this popular conception is deeply misleading. We know from previous work by Campbell-Kelly, Aspray, Akera, Olley, Priestley, Daylight, Mounier-Kuhn, and others that several computing pioneers, including Aiken, Eckert, Mauchly, and Zuse, did not depend on (let alone were they aware of) Turing's 1936 universal-machine concept. Furthermore, it is not clear whether any substance in von Neumann's celebrated 1945 `First Draft Report on the EDVAC' is influenced in any identifiable way by Turing's work. This raises the questions:</p>
<ol><li>When does Turing enter the field?</li>
<li>Why did the Association for Computing Machinery (ACM) honor Turing by associating his name to ACM's most prestigious award, the Turing Award? </li>
</ol><p>Previous authors have been rather vague about these questions, suggesting some date between 1950 and the early 1960s as the point at which Turing is retroactively integrated into the foundations of computing and associating him in some way with the movement to develop something that people call computer science.</p>
<p>In this paper, based on detailed examination of hitherto overlooked primary sources, attempts are made to reconstruct networks of scholars and ideas prevalent to the 1950s, and to identify a specific group of ACM actors interested in theorizing about computations in computers and attracted to the idea of language as a frame in which to understand computation.</p>
<p>By going back to Turing's 1936 paper and, more importantly, to re-cast versions of Turing's work published during the 1950s (Rosenbloom, Kleene, Markov), I identify the factors that make this group of scholars particularly interested in Turing's work and provided the original vector by which Turing became to be appreciated in retrospect as the father of computer science.</p>
<p><strong> </strong></p>
<p><strong> </strong></p>
</div></div></div><section class="field field-name-field-pdf field-type-file field-label-above view-mode-rss"><h2 class="field-label">PDF: </h2><div class="field-items"><div class="field-item even"><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="https://dijkstrascry.com/sites/default/files/papers/Daylightpaper91.pdf" type="application/pdf; length=350076">Daylightpaper91.pdf</a></span></div></div></section><section class="field field-name-field-tags field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">Tags: </h2><ul class="field-items"><li class="field-item even"><a href="/taxonomy/term/15" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Turing centenary</a></li><li class="field-item odd"><a href="/taxonomy/term/3" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">paper</a></li><li class="field-item even"><a href="/taxonomy/term/6" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Research</a></li></ul></section>Tue, 20 Aug 2013 09:35:02 +0000egdaylight118 at https://dijkstrascry.comhttps://dijkstrascry.com/TuringPaper#comments