User talk:D.Lazard

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Turing thesis[edit]

I don't edit so much anymore, and I don't plan to undo your edit, but on the Turing thesis article, the key to Turing's conception of computability was indeed the idea of a human working algorithmically with pencil and paper. Indeed, the key point of Turing's 1936 paper [1] was section 9, where he analyzed the work of a human computer (at the time, "computer" referred to a human doing computing), and argued that any algorithm that could be computed by a human could be computed by a Turing machine. The key reason that Turing machines are of interest, compared to other models such as Church's λ calculus, is that Turing machines allowed Turing to make this philosophical argument (referring to "states of mind", etc.) that his formal notion of computable functions captured all the functions that a human could algorithmically compute. Without that argument, Turing would not have been able to claim a solution to the Entscheidungsproblem, which is about human, rather than mechanical, computation. — Carl (CBM · talk) 01:34, 20 June 2015 (UTC)

To CBM:: I think that we are both right (or both wrong). In fact, as it is frequently the case for mathematical breakthroughs, one has to distinguish between the (philosophical ?) interpretation of the result by the original authors, and the present scientific status of the same result. What I have tried to explain is what is called "Church–Turing thesis" in modern textbooks on computability, a subarea of computer science. It is clear that the modern point of view on the thesis is not the same as that of Turing, which, itself may differ from that of Church. Nevertheless, the use of the word "machine" by Turing shows that the mechanical aspect of computability was present in his though. I'll look on Turing paper to try to find a formulation that is compatible with both original Turing thought and the modern concept of Church–Turing thesis. D.Lazard (talk) 04:44, 20 June 2015 (UTC)
What I was stating is the modern interpretation of the result; I work in computability theory myself. The Stanford Encyclopedia article [2] treats "mechanical" and "effective" as synonyms, and defines them in terms of a human with pencil and paper. That article spends significant space on the difference between Turing's thesis that Turing machines capture all algorithmic human computation, and the stronger thesis that Turing machines capture all machine computation. I would also recommend section 3 of Soare's well known paper Computability and Recursion [3]. — Carl (CBM · talk) 12:35, 20 June 2015 (UTC)

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Send on behalf of The Wikipedia Library using MediaWiki message delivery (talk) 04:31, 7 July 2015 (UTC)

Opened a dispute resolution request for the Oder of a polynomial article[edit]

I've opened a dispute resolution request for the Order of a polynomial edit dispute you're trying to start. Please contribute to the discussion in Wikipedia:Dispute resolution noticeboard#Talk:Order of a polynomial.23Disambiguating -- Mecanismo | Talk 15:20, 21 August 2015 (UTC)

Addition (Code)[edit]

Hey there. The point of the code is to show how addition is implemented in C code in a manner that is representitive of what is going on in hardware (i.e. using AND and XOR bitwise manipulations). In my original edit, I had an "as shown below" comment on this in the text, but it looks like it was deleted by another user which put the code example out of context. I have added this so it reads:

"In practice, comutational addition may achieved via XOR and AND bitwise logical operations in conjunction with bitshift operations as outlined in the C code below. "

I think it is perhaps interesting for people to see how addition is actually implemented both in software and in hardware (i.e. unrevelling the + operator). This is really basic computer science which I feel gives value to the article as it shows a critial link between software and hardware (without going into assembly). — Preceding unsigned comment added by Mwchalmers (talkcontribs) 14:59, 16 September 2015 (UTC) --Mwchalmers (talk) 15:07, 16 September 2015 (UTC)

To Mwchalmers: Please put new sections in talk page at bottom (or use "New section" button at the top of the page. Also, please your posts with four tilde (~~~~).
I have answered in advance on Talk: Addition#addition on computers
Bitwise addition in never implemented in software (except, may be, as exercise for beginners), as hardware addition is dramatically faster.
The algorithm, not the C code, may be interesting here. The Wikipedia guidelines (see MOS:CODE and MOS:ALGO) ask to write algorithms in pseudo-code, not in any specific programming language. This is specially worth here, as bitwise addition is never programmed in any programming language (except by software for designing hardware, that may be viewed as programming languages compiled into hardware). So, please, rewrite the algorithm in pseudo-code, instead of reverting. D.Lazard (talk) 15:59, 16 September 2015 (UTC)

I see your point in going with pseudocode, as the algorithm, not the C, is what is interesting here. I have written some pseudocode with comments which works well with the full-adder circuit shown in the section. I think it really adds to the section to have a pseudocode as people often associate code with computing. It is nice to provide some intuitive link between how an algorithm in code and an algoritm in hardware. I have also labeled the carry specifically as well as where the XOR and AND operations appear in the code. I have included both the iterative and recursive versions, which is interesting in itself as it implies a connection between iteration and recursion. Feel free to make changes to the pseudocode if you think it is still too C-like or the comments are too sparse. Somehow it should be clear that integer addition is implied. Mwchalmers (talk) 10:31, 17 September 2015 (UTC)