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In Scott Aaronson's answer to my question about the Extended Church-Turing Thesis, he says

I don't see how talking about "proofs" of the CT or ECT adds much light to this discussion. Such "proofs" tend to be exactly as good as the assumptions they rest on---in other words, as what they take words like "computation" or "efficient computation" to mean. So then why not proceed right away to a discussion of the assumptions, and dispense with the word "proof"?

I would like to start a "discussion of the assumptions," or a question like, "What are the right axioms for the notion of computation and algorithm." I would probably seed it with the list of axioms Dershowitz and co-authors use to prove Church-Turing Thesis, or Extended Church-Turing Thesis.

So my meta-question is this: where would the best venue be for this? It seems as though it would be a natural candidate for a blog entry, but perhaps it would be better as a community wiki on the main site, so people could vote up and down axioms/intuitions that resonated, or didn't. Any preferences/suggestions?

EDIT: thanks everyone for your input. I will ask a question, but probably next week. I don't have time to shepherd a question for the next several days.

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  • $\begingroup$ Might make an interesting blog post. Might generate an interesting discussion in the comments. $\endgroup$ Jul 29 '11 at 20:58
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A subjective question is not bad by itself but I would prefer if we don't get an opinion poll question about the suitable axioms. It would be better if you phrase it in a way that is more objective and/or a good subjective question:

Guidelines for Great Subjective Questions

  1. Great subjective questions inspire answers that explain “why” and “how”. The best subjective questions invite explanation. If you’re asking for a product recommendation of some kind, you want answers to contain detailed information about the features and how they can be used, and why you might want to choose one over the other. “How?” and “Why?” has more lasting value than a bunch of product-feature bullet points or a giant enumerated list, no matter how extensive. In contrast, the bad subjective questions let answerers get away with hit-and-run answers that maybe provide a name and a link — but fail to provide any sort of adequate explanation, context, or background.

  2. Great subjective questions tend to have long, not short, answers. The best subjective questions inspire your peers to share their actual experiences, not just post a mindless one-liner or cartoon in hopes of being rewarded with upvotes for being merely “first.” Sharing an experience takes at least one paragraph; ideally several paragraphs. If I’m asking about how to bake cookies, don’t give me a list of grocery items: milk. butter. vanilla. eggs. There is virtually nothing I can learn from a short, static list of grocery items that make up a recipe. Instead, tell me what happened the last time you made cookies from that recipe! Share your detailed experiences, so that we all might learn from them.

  3. Great subjective questions have a constructive, fair, and impartial tone. The best subjective questions avoid the all too seductive route of ranting and flamebait. They set the right tone of constructive learning and collaboration from the very outset, by emphasizing that we’re all here to learn from each other, even if we have different viewpoints or beliefs about the right way to handle what are inherently subjective decisions. We’re not here to fight each other; that’s an enormous waste of everyone’s time. There is always more than one right way.

  4. Great subjective questions invite sharing experiences over opinions. Certainly experiences inform opinions, but the best subjective questions unabashedly and unashamedly prioritize sharing actual experiences over random opinions. It’s more useful to share with us what you’ve done than what you think. Everyone has an opinon. It takes zero effort or imagination to have an opinion about anything and everything. But people who have done things, real things in the world, and have the scars and arrows in their back to show for it — now that’s worth sharing. You should be uniquely qualified to have your opinion based on the specific experiences you had. And you should share those experiences, and more specifically what you learned from your experiences, with us!

  5. Great subjective questions insist that opinion be backed up with facts and references. Opinion isn’t all bad, so long as it’s backed up with something other than “because I’m an expert”, or “because I said so”, or “just because”. Use your specific experiences to back up your opinions, as above, or point to some research you’ve done on the web or elsewhere that provides evidence to support your claims. We like you. We want to believe you. But like wikipedia itself, {{citation needed}}. And good subjective questions make this clear from the outset: back it up!

  6. Great subjective questions are more than just mindless social fun. The best subjective questions avoid the social pitfalls of “Getting To Know You” (GTKY) and mindless entertainment. Sometimes people just want to poll a community for ideas that might help solve a problem (best book, best approach). These can be okay when there is actual knowledge in the collection of answers. What isn’t okay are the social bonding questions which are designed just to impress others, such as “What is the coolest/stupidest/weirdest/funniest thing you saw/did/tasted today?”, or questions where the site’s actual topic is tacked on as a token afterthought, such as “Favorite food for programmers.” If you removed the “for programmers” part of this question, is it really unique to our profession? Could an average member of our community reasonably be expected to learn something that makes them better at their job from this question? If not, then it’s a bad subjective question.

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  • $\begingroup$ ps: I hope that after posting the question and receiving answer, you will also write a blog post about it. :) $\endgroup$
    – Kaveh
    Jul 29 '11 at 18:54
  • $\begingroup$ Hi Kaveh, I am a bit confused by your answer here. Suppose I posted the axioms of ZF, and 100 people upvoted the Axiom of Infinity but only 5 people upvoted the Axiom of Replacement, and 23 people contributed their own axioms, or links to other axiom sets like Hilbert/Bernays. What would be the problem with that? My own concern (and, I think, that of @Suresh, if I read him correctly) was that discussion not be targeted against a particular paper, and that the merits of a new, perhaps not fully peer reviewed paper, not be debated. I don't see why voting on axioms would be a problem per se. $\endgroup$ Jul 29 '11 at 19:41
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    $\begingroup$ @Aaron: If you ask “which axiom do you like?” without a clear criterion and 100 people up-voted the Axiom of Infinity (disclaimer: I do not know what it is), that would only mean that 100 people felt clicking upward arrow icon on a certain website. It might be fun, but I do not know why anyone would be interested in seeing that. $\endgroup$ Jul 29 '11 at 20:00
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    $\begingroup$ @Aaron Sterling: I agree with Tsuyoshi. What would learn from those votes? Are you just interested in seeing which axiom gets more votes on cstheory? IMHO the answers and their vote would not be interesting without supporting arguments/references. $\endgroup$
    – Kaveh
    Jul 29 '11 at 23:09
  • $\begingroup$ although GASARCH did a simple vote on P vs NP :) $\endgroup$ Jul 29 '11 at 23:18
  • $\begingroup$ @Suresh: I was thinking about it when I was writing my comment. It is fun to read it, but I didn't learn anything just from votes. $\endgroup$
    – Kaveh
    Jul 30 '11 at 1:09
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    $\begingroup$ @Suresh, Aaron: just to make that I am not misunderstood, I think a question which is not just a poll can be interesting, e.g. if the answers should also give references for the axiom with arguments that the axiom is a reasonable one, e.g. "Church Thesis is first stated by Alonzo Church in [Ref] and is reasonable/plausible axiom about computation because X, Y, Z" (even better if counter arguments are also mentioned "but there are also arguments against it like A, B, C"). $\endgroup$
    – Kaveh
    Jul 30 '11 at 3:53
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    $\begingroup$ On the other hand, a pure poll is like asking "who is your favorite computer scientist?". It is a fun and interesting question, but the answers and their votes will not be very informative (IMHO). ps: on a second thought, a poll about axioms might be more like a poll about favorite papers, so I don't know, but I think the question will be better with extra information in the answers. $\endgroup$
    – Kaveh
    Jul 30 '11 at 3:53
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    $\begingroup$ @AaronSterling sounds like you should proceed, but with caution $\endgroup$ Jul 30 '11 at 14:41
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I think you can ask a serious question on this without even going all the way to community wiki. I did a similar thing here:

Axioms necessary for theoretical computer science

I ended up asking a very specific question (has reverse mathematics been applied to cstheory) and getting very good specific answers that taught me a lot.

For the computation axioms it might be better to ask specific questions like: what basic (or philosophical) axioms have been proposed for computation? How do these axioms relate to "specific axioms from paper"? What insights have they given us? What are the limitations of "specific axioms from paper"? How could you modify "specific axioms from paper" to allow quantum computing? Stuff like that.

I think simply asking for community members to contribute individual axioms will result in something pretty chaotic. Partially because you usually want to contribute a set of axioms not a single one, anyways. Also because it is not clear what a ranked list of axioms will mean... but I think this was discussed in the comment thread under Kaveh's answer already.

I definitely support making a blog post about axioms and computation.

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It's tricky. Ordinarily, I'd not want it to be anywhere on the Q&A site, but I'm biased towards trusting the questioner in this case, and am willing to let it go as CW. But would you then have people vote for sets of axioms, or for individual axioms ?

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    $\begingroup$ I'm thinking individual axioms as the suggestion, along with a clear statement that the purpose is not to bash anyone's paper, but to produce a bellwether of the community's intuition of "computation." $\endgroup$ Jul 29 '11 at 16:51
  • $\begingroup$ I'm ok with that. might be good to refer to this meta discussion when posting to forestall controversy $\endgroup$ Jul 29 '11 at 17:19
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If you want just a poll for personal taste, please do it somewhere else. I know that many people like those silly questions like “Which paper should everyone read?” but that is at best not what Stack Exchange is for and at worst it can be a noise on the top page.

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    $\begingroup$ While one possible way of asking the question could degenerate into a popularity contest, I think the discussion thus far has suggested more meaningful ways of doing it, and of moderating the discussion. Maybe you're being a little harsh ? $\endgroup$ Jul 31 '11 at 21:51
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    $\begingroup$ @Suresh: Honestly, I got the impression from the discussion in the comments to Kaveh’s answer that Aaron really wanted a poll merely for personal taste, and that is why I wrote this answer. But if he wants something else, then this answer will not apply and I will be happy. $\endgroup$ Aug 1 '11 at 0:11

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