Turing Complete

Discussions concerned with knowledge of measurement, properties, and relations quantities, theoretical or applied.

Re: Turing Complete

Is the set of all holomorphic functions a set?

Think I'm gonna have to take a little visit over at math.stackexchange.com

(...unless some genius here wants to answer it...)

hyksos
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Re: Turing Complete

You can dish out insults but you can't take accurate criticism. Plain for all to see. Have a nice life.

Wait ... you don't know whether the collection of functions from the complex numbers to themselves having a particular property is a set? And you are holding yourself up as an authority on foundations? You are embarrassing yourself now. The collection of functions from one set to another is a subset of the powerset of their Cartesian product, right? I just saved you from embarrassing yourself on Stackexchange.

And like I say, I refrained from calling you out on your ignorance till you started attacking someone else.
Last edited by someguy1 on January 24th, 2017, 3:36 pm, edited 2 times in total.
someguy1
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Re: Turing Complete

Yeah I patiently gave pointers and even a simplified glossary for the benefit of another forum user here. For his benefit -- for his empowerment -- not mine.

This is the "thanks" I get.

hyksos
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Re: Turing Complete

The thread started rather auspiciously I thought as something that could be a learning resource for many members in related fields. Now personalities are in collision and this is hindering that original purpose. No more personal comments, please, no matter how justified they may seem. I do agree that the math requirements are high, and that it is frustrating for those who don't know what they don't know on the topic. The basic criterion of thread health is that member responses reflect that they have read the source material being cited. E.g. is someone here with formal training in higher mathematics says that you need to study some Model Theory, then you probably do.

Braininvat
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Re: Turing Complete

Braininvat » January 24th, 2017, 1:28 pm wrote:The thread started rather auspiciously I thought as something that could be a learning resource for many members in related fields. Now personalities are in collision and this is hindering that original purpose. No more personal comments, please, no matter how justified they may seem. I do agree that the math requirements are high, and that it is frustrating for those who don't know what they don't know on the topic. The basic criterion of thread health is that member responses reflect that they have read the source material being cited. E.g. is someone here with formal training in higher mathematics says that you need to study some Model Theory, then you probably do.

The individual who name-checked model theory doesn't know the set-theoretic definition of a function. If that can't be called out, then what can?
someguy1
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Re: Turing Complete

This is getting confused.

My main point to anyone here is to get textbooks on math to learn the subject from textbooks constructed specifically for learning --- and to avoid wikipedia. Wikipedia is a reference that is written in ultra-modern form. I have to include these caveats because of the fact that I keep linking it. I am linking the website for an entirely different reason than "go learn this".

You do not have to know Model Theory to read Proof Theory or learn it. Not at all. To read wikipedia you have to be comfortable with Model Theory because they write it like that . For that reason, wikipedia is bad for learning. Wikipedians are writing about Proof Theory to a particular trained audience. NOT because you must know Model Theory to learn Proof Theory and Godel's landmarks theorems, but for their own reasons.

hyksos
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Re: Turing Complete

someguy1 » January 24th, 2017, 11:23 pm wrote:You can dish out insults but you can't take accurate criticism. Plain for all to see. Have a nice life.

Wait ... you don't know whether the collection of functions from the complex numbers to themselves having a particular property is a set? And you are holding yourself up as an authority on foundations? You are embarrassing yourself now. The collection of functions from one set to another is a subset of the powerset of their Cartesian product, right? I just saved you from embarrassing yourself on Stackexchange.

And like I say, I refrained from calling you out on your ignorance till you started attacking someone else.

A user of this forum has now just accused me of 1.) dishing out insults and 2.) attacking other users.

What say you , moderators? Have I "attacked" other users? have I "dished out insults"?

Let us look at what I actually said and actually did:

hyksos » January 24th, 2017, 12:35 pm wrote:
Scott,

I honestly and swear on my mother's grave that I am 1.) Not trying to flame you. 2.) Not trying to insult you. I do not know any other way to say this to you in a way that is "nice". So I will just say it, and you can accept my words or not.

Is that "insulting and attacking" users? Forum moderators : What say you?

hyksos
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Re: Turing Complete

Wait ... you don't know whether the collection of functions from the complex numbers to themselves having a particular property is a set? And you are holding yourself up as an authority on foundations? You are embarrassing yourself now. The collection of functions from one set to another is a subset of the powerset of their Cartesian product, right? I just saved you from embarrassing yourself on Stackexchange.

If the set of holomorphic functions is a subset of the powerset of all cartesian products (as given by set theory) then please explain to the forum why the statement "Complex Analysis is a subset of ZFC" rustled your jimmies so much. The statement might be wrong in minute english detail, but the essence of its claim is mathematically sound. If you must, replace "subset" with "sub-class" or "sub-consequences" according to taste.

While you are at it, please provide to the moderators of this forum a list. The list should contain the names of the users who I have "dished out insults" towards and whom I have "attacked".

I would happy to provide to you links to the profiles of all mods and administrators of this forum to help you in the delivery of your list of my transgressions and crimes.
Last edited by hyksos on January 25th, 2017, 4:29 am, edited 1 time in total.

hyksos
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Re: Turing Complete

Braininvat » January 24th, 2017, 11:28 pm wrote: E.g. is someone here with formal training in higher mathematics says that you need to study some Model Theory, then you probably do.

For the record : I am not suggesting nor implying that anyone should learn Model Theory.

My honest, forthright and helpful suggestion to Scott Mayers is that he needs to get some exposure to Abstract Algebra if he does not have it. After getting some exposure to that subject, then he needs to either read books or take courses on Proof Theory.

Proof Theory texts will explicitly cover Godel's landmark theorems in explicit detail. (Depending on the context, this subject is sometimes called "Mathematical Logic". That is a departmental issue. It depends on context and department.)

There are other subjects which could be inserted in the mix which would further grease Scott's wheels (so to speak). Those would be just a little bit of exposure to Set Theory , and some exposure to Number Theory, particularly in how Number Theory is applied to integers. Neither of those subjects is a requirement in preparation of Proof Theory, but someone with exposure to them will pick up Proof Theory in a more "automatic" way, as it were.

hyksos
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Re: Turing Complete

I insult no one. I attack no one.

This is my help.
This is my suggestion.
This is for Scott's benefit.
This is for Scott's enrichment.
This is for the benefit and betterment of Scott.

This is honest. This is man-to-man. I attest to this entire forum that I fully believe that if these suggestions are followed, that only good things will happen.

hyksos
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Re: Turing Complete

hyksos,

I must confess that I've been a bit too interested in this dialog. You hold some rather strange beliefs, so simply ending the issue would've left some questions unanswered.

Since you've asked your own question, yes, your behavior's been out-of-line. You clearly don't understand these topics very well, though you're pretending to offer advice and understanding to others. On the whole, this offered advice and understanding is pretty poor. To not mince words, in almost all cases in which you've disagreed with Scott or/and someguy1, they were correct and you were wrong.

It might be productive to reread some of the prior comments and give them a bit more consideration. I mean, if you check my profile and someguy1's, we both have the same most active thread topic, in which we'd disagreed and had quite a great discussion as a result. Threads like this have the same potential. Just... if you catch yourself telling someone else to go take a class, that's a good opportunity to stop and give the issue more consideration.
Natural ChemE
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Re: Turing Complete

in which we'd disagreed and had quite a great discussion as a result.

That's nice. Sounds good. It almost sounds like he met your family and you went camping together.
Meanwhile, someguy1's behavior in this thread has degenerated into him making accusations that I am attacking and insulting forum users. Did you miss that part?

So you are are going to defend a user in this thread who has accused me of attacking and insulting other forum users, and then tell me my behavior is "out of line". For that reason I would say that you are picking sides arbitrarily, and you have no basis for this unwarranted complaint. For these reasons, your moderation of this forum is suspect.
Last edited by hyksos on January 25th, 2017, 9:28 am, edited 1 time in total.

hyksos
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Re: Turing Complete

I fully invite someguy1 to act as Scott Mayer's personal math tutor on this forum.

So someguy1, Scott is all yours. You can have him. Take him under your wing.

hyksos
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Re: Turing Complete

hyksos » January 25th, 2017, 8:25 am wrote:I fully invite someguy1 to act as Scott Mayer's personal math tutor on this forum.

So someguy1, Scott is all yours. You can have him. Take him under your wing.

Just out of curiosity, you get that this is a really weird thing to say, right? I mean, it doesn't seem rooted in reality, and it's unduly denigrating to Scott - again stressing that Scott seems to have a better understanding of this topic than you, which makes it strange to posture as though he's in some dire need of a "math tutor".

Though, if you wanted to ask someguy1 for pointers on your own points of confusion, that'd be an entirely normal and acceptable approach to discussions on a forum like this.

As for moderation, a thread split would probably be a good idea, with the productively on-topic posts remaining in Mathematics, and the rest put into a feedback forum thread. Such organization'll tend to be a function of when someone gets the time to do it.
Natural ChemE
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Re: Turing Complete

If anything here is disrooted in reality and weird it is Natural ChemE suddenly storming into this thread to lay down a spew of unsubstantiated claims, among these :

1.) My advice is "pretty poor".

2.) I don't understand these topics very well.

3.) My behavior is "out of line."

4.) I am "denigrating" Scott.

I specifically and in large text plain english asked all forum moderators to answer this question, none of them have yet done so. Natural ChemE is present and posting in this thread, so we can only conclude he is conveniently ignoring the question for his own nefarious reasons.

Have I attacked other users on this forum? If yes, who did I attack and when did this happen?

Have I hurled insults at other users on this forum? If yes, who did I insult , and where did this happen?

hyksos
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Re: Turing Complete

hyksos,

So you've just posted a screenshot of one of someguy1's posts in which he observes that you can dish out insults, and you're asking what he's referring to? While I can't speak for him, the post immediately before his is one of yours, and it starts out like this:
hyksos » January 24th, 2017, 2:18 pm wrote:Oh yes well pardon me for "subset of ZFC". Let me be more precise so as to your cure the troll's little tummy ache on this fine point.
Referring to another user as a "troll" with a "little tummy ache" would seem to qualify.

Could you help me to understand why you had to ask that question? I mean, you took the time to screenshot and annotate his post, so I'm inclined to think that you're trying.
Natural ChemE
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Re: Turing Complete

I neither have the time nor the inclination to delicately and rigorously demonstrate that within the universe of consequences of ZFC's deductive system, that there will exist theorems that are stating things which are isomorphic to theorems in Complex Analysis. In this sense, Complex Analysis in (in some way) "contained inside of" the universe of consequences of ZFC.

someguy1 knows that is precisely what I meant, and for that reason, he is not acting in good faith.

As a moderator, neither are you acting in good faith. How could you possibly read someguy1's posts and not detect abusive and inflammatory language? You must be blind.

If you believe that someguy1 is some sort of innocent bystander whom I have "brutally attacked and insulted" you are absolutely wrong. IF that's what you are claiming is happening here , you are simply biased and taking sides. You are no longer even moderating. You are now just using your moderator powers here to push people around be abusive.

hyksos
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Re: Turing Complete

I will respond to questions in private message from anyone whom I believe is acting in good faith. I will not be forced by moderators to feed trolls. I will not be forced to immerse myself in petty flame wars under the threat of a forum ban.

I am no longer participating in this thread. All outstanding questions about mathematics should be directed at the resident "experts", (whoever those may be.)

I intend to follow the rules of responding to pointed questions in any other section of this forum, but no longer in this particular thread.

hyksos
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Re: Turing Complete

hyksos,

With regards to math, your characterization of ZFC's on-par with gibberish. I don't say this to be mean; just, as an objective observer, I can't make heads or tails of what you're trying to say. If you're suspicious that members of this forum are in a conspiracy to suppress your truth, I'd suggest asking folks elsewhere, e.g. on StackExchange's Math forum. Please feel free to link another discussion if you find others who agree with you. I mean, you won't, but still.

hyksos » January 26th, 2017, 12:06 am wrote:You are now just using your moderator powers here to push people around be abusive.

This is difficult to understand for the following reasons:
1. I haven't used a single mod power, nor threatened to use them.
3. I'm only here because you requested a mod respond.
Do you think it's possible that, rather than everyone else being evil and wrong, you might have some personal reflection to do?
Natural ChemE
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 Braininvat liked this post

Re: Turing Complete

Water under the bridge so perhaps I shouldn't bother to post this. But my motives were questioned. If my motives were unclear I'd at least try to explain where I was coming from. @hyskos Please don't feel the need to respond if you prefer not to. I'll stipulate that you are unhappy with my posts and that nothing I write will change your opinion regarding my good faith or lack thereof.

@hyskos, My posts were influenced by what you wrote here:

hyksos » January 18th, 2017, 5:44 am wrote:Mathematics does not operate by these social rules.

Mathematics is qualitatively different from all other scientific disciplines. I could list the reasons, but the one that sticks out the most is that the discipline of Higher Math is obsessive about very precise definitions.

I was struck by what seems to be a double standard.

When others speak casually, you explain the need for absolute mathematical precision.

When you are criticized for speaking casually, you say that your meaning is obvious and that the critic is acting in bad faith.

That's a double standard.

I challenged you on the "subset" remark not because I didn't understand what you meant, but because it was inconsistent with your remarks on precision. You responded with the defense of casualness and metaphor. Yet when others speak in metaphor you demand precision.

Likewise when I pointed out that you had made a factual error (Russell and Whitehead$^*$), you accused me of "hair splitting." When others are wrong they should read books. When you are wrong, the things you're wrong about don't matter because they're irrelevant and it's bad faith to bring them up.

That's a double standard.

I wish to state for the record that my motive in posting as I did was not to question @hyskos's math or history, but to call out the double standard.

That said, I came to this thread late and jumped in with criticism. I can see how that might have been perceived as an attack out of the blue. For that I apologize. I should have made a more gentle entrance into an ongoing thread.

$^*$ Regarding R&W, Principia Mathematica (PM) is about type theory and not set theory. Type theory is based in logic, whereas modern set theory goes beyond logic to add the axioms of set theory. It's a completely different thing. PM is irrelevant in the development of mainstream twentieth century math. If you are unaware of that and claiming the opposite, that is a material error on your part and your proper response should be to update your knowledge, not question my good faith. PM is hugely important in twentieth century logic. It's irrelevant to twentieth century math. PM has nothing to do with set theory in any form whatsoever. If PM were about set theory in any form at all, your attack on me would have been perfectly correct. If PM were about early set theory and you called it ZFC, I'd be acting in bad faith to make a big deal out of it. But PM is not about set theory at all and your attack is wildly off the mark. Your error is material. As you are placing your technical argument in the context of your historical narrative, errors in the latter cast doubt on the credibility of the former. It's perfectly appropriate for me to have brought it up.
Last edited by someguy1 on January 27th, 2017, 10:56 pm, edited 4 times in total.
someguy1
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Re: Turing Complete

Natural ChemE » January 25th, 2017, 6:15 am wrote:I mean, if you check my profile and someguy1's, we both have the same most active thread topic, in which we'd disagreed and had quite a great discussion as a result.

Hi @NCE, Thank for the support, much appreciated.

I've had some thoughts about our convo of last year. If I had it to do over again I would have focussed obsessively on one point at a time, instead of trying to refute all at once everything you wrote that I disagreed with. That led to the conversation going all over the place and never getting anywhere.

The one point I wanted to pin you down on was your claim that because there exists a model in which CH is true, that's the end of the story as far as you're concerned, and CH is true.

That's bad logic. There's a model of geometry that's Euclidean, but non-Euclidean geometry turns out to be a better model of the world we live in. There exists an Abelian group, but not all groups are Abelian.

I wonder if you've had any time to think about this and if you've seen the error of this particular line of argument yet. If you split off a new thread I would love to focus on this one particular issue, which is what I should have done last time. If not I certainly understand.
someguy1
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Re: Turing Complete

someguy1,

Unfortunately I don't have time to engage in fun discussions right now. Yet more unfortunately, I love such discussions more than fat kids love chocolate. And, let me just say, yum! to chocolate.

someguy1 » January 27th, 2017, 9:11 pm wrote:The one point I wanted to pin you down on was your claim that because there exists a model in which CH is true, that's the end of the story as far as you're concerned, and CH is true.

That's bad logic. There's a model of geometry that's Euclidean, but non-Euclidean geometry turns out to be a better model of the world we live in. There exists an Abelian group, but not all groups are Abelian.

I'd agree that that'd be bad logic. I'd spent a lot of time talking about constructivism because I think that it's needed to explicitly specify the model that we're talking about. I'd linked Is the Continuum Hypothesis a Definite Mathematical Problem, Solomon Feferman (2011), though I am somewhat confused by why such a simple point requires so much discussion that someone would actually give a presentation on it.

The CH is easy to prove because we can select a model in which it's easy to prove; we can also disprove it by selecting a model in which it's easy to disprove. It all boils down to how the set of all integers and reals are constructed. When classical mathematicians refused to specify a construction, they were merely beating their heads against ambiguity, not complexity.

Anyway, please be aware that I'm not saying that the CH is true across all models; it's not.

PS - Yeah, we'll probably have to split this thread to organize it a little better. Everyone's always short on time, so we're sometimes slow to get to it.
Natural ChemE
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Re: Turing Complete

Natural ChemE » January 27th, 2017, 9:22 pm wrote:... I'd spent a lot of time talking about constructivism because I think that it's needed to explicitly specify the model that we're talking about.

I believe you're confusing constructivism with the constructible universe. Two radically different things with similar sounding names. Gödel never had constructivism in mind and the constructible universe is simply not the same thing. I'd love to go into more detail but it would be inappropriate in this thread.

If you split off a new CH thread I'd be glad to tell you why constructivism has nothing to do Gödel's constructible universe. Also Feferman's paper is interesting but not too relevant since it doesn't support your point, it makes a a different point.
someguy1
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