IS Forum
Forum Index Register Members List Events Search Today's Posts Mark Forums Read Help

Go Back   International Skeptics Forum » General Topics » Science, Mathematics, Medicine, and Technology
 


Welcome to the International Skeptics Forum, where we discuss skepticism, critical thinking, the paranormal and science in a friendly but lively way. You are currently viewing the forum as a guest, which means you are missing out on discussing matters that are of interest to you. Please consider registering so you can gain full use of the forum features and interact with other Members. Registration is simple, fast and free! Click here to register today.
Reply
Old 16th February 2014, 11:22 AM   #2361
W.D.Clinger
Philosopher
 
W.D.Clinger's Avatar
 
Join Date: Oct 2009
Posts: 5,759
Originally Posted by BurntSynapse View Post
...which tells us nothing about whether the rejection killed the dichotomy or whether the distinction survived despite that rejection, being regarded as useful for, well: drawing distinctions. Carnap was aware of Quine's objections, but justified maintaining the dichotomy on utilitarian grounds - which seem more in line with my work.
The analytic/synthetic dichotomy is sustainable in some particular circumstances where "analytic" can be identified with an objectively definable notion such as "provable", "valid", or some such. In those common cases, however, the analytic/synthetic distinction just adds misleading synonyms to existing technical nomenclature. When no objectively definable notion of analytic is available, then Quine's objections hold with full force and the analytic/synthetic dichotomy just adds muddle. In my opinion, therefore, it's hard to find any real use for the dichotomy.

Originally Posted by BurntSynapse View Post
It would be very helpful to know what "the ambiguity" is, and some hint about what you'd like me to do about it?
Cite your sources instead of plagiarizing them.

Originally Posted by BurntSynapse View Post
Originally Posted by W.D.Clinger View Post
I'd like to call attention to Raatikainen's review of a cleverly titled book by Torkel Franzén: Gödel's Theorem: An Incomplete Guide to Its Use and Abuse. In that review, Raatikainen applauds Franzén's refutation of BurntSynapse's argument:
To me, he's talking about arguments with regard to mathematics which attack it as unreliable. I don't recognize any of those arguments as opinions I share.
Some of us had somehow gotten the impression you were trying to use Gödel's incompleteness theorems to support your belief that physicists' use of vector math entails risk of "undocumented assumptions" in physics.

Originally Posted by BurntSynapse View Post
I regard uses of math different than math. Risky use does not mean the math is risky in and of itself in any way, and should not be taken as such.
When using math, there is the obvious and mundane risk that someone (e.g. a physicist) might make a mistake. Had you been talking about that risk, everyone would have agreed with you at the outset and we would not be having this conversation.

There is a smaller risk that someone (typically a mathematician) might make a mistake that gets past peer review and enters a paper that describes faulty mathematics upon which physicists might eventually rely. Mathematicians make a fair number of such mistakes, but the risk here is small because most (though not all) of the math physicists rely upon has been in widepread use for a long time and is pretty thoroughly debugged. I thought at first that this was the kind of risk you were talking about in vector math, but whenever I say anything about this kind of risk you say it has nothing to do with the risk you're talking about.

Gödel's incompleteness theorems have nothing to do with risk in math or physics. When you dragged Gödel into the conversation, it was a clear signal you didn't know what you were talking about.

There is a small risk of inconsistency in ZF, and I suppose there may be some theoretical risk that even Peano arithmetic is inconsistent. If you were saying those risks are undocumented, you'd be as wrong as it's possible to be.
(Pro tip: Refusing to explain your position with any real clarity makes it easier for you to say critics are attacking a position you don't hold, but it is possible to protest so often as to rule out all reasonable positions you could have held.)
Originally Posted by BurntSynapse View Post
My read of Gödel's incompleteness theorems, (first learned from Gödel, Escher, Bach and as described therein) is that the incompleteness he describes in dialog form is analogous to the project management principles of inherently incomplete documentation, and the issue that PM standards are limited in their ability to define when to apply any particular guideline.
That's a fairly bizarre misreading of Gödel's incompleteness theorems. If you tell us which section(s) of Hofstadter's book led you to that impression, perhaps we can help you to debug your thinking.

Originally Posted by BurntSynapse View Post
Originally Posted by W.D.Clinger View Post
You continue to pretend my characterization of your opinion as a grotesque distortion of Quine's theory was unsupported by specifics or argument. Fair-minded readers who examine that post will conclude otherwise.
A) It's not pretending, and
B) it's not my objection.

It's more that the specifics seem to attack opinions that I don't hold.
It does take a certain amount of intellectual sophistication to see any connection between Burton Dreben's refutation of the claim that Quine's theory of underdetermination leads to thinking there's as much evidence for Zeus as for electrons and your own claim that Quine's theory of underdetermination makes it hard to tell whether falling is better explained by Zeus or by a theory of gravity.
(Pro tip: When complaining about attacks on opinions you don't hold, your habit of mangling or deleting links in the attacks you quote could lead readers to suspect you are trying to make it harder for them to view the evidence. In your quotation of my words above, I took the liberty of restoring the link you deleted.)
W.D.Clinger is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 16th February 2014, 12:18 PM   #2362
BurntSynapse
Thinker
 
Join Date: Jul 2008
Posts: 247
Originally Posted by dlorde View Post
Wow, excellent obfuscating jargon!

Although jargon can also be used to concisely express complex technical ideas...
Obfuscating suggests intention to deceive, which is not my intention here. Obviously, we are all certain to be wrong, less-developed, and ignorant of many things from future perspectives, (assuming we grow).

I affirm as if I were in a court of law: I am trying tell the truth, the whole truth, and nothing but the truth.

If something seems unclear, knowledgeable participants in the discussion can help - there is no weakness in asking.

Last edited by BurntSynapse; 16th February 2014 at 12:21 PM.
BurntSynapse is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 16th February 2014, 12:32 PM   #2363
dlorde
Philosopher
 
dlorde's Avatar
 
Join Date: Apr 2007
Posts: 6,864
Originally Posted by BurntSynapse View Post
Obfuscating suggests intention to deceive...
Not at all. It just means the jargon you posted made your meaning obscure, unclear, or unintelligible. I have no idea why you do it.
__________________
Simple probability tells us that we should expect coincidences, and simple psychology tells us that we'll remember the ones we notice...
dlorde is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 16th February 2014, 02:17 PM   #2364
Perpetual Student
Illuminator
 
Perpetual Student's Avatar
 
Join Date: Jul 2008
Posts: 4,852
I just completed Max Tegmark's book "Our Mathematical Universe," wherein he describes his idea of a four level multiverse as well as the notion that the universe is mathematics.
Tegmark makes the latter claim observing that at the most fundamental level all we have is mathematical structure to describe nature. For example, the electron as nothing more than the mathematical structure describing it, since all properties of an electron can be completely described mathematically. He then invokes the mathematical concept of isomorphism to conclude the electron is the mathematical structure describing it. It's a provocative idea.
I would be interested to learn to what degree the physicists here would find his conjectures to be "crackpot" as opposed to, say, "interesting speculation."
__________________
It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.
- Richard P. Feynman

ξ
Perpetual Student is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 16th February 2014, 04:10 PM   #2365
The Man
Unbanned zombie poster
 
The Man's Avatar
 
Join Date: Jun 2007
Location: Poughkeepsie, NY
Posts: 18,384
Originally Posted by Perpetual Student View Post
I just completed Max Tegmark's book "Our Mathematical Universe," wherein he describes his idea of a four level multiverse as well as the notion that the universe is mathematics.
Tegmark makes the latter claim observing that at the most fundamental level all we have is mathematical structure to describe nature. For example, the electron as nothing more than the mathematical structure describing it, since all properties of an electron can be completely described mathematically. He then invokes the mathematical concept of isomorphism to conclude the electron is the mathematical structure describing it. It's a provocative idea.
I would be interested to learn to what degree the physicists here would find his conjectures to be "crackpot" as opposed to, say, "interesting speculation."

Well, in a lot of ways "crackpot" is often just an over application of, or devotion to, an "interesting speculation". When the mathematical description of an electron repels the same mathematical description of another electron I might go with "the electron is the mathematical structure describing it". Until then the electron has a property called charge which we can describe mathematically but it is still a property the electron has and those mathematical descriptions do not. So while the electron has its properties and is described by them in its interactions. The mathematics just describes those properties and interactions not actually having the properties of the electron (like charge) and having other properties the electron itself does not have (like the ability to be easily manipulated). One of the problems with this 'isomorphic' electron is that our mathematics generally describes idealized electrons and/or an electron just within some limitations. Indeed the mathematics is our best description of the electron (idealized and limited) and that is where those isomorphic aspects remain.
__________________
BRAINZZZZZZZZ
The Man is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 16th February 2014, 05:05 PM   #2366
Reality Check
Penultimate Amazing
 
Join Date: Mar 2008
Location: New Zealand
Posts: 28,521
Originally Posted by BurntSynapse View Post
Not confused, nor do I think it funny, nor do I think including a name leaves a person unable to ask for any details about which they have any question.
Who is this imaginary person that you are talking about, BurntSynapse .
People in this thread have asked you questions about your name dropping, e.g. my questions:
BurntSynapse, Please define Nersessian's "concrete problem"
First asked 29 January 2014.

BurntSynapse, please cite, quote or describe the "Nersessian Model"/" Representation"/"the main thrust of Creating Scientific Concepts
First asked 5 February 2014
Reality Check is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 16th February 2014, 06:35 PM   #2367
Perpetual Student
Illuminator
 
Perpetual Student's Avatar
 
Join Date: Jul 2008
Posts: 4,852
Originally Posted by The Man View Post
Well, in a lot of ways "crackpot" is often just an over application of, or devotion to, an "interesting speculation". When the mathematical description of an electron repels the same mathematical description of another electron I might go with "the electron is the mathematical structure describing it". Until then the electron has a property called charge which we can describe mathematically but it is still a property the electron has and those mathematical descriptions do not. So while the electron has its properties and is described by them in its interactions. The mathematics just describes those properties and interactions not actually having the properties of the electron (like charge) and having other properties the electron itself does not have (like the ability to be easily manipulated). One of the problems with this 'isomorphic' electron is that our mathematics generally describes idealized electrons and/or an electron just within some limitations. Indeed the mathematics is our best description of the electron (idealized and limited) and that is where those isomorphic aspects remain.
But the mathematics does describe electric charge and all its consequences. Do not the quantum field equations for electrons apply to all situations describing the underlying behavior of electrons, not just limited and idealized ones? Isn't the idealization you mention used for clarity and computational purposes?
__________________
It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.
- Richard P. Feynman

ξ
Perpetual Student is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 16th February 2014, 07:19 PM   #2368
BurntSynapse
Thinker
 
Join Date: Jul 2008
Posts: 247
Originally Posted by W.D.Clinger View Post
The analytic/synthetic dichotomy is sustainable in some particular circumstances where "analytic" can be identified with an objectively definable notion such as "provable", "valid", or some such.
As your references pointed out convincingly, objective definition appears beyond reach, but where we seem to disagree here is whether subjective, relative definition is permissible which justifies the distinction. If tons of people agree, but objective criteria prove difficult, shall we assert no such distinction exists? Kassler claims philosophers definitions are not the same as lexicographers.

Kassler’s explanation: “Mere agreement about the cases, like "this counts as science while this as pseudo-science," even if almost all of us agree and agree confidently, won't tell us what our criteria are, much less how good they are. So a definition would be lovely, yet good definitions are hard to come by. We don't always need a definition in order to draw a confident distinction.”


Originally Posted by W.D.Clinger View Post
In those common cases, however, the analytic/synthetic distinction just adds misleading synonyms to existing technical nomenclature.
When we say the distinction "just adds misleading synonyms", it seems to conflict with Kassler’s claims: “If we have necessary conditions, we can confidently rule certain things out from counting as bourbon or as science. We can say, here are the necessary conditions, this thing doesn't meet a necessary condition, hence it's not science. Similarly, if we have sufficient conditions, we can definitively rule certain things in.”
For transdisciplinary linking, this seems significant.

Originally Posted by W.D.Clinger View Post
When no objectively definable notion of analytic is available, then Quine's objections hold with full force and the analytic/synthetic dichotomy just adds muddle.
I think you're repeating for emphasis, and I acknowledge your objection is both substantial and defensible. I suspect we further agree the importance of the objectively definable criteria you present (as one of the math & physics experts here) is less important within utilitarian perspectives, where we are concerned with doing something different than formally proving.

We may be unable to define pornography or childhood with any objective precision, but we do want some legal restrictions, especially when those attributes intersect.

Originally Posted by W.D.Clinger View Post
Cite your sources instead of plagiarizing them.
Good advice & I'll work on doing better with that.

As I said VERY early: the only idea I can claim (AFAIK) is treating physics as an information system for providing decision-relevant information...or something pretty close to that.

Originally Posted by W.D.Clinger View Post
Some of us had somehow gotten the impression you were trying to use Gödel's incompleteness theorems to support your belief that physicists' use of vector math entails risk of "undocumented assumptions" in physics.
Yes, that seems accurate as an illustration of where completeness for rules governing the application of rules can never be totally documented, it must be assumed. Reminder: this is exactly what your critic of the mis-use of Gödel, Escher, Bach stated. His argument, IMO, reflect the utilitarian view that functionality trumps objective definition...even going so far as to claim it can make absolutely certain claims, which seems to contravening the “always subject to revision or incorporation in a larger theory” condition required in science.

Originally Posted by W.D.Clinger View Post
When using math, there is the obvious and mundane risk that someone (e.g. a physicist) might make a mistake. Had you been talking about that risk, everyone would have agreed with you at the outset and we would not be having this conversation.
Perhaps, but I'm concerned with underdetermination regarding which math or model to use. My reading is that historically there’s nothing within geo-centric math, the model itself, or its related theories that will tell us it should be excluded, or included. From http://en.wikipedia.org/wiki/Tarski%...bility_theorem : “…truth in the standard model of the system cannot be defined within the system”.
Quine’s web of belief explained how theories are protected from disconfirming evidence, and this protection seems to lie outside the model or math.

I find the argument that quaternions were less risky compelling because advocates provided arguments which seem compelling even if I don't understand them, while critics' denials seem to lack the same depth. This criterion lies outside the math, even outside the mathematicians. I also tend to judge based on how many top experts go from one side to the other, and I even advocate this as a good heuristic. I tell people: “Want to know if climate change/religion/autism links to vaccines are real? Top experts usually only go one way at a time – and we should not blindly follow, but we should follow.”

I've never spoken to a quaternion expert who didn't have a solid grounding in vectors, and then eschewed Q's for reasons that the techniques were more capable. I can't prove they’re better for anything, but if I have to provide some sort of example for a new approach that has does not seem to have been done yet, Q’s are the first pain-reliever I reach for. Better criteria & examples are invited.

Originally Posted by W.D.Clinger View Post
There is a smaller risk that someone (typically a mathematician) might make a mistake that gets past peer review and enters a paper that describes faulty mathematics upon which physicists might eventually rely.
Yeah...but we agree this is very small, and I hope we agree different than a mistake in which mathematics to use.

Originally Posted by W.D.Clinger View Post
Mathematicians make a fair number of such mistakes, but the risk here is small because most (though not all) of the math physicists rely upon has been in widepread use for a long time and is pretty thoroughly debugged. I thought at first that this was the kind of risk you were talking about in vector math, but whenever I say anything about this kind of risk you say it has nothing to do with the risk you're talking about.
Yup...and I said it again above. The technique or tool and its selection are related, but different, IMO.

Originally Posted by W.D.Clinger View Post
Gödel's incompleteness theorems have nothing to do with risk in math or physics.
I think given sufficiently strict definitions, I’d agree, but the Tarski stuff does seem awfully close to what I’m saying. I’d be interested to know what Quine wrote in the last chapter of Mathematical Logic described at: http://en.wikipedia.org/wiki/Willard_Van_Orman_Quine




Originally Posted by W.D.Clinger View Post
When you dragged Gödel into the conversation, it was a clear signal you didn't know what you were talking about.
You think? Hopefully repeated agreement with my limitless inadequacies will enable critics to take yes for an answer, and help compensate for them.
I remember a conversation from Gödel, Escher, Bach where there was an infinite regress of "Suppose I agree with all those, and still don't accept X" (note: trying to remember from approx. 35 years ago.)

I'm no mathematician, physicist, or HPS expert. I am an expert in designing standards for successful delivery of a defined goal, with lots of experience in making it happen.

Originally Posted by W.D.Clinger View Post
There is a small risk of inconsistency in ZF, and I suppose there may be some theoretical risk that even Peano arithmetic is inconsistent. If you were saying those risks are undocumented, you'd be as wrong as it's possible to be.
OK! That's delightfully different than a previous "you're wrong as it's possible to be".

I'm not arguing that sort of risk. I refer to the undocumented risk inherent in using cognitive frames without any awareness of how they are reconfigured during paradigm change.


Originally Posted by W.D.Clinger View Post
(Pro tip: Refusing to explain your position with any real clarity makes it easier for you to say critics are attacking a position you don't hold, but it is possible to protest so often as to rule out all reasonable positions you could have held.)
This sounds like a generalization of the all the particulars for which we cannot and (IMO) should not be trying to establish clarity, such as specific impacts far in the future.

Originally Posted by W.D.Clinger View Post
That's a fairly bizarre misreading of Gödel's incompleteness theorems. If you tell us which section(s) of Hofstadter's book led you to that impression, perhaps we can help you to debug your thinking.
Described above.

Originally Posted by W.D.Clinger View Post
“My claim” actually comes from Kassler’s explanation of why Quine advocates “simplicity and conservatism” as criteria for preferring different webs of belief. This seems related to underdetermation and incompleteness, but I don’t think any segments of the PMBOK on risk management are going to be rewritten if that perception proves illusory.

Originally Posted by W.D.Clinger View Post
(Pro tip: When complaining about attacks on opinions you don't hold, your habit of mangling or deleting links in the attacks you quote could lead readers to suspect you are trying to make it harder for them to view the evidence. In your quotation of my words above, I took the liberty of restoring the link you deleted.)
[/quote]
My apologies for invoking Hanlon's Razor again, and I'd really appreciate more focus on substance than form, unless agreement on even the smallest point is prohibited by some rule I don't share.
If there is a way to easily include sub-quotes that otherwise get deleted, I’d appreciate any help with that.
BurntSynapse is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 16th February 2014, 07:30 PM   #2369
BurntSynapse
Thinker
 
Join Date: Jul 2008
Posts: 247
Originally Posted by Reality Check View Post
I thought I'd already given this link:
http://www.amazon.com/Creating-Scien.../dp/0262515075

I also thought I'd quoted and/or summarized bits from that page:
How do novel scientific concepts arise? In Creating Scientific Concepts, Nancy Nersessian seeks to answer this central but virtually unasked question in the problem of conceptual change. She argues that the popular image of novel concepts and profound insight bursting forth in a blinding flash of inspiration is mistaken. Instead, novel concepts are shown to arise out of the interplay of three factors: an attempt to solve specific problems; the use of conceptual, analytical, and material resources provided by the cognitive-social-cultural context of the problem; and dynamic processes of reasoning that extend ordinary cognition. Focusing on the third factor, Nersessian draws on cognitive science research and historical accounts of scientific practices to show how scientific and ordinary cognition lie on a continuum, and how problem-solving practices in one illuminate practices in the other. Her investigations of scientific practices show conceptual change as deriving from the use of analogies, imagistic representations, and thought experiments, integrated with experimental investigations and mathematical analyses. She presents a view of constructed models as hybrid objects, serving as intermediaries between targets and analogical sources in bootstrapping processes. Extending these results, she argues that these complex cognitive operations and structures are not mere aids to discovery, but that together they constitute a powerful form of reasoning--model-based reasoning--that generates novelty. This new approach to mental modeling and analogy, together with Nersessian's cognitive-historical approach, make Creating Scientific Concepts equally valuable to cognitive science and philosophy of science.

Last edited by BurntSynapse; 16th February 2014 at 07:31 PM.
BurntSynapse is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 16th February 2014, 07:44 PM   #2370
BurntSynapse
Thinker
 
Join Date: Jul 2008
Posts: 247
Originally Posted by dlorde View Post
Not at all. It just means the jargon you posted made your meaning obscure, unclear, or unintelligible. I have no idea why you do it.
To me, jargon is only meaningless if I'm unwilling to do some minimal research. If the learning curve is too steep, I ask for help understanding.

Example, when I didn't understand ZF, I didn't think the user had done anything unusual, assuming it was an exemplar for the topic in his field.

A few back & forths with Wikipedia helped me get the gist...and I think the concept stuck better than if he'd just explained.
BurntSynapse is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 16th February 2014, 08:40 PM   #2371
Reality Check
Penultimate Amazing
 
Join Date: Mar 2008
Location: New Zealand
Posts: 28,521
Talking "Creating Scientific Concepts" turns out to be irrelevant

Originally Posted by BurntSynapse View Post
I thought I'd already given this link:
http://www.amazon.com/Creating-Scien.../dp/0262515075
Which ignores the first question:
BurntSynapse, Please define Nersessian's "concrete problem"
First asked 29 January 2014.

And is a general description of the book which makes the answer to:
BurntSynapse, please cite, quote or describe the "Nersessian Model"/" Representation"/"the main thrust of Creating Scientific Concepts"

The "Nersessian Model"/" Representation"/"the main thrust of Creating Scientific Concepts" is not relevant to this thread !
The book is an analysis of historical novel scientific concepts arising, not a proposal to improve current scientific research.
Anyone who has learned about the history of science knows that the popular image of progress by Aha! moments is mostly wrong.
Reality Check is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 16th February 2014, 09:24 PM   #2372
W.D.Clinger
Philosopher
 
W.D.Clinger's Avatar
 
Join Date: Oct 2009
Posts: 5,759
In an attempt to improve the focus of this conversation, I'm going to ignore several side issues that belong in the subforum devoted to Religion & Philosophy.

Originally Posted by BurntSynapse View Post
Originally Posted by W.D.Clinger View Post
Some of us had somehow gotten the impression you were trying to use Gödel's incompleteness theorems to support your belief that physicists' use of vector math entails risk of "undocumented assumptions" in physics.
Yes, that seems accurate as an illustration of where completeness for rules governing the application of rules can never be totally documented, it must be assumed. Reminder: this is exactly what your critic of the mis-use of Gödel, Escher, Bach stated. His argument, IMO, reflect the utilitarian view that functionality trumps objective definition...even going so far as to claim it can make absolutely certain claims, which seems to contravening the “always subject to revision or incorporation in a larger theory” condition required in science.
Yowza. What you said there is half wrong and the other half bafflegab.

Gödel's completeness theorem (not his incompleteness theorems) proved the completeness of certain rules governing application of the inference rules for first order logic. That's not an assumption, it's a theorem, and that theorem provides unassailable documentation of the fact.

As for "your critic of the mis-use of Gödel, Escher, Bach", which critic do you think you're talking about? I was talking about Torkel Franzén's criticism of the misuse of Gödel's incompleteness theorem by people like you. Franzén wasn't talking about Hofstadter's book.

No matter which critic you think you were discussing, what you wrote about that critic's claims was pure bafflegab. Your description of the criticism bears absolutely no resemblance to Franzén's actual criticism (or any other critic I've cited or quoted, so far as I know).

Originally Posted by BurntSynapse View Post
I find the argument that quaternions were less risky compelling because advocates provided arguments which seem compelling even if I don't understand them, while critics' denials seem to lack the same depth. This criterion lies outside the math, even outside the mathematicians. I also tend to judge based on how many top experts go from one side to the other, and I even advocate this as a good heuristic. I tell people: “Want to know if climate change/religion/autism links to vaccines are real? Top experts usually only go one way at a time – and we should not blindly follow, but we should follow.”

I've never spoken to a quaternion expert who didn't have a solid grounding in vectors, and then eschewed Q's for reasons that the techniques were more capable. I can't prove they’re better for anything, but if I have to provide some sort of example for a new approach that has does not seem to have been done yet, Q’s are the first pain-reliever I reach for. Better criteria & examples are invited.
Better criteria and examples were provided months ago. The experts who have replied to you within this thread were unanimous in saying there's nothing wrong with quaternions or with quaternion formulations of Maxwell's equations, but were also unanimous in explaining why vector formulations are now preferred: the vector formulations generalize to higher dimensions (needed for example in relativity) and to more powerful mathematics (including tensor algebra and differential geometry), while the quaternion formulations do not.

When you say you favor quaternions over vector math because you "judge based on how many top experts go from one side to the other", you reveal flaws in your judgment and strong bias in your selection of experts. From our academic training and professional experience, it's virtually certain that I and many of your other critics within this thread are far more aware of what real experts say about quaternions than you are. Nevertheless you continue to prefer your own uninformed judgment to that of domain experts, even after the domain experts have provided you with convincing technical reasons for their informed opinions.

That is not a hallmark of intelligent project management.

Originally Posted by BurntSynapse View Post
Originally Posted by W.D.Clinger View Post
Gödel's incompleteness theorems have nothing to do with risk in math or physics.
I think given sufficiently strict definitions, I’d agree, but the Tarski stuff does seem awfully close to what I’m saying. I’d be interested to know what Quine wrote in the last chapter of Mathematical Logic described at: http://en.wikipedia.org/wiki/Willard_Van_Orman_Quine
Your mention of Tarski here was useless name-dropping. So far as I know, the only reference to Tarski within this thread had been my reference to Tarski's theorem, which is Theorem 17.3 in Boolos et al., Computability and Logic, fifth edition.

Your mention of Quine was only marginally better. You cited the Wikipedia article on Quine and referred to the last chapter of a specific book, Mathematical Logic, but you didn't say why. I suspect your only knowledge of that chapter comes from the Wikipedia article, which says the chapter deals with Gödel's incompleteness theorem [sic] and Tarski's indefinability theorem. That material was covered in chapters 17 and 18 of the fifth edition of Boolos et al., which I have already summarized here in considerable detail. Quine's treatment of this material is nowhere near as good.

Originally Posted by BurntSynapse View Post
Originally Posted by W.D.Clinger View Post
When you dragged Gödel into the conversation, it was a clear signal you didn't know what you were talking about.
You think? Hopefully repeated agreement with my limitless inadequacies will enable critics to take yes for an answer, and help compensate for them.
I remember a conversation from Gödel, Escher, Bach where there was an infinite regress of "Suppose I agree with all those, and still don't accept X" (note: trying to remember from approx. 35 years ago.)
Okay. I (literally ) cracked open my paperback copy this afternoon and found nothing that could have led to your misreading Gödel's incompleteness theorems as "analogous to the project management principles of inherently incomplete documentation, and the issue that PM standards are limited in their ability to define when to apply any particular guideline." That misreading also seems to be a long way from any conversation Hofstadter might have invented about an infinite regress of contrariness.

If you've been straight with us concerning the sources of your interpretation of Gödel's incompleteness theorems, then you would do well to start over with the knowledge that you never really understood those theorems, and try not to make the same mistakes next time.

Originally Posted by BurntSynapse View Post
I'm not arguing that sort of risk. I refer to the undocumented risk inherent in using cognitive frames without any awareness of how they are reconfigured during paradigm change.
Your participation here has demonstrated that risk most convincingly. Your critics have shown considerably greater awareness than you have.

We've seen that with respect to two specific paradigm changes I had cause to mention above: (1) the shift from quaternions to vector math and (2) the shift from Hilbert's program to Gödel's incompleteness theorems.
W.D.Clinger is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th February 2014, 04:02 AM   #2373
dlorde
Philosopher
 
dlorde's Avatar
 
Join Date: Apr 2007
Posts: 6,864
Originally Posted by BurntSynapse
Originally Posted by dlorde View Post
Not at all. It just means the jargon you posted made your meaning obscure, unclear, or unintelligible. I have no idea why you do it.
To me, jargon is only meaningless if I'm unwilling to do some minimal research. If the learning curve is too steep, I ask for help understanding.
Sometimes it's just poor communication. In this case, it didn't really matter.
__________________
Simple probability tells us that we should expect coincidences, and simple psychology tells us that we'll remember the ones we notice...
dlorde is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th February 2014, 05:31 AM   #2374
BurntSynapse
Thinker
 
Join Date: Jul 2008
Posts: 247
Originally Posted by W.D.Clinger View Post
Yowza. What you said there is half wrong and the other half bafflegab.
Typically, "what you said" is used here to criticize things I actually did not say and don't believe, while questions to get at the root of how & where such criticisms got off the rails are ignored. This is accompanied by protestations that my opinion is not properly explained. Here I use the term "criticism" loosely, since insult seems more appropriate for terms like "bafflegab" and demeaning categorization of myself with "people" ascribed various defects.

Originally Posted by W.D.Clinger View Post
Gödel's completeness theorem (not his incompleteness theorems) proved the completeness of certain rules governing application of the inference rules for first order logic.
Even if true, says nothing clearly related to my claims. I've never argued against this point - at all. How does this support the argument that Nersessian's model "enables more targeted, intelligent management of research programs"?

Originally Posted by W.D.Clinger View Post
That's not an assumption, it's a theorem, and that theorem provides unassailable documentation of the fact.
AFAICT, this is unrelated to any of my opinions.

Originally Posted by W.D.Clinger View Post
As for "your critic of the mis-use of Gödel, Escher, Bach", which critic do you think you're talking about?
Unless I'm very much mistaken, I'm talking about Panu Raatikainen, under whose name you posted his claims about "absolutely certain knowledge about the truth of the axioms of the system" which I consider to violate a necessary condition of science.

Originally Posted by W.D.Clinger View Post
I was talking about Torkel Franzén's criticism of the misuse of Gödel's incompleteness theorem
If the fact that Torkel Franzén said it is so much more important to you than what either the idea's meaning, validity, or potential value:
A) we have very different priorities regarding proper "focus" and
B) you should quote Torkel Franzén.

Originally Posted by W.D.Clinger View Post
Franzén wasn't talking about Hofstadter's book.
Gossiping (obsessively) over form and who said what to whom, excluding content smacks of desperation to avoid the issues.

Originally Posted by W.D.Clinger View Post
No matter which critic you think you were discussing...
Panu Raatikainen... http://www.ams.org/notices/200703/rev-raatikainen.pdf

Originally Posted by W.D.Clinger View Post
what you wrote about that critic's claims was pure bafflegab.
Next, you will almost certainly claim that it is also wrong, despite the fact that bafflegab CANNOT be wrong since meaningless gibberish is not truth functional.

Originally Posted by W.D.Clinger View Post
Your description of the criticism bears absolutely no resemblance to Franzén's actual criticism (or any other critic I've cited or quoted, so far as I know).
False in as many ways as one wishes to invest the time in citing, assuming the prior criticism of bafflegab is false, and there is some truth functional claim. Saying "bafflegab bears absolutely no resemblance" is silly. Inviting pedantically silly refutation:
The bafflegab resembles the criticism in that both of them:
- appear online
- were typed by mortals on keyboards using electricity
- include vowels interspersed with consonants,
Etc., ad infinitum.

"Bafflegab" is not any more magic than "focus" or ignoring refutation at providing objections that can be taken seriously.

Hand waving to "your writing", and "your posts are evidence for/against X" at some point begin to feel intellectually dishonest to me.

Originally Posted by W.D.Clinger View Post
Better criteria and examples were provided months ago.
Hand wave.

Originally Posted by W.D.Clinger View Post
The experts who have replied to you
I suspect these the same experts I requested to be identified when they were invoked earlier in a similar fashion. The request was snipped and ignored, as I recall.

Originally Posted by W.D.Clinger View Post
within this thread were unanimous in saying there's nothing wrong with quaternions or with quaternion formulations of Maxwell's equations, but were also unanimous in explaining why vector formulations are now preferred: the vector formulations generalize to higher dimensions (needed for example in relativity) and to more powerful mathematics (including tensor algebra and differential geometry), while the quaternion formulations do not.
You seem to imply there is some aspect of any of this with which I disagree. AFAICT, this has no relation to any of my opinions, and you don't present any obvious links to them.

Originally Posted by W.D.Clinger View Post
When you say you favor quaternions over vector math because you "judge based on how many top experts go from one side to the other", you reveal flaws in your judgment and strong bias in your selection of experts.
The most important distinction to me of my explicitly acknowledged bias is my awareness of it. Without that awareness, I think we tend to easily slip into fallacy and dogmas we cannot perceive, attacking others for failings we ourselves share.

Originally Posted by W.D.Clinger View Post
From our academic training and professional experience, it's virtually certain that I and many of your other critics within this thread are far more aware of what real experts say about quaternions than you are.
As if I've not claimed that many times. The only reason this is not a bad appeal to authority is that it isn't being used to support any detectable position, although the implied message seems to be my claims are bad in just about every possible way, no matter what.

Originally Posted by W.D.Clinger View Post
Nevertheless you continue to prefer your own uninformed judgment to that of domain experts, even after the domain experts have provided you with convincing technical reasons for their informed opinions.
There are many expert arguments given in this thread. If, like these objections, they do not criticize any identifiable "uninformed judgment" I hold, then it does seem proper to acknowledge their correctness in the point they make while maintaining my current stance.

Accusing me of being associated with "people like X" who are described as having opinions I lack is not a compelling objection, and IMO, undermines the credibility of the critic, since they either cannot see or recognize the irrelevance of their expertly-supported point.


Originally Posted by W.D.Clinger View Post
That is not a hallmark of intelligent project management.
True it is completely irrelevant.


Originally Posted by W.D.Clinger View Post
Your mention of Tarski here was useless name-dropping. So far as I know, the only reference to Tarski within this thread had been my reference to Tarski's theorem, which is Theorem 17.3 in Boolos et al., Computability and Logic, fifth edition.
This seems to argue Tarski's idea is irrelevant because it had not been mentioned before, which seems an unusual criteria for establishing these claims of "useless" and "name-dropping".

Originally Posted by W.D.Clinger View Post
Your mention of Quine was only marginally better. You cited the Wikipedia article on Quine and referred to the last chapter of a specific book, Mathematical Logic, but you didn't say why.
I'd intended the context of the immediately preceding sentence to make the relation clear. Underdetermination regarding which math or model to use does seem related by some thinkers to incompleteness, rejected by others & some here.

Originally Posted by W.D.Clinger View Post
Okay. I (literally ) cracked open my paperback copy this afternoon and found nothing that could have led to your misreading Gödel's incompleteness theorems as "analogous to the project management principles of inherently incomplete documentation, and the issue that PM standards are limited in their ability to define when to apply any particular guideline."
Math studies found inherent incompleteness, PM studies found inherent incompleteness, HPS studies found incompleteness.

If a reader cannot find any plausible analogies, I'm probably not a good resource to assist further.


Originally Posted by W.D.Clinger View Post
If you've been straight with us concerning the sources of your interpretation of Gödel's incompleteness theorems, then you would do well to start over with the knowledge that you never really understood those theorems, and try not to make the same mistakes next time.
This comment suggests no distinction between the content of the theorems (about which I've consistently declared my complete ignorance) and their value to illustrate an important epistemological truth in scientific development efforts.

Arguments against math claims I don't make, cannot make, have not made, and repeatedly declared that I've not made them - these arguments seem emotionally motivated and quite misguided. If one wishes to show that the principle of incompleteness appearing in multiple fields by multiple means absolutely cannot be considered a plausible clue for directing research, then it seems one should try to make that case.

Name-calling, hand waving, determination to object no matter how spurious or fallacious the objection, focus on names, spelling, style, and the host of other distractions suggest a very weak position indeed.

Last edited by BurntSynapse; 17th February 2014 at 05:44 AM.
BurntSynapse is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th February 2014, 06:30 AM   #2375
tsig
a carbon based life-form
 
Join Date: Nov 2005
Posts: 39,049
Originally Posted by Reality Check View Post
Which ignores the first question:
BurntSynapse, Please define Nersessian's "concrete problem"
First asked 29 January 2014.

And is a general description of the book which makes the answer to:
BurntSynapse, please cite, quote or describe the "Nersessian Model"/" Representation"/"the main thrust of Creating Scientific Concepts"

The "Nersessian Model"/" Representation"/"the main thrust of Creating Scientific Concepts" is not relevant to this thread !
The book is an analysis of historical novel scientific concepts arising, not a proposal to improve current scientific research.
Anyone who has learned about the history of science knows that the popular image of progress by Aha! moments is mostly wrong.
Do you mean that the apple never fell on Newton's head inspiring the Law of Gravity? If that was a lie then all science must be a lie since all science ultimately comes from Newton's head.

Because scientists lie all science is a lie so my woo* is true.

*The Co-inhabiting, Co-joined, Co-operating Purposefuly Organised Universe.

(C3 PO U)
tsig is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th February 2014, 06:35 AM   #2376
tsig
a carbon based life-form
 
Join Date: Nov 2005
Posts: 39,049
Originally Posted by BurntSynapse View Post
>sniped for Gab<
Name-calling, hand waving, determination to object no matter how spurious or fallacious the objection, focus on names, spelling, style, and the host of other distractions suggest a very weak position indeed.
There was this guy called Gabbey but everyone called him Gab it was so easy to fool him that everyone baffled Gab.

Last edited by tsig; 17th February 2014 at 06:37 AM.
tsig is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th February 2014, 06:44 AM   #2377
W.D.Clinger
Philosopher
 
W.D.Clinger's Avatar
 
Join Date: Oct 2009
Posts: 5,759
In his most recent post, BurntSynapse continued to complain that my criticism is directed toward opinions he does not hold. I will refute his protests by examining only his first complaint in detail; his subsequent complaints were no more justified than his first.

Originally Posted by BurntSynapse View Post
Originally Posted by W.D.Clinger View Post
Yowza. What you said there is half wrong and the other half bafflegab.
Typically, "what you said" is used here to criticize things I actually did not say and don't believe, while questions to get at the root of how & where such criticisms got off the rails are ignored. This is accompanied by protestations that my opinion is not properly explained. Here I use the term "criticism" loosely, since insult seems more appropriate for terms like "bafflegab" and demeaning categorization of myself with "people" ascribed various defects.

Originally Posted by W.D.Clinger View Post
Gödel's completeness theorem (not his incompleteness theorems) proved the completeness of certain rules governing application of the inference rules for first order logic.
Even if true, says nothing clearly related to my claims. I've never argued against this point - at all. How does this support the argument that Nersessian's model "enables more targeted, intelligent management of research programs"?

Originally Posted by W.D.Clinger View Post
That's not an assumption, it's a theorem, and that theorem provides unassailable documentation of the fact.
AFAICT, this is unrelated to any of my opinions.

That's enough. Let's look at BurntSynapse's very first sentence in the paragraph I was criticizing:

Originally Posted by BurntSynapse View Post
Yes, that seems accurate as an illustration of where completeness for rules governing the application of rules can never be totally documented, it must be assumed.

That sentence is not bafflegab. It is, however, completely wrong.

There are thousands of systems in which "completeness for rules governing the application of rules" has been totally documented. Most of those systems are quite trivial, and the documentation often takes the form of a computer program that applies the rules. Consider, for example, the rules that specify the context-free syntax of a programming language. Those rules correspond to productions of the context-free grammar (CFG) for the language, which is usually documented. There are many viable sets of rules for applying those rules, giving rise to different kinds of parsers, e.g. LL(1), SLR(1), LALR(1), LR(1) and so forth, but we have mathematical theorems that tell us each of those particular kinds of parsers is complete (will accept every correct program and will reject every program that contains context-free syntax errors), so the completeness of the parsers' rules for applying the rules of the CFG is documented (by those theorems). That's why programmers accept a compiler's report of syntax errors as definitive: In modern compilers, where the parser has been generated directly from the CFG by a modern parser generator, it would be absurd to protest that the compiler's algorithm for applying the rules of the CFG isn't complete enough to accept the program being rejected.

That's an entire class of mundane counterexamples to BurntSynapse's claim.

The counterexample I actually offered was more interesting and relevant to the discussion: Gödel's completeness theorem proved the completeness of certain rules governing application of the inference rules for first order logic.

BurntSynapse responded to that counterexample by saying "Even if true, says nothing clearly related to my claims."

The "Even if true" part was interesting. Instead of checking for himself whether what I had said was true, BurntSynapse took a wild and hopeless shot at my credibility.

As for the "says nothing clearly related to my claims", that's a funny way of acknowledging Gödel's completeness theorem as a clear counterexample to BurntSynapse's claimed impossibility of documenting "completeness for rules governing the application of rules", and his claim that said completeness "must be assumed". Gödel didn't assume the completeness of a set of rules for proving validity in first order logic. He proved it.

The rest of BurntSynapse's recent post was just as bad as its opening sentences. Point-by-point rebuttal would be both futile and redundant.
W.D.Clinger is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th February 2014, 10:07 AM   #2378
Cuddles
Penultimate Amazing
 
Join Date: Jul 2006
Posts: 18,774
Originally Posted by BurntSynapse View Post
We all are experts in something.
And there we have it. Ultimately, there is so much crackpot physics because people like BurntSynapse believe the above. In reality, the majority of people are not experts in anything. But people like BurtSynapse often make the mistake of thinking they know more than they actually do and, importantly, more than the actual experts they tend to argue with. The Dunning-Krueger effect is fairly well known here, but it's quite unusual for someone to admit to knowingly being a victim of it.

Originally Posted by Perpetual Student View Post
I just completed Max Tegmark's book "Our Mathematical Universe," wherein he describes his idea of a four level multiverse as well as the notion that the universe is mathematics.
Tegmark makes the latter claim observing that at the most fundamental level all we have is mathematical structure to describe nature. For example, the electron as nothing more than the mathematical structure describing it, since all properties of an electron can be completely described mathematically. He then invokes the mathematical concept of isomorphism to conclude the electron is the mathematical structure describing it. It's a provocative idea.
I would be interested to learn to what degree the physicists here would find his conjectures to be "crackpot" as opposed to, say, "interesting speculation."
Yeah, it's pretty much crackpot. Maths is essentially just a language. It's a very precisely defined language that is far more useful for accurately describing the world than naturally evolved human languages, but it's still nothing more than that. Saying an electron is the maths makes no more sense than saying an electron is the English. It's not just not interesting speculation, it's not even a meaningful sentence.
Cuddles is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th February 2014, 10:14 AM   #2379
Perpetual Student
Illuminator
 
Perpetual Student's Avatar
 
Join Date: Jul 2008
Posts: 4,852
Originally Posted by Cuddles View Post
<...>
Yeah, it's pretty much crackpot. Maths is essentially just a language. It's a very precisely defined language that is far more useful for accurately describing the world than naturally evolved human languages, but it's still nothing more than that. Saying an electron is the maths makes no more sense than saying an electron is the English. It's not just not interesting speculation, it's not even a meaningful sentence.
Mathematics is much more than "essentially just a language." Since your premise is wrong, that which follows is relatively worthless.
__________________
It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.
- Richard P. Feynman

ξ
Perpetual Student is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th February 2014, 10:58 AM   #2380
Cuddles
Penultimate Amazing
 
Join Date: Jul 2006
Posts: 18,774
Originally Posted by Perpetual Student View Post
Mathematics is much more than "essentially just a language."
No it isn't.

Quote:
Since your premise is wrong, that which follows is relatively worthless.
I'm sure I've said this before, but perhaps you shouldn't bother asking questions if you're just going to argue with and insult the people who actually take the trouble to answer them for you.
Cuddles is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th February 2014, 11:38 AM   #2381
Perpetual Student
Illuminator
 
Perpetual Student's Avatar
 
Join Date: Jul 2008
Posts: 4,852
Originally Posted by Cuddles View Post
No it isn't.



I'm sure I've said this before, but perhaps you shouldn't bother asking questions if you're just going to argue with and insult the people who actually take the trouble to answer them for you.
No insult was intended. My question had to do with Tegmark's MUH conjecture. Your naďve view of mathematics does not even allow for any discussion of that question. Perhaps if you gained a little perspective concerning the richness and scope of mathematics, you might be able to have an informed opinion. This might be a good place to start: LINK
Let me know if I can be of any assistance.
__________________
It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.
- Richard P. Feynman

ξ
Perpetual Student is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th February 2014, 11:44 AM   #2382
The Man
Unbanned zombie poster
 
The Man's Avatar
 
Join Date: Jun 2007
Location: Poughkeepsie, NY
Posts: 18,384
Originally Posted by Perpetual Student View Post
But the mathematics does describe electric charge and all its consequences. Do not the quantum field equations for electrons apply to all situations describing the underlying behavior of electrons, not just limited and idealized ones? Isn't the idealization you mention used for clarity and computational purposes?
Ok, so what math describes what the value of the electron (or elemental) charge is actually? Currently (no pun intended) it is a measured value and given aspects of quantum field theory the value we do measure is shielded to some degree (by virtual pairs) and less than the value the electron carries. How much less we just don’t know. Cuddles is quite correct above, math is essentially just a language, a formalized, standardized and logically consistent language but a language none the less. I actually considered making the “electron is the English” remark in my previous post but decided instead to just focus on what the isomorphic descriptor explicitly excludes. Namely the very differences that make a description (even mathematical) of an electron just a, well, description and not an electron. To try to put it more succinctly it would be an extremely crappy description of an electron that didn’t map to the electron, or the electron to it, in some ways or others. So that there is a morphism between them should not only be of no surprise but is the actual intent of and how we gain that description (by examining the electron’s properties). Between the two, one being the objective and observed object, the electron, and the other being the “category” ”object” of its mathematical description. The only way to lose that distinction is to deliberately ignore it and how that description was obtained (by objectively observing the electron).
__________________
BRAINZZZZZZZZ
The Man is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th February 2014, 11:49 AM   #2383
BurntSynapse
Thinker
 
Join Date: Jul 2008
Posts: 247
Originally Posted by W.D.Clinger View Post
That sentence is not bafflegab. It is, however, completely wrong...Consider, for example, the rules that specify the context-free syntax of a programming language.
I read this to stipulate a programming language context. If you don't, why not?
BurntSynapse is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th February 2014, 12:13 PM   #2384
Perpetual Student
Illuminator
 
Perpetual Student's Avatar
 
Join Date: Jul 2008
Posts: 4,852
Quote:
Cuddles is quite correct above, math is essentially just a language, a formalized, standardized and logically consistent language but a language none the less.
Therein lies the problem. Your view of mathematics is uninformed. Perhaps you too might benefit from this:
LINK
__________________
It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.
- Richard P. Feynman

ξ
Perpetual Student is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th February 2014, 12:35 PM   #2385
steenkh
Philosopher
 
steenkh's Avatar
 
Join Date: Aug 2002
Location: Denmark
Posts: 7,259
Originally Posted by Perpetual Student View Post
Therein lies the problem. Your view of mathematics is uninformed. Perhaps you too might benefit from this:
LINK
Sure, mathematics is complex, but could you point out precisely what you find of relevance in this article?
__________________
Steen

--
Jack of all trades - master of none!
steenkh is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th February 2014, 02:41 PM   #2386
The Man
Unbanned zombie poster
 
The Man's Avatar
 
Join Date: Jun 2007
Location: Poughkeepsie, NY
Posts: 18,384
Originally Posted by Perpetual Student View Post
Therein lies the problem. Your view of mathematics is uninformed. Perhaps you too might benefit from this:
LINK
What problem would that be, the question you asked about or just something else? That we might hold different views in no way makes either of those views necessarily uninformed. Did your question benefit from that article? If not (and I suspect not) then your view remains uninformed to that question even by that article. As such, you sought additional information elsewhere. If you feel that article or a particular view of mathematics is relevant to the question you asked you could try to be more specific (as a steenkh suggests) and you may just answer your own question in a way that you do feel more satisfying. Otherwise a slightly different view may be the only way to answer your question.

Frankly I don't see the view of mathematics as being all that important to the distinguishing factor between a description and that which is described (unless of course one is describing a description). A similar distinction is between having a fever and being diagnosed with a fever in a response to a question from BurntSynapse before. While perspectives such as mathematics as more of a philosophy, a mental process, natural process or natural order of things can obscure that distinction they can't eliminate it. Mathematics as a language does help make the distinction obvious but I don't see that perspective as being required. That is in fact the primary reason I didn't reference mathematics as a language or make the 'electron is the English' remark I had considered making in my response to your question.
__________________
BRAINZZZZZZZZ
The Man is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th February 2014, 04:51 PM   #2387
BurntSynapse
Thinker
 
Join Date: Jul 2008
Posts: 247
Your mention of fever got my curiosity.
Originally Posted by The Man View Post
Originally Posted by BurntSynapse View Post
Once a paradigm shift is complete, a scientist cannot, for example, reject the germ theory of disease to posit the possibility that miasma causes disease or reject modern physics and optics to posit that aether carries light.

If you see anything in that or any other generally accepted definition which includes a "past-only" restriction, please cite it.
Really?!?! It’s the very distinction you and apparently Kuhn are citing, “Once a paradigm shift is complete”.
Generally, distinguishing a type of X (the completed paradigm shift) is not defining X (the paradigm shift).

Paradigm shifts are processes over time, and it would seem very strange not to allow consideration of what is going on during that process. Discussing the state "after a process is complete" seems common & ordinary.

We may use process verbs as nouns, referring to things such as "a birth" in the past, but there's nothing inherent in most definitions that prohibit us from saying a birth will be like this in the future, is proceeding like that right now, or took place some other way a century ago.

If there are examples of such definitions, I'm not aware of them. There are some who argue they're only identifiable in the past, but these seem only to apply to successful paradigm changes, such as for the scientific community overall.

Last edited by BurntSynapse; 17th February 2014 at 04:54 PM.
BurntSynapse is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th February 2014, 06:07 PM   #2388
The Man
Unbanned zombie poster
 
The Man's Avatar
 
Join Date: Jun 2007
Location: Poughkeepsie, NY
Posts: 18,384
Originally Posted by BurntSynapse View Post
Your mention of fever got my curiosity.
Glad to hear it.

Originally Posted by BurntSynapse View Post
Generally, distinguishing a type of X (the completed paradigm shift) is not defining X (the paradigm shift).
Are incomplete paradigm shifts, you know where the paradigm hasn’t actually shifted, a paradigm shift? If that is the case then they happen all the time. Often it is a distinguishing feature that, well, defines X.

Originally Posted by BurntSynapse View Post
Paradigm shifts are processes over time, and it would seem very strange not to allow consideration of what is going on during that process. Discussing the state "after a process is complete" seems common & ordinary.
While attempting to discuss paradigm shifts where the paradigm hasn’t shifted makes them so “common & ordinary” as to be meaningless. If you don’t like the definition you gave then get a new one but don’t try to make it meaningless or try claim that anyone intends “not to allow consideration of what is going on during that process”.

Originally Posted by BurntSynapse View Post
We may use process verbs as nouns, referring to things such as "a birth" in the past, but there's nothing inherent in most definitions that prohibit us from saying a birth will be like this in the future, is proceeding like that right now, or took place some other way a century ago.

If there are examples of such definitions, I'm not aware of them. There are some who argue they're only identifiable in the past, but these seem only to apply to successful paradigm changes, such as for the scientific community overall.
I just used the definition you gave. Funny how that part of what I quoted from you is missing from your quote above. Heck, take all the unsuccessful “paradigm changes” you want, stack them up against the definition you gave and see how they fare.
__________________
BRAINZZZZZZZZ
The Man is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th February 2014, 07:32 PM   #2389
Max Tegmark
New Blood
 
Join Date: Feb 2014
Posts: 6
Thanks Cuddles for raising this important question about whether mathematics is invented or discovered - a famous controversy among mathematicians and philosophers. You’re quite right we humans invent the *language* of mathematics (the symbols, our human names for the symbols, etc.), but it’s important not to confuse this language with the *structures* of mathematics that I focus on in the book. For example, any civilization interested in Platonic solids would discover that there are precisely 5 such structures (the tetrahedron, cube, octahedron, dodecahedron and icosahedron). Whereas they’re free to invent whatever names they want for them, they’re *not* free to invent a 6th one – it simply doesn’t exist. It's in the same sense that the mathematical structures that are popular in modern physics are discovered rather than invented, from 3+1-dimensional pseudo-Riemannian manifolds to Hilbert spaces.
Max Tegmark is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th February 2014, 07:32 PM   #2390
BurntSynapse
Thinker
 
Join Date: Jul 2008
Posts: 247
Originally Posted by The Man View Post
Are incomplete paradigm shifts, you know where the paradigm hasn’t actually shifted, a paradigm shift?
AFAIK, the term "incomplete paradigm shift" is most often used to refer to a situation where some, but not all members of the community adopt a new cognitive frame. I think it also could apply to intermediate models of an individual where a researcher's conceptualizations are in flux during what Nersessian calls a "bootstrapping process".

Originally Posted by The Man View Post
If that is the case then they happen all the time. Often it is a distinguishing feature that, well, defines X.
Recategorization of exemplars is regarded by some as an internal characteristic that while not entirely undisputed (http://www.sciencedirect.com/science...69848612000593), seems as good as any for distinguishing the "duck-rabbit gestalt switch", with Resident Evil example, see: http://jhaponline.org/jhap/article/view/21/20

The figure doesn't change, but we see a rabbit, then a duck.


Originally Posted by The Man View Post
While attempting to discuss paradigm shifts where the paradigm hasn’t shifted makes them so “common & ordinary” as to be meaningless.
I'm not entirely sure what is meant here by common & ordinary, but the lack of clarity on the term seems to be cited as leading to replacement of the term "paradigm" itself by more technical terms.

Originally Posted by The Man View Post
If you don’t like the definition you gave then get a new one but don’t try to make it meaningless or try claim that anyone intends “not to allow consideration of what is going on during that process”.
New, better definitions are available, but feature terms unknown to most audiences.

Originally Posted by The Man View Post
I just used the definition you gave. Funny how that part of what I quoted from you is missing from your quote above. Heck, take all the unsuccessful “paradigm changes” you want, stack them up against the definition you gave and see how they fare.
Fair enough, I should not have used the original definition for modern uses it can't support.
BurntSynapse is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2014, 06:35 AM   #2391
W.D.Clinger
Philosopher
 
W.D.Clinger's Avatar
 
Join Date: Oct 2009
Posts: 5,759
pointlessness

Originally Posted by BurntSynapse View Post
Originally Posted by W.D.Clinger View Post
That sentence is not bafflegab. It is, however, completely wrong...Consider, for example, the rules that specify the context-free syntax of a programming language.
I read this to stipulate a programming language context. If you don't, why not?
Who would have stipulated that? I haven't. Have you? If so, where?

You made a general claim. Any counterexample refutes your general claim. That's critical thinking 101.

My first counterexample was Gödel's completeness theorem. When you wrote "Even if true", you revealed your ignorance of Gödel's completeness theorem. I then provided an entire class of mundane counterexamples drawn from the familiar world of programming languages (which, by the way, is closely connected to the world of logic and mathematics).

It's possible, of course, that your general claim wasn't intended to be general. You phrased it as a general claim, but you often say things you later reject as misinterpretations of or irrelevant to your position.

By the way, why do you write so much about matters you later claim are irrelevant to your position? I have no idea, for example, why you think your "stipulate" question could have any bearing on your position or mine.
(Pro tip: When you ask irrelevantly silly questions, or express doubt ("Even if true") about well-known facts, you can appear quarrelsome.)
Most of your claims seem quite silly to me: Whether true or false, they seldom advance your argument.

In this case, I think you were still trying to pretend you understood some basic idea of Gödel's incompleteness theorems, even within a post in which you disclaimed real knowledge of those theorems and revealed complete ignorance ("Even if true") of Gödel's completeness theorem. But why?

For that matter, why did you drag Gödel into this conversation at all? You did so because you thought his incompleteness theorems somehow supported your claim of undocumented assumptions creating risk that's somehow related to the risk of vector math you hallucinated. All of that has been thoroughly debunked, yet you cling to your conviction that quaternions are somehow safer, based on your own (clearly uninformed) reading of "experts" you have never named or cited. You are now on the defensive about Gödel, but you have only yourself to blame for that. Had you not tried to attach your argument to Gödel's prestige through name-dropping, your ignorance of Gödel's theorems would never have come to light.

And why did you drag Quine into this conversation? You didn't know about his rejection of the analytic/synthetic distinction, and you cling to a grotesquely distorted view of his theory of underdetermination. With such a poor understanding of Quine's philosophy, what did you hope to accomplish by dropping his name?

You're still dropping names, but they're becoming more and more obscure. In your recent posts, you've mentioned Kassler six times, apparently because you believe he/she is an authority on Quine. To give you some idea of Kassler's obscurity: a Google search on "Kassler"+"Quine" yields this thread as the top hit.

It's possible, of course, that you misspelled this person's name all six times.
(Pro tip: Misspelling the names you drop does not create an impression of superiority or competence.)
W.D.Clinger is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2014, 06:43 AM   #2392
The Man
Unbanned zombie poster
 
The Man's Avatar
 
Join Date: Jun 2007
Location: Poughkeepsie, NY
Posts: 18,384
Originally Posted by BurntSynapse View Post
AFAIK, the term "incomplete paradigm shift" is most often used to refer to a situation where some, but not all members of the community adopt a new cognitive frame. I think it also could apply to intermediate models of an individual where a researcher's conceptualizations are in flux during what Nersessian calls a "bootstrapping process".
So that would not meet the definition of a paradigm shift that you cited.


Originally Posted by BurntSynapse View Post
Recategorization of exemplars is regarded by some as an internal characteristic that while not entirely undisputed (http://www.sciencedirect.com/science...69848612000593), seems as good as any for distinguishing the "duck-rabbit gestalt switch", with Resident Evil example, see: http://jhaponline.org/jhap/article/view/21/20

The figure doesn't change, but we see a rabbit, then a duck.
So what, the definition you gave has a defining feature.


Originally Posted by BurntSynapse View Post
I'm not entirely sure what is meant here by common & ordinary, but the lack of clarity on the term seems to be cited as leading to replacement of the term "paradigm" itself by more technical terms.
Well, what did you mean by that phrase?

Originally Posted by BurntSynapse View Post
New, better definitions are available, but feature terms unknown to most audiences.
Great, so cite one that you would actually want to use instead of one you evidently just don't like anymore. Don't worry, some of us here know a whole crap load of terms and are quite good at helping others get to know them.

Originally Posted by BurntSynapse View Post
Fair enough, I should not have used the original definition for modern uses it can't support.
"modern uses it can't support."? Is it now used to support something other than a paradigm shift? Are paradigm shifts different now in some critical way than they were before? In either case that would make applying aspects from the history of paradigm shifts less relevant as they similarly wouldn't "support" these purported "modern uses".
__________________
BRAINZZZZZZZZ
The Man is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2014, 07:01 AM   #2393
BurntSynapse
Thinker
 
Join Date: Jul 2008
Posts: 247
Originally Posted by Max Tegmark View Post
...it’s important not to confuse this language with the *structures* of mathematics that I focus on in the book. For example, any civilization interested in Platonic solids would discover that there are precisely 5 such structures (the tetrahedron, cube, octahedron, dodecahedron and icosahedron).
It seems odd to claim such broad reach for ideas that apply to such restricted domains. Stipulating "Platonic solids" seems artificially narrow. We would have to rule out infinities of other conditions, like pi dimensions, wouldn't we?

The fact that counting things on our fingers was an evolutionary advantage seems a suspiciously weak foundation for assuming reality is ultimately structured that way. I'm not saying we should toss the SM, but it does seem wise to be on the lookout for contextual assumptions which are natural for us to ignore, often all-but impossible to recognize. I can't say what makes me see a duck or a rabbit first, or what exactly prompts a change. When we've never seen lines, planes, or Platonic solids in nature, caution seems warranted.

Originally Posted by Max Tegmark View Post
Whereas they’re free to invent whatever names they want for them, they’re *not* free to invent a 6th one – it simply doesn’t exist. It's in the same sense that the mathematical structures that are popular in modern physics are discovered rather than invented, from 3+1-dimensional pseudo-Riemannian manifolds to Hilbert spaces.
What about polychorons - could they count? http://en.wikipedia.org/wiki/Polychoron

It seems to me "understanding" only occurs within some framework, somewhat like "parenthood" is understood in terms of having children.

As I understand science, such frameworks should (at least in in principle), always be subject to revision.

From http://plato.stanford.edu/entries/sc...determination/ Quine argues: "...even of pure mathematics and logic, [it] is a man-made fabric...".

Last edited by BurntSynapse; 18th February 2014 at 07:13 AM.
BurntSynapse is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2014, 07:16 AM   #2394
TjW
Penultimate Amazing
 
Join Date: Mar 2005
Posts: 11,097
Originally Posted by The Man View Post
"modern uses it can't support."? Is it now used to support something other than a paradigm shift? Are paradigm shifts different now in some critical way than they were before? In either case that would make applying aspects from the history of paradigm shifts less relevant as they similarly wouldn't "support" these purported "modern uses".
So there's been a paradigm shift in paradigm shifts?
TjW is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2014, 08:01 AM   #2395
BurntSynapse
Thinker
 
Join Date: Jul 2008
Posts: 247
Originally Posted by The Man View Post
So that would not meet the definition of a paradigm shift that you cited.
Correct. Kassler quotes some author as finding 26 different meanings of "paradigm" in Kuhn's work - perhaps even with just SSR.

Originally Posted by The Man View Post
Well, what did you mean by that phrase?
That the usage I describe seems very common in HPS material I've read...like "problem". I've heard different reasons for moving away from "paradigm shift" that have convinced me that more technical concepts and jargon enable better analysis, more detailed understanding, and more precise reasoning we are getting into. Since my field is application, my interest in definitions leans more toward lexicographers, and whether that sort of definition meets acceptable scoping criteria.

Originally Posted by The Man View Post
Great, so cite one that you would actually want to use instead of one you evidently just don't like anymore.
My current preference for distinguishing potentially revolutionary cognitive frames by whether and how they tend to recategorize exemplars in ways impossible in previous frames. I suspect HPS people will continue improving and expanding on that, if they haven't already. Perhaps its already frowned on by some, but the last critique I read seemed weak.

Originally Posted by The Man View Post
"modern uses it can't support."? Is it now used to support something other than a paradigm shift?
The meanings and use have changed, and current uses seem different (and better) than uses from decades ago.

Confusion over whether some meanings of 'paradigms" & "shifts" support or should support various claims is exactly the kind of confusion that lead to clarifications like development of the recategorization criterion in the late 90's & early 2000's.

Originally Posted by The Man View Post
Are paradigm shifts different now in some critical way than they were before?
To dive into that, we should probably use more modern, precise terms and concepts. Human cognitive processes are regarded as utilizing the same basic mental machinery, and as Nersessian points out, external cultural resources and other factors change.

Originally Posted by The Man View Post
In either case that would make applying aspects from the history of paradigm shifts less relevant as they similarly wouldn't "support" these purported "modern uses".
That conclusion hits the nail quite squarely, I'd say.

Last edited by BurntSynapse; 18th February 2014 at 08:09 AM.
BurntSynapse is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2014, 08:14 AM   #2396
BurntSynapse
Thinker
 
Join Date: Jul 2008
Posts: 247
Originally Posted by TjW View Post
So there's been a paradigm shift in paradigm shifts?
Nice
BurntSynapse is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2014, 08:41 AM   #2397
BurntSynapse
Thinker
 
Join Date: Jul 2008
Posts: 247
Originally Posted by W.D.Clinger View Post
Who would have stipulated that? I haven't. Have you? If so, where?
Referring to "X of Y" seems to specify instance X within the context of domain Y.

Originally Posted by W.D.Clinger View Post
Consider, for example, the rules that specify the context-free syntax of a programming language.
We are asked to consider things that fall within the category of what we might call "rules".

The rules category seems here further qualified by stipulating we are only considering rules that "specify".

The domain is then further narrowed to only those specifying rules which apply to "syntax".

The kind of syntax under consideration is further refined to those in "context-free" categories...and so on.

This seems like providing alot of (IMO necessary) contextual support for whatever claims are going to be made, and it seems like this is needed for the claim to be interpreted and meaningful. "Meaning" certainly seems like it has to be relative to something, and Quine's "web of belief" seems like a good model for that.

It may well be wrong, but it it intelligible?

Last edited by BurntSynapse; 18th February 2014 at 09:08 AM.
BurntSynapse is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2014, 09:41 AM   #2398
Perpetual Student
Illuminator
 
Perpetual Student's Avatar
 
Join Date: Jul 2008
Posts: 4,852
Originally Posted by BurntSynapse View Post
It seems odd to claim such broad reach for ideas that apply to such restricted domains. Stipulating "Platonic solids" seems artificially narrow. We would have to rule out infinities of other conditions, like pi dimensions, wouldn't we?

The fact that counting things on our fingers was an evolutionary advantage seems a suspiciously weak foundation for assuming reality is ultimately structured that way. I'm not saying we should toss the SM, but it does seem wise to be on the lookout for contextual assumptions which are natural for us to ignore, often all-but impossible to recognize. I can't say what makes me see a duck or a rabbit first, or what exactly prompts a change. When we've never seen lines, planes, or Platonic solids in nature, caution seems warranted.
The point is that the platonic solids are the only regular, convex polyhedrons with congruent faces of regular polygons that can exist within the context of three dimensional Euclidean geometry. Change the context and some other mathematical realities and relationships will result.
Quote:
What about polychorons - could they count? http://en.wikipedia.org/wiki/Polychoron

It seems to me "understanding" only occurs within some framework, somewhat like "parenthood" is understood in terms of having children.

As I understand science, such frameworks should (at least in in principle), always be subject to revision.

From http://plato.stanford.edu/entries/sc...determination/ Quine argues: "...even of pure mathematics and logic, [it] is a man-made fabric...".
The same would be true of polychorons, in that any civilization interested in polychorons would discover the same characteristics we have.
__________________
It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.
- Richard P. Feynman

ξ
Perpetual Student is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2014, 09:47 AM   #2399
Dancing David
Penultimate Amazing
 
Dancing David's Avatar
 
Join Date: Mar 2003
Location: central Illinois
Posts: 39,700
Originally Posted by BurntSynapse View Post
Maybe any or all. I'm willing to take any of the 3 and let you pick which. All I need is to understand what is meant by the term "your pet theory", assuming this refers to concept(s) I actually believe...

Also, we'd probably need to have a shared definition of "show", so that we agree on whether something explains something else adequatlely.

I tend to use possible worlds semantics for justification but here, larger issues of modal logic looms large and consistently present the greatest obstacles. I'm not sure how to overcome those.

Ideas?
Hi BurntSynapse

Please explain exactly how the many pet theories you have would have helped Edwin Hubble and his research assistant in their paradigm shift. Actually two paradigm shifts but teh Hubble constant is teh big one.

Then explain how your pet theories would have helped Alan Guth (which is unfair), so I will say Ernest Rutherford instead who was involved in a huge paradigm shift.

I am asking how all the different things you claim would help research and in particular paradigm shift would have any practical application.

Guth was unfair because it is a theoretical paradigm shift, so i chose two very utilitarian examples of research Hubble and the spectroscopy and then Rutherford and the alpha particle experiment.

These are two of the biggest paradigm shifts in the last century, my point being you have a bad understanding of what leads to paradigms shifts, which is why i think you should read Kragh's Quantum generations.
__________________
I suspect you are a sandwich, metaphorically speaking. -Donn
And a shot rang out. Now Space is doing time... -Ben Burch
You built the toilet - don't complain when people crap in it. _Kid Eager
Never underestimate the power of the Random Number God. More of evolutionary history is His doing than people think. - Dinwar
Dancing David is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 18th February 2014, 09:50 AM   #2400
Dancing David
Penultimate Amazing
 
Dancing David's Avatar
 
Join Date: Mar 2003
Location: central Illinois
Posts: 39,700
Originally Posted by BurntSynapse View Post
Not confused, nor do I think it funny, nor do I think including a name leaves a person unable to ask for any details about which they have any question.
So ask the name you dropped in the Plato's cave has any real bearing on research.

And then ask them the difference between a poetic allusion in an interview and something with practical applications.
__________________
I suspect you are a sandwich, metaphorically speaking. -Donn
And a shot rang out. Now Space is doing time... -Ben Burch
You built the toilet - don't complain when people crap in it. _Kid Eager
Never underestimate the power of the Random Number God. More of evolutionary history is His doing than people think. - Dinwar
Dancing David is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Reply

International Skeptics Forum » General Topics » Science, Mathematics, Medicine, and Technology

Thread Tools

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Forum Jump


All times are GMT -7. The time now is 08:27 PM.
Powered by vBulletin. Copyright ©2000 - 2024, Jelsoft Enterprises Ltd.

This forum began as part of the James Randi Education Foundation (JREF). However, the forum now exists as
an independent entity with no affiliation with or endorsement by the JREF, including the section in reference to "JREF" topics.

Disclaimer: Messages posted in the Forum are solely the opinion of their authors.