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I use Wikipedia regularly. When I need a little clarification for something for a class, particularly history (the teacher is a bit flaky, the readings and assignments rarely match up), I hop on wiki. However, I don't consider it a source suitable for a research paper.

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When wikipedia has good citations, it's as good as a book with good citations. When it doesn't, it's as good as a book without good citations. The reason it doesn't usually make sense to cite it in a paper is that wikipedia doesn't ever present original research, so you can typically cite something more direct.

 

Somebody did a study of science articles a few years ago (before the big push for citations on wikipedia) and found that there were more errors in Encyclopedia Brittanica than in Wikipedia.

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Originally Posted By: CRISIS on INFINITE SLARTIES
Somebody did a study of science articles a few years ago (before the big push for citations on wikipedia) and found that there were more errors in Encyclopedia Brittanica than in Wikipedia.


it also found that the wikipedia articles were generally more poorly written and structured and the errors that were there were more likely to be serious, though

anyway i've cited wikipedia exactly once and that was to use it as a primary source in an essay about online communities

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Originally Posted By: Secret message follows:
The problem quickly became that most sources that I could cite were not available to the public, while a great deal of Google-indexed material was either Wikipedia mirrors or clearly Wikipedia-based.
I think Wikipedia accepts citing print sources; certainly a lot of the articles already do.

Originally Posted By: Master1
However, I don't consider it a source suitable for a research paper.
It's not a good source for a research paper, for the same reason as Encyclopedia Britannica is not a good source for a research paper. Encyclopedias are tertiary sources; for a research paper, you really want primary sources and perhaps some secondary sources.

Originally Posted By: CRISIS on INFINITE SLARTIES
Somebody did a study of science articles a few years ago (before the big push for citations on wikipedia) and found that there were more errors in Encyclopedia Brittanica than in Wikipedia.
I remember reading about that in the Discover magazine.

Originally Posted By: Lilith
it also found that the wikipedia articles were generally more poorly written and structured and the errors that were there were more likely to be serious, though
I have found articles to be poorly written at times, yes. The worst is when the article presents its topic in a way that expects the reader to already be familiar with it.

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Originally Posted By: Celtic Minstrel
Originally Posted By: Lilith
it also found that the wikipedia articles were generally more poorly written and structured and the errors that were there were more likely to be serious, though
I have found articles to be poorly written at times, yes. The worst is when the article presents its topic in a way that expects the reader to already be familiar with it.


I've found that to be more a problem in their mathematics articles than their science article, but I pretty much agree.

I could also defend Wikipedia by redirecting you to their excellent articles on pop culture, but that might have given me a brain aneurysm.

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Wikipedia is often good at technical subjects, but it's also very technical on technical subjects. Want a high school level approach? Good luck. Recently there's apparently been a push for separate beginner-level articles, but since they're of less interest to the experts who could write them, they're likely to lag.

 

—Alorael, whose citation problem wasn't that he couldn't cite. It was that other editors couldn't check his citation and so fell back on more accessible and more numerous (but wrong) non-technical articles.

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Originally Posted By: Celtic Minstrel
Originally Posted By: Master1
However, I don't consider it a source suitable for a research paper.
It's not a good source for a research paper, for the same reason as Encyclopedia Britannica is not a good source for a research paper. Encyclopedias are tertiary sources; for a research paper, you really want primary sources and perhaps some secondary sources.
This.

This, this, this.

Whenever instructors tell their students not to cite Wikipedia, they're doing their students a disservice by implying that Wikipedia is unsuitable because it's online, or because it can be edited by anyone.

(Also, instructors make a big deal about providing access dates for online works cited, which is good, but they should be just as finicky in asking for edition numbers for encyclopedias and textbooks.)

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News flash, folks: Wikipedia is a great platform for continuing research, but check out some of the links ... you can randomly enter anything as a "link" and unless a diligent editor is checking, you can get away with it. As a former English teacher, I banned Wikipedia as source. Instead, I suggested it as a launching pad for further investigation.

 

Ahh, many Fs were given that fateful first paper to students who neglected to cite other sources than Wikipedia ... good times, let me tell you.

 

And Dintiradan, MLA formatting requires edition numbers for all serialized works, including periodicals and reference books.

 

MissSea =)

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I edit wikipedia to my liking all the time. So do a million other people. Don't use it as a source, and barely use it to learn from.

 

That being said, threads here go off topic faster than anything I've seen.

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Originally Posted By: Txgangsta
Don't use it as a source, and barely use it to learn from.

That's not quite right. Wikipedia isn't entirely trustworthy, but it's both roughly as good as and much broader than good encyclopedias. Don't use it as a source because it's encyclopedic; use it to learn trivia, but don't rely on it for thorough knowledge. Why? Because it's an encyclopedia! But rejecting it entirely? Maybe if there were evidence for it being especially bad, but the evidence is largely in its favor.

MissSea, the link problem isn't such a large problem. You can enter bogus information and defend it with a bogus citation, but anyone following up on citations links for more information should be able to separate the real sources for the wiki vandalism links. And I'd say that if your students were getting F's for citing Wikipedia maybe you needed to make it a bit clearer that they couldn't.

—Alorael, who has, as a tutor, seen many citation catastrophes. Very often it's because students are given a laundry list of unacceptable citation behaviors. Don't ever use information without citing a source. Don't cite "bad" sources. (But what if they use trivial information from a bad source?) Don't rely on just a couple of sources. Very rarely are students actually taught why to cite, other than to avoid being penalized for plagiarism and to meet required citations for an assignment. It would be nice to have students learn the benefits of building off others' work and how solid sources strengthen an argument.

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Originally Posted By: Alorael
Originally Posted By: Txgangsta
Don't use it as a source, and barely use it to learn from.

That's not quite right. Wikipedia isn't entirely trustworthy, but it's both roughly as good as and much broader than good encyclopedias. Don't use it as a source because it's encyclopedic; use it to learn trivia, but don't rely on it for thorough knowledge. Why? Because it's an encyclopedia! But rejecting it entirely? Maybe if there were evidence for it being especially bad, but the evidence is largely in its favor.

And yet again I find myself in agreement with Alorael.

Originally Posted By: Alorael
And I'd say that if your students were getting F's for citing Wikipedia maybe you needed to make it a bit clearer that they couldn't.

There are some students out there who simply must find things out the hard way, no matter how much you try to help them.

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Originally Posted By: Lilith
Originally Posted By: CRISIS on INFINITE SLARTIES
Somebody did a study of science articles a few years ago (before the big push for citations on wikipedia) and found that there were more errors in Encyclopedia Brittanica than in Wikipedia.


it also found that the wikipedia articles were generally more poorly written and structured and the errors that were there were more likely to be serious, though

anyway i've cited wikipedia exactly once and that was to use it as a primary source in an essay about online communities


A lot of the physics articles are really bad (not to mention rambley and incoherent). In fact, I know a few big-name experts in their fields who've corrected major errors in some of them, or written/re-written some of them, only to have their changes reverted, or had serious errors introduced. In fact, many physics pages that I know of like this now claim they 'need attention from an expert' :-/. In fact, I don't personally know any physicists who edit wikipedia anymore.

Many errors make articles fundamentally wrong, or contain serious misconceptions, or are deeply misleading.

Not to mention there are numerous articles on crackpot theories, that one would never guess were crackpot based on the articles. And these are impossible to edit, because the people who believe in the crazy theories are always far more numerous than the competent physicists (and have far more time on their hands).

From what I've seen, math articles tend to contain fewer serious explicit errors, but are written very confusingly, misleadingly, and contain just as many misconceptions / incorrect explanations.

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The thing that's useful about Wikipedia is its organization of information, in one place, in a coherent and uniform fashion. What is relatively undeveloped is its discernment of what is and is not useful information -- it does this to basically the same degree that craigslist polices its listings.

 

I like that analogy because, much like craigslist, wikipedia is a very useful service despite the existence of scams and frauds and illegal activities. To the degree that you have knowledge about a subject, these may be easier or harder to spot. For example, somebody from elsewhere in the world who looked at a random apartment listing would not think anything special of a Beacon Hill studio listing for $500 a month, but for someone with basic knowledge of Boston apartment prices and craigslist advertising trends, it is an obvious scam. Similarly, I'd like to think that I have enough general knowledge about U.S. military history not to be taken in by the Upper Peninsula Wars, but I wouldn't trust my evaluation of a physics article.

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Originally Posted By: Master1
So we have concluded that Wikipedia is fine for a cursory or even deeper inquiry, but is not sufficient to make you an expert.


Opinions of a few people on a gaming forum != legitimate criticism of Wikipedia.

Especially when people make general statements along the lines of "Well I knew a guy who knew a guy who said it's wrong".

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Originally Posted By: Dantius
Originally Posted By: Master1
So we have concluded that Wikipedia is fine for a cursory or even deeper inquiry, but is not sufficient to make you an expert.


Opinions of a few people on a gaming forum != legitimate criticism of Wikipedia.

Especially when people make general statements along the lines of "Well I knew a guy who knew a guy who said it's wrong".


How about:
"I am an expert in high energy theoretical physics who has published string theory papers, who additionally has a degree in math, and I can say, in my expert opinion, the math and physics articles in wikipedia are riddled with errors and are generally of poor quality." wink

So now you too can say you know a guy on the internet who says they suck!

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To comment on the mathematical articles. Having many different people edit an article over a period of time has made some of the articles incoherent. Unlike printed matter, there is no proof reading. Different people find different ideas or inferences 'obvious' and explanations can be added / removed depending on a particular individual's view. To the reader the article may not flow properly (as successive sentences may be in entirely different styles) and inaccuracies can be introduced by editing one part of an article without being aware of other parts on which it depends.

 

In fairness, some preprints and even published textbooks or monographs can be as poorly written and presented. Mathematicians as a class are not noted for their communication skills (clearly this is a generalization, and there exist counter examples).

 

My experience has been that the other types of articles usually contain much more detail e.g. the articles on various countries and cities, and the articles on popular media (tv shows and so on). But, I look at those as a casual reader who's merely curious about the subject, without any serious interest in them, which means I don't see the flaws (unless they're really bad).

 

I am still, in principle, a supporter of the wikipedia concept since it is a very accessible source of information on a wide range of topics (democratization of knowledge and all that). And wiki is a great source of trivia. However, I think anyone with a professional level of interest in a particular subject is bound to find it frustrating. It operates in the same space as a tabloid newspaper.

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Again, where Wikipedia shines isn't in providing good information. It's in providing some information about any subject. Economics of a third world country, current political crisis, biography of guys who have been dead for hundreds of years, or obscure bands playing obscure kinds of music? Or fictional third-world economists who have been dead for hundreds of years due to the machinations of obscure bands? Wikipedia has it. And it has lists of lists of similar things.

 

—Alorael, who missed Slarty's question. It was years ago, and it was on the stub-level article for Pneumocystis carinii, which no longer exists at all. The article insisted that P. carinii infects cats. It doesn't; it infects rats. Of course, Wikipedia now claims that "the older name Pneumocystis carinii, (which now only applies to the Pneumocystis variant that occurs in animals), is still in common usage," which is true but not true enough. Many species have their own corresponding species of Pneumocystis. P. carinii doesn't infect animals, it infects rats and only rats.

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And then there's it's counterpart full with fallacies and conspiracy theories:

The UNCyclopedia

with ideas such as the "cat with buttered toast engine"

and the "Stormtroopers vs. Red Shirts" engine

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Originally Posted By: Micawber
To comment on the mathematical articles. Having many different people edit an article over a period of time has made some of the articles incoherent. Unlike printed matter, there is no proof reading.


Yeah, but the problem is more than no proofreading, but no internal consistency, articles can switch between writing styles, and, worse, conventions, randomly throughout an article. It really takes an expert to spot these consistently, and be able to fix them.

Quote:

In fairness, some preprints and even published textbooks or monographs can be as poorly written and presented. Mathematicians as a class are not noted for their communication skills (clearly this is a generalization, and there exist counter examples).


Yeah, I would argue that the vast majority of math, and of physics texts are not so good. Still, much better than wikipedia, though.

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Originally Posted By: cfgauss
Originally Posted By: Micawber
To comment on the mathematical articles. Having many different people edit an article over a period of time has made some of the articles incoherent. Unlike printed matter, there is no proof reading.


Yeah, but the problem is more than no proofreading, but no internal consistency, articles can switch between writing styles, and, worse, conventions, randomly throughout an article. It really takes an expert to spot these consistently, and be able to fix them.


Yes, and certain people don't read things fully before responding.

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Originally Posted By: cfgauss
Quote:
In fairness, some preprints and even published textbooks or monographs can be as poorly written and presented. Mathematicians as a class are not noted for their communication skills (clearly this is a generalization, and there exist counter examples).

Yeah, I would argue that the vast majority of math, and of physics texts are not so good. Still, much better than wikipedia, though.

I would argue that the vast majority of all textbooks are pretty bad. I think it's mostly inherent to the conflict between how textbooks are written and how humans actually learn things, rather than stemming from writers with poor communication skills (though that may sometimes be a factor too). Meaningful learning is a process of building up information, applying your own thinking to it, making connections, sorting out patterns, and building up your own internal understanding of the subject. Textbooks tend to provide information discretely and disconnectedly. IMHO, most textbooks would be better off in the form of a story or a novel, with periodic breaks for exercises and the like. (I know of one example of this: Sophie's World, a novel about the history of philosophy written by a high school philosophy teacher. But it's a good novel on its account, too.)

The one major exception I can think of is foreign language textbooks: while there is plenty of fluff out there whose curriculum is dictated by a café menu, there are also a lot of good language texts. I think this is because the content of languages isn't up for debate. Some books will present infinitives right away and others will save them for later, but an infinitive is an infinitive, a noun is a noun, and how you say it is how you say it. There is nothing to interpret and there are no value judgments to make. Compare this to, say, history textbooks. For secondary school books, what gets included is either totally arbitrary and unscholarly (ancient history) or rigidly politically determined and unscholarly (national history) -- and in neither case is anything interesitng said. It's harder to overlay a clear-cut structure like "vocabulary here, grammar there" onto other subjects.

I think I'm going to stop here before I rant any further.

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Originally Posted By: CRISIS on INFINITE SLARTIES

The one major exception I can think of is foreign language textbooks: while there is plenty of fluff out there whose curriculum is dictated by a café menu, there are also a lot of good language texts. I think this is because the content of languages isn't up for debate. Some books will present infinitives right away and others will save them for later, but an infinitive is an infinitive, a noun is a noun, and how you say it is how you say it. There is nothing to interpret and there are no value judgments to make. Compare this to, say, history textbooks. For secondary school books, what gets included is either totally arbitrary and unscholarly (ancient history) or rigidly politically determined and unscholarly (national history) -- and in neither case is anything interesitng said. It's harder to overlay a clear-cut structure like "vocabulary here, grammar there" onto other subjects.

I think I'm going to stop here before I rant any further.
Wouldn't/Couldn't this apply to math too? And if not, Why?

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Originally Posted By: CRISIS on INFINITE SLARTIES
It's harder to overlay a clear-cut structure like "vocabulary here, grammar there" onto other subjects.


But you can! Take a calculus textbook, for instance. Start with limits and continuity, move up to derivatives, then onto the Fundamental Theorem and definite integration. Then antiderivates, differential equations, maybe a little multivariable calculus if it's a higher level, and a few other things you want to tack on anywhere, such as Taylor polynomials and Fourier series. I mean, it's not like you can just say "Eh, we'll teach limits after we do diff eq's" just for the hell of it. There's definitely a progression of knowledge.

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Ratt: Hmm. A good question. I think the difference is as follows: anyone learning a foreign language has already picked up at least one language. However unconsciously, they already have the structures to mentally grasp what a word is, ways that words can be combined, how different speech sounds can be combined, etc. The specifics are all different, of course, but except for radically different pieces of grammar, the structures all exist and don't have to be built from the ground up. However, I doubt that most people have any pre-existing structures to slide negative numbers, logarithms, or derivatives into, when they first learn about those topics.

 

Dantius: That's not what I was saying at all. What does separating vocabulary and grammar have to do with a progression of knowledge?

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Originally Posted By: Dantius
But you can! Take a calculus textbook, for instance. Start with limits and continuity, move up to derivatives, then onto the Fundamental Theorem and definite integration. Then antiderivates, differential equations, maybe a little multivariable calculus if it's a higher level, and a few other things you want to tack on anywhere, such as Taylor polynomials and Fourier series. I mean, it's not like you can just say "Eh, we'll teach limits after we do diff eq's" just for the hell of it. There's definitely a progression of knowledge.


The way I learned calculus (note, I'm still learning it, but I've taken AP AB) we did continuity a bit later, after most of differentiation. We also did antiderivatives before the fundamental theorem and definite integrals, seeing as antiderivatives are needed for definite integrals.

And I think Slarty was talking about different ways of presenting information, rather than different orders. There are a number of ways a person can think about any given aspect of calculus, and each text book generally presents one, which may not work for everyone. Language is different because an infinitive is an infinitive. Yes, there can still be variations in its description, but language is much more uniform than other subjects.

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Originally Posted By: CRISIS on INFINITE SLARTIES
Ratt: Hmm. A good question. I think the difference is as follows: anyone learning a foreign language has already picked up at least one language. However unconsciously, they already have the structures to mentally grasp what a word is, ways that words can be combined, how different speech sounds can be combined, etc. The specifics are all different, of course, but except for radically different pieces of grammar, the structures all exist and don't have to be built from the ground up. However, I doubt that most people have any pre-existing structures to slide negative numbers, logarithms, or derivatives into, when they first learn about those topics.
I meant more of the fact that basic to intermediate math is, for lack of a better expression, universal. There is the same amount of debate about what is or isn't worthy of inclusion as in language, maybe even less. But since you took the time to respond...

Well I would argue that people already have a semi-grasp of language but only in so much as they understand the concept of words (nouns, adjectives, verbs, etc.). Grammar structure however can be as alien as negative numbers etc. I'm sure you've heard a spanish-speaking person say something similar to "Where we can sit?" in stead of "Where can we sit" or, I believe, Russians leaving out "a" or "the" because that idea doesn't exist in their language.

When you get down to it I believe that language and math are both ways to express abstract ideas. Once you have a grasp of basic concepts (words and addition) you can apply it to other concepts (grammar structure and algebra).

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There are a lot of underlying structures that are common across languages, even when the surface forms look fairly different. There are also some structures that are actually different in more significant ways. So I would agree that certain pieces of grammar structure -- including both the ones you mention, use of word order vs. affixes because it has far-reaching impact, and use of determiners like "a" because it's complex and idiosyncratic -- would have the same issues as some math concepts. But I hold that most pieces of language have an antecedent to aid in their uptake, even if it isn't at all apparent. With math you eventually get to topics where almost everything needs a brand new box, there's nothing to compare it to. So maybe negative one, that you can connect to what you know about objects or scores or money, but the square root of negative one, well, that's a unicorn.

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Originally Posted By: CRISIS on INFINITE SLARTIES
But I hold that most pieces of language have an antecedent to aid in their uptake, even if it isn't at all apparent. With math you eventually get to topics where almost everything needs a brand new box, there's nothing to compare it to. So maybe negative one, that you can connect to what you know about objects or scores or money, but the square root of negative one, well, that's a unicorn.


This is only the picture you get from bad math books and teaching wink. The seemingly new ideas didn't come out of nowhere, after all. They were all developed as fairly obvious solutions to problems, or slight changes in thinking about things, etc, and later were developed progressively into something that was more general and didn't 'need' the connections to what it came from. So they don't get taught, and everyone just assumes you'll pick up on them eventually.

Sometimes people do, sometimes not. This leads to embarrassing situations where some math PhDs (or, in the analogous story for physics, physics PhDs!) can't justify some fairly basic statements in their field.

So people have the ability to understand plenty of complex, seemingly abstract mathematical ideas if they've learned the requirements reasonably well. And often the requirements are pretty slim depending on the topic and level of detail you want to understand it in. I have fun teaching my grade-school aged nieces and nephews graduate level math occasionally, and they seem to get it pretty well wink.

Originally Posted By: CRISIS on INFINITE SLARTIES

I would argue that the vast majority of all textbooks are pretty bad. I think it's mostly inherent to the conflict between how textbooks are written and how humans actually learn things, rather than stemming from writers with poor communication skills (though that may sometimes be a factor too).


That's part of it, but if you aren't writing in a way amicable to how people learn, I'd call that poor communication skills wink.

Quote:
Meaningful learning is a process of building up information, applying your own thinking to it, making connections, sorting out patterns, and building up your own internal understanding of the subject. Textbooks tend to provide information discretely and disconnectedly.


But part of a reason for that style is that, once someone's an expert at the basics, it's the best and most efficient style to use. So, picking up a graduate level book on a subject you already know, this can work well. The trouble is that this is the worst way to write books for people who aren't already experts!

Quote:

IMHO, most textbooks would be better off in the form of a story or a novel, with periodic breaks for exercises and the like.


This wouldn't work so well for math or science used literally, but when I give people advice on how, e.g., to write talks, I do always tell them that their talk should tell a story. It should have all the classical components of a story, just suitably adapted! Your characters get to be equations or laws instead of people wink.

When I see most talks (or read most chapters in books) I come away thinking: what was the point of that? What was the 'moral' of this story? What important things should I take away from that? How can I use that to do something? What did it do by itself? Often the answers to these question, based on the talk/book are "I dunno." I think writing things like you're writing a very abstract story answers these kinds of questions automatically and leads to much better material.

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Originally Posted By: cfgauss
This wouldn't work so well for math or science used literally, but when I give people advice on how, e.g., to write talks, I do always tell them that their talk should tell a story. It should have all the classical components of a story, just suitably adapted! Your characters get to be equations or laws instead of people wink.

When I see most talks (or read most chapters in books) I come away thinking: what was the point of that? What was the 'moral' of this story? What important things should I take away from that? How can I use that to do something? What did it do by itself? Often the answers to these question, based on the talk/book are "I dunno." I think writing things like you're writing a very abstract story answers these kinds of questions automatically and leads to much better material.


I think this also has to do how you write the story. Admittedly it would probably be hard to express the concepts of higher math, physics, chem, and maybe bio, but I could see it potentially working for calculus and beginning physics (basically talking through derivations), and working very well for biology. I base this on my experience reading "The Goal" by Eliyahu Goldratt, which teaches lean manufacturing through story. If you actually ask questions about what you should take away, you benefit tremendously.

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I don't think I was explaining myself very well as far as the ease of translating (not literally) the building blocks of language. Let me try and explain it more concretely with one example:

 

If you are a fluent, native English speaker (or a speaker of most any language), you know how to distinguish nouns and verbs grammatically. You know how to do this even if you never learned what a noun or a verb is. In fact, you know how to do this correctly even if you were taught incorrect definitions ("action word" and "person, place, or thing"). You might not be able to answer technical questions about nouns and verbs on paper, but you can USE them correctly -- even in unusual and intricate situations. You understand those two categories of words, even if you don't have the vocabulary to talk about them.

 

So, when you learn a foreign language, when you are putting together the paradigm for that language in your head, you can -- and do -- reuse most of the parts of the English paradigm. So if you get no explanation, or a bad explanation, of how nouns and verbs work, it doesn't really matter, because you already have the mental tools to use them. On the other hand, if you get no explanation, or a bad explanation, of what exactly the square root of negative one is, it takes a lot more work to make up that ground yourself. Many people can do that on their own, but not everybody -- and that's the difference with languages.

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Originally Posted By: The Ratt
I think this also has to do how you write the story. Admittedly it would probably be hard to express the concepts of higher math, physics, chem, and maybe bio, but I could see it potentially working for calculus and beginning physics (basically talking through derivations), and working very well for biology.


Kind of tangential, but this reminds me that Greg Egan managed to write a story where an injection from the real line to a set of measure zero was critical to the plot. I can only assume that he did this because someone dared him to.

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Originally Posted By: CRISIS on INFINITE SLARTIES
I don't think I was explaining myself very well as far as the ease of translating (not literally) the building blocks of language. Let me try and explain it more concretely with one example:

If you are a fluent, native English speaker (or a speaker of most any language), you know how to distinguish nouns and verbs grammatically. You know how to do this even if you never learned what a noun or a verb is. In fact, you know how to do this correctly even if you were taught incorrect definitions ("action word" and "person, place, or thing"). You might not be able to answer technical questions about nouns and verbs on paper, but you can USE them correctly -- even in unusual and intricate situations. You understand those two categories of words, even if you don't have the vocabulary to talk about them.

So, when you learn a foreign language, when you are putting together the paradigm for that language in your head, you can -- and do -- reuse most of the parts of the English paradigm. So if you get no explanation, or a bad explanation, of how nouns and verbs work, it doesn't really matter, because you already have the mental tools to use them. On the other hand, if you get no explanation, or a bad explanation, of what exactly the square root of negative one is, it takes a lot more work to make up that ground yourself. Many people can do that on their own, but not everybody -- and that's the difference with languages.


I'm not sure if I totally agree here. People learn their native language only how they're taught it - if taught incorrectly then one will speak that way. I live in a country where I don't really speak the language and also I didn't learn so much the parts of speech at school and what they are called. So when I try to assemble a sentence myself in German I often get the order wrong, however I can get it right, if I've learnt a particular phrase, by keeping the structure of the phrase and substituting the words I want. When someone tries to explain to me why a sentence is how it is grammatically my brain fogs up since I didn't learn grammar that way.

When you speak of 'building blocks' of language I think they are more varied and fundamental than you mention - being able to distinguish between nouns and verbs only gets you so far and could be equated with, say, addition and subtraction. There are a myriad of other things that you have to be made aware of and actually learn, same as learning that there is a square root and the what, how and why's of it.

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Originally Posted By: waterplant
People learn their native language only how they're taught it - if taught incorrectly then one will speak that way.

People aren't taught native languages: native languages are languages you learn growing up, by observation and experience. Some parents and schools may seek to enrich this learning, but children learn languages to complete fluency without any instruction.

Quote:
I live in a country where I don't really speak the language

Which means it's not your native language. Right?

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and also I didn't learn so much the parts of speech at school and what they are called. So when I try to assemble a sentence myself in German I often get the order wrong, however I can get it right, if I've learnt a particular phrase, by keeping the structure of the phrase and substituting the words I want. When someone tries to explain to me why a sentence is how it is grammatically my brain fogs up since I didn't learn grammar that way.

Yes, but you are clearly 100% capable of assembling sentences fluently in English, so you can tell nouns and verbs apart (and a million other things -- see below). Analysis of language is one thing and actually learning and speaking it is something else. Most language learners mainly learn the latter, and most textbooks mainly teach the latter.

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When you speak of 'building blocks' of language I think they are more varied and fundamental than you mention - being able to distinguish between nouns and verbs only gets you so far and could be equated with, say, addition and subtraction.

Certainly true -- if anything, an understatement. Language is incredibly complex.

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There are a myriad of other things that you have to be made aware of and actually learn, same as learning that there is a square root and the what, how and why's of it.

It's not the same. When learning a new language, you learn a lot of vocabulary that you can use just like the vocabulary in your old language, and you learn a lot of grammar, most of which is also parallel to the grammar in your old language. When you study math, you constantly encounter concepts that are -not- just another flavour of a category of things you already how to use, but rather are totally new things that require you to understand them differently.

If you are talking about learning grammar or linguistics in the abstract, then yes, I'd agree that's very similar to learning math. However, that is also quite different from the goals of most foreign language learners and courses.

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Part of the difference here is that learning a language is more like learning to ride a bicycle or change a tire than like learning calculus or the history of the American Civil War. Nobody is really trying to understand how to ride a bicycle; the goal is competent performance, of a task whose requirements are treated as arbitrary.

 

It is possible to understand bicycles. But it's really not that easy. And understanding doesn't help you all that much with performance. So nobody much bothers with laying out the axioms of bicycle riding, surveying their historical sources, situating bicycle riding within a larger context, and tracing all the logical consequences of gears and handbrakes.

 

Languages are considerably more complex than bicycles. There may possibly be a coherent deep logic to them, if you believe Noam Chomsky, but even if so, it's awfully difficult to perceive. The answer to most questions about why a language works thus-and-so is, Just Because. So you just learn to perform the task of following the rules. In practice, there is not much to understand. It's learning to do.

 

It's not easy to see what Civil War history might have as a task to be performed. Not repeating past mistakes, if anything analogous should arise during your own term as President? Staying in character in a re-enactment weekend? These are not really major issues, so understanding is the main point of history.

 

Calculus does also have tasks to perform, and to a great extent one can simply learn the rules and apply them. And I guess a lot of people do. If you really use calculus a lot, though, at some point it really will help to understand it better. This would seem to say something about how math is a special kind of subject.

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You can study abstract mathematics with only the most tangential ties to anything present in the physical world, and you can study the history of the spread of crop cultivation among ancient civilizations. Both are very unlikely to help you with any task you encounter, but they're still not very similar.

 

Math is all about deduction. In fact, the only input that has any connection to reality in coming up with mathematics is the set of axioms you're using, and it's quite possible (but not easy!) to instead choose a set of axioms with very little connection to anything observable. Other disciplines tend to be very concerned with inductive reasoning. History relies entirely on describing and understanding what happened. Language and linguistics are can be descriptive or experimental, but they're rarely deductive. There are really very few fields that have so few inherent ties to observation.

 

—Alorael, who could bring up some mathematician jokes about "solving" problems in ways that are mathematically sound but practically lacking. It's usually about mocking math, but it's a good way to think about how a the field really doesn't care at all about real things (except real numbers, which are entirely imaginary, but which are by definition not actually imaginary numbers). Oh, and for bonus points, consider the interactions between abstract, deductive reasoning and postmodern deconstruction.

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Originally Posted By: Randomizer
First assume a spherical problem ...


Heh, that reminds me of a joke where various professions are asked to "prove" that all odd number are prime:

Professor: 3 is prime, 5 is prime, 7 is prime. The rest are left as an exercise to the student.

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Originally Posted By: demons will charm you
You can study abstract mathematics with only the most tangential ties to anything present in the physical world


No such thing exists. Unless by "only the most tangential ties to anything present in the physical world" you mean "the source of all physical laws" wink. Even number theory, notorious for having no physical applications until crypto applications were found, has many applications in physics! Not directly (as if that would even mean anything...), but it can occasionally be helpful in some areas, depending on one's point of view and description.

That's not to say you can't study math ignorant of any applications--which is what most mathematicians do. But it's all part of Reality's sick, twisted plan to have it all interconnected in surprising, amoral ways!

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Both are very unlikely to help you with any task you encounter, but they're still not very similar.


Hey, I find it fun to find every-day applications for sophisticated math! And you can always do it if you think about it enough.

One can argue that knowing that bubbles form a suspiciously efficient (close to piecewise linear) packing arrangement is not useful, but, hey, what happens when your kid asks you how long the bubbles in his bubble bath will last?

Well, understanding the irregular, but suspiciously familiar packing arrangement, and basics about minimal surface shapes, and how the time they last relates to allowed fluctuations and how a fluctuation in one affects its neighbors, you can easily estimate the rate at which bubbles collapse! wink

Of course, the real answer to "you can't use sophisticated math/physics in your everyday life" is "you can, but no one cares." Really, people barely care about what reading accomplishes in your every day life, and a third to a half of people are not proficient at basic reading, either, so what can you really ask for?

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Math is all about deduction.


Which is half of why it's the exclusive way to describe reality!

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Other disciplines tend to be very concerned with inductive reasoning.


Like math for example! Which is the other half of the reason.

At any rate, as people in other fields are learning more and more (then, forgetting, re-learning, forgetting again...) hardcore math and scientific reasoning is applicable to anything. One could very easily apply any number of mathematical topics to understanding history, e.g.

There have been a few people who've applied things like game theory to understand historical events, but the problem is that there is no academic audience for this kind of work. The historians believe, incorrectly, that you can not model real events with math properly, or that you can't get 'hidden' information out of events with math, so they don't care what the mathematicians can do. Mathematicians believe (often incorrectly) that the historian's conclusions aren't sound, and their information isn't trustworthy enough. So you end up with both sides without enough tools to do anything interesting, and who don't care enough to learn what the other has to say! And from an "economic" point of view, there's no reason for either side to learn the other's side.

Although there is a field of mathematical analysis of present events, which is one of the reason for various intelligence agencies being the largest employers of mathematicians, in addition to their cryptographic and data analysis and mining skills.

So I would surely argue that any field could (and should) really be done best with hardcore math. After all, that's the only way you can be sure (with a calculable degree of certainty!) that you're correct.

But they don't, which goes back to SoT's comment,
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It is possible to understand bicycles. But it's really not that easy. And understanding doesn't help you all that much with performance. So nobody much bothers with laying out the axioms of bicycle riding, surveying their historical sources, situating bicycle riding within a larger context, and tracing all the logical consequences of gears and handbrakes.


As far as the average person is concerned, there's no benefit to them to understand bicycles. There is a benefit, and it can be significant. It's just that for the average person, and in their domain of use, the benefit from having a basic understanding (plus arbitrary guesses for any non-basic information), is not that much smaller than having a complete understanding. This is because the perceived improvement of learning the more sophisticated things is basically weighted by how difficult we think it will be to learn.

That's why, e.g., a lot of people complain about "windows" doing stupid things (regardless of the things being done being windows's fault) but do not bother to learn how to avoid these problems, or how to make their computer run better. And if they do, it's all cargo-cult reasoning (let's randomly run a registry "cleaner" to make my computer faster!) and not real reasoning (let's examine all running processes and see who's taking up the most CPU time and see what they're doing). Understanding how a computer works in enough detail to make sure it always runs well requires technical sophistication; it's just much easier to blame Bill Gates and stupid "M$" than to understand how to fix things, even though there is an obvious benefit.

This is something the economists study (occasionally, oddly enough, with rather sophisticated math). From a (over)simplified, more physics/engineering point of view, the bulk behavior is calculated by an expectation value that looks schematically like:
(sum over i)[ (perceived benefit of ith action)*(perceived difficulty coefficient of ith action) ]
with some additional normalizations, etc.

E.g., the classical "I ain't never needed no reading before! I got along fine all my life without yer book lernin'!" (This is something that may seem stupid to you younger readers, but it's something I'll bet most older ones have heard actually used in real life by adults who refuse to learn to read!) These people assume it will be very difficult to learn to read, and are completely ignorant of the benefits. (high difficulty)*(low benefits) = (won't learn to read), (no difficulty)*(I already don't know how to read) = (won't learn to read) so the expected value is "I won't learn to read"!

This goes back to the original comments (see, I was going somewhere with this!) that one could, and should, ideally, (ultimately) approach all subjects in an identical top-down axiomatic way. Including, language, history, bicycles, soap bubbles etc.

It's just that the perceived difficulty in doing so is greater than the perceived gains. So, the typical person won't. This is why so many people consistently misuse "their/there"--they could do it right, but, they ask, "what does it get me." Well, you don't look like a moron, but, lacking the understanding of how stupid it makes them look to get it wrong 50% of the time, the perceived improvement is small, and the perceived difficulty is large, so they don't.

So this discussion about if other topics can be addressed in the same way or not doesn't mean anything. They can. The question is if most people find it sufficiently convenient (and the answer is that they do not).

But it is the case that with properly done science, you cannot escape the correct way of doing it and expect to be successful (outside of writing crackpot pop-sci books, anyway).

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tl;dr, although, in all fairness, tl;idc would be better.

 

Mandatory Internet response aside, I don't disagree that high level math can on rare occasions be useful, but I can't think of any scenario in everyday life that could be answered better by simpler methods. For instance, when your kid asks how long the bubbles will last, get him a stopwatch and teach him how to find averages. It will be far more useful to him than explaining advanced mathematics to him, because he's certainly not going to care about the rate of change of the quantity of the bubbleswith respect to time.

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Mathematics as a tool are very useful. We'd all be in trouble without arithmetic, and most people can find uses for algebra here and there. Statistics is a requirement for understanding all the lies politicians tell. You can apply all kinds of math to all kinds of things! That's not what I'm arguing.

 

History is derived from what happened and what happens. Math is not derived from things. Physics, which relies heavily on mathematics, does have as its basis observation of what happens. Math doesn't care; it can't care. It's deductive! Mathematicians may pursue branches because they are practically relevant, but the branches themselves exist and are true regardless of their ties to the real world.

 

Don't read this as an attack on the relevance of math. It's about the underpinnings of disciplines. Everything else is, at base, drawn from inductively determined truths. Math isn't, except to the degree that the axioms most commonly used are those that seem to be true in reality.

 

—Alorael, who doesn't think Dantius is right. While it's always nice to teach the virtues of observation and empiricism, there are also times when you want to know something without actually having to do it. You may one day find yourself jury-rigging a contraption of some sort and wish you'd paid more attention to related rates.

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Eh, the only reason I'd use science in the bathtub is to keep my hypothetical kids in line. "Your brother splashed around a lot during his bath, so you have to be the control group and keep very still during yours."

 

('Science in the bathtub' would be a good name for a band.)

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Hypothetical kids have a very short attention span, they would quickly forget that you told them that they're in a control group and need to keep very still.

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Originally Posted By: demons will charm you
History is derived from what happened and what happens. Math is not derived from things. Physics, which relies heavily on mathematics, does have as its basis observation of what happens. Math doesn't care; it can't care. It's deductive! Mathematicians may pursue branches because they are practically relevant, but the branches themselves exist and are true regardless of their ties to the real world.


But this isn't correct. Math studies relationships and it does not matter what those relationships specifically are, or if they are inductive, deductive, or other. It doesn't matter if the relationship is numerical equality, causation, groupings into similar classes, logical implication, etc.

Most of what pure mathematicians study are these relations abstractly, without context, but in principle it's always trivial to add context ("this is a C*-algebra" vs. "this is the C*-algebra of quantum mechanical observables").

History is all about relationships: someone did this, this happened then this, this happened because of this, etc. This is the very natural domain of math, and studying these kinds of relationships is no different than any others.

Similarly, physics is described exclusively by math because it's all about relationships: I measure this then this happens, something happens what caused it, etc.

Really, more generally, and from a more 'physical' point of view, any science is all about observables of some kind. It doesn't matter if they're complex, "the fall of the Roman empire" or elementary, "I just saw a 100 GeV cosmic ray." What's important is that as long as there are some kind of relationships between events, you can write, e.g., conditional probabilities,
P(event one | event two)
and calculate 'equations of motion' that relate "if I saw this, these are the likely next possible outcomes." It makes no difference if you're calculating the possible energy states given that you have an electron in a hydrogen atom, or the possible outcomes of increased government spending, or are using them to understand how the fall of the Roman empire affected Europe. The formal structure is the same either way.

The only difference is if people know math can be mutatis mutandis applied to their field, too. And the reasons they don't know this are what I outlined before.

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Everything else is, at base, drawn from inductively determined truths. Math isn't, except to the degree that the axioms most commonly used are those that seem to be true in reality.


There's really no difference here. It's the difference between "starting at the beginning" and "starting in the middle." You can do each either way if you know the right things. Sometimes it's very useful to do math research inductively, and sometimes it's useful do do physics deductively.

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Originally Posted By: cfgauss
It makes no difference if you're calculating the possible energy states given that you have an electron in a hydrogen atom, or the possible outcomes of increased government spending, or are using them to understand how the fall of the Roman empire affected Europe. The formal structure is the same either way.


I hate to break it to you, but Hari Seldon isn't real.

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Originally Posted By: cfgauss
But this isn't correct. Math studies relationships... History is all about relationships... Similarly, physics is described exclusively by math because it's all about relationships...

This makes no sense logically: if relationships are the only reason physics is described by math, then why can't physics be described by history? The answer is that, while on one level math, history, and physics are all about relationships, there are other differences between those disciplines that are TOTALLY relevant to this conversation. That relationships are essential is an accurate, but inadequate definition of any of those disciplines.

Originally Posted By: demons will charm you
Mathematicians may pursue branches because they are practically relevant, but the branches themselves exist and are true regardless of their ties to the real world... Everything else is, at base, drawn from inductively determined truths. Math isn't, except to the degree that the axioms most commonly used are those that seem to be true in reality.
I think you could say this about many fields by drawing a distinction between the platonic form of the field's domain, and the way it is substantiated/instantiated in the flesh (a distinction which is actively pursued in some fields). In particular I'm thinking of computer science and linguistics. I'm not sure how different it is to start with the given axiom of ordinal numbers and the most basic, can't-be-defined-in-terms-of-other-operations operations, than it is to start with the basic axioms of a syntactic theory (the most basic components and the most basic operations), or the simplest components of a programming language, etc. CS and Lx tend to provoke more practically relevant research than math, but less than other fields. It's not a coincidence that I have tended to group those fields together (under "abstract sciences") in demographic surveys here. However, I think you could apply that division to most fields, it just isn't done so much.

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Originally Posted By: Student of Trinity
I hate to break it to you, but Hari Seldon isn't real.


laugh Some day! Unfortunately not for a while since such a thing would be prohibitively complicated wink. We've got to work on some AIs to help us out first.

Originally Posted By: CRISIS on INFINITE SLARTIES
This makes no sense logically: if relationships are the only reason physics is described by math, then why can't physics be described by history?


This reasoning is fallacious. a implies b doesn't mean b implies a, which is what you're saying here. E.g., language describes what I look like, but what I look like doesn't describe language. (Unless you mean the formal structure is applicable in both places, then, it does, but see below.)

Math is the 'largest' set (by construction) in the 'space' of all sets of relationships. I can describe other things by making isomorophisms between subsets of relations in math and subsets of whatever field I want to describe.

So, e.g., there's an isomorphism between observables in ordinary quantum mechanics and elements of C*-algebras, and partial differential equation describing time evolution, and conditional probabilities. There is also an isomorphism between, e.g., historical events and conditional probabilities. That doesn't mean that there is a canonical isomorphism between historical events and quantum observables, even though quantum mechanics is probabilistic. It just means they're described by the same language.

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