Differences between Chinese and Western education systems

[Ecofarm]

I think you're trying to say that quantifiability and abstraction don't go together.

Defined context and abstraction don't go together. It's really the context part I have a problem with, it leads to the definition of abstract being, well, abstract; because it was incorrect.

 

[nihilistic]

Postmodernist interdisciplinary ecology major. I'll try to make it simple: the context of math is defined exactly. Exactly. There are no unknowns.

As far as it being abstract in the sense of not relying on other things, well, sure.

In other words, you don't know what you are talking about. Math that "does not have any unknowns" is over after grade school.

I think this is a fairly accurate meaning for what I'm saying. Saying that Shakespeare is portraying belonging through his use of the mystical forest in 'As You Like It' is more abstract (apart from concrete realities) than gravity, or 2 + 2 = 4.

It is supporting the point of purity.

But in actuality there is indeed a shakespeare who wrote a play called "As you like it" inside of which includes a description of a "Forest of Arden". Had the dice of history/cosmology been rerolled, that example of yours has 0 chance to remain intact or even to exist, but math will remain unchanged. That is the point of "abstraction". As for your claim of "purity" as the subject of the xkcd cartoon, what purity are you referring to if not the purity of abstraction?

 

[Camikaze]

But in actuality there is indeed a shakespeare who wrote a play called "As you like it" inside of which includes a description of a "Forest of Arden". Had the dice of history/cosmology been rerolled, that example of yours has 0 chance to remain intact or even to exist, but math will remain unchanged. That is the point of "abstraction". As for your claim of "purity" as the subject of the xkcd cartoon, what purity are you referring to if not the purity of abstraction?

My point with Shakespeare was that it could be interpreted to be a number of things, and not just about, say, belonging. And I'm using the word pure to mean exactly what you described- maths remaining intact. As Dachs so eloquently put it, maths is quantifiable, as opposed to an abstraction. It is tangible, as opposed to metaphysical. That is what you're saying, I think, and it is what I am trying to say. The purity in the cartoon I am referring to is this purity, this fact that Maths would remain intact.

 

[Dachs]

As Dachs so eloquently put it, maths is quantifiable, as opposed to an abstraction. It is tangible, as opposed to metaphysical.

Please note that I'm not attempting to claim that that is a dichotomy, just that I was helping you put your position into better words.

 

[PiMan]

Math that "does not have any unknowns" is over after grade school.

True in the strictest sense, but those unknowns are very specifically defined unknowns. As variables, as uncertainties, and as approximations (I'm probably missing something), but they are all defined. Even the undefined is specifically defined as undefined (see: divide by 0).

 

[Camikaze]

Please note that I'm not attempting to claim that that is a dichotomy, just that I was helping you put your position into better words.

Yeah, well thanks for the articulation anyway.

 

[nihilistic]

My point with Shakespeare was that it could be interpreted to be a number of things, and not just about, say, belonging. And I'm using the word pure to mean exactly what you described- maths remaining intact. As Dachs so eloquently put it, maths is quantifiable, as opposed to an abstraction. It is tangible, as opposed to metaphysical. That is what you're saying, I think, and it is what I am trying to say. The purity in the cartoon I am referring to is this purity, this fact that Maths would remain intact.

The word you are looking for is "arbitrary", not "abstract". You are saying that shakespeare can mean whatever you want it to mean, sure. Who cares about BS? As for the alphabet soup of more and more qualifiers such as "quantifiable", "metaphysical", "tangible", etc, do you really want me to define every one of them down and ask you that same question again of "do you really mean that"? Or are you saying that perhaps I should prepare a buzzword bingo?

 

[Sharwood]

Please note that I'm not attempting to claim that that is a dichotomy, just that I was helping you put your position into better words.

Flip-flopper.

 

[Ecofarm]

do you really want me to define every one of them down and ask you that same question again of "do you really mean that"?

I would like you to explain how math is context-free.

What subject are you talking about that can be classified as more abstract or context-free than math?

You are saying that it exists without outside context? Perhaps you are saying it can fit into any context, but the context of math itself is the most defined context known. Physics is more likely to discover a previously unknown by a factor of power.

 

[nihilistic]

True in the strictest sense, but those unknowns are very specifically defined unknowns. As variables, as uncertainties, and as approximations (I'm probably missing something), but they are all defined. Even the undefined is specifically defined as undefined (see: divide by 0).

Well, yes you are. Just to keep it easy I'll stick to a question in the ultra basic area of calculus: find the integral with respect to x of e^(-x^2).

 

[Dachs]

Flip-flopper.

Yeah, I'm so unreliable. I went from having no stated position to not having a stated position.

 

[Sharwood]

Yeah, I'm so unreliable. I went from having no stated position to not having a stated position.

Like a true politician.

 

[nihilistic]

I would like you to explain how math lacks context.

Read up on wikipedia or take a course in logic.

 

[Ecofarm]

That's math as a language, not as a science. Note: grammer. If you want to say math is a context-free language, fine. But the context of math is clearly defined.

Try looking up context-free math:

No article title matches

Your article begins:

"In formal language theory..."

What's "formal language theory"?

Formal language theory is a field of computer science which studies formal languages.[1] These languages are often arranged via the Chomsky hierarchy, which classifies langauges based on the types of formal grammars that define them.

There, I wikied. Just because Chomsky says that math is a context-free language, utilizing context-free grammer DOES NOT MEAN that math is context-free.

 

[Sharwood]

That's math as a language, not as a science. Note: grammer.

Note: spelling.

 

[nihilistic]

That's math as a language, not as a science. Note: grammer.

That's what you don't get: math is not a science. It does not depend on real-world observations. It is a philosophy.

 

[Ecofarm]

Great, now math is not a science; it's a way of thinking. Fantastic. Chomsky told you this?

 

[Tee Kay]

Great, now math is not a science; it's a way of thinking. Fantastic. Chomsky told you this?

It is a way of thinking. I'm not aware of any case of "maths for maths' sake" with the exception of mathematicians.

 

[Bill3000]

Great, now math is not a science; it's a way of thinking. Fantastic. Chomsky told you this?

You do know who Chomsky is within linguistics, correct? You are saying the equivalent of "Einstein told you this?" to a physicist regarding special relativity.

 

[Ecofarm]

@bill: no.

But I'm not buying into math = philosophy.

Fifty is a philo major, right? Ask him if there are any mathematicians in his department.