07 Aug 15
Originally posted by FabianFnasThe argument requires understanding of "greater than" and "less than," along with the basic arithmetic operations of multiplication, division, and subtraction. Anyone with at least a grade-school education should possess that understanding. The most advanced notion in the argument, really, is that of a "real number," and the one thing taken as axiomatic is that for every positive real number there exists a positive integer greater than it. That's essentially the Archimedean Property, which is equivalent to the Completeness Axiom of the real number system -- and so it is fair to use. You can easily read the entire argument out loud using plain English.
I've never doubted that.
The real problem is to explain this so everyone can understand it, even those who lack mathematical education. Can you do that...?
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07 Aug 15
The post that was quoted here has been removed
Given his continuing record of abuse and lies against me, I regard Googlefudge with absolute disdain.
So when Googlefudge regards me as 'rude' toward him, I could not care less.
So you continue to be rude to and about me, as well as insulting, mistaken, and incorrect.
Which is why our interactions are always hostile. I assure you that your contempt for me is nothing
compared to mine for you. I don't need to reiterate it in ever post however, unlike you.
In contrast to Googlefudge, Sonhouse has written that he understood what I meant in my earlier post.
I understood your post perfectly, because like Sonhouse I have a mathematical and science background.
Given that the argument is about explanations for people who do NOT have a mathematical background
arguing that someone with such a background understood you does nothing to make your point.
Googlefudge has condemned me for 'bragging' when I write that I learned mathematics from
books in a foreign language. In fact, I was born into a minority community in my society,
and so, like others in my family, I had to learn a foreign language when I was sent to school.
Does Googlefudge (who's apparently an extremely insecure and resentful Westerner)
expect that I must lie about my family's linguistic background in order to appease him?
I am neither insecure, or resentful. I have a whole bunch of obstacles I overcame that I could mention
every time a topic comes up, but I don't because I am not insecure and don't need to brag about it.
Unlike you. You brag about your abilities and 'superiorities' constantly.
YOU are the one who is evidently insecure.
One of my uncles (whose father had only a few years of schooling) earned a PhD and
became a scientist of some distinction. He used to teach mathematics at a famous university.
Would Googlefudge now like to accuse me of lying about my uncle?
Would Googlefudge expect my uncle also to lie about his linguistic origins?
No, because whether it's true or not is not the point. I neither know nor care if it's true.
The fault I point out is your constant bragging about your abilities, not that you lie about having them.
I typically take people at their word unless I have a good reason not to when they talk about their past
or education/etc.
So no, I wouldn't like to accuse you of lying [at least, not about this]. [Just of bragging]
I would like to enquire if you would like to reconsider your response given that you have proven you didn't
understand mine?
And, knowing nothing about how Timothy Gowers teaches or the experiences of his students,
Googlefudge has condemned Timothy Gowers as a 'lousy teacher' for almost everyone.
I suspect that Googlefudge would struggle mightily to learn in a class under Timothy Gowers,
for which Googlefudge presumably would completely blame Timothy Gowers, not himself.
I don't know Timothy Gowers, but I have gotten on well before with teachers who were
considered extremely demanding.
Wrong again. You really should have learned by now.
Again. I have a mathematical and science background and had no problems with 'demanding teachers'.
That is not the point.
As I said very clearly, because I know how hard you find comprehending my posts due to your massive bias
against me, I was talking about the ability to teach people who are NOT brilliant and/or naturally adept at a subject.
And your statement of his position shows him [if it's true, which I am assuming, contrary to your belief that I don't
take you at your word] to believe and advocate things I know to be false. It takes both effort and ability and if you
don't have one it doesn't matter how much of the other you have.
While I don't idealize Chinese students (I have known some who are lazy or stupid), I would like to say
that teaching them is more enjoyable than attempting to teach arrogant Westerners like Googlefudge.
My teachers all liked me, I worked hard and was near or at the top of my class.
Also, not arrogant, unlike you.
So utterly wrong again. Will you ever learn?
While I suspect that Googlefudge would like to sneer at the culture of my upbringing
YOU SUSPECT WRONGLY!
You see I think you despise an imaginary me that lives only in your imagination because every single time you
'guess' or 'suppose' or 'suspect' something about me or my beliefs/intentions you are wrong.
I would like to say that I grew up in a world with less tolerance of human error or weakness
If you are the result then that is nothing to brag about.
Education and learning should be fun, exciting, engaging. Not a harrowing experience designed to destroy the weak.
Thinking otherwise just means you have your priorities wrong.
Again, I regard Googlefudge with absolute disdain
And again, there is nobody here who doesn't already know that.
Given that nobody of consequence has joined in your "let's hate googlefudge" club, apparently nobody else cares.
And given that you are utterly wrong about me at every turn... Well that might give you a hint as to why.
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07 Aug 15
The post that was quoted here has been removedWhy do you not talk directly with the person you are arguing with? This third person referencing is certainly the sign of a personality disorder. It is though you believe you are on a podium lecturing to an audience of devout followers?!?
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08 Aug 15
The post that was quoted here has been removed
There are major cultural differences between me and Googlefudge an extremely narrow-minded
ethnocentric (probably white) Briton.
Wrong from the first sentence. You are biased, I am not however narrow-minded.
I expect that Googlefudge believes that his culture
must be far superior ('Rule Britannia!' ) to the culture(s) of my most modest upbringing.
WRONG. this is going to be a running theme.
I am not here to argue about that in general.
Good, because you're wrong, so arguing about it would be pointless... much like mentioning it in the first place.
I don't claim to be or even aspire to be a
'civilized Westerner', so some such Westerners may feel free to start sneering at me now.
I think you are arguing with a cartoon... Or possibly republicans. I'm neither.
Most of this post will concern how cultural differences affect our attitudes toward mathematics,
citing me and Googlefudge as examples. (I know that Googlefudge does not represent all Westerners.)
Given your [in]accuracy thus far, this should be impressively ignorant.
First of all, Googlefudge has condemned me for 'bragging' because I have written that I
can speak more than one language.
WRONG. I called you out for bragging because you consistently tout your own abilities and superiority
and 'brag' about the challenges you claim to have overcome.
This is also not true as that was not the thing you were bragging about at the time.
Googlefudge seems to regard this achievement as
so extraordinarily difficult or unlikely for me that he apparently suspects me of lying about it.
WRONG and WRONG and a LIE. It's neither extraordinarily difficult nor do I suspect you of lying about it.
In fact I have expressly stated that I am not accusing you of lying about it so your accusation is a lie as well
as wrong.
Actually, it's *normal* in my family to speak more than one language. Even people with
hardly any formal education can speak more than one language. We tend to grow up using
more than one language. It's natural for us, *not* a 'bragging' attempt to impress Googlefudge.
When parents have different mother tongues, their children tend to be exposed to more
than one language at home. As an apparently extremely ethnocentric Briton, Googlefudge
may be ignorant of the fact that speaking more than one language Is common in other societies.
WRONG. I am well aware that it is common for people to speak multiple languages, neither being
ignorant nor an idiot. If nothing else, my school had an exchange program with a school in India where
speaking 5+ languages was the norm. And it's not like discovering that was a surprise to me at the time.
Your arrogant presumptive ignorance about me and my knowledge and beliefs is apparently boundless.
Googlefudge has condemned me for allegedly being terrible at teaching mathematics
and having no comprehension of what being a good mathematics teacher involves.
Based on what you said "I have no sympathy for people who complain it's too hard for them to learn even the
most basic mathematical notation." and " Given that I found it almost effortless to learn school mathematics,
I naturally find it harder to understand the learning difficulties of less gifted students." I did indeed
accuse you of being bad at teaching. Specifically teaching people who were not as 'gifted' and those who
have learning difficulties [of whatever type]. Being a 'good teacher' is not about being able to impart ideas to
the best, they tend to be able to excel regardless [although a good teacher always helps] it is in fact about
being able to pass on and explain ideas to those who are NOT brilliant and/or gifted.
That requires an understanding you demonstrably do not have.
I attended a conference where I was introduced to some of the most
highly regarded mathematics teachers (all men) in Japan. In contrast to Googlefudge's
usual sneering and insulting of me, these Japanese mathematics teachers treated me
with great respect, even deference.
Well done, you managed to get treated with deference by people of a society where having a bad social
interaction is unthinkable and shameful.
Also, this is irrelevant, you are still talking about professionals and experts and not students.
It's also, still, bragging. Are you capable of making arguments without bringing in supposed others who think
you are awesome??
I was very impressed by their dedication to their profession,
and I was able to observe some of the ways they taught mathematics--which was in stark
contrast to the sloppy 'dumbed down' iinformality preferred by Googlefudge, a non-mathematician.
You have absolutely no idea what I prefer. In fact you are utterly, deliberately, and persistently ignorant of what I think
on just about every subject. Although you do seem to have grasped that I don't like you, that's about the
only thing you have right.
Teaching mathematics to maths students in a maths class is not actually what this argument is about.
You have no clue whatsoever about my views on good maths education because you have never stopped to
ask me.
You just arrogantly assume you know my views, and arrogantly and ignorantly assume that they are right.
I would be happy to stand alongside these Japanese teachers in opposition to Googlefudge.
You are arguing against a fictional straw man character. not me.
However hard that Googlefudge
(rated 1007 RHP) trained at chess, I doubt he ever come close to my level of play.
Classy. I don't know, I've never actually 'trained' at chess at all, it's not my preferred game style.
However while you might be correct that there is no amount of training I could do to beat you... You could
also be in for a nasty surprise. You really have no clue.
I would concur with Googlefudge
that effort alone is not necessarily enough for achievement.
Thus putting you at odds with the statements you attributed to Gowers. Fields medal and all.
But Timothy Gower's attitude of "the most important factor--by far--for success in mathematics
is hard work, not innate talent' is universally accepted in East Asian mathematical cultures.
Argumentum ad-populum.
I never denied hard work was important, Quite the opposite. However his claim as stated by you was not
"most important by far", it was the ONLY requirement. Also, "Most important by far" is also not correct.
Recent [ish] research shows that actually talent [here standing in for every factor other than hard work]
plays a much bigger part than previously thought and that telling students that they can achieve anything
if they just work hard enough is [for a significant number] not only not true, it's deeply harmful. Some
people [sadly] just cannot succeed at certain tasks/activities/etc no matter how hard they try. Others will
be able to, but with vastly more work than those with higher levels of talent. And this has implications for
teaching.
It's a far cry from Googlefudge's attitude that apparently emphasizes the importance of
innate talent and attributes responsibility for failure to the teacher, not to the student.
WRONG. re-above.
Failure can be the students fault, the teachers fault, and/or both/neither.
A bad teacher can do immense harm, and claiming otherwise makes good teachers pointless.
If a teacher cannot effect a students performance they are worthless.
This is evidently not true, and teachers are very important. The biggest difference being to those
who are less gifted as they need the most help/inspiration/etc.
While I have some criticisms
of how mathematics has been taught in eastern Asia or eastern Europe, I would *not*
wish to lower one's standards to appease an extremely arrogant 'intellectually lazy'
Westerner like Googlefudge. ..../.....
By the way, one of my very young relatives (not yet old enough to attend school) has
begun speaking in more than one language. When she's older, will she take enough
care to conceal that fact from Googlefudge to prevent him denouncing her for 'bragging'?
Or perhaps we shall advise her that this is no longer the 19th century (some older men
in my family have deep bitterness toward British imperialism and racism), so she need
not fear the arrogant sneering from the likes of a Googlefudge
You still have no clue what my standards are. YOU are Arrogant and ignorant to the last.
So. to sum up...
You have no clue what my views are, yet arrogantly and ignorantly assume that you do.
You accuse me if being ignorant of things I know, thus demonstrating your own ignorance of me.
You hold yourself as superior while making empty strawman attacks and committing logical fallacies
and making endless and irrelevant diversions so that you can brag some more about your accomplishments
all the while lying about me, my statements, and my beliefs.
And you do it all while accusing me of being a liar.
You do it while accusing me of being arrogant and ignorant.
I say that you are the kettle calling the silverware black.
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The post that was quoted here has been removedOh get over yourself.
I read Sonhouse's post as clearly referring to your earlier proof.
If that's not what he was talking about then I was wrong.
But honestly so.
This is exactly the same crap you came out with when we first fell out.
You accused me of lying when I simply took a different meaning from a post than
the one you saw. I admitted that I might have been wrong in my interpretation, although
I maintained that it was still a reasonable interpretation [and still do].
However what I did both then and now was not dishonest or lying or distortions.
Your inability to accept the concept that people can have different [legitimate] points of view,
or simply make mistakes, without being either dishonest or lying is one of your bigger flaws.
Which is saying something.
I have no need to lie or dissemble or distort.
And wouldn't even if I did have such a need.
If I am wrong I admit it, Unlike you.
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08 Aug 15
The post that was quoted here has been removedDo, by all means show us your proof that indicates you know what I believe and think
and value that goes beyond what I say I think and value.
Oh, yes, that's right, my words are the ONLY evidence you have.
I know what I think and believe, and you don't.
You only know what I think, believe, and know when I TELL YOU what I think and believe.
[and then only when you actually read what I write, and understand it correctly, and then believe it]
Thus, when it comes to who is right about what I think. My words are as close as you are going
to get in the way of proof on this site.
Given that it is you making claims about my thoughts and beliefs, it is up to you to meet the burden
of proof that demonstrates that you are right.
If you cannot do that, and you cannot do that, then you owe me an apology for claiming so many
things about me and my beliefs that you have no possible way of knowing.
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08 Aug 15
The post that was quoted here has been removedI NEVER claimed to be a mathematician... and why you would bring up the fact that I made a poor attempt at a pure mathematics problem is beyond me. I enjoy the subject immensely, but I'm just an mechanical engineer, with an undergraduate minor in the field; Thus my exposure to the subject as a whole has been limited. I know I'm good at/and ENJOY solving problems in my fields scope. Regardless of what you may think, I don't need YOUR approval to continue to do so.
Best of luck to you in your hopelessly lonely life.
08 Aug 15
Originally posted by SoothfastHey Sooth, I see by your profile you live in Pa. What part of that bitterly cold place do you live? I live in the south end of the Pocono Mountains north of Allentown.
The argument requires understanding of "greater than" and "less than," along with the basic arithmetic operations of multiplication, division, and subtraction. Anyone with at least a grade-school education should possess that understanding. The most advanced notion in the argument, really, is that of a "real number," and the one thing taken as axiomatic ...[text shortened]... and so it is fair to use. You can easily read the entire argument out loud using plain English.
My job takes me about 80 miles away deep in the heart of New Jersey, where we are developing an American method of making a product almost everyone interacts with several times a week.
Do you teach math at Penn State? Maybe State College?