Originally posted by jrootham: [b] At this point I would say that it is an open question as to whether there is a fundamental connection between mathematics and the world, or it is just coincidence that the world can be described mathematically. [/b]

Mathematics is a human creation designed (among other things) to [i]model[/i] various aspects of the physical world. While the math may be flawless, the mapping of the model to the world may be imperfect.

[i]Example:[/i]

Q: The Canadian government sends 2,000 troops to Afghanistan. The Canadian government miraculously develops a conscience and withdraws 1,956 troops from Afghanistan in time for Christmas 2006. How many Canadian troops are left in Afghanistan?

Very interesting discussion, but very pointless. Single moms with difficult kids haven't been counted, considered or helped in this discussion. No solution was given for the burgeoning numbers of homeless and working poor. The difficulties faced by the disabled, ditto. I think math is all manipulated crap in Economics, but Economics 100 is a tool whereby the Right of Wing influence impressionable young men and women with Marketplace Dogma (otherise known as doggie do). I wonder if anyone has actually stepped on the moon. Could rookie small-plane pilots fly a big plane into a couple of highrises? My cell phone won't work on the ski hill, so I doubt it could work at a few miles up in the sky. I think that so-called rational thought is over-rated, while instinct and intuition are under-rated. People print or type instead of write, and their brains slow down accordingly, leaving little time for imagination, resourcefulness and critical thought. I think we vastly underestimate the universe. Infinity is a fact--we're here. So that suggests a Universe of at least a plus One. If a Black Hole sucked us all up tomorrow, we've been. That can't be undone. So anything could be possible, eh? One might be the only number that we need bother with, for those of us who hated Chi Hypotheses. You are probably thinking I need a nap after skiing...

Among historians of mathematics, Dirk Struik (1894-2000) was probably one of the best to connect progressive values with mathematics.

See, for example, G Alberts, On connecting socialism and mathematics : Dirk Struik, Jan Burgers, and Jan Tinbergen, Historia Math. 21 (3) (1994), 280-305. Now that would be an interesting read.

In any case, a good history of mathematics would be one place to start. Over here is the MacTutor History of Mathematics archive.

You might also look at [i]Applied Mathematics.[/i] This has traditionally been divided into 3 major areas: approximation theory, differential equations, and applied probability. To take just one example, the design of a dam (for generating hydroelectric power) requires the solution to a number of differential equations. It has something to do with how strong the base of the dam has to be to hold back the water. But of course a dam might be seen as not progressive at all, depending on the circumstances.

Of course engineering is basically applied mathematics (and physics). Building and house construction, bridges, etc. are all partly the result of some practical application of mathematical techniques.

In history, the French Revolution is also associated with a number of famous scientists and mathematicians. That's certainly a progressive use of higher [i]mathematicians.[/i] [img]biggrin.gif" border="0[/img]

As a person of social concience I've always felt, and with great passion, that xn + yn = zn has no non-zero integer solutions for x, y and z when n > 2, but you know I've just never been able to prove it. This disturbs me.

Here in BC we have 40% superminoritys oppressing the majority. (By government edict). I have argued against people (well discribed by Brett Mann below) that 40% superminoritys violate the 1 person 1 vote foundation principle of democracy. (Making 40 votes for one thing = 60 votes for something else clearly violates parity). But the mathematically and ethicly challenged deny any violation! The true devastation brought on by argueing with people incapable of rational thought is difficult to discribe! There must be a mathematical equation which explains why these people exist and are so conservative and are so cold bloodedly resilute in their resistance to reason. Should i put a 60% "supermajority" mathematics question in humanitys and science? (The people in politics are unconcerned).

quote: Originally posted by Brett Mann: [b]The very fact that this question can even be asked is disturbing. It is my belief that somewhere in the past two or three decades, a thread of anti-intellectualism and even anti-rationalism has crept into leftist thinking. It used to be that right wing USians had a monopoly on anti-intellectualism. There even was a group that proudly called themselves the "know-nothings" in the 1930s or so. The term "pointy-headed intellectual" was introduced by American reactionaries. The denial of global warming, the rejection of evolution, are directly traceable to a contempt for science, knowledge and learning. And a corrosive cynicism which distrusts everything (even mathematics!) is likely the legacy of post-modern, deconstructionist philosophy. Ken's question reveals a current of thinking on the left which desperately needs to be re-examined.[/b]

Originally posted by Ken Burch: [b]Just so that people don't come to the wrong conclusions about me, I'm not here to DEFEND the idea that higher mathematics is reactionary, it's a belief that I'm trying to move past.

My position here is NOT "Death to the Quadratic Equation".

I'm trying to learn other ways to see this discipline.

[ 13 December 2006: Message edited by: Ken Burch ][/b]

It's neither reactionary nor revolutionary. Approaching mathematics with such preconceptions will inhibit your learning it. It has to be approached on its own terms.

If I had to explain it to laymen, I would say it's primarily an aesthetic pursuit, a "glass bead game" (to use terminology from Hermann Hesse). For those immersed in, there's nothing quite so intoxicating or addictive.

Most school and lower-division college texts are egregiously written. The roots of the subject -- which continue to motivate its development -- really lie in a sort of "quantitative philosophy," a semi-mystical approach going back to Pythagoras and Diophantus. And there's no better place to start. The second edition of John Stillwell's "Mathematics and its History" was published two years ago. Work your way slowly through that book with quiet patience. At the end you will be a different man.

[ 21 December 2006: Message edited by: slybackstabber ]

I am happily immune from being immersed in higher mathematics. My ability to forget what I have learned in a mathematics context knows no limits.

It makes perfect sense, and if asked immediately after being told, I can follow almost any mathematical process to its conclusion.

However, if asked 5 minutes after being told, a period of time in which I've had a full cycle of [grocery list revision, vague horniness, thought about somebody I haven't seen in years, experienced existential angst, looked at my feet, blinked, thought about blinking, thought negative thoughts towards the powers that be] then I haven't a ghost of a chance.

I once wrote a mathematics exam in university where I studied intensely and at great pains to myself. I carried a vast a fragile latticework of understanding into the test and managed to write it all down as quickly as possible. By the time I had handed in the test and left the room, the latticework had shattered and I couldn't have begun to describe what I had once known.

On the other hand, I play a mean scrabble. [img]wink.gif" border="0[/img]

Originally posted by Ken Burch: [b]I've come to realize that probably one reason I struggled with algebra, geometry et.al., was that it seemed to me that these were basically reactionary academic disciplines, useful for designing weaponry or potentially repressive computer technology, but not with any obvious humanistic or social positive uses.[/b]

Do you live in a house? Do you use the Internet? If so, you're using applications of algebra, geometry, and other forms of mathematics.

quote: [b]I also feel this could be useful in developing better ways of teaching higher mathematics if such uses could be found.[/b]

Algebra and geometry are definitely not higher mathematics. The ancient Babylonians and Egyptians knew about them, and we teach them to adolescents today. Higher mathematics consists of subjects taught in universities like Analytic Number Theory, Complex Variables, Group Theory, Manifolds, Real Analysis, and Topology.

I am seriously dumbfounded by what a emaciated idea of what "math" is that the orginal poster (and others afterwards) displayed.

"Yeah... math... you know... like nuclear missiles and evil computer systems and shit..."

I can't begin to express how my consternation at finding another enclave of stupid people among the generally more intelligent left wing of Canadian society. Ugh.

We should start using newmath. We'll limit math to such the point that those god damned theoretical physics kids can't challenge the good old idea that God tells invisible bats with heavy weights on their feet to hold us to the Earth.

Originally posted by Ken Burch: [b]I've come to realize that probably one reason I struggled with algebra, geometry et.al., was that it seemed to me that these were basically reactionary academic disciplines, useful for designing weaponry or potentially repressive computer technology, ...[/b]

Nothing to do with the fact that you can't do maths?

Originally posted by eco-robot: [b] I can't begin to express how my consternation at finding another enclave of stupid people among the generally more intelligent left wing of Canadian society. Ugh.[/b]

Yes and trigger-jerky venom from a self-superior 20-year-old who's obviously seen so much of the world is just so much better. Thanks for your "contribution".

Originally posted by eco-robot: [b]I can't begin to express how my consternation at finding another enclave of stupid people among the generally more intelligent left wing of Canadian society. Ugh.[/b]

Well, then, you won't be needing your account here anymore. E-mail me when you're ready to participate on babble respectfully, and I'll unlock your account.

Originally posted by Kevin_Laddle: Thanks to mathematics, the United States was building rocket ships to collect pebbles on the moon while they had [b]hundreds of millions[/b] of their own citizens at home starving to death.[/QB]

I take it that you were as bad at math as Mr. Burch? [img]wink.gif" border="0[/img]

Originally posted by Sans Tache: [b]Mathematics is the search for the truth. The truth has no right or wrong, no left or right, it is, well, the truth.

If someone asks an accountant to add 2 + 2, the accountant will in turn ask, what would you like the answer to be? If a mathematician is solving a problem, there is only one answer.[/b]

This is one of the primary differences between lower and higher math. When you take arithmetic and algebra in middle school, you're taught absolutes like that. When you take Number Theory and Abstract Algebra in university, you learn that there are infinitely many arithemetic and algebraic systems. By choosing the appropriate algebra, you can have 2+2=0 or whatever you want.

Many such algebras aren't even commutative, i.e. a+b != b+a in those algebras. That turns out to be quite useful in physics, as quantum mechanics is described by a non-commutative algebra. The Heisenberg Uncertainty Principle is simply a precise description of the non-commutativity of position and momentum.

Originally posted by unionist: [b]Ken, you are so profoundly wrong about this that I wouldn't know where to start. Mathematics has applications to every single branch of human thought and activity - no known exceptions. Here is a [url=http://www.fields.utoronto.ca/programs/scientific/03-04/mathmedicine/]ra... example.[/url] When I retire, I'll devote my full time to answering your question.[/b]

I can't believe this ones still going on, I thought you clarified weeks ago. All I could add is a certain amount of mathematical reduction is essential for any sociological comparisons, but the real work still resides in the accuracy of the opening observations and the consistency any following narratives. Damn...I might be ready for my degree now. < [img]biggrin.gif" border="0[/img]

Originally posted by Ken Burch: [b]There was really no reason for the venom this thread produced.[/b]

I think we so often hear people trying to downplay basic education, that many people are pretty sensitive to the idea that math isn't important for all people to learn.

This is easily the most inane thing I have read in weeks. The reason why Ken could not handle math was not because it is used for evil. It's because he was bad at math. It's like me saying "I think one of the reasons I was never good at running fast was because fast running is often used for robbing." Rather, it's about me being a bad athlete.

Well this is nothing if not the wierdest little thread to come by in a while. Just dropped by in the unlikely event that it needed some moderatin', but obviously not. I had actually forgotten that I had contributed some wisdom of my own a while back.

There's humour, there's drama, there's some sort of ersatz Marxist dialectic. Not much math. Sometimes it approaches being transcendentally sublime (but wisely stops just short).

There was really no reason for the venom this thread produced.[/b]

Well, you kind of walked into a subject that has been debated quite a bit over the years here, and it goes beyond just math and can be politically charged.

I'm not good at cipherin' myself. I mean, I could learn all the high school math-- at a slightly slower pace than the fair to middlin' students. But my main problem is in retention.

Cripes, I can remember details from my grade six history book. I've memorized "The Creamation of Sam McGee", "The Highwayman" and a few soliloquay's from Shakespear, but if I don't use math in the same week I learn it, it's gone. My math exams, obviously, were awful. Except for the most recently learned section.

But mathematics is the only truth we know. The rest of our truths are just our best guesses. So, it's probably pretty important.

The broader idea, that higher mathematics and what we call "pure science" is a waste of time and resources is an unfortunate debate that crops up from time to time, and those that think pure science is a waste of time, or that science is evil, generally end up slinking away after being pointed to the errors of their ways.

I'm not sure how often that's happened, or what the percentages are, but those of us who champion science over ludditism or post modernism, religion , and other superstitions always give more than a good account of ourselves.

Keeping track of that stuff would be like, math, so it's beyond me.

But mathematics is the only truth we know. The rest of our truths are just our best guesses. So, it's probably pretty important.

I think I'll give Tommy the last word on this, being as it's probably as close to an absolute truth as has been uttered on this little site. I have recieved private communication which has convinced me that this thread has outstayed it's time upon the stage, and I shall respect that communication with acquiescence.

Mathematics is a human creation designed (among other things) to [i]model[/i] various aspects of the physical world. While the math may be flawless, the mapping of the model to the world may be imperfect.

[i]Example:[/i]

Q: The Canadian government sends 2,000 troops to Afghanistan. The Canadian government miraculously develops a conscience and withdraws 1,956 troops from Afghanistan in time for Christmas 2006. How many Canadian troops are left in Afghanistan?

A: None.

Very interesting discussion, but very pointless. Single moms with difficult kids haven't been counted, considered or helped in this discussion. No solution was given for the burgeoning numbers of homeless and working poor. The difficulties faced by the disabled, ditto. I think math is all manipulated crap in Economics, but Economics 100 is a tool whereby the Right of Wing influence impressionable young men and women with Marketplace Dogma (otherise known as doggie do). I wonder if anyone has actually stepped on the moon. Could rookie small-plane pilots fly a big plane into a couple of highrises? My cell phone won't work on the ski hill, so I doubt it could work at a few miles up in the sky. I think that so-called rational thought is over-rated, while instinct and intuition are under-rated. People print or type instead of write, and their brains slow down accordingly, leaving little time for imagination, resourcefulness and critical thought. I think we vastly underestimate the universe. Infinity is a fact--we're here. So that suggests a Universe of at least a plus One. If a Black Hole sucked us all up tomorrow, we've been. That can't be undone. So anything could be possible, eh? One might be the only number that we need bother with, for those of us who hated Chi Hypotheses. You are probably thinking I need a nap after skiing...

And I feel that so-called feelings are not strongly enough felt.

Merry Christmas.

Right you are, Unionist! Here's to depth of feeling and of thought! Merry Christmas to you, too!

Among historians of mathematics, Dirk Struik (1894-2000) was probably one of the best to connect progressive values with mathematics.

See, for example, G Alberts, On connecting socialism and mathematics : Dirk Struik, Jan Burgers, and Jan Tinbergen, Historia Math. 21 (3) (1994), 280-305. Now that would be an interesting read.

In any case, a good history of mathematics would be one place to start. Over here is the MacTutor History of Mathematics archive.

[url=http://www-history.mcs.st-andrews.ac.uk/]History of Math archive[/url]

You might also look at [i]Applied Mathematics.[/i] This has traditionally been divided into 3 major areas: approximation theory, differential equations, and applied probability. To take just one example, the design of a dam (for generating hydroelectric power) requires the solution to a number of differential equations. It has something to do with how strong the base of the dam has to be to hold back the water. But of course a dam might be seen as not progressive at all, depending on the circumstances.

Of course engineering is basically applied mathematics (and physics). Building and house construction, bridges, etc. are all partly the result of some practical application of mathematical techniques.

In history, the French Revolution is also associated with a number of famous scientists and mathematicians. That's certainly a progressive use of higher [i]mathematicians.[/i] [img]biggrin.gif" border="0[/img]

[ 17 December 2006: Message edited by: N.Beltov ]

As a person of social concience I've always felt, and with great passion, that xn + yn = zn has no non-zero integer solutions for x, y and z when n > 2, but you know I've just never been able to prove it. This disturbs me.

Andrew Wiles and Nick Katz solved Fermat's Last Theorem in

~~1994~~1995. But I bet you knew that.[url=http://en.wikipedia.org/wiki/Fermat's_last_theorem]It's been done![/url]

[ 16 December 2006: Message edited by: N.Beltov ]

Well, I just said I couldn't prove it. I was merely a liberal arts major.

Here in BC we have 40% superminoritys oppressing the majority. (By government edict).

I have argued against people (well discribed by Brett Mann below) that 40% superminoritys violate the 1 person 1 vote foundation principle of democracy. (Making 40 votes for one thing = 60 votes for something else clearly violates parity).

But the mathematically and ethicly challenged deny any violation! The true devastation brought on by argueing with people incapable of rational thought is difficult to discribe!

There must be a mathematical equation which explains why these people exist and are so conservative and are so cold bloodedly resilute in their resistance to reason.

Should i put a 60% "supermajority" mathematics question in humanitys and science? (The people in politics are unconcerned).

It's neither reactionary nor revolutionary. Approaching mathematics with such preconceptions will inhibit your learning it. It has to be approached on its own terms.

If I had to explain it to laymen, I would say it's primarily an aesthetic pursuit, a "glass bead game" (to use terminology from Hermann Hesse). For those immersed in, there's nothing quite so intoxicating or addictive.

Most school and lower-division college texts are egregiously written. The roots of the subject -- which continue to motivate its development -- really lie in a sort of "quantitative philosophy," a semi-mystical approach going back to Pythagoras and Diophantus. And there's no better place to start. The second edition of John Stillwell's "Mathematics and its History" was published two years ago. Work your way slowly through that book with quiet patience. At the end you will be a different man.

[ 21 December 2006: Message edited by: slybackstabber ]

I am happily immune from being immersed in higher mathematics. My ability to forget what I have learned in a mathematics context knows no limits.

It makes perfect sense, and if asked immediately after being told, I can follow almost any mathematical process to its conclusion.

However, if asked 5 minutes after being told, a period of time in which I've had a full cycle of [grocery list revision, vague horniness, thought about somebody I haven't seen in years, experienced existential angst, looked at my feet, blinked, thought about blinking, thought negative thoughts towards the powers that be] then I haven't a ghost of a chance.

I once wrote a mathematics exam in university where I studied intensely and at great pains to myself. I carried a vast a fragile latticework of understanding into the test and managed to write it all down as quickly as possible. By the time I had handed in the test and left the room, the latticework had shattered and I couldn't have begun to describe what I had once known.

On the other hand, I play a mean scrabble. [img]wink.gif" border="0[/img]

On the brighter side, you are therefore convesant with the mathematical concept "infinite".

Do you live in a house? Do you use the Internet? If so, you're using applications of algebra, geometry, and other forms of mathematics.

Algebra and geometry are definitely not higher mathematics. The ancient Babylonians and Egyptians knew about them, and we teach them to adolescents today. Higher mathematics consists of subjects taught in universities like Analytic Number Theory, Complex Variables, Group Theory, Manifolds, Real Analysis, and Topology.

This idiotic thread was made possible by math.

I am seriously dumbfounded by what a emaciated idea of what "math" is that the orginal poster (and others afterwards) displayed.

"Yeah... math... you know... like nuclear missiles and evil computer systems and shit..."

I can't begin to express how my consternation at finding another enclave of stupid people among the generally more intelligent left wing of Canadian society. Ugh.

We should start using newmath. We'll limit math to such the point that those god damned theoretical physics kids can't challenge the good old idea that God tells invisible bats with heavy weights on their feet to hold us to the Earth.

Nothing to do with the fact that you can't do maths?

[img]biggrin.gif" border="0[/img]

Yes and trigger-jerky venom from a self-superior 20-year-old who's obviously seen so much of the world is just so much better. Thanks for your "contribution".

Well, then, you won't be needing your account here anymore. E-mail me when you're ready to participate on babble respectfully, and I'll unlock your account.

Until then - bye.

[ 23 January 2007: Message edited by: Michelle ]

I take it that you were as bad at math as Mr. Burch? [img]wink.gif" border="0[/img]

This is one of the primary differences between lower and higher math. When you take arithmetic and algebra in middle school, you're taught absolutes like that. When you take Number Theory and Abstract Algebra in university, you learn that there are infinitely many arithemetic and algebraic systems. By choosing the appropriate algebra, you can have 2+2=0 or whatever you want.

Many such algebras aren't even commutative, i.e. a+b != b+a in those algebras. That turns out to be quite useful in physics, as quantum mechanics is described by a non-commutative algebra. The Heisenberg Uncertainty Principle is simply a precise description of the non-commutativity of position and momentum.

Heh. [img]wink.gif" border="0[/img]

I'm betting he meant to say people on earth rather than American citizens.

Ken, Unionist right away gave the only reason you need to buckle down and learn math. Otherwise you might end up working at Verizon Wireless

[url=http://www.abandonedstuff.com/2006/12/11/verizoncentsless/]http://www.ab...

I'll find the book Unionist suggests and read it.

And once again, I wasn't starting this thread to ATTACK mathematics. I was trying to move beyond a limitation in my own thinking.

There was really no reason for the venom this thread produced.

I can't believe this ones still going on, I thought you clarified weeks ago. All I could add is a certain amount of mathematical reduction is essential for any sociological comparisons, but the real work still resides in the accuracy of the opening observations and the consistency any following narratives. Damn...I might be ready for my degree now. < [img]biggrin.gif" border="0[/img]

I think we so often hear people trying to downplay basic education, that many people are pretty sensitive to the idea that math isn't important for all people to learn.

I don't think that was ever Ken's intent. Everyone knows that mathemetatics essential....even to lowly shepherds like me.

This is easily the most inane thing I have read in weeks. The reason why Ken could not handle math was not because it is used for evil. It's because he was bad at math. It's like me saying "I think one of the reasons I was never good at running fast was because fast running is often used for robbing." Rather, it's about me being a bad athlete.

well said Peter, that sums it up.

Well this is nothing if not the wierdest little thread to come by in a while. Just dropped by in the unlikely event that it needed some moderatin', but obviously not. I had actually forgotten that I had contributed some wisdom of my own a while back.

There's humour, there's drama, there's some sort of ersatz Marxist dialectic. Not much math. Sometimes it approaches being transcendentally sublime (but wisely stops just short).

You see OldGoat, there you go with the math: "Some of this, some of that." Regressive.

Well, you kind of walked into a subject that has been debated quite a bit over the years here, and it goes beyond just math and can be politically charged.

I'm not good at cipherin' myself. I mean, I could learn all the high school math-- at a slightly slower pace than the fair to middlin' students. But my main problem is in retention.

Cripes, I can remember details from my grade six history book. I've memorized "The Creamation of Sam McGee", "The Highwayman" and a few soliloquay's from Shakespear, but if I don't use math in the same week I learn it, it's gone. My math exams, obviously, were awful. Except for the most recently learned section.

But mathematics is the only truth we know. The rest of our truths are just our best guesses. So, it's probably pretty important.

The broader idea, that higher mathematics and what we call "pure science" is a waste of time and resources is an unfortunate debate that crops up from time to time, and those that think pure science is a waste of time, or that science is evil, generally end up slinking away after being pointed to the errors of their ways.

I'm not sure how often that's happened, or what the percentages are, but those of us who champion science over ludditism or post modernism, religion , and other superstitions always give more than a good account of ourselves.

Keeping track of that stuff would be like, math, so it's beyond me.

[img]wink.gif" border="0[/img]

I think I'll give Tommy the last word on this, being as it's probably as close to an absolute truth as has been uttered on this little site. I have recieved private communication which has convinced me that this thread has outstayed it's time upon the stage, and I shall respect that communication with acquiescence.

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