If I'm wrong about this, I'd appreciate it if people could show me how this discipline can have progressive uses.

Take your post on babble for example. It would clearly be impossible without the internet. Taken in context, is this a net positive or a net negative? On the down side, the internet causes people to gain weight, procrastinate more, and gives an avenue for paedophiles and racists. On the other hand, it's responsible for the fact the 1990s were a better economic period than the 1980s, it's spreading literacy, gives an alternative to mainstream media, allows faster communication, apparently 20% of new married couples met on dating sites, et cetera. Overall, I would guess the internet is a positive.

You could make similar arguments for the airplane, for statistical theory, for food preservation and for combustion. How about the German V2 rocket. It killed so many people. But that same technology helped put a man on the moon, helped put weather sattelites up in space so we could study the atmosphere, and helped us set up a system of telecommunication through sattelite that you can communicate with people all over the world. Was it the technology that was moral/immoral, or the people?

I think you have to take a very holistic approach to the social impact of technology. There's a very long and convoluted chain between the purest of scientists who study esoteric abstractions for abstractions sake, and your common citzen demanding new products or governments demanding new weapons. It is society which decides how technology will be used.

Equivalently though, it is technology which is helping shape ethics. A philosopher, generally, would like a paper and pencil. Moving to more contemporary times, statistics are a primary tool of research in the social sciences, and there's very much an interplay between neurology, psychology, and sociology; if you try and have one without the other eventually you'll hit an intellectual dead end.

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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.

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I agree. The uses of mathematics are primarily to serve the elites and powerful within society. Thanks to mathematics, the United States was building rocket ships to collect pebbles on the moon while they had hundreds of millions of their own citizens at home starving to death. Mathematics is great for building nuclear war heads, weapons technology, software to line the pockets of millionaire fat cats, or creating non-sense to feed the bullshit rationale for junk sciences such as economics. But for the poor working family just trying to get by, mathematics has very little to offer.

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Let's talk about the average Joe.

- Back around 100 or so years ago for average joe, the infant mortality rate in North America was around 200 per thousand.
- Life expectancy was around 50.
- There were no effective birth control methods other than abstinence. Typical marriage age for average Joe was 20.
- Horse, and sometimes boat, were the means of travel.
- If average joe was lucky enough to know how to write, he could write letters to communicate.
- It was harder for average Joe to get heating in the winter.

Chemistry pollutes our planet and makes explosive weaponry available for wars. It provides Big Pharma with new ways to make money off our diseases. It allows Monsanto to control our agriculture with pesticides and fertilizer. It gave us plastic.

And don't even get me started on physics.

ETA for Michelle's benefit:

[ 14 December 2006: Message edited by: M. Spector ]

Language has caused empire. Language has allowed the few to conspire to control the many. Language allows for ideology and brainwashing. If not for language there'd be no words like "us" and "them". And clearly, without language we wouldn't have run into all the problems of algebra and chemistry.

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Originally posted by 500_Apples:
Kevin Laddle wrote:

Let's talk about the average Joe.

- Back around 100 or so years ago for average joe, the infant mortality rate in North America was around 200 per thousand.
- Life expectancy was around 50.
- There were no effective birth control methods other than abstinence. Typical marriage age for average Joe was 20.
- Horse, and sometimes boat, were the means of travel.
- If average joe was lucky enough to know how to write, he could write letters to communicate.
- It was harder for average Joe to get heating in the winter.

Now that I'm done writing this, I simply you're joking Mr. Laddle.

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But what does all of this have to do with mathematics? In a round about way, I realize you could make some abstract connection, but the same is true of anything if you want to reach far enough.

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 ]

Research into global climate change is heavily dependent on mathematical models.

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Originally posted by Gir Draxon:

Research into global climate change is heavily dependent on mathematical models.

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Thinking has been used to develop weapons to kill millions of people, and to scrounge up rationalizations and propaganda for doing the killing in the first place.

Typically, thought has been a tool of the ruling class to come up with all sorts of ways to oppress the masses. Or they shut other people out of their thoughts just to be exclusive and petty.

Maybe you can use thoughts to do some good things but most people only use their thoughts to imagine doing dirty things to their secretaries.

[ 14 December 2006: Message edited by: Rabelais ]

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Originally posted by quart o' homomilk:
End the oppressive burden of thought!

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This whole post made me burst out laughing, especially the part about thoughts being used to think dirty things about their secretaries.

Seriously though - I'm really kind of surprised at some of these posts, unless they're so subtly satirical that I'm a patsy. I mean, I can tell that a couple of them besides homomilk's are satirical but a couple of them have me scratching my head.

Are some of us really advocating that the advanced study of some of the natural sciences and mathematics are bad? I've never been good at math, never my strong point, but I KNOW there is a beauty to it that I'm missing out on and it's always been kind of a sad thing for me. (I recognize this because I've read people who ARE into it talking about it and I think, wow, they're really inspired by this stuff, and during those few "flashes" where I "get it" when things are explained to me by someone who is passionate about it, whether in print or in person, I think, wow, this is really neat.)

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But what does all of this have to do with mathematics? In a round about way, I realize you could make some abstract connection, but the same is true of anything if you want to reach far enough.

My point is merely that mathematics has historically been a tool utilized by the elites in society for their own benefit. All of the famous Greek mathematicians, for instance, were aristocrats. They had an interest in keeping their craft out of the hands of the peasants in the same way they wanted to keep them dumb, hungry, and illiterate.

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The starting point for modern medicine are the microscope, computer modelling, and statistics. Both of which are impossible without mathematics. The microscope is an application of optics, which is a discipline heavily depend on mathematics.

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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.

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Most pure mathematicians regard their work as being analogous to art, with no direct application. Professor Godfrey Harold Hardy FRS (February 7, 1877 – December 1, 1947), for eample, would often brag about how useless his work was, and that it could only be used for other math. Of course, 100 years later, his work is at the foundation of cryptography. There was an exception to this attitude though: Hardy is also known for formulating the Hardy-Weinberg principle, a basic principle of population genetics, independently from Wilhelm Weinberg in 1908. He played cricket with the geneticist Reginald Punnett who introduced the problem to him, and Hardy thus became the somewhat unwitting founder of a branch of applied mathematics.

A quote:

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Hardy preferred his work to be considered pure mathematics, perhaps because of his detestation of war and the military uses to which mathematics had been applied. He made several statements similar to that in his Apology:

"I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world."[1]
However, aside from formulating the Hardy-Weinberg law in population genetics, some of his work in number theory are reported to have found practical application in cryptography.
http://en.wikipedia.org/wiki/G._H._Hardy

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n general you don't know what the applications are when you go into something brand new. If it's poorly understood, how could you know the applications? To be really good at something, you can't really do it as a means to an end, you have to do it as an end in itself. Scientists and mathematicians who are really talented and productive love the subject matter. If you want to know how to approach the subject, the best way is to simply see the equations for how beautiful they really are, to look for the reasons the methods work, and to try and make your solutions more elegent.

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"Physics is like sex. Sure, it may give some practical results, but that's not why we do it." - Richard Feynman

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Originally posted by 500_Apples:
Kevin Laddle I ask you again if you're serious?

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Originally posted by Kevin_Laddle:
My point is merely that mathematics has historically been a tool utilized by the elites in society for their own benefit.

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Originally posted by Kevin_Laddle:
I'm of the belief that all information; university studies, formulas for creating new pharmaceutical cures, technologies that could save lives, etc should be free to all. These are things that belong to all of human kind, and I do not think we should be excluding some.

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Pure mathematics is the most democratic discipline. You only need a writing instrument and something to write on in order to engage in pure mathematics: a pen and napkin will suffice, or a stick and a piece of ground to make marks on.

Here's a joke.

The provost and the dean are meeting with the chair of the department of physics, who is trying to get money out of them for new lab equipment.

I don't look at math as being an elitist subject per se. I knew an NDP'er who ran for election in my hometown many years ago. During his high school years, Karl Morin-Strom won several provincial and national mathematics competitions and went on to obtain a PhD in math before working with the NDP. There is no shortage of left-brained lefties, imo. Einstein etc.

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Originally posted by Martha (but not Stewart):
The provost says, "Why can't you physicists be like the mathematicians? All they need is a pencil, some paper, and a wasterpaper basket." But then the dean adds, "Better yet, why can't you physicists be like the philosophers? They don't even need the wastepaper basket."

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Haha! I love philosophy jokes.

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Originally posted by Brett Mann:
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.

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Your utterly baseless and (I would say) slanderous "belief" is similar to your belief that the "Left" is blind to the threat that "Al Qaeda" poses to civilization as we know it.

The posts in this very thread should suffice to refute your anti-intellectualist straw man.

"It's not that important whether Mr. Summers is right or wrong. What's important is the attempt by some of the academic elite to stifle inquiry. Universities are supposed to be places where ideas are pursued and tested, and stand or fall on their merit. Suppression of ideas seen as out of the mainstream has become all too common at universities. The creed of the leftist religion is that any difference between people is a result of evil social forces. That is a vision that can return us to the Dark Ages".

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Originally posted by Brett Mann:
Utterly baseless? Do a search on "anti-intellectualism" and see what you come up with.

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Every time you amaze me, you then come back to amaze me some more.

The Washington Times was founded and is owned by right-wing fanatic cult-leader Sun Myung Moon.

The article you quote is written by the late unlamented Walter E. Williams, that luminary of impartial observation and enlightened opinion:

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Dr. Williams is also an outspoken critic of the minimum wage and affirmative action, believing that both practices are detrimental to blacks. Dr. Williams especially emphasizes his belief that racism and the legacy of slavery in the United States are overemphasized as problems faced by the black community and do not adequately explain the situation blacks face today.

Like most conservatives and libertarians, Dr. Williams criticizes gun control as endangering the innocent and failing to reduce crime.

Dr. Williams praises capitalism (of a laissez-faire variety) as being the most moral and most productive system man has ever devised.

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And Brett, once again, I started this thread in order to gather evidence to help refute the perception I had about mathematics, not to justify that perception. I had realized that what I thought about this couldn't actually be right and I was trying to move past it intellectually. OK?

[ 15 December 2006: Message edited by: Ken Burch ]

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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.

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Originally posted by Ken Burch:
Walter E. Williams may be unlamented, but as far as I know the man is NOT late. I've seen his column in the Anchorage newspaper(well, the half-page remnant of the OLD right-wing Anchorage newspaper that is published in the moderate Anchorage newspaper...)within the last week or so.

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You're right - just wishful thinking I guess. He's still enriching humanity's treasury of tripe and trash. Here is his restrained and dispassionate tribute to Milton Friedman, entitled Death of a Giant:

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While the man is gone, those of us who hold personal liberty as society's highest end will always remember his steadfast support of the principles of personal liberty. [...]

During my guest-hosting stints on the Rush Limbaugh show, Professor Friedman was a guest on several occasions. His responses to caller questions demonstrated the real teacher in him -- the ability to explain complex phenomena in a way that ordinary people can readily understand.

In terms of his scholarly output and worldwide contributions to ideas on liberty, Professor Milton Friedman was the 20th century's greatest economist.

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Originally posted by Brett Mann:
I'm old school. I believe in right and wrong.

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But seriously, does not postmodern thought tend to undermine the concept of an objective reality which exists beyond all our constructions?

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Consider this helpful gloss by the always aweseome Judith Butler:

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Derrida made clear in his short book on Walter Benjamin, The Force of Law (1994), that justice was a concept that was yet to come. This does not mean that we cannot expect instances of justice in this life, and it does not mean that justice will arrive for us only in another life. He was clear that there was no other life. It means only that, as an ideal, it is that towards which we strive, without end. Not to strive for justice because it cannot be fully realised would be as mistaken as believing that one has already arrived at justice and that the only task is to arm oneself adequately to fortify its regime. The first is a form of nihilism (which he opposed) and the second is dogmatism (which he opposed). Derrida kept us alive to the practice of criticism, understanding that social and political transformation was an incessant project, one that could not be relinquished, one that was coextensive with the becoming of life and the encounter with the Other, one that required a reading of the rules by means of which a polity constitutes itself through exclusion or effacement.

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It can be used to manipulate/understand the world for good or evil, but that good or evil comes from us, not the math.

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Originally posted by arborman:
What a bizarrely absurd thread. Math? Math is a value neutral tool for understanding the world.

It can be used to manipulate/understand the world for good or evil, but that good or evil comes from us, not the math.

Sheesh.

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I missed that one, thanks arborman. There is no good or evil in mathematics, just the truth.

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Originally posted by arborman:
What a bizarrely absurd thread. Math? Math is a value neutral tool for understanding the world.

It can be used to manipulate/understand the world for good or evil, but that good or evil comes from us, not the math.

Sheesh.

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Originally posted by EriKtheHalfaRed:
Yes yes, we all agree on that, its value neutral like any other intellectual tool but of course can also be misused like any other tool.

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Also, note that this is a very different thing than the popular definition of truth. That definition is that something is true if the world (universe, whatever) works that way.

Further note that the natural sciences do not have the concept truth or proof. There is only consistent with the best available theory. Some of those theories are considered to be very good, but none reach the standard of proof that mathematics holds.

The connection between math and the world is a very interesting one. 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.

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Originally posted by unionist:

I'm new school. I believe in right is wrong.

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Who knew people were this touchy about anything that even sounded like it was questioning the legitimacy of math(which, by the way, I wasn't actually doing)?

Michelle, can you please lock this? The whole thing took a turn I never intended it to take.

[ 16 December 2006: Message edited by: Ken Burch ]

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Originally posted by jrootham:
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.

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

Example:

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?

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Originally posted by Merryblue:
I think that so-called rational thought is over-rated...

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

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.

History of Math archive

You might also look at Applied Mathematics. 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 mathematicians.

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

It's been done!

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

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Originally posted by Brett Mann:
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.

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Originally posted by Ken Burch:
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 ]

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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 ]

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.

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My ability to forget what I have learned in a mathematics context knows no limits.

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Originally posted by Ken Burch:
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.

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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.

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I also feel this could be useful in developing better ways of teaching higher mathematics if such uses could be found.

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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..."

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Originally posted by Ken Burch:
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, ...

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

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Originally posted by eco-robot:

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.

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Originally posted by eco-robot:
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.

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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 ]

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

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Originally posted by Sans Tache:
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.

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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.

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Originally posted by Free_Radical:

I take it that you were as bad at math as Mr. Burch?

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Heh.

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Originally posted by unionist:
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 random example. When I retire, I'll devote my full time to answering your question.

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

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

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Originally posted by Ken Burch:

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

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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.

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

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