Math: Progressive or Reactionary?

This reminds me of a website I saw once where the writer claimed to have stood up and walked out of a calculus class because the instructor couldn't tell him how it was a Christian calculus class (at a Christian college). Maybe linked from here.

Anyhow, this case in particular shows that ideologues on both sides of the spectrum are clueless when it comes to science and mathematics. They think that just because they can talk away everything in their own interests that they can talk past reality as well. "Progressive math" and "feminist algebra" belong with "Intelligent Design" and "Christian calculus" in Lysenko's dustbin, but all too many people will buy into them in the meantime.

Define the word 'is'? ;)

They say that if you remember the sixties, you weren't there. But I do, and I was.

I clearly remember a "progressive" neoluddite rant about how "we've got to get ourselves back to the garden" by a fool who was trashing science and technology in terms that, in retrospect, were eerily similar to the Unabomber Manifesto.

After I picked up my dropped jaw, I politely said: "Do you have any sense of irony from the fact that you just said that while listening to electric guitars on an upscale sound system in an airconditioned room?"

He did not.

The next year, in grad achool, I spent a frustrating 2 hours trying to convince an equally stoned fool that there was no such thing as "the dark side of the moon." I'd even tried role-playing. "Okay, you're the sun, and you stand here and shine this flashlight on me, the Earth. And this baketball I'm holding is the Moon, see...?"

I like your credo: "Math is." Would make a good Coat of Arms for your blog...

"Against stupidity, the gods themselves contend in vain." [Schiller, cf. Asimov]

Evolution has always been attacked. Science has recently come under attack. And now math gets attacked.

The fruitcakes are restless.

What's next, the metric system? Counting? Spelling? The compass rose?

Exactly what is Christian about agriculture? Oh, no, farming is wide open to attack. And so is gardening, lawn care, and taking out the garbage.

It's a bit of a sad fact that, although anti-intellectualism is currently in America today associated chiefly with the Right (and a lot of intellectual types on the Left take open pride in this), there's no particular reason why it has to be this way; anti-intellectualism can infect basically any political philosophy you care to name, and at one time or another in history, it usually has.

We even see anti-intellectualism crop up among intellectuals-- maybe even mostly there, as intellectual types have a habit of deciding that their kind of intellectual is the only valid one, and all those other kinds of intellectuals must be doing something wrong. (Or, more often maybe, intellectuals who've gotten really into one field of study have an unfortunate tendency to decide that any field of study they don't personally understand must be worthless or evil.)

And that's exactly what we're seeing here: anti-intellectualism, in the form it takes when it infects the Left-- Leftist intellectuals no less, it looks like. And the way that this came about is hopelessly brazen and undisguised as the OP puts it: I have trouble understanding algebra, therefore I'm realizing it must be Bad. (And then of course as the thread goes on we get that little whiff of Lysenkoism as we run into the always-hilarious process of ideologues trying to figure out which ideology some branch of science is more compatible with, as if that would make it any more or less true...)

There really isn't anything much we can do about this, I guess. About the only thing we can do is remain vigilant to watch for anti-intellectualism encroaching, and try to ensure that it isn't allowed to take a foothold in whatever little corner of the ideological spectrum which we happen to occupy and therefore are in the best position to beat it back from. I'm not sure how we go about preventing it from gaining a foothold, mind you. Yell at it, I guess. Which means I guess MarkCC is on the right track here.

This is interesting debate but it needs to be brought back to the fundamentals of math.

So, since we are talking math, I thought I would put forth a tangential subject: Math Rock. I think mathematicians should take a closer look at it and perhaps study its finite characteristics to see if it may reveal any secrets, previously undiscovered sequences in note structure and provide insight to those of us who are not mathematicians.

I'm writing an article for my website on Math Rock so any feedback would be great!

Thanks
Phil at IRC
http://www.indierockcafe.com
http://www.monkeytypesthebible.com

I had a similar argument with a friend a few months ago about physics. His 'ultra-liberalistic' view was that much of our funding comes from the defense department, and that very few physicists seem troubled by that status quo. Part of his conclusion was that ethics should be taught IN physics classes, so that we'll steer clear of the 'wrong sort' of research. My response went a little further than MCC's, in that I said that it is genuinely dangerous to try and integrate ethics, or politics, into science. Should we ignore scientific truths because we find them unethical? Reality is reality - science is not tainted or invalidated by what some choose to do with that knowledge.

I think that anything I might say here has already been said more eloquently than I would be able to. All I have to add is that things like this really make me sick / sad / disgusted.

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

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

What are some positive humanistic and social uses of math?

Here's an easy one that your letter writer would probably understand.

Cooking.

I use algebra all the time when I cook. I'm always figuring out how to scale the amounts of ingredients that we need for different recipes. And calculating the amounts of ingredients, simple though it may be, is a very positive, and important use of math.

altho I assume s. rivlin intended his/her question to be humorous, I've been struggling with a variant on it and would appreciate inputs.

in discussions of such things as "truth", "reality", etc, people routinely use 2+2=4 as an example. but altho I can see gravity as "existing" in nature without the human addition of a "law of gravity", this isn't clear to me for math. take the simple case of integer arithmetic. why would nature need to add or subtract? the rules of such operations appear to be of interest only to intelligent creatures. and to take it a level further, altho it seems clear that any such creatures will come up with rules for doing such operations that necessarily will be in some sense equivalent (same "category"?), must they also come up with higher level abstractions like galois fields? ie, is there a point beyond which there is creativity rather than "mere" discovery, something analogous to art?

sorry if this is nonsensical. I'm philosophically near-illiterate, and altho trained, not much of a mathematician either, at least modulo present company.

-charles

Long ago, I learned a bit of wisdom from Jack Handley, who said that any time I had a difference of opinion with somebody, I should walk a mile in their shoes. That way, if I still disagreed with them, I'd be a mile away and have their shoes.

I'm finding it difficult to get into this person's shoes. First of all, he's arguing from adverse consequences, which just ain't valid: the fact that the Bomb killed hundreds of thousands of people doesn't mean that the principles of nuclear physics are in any way invalid. On the contrary: the hellish fires of Hiroshima is a doleful reminder of just how well we can understand the world, if we only try.

Second, listen to what the fellow says:

I've come to realize that probably one reason I struggled with algebra, geometry et.al., [sic] was that it seemed to me that these were basically reactionary academic disciplines [...]

Isn't this a tacit admission that he is passing judgment on something he does not understand (or did not understand for a long time)?

"Math is." Meaning, "math is a rational tool of logic, neither good nor bad in and of itself."

I've had to very vehemently and incessantly make this point to some of my friends on the left (the ones that are more right brain dominant), although I'm usually talking about science and logic and general, and not specifically about math ... but the principle is identical.

And to some of my friends on the right (the one's that are left brain dominant), I've also had to vehemently and incessantly make the point that logic, science, math, etc., aren't enough by themselves to make for good behavior or a good society.

Seems to me that wholebrain, general purpose biocomputers are the ideal, with areas of specialities as subsets of importance to that.

Logic without values is oppressive; values without logic is "woo."

Or maybe I should have written, "Logic without values can be USED oppressively; values without logic is mere 'woo.'"

To give one of a million answers to the idiot's question some of the most beautiful works of art produced by painters like da Vinci (who by the way is not a code!)and Dürer were only possible because mathematicians like da Vinci and Dürer discovered the mathematical rules of linear perspective.

I followed the link, and to be fair almost every single person who replied to that remark explained either gently or rudely that the person was spouting nonsense. For any given nutty opinion, the answer to the question "can I find someone who spouts that opinion on the Internet?" is always "yes".

Blake Stacey says:

Second, listen to what the fellow says:

I've come to realize that probably one reason I struggled with algebra, geometry et.al., [sic] was that it seemed to me that these were basically reactionary academic disciplines [...]

Isn't this a tacit admission that he is passing judgment on something he does not understand (or did not understand for a long time)?

Not so much. It's saying "I thought they were evil so (of course!) I had trouble learning them." His not understanding them is the judgment.

I read the thread to the bitter end, and the original poster basically completely backs away from his statement. So victory has already been achieved.

take the simple case of integer arithmetic. why would nature need to add or subtract? the rules of such operations appear to be of interest only to intelligent creatures.

I don't know if this helps but I found this article. I realize its a childrens site but it have interesting info.

This reminds me of some people I went to high school with who loved to proclaim that the only thing scientists were good for is to make bigger and better bombs.

This reminds me of some people I went to high school with who loved to proclaim that the only thing scientists were good for is to make bigger and better bombs.

I think it's ironic beyond words when people say things like that over the internet.

Oh Mark, please don't take guys like him seriously. You should appreciate them when you find them. They are those truly pathetic creatures, the one-dimensional minds.

Take the dot product of mathematics and "progressivism". If it's positive, mathematics is "good". Otherwise, mathematics should be discarded. How sad!

It must be terrible to have to live with such limited mental horizons.

Pleased to have found your blog - am not "in math" but respect your content and angle. May I link from my Maryland politics site?

Here is an inquiry for the math-phobic commentator. One way to determine energy-efficient distribution systems for goods, such as on a rail network with limited capacities and high energy costs, is to use linear algebra/matrices. Often the most efficient routes are not intuitive.

Math - specifically statistics - can be used to determine patterns of suspected bad faith discrimination against minorities or others.

Math is central to agriculture, optics, construction of social service facilities, taxation, transit planning, etc. Not everyone is cut out for math, I took Linear Algebra in college and it was my worst grade in my liberal-arts career there. But math is not automatically about right-wing politics or militarism. Jeesh.

Isn't chemistry, at the ball-and-stick atomic level, basically integer arithmetic? Not to offend any chemists in the audience, but it really looks like an implementation of the integers. This atom has four hooks, this atom has two, and so forth. On the nuclear level, the identity of each atom is determined by the integer number of pieces it contains.

At the deepest level, all the evidence we have collected to date indicates that the fundamental behaviors of Nature are mathematical. They can be described in no other way. Read Feynman's Character of Physical Law for details on this point; the moral is that Nature needs to know math in order to figure out what to do next.

ryan s -

tnx for the link. not quite on point, but interesting. I wonder if the fact that the various testees had problems at four and beyond says anything about primes. probably not, but it's surprisingly (to me) small number to pose a problem.

-c

But the question isn't whether mathematics is accurate, but whether its existence is progressive.

A colorable argument can be made that mathematics, as well as most disciplines which have practical applications, are regressive.

They increases the relative value of capital investment to labor either by allowing the purchase of more efficient capital products made with applied knowledge or purchasing education. If you have Marxist economic beliefs (and thus believe very strange things about how labor markets work), increasing the marginal productivity of a unit of labor is a bad thing for laborers since it means that less of them are necessary to achieve the same level of production so their wages will drop due to excess labor.

If you have social constructionist beliefs about power (which have some truth to them but can be taken to absurd extremes), specialized knowedge creates elites, maintained by jargon and titles, which can shape the public's subjective impression of reality toward their ends.

Math is a tool. Is a screwdriver either regressive or progressive? Of course not. The effcts of a screwdriver's use depend entirely on how it's used, what it's used for, what is the goal of the person or persons using it.

Don't conflate objects (even conceptual ones like mathematics) with intentions.

A colorable argument can be made that... disciplines which have practical applications, are regressive... If you have Marxist economic beliefs

I frankly doubt Marxism is something which actually exists in the real world at this exact time.

Yet, if you really are a red-blooded Marxist, you have to acknowledge that capitalism is necessary. The ideal socialist state cannot arise until workers are brought together in vast industrial armies, surrounded by material wealth. All tools which advance society to this point are, perforce, good things, because they bring us closer to the desired conclusion. Because industrial capitalism cannot survive without math, math is good.

Furthermore, try figuring out what should come from each according to his abilities and go to each according to his needs without basic algebra.

Knowledge can build elites up, but like rock and roll tells us, there's a time to build up and a time to tear down. Knowledge helps with the second part too.

I remember an example in Gonick and Smith's Cartoon Guide to Statisics which relates directly to the issue of political progressivism. In several court cases argued in the Deep South, the story goes, the defendants appealed on the grounds that the jury selection had been racially biased. To give precise figures, on an eighty-person panel of potential jurors, only four were African-American, while the population at large was roughly evenly split.

The statistician called as an expert witness showed that the probability of this happening by chance (which you can work out as 80 Bernoulli trials) is less than the probability of three successive royal flushes in poker.

The judge says something and then orders his own comments struck from the record. Gonick and Smith are assured by their correspondent that the remark ran something like, "If I was in that poker game, I'd have started shootin' after the second royal flush."

Political progressivism!

This reminds me of a paragraph in GM Hardy's Mathematician's apology:

"Real mathematics has no effects on war. No one has yet discovered any warlike purpose to be served by the theory
of numbers or relativity, and it seems very unlikely that anyone will do so for many years. It is true that there are branches of applied mathematics, such as ballistics and aerodynamics, which have been developed deliberately for war and demand a quite elaborate technique: it is perhaps hard to call them 'trivial', but none of them has any claim to rank as 'real'. They are indeed repulsively ugly and intolerably dull; even Littlewood could not make ballistics respectable, and if he could not who can?"

I think Hardy is making essentially the same point as the maligned poster. He is suggesting that math that's harmful is boring, and this is our tipoff that we shouldn't practice it.

A lot of math that is boring is helpful, however.

Eh, Hardy was an asshole who maligned applied mathematics at every opportunity. I'd love to see the look on his face if he knew that so much of the 'pure' math he worked on during his life is finding a ton of application these days. ^_^

Eh.

See, when I see stuff like this, it doesn't actually anger me any more. Alan Sokal has already done sufficiently broad blasting of variations on this woo that it's not even interesting any more. If stuff like this still upsets, reading some of Sokal's stuff can be very relaxing (especially "What the Social Text Affair Does and Does Not Prove").

What does make me flinch in the bit you quoted is the idea that "algebra, geometry et.al." are "higher mathematics". He just has no idea...

Now, there is a way to change his criticism to a point that may, in fact, be vaguely valid. However, that's sufficiently far from the original that it's no longer fair to call it the same objection.

MarkXIV: "specialized knowedge creates elites, maintained by jargon and titles, which can shape the public's subjective impression of reality toward their ends."

You seem to be implying that such elites would otherwise not exist! (1. Chieftains &rarr politicos 2. priestly types in general 3. Celebrities.) And shaping public perceptions? We only wish!

Eh, Hardy was an asshole who maligned applied mathematics at every opportunity. I'd love to see the look on his face if he knew that so much of the 'pure' math he worked on during his life is finding a ton of application these days. ^_^

Or that these days he is probably best remembered as being the Hardy of the Hardy-Weinberg principle in genetics due to a very short letter to Science that he wrote in 1908 and which involved no more complicated math than simple algebra.

That's the way these things go sometimes, I'm afraid. Many people want to conflate scientific and mathematical observations with some sort of political or theological or social agenda--not realizing that the disciplines are complete, in and of themselves, without needing an agenda.

Math, Science--they're tools, just like a hammer, to be used however you want to use them.

If the only uses you can think of for math are destructive ones, then I'd say that says more about your dangerous nature than math's.

In your several posts you've mentioned getting angry - it's bad for health (seriously) ... better first say and think "hmmm... how interesting"

Kathy Sierra explains:
http://headrush.typepad.com/creating_passionate_users/2006/12/two_more_…

I've come to realize that probably one reason I struggled with history, social studies et.al., was that it seemed to me that these were basically reactionary academic disciplines, useful for designing dogmatic ideologies or potentially repressive social systems, but not with any obvious humanistic or practical positive uses.

Seriously, it seems to me that the fruit of the social sciences are far more suspcious-looking.

Re DiPietro

I hope that Mr. DiPietro is not making the sssumption that I agree in any way, shape form or regard with folks who believe that scientists are only good for making bigger and better bombs. I didn't go on to achieve a PhD in physics by agreeing with these sadly deluded folks.

Ok. I don't always agree with Mark C. on Scienceblogs, but often we have similar opinions. But today, we're dead on in agreement.

I saw the other day a map of the average IQ of the world's nations. (Disclaimer: I don't believe in the IQ test being the end all be all of a metric for intelligence, but it does say a little)

http://en.wikipedia.org/wiki/Image:AverageIQ-Map-World.png

You do have to take that with some salt, possibly even with the whole salt shaker. But, it was no surprise that Japan is one of the leading IQ countries. China took me by surprise. I have a hard time believing that all 1.5 billion or so Chinese average out above 100. Possibly, and likely, in their cities this is so, but in the countryside where their government keeps them technologically and socially crippled, mmm, don't know, but I don't think it's likely.

Better, is America. Average 100. Sure, I've heard that all along. But, from what I can tell by talking to people I really doubt it. People are proud of being ignoramus. Truly. They enjoy stances with comfort of, "math and science are worthless, etc." As a matter of fact, people are sooo fucking stupid, they tolerate the birth of a museum that celebrates that the Earth is 10,000 years old, and that dinosaurs lived with man. WTF, talk about failing 7th grade science class.

But today, today takes the proverbial cake. This fucking moron, puts forth that math's only purpose to serve the rich and the government, by a) making people richer, b) making weapons of mass destruction. (Deer in the headlight look) Surely, you're Joking. Nope, he's not, and what's worse are the others that agree with him. (Look in a deer's eyes as he rolls over the top of the car)

I'm really tired of people thinking, believing, and continuing to be "stupid cool". This stupid cool stance, is what is KILLING US AND THE FUCKING PLANET!!!! Not government, NOT MATH, these STUPID FUCKERS are KILLING THE PLANET AND US!!! Because they refuse to get EDUCATED!! Why? Pick you're reason FEAR OF FAILURE, fear of being mortal like all us scientists, fear of hard work and pain for gain, etc. If they could overcome themselves, we could have a populace mature and educated enough to be the leading super power of the world. OUR FAILURE IN GOVERNMENT IS A DIRECT RELATION WITH THE EDUCATION OF OUR POPULACE. And you'll need fucking MATH, to understand that word DIRECT bitches.

It's unbelievable how I studied yesterday Rudin's text for pleasure, and then, I go online this morning and have to read about how the fucking "missing links" are still among us. Unbelievable.

Please forgive all my typos in this fucking rage. I need go study!

Eric Rand Jr:

Math, Science--they're tools, just like a hammer, to be used however you want to use them.

A pure mathematician once said to me that he thought mathematics was like art. While I can certainly appreciate what he was saying, I too prefer to think of mathematics (and science) as a tool [*]--like the chisel used in sculpting Michelangelo's David, or the swordsmith's hammer used in forging a sword. But the tool itself has no intrinsic "goodness" or "badness".

So having said that, let's try a little word substitution:

I've come to realize that probably one reason I struggled with hammers, saws and other tools, was that it seemed to me that these were basically nasty things, useful for making swords, spears or other potentially dangerous stuff, but not with any obvious humanistic or social positive uses.

Crank!

[*] But even a tool can be beautiful!

Now I happen to love math, and I can even construct an argument about how math is (politically) progressive. That said, I happen to disagree with you that "math is" or that "It's unavoidable." Math is a human construct. You even admit as much when you point out that math is a way of describing things by using rules. (I will disagree with that point later.) Math is not an aspect of the world, it is not a "natural" force (except that everything is natural). We make the rules and we make the descriptions (mappings). Some math is useful at helping us describe and understand the world, some is not. We tend to concentrate on that aspect of the mathamatical "universe" that helps us describe our experiential world.

As for the unnammed original writer, he is partially right even if ultimately wrong. Again, as you say, Math is a rule based system. Rule based systems are not the only way to go (though they seem to be the only *formal* way to go). And math is very formal. From a socio-political standpoint there are other system other than formal rule based ones and there are good reasons for someone to object to such a system. That math is not a socio-political system is something that *both* sides can forget. You might take a look at the history of people attempting to reform society using the authority of math and science and "logic". Amusingly enough those reforms have come from both the left and the right.

As I said before, I disagree that math is a way to describe things using rules. Math itself is simply a way, a game almost, for constructing "statements" (or, even, strings) using a formal rule based system. Start with some basic operators and you can build ever more complex statements. Now as it happens we can use some of this to then describe the experiential world. Why there is this "unreasonable" (not my term) coorelation between math and the natural world is a wonder and an unknown. There are those who think it is an important aspect of the world. There are othes, and I lean in this direction, that think it is just natural selection. That is, we choose and use those maths that help us in the world, those that do not help us do not get explored as deeply. There are strong mathamatical claims that the "universe" of math is far larger than we have explored and far less "relevant" to the natural world.

Getting angry is the first step. Scream at us, because we can sympathize. Try not to scream at the schoolchildren, though.

math_man wrote:

Better, is America. Average 100. Sure, I've heard that all along. But, from what I can tell by talking to people I really doubt it. People are proud of being ignoramus. Truly. They enjoy stances with comfort of, "math and science are worthless, etc." As a matter of fact, people are sooo fucking stupid, they tolerate the birth of a museum that celebrates that the Earth is 10,000 years old, and that dinosaurs lived with man. WTF, talk about failing 7th grade science class.

Keep in mind that ignorance does not mean that one is incapable of being intelligent. IQ is just a measure of cognitive ability--the capacity that a person has to solve problems.

Ignorance is when you decide not to use your problem-solving ability to question what you know.

A year or so ago, my grandfather took me to visit one of his old friends who worked at a university. The gentleman in question was one of the smartest people whom I've met--he had a great outlook on life, a well-paying job in the IT department, and a couple of degrees hanging up on the wall. He was also a creationist.

Was he intelligent? Absolutely. Did he have a high IQ? Most definitely. Was he ignorant of basic biology? Yes, by his own choice.

You choose whether to be ignorant or not; it has no relation to your intelligence. All it requires is that you be closed-minded about some aspect or other of the world.

Why do they choose ignorance? There's various reasons, and each individual has their own. Some have been indoctrinated at a young age, and lack the desire to question their own beliefs, because their beliefs work for them. Others are afraid of questioning their beliefs--whether they fear damnation, or just uncertainty in general, is open to question. Still others have been given a mistaken impression about what the 'other side' holds, or were never taught properly. Others never learned certain critical thinking skills.

How do we fix ignorance? By talking to people, and asking them--politely--to question their beliefs. Ask them why they believe as they do. Ask them to think about whether their reason for believing is appropriate. Learn to see things from their point of view, and teach them how to see from yours.

Once someone's mind is open, they can be educated--not before.

I agree, when their minds are open. Forgive my rage. I was in the military at the beginning of all this, prior to my education.

Unfortunately, sometimes, it takes a hard knock to open minds. Sometimes some people are only reached when someone is enraged at them.

Those in schools are different from the start. They've taken a first step. But, to the average populace, sometimes, a strong sentence here or there does actually get their attention.

I thought I made my disclaimer clear about what I thought of IQ. I do concur it is almost entirely BS.

I do concur their are some well educated people who should be on the receiving end of my rant.

I do concur you must be open and questioning of everything. I am not naive enough to think there is an absolute measure of any kind.

BUT, a strong but. The current state of affairs, the situation America is in, and the crap we're doing to this planet, IS a good overall measure of the effectiveness of our teaching and how well educated people are. So...

FUCK this politcally correct BULLSHIT!! These fucking morons need to wake the FUCK UP!!!! In ALL SECTORS!!!

Cooking.

One can also predict precise cooking times for substantial pieces of meat, fish, eggs. Math rock, and math cook.

it's surprisingly (to me) small number to pose a problem.

If the context is to choose between food sources in a competitive environment, as the tests suggest, it isn't terribly surprising if it maxes out early. The greatest advantage will be to distinguish between 2 and 1, or 3 and 2, insects or apples.

Btw, birds do much better on these tests, some species can distinguish between 6 and 7 IIRC. Seed for thoughts. :-)

Better, is America. Average 100.

Actually, that map claims 85-90 across Americas. And Australia 60?! Hmm. According to the discussion, the map is based on fabulation (no real source), not measurement. Likewise, some of the articles it is linked from is placed under the Wikipedia category of "Articles with unsourced statements".

You know, I think I'll agree with Wikipedia's tagging the map for deletion. And here it isn't math that is needed, but discrimination.

OTOH, IQ maps and other test interpretations could easily be the next topic on Mark's Bad Math list. Perhaps followed up with the difference between the unusable race concept and the useful population concept some sciencebloggers discussed recently, making room for showing some nifty multidimensional scattergrams.

math_man wrote:

I agree, when their minds are open. Forgive my rage. I was in the military at the beginning of all this, prior to my education.

No problem; getting upset at ignorance is a very human trait--because it's quite difficult to understand why someone would choose not to live up to their full potential.

BUT, a strong but. The current state of affairs, the situation America is in, and the crap we're doing to this planet, IS a good overall measure of the effectiveness of our teaching and how well educated people are. So...

I'd say that, perhaps, it might be a good idea to help out the education sector, and teach the teachers better ways to teach their students--how to engage their attention, how to keep them interested, all that sort of thing.

And, of course, make sure that the teachers know the concepts properly themselves.

Teach people how to think, rather than how to memorize lists of random 'facts'.

At least, that's my view on how to start.

And by the way, if you're not enraged at our current state of affairs. If you're not mad that people don't understand the importance of mathematics. If you're not mad about this movement against science. If you're not mad at America illegally invading Iraq. If you're not mad that this Administration has ruined a large part of our government. If you're not mad that NY had 60 degree weather in January. If you're not mad that people sit there and take it with a smile. If you're simply not mad at any of this...

Then you're probably not mad at the fact that this poor kid's sentence proclaiming utter stupidity about the importance of mathematics actually, relates to why people allow any of this happen.

It's simply a matter that we have FAILED to educate people. And we have allowed the uneducated control of government and education.

I'm speechless.

math_man wrote:

Then you're probably not mad at the fact that this poor kid's sentence proclaiming utter stupidity about the importance of mathematics actually, relates to why people allow any of this happen.

I'm not mad, because I can see why he wrote what he did, and how to change the situation.

I am somewhat sad that other people don't feel that a proper education is as important as it is, and I'm sad at the state of what an education is considered to be--but I can see how to change it, and I accept that the process will be a long, slow one.

But then again, that's just my point of view--that educating people gradually, one at a time, and encouraging them to teach other people about the same thing will eventually result in a change in public perception.

(Sneaky? Underhanded? Hijacking personal relationships for the transmission of information? Of course; how do you think word-of-mouth advertising works, anyway? ;-þ )

If you're not mad that NY had 60 degree weather in January.

For what it's worth, this doesn't make me mad. It's a single month in a single city. Weather is inherently chaotic. Now, what *does* make me angry are the long-term trends that we can clearly see, after all the random variation has been ironed out.

I mean, if I was going to use today's weather to confirm or deny global warming, I'd say it's false. We're too cold down here right now. >_<

« Faire des mathématiques, c'est donner le même nom à des choses différentes. »
Henri Poincaré

Everyone is laying into the guy, but I can see where someone gets this impression. The picture the average person gets of mathematics is that it is the way it is because your math teacher said so, that it is an arbitrary set of rules, that it is an attempt to reduce the richness of experience to dry numbers, that it is (assume 50's documentary narrator voice) "a TOOL IN MAN'S CONTINUING MASTERY OVER NATURE".

Most people have never seen how mathematics is part of the attempt to understand (not necessarily control) this world we find ourselves in, how it is like a music that can only be read, how it arises from a creative tension of discovery and invention. They don't see that mathematics, like science, requires no authority, and is in this way subversive.

Freeman Dyson has a great essay on science as subversion, in which he talks about his schooldays where learning was about submitting to authority. Math and science were liberating, because they transcended the petty authority of his schoolmasters.

yagwara:
That is a sad truth, but it doesn't click with what the person said. They're explicitly connecting mathematics to death and repression, not just saying it's boring or useless.

It truly is a tragedy that people don't understand how beautiful math can be, but it's a different issue.

I think the issue is connected. There's an ongoing perception that going "by the numbers" (i.e. behaving in a way suggested by mathematics) is somehow failing to be compassionate, and because of this, they think of mathematics as "harsh" and "ugly".

When I was in elementary school, my teacher said we could not subtract five from three, so I raised my hand and asked, "Why can't we say it's minus two?" Years later, in high school, negative numbers were fine, but we couldn't take square roots of them. So, I raised my hand and asked, "Why can't we use complex numbers?"

In eleventh grade, we wasted a year with a class known as "pre-calculus". I honestly don't know the point of it; when we weren't re-hashing the stuff we'd learned the previous year in Algebra II, we were huddling in the back of the room, playing Twenty Questions. Among the topics we slogged through, we did a whole stack of worksheets on limits. "Find the limit as x tends to three of. . . ." Many of these problems had a peculiar structure in common: they were all quotients with a subtraction on top. Nobody really had a clue why the balance of problems looked like that, except those half-dozen of us who had already learned calculus. Recognizing them all as derivatives of polynomial and trigonometric functions, we could breeze through them in a line of work apiece, never making a mistake, while everyone else spent six lines on each problem and screwed up a hefty fraction of them.

Of course, you can tell what happened: we got in trouble for "not doing it the way we do in this class."

All in all, mathematics provided an excellent way to stick thorns in my math teachers, and if that's not liberating, I don't know what is.

lytefoot:

Yeah, that's what I was thinking. There are a number of dichotomies that, in most people's minds, are aligned together: rigid/flexible, authoritarian/independent, narrow/open, right/left. Unfortunately many people also include rational/creative and math/art in this family.

Not that I think any of those are dichotomies, much less correlated ones.

I would disagree that politics + science is inherently evil. The reason for bringing ethics into science classes is that, although science may be true, science is done by humans, who, whether we like to admit it or not, are influenced by human culture, sometimes in subtle and almost imperceptible ways. The truth of science only emerges out of the consensus of the scientific community (peer-reviewing etc), and in this way the search for truth is always in process as that community changes and grows. Politics in science is not a bad idea because science is done by humans who have politics, you can't escape that.

I believe the lesson here is that people who divide the world into "progressive" and "reactionary" categories are complete morons.

By the way, in case I haven't said it before:

Mr. Chu-Carroll, thank you. Thank you for what you do, both professionally and on this blog. (Although I've only directly benefitted from this blog, so the first point is just by extension.)

The novel "Zen and the Art of Motorcycle Maintenance," one of my favorite books, is a 30-year-old classic dealing with these issues (the divides classic/romantic, rational/emotional, left-right, etc.) as it's theme.

The polarities in life are often reflected as a split in the human mind, and the challenge for each one of us is to integrate these disparate elements into a consistent pov, as part of a healthy and functioning whole personality. Most fail to do this, most barely have the time or inclination to even try, and yet our future as a race depends on it.

If you're not mad at America illegally invading Iraq.
I will let that go.
If you're not mad that this Administration has ruined a large part of our government.
I will let this go.

It's simply a matter that we have FAILED to educate people. And we have allowed the uneducated control of government and education.
This, I will not let go.
I work at a inner city school district. I have seen countless programs to help children learn and focus on school. I have seen countless teaching styles. The one major factor that must happen for education is parenting. If the child goes home and the parents say that they are stupid or they don't need education THEN education will fail. I have seen a superintendent go to the parents directly in an effort to help their child succeed. Even visiting them at their homes. Most of then gave him a few choice words and told him, in a not so nice way, to leave. Now, how is a child going to progess in any educational environment like this? Yes, there are SOME success stories, but not many. Years and years ago some parents may not have known what math is, or does, but they knew that education was needed. If your parents are behind you then a child will succeed. If your parents are against you most likely you will fail. I don't care what program, administration, or books you have it will fail.

I agree. It is the parents faults too, and maybe mostly. But... we the system failed to educate the parents too, eh.

It doesn't matter whose fault it is. We need a truly existential stance of, "everyone of us is equally at fault; because they.. willingly, neglegently, ingornantly, etc., etc." whatever.

If this planet burns up, or we nuke it. Who gives a fuck whose fault it is. Don't like my language? I don't like how this planet is teetering on the brink of destruction at humanities will.

Hawkings, one of our super minds, has been blogging again, as you may now, about how screwed up this is. Now if this man, who's done more to help advance humanity than probably the sum of all us raised to the nth, has to take time, again, to talk to us, something is terribly wrong.

So, yes. We failed. Consider this. You're looking at a local picture, in a local period of time. Great. The universe is global though, it doesn't matter what the microanalysis is in this part or that part. The major movement of the system is towards destruction.

The reason. People aren't educated. Simple. That's why. There's an infinite number of things they could be uneducated about, but that's the point, something is missing. Or something is blocking it.

What we need is a massive movement. Similar to other massive movements in history.

While I agree we can change people one by one, via, blogs or conversations. The facts remain, that people like Rosa Parks and the just celebrated King, were volitile, and highly upset, and they did NOT settle for slow change.

And the facts are, while I hate to see a people supressed, it won't matter at all if we're not around anymore.

What's more ironic, is this "stupid cool" attitude, mixed with politically correct fear, has almost turned our nation into an OPEN slavery. Yes, they've always sought control, but we've outright, publicly given it to them with this administration.

And all those who voted for, obvious, uneducated.

Let's not point fingers, let's not be passive, let's not waste anymore time.

Let's get fired, and let us who are in a situation to leave massive impacts on this system, do so! Yeah, you, education community. It is your title, no?

Parents are stupid like a rock, fuck them. Lets listen to the our brothers in Japan. It's time the education community takes back it's rights and pride. It's time we raise OUR voices, and tell EVERYONE, what they NEED to know.

Don't care. It has to be done. Otherwise, well... It's either a slow 100 yr heat death, or a really quick instant heat death. Personally, I don't like either. So I rather raise my voice.

You?

The human race has had compassionate and intelligent teachers from the beginning, but all their efforts are constantly being foiled by a few frustratingly immutable facts and all the many complications that are derived from them:

1) The unprincipled have a short-term advantage over the principled; their lies and ruthlessness in gaining power causes them to tend to rise to the top of hierarchical power structures.

2) Being ruled by morally unfit scum, our societies are affected negatively in countless ways, from poor parenting to poor citizenship.

3) Each new generation has to re-learn many of the most important lessons.

4) Psychological change takes time, and our lives are short.

5) Many of the most important lessons concern subjective qualities (like love or values or other psychological elements), and are often therefore somewhat unsolvable by obvious facts or sheer logic.

6) Fear is one of the chief motivators for living creatures, and is used to manipulate us by the unprincipled powerful.

Virtue and reason, like many things valuable, are rare, but all the more worth the struggle. Me? I'm with you, math_man.

For John Armstrong, who remembered it:

The "Christian calculus" thing is posted here on my blog.

Zeno wrote:

The "Christian calculus" thing is posted here on my blog.

I kind of have to laugh at that...it's amazing the lengths that people will go through to appropriate something 'good' as 'their own' sometimes...

Near the begining, there was: 'That's it: just "Math is". Math is a way of describing things using rules.' But you try and do it, and you find out that Math is Set Theory (more or less, but mostly more). If you want to do Math professionally, you are advised to do Set Theory (cf. the forces that act towards taking an interest in String Theory in Physics).

So, Is Set Theory Progressive or Reactionary? Well, such social structures (which demand conformity for no other reason than they're the only game in town because they demand it) could hardly be progressive; but the more important question is, Is Set Theory true? That is, is it OK for we scientifically-minded souls? Do its formal structures (probably) correspond with those that underlie objective, physical reality?

Now, because it's the only game in town, it has hardly been advertised that it (Maths) doesn't really care anymore. Most Mathematicians want to think of themselves as Platonists, studying the structures that would be true in all possible worlds, but more and more they must settle for Formalism, studying structures that are interesting because they (Mathematicians) study them. Why have they felt compelled to make that shift? Because there are scientifically compelling reasons why Set Theory is NOT true. (No wonder String Theory is making such slow progress; even if its basic approach was OK as physics, it has been presuming the wrong Math!) For example, see the modern physical instantiation of Levy's paradox (at http://www.geocities.com/potential_continuity/infiniteprobes.html). In short, although Math Is, the way that it is being done now, and the thing that it is now, are Reactionary.

The "Math is reactionary" thread linked to, and some of the comments listed above, are deeply disturbing. The denial of objective reality seems to have cut deeply into our society, and is corrosive of all science and learning, while the assumption that all those who disagree with you on specific issues are being willfully ignorant is equally corrosive of democratic political discourse. And it is very hard for me to see how we are going to solve any of our problems without objective science and democratic dialog.

While I agree with tschafer, I would like to emphasize that when there is a systematic presumption (such as that Set Theory is the Foundation of Mathematics) that lacks realistic justification (as anything other than a definition of a new entity going rather deceptively by an old name) and which cannot be discussed seriously (except outside scientific mathematics, and alongside all sorts of real oddities, within philosophy) then we might be losing the objectivity of our science; and that that is a potential problem because of the value of objective science (that I mention because of the invaluably democratic nature of such sites as this).

tschaefer wrote:

The denial of objective reality seems to have cut deeply into our society, and is corrosive of all science and learning, while the assumption that all those who disagree with you on specific issues are being willfully ignorant is equally corrosive of democratic political discourse. And it is very hard for me to see how we are going to solve any of our problems without objective science and democratic dialog.

If you'll pardon a bit of philosophizing, my opinion (shaded as it is by my own personal perceptions) is that the current state of denial towards reality is being driven by a focus of "should" rather than "is"--of people saying, "This is the way things should be" or "These things should not happen" rather than "This is how things are;" when one talks about "should," one is colouring their observations with their own personal perceptions, rather than seeing what "is."

This is pretty much the opposite of science; science is, after all, the study of what is, as is mathematics--one plus one is two; there's no "should" about it.

Why do people focus more on "should" than "is"? That, I'm not quite sure about. It may be because of the purposeful polarization of politics; it may be because of a lack of emphasis in math and science education; it may be because of the rise in popularity of certain fundamentalist denominations and their evangelical insistence on reforming the world into their own image; it may be because of the large amounts of money spent on studies comissioned by special interest groups; it may be because of all of these factors, or some, or none.

What is apparent, though, is that if there is a trend towards subjectivity of observers, then progress in math and science will suffer. Conversely, if there are advocates of objectivity--of removing the relevance of the researcher from the relevance of the research--who loudly and publically advocate extreme objectivity and dispassionate analysis of facts, then scientific and mathematical progress will thrive.

Science and mathematics are not political in and of themselves: they are a way of describing what is, and how it works. Politics--what "should" or "should not" be--has no place in this paradigm.

Eric, does science not care about the nature of the researcher(s)? It's a largely peer-reviewed process, so the status of the researchers (as peers or not) is important. (Not to mention that a large part of getting that status is getting funded, by non-scientists.) Also, fundamentalists often talk of the way the world is (e.g. Jesus is the Son of God), maybe more so than scientists (who talk of how it seems to be, or probably is, given only a restricted range of hypotheses, amongst which repetitions of experiments might discriminate). And what of the idea (common amongst scientists) that we should be more scientific? In short, I suggest that this whole area (like so many things) is much more complicated than many people presume (which is why I like maths (rather than set theory)).

Enigman wrote: does science not care about the nature of the researcher(s)? It's a largely peer-reviewed process, so the status of the researchers (as peers or not) is important.

I consider that to be more a method of ensuring that one's personal viewpoints are not impressing themselves on the research than any endorsement of specific persons or institutions. The peer-review process is meant to encourage objectivity, rather than subjectivity. True, one must be careful in selecting the peers--but that is mostly so that the people who have the appropriate support structure to perform the review are selected to review things within their area of expertise; one would not have a biochemist reviewing an animal-behaviour paper.

Also, fundamentalists often talk of the way the world is (e.g. Jesus is the Son of God), maybe more so than scientists (who talk of how it seems to be, or probably is, given only a restricted range of hypotheses, amongst which repetitions of experiments might discriminate).

Fundamentalists are speaking of their faith--their particular viewpoint of how the world works. The very concept of G-d has no place in science--how can one devise a test to determine anything about a supposedly omnipotent being, who can alter the test results undetectably?--and as such is a matter of faith, rather than observation.

A fundamentalist mindset also has no place in science: it is considered a virtue for a fundamentalist to be closed-minded to any alternate hypothesis, and to allow only the 'approved' viewpoint into their head; this is the opposite of the open-minded viewpoint (and the demand that one revise one's hypotheses if the evidence does not fit) that science requires.

For a fundamentalist, their faith in how the world "should" be overrides any evidence as to how the world *is*. There is no objectivity, no requirement to remain detatched.

And what of the idea (common amongst scientists) that we should be more scientific?

That is a matter of philosophy, and debate over procedure--not something of science itself.

Previous poster says: "The very concept of G-d has no place in science--how can one devise a test..." and thereby contradicts himself on the main point of his posting. That is, science deals with 'is' not 'should'. Since there is no test, we cannot know that there is not a God. Science can only work with hypothetical world-views, not with nothing but verifiable facts, and so the possible patterns that such facts could be evidence for are important. Since we cannot exclude God, such concepts must be included. To do otherwise would be to impose, as a matter of faith, an atheistic viewpoint. And of course that would be wrong, not to be open. After all, love is trust, and one could hardly be trustworthy were one not truthful, and the single-minded pursuit of truth is science. That is, scientists are, as such, lovely. Indeed, science, like love and truth, will set us free. And mathematics, insofar as it is part of science (i.e. platonistic), will too. (Only I note that formalistic mathematics, being effectively akin to faith, is NOT progressive.)

I ought to control my urge to keep commenting upon this topic, but I ought also to say that I think that Eric's use of the is/should divide, to help us to make sense of the modern flight from realism, is interesting, even important. Many reasonable people do associate realism with faith in the findings of science, rather than with faith in religious tradition, so it is important to note that science is a method, not a set of true theories. For the believer, to say that JC is God is to speak of what is, just as we may say that water is molecular. Conversely, much of what scientists say is not about what is, but about what we could get away with approximating reality to, given that we want a simple picture of reality to work with (that 'could' becoming a 'should' for scientists working within commercial constraints, with what can be publically justified, etc.). Science has a better track-record than religion, when it comes to pursuing the truth, but it is worth noting that there are scientific fundamentalists as well as religious ones (no less so, nowadays), and that no believer wants to hold onto a false belief.

Quote: Isn't chemistry, at the ball-and-stick atomic level, basically integer arithmetic? Not to offend any chemists in the audience, but it really looks like an implementation of the integers. This atom has four hooks, this atom has two, and so forth. On the nuclear level, the identity of each atom is determined by the integer number of pieces it contains. (end quote)

I always loved quantum mathermatics. :) The whole concept that protons, neutrons, electrons (and thier anti-matter counterparts, the positron, negatron, and neutrino)are made up of smaller componants, each with a PARTIAL positive or negative charge (ie, +3 AND -7, +1/3, -4/5, etc.) and that how they go together determines what kind of sub-particle you get! Plus the idea that, at that level of reality, those things aren't 'solid objects' but globs of energy behaving in determinable ways, something that my parents still can't quite seem to grasp. The sci-fi geek that I never grew out of just glows at the idea that matter isn't actually matter, just energy held in shape by valence feilds and quantum forces.