Just wanted to say don’t overrate yourself.
On another note, yeah, bias and outright mockery of so called “soft sciences” aren’t anything new as I’m sure you should know.
There are many things the soft sciences need to get mocked for. Actually the soft sciences need to be continually mocked until they grow a pair. Neither Anthropologists or Sociologist do a good job of claiming their turf against ignorant people. So at the end of the day its whatever with us: idiots and uninformed people will continually say crazy shit about groups and we never educate anybody on why that’s an awful thing.
Really. So if you have four dimes and I take one away, do you have approximately three dimes remaining? The answer is no. You have exactly three dimes remaining. the statement “all numbers are infinite” is meaningless fluff you are saying to try to convince people here that you have some idea of what you are talking about. But it’s obvious to anybody who has taken a second semester calculus class you don’t.
Take the number 3, or any integer really. Yes it can be written as 3.000000…, with infinitely many zeros to the right. But do you even know what those zeros represent? The number 3.000000… is really just the same thing as
So guess what, when it comes to integers, the whole “all numbers are infinite” line is complete rubbish. You have exactly (and not approximately) three dimes left.
Maybe if you are trying to estimate your unknown population mean, but if you have four dimes and I take one of those dimes away, you will always have three dimes left (as I just demonstrated) 100% of the time. Furthermore, even if the distance between two things that I was measuring right in front of me was an irrational value that I was approximating, then it is impractical to obsess over how much precision I have lost because I stopped calulating digits after the 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999th
significant digit. And even if for some bizarre reason I needed MORE precision, then I would just calculate more digits until I got the precision I needed.
This is a vacuous statement. It is logically equivalent to saying “if there was a martian on the moon, I wouldn’t have multiple pencils.” And it is logical for problems to have multiple possible solutions. A quadratic polynomial for instance, can have up to two roots. It’s not “wrong” for it to have this property (since wrong implies some kind of morality) and it is certainly not false.
Then your sources are (VERY) outdated, considering the New Math is a failed math educational reform movement from the 1960’s that has already run its course. Currently it is 2012 and no textbook author would dare go back to that standard. Pretty much any standard textbook today has various problems that apply mathematics in the section to real-world problems in physics, finance, biology, etc… It seems that you never bothered to read your math textbooks because if you had, you would have noticed this.
I am totally not being “mean” when I say this (though you will interpret it as such): Matriarch, you are the poster child for why algebra is necessary. Your misinformed, specious, and at times baffling views on mathematics serve as a prototype of what happens when a sense of quantitative literacy is left undeveloped.
Math is logic, If I have 4 objects and I remove 1 object I should have a number of objects one less than 4 objects which is 3.
I mean if you have done mathematical proofs you understand how much logic there is. I mean here is a simple one.
If n is an integer then prove that if n^2 is an even number, prove n is an even number.
Straight up this is actually a hard problem to prove as given, but we logically rearrange the problem. Instead of starting with n^2 we start with n. For n there are two possibilities for what n can be. n can be odd or n can be even. So if we examine this problem by squaring n we can find if this is true.
Assume n is even and can be written as 2J where J is an integer
n^2= nn = (2J)(2J)=2(2JJ)
Therefore if n is even this implies n^2 is even
Assume n is odd and can be written as 2J+1
n^2=nn=(2J+1)(2J+1)=4JJ+4J+1=2(2J*J+2J)+1
Therefore if n is odd then n^2 is odd
We conclude that if n is odd then n^2 must be odd and if n is even n^2 is even so logically we can deduce that if n^2 is even then it is only possible for n to be even.
That’s the kind of logic that goes into math.
This is the irony. I was going to reply to the “infinite zeroes” and “multiple solutions” statements, but I just said fuck it, and decided to write her off because as has been shown many times she truly doesn’t get it. Of course a quadratic has multiple solutions, because the “solution” to a quadratic is when it hits zero. The shape of a parabola and common sense should tell a person that this is reasonable. The physical analog to this is kicking a ball off of the ground into the air with t =0 being the initial kick. The model will have two solutions because the ball is on the ground twice.
What I really enjoyed is the hypocrisy of arguing that math should always have real world applications, yet taking issue with approximations being made.
I’d love an example please, the whole point in math and the reason a lot of people like that is there aren’t multiple possible solutions EVER. The answer is ALWAYS defined. There can be multiple descriptions of the same right answer, there can be multiple answers, but it’s not like “well you can choose this or this, or this” each of the answers is solid and there, not just a “possible” answer. When you take the quadratic of something it’s not “this point or this point”, it’s “this point AND this point”, if it was on a test and you just gave one it’d be partial credit at best.
1/3 = .33333333333 repeating to infinity
2/3 = .66666666666 repeating to infinity
1/3 + 2/3 = 1
so 1 can also be written as .99999999999999999 repeating on to infinity
doesn’t mean 1 is infinite, it is a finite number. so is 1/3 and 2/3.
You guys can abstract physical objects into numbers all you want, but it’s merely an imperfect abstraction.
You can say that we have 3 dimes, but that’s only a partial representation of what those dimes actually are in the physical world. That’s what I meant when I said numbers are limited in their function. To think of it in another way, each of those dimes are physically unique (unless you want to count repeated molecular structures in quantum physics, but that gets into different realities and really crazy stuff), so while adding them together might be useful, it is in no means fully representing those dimes.
If I have 1 dime the size of the Empire State Building, and two dimes in my hand, I still have 3 dimes. But quantifying them by just saying “I have 3 dimes in total” doesn’t mean much. This is because every instance of ‘having 3 dimes’ is completely unique. We could theoretically have an infinite variety of 3 dimes.
If numbers attempt to represent those dimes in terms of mass or dimension, then you face the infinite number having to be rounded issue. What you round off and consider unimportant is completely subjective. The more decimal places a number takes up, the more accurately it represents an object in physical space. But you cannot work with infinite numbers, so math approximates.
While it’s certain that some number abstractions are more accurate than others, all of those abstractions in truth have a probability of accurate reflection. In essence, you’re saying “For what we’re doing now, rounding this number here will suffice in the vast majority of circumstances.” However, it will never be 100% truth. Something might have a 99.99999999999999999999999999999999999% chance of being right, but there’s still that chance it’s wrong.
Think about that the next time you get on a plane.
Engineer 1: "Hey guys what are the chances the wings just fall off?"
Engineer 2: "Hmm…according to these calculations about x%"
Engineer 3: “That’s low enough to pass, build it and put people on it.”
This is precisely why there will always be math errors, and why anything based on math will never fully reflect or understand the physical world (sorry science). So why do we use it? Because it’s the best thing we have. Who knows, maybe someday math itself will be phased out because of these limitations.
The pure arrogance displayed by many math savvy people astounds me. Get the fuck off your pedestal. You’re not somehow superior to other modes of thinking, just different. And whenever anyone speaks out against math the zealots come out in droves like some hyper-conservative church stuck in steep religious doctrine. But if you want to keep white-knighting math (math must be a real sexy bitch), that’s your freedom. Just don’t expect me to listen to it.
True, he was specifically writing about New Math, but I think a lot of what he says still applies today. I know that when I read it last year, along with “Why the Professor Can’t Teach”, it didn’t seem all that dated. His example about incidence/reflection illustrates the problem with “applications”. It’s just lazy to give a formula, say for the surface area of a sphere, and then ask for the surface area of the Earth given its mean radius. That doesn’t really teach anything, but so many of the application problems in lower level algebra books have problems like this. What’s the difference between plugging the radius into a calculator and pushing some buttons, or looking it up online? Once you get to trig and calculus the examples get better, but we’re losing students far before that point.
I think high school students are perfectly capable of digesting a proof of the surface area of a sphere, with some technical gaps, that will not only be more meaningful to them, but will illustrate what math is all about in the first place. But this takes longer and a teacher wouldn’t be allowed to slow down because then they won’t get to cover the 200 other topics in the syllabus.
A lot of New Math stuff is still around, too. Making them memorize the symbols N, Z, Q, R-which I don’t mind so much because they save time- set theory, truth tables, implication, converse, contrapositive, the **inverse **of A->B (it’s ~A->~B…have you heard of that, because I don’t think that’s ever come up for me), functions as special types of relations including problems like “is {(1,2),(3,8),(2,8)} a function? why or why not?”. Well, since they’re getting technical just for the sake of getting technical, a function from what set into what set? It’s definitely not a function from {0,1} into R, so even their attempts to be precise are bad. Or what about asking “is 3 an element of {integers}”? Well, no, since {integers} consists of one element-a word. These are real examples from books I’ve had to use.
New Math emphasized number sets and the bootstrapping from one to the next. Q is formed from ordered pairs of elements of Z with some restrictions and correctly defined operations, and so on. No book goes into that much detail now, but the idea lives on and has authors rewriting math history. How many times have you heard someone say that i was “invented” to solve x^2=-1? I’ve heard it a lot and seen it in plenty of textbooks. It’s a nice little story, but it’s wrong and it probably discourages a student who doesn’t think he’d be clever enough to think of something like that. Well, *nobody *thought of it, ever. People just stumbled upon it.
Probably went a little off topic there, but Kline’s views aren’t irrelevant because New Math is gone. There’s still very little motivation and a reliance on memorization/plugging into a formula, at least at the lower levels of math (and they’re usually even given the formula they need to use as well lol).
I’d say the arrogance of math is pretty well earned considering just about every important discovery in human history.
But that isn’t a problem with math that is a problem with definition of a dime. If I define dimes as small round objects used as US currency and is equivalent to 10 US cents, then I have 2 dimes and a giant hunk of metal.
And Math covers that, its called units. I’ve used a similar example in teaching chemistry to freshmen where I give them the case of
30+30 = 1
And ask how does this problem make sense? It makes sense if 30 Minutes + 30 Minutes = 1 Hour. But see it wasn’t a case of the math failing, it was a case of me failing to explain the logic.
See changing the definition doesn’t invalidate the math and in any case you still have 3 objects.
No the problem with the math is what we choose to represent with the math. As a theoretical chemist the reason certain models fail is because they neglect forces or interactions that exist in the real world. Most models are made for simplicity and are often based on assumptions about a system. It gives us a starting point to understanding a system and it is quite successful. In fact I just finished a journal article about the problems with classical nucleation theory. So I might be what you call an expert on this matter.
See the problem with your line of reasoning is that you miss the concept of generalization. We generalize a system to make things easier on ourselves. For instance let’s take a coin flip. If we completely knew every force that was being applied to the coin and all the conditions we could tell you if it would land on heads or tails. The problem is that to do that it would be much more work than it is worth so instead we generalize it by using probability. We can’t predict exactly that it is going to land on heads or tails, but we can predict that if neither side is favored we should expect to get close to half of them to land on heads and half to land on tails.
Likewise the problem with any model that fails is it overly generalizes the system, or that the system is more complex than the model used. But don’t be mislead, the models work when the system behaves as the model predicts.
If anything the only problem with the math is that we as humans have finite lives and can not spend the time required to create a perfect model.
Considering we are responsible for the computer you are typing on, we will be as fucking arrogant as we fucking like.
Lol at comments like this because they don’t help.
I don’t think that Math is wrong so much as people have an aversion to being told they are predictable at some level. What they don’t understand is that most humans are entirely predictable once you understand the culture they are in. I could go on some godlike dissertation worthy rant on Culture but it helps nobody (and it leaves me out of a dissertation topic). Similarly heavy math people kinda forget the imperfect models they create when it comes to human interactions. Kinda how some engineers have been known to do shit in the way least convenient to people by not talking to them.
This thread is looking real pop-corn right now.
You honestly think she is going to change her view point because of an internet forum? I’ve been around the block long enough to know better.
I’ll say math and the related fields are better than most schools of thought because it has produced results and that is the ultimate measuring stick of the success of a school of thought.
People are creatures of habit, but at the same time they are capable of changing said habits.
[media=youtube]kpCJyQ2usJ4[/media]
Sal Khan is one of the best men out there right now.
BTW “real world applications”
[media=youtube]mt6Nq0dzFjo[/media]
I’m an econometrics student and I use algebra all the time to actually solve real world economic and logistic problems.
But even if you don’t have to use algebra in it’s high school format (meaning solve for x type of stuff) in real life like I do, then algebra is still one of the most important subjects in schools. Because the way I see it is that algebra schould teach you about abstract problem solving, which is the only subject in schools that teach this. Let’s say there comes a problem (even in the real world) that you’ve never seen before and that the books never taught you how to solve, which happens all the time with algebraic equations. Then you shouldn’t give up, but instead stop and think about how you’re going to solve it, just as in the real world. And algebra should teach you that.
yes math is beautiful and that’s something else people forget. why not study it because it is amazing? for example:
[media=youtube]G_GBwuYuOOs[/media]
the mandelbrot set is generated using a simple equation. once i realized how easy it was, i wrote out some code to produce a mandelbrot set and a julia set, added in some color cycling, and just got high and jerked off to my own creation. now THATS practical application
Math is a tool; nothing more and nothing less. The tool is only as good as the person using it, the job it is used for and the techniques used by the person with the tool to do the job. Saying math has a high success rate is like saying hammers have a high success rate when used at hammering. I assure that qualitative techniques have a better success rate at understanding the nuances of a culture than math does because qualitative techniques are the best tool for parts of the job. Just how anthropologists/sociologist also use math for other parts to flesh out the whole picture.
Aside from being a gross case of self-serving bias, it is an extremely unnecessary one. Students need to know that they are being handed a insanely versatile hammer and then taught how to work it. Most people don’t need high level math; but there are a good deal of math they do need to learn. If we sat down to take note of all the fun things anthropology has given us through out the years (even to that time where we were doing anthropological research without calling it that), we’d also could say many great deals about how beneficial it is to mankind.
Yeah, you have totally explained all of the world’s history with that. There is no way to appreciate how stupid this sentence is. It says nothing, it explains nothing. Let me give you one that is.
You see for the people who like science are never really wrong. It is because we understand what science does. This means that whenever somebody pretends to call us out on something, all we have to say is “Upon further research…”
Math is a thought process as well as a tool. When you see math as nothing more than symbols on a page you will never truly master it. It is when you can see beyond the symbols that you start to appreciate what math can be.
Learning about our own mind and our own culture is interesting, but at the same time there is so much of it that if we were ignorant about we wouldn’t be much worse off.
And even as a scientist I still talk about those just the same, I hated sociology classes because they were a total waste of time since they didn’t teach me anything I couldn’t come to on my own. Not to mention they were very rarely politically unbiased.
It says everything if you take the time to think about it. People have habits. If you do anything competitive you see this on a small scale, but one thing I have found is that even the worst of habits can be changed if the player is aware of his own habits and puts forth the effort to retrain himself into new habits.
The problem is that all too often people are in positions where changing their habits is an annoyance for them. For instance people would be healthier if they simply took the stairs more often, but of course this is an inconvenience because the elevator is much easier. All too often it takes some life shattering event for people to change their habits and in this case it could be a family member having a heart attack. The motivation to change is one of the hardest things to come by.
On a cultural scale changing cultural habits require the changing of the individuals habits. If one person has so much trouble changing, what are the chances of 1 million individuals changing? Not as likely to happen. As a result that is why history repeats because by the time a population can adjust for disaster it is often too late.
Then you have the problem where the experience of the last generation is wiped and the new generation has to relearn the experience and wisdom that the last generation had to learn. Having your grandpa tell you how horrible war is will never be as effective as you having experienced it.
We are wrong all the time, but when we are wrong we try to figure out what went wrong and figure out how to improve on it.
Algebra made me lose my job! I was all like “damn I’m so good at being a network administrator” and like 6 months later, the dude in charge of the company is like “you have no educational background! GET OUT!!” so now I’m going back to college because I can’t even do high school algebra but I can network the shit out of stuff!! DJASF;DSJFKLSFJKLJD;SFJSFJ;DASL!!
Now going back to school, Algebra is awesome!! Why did I neglect this subject so much??? Yeah sure, I feel like it’s enforced a little too heavily for subjects not needed, but for the most part it’s helpful. It help me beat some random Akuma player at that 25th anvs tournament… twice! Yeah sure I was high out of my mind, and yeah the Akuma player did suck, but if it wasn’t for Algebra… I WOULD HAVE LOST!!
I get the strange impression I have a leech, I should go to the doctors to get that looked at.