I'm glad things worked out well for your mother, and it's too bad the school administration couldn't be flexible. But that's the way things are going at the moment: with "No Child Left Behind" and whatnot, teachers are supposed to be "highly qualified", with documentation, and even taking classes/workshops on an ongoing basis...
Since she is an experienced teacher with extremely good recommendations, I wonder if it would have been possible to get a master's degree very quickly by turning in a portfolio? Obviously there still would have been a few hoops to jump through and maybe some fees (I dunno), but presumably it would have taken very little time (compared to years and years of grad school). Just a thought.
Well, it seems to me that activities like this competition contribute a lot to education. Think of it like a science fair, say. The high school and college students who participated in teams in this race have surely learned a ton about building a vehicle, testing it, fuel efficiency, aerodynamics... not to mention plain old teamwork.
Sure, they're learning these things in a specialized context. Just like how homework problems in math or programming class are always very specific problems that never quite match up with how those disciplines are used in the "real world". Doing a few calculus problems doesn't make you a mathematician and taking part in one competition like this doesn't make you an automotive engineer. But it seems to me that activities like this would help a student a lot, both to learn things about the field, and to give encouragement...
So I've rambled on again. I guess my point is just that there can be a lot of value to an activity like this. Even if it doesn't lead to better cars, it will hopefully lead to better engineers.
At the university where I teach, a large proportion of the student body doesn't pay tuition, but instead is supported by the state of Louisiana. The money for this comes out of taxes. Which means that I, as a professor, am paying a large number of my students to be here. So I guess I'm their boss...
Out of curiosity, what topic was taught in this way? Seems to me it would require the students to be pretty well-prepared for class.
This morning in my college algebra class, my students were barely able to handle the idea of discussing even functions AND odd functions in the same hour, despite my having told them last time that we'd be covering that. Too much information; none of them bothered to prepare for class. If I tried to run a class discussion, I don't think we'd ever cover anything. Or maybe it would work fine, I don't know.
I've never done this before, but: Dawn's First Post!
hehehe
Well, nice post, and nice articles.
The exercise was like taking a recording of a stadium full of loud people, then subtracting the noise of every person except one to hear the voice of that single individual.
I'm impessed. Even if they're wrong, it still seems to me like an impressive attempt to push the envelope on observations.
Yes, it is amusing, you're right. Was it meant as a joke? Sorry, I didn't pick up on the intent. As a serious article, I'm not buying it. As a joke, OK. I think you enjoyed it more than I did.:-)
I love Slate and I read it every day, but this article is not convincing for me. His main point is that George Lucas got all meta about plot; the Force represents Plot; the Emperor represents the author's attempt to control the plot, and Jar Jar represents the inventive whimsy of the characters. Sounds to me like "Moby Dick is actually the Republic of Ireland". Sorry.
Good question. Here's my attempted answer but maybe someone else will have a better one.
First of all, you have to look out for circular logic: "If f(-sqrt(2)) = 2, then (-sqrt(2))^f(-sqrt(2)) = 2". Tempting but wrong.
Well, just because it's not a proof doesn't mean -sqrt(2) is not a solution. To really address that, you have to go back to the original question.
x^x^x^x^...
has to be defined carefully. The only way I can imagine to define it is
lim_{n\to \infty} x^(x^(x^...)) (x appearing n times)
The solution other people have posted works out something like this: Call that limit f(x); it might be 0, infinity, non-convergent, or convergent to a finite value. For example, f(1) = 1 and f(2) = infinity (the sequence of finite exponential towers grows without bound).
For some values of x, f(x) is undefined because x^x is undefined, and so every term in the sequence is undefined (they each have an (x^x) up at the top of the tower). For example, 0^0 is not defined, and so f(0) is not defined; similarly (-sqrt(2))^(-sqrt(2)) is not defined: if y0, then y^(p/q) is defined if q is odd, but what on earth is it otherwise? Should we take a limit of y^(p/q) as p/q \to -sqrt(2), with q odd? Ugh. I don't remember real analysis well enough to say whether that limit would converge. I guess when I say -sqrt(2)^-sqrt(2) is "undefined" what I mean is that the arithmetic operation ^ is undefined; but maybe there's some sort of gruesome "continuous extension".
Well, if f(-sqrt(2)) is undefined, then that means -sqrt(2) is not a solution to the problem (which after all was "solve f(x)=2").
I mean, this f satisfies the functional equation x^F(x) = F(x). Your argument shows that if g is a function satisfying that equation and x is a real number such that g(x) = 2, then x = +/- sqrt(2). But -sqrt(2) is not in the domain of our function f.
As someone else pointed out, it's also not obvious that if g(sqrt(2)) is defined then necessarily g(sqrt(2)) = 2. A priori, g(sqrt(2)) could be 4, 8, 16, or any power of two.
Very nice! Nicely written and explained. I don't think it's hand wavy. If anyone is paranoid about whether you might be off by one anywhere in your count, then fine, give each non-counter more tokens...
While I recognize that there are real issues here, I must say that my first reaction was: I wonder if GPS might be able to kill off paintings of lighthouses...
True. I think the point was that three big meals a day is better than one or two really big meals.
Right now I am trying to have four reasonably healthy small meals, rather than three big meals and an unhealthy snack. I guess each person has to find an eating plan that works with his/her daily schedule.
Re:Money not the bottleneck.
on
HIV Vaccine
·
· Score: 1
"ACHAP PEPFAR overload"?!? Gee, why didn't I think of that?;-)
Slashdot Mirror
Maybe they're seeking the death penalty? /ducks
I'm glad things worked out well for your mother, and it's too bad the school administration couldn't be flexible. But that's the way things are going at the moment: with "No Child Left Behind" and whatnot, teachers are supposed to be "highly qualified", with documentation, and even taking classes/workshops on an ongoing basis...
Since she is an experienced teacher with extremely good recommendations, I wonder if it would have been possible to get a master's degree very quickly by turning in a portfolio? Obviously there still would have been a few hoops to jump through and maybe some fees (I dunno), but presumably it would have taken very little time (compared to years and years of grad school). Just a thought.
Well, it seems to me that activities like this competition contribute a lot to education. Think of it like a science fair, say. The high school and college students who participated in teams in this race have surely learned a ton about building a vehicle, testing it, fuel efficiency, aerodynamics... not to mention plain old teamwork.
Sure, they're learning these things in a specialized context. Just like how homework problems in math or programming class are always very specific problems that never quite match up with how those disciplines are used in the "real world". Doing a few calculus problems doesn't make you a mathematician and taking part in one competition like this doesn't make you an automotive engineer. But it seems to me that activities like this would help a student a lot, both to learn things about the field, and to give encouragement...
So I've rambled on again. I guess my point is just that there can be a lot of value to an activity like this. Even if it doesn't lead to better cars, it will hopefully lead to better engineers.
LOL. Thin-skinned troll.
Troll.
It would be ironic if noone responded on your wedding day...
*kapow*
my head asplode
So, do you have one of those jobs where you copy 17 MB from one folder to another...? ;-)
# Minor_trolls)
(http://en.wikipedia.org/wiki/Naked_and_petrified
At my university I'm required to take attendance records and store them for 5 years after the end of the semester.
At the university where I teach, a large proportion of the student body doesn't pay tuition, but instead is supported by the state of Louisiana. The money for this comes out of taxes. Which means that I, as a professor, am paying a large number of my students to be here. So I guess I'm their boss...
Out of curiosity, what topic was taught in this way? Seems to me it would require the students to be pretty well-prepared for class.
This morning in my college algebra class, my students were barely able to handle the idea of discussing even functions AND odd functions in the same hour, despite my having told them last time that we'd be covering that. Too much information; none of them bothered to prepare for class. If I tried to run a class discussion, I don't think we'd ever cover anything. Or maybe it would work fine, I don't know.
There's a review of various energy drinks on Slate.com: http://www.slate.com/id/2126591/
I've never done this before, but: Dawn's First Post!
hehehe
Well, nice post, and nice articles.
The exercise was like taking a recording of a stadium full of loud people, then subtracting the noise of every person except one to hear the voice of that single individual.
I'm impessed. Even if they're wrong, it still seems to me like an impressive attempt to push the envelope on observations.
Yes, it is amusing, you're right. Was it meant as a joke? Sorry, I didn't pick up on the intent. As a serious article, I'm not buying it. As a joke, OK. I think you enjoyed it more than I did. :-)
I love Slate and I read it every day, but this article is not convincing for me. His main point is that George Lucas got all meta about plot; the Force represents Plot; the Emperor represents the author's attempt to control the plot, and Jar Jar represents the inventive whimsy of the characters. Sounds to me like "Moby Dick is actually the Republic of Ireland". Sorry.
Good question. Here's my attempted answer but maybe someone else will have a better one.
First of all, you have to look out for circular logic: "If f(-sqrt(2)) = 2, then (-sqrt(2))^f(-sqrt(2)) = 2". Tempting but wrong.
Well, just because it's not a proof doesn't mean -sqrt(2) is not a solution. To really address that, you have to go back to the original question.
x^x^x^x^...
has to be defined carefully. The only way I can imagine to define it is
lim_{n\to \infty} x^(x^(x^...)) (x appearing n times)
The solution other people have posted works out something like this: Call that limit f(x); it might be 0, infinity, non-convergent, or convergent to a finite value. For example, f(1) = 1 and f(2) = infinity (the sequence of finite exponential towers grows without bound).
For some values of x, f(x) is undefined because x^x is undefined, and so every term in the sequence is undefined (they each have an (x^x) up at the top of the tower). For example, 0^0 is not defined, and so f(0) is not defined; similarly (-sqrt(2))^(-sqrt(2)) is not defined: if y0, then y^(p/q) is defined if q is odd, but what on earth is it otherwise? Should we take a limit of y^(p/q) as p/q \to -sqrt(2), with q odd? Ugh. I don't remember real analysis well enough to say whether that limit would converge. I guess when I say -sqrt(2)^-sqrt(2) is "undefined" what I mean is that the arithmetic operation ^ is undefined; but maybe there's some sort of gruesome "continuous extension".
Well, if f(-sqrt(2)) is undefined, then that means -sqrt(2) is not a solution to the problem (which after all was "solve f(x)=2").
I mean, this f satisfies the functional equation x^F(x) = F(x). Your argument shows that if g is a function satisfying that equation and x is a real number such that g(x) = 2, then x = +/- sqrt(2). But -sqrt(2) is not in the domain of our function f.
As someone else pointed out, it's also not obvious that if g(sqrt(2)) is defined then necessarily g(sqrt(2)) = 2. A priori, g(sqrt(2)) could be 4, 8, 16, or any power of two.
Very nice! Nicely written and explained. I don't think it's hand wavy. If anyone is paranoid about whether you might be off by one anywhere in your count, then fine, give each non-counter more tokens...
What do you think proportional means? Learn some math.
Yeah, well, 90% of everything is Sith...
(supposed to be "crap", not "shit", i know.... tryin' my hardest...)
This is mentioned on http://www.crazyapplerumors.com/archives/000429.ht ml#000429.
Silliness. Enjoy!
Here is a short tip on how to enable Flash blocking for OmniWeb and Camino:
0 313224837662
http://www.macosxhints.com/article.php?story=2005
I don't know about Safari or image-blocking, sorry.
HTH
While I recognize that there are real issues here, I must say that my first reaction was: I wonder if GPS might be able to kill off paintings of lighthouses...
True. I think the point was that three big meals a day is better than one or two really big meals.
Right now I am trying to have four reasonably healthy small meals, rather than three big meals and an unhealthy snack. I guess each person has to find an eating plan that works with his/her daily schedule.
"ACHAP PEPFAR overload"?!? Gee, why didn't I think of that? ;-)
it can lead to sex, and sex can lead to dancing.