These claims often occur, even publicly (remember, what was it, the IBM researcher who claimed to have solved the N=?NP problem?) but it is rare for them to be true. But, it would be fabulous for another one of these problems to have been solved.
Mathematicians have already learned to factor primes numbers. For instance, consider the imaginary number i=sqrt(-1). Then we have 3=(2+i)(2-i), 5=(2+i)(2-i), 17=(4-i)(4+i), and so on.
We often say that immediately after starting to job on the track we are on first lap. Then we reach our second, then our third, and so on, updated each time we cross the starting point. But I hate this and would much rather start with zero. Does anyone else feel the same way? I liked to say to myself, "I've completed no laps," then "I've completed one lap," and so on, instead of "I'm on my first lap," and "I'm on my second lap." Better to count what one has already done instead of what one plans to do.
Couldn't there be some sort of feedback with the number of wiki edits and the amount of advertising done? I mean, you won't get as many edits if you don't do as much advertising.
I thought of this too, but malapropism is only used when the effect is humorous.
I used to think malapropism meant a humorous mis_pronunciation_, so I'd say malaprapism instead of malapropism. Little did I know that malapropism is a humorous misuse of a word. [/layered-self-referential-irony]
I remember a great evening with the family when we were reading reviews for laxatives and other products like it. It's just so funny for people to be open about their, er, regular habits. Some samples:
"I used to be constipated for several days at a time for over 20 years before I started taken Swiss Kriss herbal laxative. I gave this herbal laxative 5 stars, because it works every time I use it. I never cramp. It's just a smooth move everyone should try."
"I have ALWAYS had a problem with constipation. Even when I was a child I had problems. Now at 55, I have learned I'm allergic to all DAIRY products which has helped tremendously, but still have a problem with constipation. Swiss Kriss is the ONLY product that my doctor will let me take every day. I take FOUR tablets at bedtime and I do not have any problems. I recommend it highly! BUT, until you know how many you will need to take, I'd only start out taking ONE tablet and then adding to it, only if needed."
"I actually never heard of this product till I read a biography about Louis Armstrong recently. Amongst Louis' many quirks and talents, he was actually a very health-conscience guy. He was into various techniques to keep his weight down and in general, stay healthier. This product was something he liked so much, swore by in fact, that he'd offer little packets of it to friends and associates he'd meet (even offering some to the British Royal Family during his visit in the U.K.). He also did a few commercials for them. Sooo, how could I pass that up?! I tried it myself and Pops had it right. This stuff has been around for a looong time and still works like a charm."
"I went to my favorite restaurant and ordered one of everything on the left on the menu...I felt...a feeling, I sensed an urgency, like a clogged pipe was my colon after that meal I've always had 'butt' issues btw I drove slowly through the bad side of town looking for a drugstore, looking for a way out of my 'condition.' I managed to locate an all night drive thru pharmacy with the word 'relief' posted clearly in the window. I parked, got out of my vintage Studebaker and proceeded to bang on the window pleading for a product that would take my pain away. [...] These pills do work...they just work too good...YOUR LIFE WILL BE FOREVER ALTERED AFTER USING THIS...THIS...'product.' Why is it $5.49 a bottle? I wouldn't pay more than $5.38."
Many of the math graduate courses I've taken had no followed textbook or even official course notes, and in those classes it was essential to take notes. I remember going back through my notes at the end of the day or the next day to rework them, and that helped a lot in understanding. I think the pace of the classes were fast enough, at least for some of them, or my knowledge at the time incomplete enough, that the pace of class was too fast. So I had to "preserve" it, perhaps without understanding all the details, and then review.
Come to think of it, I think I've only had one to three courses that diligently followed a textbook. Math is a funny subject to learn, I suppose, as powerpoint I feel is very bad for it. Sometimes you can learn entirely new things just by taking with another person, and I think that is the coolest thing ever. No writing ever done! All the visualization is done in the brain. However, to really understand the material, you need to work it out, as your brain cannot keep all the necessary information in your head at once.
Hofstadter's law: It always takes longer than you expect, even when you take into account Hofstadter's Law.
— Douglas Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid
It's not strictly impossible to predict the future. We do it all the time in science--no one is surprised that we can determine ahead of time what the period of a pendulum is. The question here is why the science for how quickly a task on a computer is complete is so poor.
Many of those are philosophical questions that one might argue cannot ever be satisfactorily answered. If there is an implicative structure to the universe (A is caused by B which is caused by C... ) eventually you will reach some cause to which we don't have an explanation (... which is caused by Z). Take the appearance of the color blue--we can say many scientific things about the color blue, but its actual color? Is there an explanation? So some things we are forced to take as is. It may be true we DON'T have to take things like gravity just as they are but we have reasons to believe if not, something else will replace it.
You have a very good point, and I get annoyed as well, but consider this. What does it mean that a dog learns how to bounce off the wall? The fact of the matter is that the dog has some procedure for determining its position that can also be figured out using calculus. That's the amazing thing.
There was actually an Mathematical Monthly article called "Can Dogs Do Calculus." In it, the dog would seem to solve this optimization problem, though it turns out there is a simpler explanation for their behavior. However, knowing it gives insight to the calculus problem.
I agree the quadratic formula is not that important to memorize for the majority of math students. Completing the square is good enough, at any rate, and that's how you come up with the quadratic formula anyways. However, knowing the difference between sin and cos is more basic and more fundamental. If you can't remember them, then you probably don't understand the unit circle and that x goes with cosine and y with sin, and that is conceptually an important understanding.
Slashdot Mirror
Mod mistake, commenting to fix.
These claims often occur, even publicly (remember, what was it, the IBM researcher who claimed to have solved the N=?NP problem?) but it is rare for them to be true. But, it would be fabulous for another one of these problems to have been solved.
Annnnnnddd... the first factorization is wrong. It should be 2=(1+i)(1-i).
Mathematicians have already learned to factor primes numbers. For instance, consider the imaginary number i=sqrt(-1). Then we have 3=(2+i)(2-i), 5=(2+i)(2-i), 17=(4-i)(4+i), and so on.
We often say that immediately after starting to job on the track we are on first lap. Then we reach our second, then our third, and so on, updated each time we cross the starting point. But I hate this and would much rather start with zero. Does anyone else feel the same way? I liked to say to myself, "I've completed no laps," then "I've completed one lap," and so on, instead of "I'm on my first lap," and "I'm on my second lap." Better to count what one has already done instead of what one plans to do.
does it run linux?
Did anyone catch the off-by-one error in this post? Yes, the number of times this joke has been posted is now two.
that Greenland is called Green again?
Couldn't there be some sort of feedback with the number of wiki edits and the amount of advertising done? I mean, you won't get as many edits if you don't do as much advertising.
I thought of this too, but malapropism is only used when the effect is humorous. I used to think malapropism meant a humorous mis_pronunciation_, so I'd say malaprapism instead of malapropism. Little did I know that malapropism is a humorous misuse of a word. [/layered-self-referential-irony]
I remember a great evening with the family when we were reading reviews for laxatives and other products like it. It's just so funny for people to be open about their, er, regular habits. Some samples:
"I used to be constipated for several days at a time for over 20 years before I started taken Swiss Kriss herbal laxative. I gave this herbal laxative 5 stars, because it works every time I use it. I never cramp. It's just a smooth move everyone should try."
"I have ALWAYS had a problem with constipation. Even when I was a child I had problems. Now at 55, I have learned I'm allergic to all DAIRY products which has helped tremendously, but still have a problem with constipation. Swiss Kriss is the ONLY product that my doctor will let me take every day. I take FOUR tablets at bedtime and I do not have any problems. I recommend it highly! BUT, until you know how many you will need to take, I'd only start out taking ONE tablet and then adding to it, only if needed."
"I actually never heard of this product till I read a biography about Louis Armstrong recently. Amongst Louis' many quirks and talents, he was actually a very health-conscience guy. He was into various techniques to keep his weight down and in general, stay healthier. This product was something he liked so much, swore by in fact, that he'd offer little packets of it to friends and associates he'd meet (even offering some to the British Royal Family during his visit in the U.K.). He also did a few commercials for them. Sooo, how could I pass that up?! I tried it myself and Pops had it right. This stuff has been around for a looong time and still works like a charm."
"I went to my favorite restaurant and ordered one of everything on the left on the menu...I felt...a feeling, I sensed an urgency, like a clogged pipe was my colon after that meal I've always had 'butt' issues btw I drove slowly through the bad side of town looking for a drugstore, looking for a way out of my 'condition.' I managed to locate an all night drive thru pharmacy with the word 'relief' posted clearly in the window. I parked, got out of my vintage Studebaker and proceeded to bang on the window pleading for a product that would take my pain away. [...] These pills do work...they just work too good...YOUR LIFE WILL BE FOREVER ALTERED AFTER USING THIS...THIS...'product.' Why is it $5.49 a bottle? I wouldn't pay more than $5.38."
Many of the math graduate courses I've taken had no followed textbook or even official course notes, and in those classes it was essential to take notes. I remember going back through my notes at the end of the day or the next day to rework them, and that helped a lot in understanding. I think the pace of the classes were fast enough, at least for some of them, or my knowledge at the time incomplete enough, that the pace of class was too fast. So I had to "preserve" it, perhaps without understanding all the details, and then review. Come to think of it, I think I've only had one to three courses that diligently followed a textbook. Math is a funny subject to learn, I suppose, as powerpoint I feel is very bad for it. Sometimes you can learn entirely new things just by taking with another person, and I think that is the coolest thing ever. No writing ever done! All the visualization is done in the brain. However, to really understand the material, you need to work it out, as your brain cannot keep all the necessary information in your head at once.
Or does it sound like they autotuned his voice?
Hofstadter's law: It always takes longer than you expect, even when you take into account Hofstadter's Law. — Douglas Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid
It's not strictly impossible to predict the future. We do it all the time in science--no one is surprised that we can determine ahead of time what the period of a pendulum is. The question here is why the science for how quickly a task on a computer is complete is so poor.
Many of those are philosophical questions that one might argue cannot ever be satisfactorily answered. If there is an implicative structure to the universe (A is caused by B which is caused by C ... ) eventually you will reach some cause to which we don't have an explanation (... which is caused by Z). Take the appearance of the color blue--we can say many scientific things about the color blue, but its actual color? Is there an explanation? So some things we are forced to take as is. It may be true we DON'T have to take things like gravity just as they are but we have reasons to believe if not, something else will replace it.
In fact, my professor suggests that there's not much promise writing a thesis relating to fractal dimension! Not a new field indeed.
You have a very good point, and I get annoyed as well, but consider this. What does it mean that a dog learns how to bounce off the wall? The fact of the matter is that the dog has some procedure for determining its position that can also be figured out using calculus. That's the amazing thing. There was actually an Mathematical Monthly article called "Can Dogs Do Calculus." In it, the dog would seem to solve this optimization problem, though it turns out there is a simpler explanation for their behavior. However, knowing it gives insight to the calculus problem.
What about hard work and intelligence? I wish they just hand me my PhD, except then it wouldn't be worth anything.
This only confirms that lego has indeed sold out.
I agree the quadratic formula is not that important to memorize for the majority of math students. Completing the square is good enough, at any rate, and that's how you come up with the quadratic formula anyways. However, knowing the difference between sin and cos is more basic and more fundamental. If you can't remember them, then you probably don't understand the unit circle and that x goes with cosine and y with sin, and that is conceptually an important understanding.