I think some form of categorization for pornography is great. It does not diminish the rights for pornography to be seen, it simply requires them to be defined by having a.xxx domain. The enforcement of this law in its entirety would be difficult, but for a large amount of commercial porn sites it could be controlled. This would give potential for the internet to be cleaned up, quite a bit in my opinion. And it should make it easier to find porn. lolllll
Personally, I enjoy the sticker. I think the whole ordeal points to the fact of how incredibly clueless some people are about truth, theory, and proof. This is inherently a philosophical issue - how do we know what is true? How can we prove things? I find the sticker as an ironic epistemological statement, which works against the people who would use the sticker in the first place. I think the sticker is a great starting point for epistemological discussions regarding creationism, evolutinary theory, science, and religion.
To me it is such a sad thing when science and religion are considered totally opposing viewpoints. Of course, Christian fundamentalism is in radical opposition to most of science (for its dogmatism), but science and religion both need to be recognized as pursuits for truth.
The real questions that need to be debated are the epistemological ones which lie above both science and religion. I find it hilarious that a judge is demanding a sticker encouraging critical thinking to be removed. People need to stop seeing religion as science as oppoising teams like in football. It's incredible to me that many people enthusiastic about the scientific method have such immature attitudes. Now let's all study some philosophy and have critical discussions, rather than root for our team at the Science vs. Religion Super Bowl.
I would just like to note that you have correctly stated the modern view of mathematics, but before the modern view mathematics was much more based on intuitive observations. Euclidean geometry was very much grounded in the intuitive observations of space. Although there was still an emphasis on the process of deduction, mathematics then was still related to observation. It was only until the axioms of Euclidean geometry were studied and challenged that mathematics started to be viewed simply as the logical consequences of deduction from axioms. This was because after challenging the axioms of Euclid, Non-Euclidean geometries were created, in which the axioms did not obey our normal intuitive observations. Thus the focus shifted to the deduction process from the axioms, rather than the intuitive meaning of the axioms. For a more detailed account of this movement, I refer you to a book by Howard Eves called Foundations and Fundamental Concepts of Mathematics.
I disagree. The point is that his misconduct was in the field of which his PhD was granted.
A PhD signifies that you are capable of research and that you are competent in your given field (hopefully). Schoen has showed he is not capable of either. He is not capable of research (he falsifies his results and data) and he is also certainly not competent in his own field. Understanding the concepts of physics at a PhD level does not immediately infer competence. Being competent also means knowing that making up data and conclusions are not parts of the scientific method. We are talking about fundamental knowledge he should have (the scientific method).
I am very happy with the university's decision, because I think they are retaining some dignity as to what a PhD should actually mean. It would be a tragedy to see a PhD reduced to some inflated IT certificate.
A PhD should not be a judge of personal character, but it should be a judge of their competence and legitamacy in the field of their PhD. Schoen has clearly disputed the meaning of his PhD.
I would tend to agree that learning calculus from Kiesler would be rather impractical these days. The methods used in Kiesler are from Nonstandard Analysis, which is aptly named because they are quite "nonstandard." Most mathematicians, AFAIK, are not trained in this at all.
Almost everyone learns the epsilon-delta limit approach to calculus. This is probably due to historical reasons, as it was the first way to put calculus on a rigorous footing. Nonstandard Analysis came later, and although it was more intuitive people didn't pick up on it because epsilon-delta provided just as much rigor with a lot more familiarity.
I would not knock on the methods of Nonstandard Analysis entirely, however. It provides a much more intuitive way to understanding calculus. In fact, the calculus of Newton and Leibniz was much more similar to the methods of nonstandard analysis than what is taught today. I'm not a professional mathematician, but I am aware of the fact that theorems are generally easier and more elegant to prove in nonstandard analysis.
I definitely agree with the reviewer in that what is so great about Kiesler is that by his use of nonstandard analysis, it is able to understand dy and dx much better than in the standard calculus teaching.
As I have experienced, what is most tragic about the teaching of the calculus is that the fundamental ideas of infinity, infinitesimals (or limits), and continuity are not given nearly enough attention. In order to truly understand calculus, these ideas must be understood thoroughly on a conceptual basis. This is possible through epsilon-delta, but it is often considered much too sophisticated for a beginning student of calculus to understand (which is fairly correct; remember that the rigorization of calculus took many, many years of work from the most brilliant mathematicians). Nonstandard analysis can provide the pedagogical bridge for this.
BTW - I forget to mention Smooth Infinitesimal Analysis, which is a different way of allowing the use of inifinitesimals in a rigorous manner. It differs from nonstandard analysis in that its development came through category theory versus logic. I believe John L. Bell wrote a wonderful little book on the subject. (Google "infinitesimal analysis john bell" and you can find the book).
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I think some form of categorization for pornography is great. It does not diminish the rights for pornography to be seen, it simply requires them to be defined by having a .xxx domain. The enforcement of this law in its entirety would be difficult, but for a large amount of commercial porn sites it could be controlled. This would give potential for the internet to be cleaned up, quite a bit in my opinion. And it should make it easier to find porn. lolllll
Personally, I enjoy the sticker. I think the whole ordeal points to the fact of how incredibly clueless some people are about truth, theory, and proof. This is inherently a philosophical issue - how do we know what is true? How can we prove things? I find the sticker as an ironic epistemological statement, which works against the people who would use the sticker in the first place. I think the sticker is a great starting point for epistemological discussions regarding creationism, evolutinary theory, science, and religion.
To me it is such a sad thing when science and religion are considered totally opposing viewpoints. Of course, Christian fundamentalism is in radical opposition to most of science (for its dogmatism), but science and religion both need to be recognized as pursuits for truth.
The real questions that need to be debated are the epistemological ones which lie above both science and religion. I find it hilarious that a judge is demanding a sticker encouraging critical thinking to be removed. People need to stop seeing religion as science as oppoising teams like in football. It's incredible to me that many people enthusiastic about the scientific method have such immature attitudes. Now let's all study some philosophy and have critical discussions, rather than root for our team at the Science vs. Religion Super Bowl.
I would just like to note that you have correctly stated the modern view of mathematics, but before the modern view mathematics was much more based on intuitive observations. Euclidean geometry was very much grounded in the intuitive observations of space. Although there was still an emphasis on the process of deduction, mathematics then was still related to observation. It was only until the axioms of Euclidean geometry were studied and challenged that mathematics started to be viewed simply as the logical consequences of deduction from axioms. This was because after challenging the axioms of Euclid, Non-Euclidean geometries were created, in which the axioms did not obey our normal intuitive observations. Thus the focus shifted to the deduction process from the axioms, rather than the intuitive meaning of the axioms. For a more detailed account of this movement, I refer you to a book by Howard Eves called Foundations and Fundamental Concepts of Mathematics .
I disagree. The point is that his misconduct was in the field of which his PhD was granted.
A PhD signifies that you are capable of research and that you are competent in your given field (hopefully). Schoen has showed he is not capable of either. He is not capable of research (he falsifies his results and data) and he is also certainly not competent in his own field. Understanding the concepts of physics at a PhD level does not immediately infer competence. Being competent also means knowing that making up data and conclusions are not parts of the scientific method. We are talking about fundamental knowledge he should have (the scientific method).
I am very happy with the university's decision, because I think they are retaining some dignity as to what a PhD should actually mean. It would be a tragedy to see a PhD reduced to some inflated IT certificate.
A PhD should not be a judge of personal character, but it should be a judge of their competence and legitamacy in the field of their PhD. Schoen has clearly disputed the meaning of his PhD.
I would tend to agree that learning calculus from Kiesler would be rather impractical these days. The methods used in Kiesler are from Nonstandard Analysis, which is aptly named because they are quite "nonstandard." Most mathematicians, AFAIK, are not trained in this at all.
Almost everyone learns the epsilon-delta limit approach to calculus. This is probably due to historical reasons, as it was the first way to put calculus on a rigorous footing. Nonstandard Analysis came later, and although it was more intuitive people didn't pick up on it because epsilon-delta provided just as much rigor with a lot more familiarity.
I would not knock on the methods of Nonstandard Analysis entirely, however. It provides a much more intuitive way to understanding calculus. In fact, the calculus of Newton and Leibniz was much more similar to the methods of nonstandard analysis than what is taught today. I'm not a professional mathematician, but I am aware of the fact that theorems are generally easier and more elegant to prove in nonstandard analysis.
I definitely agree with the reviewer in that what is so great about Kiesler is that by his use of nonstandard analysis, it is able to understand dy and dx much better than in the standard calculus teaching.
As I have experienced, what is most tragic about the teaching of the calculus is that the fundamental ideas of infinity, infinitesimals (or limits), and continuity are not given nearly enough attention. In order to truly understand calculus, these ideas must be understood thoroughly on a conceptual basis. This is possible through epsilon-delta, but it is often considered much too sophisticated for a beginning student of calculus to understand (which is fairly correct; remember that the rigorization of calculus took many, many years of work from the most brilliant mathematicians). Nonstandard analysis can provide the pedagogical bridge for this.
BTW - I forget to mention Smooth Infinitesimal Analysis, which is a different way of allowing the use of inifinitesimals in a rigorous manner. It differs from nonstandard analysis in that its development came through category theory versus logic. I believe John L. Bell wrote a wonderful little book on the subject. (Google "infinitesimal analysis john bell" and you can find the book).