John Gabriel
2017-03-29 01:32:36 UTC
9/21/2016 A Harvard alumnus comments! | The New Calculus
Just a few weeks ago, some ignoramus posted a question on that ridiculous site Quora.
The question was:
“What do people think of John Gabriel’s New Calculus, which claims it is the only rigorous formulation of calculus”.
Quora is a question and answer site, that is run by a group of mainstream academics and their sock puppets. They control both the questions and answers. Those who post questions or comments with opposing views, have both their questions and comments mercilessly edited, and deleted if need be. In a sense, it’s Wikipedia-esque, in that the questions and answers are the views of mainstream academics. Nothing that is different or new is tolerated.
One of the fools who sits atop the trash heap, is one Prof. Jack Huizenga, a Harvard alumnus and mathematics teacher at Illinois University. The following link contains a snapshot of Huizenga’s comment: The ridiculous comment at the ridiculous site Quora.
In this very first post, I will address the comments made by this ignoramus (Huizenga) and horrify those, who will realise that this dimwit actually teaches mathematics!
There has been a completely rigorous notion of limit for well over a hundred years. – Huizenga
The great mathematics historian Carl Boyer had this to say:
"Cauchy had stated in his Cours d'analyse that irrational numbers are to be regarded as the limits of sequences of rational numbers. Since a limit is defined as a number to which the terms of the sequence approach in such a way that ultimately the difference between this number and the terms of the sequence can be made less than any given number, the existence of the irrational number depends, in the definition of limit, upon the known existence, and hence the prior definition, of the very quantity whose definition is being attempted.
That is, one cannot define the number 'square root of 2', as the limit of the sequence 1, 1.4, 1.41,1.414, ... because to prove that this sequence has a limit one must assume, in view of the definitions of limits and convergence, the existence of this number as previously demonstrated or defined. Cauchy appears not to have noticed the circularity of the reasoning in this connection, but tacitly assumed that every sequence converging within itself has a limit." - The History of Calculus and its Conceptual Development' (Page. 281) Carl B. Boyer
I doubt that Huizenga ever read this book, and if he did, there is no doubt he did not understand it. Not only has the notion of limit never been rigorous, but it was never challenged by any intelligent mathematician.
Rigorous treatments of infinitesimals are a bit more tricky, but have also been made. – Huizenga
One can only assume the moron is referring to the abortion of non-standard analysis, by a failed Jewish mathematician called Abraham Robinson. Even today, there are many academics (including PhDs) who do not accept non-standard analysis. In my opinion, it is pure rot because infinitesimals
don’t exist.
Reformulations of calculus as attempted in New Calculus, are essentially no interest to mathematicians, as the field of calculus is already extremely well understood and rigorous. – Huizenga
The buffoon wrongly assumes that the New Calculus is only a reformulation, which is evidently false. He goes on to talk about what interests mathematicians, but how could he know? Huizenga is not a mathematician, he is a teacher with no great works behind his name, unless of course one calls his juvenile papers on algebraic geometry a work of any kind.
Needless to say, if calculus were already extremely well understood, we would not have other mathematics PhDs making statements as follows:
Clearly, our calculus course does not prepare scientists in other fields to recognize, understand, and utilize the calculus that many of their fields are based upon. Thus, when it comes to calculus, we don’t get it the first time around, our colleagues don’t get it, and our students are still not getting
it. It’s no wonder that one of the most common occurrences in higher education is that of a non mathematics faculty member discovering that something they were doing is calculus. And at the very least, we feel justified in asserting that there still is a crisis in calculus instruction. – Knisley (Crisis in calculus education)
Knisley goes on to say:
However, in the calculus curriculum, many of the associations are circular. All too often a given concept is associated with a concept that is defined in terms of the original concept. Such connections increase the complexity of a concept without shedding any insight on the concept itself. Not surprisingly, concepts motivated with circular associations are the ones most often memorized with little or no comprehension. – Knisley (Facing the crisis in calculus education)
As for calculus being rigorous, we will hold off on that one until you have read and studied my New Calculus.
There is no point in trying to remove limits or infinitesimals from a discussion of calculus. – Huizenga
It’s easy to see that our moron academic knows nothing about Newton’s calculus and how he (Newton) arrived at the knowledge of it. The author’s main objection to the standard treatment of calculus via real analysis seems to be that he does not understand it. – Huizenga
Well, that’s certainly news to me. I have never made such a claim on the internet or anywhere else. I reject real analysis, not because I don’t understand it (few can ever understand it as well as I), but because it deals with a topic about a non-existent concept – the real number. Real numbers do not exist, because irrational numbers do not exist. In fact, until I arrived on the scene, no one before me and after Euclid, understood what is a number.
In the following comment I debunk the concept of Dedekind cuts and Cauchy sequences:
https://drive.google.com/open?id=0B-mOEooW03iLSTROakNyVXlQUEU
Our buffoon continues:
The errors in New Calculus are too numerous for it, to be worth going through the whole text. – Huizenga
It’s rather funny that he should say this, because he goes on to show that there is not a single error. Unsurprisingly, the baboon dismissed the rest of the text because he could not understand it up till that point. Huizenga mentions that one has to consider an (m,n) pair which is outright false.
In fact, if he had only continued to study and reread the text carefully, he would have soon realised that the values of m and n play no role in that of the gradient. Tsk, tsk.
His definition therefore presupposes that we know the slope of the tangent line (and that we have a notion of a tangent line to a graph of an arbitrary function) and merely computes the slope of a parallel secant line. This is incredibly circular. – Huizenga
Of course we know the slope of the tangent line, provided we know the slope of a parallel secant line. This is grade 8 mathematics! What he states in parenthesis is even more amusing. It demonstrates clearly that he, like many of his colleagues never understood calculus:
If a given function is not continuous and smooth, then any of the methods of calculus are null and void.
One, and only one tangent line exists at every point, provided the function is continuous and smooth, and a given point is not a point of inflection, that is, only half-tangent lines are possible at points of inflection. Our moron then continues to quote the example of the cubic, where there is no
tangent line at x=0 (because an inflection point exists at x=0). Unlike Newton's flawed formulation, the New Calculus handles this correctly.
He further goes to great length to try and convince the reader that he can actually divide the numerator in his difference quotient by m+n. – Huizenga
I don’t go to any great lengths. The proof that every term in the numerator has a factor of m+n can be shown by a high school student. It requires no special knowledge. The first page of the New Calculus website http://thenewcalculus.weebly.com has many examples on this, and includes links
to dynamic Geogebra applets which prove conclusively that it is based on sound analytic geometry.
It is legal to do this in the New Calculus, but illegal in Cauchy's flawed formulation.
That m+n is a factor of every term in the numerator finite difference f(x+n)-f(x-m) can be seen by anyone with a modicum of intelligence, but our chump Huizenga lacks even this. The chump way to see this fact, is to investigate actual functions using the finite difference, and it is soon realised, that this fact is true for all functions. It gets slightly more complicated in the case of terms containing only m and/or n, but this is easy to prove by mathematical induction and constructive proofs, as I have shown in my article
https://drive.google.com/open?id=0B-mOEooW03iLWldTU1ZkTDVQR0E
The easiest proof is given with the equation of a straight line, say f(x)=kx+p. We have from the New Calculus derivative definition: f ' (x) = {k(x+n)+p - [k(x-m)+p] } / (m+n) =k(m+n) / (m+n) = k. Observe that m and n play no role in the value of k which is the gradient. What amuses me, is that so many grade 8 students understand this, and most PhD chumps just don't get it!
Of course the New Calculus is likely to be revised over time to address concerns brought up by people. As this happens, I am confident it will look more and more like standard calculus (or the theory of the symmetric derivative which is closely related). – Huizenga
Another presumptuous claim by our buffoon Huizenga, because the New Calculus has never been revised and there are no plans to revise it whatsoever. There is no need to revise theory that is based on well-defined concepts. It will stand the test of time, just as Euclid’s Elements did.
The statement in parenthesis is quite amusing because it once again demonstrates the lack of understanding displayed by Huizenga. The New Calculus is not just about a new derivative definition, but also about a new integral definition, and much more (*). He might have gotten to that information had he continued studying the text. But ‘open-minded’ academic that he is not, he
ceased to continue, when he could no longer understand what he was reading.
The new calculus derivative definition has nothing in common with the symmetric derivative which Huizenga clearly does not understand. The symmetric derivative requires no special relationship exist between m and n. In fact, the symmetric derivative is used mostly in numeric differentiation.
(*) There are many new methods and theorems in the New Calculus that are not possible using Newton's flawed formulation.
And that covers his comment at Quora. In fact, he proves by all his statements, that there are no errors in the New Calculus, only serious issues in his ability to comprehend.
This same moron thinks that the derivative of sin(x) is not always cos(x). He also fancies that the sine function can take degrees as input, which is outright false. The trigonometric ratios operate only on radian input.
Comments are unwelcome and will be ignored.
Posted on this newsgroup in the interests of public education and to eradicate ignorance and stupidity from mainstream mythmatics.
***@gmail.com (MIT)
***@psu.edu (HARVARD)
***@mit.edu (MIT)
***@math.okstate.edu (David Ullrich)
***@clarku.edu
***@gmail.com
Just a few weeks ago, some ignoramus posted a question on that ridiculous site Quora.
The question was:
“What do people think of John Gabriel’s New Calculus, which claims it is the only rigorous formulation of calculus”.
Quora is a question and answer site, that is run by a group of mainstream academics and their sock puppets. They control both the questions and answers. Those who post questions or comments with opposing views, have both their questions and comments mercilessly edited, and deleted if need be. In a sense, it’s Wikipedia-esque, in that the questions and answers are the views of mainstream academics. Nothing that is different or new is tolerated.
One of the fools who sits atop the trash heap, is one Prof. Jack Huizenga, a Harvard alumnus and mathematics teacher at Illinois University. The following link contains a snapshot of Huizenga’s comment: The ridiculous comment at the ridiculous site Quora.
In this very first post, I will address the comments made by this ignoramus (Huizenga) and horrify those, who will realise that this dimwit actually teaches mathematics!
There has been a completely rigorous notion of limit for well over a hundred years. – Huizenga
The great mathematics historian Carl Boyer had this to say:
"Cauchy had stated in his Cours d'analyse that irrational numbers are to be regarded as the limits of sequences of rational numbers. Since a limit is defined as a number to which the terms of the sequence approach in such a way that ultimately the difference between this number and the terms of the sequence can be made less than any given number, the existence of the irrational number depends, in the definition of limit, upon the known existence, and hence the prior definition, of the very quantity whose definition is being attempted.
That is, one cannot define the number 'square root of 2', as the limit of the sequence 1, 1.4, 1.41,1.414, ... because to prove that this sequence has a limit one must assume, in view of the definitions of limits and convergence, the existence of this number as previously demonstrated or defined. Cauchy appears not to have noticed the circularity of the reasoning in this connection, but tacitly assumed that every sequence converging within itself has a limit." - The History of Calculus and its Conceptual Development' (Page. 281) Carl B. Boyer
I doubt that Huizenga ever read this book, and if he did, there is no doubt he did not understand it. Not only has the notion of limit never been rigorous, but it was never challenged by any intelligent mathematician.
Rigorous treatments of infinitesimals are a bit more tricky, but have also been made. – Huizenga
One can only assume the moron is referring to the abortion of non-standard analysis, by a failed Jewish mathematician called Abraham Robinson. Even today, there are many academics (including PhDs) who do not accept non-standard analysis. In my opinion, it is pure rot because infinitesimals
don’t exist.
Reformulations of calculus as attempted in New Calculus, are essentially no interest to mathematicians, as the field of calculus is already extremely well understood and rigorous. – Huizenga
The buffoon wrongly assumes that the New Calculus is only a reformulation, which is evidently false. He goes on to talk about what interests mathematicians, but how could he know? Huizenga is not a mathematician, he is a teacher with no great works behind his name, unless of course one calls his juvenile papers on algebraic geometry a work of any kind.
Needless to say, if calculus were already extremely well understood, we would not have other mathematics PhDs making statements as follows:
Clearly, our calculus course does not prepare scientists in other fields to recognize, understand, and utilize the calculus that many of their fields are based upon. Thus, when it comes to calculus, we don’t get it the first time around, our colleagues don’t get it, and our students are still not getting
it. It’s no wonder that one of the most common occurrences in higher education is that of a non mathematics faculty member discovering that something they were doing is calculus. And at the very least, we feel justified in asserting that there still is a crisis in calculus instruction. – Knisley (Crisis in calculus education)
Knisley goes on to say:
However, in the calculus curriculum, many of the associations are circular. All too often a given concept is associated with a concept that is defined in terms of the original concept. Such connections increase the complexity of a concept without shedding any insight on the concept itself. Not surprisingly, concepts motivated with circular associations are the ones most often memorized with little or no comprehension. – Knisley (Facing the crisis in calculus education)
As for calculus being rigorous, we will hold off on that one until you have read and studied my New Calculus.
There is no point in trying to remove limits or infinitesimals from a discussion of calculus. – Huizenga
It’s easy to see that our moron academic knows nothing about Newton’s calculus and how he (Newton) arrived at the knowledge of it. The author’s main objection to the standard treatment of calculus via real analysis seems to be that he does not understand it. – Huizenga
Well, that’s certainly news to me. I have never made such a claim on the internet or anywhere else. I reject real analysis, not because I don’t understand it (few can ever understand it as well as I), but because it deals with a topic about a non-existent concept – the real number. Real numbers do not exist, because irrational numbers do not exist. In fact, until I arrived on the scene, no one before me and after Euclid, understood what is a number.
In the following comment I debunk the concept of Dedekind cuts and Cauchy sequences:
https://drive.google.com/open?id=0B-mOEooW03iLSTROakNyVXlQUEU
Our buffoon continues:
The errors in New Calculus are too numerous for it, to be worth going through the whole text. – Huizenga
It’s rather funny that he should say this, because he goes on to show that there is not a single error. Unsurprisingly, the baboon dismissed the rest of the text because he could not understand it up till that point. Huizenga mentions that one has to consider an (m,n) pair which is outright false.
In fact, if he had only continued to study and reread the text carefully, he would have soon realised that the values of m and n play no role in that of the gradient. Tsk, tsk.
His definition therefore presupposes that we know the slope of the tangent line (and that we have a notion of a tangent line to a graph of an arbitrary function) and merely computes the slope of a parallel secant line. This is incredibly circular. – Huizenga
Of course we know the slope of the tangent line, provided we know the slope of a parallel secant line. This is grade 8 mathematics! What he states in parenthesis is even more amusing. It demonstrates clearly that he, like many of his colleagues never understood calculus:
If a given function is not continuous and smooth, then any of the methods of calculus are null and void.
One, and only one tangent line exists at every point, provided the function is continuous and smooth, and a given point is not a point of inflection, that is, only half-tangent lines are possible at points of inflection. Our moron then continues to quote the example of the cubic, where there is no
tangent line at x=0 (because an inflection point exists at x=0). Unlike Newton's flawed formulation, the New Calculus handles this correctly.
He further goes to great length to try and convince the reader that he can actually divide the numerator in his difference quotient by m+n. – Huizenga
I don’t go to any great lengths. The proof that every term in the numerator has a factor of m+n can be shown by a high school student. It requires no special knowledge. The first page of the New Calculus website http://thenewcalculus.weebly.com has many examples on this, and includes links
to dynamic Geogebra applets which prove conclusively that it is based on sound analytic geometry.
It is legal to do this in the New Calculus, but illegal in Cauchy's flawed formulation.
That m+n is a factor of every term in the numerator finite difference f(x+n)-f(x-m) can be seen by anyone with a modicum of intelligence, but our chump Huizenga lacks even this. The chump way to see this fact, is to investigate actual functions using the finite difference, and it is soon realised, that this fact is true for all functions. It gets slightly more complicated in the case of terms containing only m and/or n, but this is easy to prove by mathematical induction and constructive proofs, as I have shown in my article
https://drive.google.com/open?id=0B-mOEooW03iLWldTU1ZkTDVQR0E
The easiest proof is given with the equation of a straight line, say f(x)=kx+p. We have from the New Calculus derivative definition: f ' (x) = {k(x+n)+p - [k(x-m)+p] } / (m+n) =k(m+n) / (m+n) = k. Observe that m and n play no role in the value of k which is the gradient. What amuses me, is that so many grade 8 students understand this, and most PhD chumps just don't get it!
Of course the New Calculus is likely to be revised over time to address concerns brought up by people. As this happens, I am confident it will look more and more like standard calculus (or the theory of the symmetric derivative which is closely related). – Huizenga
Another presumptuous claim by our buffoon Huizenga, because the New Calculus has never been revised and there are no plans to revise it whatsoever. There is no need to revise theory that is based on well-defined concepts. It will stand the test of time, just as Euclid’s Elements did.
The statement in parenthesis is quite amusing because it once again demonstrates the lack of understanding displayed by Huizenga. The New Calculus is not just about a new derivative definition, but also about a new integral definition, and much more (*). He might have gotten to that information had he continued studying the text. But ‘open-minded’ academic that he is not, he
ceased to continue, when he could no longer understand what he was reading.
The new calculus derivative definition has nothing in common with the symmetric derivative which Huizenga clearly does not understand. The symmetric derivative requires no special relationship exist between m and n. In fact, the symmetric derivative is used mostly in numeric differentiation.
(*) There are many new methods and theorems in the New Calculus that are not possible using Newton's flawed formulation.
And that covers his comment at Quora. In fact, he proves by all his statements, that there are no errors in the New Calculus, only serious issues in his ability to comprehend.
This same moron thinks that the derivative of sin(x) is not always cos(x). He also fancies that the sine function can take degrees as input, which is outright false. The trigonometric ratios operate only on radian input.
Comments are unwelcome and will be ignored.
Posted on this newsgroup in the interests of public education and to eradicate ignorance and stupidity from mainstream mythmatics.
***@gmail.com (MIT)
***@psu.edu (HARVARD)
***@mit.edu (MIT)
***@math.okstate.edu (David Ullrich)
***@clarku.edu
***@gmail.com