Wolfgang Mueckeheim is a decent human being. Although he is one of the smartest mainstream academics I've met (Wildberger is the other), some of his thoughts on important mathematics concepts are not correct.

The majority of his comments at the following link are worth reading and I'd say I would agree with perhaps 60% of them:

https://www.quora.com/profile/Wolfgang-Mueckenheim-1

BUTTTTT.....

The following 2 comments are incorrect:

1. Mathematics - at last reasonable mathematics - is abstracted from physical reality. That begins with counting and drawing lines. If other universes exist, then they will probably have the same physics and therefore the same mathematics.

“Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.” [V.I. Arnold: "On teaching mathematics" (1997)]

-------------------------

Mathematics is entirely abstract and has nothing to do with the physical world. Mathematics is the science of (abstract) measure and number. The quote by Arnold is just plain ignorant.

2. What is a number? A number is an idea. An idea is a thought. What is a thought that no-one can think? Certainly nothing belonging to a scientific worldview.

How can an irrational number be thought? Like anything else it can be thought by a finite name, sound, or picture like π or √17 . (Infinite digit sequences without finite formulas would require an infinite amount of information. That is not available.) How many finite names can exist? Not more than countably many. Therefore there are at most countably many irrational numbers. The rest is not belonging to a scientific worldview.
-------------------------------------
A number is a name given to a (abstract) measure that describes a magnitude or size.

Number is a noumenon - a thing as it is in itself, as distinct from a thing as it is knowable by the senses through phenomenal attributes. However, a number can be "knowable" or "realised" through thought. While this word noumenon was coined by Kant, it was not his idea, but Plato's. We know that noumenon is just another word for the abstract "ideal form" from which all other concepts and things are instantiated.

The paragraph about "irrational number" is somewhat scatterbrained because WM assumes there is such a thing as "irrational number", which is untrue. Each sentence in the second paragraph contradicts all the previous sentences..

Eram semper recta <thenewcalculus@gmail.com> wrote:

[ .... ]

> The paragraph about "irrational number" is somewhat scatterbrained
> because WM assumes there is such a thing as "irrational number", which
> is untrue. ....

John, I keep having to remind you that you don't understand what it
means for a mathematical entity to exist or not. That understanding is
part of the maths education you missed out on.

In actual fact, irrational numbers do indeed exist.

--
Alan Mackenzie (Nuremberg, Germany).

On Monday, 5 July 2021 at 08:42:41 UTC-4, Eram semper recta wrote:
> Wolfgang Mueckeheim is a decent human being. Although he is one of the smartest mainstream academics I've met (Wildberger is the other), some of his thoughts on important mathematics concepts are not correct.
>
> The majority of his comments at the following link are worth reading and I'd say I would agree with perhaps 60% of them:
>
> https://www.quora.com/profile/Wolfgang-Mueckenheim-1
>
> BUTTTTT.....
>
> The following 2 comments are incorrect:
>
> 1. Mathematics - at last reasonable mathematics - is abstracted from physical reality. That begins with counting and drawing lines. If other universes exist, then they will probably have the same physics and therefore the same mathematics.
>
> “Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.” [V.I. Arnold: "On teaching mathematics" (1997)]
>
> -------------------------
>
> Mathematics is entirely abstract and has nothing to do with the physical world. Mathematics is the science of (abstract) measure and number. The quote by Arnold is just plain ignorant.
>
> 2. What is a number? A number is an idea. An idea is a thought. What is a thought that no-one can think? Certainly nothing belonging to a scientific worldview.
>
> How can an irrational number be thought? Like anything else it can be thought by a finite name, sound, or picture like π or √17 . (Infinite digit sequences without finite formulas would require an infinite amount of information. That is not available.) How many finite names can exist? Not more than countably many. Therefore there are at most countably many irrational numbers. The rest is not belonging to a scientific worldview.
> -------------------------------------
> A number is a name given to a (abstract) measure that describes a magnitude or size.
>
> Number is a noumenon - a thing as it is in itself, as distinct from a thing as it is knowable by the senses through phenomenal attributes. However, a number can be "knowable" or "realised" through thought. While this word noumenon was coined by Kant, it was not his idea, but Plato's. We know that noumenon is just another word for the abstract "ideal form" from which all other concepts and things are instantiated.
>
> The paragraph about "irrational number" is somewhat scatterbrained because WM assumes there is such a thing as "irrational number", which is untrue. Each sentence in the second paragraph contradicts all the previous sentences.

You can learn what it means to be a number and ignore the nonsense by Prof. W Mueckenheim who is as clueless as most other academics in thee mainstream:

https://www.academia.edu/49478620/What_exactly_is_a_number_in_mathematics

måndag 5 juli 2021 kl. 14:42:41 UTC+2 skrev Eram semper recta:
> Wolfgang Mueckeheim is a decent human being. Although he is one of the smartest mainstream academics I've met (Wildberger is the other), some of his thoughts on important mathematics concepts are not correct.
>
> The majority of his comments at the following link are worth reading and I'd say I would agree with perhaps 60% of them:
>
> https://www.quora.com/profile/Wolfgang-Mueckenheim-1
>
> BUTTTTT.....
>
> The following 2 comments are incorrect:
>
> 1. Mathematics - at last reasonable mathematics - is abstracted from physical reality. That begins with counting and drawing lines. If other universes exist, then they will probably have the same physics and therefore the same mathematics.
>
> “Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.” [V.I. Arnold: "On teaching mathematics" (1997)]
>
> -------------------------
>
> Mathematics is entirely abstract and has nothing to do with the physical world. Mathematics is the science of (abstract) measure and number. The quote by Arnold is just plain ignorant.
>
> 2. What is a number? A number is an idea. An idea is a thought. What is a thought that no-one can think? Certainly nothing belonging to a scientific worldview.
>
> How can an irrational number be thought? Like anything else it can be thought by a finite name, sound, or picture like π or √17 . (Infinite digit sequences without finite formulas would require an infinite amount of information. That is not available.) How many finite names can exist? Not more than countably many. Therefore there are at most countably many irrational numbers. The rest is not belonging to a scientific worldview.
> -------------------------------------
> A number is a name given to a (abstract) measure that describes a magnitude or size.
>
> Number is a noumenon - a thing as it is in itself, as distinct from a thing as it is knowable by the senses through phenomenal attributes. However, a number can be "knowable" or "realised" through thought. While this word noumenon was coined by Kant, it was not his idea, but Plato's. We know that noumenon is just another word for the abstract "ideal form" from which all other concepts and things are instantiated.
>
> The paragraph about "irrational number" is somewhat scatterbrained because WM assumes there is such a thing as "irrational number", which is untrue. Each sentence in the second paragraph contradicts all the previous sentences.
he is just as weong as you are, you are all cranks.

On Monday, 5 July 2021 at 08:42:41 UTC-4, Eram semper recta wrote:
> Wolfgang Mueckeheim is a decent human being. Although he is one of the smartest mainstream academics I've met (Wildberger is the other), some of his thoughts on important mathematics concepts are not correct.
>
> The majority of his comments at the following link are worth reading and I'd say I would agree with perhaps 60% of them:
>
> https://www.quora.com/profile/Wolfgang-Mueckenheim-1
>
> BUTTTTT.....
>
> The following 2 comments are incorrect:
>
> 1. Mathematics - at last reasonable mathematics - is abstracted from physical reality. That begins with counting and drawing lines. If other universes exist, then they will probably have the same physics and therefore the same mathematics.
>
> “Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.” [V.I. Arnold: "On teaching mathematics" (1997)]
>
> -------------------------
>
> Mathematics is entirely abstract and has nothing to do with the physical world. Mathematics is the science of (abstract) measure and number. The quote by Arnold is just plain ignorant.
>
> 2. What is a number? A number is an idea. An idea is a thought. What is a thought that no-one can think? Certainly nothing belonging to a scientific worldview.
>
> How can an irrational number be thought? Like anything else it can be thought by a finite name, sound, or picture like π or √17 . (Infinite digit sequences without finite formulas would require an infinite amount of information. That is not available.) How many finite names can exist? Not more than countably many. Therefore there are at most countably many irrational numbers. The rest is not belonging to a scientific worldview.
> -------------------------------------
> A number is a name given to a (abstract) measure that describes a magnitude or size.
>
> Number is a noumenon - a thing as it is in itself, as distinct from a thing as it is knowable by the senses through phenomenal attributes. However, a number can be "knowable" or "realised" through thought. While this word noumenon was coined by Kant, it was not his idea, but Plato's. We know that noumenon is just another word for the abstract "ideal form" from which all other concepts and things are instantiated.
>
> The paragraph about "irrational number" is somewhat scatterbrained because WM assumes there is such a thing as "irrational number", which is untrue. Each sentence in the second paragraph contradicts all the previous sentences.

Students:

So you see, even the best of mainstream academics suffers from brain damage.. You can escape all this nonsense by studying what I tell you.

Only I and I alone can lead you to perfect understanding.

I am a genius and I do know better than anyone else. No arrogance here, but a quiet, calm confidence.

On Saturday, July 17, 2021 at 2:49:53 PM UTC+1, Eram semper recta wrote:

"Only I and I alone can lead you to perfect understanding. ... I am a genius and I do know better than anyone else. No arrogance here, but a quiet, calm confidence."

Oh Mr Gabriel you comedy legend you. Students might think you are being serious. Students, what Mr Gabriel meant to say was that Mueckeheim is not a good representative of mainstream mathematical views and that if your want to do well in understanding mathematics and its applications then some excellent choices of books include:

1) Infinity: a very short introduction, by Ian Stewart. A pocket book to help get your intuitions in order.

2) Higher Arithmetic, an algorithmic introduction to number theory, by Howard Edwards. A charming and short constructivist introduction to number theory. Includes a brief look at the mathematical machinery of RSA encryption system. Is well complimented by the pocket book, Cryptography: a very short introduction, by Piper and Murphy.

3) Elementary Linear Algebra 8e, by Howard Anton. Tried and tested linear algebra text, proceeds at gentle pace and has some focus on geometrical aspects.

4) Groups, by Jordan and Jordan, nice and relatively short introduction to group theory, without getting bogged down in ring theory and other algebraic structures.

5) Geometry, by Brannan et al. Solid introduction to the klein/transformation approach to geometry (affine, projective, inversive and non-euclidean) after a brief look at conic sections. Utilizes the linear algebra from Anton's book and the group theory from the Jordan and Jordan book. The book is designed for self-study (being produced by the Open University in the UK), and is one of the better books on undergraduate level geometry out there.

6) Calculus: a complete course, 9e, by Robert Adams. One of the most rigorous and comprehensive undergraduate calculus books. Gives a modern account of numerical integration, approximation methods, and multivariable calculus with aspiring mathematical physicists in mind.

7) A Course in Pure Mathematics (centenary edition), by G.H. Hardy. A classic undergraduate introduction to real analysis. Neither the easiest nor the hardest book to approach that topic. Either of 'Fundamentals of Mathematical Analysis, 2e by Haggarty, Or Mathematical Analysis: a straightforward approach, by Binmore, are easier and slimmer introductions.

8) Elementary Differential Geometry, 2e, by Andrew Pressley. Differential geometry is one of the most beautiful branches of mathematics, is a good entry way into the calculus of variations and is connected to Einstein's brilliant theory of General Relativity. Pressley's book is the best undergraduate introduction that I have come across.

9) A First Course in Probability, 6e, by Sheldon Ross. Best undergraduate introduction to probability ever published in English. Enough said.

9) Game Theory: mathematical models of conflict, by Antonia Jones. A branch of applied maths that requires mathematical rigor but has nothing to do with physics, and is quite quirky. Looks at some implications of transfinite set theory, and includes a solid account of linear programming (also has solutions to most exercises). Can be complimented by the pocket book, Choice Theory: a very short introduction, by Michael Allingham.

10) An Introduction to Linear Analysis, by Kreider et al. Covers many of the essential analytic (as opposed to numerical or geometrical) methods of mathematical physics, (except for the calculus of variations), but for mathematics undergraduates.

11) Complex Analysis for Mathematics and Engineering, 4e, by Mathews and Howell. Well designed for applied mathematicians as it balances rigor and visual intuition quite well. Covers topics of interest for applications.

There are many others of course, but this is a good starting collection. Don't waste your time with any self-proclaimed 'lone genius' types online, and their silly manifestos, especially when they lack peer reviewed achievements or any hard evidence of their intellectual prowess. In particular if they are evolution deniers or general relativity deniers and lack degrees in a relevant areas, then they are scientifically illiterate and aren't worth your time. If you want to look up some real geniuses, research Roger Penrose or Paul Erdos.

Have a Wonderful Day
QB

Remain Calm and Keep Loving Real Analysis
[Recommended Book of the Day: Essential Topology, by Martin Crossley]

On Monday, 5 July 2021 at 08:42:41 UTC-4, Eram semper recta wrote:
> Wolfgang Mueckeheim is a decent human being. Although he is one of the smartest mainstream academics I've met (Wildberger is the other), some of his thoughts on important mathematics concepts are not correct.
>
> The majority of his comments at the following link are worth reading and I'd say I would agree with perhaps 60% of them:
>
> https://www.quora.com/profile/Wolfgang-Mueckenheim-1
>
> BUTTTTT.....
>
> The following 2 comments are incorrect:
>
> 1. Mathematics - at last reasonable mathematics - is abstracted from physical reality. That begins with counting and drawing lines. If other universes exist, then they will probably have the same physics and therefore the same mathematics.
>
> “Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.” [V.I. Arnold: "On teaching mathematics" (1997)]
>
> -------------------------
>
> Mathematics is entirely abstract and has nothing to do with the physical world. Mathematics is the science of (abstract) measure and number. The quote by Arnold is just plain ignorant.
>
> 2. What is a number? A number is an idea. An idea is a thought. What is a thought that no-one can think? Certainly nothing belonging to a scientific worldview.
>
> How can an irrational number be thought? Like anything else it can be thought by a finite name, sound, or picture like π or √17 . (Infinite digit sequences without finite formulas would require an infinite amount of information. That is not available.) How many finite names can exist? Not more than countably many. Therefore there are at most countably many irrational numbers. The rest is not belonging to a scientific worldview.
> -------------------------------------
> A number is a name given to a (abstract) measure that describes a magnitude or size.
>
> Number is a noumenon - a thing as it is in itself, as distinct from a thing as it is knowable by the senses through phenomenal attributes. However, a number can be "knowable" or "realised" through thought. While this word noumenon was coined by Kant, it was not his idea, but Plato's. We know that noumenon is just another word for the abstract "ideal form" from which all other concepts and things are instantiated.
>
> The paragraph about "irrational number" is somewhat scatterbrained because WM assumes there is such a thing as "irrational number", which is untrue. Each sentence in the second paragraph contradicts all the previous sentences.

Refreshed due to troll activity.