There are sometimes great controversies in the world where I feel that the wrong side won.

Pure mathematics is one example. Pure mathematics now only proceeds by the process of definition to axiom to proof. In our modern world it’s hard to believe there is any other way. But 100 years ago there was still a raging controversy about whether this was the correct way to advance pure mathematics. The losing side believed that pure mathematics should proceed by the scientific method of: hypothesis to test to acceptance. I think the wrong side won. It has lead to progress in pure mathematics being blocked; each pure mathematician can only hope to make one or at most two important proofs in his/her lifetime, whereas Hilbert propounded 23 important hypotheses in a single lecture.

Now on to music teaching. Although I refer to my “shopping list” as my Chopin-Liszt, there are great differences between the two approaches to learning piano music. And I think the wrong side won. Liszt, and before him Czerny and Hanon, belong to what is loosely called the school of velocity, where virtuosity is everything. It is said that Liszt used to play scales and similar finger exercises every day and found it so boring that he would read a book while he was playing. On the other hand, Chopin is said to have hated scales and finger exercises and believed that the best way to learn technique was within pieces of music that are worth learning to play.

Chopin lost.

Honestly, I would much prefer to listen to a piece by Chopin than one by Hanon, Czerny or even Liszt. At my advanced age, I feel that all scales give students is early arthritis.

Since 1887, the AMEB in Australia has insisted on all pianists (and all players of other instruments) at all grades practicing scales ad nauseum. And up until ten years ago, the pieces in the grade books were deliberately chosen to get worse in quality with each successive grade, so that by seventh grade there was only one piece in the whole grade that was actually worth playing. For List A for instance you had the choice of Bach, Bach, Bach or Bach – chosen from the worst pieces Bach ever wrote. OK, I exaggerate slightly, but only slightly.

From about ten years ago, the “Piano for Leisure” series came as a breath of fresh air. Finally there are pieces in upper grades that are actually worth playing. It needs to be renamed “Piano for Pleasure”, “Leisure” gives the entirely wrong impression of indolence, but all of these pieces are still bl__dy hard to play, like the best Chopin.

Music theory by the AMEB is even worse. It teaches students to write music in the style of Palestrina, Palestrina, Palestrina or Palestrina, as bastardised by Lovelock.

Now to change an impression. Liszt never taught his students to play scales. His classes were masterclass style. He would let a student play the piece of his choice, in whatever style the student wanted, until Liszt got fed up with the playing and booted the student off completely – switching to the next student.

So on to the questions.

What do you know about the history of music teaching?
Who was the bastard who started teaching major, harmonic minor and melodic minor scales to all his students?
Why did Chopin lose?

I suppose the most important differences are those between types of students. Those wanting a full “professional” musical education in the classical tradition would be well advised to practise their scales etc.

But there are many other music students looking for specific personal improvement, for their own purposes, who can choose from the variety of private tutors etc out there these days.

I still want some fiddling lessons at some stage this year, primarily to help improve my bowing, which will mean travelling to Launceston a couple times a month.

> Those wanting a full “professional” musical education in the classical tradition would be well advised to practise their scales etc.

I tend to disagree. I think Chopin was right. And Hilbert.

mollwollfumble said:

> Those wanting a full “professional” musical education in the classical tradition would be well advised to practise their scales etc.

I tend to disagree. I think Chopin was right. And Hilbert.

From a practical point of view, the difference between professional classical pianists and the rest of humanity can be summed up by the number of hours of hard work put into practice and rehearsal, and that inevitably includes a lot of boring stuff.

How can we test these competing hypotheses?

dv said:

How can we test these competing hypotheses?

And your answer is?

I suspect that professional musicians do a lot less practice than may be thought. Like perhaps playing through a piece twice before final performance. But that’s not the point. The point is whether practice is better spent learning to play good pieces well, or whether practice should be wasting time playing the same rubbish over and over again.

And who thought that playing the same rubbish over and over again is a good idea?

mollwollfumble said:

dv said:

How can we test these competing hypotheses?

And your answer is?

It wasn’t a rhetorical question.

dv said:

How can we test these competing hypotheses?

Should be quite easy. Compare two piano students, one who only practises in his favourites key(s), and another who has made it his business to become proficient in any key, by fully familiarising himself with the associated scales.

Then hand them scores covering all keys and ask them to play. Judge the resulting musicianship.

Bubblecar said:

dv said:

How can we test these competing hypotheses?

Should be quite easy. Compare two piano students, one who only practises in his favourites key(s), and another who has made it his business to become proficient in any key, by fully familiarising himself with the associated scales.

Then hand them scores covering all keys and ask them to play. Judge the resulting musicianship.

But what if one of the students would have been quite shit no matter which training regime they used?

sibeen said:

Bubblecar said:

dv said:

How can we test these competing hypotheses?

Should be quite easy. Compare two piano students, one who only practises in his favourites key(s), and another who has made it his business to become proficient in any key, by fully familiarising himself with the associated scales.

Then hand them scores covering all keys and ask them to play. Judge the resulting musicianship.

But what if one of the students would have been quite shit no matter which training regime they used?

Weed those ones out first.

Bubblecar said:

sibeen said:

Bubblecar said:

Should be quite easy. Compare two piano students, one who only practises in his favourites key(s), and another who has made it his business to become proficient in any key, by fully familiarising himself with the associated scales.

Then hand them scores covering all keys and ask them to play. Judge the resulting musicianship.

But what if one of the students would have been quite shit no matter which training regime they used?

Weed those ones out first.

What if one is better technically, but the other is more creative?

The Rev Dodgson said:

Bubblecar said:

sibeen said:

But what if one of the students would have been quite shit no matter which training regime they used?

Weed those ones out first.

What if one is better technically, but the other is more creative?

Since the point here is just to judge technical proficiency, we needn’t worry our little heads too much about other factors.

Bubblecar said:

The Rev Dodgson said:

Bubblecar said:

Weed those ones out first.

What if one is better technically, but the other is more creative?

Since the point here is just to judge technical proficiency, we needn’t worry our little heads too much about other factors.

But is it? You speak as if these things were quite separate.

But I know nothing of this subject.

The different scales and their purpose remain a mystery to me.

So I will leave it to Douglas Hofstadter to comment (who, in spite of the title of his first book, is very fond of Chopin I believe):

“I can’t help but recall, at this point, a horribly elitist but very droll remark by one of my favorite writers, the American “critic of the seven arts”, James Huneker, in his scintillating biography of Frédéric Chopin, on the subject of Chopin’s étude Op. 25, No. 11 in A minor, which for me, and for Huneker, is one of the most stirring and most sublime pieces of music ever written: “Small-souled men, no matter how agile their fingers, should avoid it.”

https://www.goodreads.com/author/quotes/3034502.Douglas_R_Hofstadter

The Rev Dodgson said:

Bubblecar said:

The Rev Dodgson said:

What if one is better technically, but the other is more creative?

Since the point here is just to judge technical proficiency, we needn’t worry our little heads too much about other factors.

But is it? You speak as if these things were quite separate.

But I know nothing of this subject.

The different scales and their purpose remain a mystery to me.

So I will leave it to Douglas Hofstadter to comment (who, in spite of the title of his first book, is very fond of Chopin I believe):

“I can’t help but recall, at this point, a horribly elitist but very droll remark by one of my favorite writers, the American “critic of the seven arts”, James Huneker, in his scintillating biography of Frédéric Chopin, on the subject of Chopin’s étude Op. 25, No. 11 in A minor, which for me, and for Huneker, is one of the most stirring and most sublime pieces of music ever written: “Small-souled men, no matter how agile their fingers, should avoid it.”

https://www.goodreads.com/author/quotes/3034502.Douglas_R_Hofstadter

Of course expression and the associated comprehension is very important for those aspiring to be fine musicians, but they’re not going to have much opportunity to concentrate on those aspects if they’re just struggling with playing the right notes fluently.

This is where there’s no substitute for “practice, practice, practice”.

mollwollfumble said:

There are sometimes great controversies in the world where I feel that the wrong side won.

Pure mathematics is one example. Pure mathematics now only proceeds by the process of definition to axiom to proof. In our modern world it’s hard to believe there is any other way. But 100 years ago there was still a raging controversy about whether this was the correct way to advance pure mathematics. The losing side believed that pure mathematics should proceed by the scientific method of: hypothesis to test to acceptance. I think the wrong side won. It has lead to progress in pure mathematics being blocked; each pure mathematician can only hope to make one or at most two important proofs in his/her lifetime, whereas Hilbert propounded 23 important hypotheses in a single lecture.

What are you proposing? That we get rid of rigour in mathematics? What good is an unproven hypothesis? It should be noted that the scientific method is flawed by its inability to prove anything.

mollwollfumble said:

Who was the bastard who started teaching major, harmonic minor and melodic minor scales to all his students?

I don’t know who invented the diatonic scale, but it should be noted that the diatonic scale is harmonically correct. For example, if one considers the major scale, then the primary triads I, IV, and V are all major chords and completely define the scale.

KJW said:

mollwollfumble said:

There are sometimes great controversies in the world where I feel that the wrong side won.

Pure mathematics is one example. Pure mathematics now only proceeds by the process of definition to axiom to proof. In our modern world it’s hard to believe there is any other way. But 100 years ago there was still a raging controversy about whether this was the correct way to advance pure mathematics. The losing side believed that pure mathematics should proceed by the scientific method of: hypothesis to test to acceptance. I think the wrong side won. It has lead to progress in pure mathematics being blocked; each pure mathematician can only hope to make one or at most two important proofs in his/her lifetime, whereas Hilbert propounded 23 important hypotheses in a single lecture.

What are you proposing? That we get rid of rigour in mathematics? What good is an unproven hypothesis? It should be noted that the scientific method is flawed by its inability to prove anything.

I learnt today that the Catalan conjecture was proved about 15 years ago. That’s what I like about maths, if something is proved then that’s it. Dust off your hands and walk away, this one is done.

sibeen said:

KJW said:

mollwollfumble said:

There are sometimes great controversies in the world where I feel that the wrong side won.

Pure mathematics is one example. Pure mathematics now only proceeds by the process of definition to axiom to proof. In our modern world it’s hard to believe there is any other way. But 100 years ago there was still a raging controversy about whether this was the correct way to advance pure mathematics. The losing side believed that pure mathematics should proceed by the scientific method of: hypothesis to test to acceptance. I think the wrong side won. It has lead to progress in pure mathematics being blocked; each pure mathematician can only hope to make one or at most two important proofs in his/her lifetime, whereas Hilbert propounded 23 important hypotheses in a single lecture.

What are you proposing? That we get rid of rigour in mathematics? What good is an unproven hypothesis? It should be noted that the scientific method is flawed by its inability to prove anything.

I learnt today that the Catalan conjecture was proved about 15 years ago. That’s what I like about maths, if something is proved then that’s it. Dust off your hands and walk away, this one is done.

That’s the ideal. But I would like to see the requirement that mathematical proofs be carried out by symbol manipulation using a machine. Only if this requirement is satisfied can a mathematical proof be regarded as rigorous.

KJW said:

mollwollfumble said:

There are sometimes great controversies in the world where I feel that the wrong side won.

Pure mathematics is one example. Pure mathematics now only proceeds by the process of definition to axiom to proof. In our modern world it’s hard to believe there is any other way. But 100 years ago there was still a raging controversy about whether this was the correct way to advance pure mathematics. The losing side believed that pure mathematics should proceed by the scientific method of: hypothesis to test to acceptance. I think the wrong side won. It has lead to progress in pure mathematics being blocked; each pure mathematician can only hope to make one or at most two important proofs in his/her lifetime, whereas Hilbert propounded 23 important hypotheses in a single lecture.

What are you proposing? That we get rid of rigour in mathematics? What good is an unproven hypothesis? It should be noted that the scientific method is flawed by its inability to prove anything.

Who needs proof? Proof is nice, but it’s very far from the be all and end all of mathematics. Proof has no role in applied mathematics at all, nor should it.

Think of a pure mathematics that is 50% based on the principle of “best so far”. Take cryptography for example, a code doesn’t have to be provably uncrackable to be useful. All it needs is to be uncrackable by all methods tried so far.

Think of the digits of pi for example. “Best so far” suffices until a more accurate result is found.

Or take another example. “It is impossible to cut an octagon into 4 simply connected pieces that can be reassembled into a square” was hypothesised in the year 1907, but 110 years later it has still not been proved. Why not just give it the benefit of the doubt and say “OK to accept it as true until proved otherwise”?

mollwollfumble said:

Who needs proof? Proof is nice, but it’s very far from the be all and end all of mathematics. Proof has no role in applied mathematics at all, nor should it.

Think of a pure mathematics that is 50% based on the principle of “best so far”. Take cryptography for example, a code doesn’t have to be provably uncrackable to be useful. All it needs is to be uncrackable by all methods tried so far.

Think of the digits of pi for example. “Best so far” suffices until a more accurate result is found.

Or take another example. “It is impossible to cut an octagon into 4 simply connected pieces that can be reassembled into a square” was hypothesised in the year 1907, but 110 years later it has still not been proved. Why not just give it the benefit of the doubt and say “OK to accept it as true until proved otherwise”?

The problem is that mathematical theorems, including those used by applied mathematics, rest on other mathematical theorems, and if there is doubt all the way up the chain, then it becomes more likely that the new mathematical theorem will be wrong. And surely a wrong theorem isn’t useful at all. Or are you suggesting that every new mathematical theorem undergo thorough testing? This seems like a lot of work compared to proving it from theorems that are guaranteed to be true.

mollwollfumble said:

Take cryptography for example, a code doesn’t have to be provably uncrackable to be useful. All it needs is to be uncrackable by all methods tried so far.

Much of the problems in the field of information technology is caused by hackers exploiting weaknesses in computer code.

mollwollfumble said:

Think of the digits of pi for example. “Best so far” suffices until a more accurate result is found.

But what if the digits that have already been given are actually wrong?

mollwollfumble said:

Or take another example. “It is impossible to cut an octagon into 4 simply connected pieces that can be reassembled into a square” was hypothesised in the year 1907, but 110 years later it has still not been proved. Why not just give it the benefit of the doubt and say “OK to accept it as true until proved otherwise”?

And how does this benefit anybody in the real word?

It is worth noting that theorems like this have often been proven in special cases, but that it’s the general case that remains unproven. If the special case is all that you need, then you can be satisfied that it has been proven, and that the doubt that applies to the general case doesn’t apply to you.

KJW said:

The problem is that mathematical theorems, including those used by applied mathematics, rest on other mathematical theorems, and if there is doubt all the way up the chain, then it becomes more likely that the new mathematical theorem will be wrong. And surely a wrong theorem isn’t useful at all. Or are you suggesting that every new mathematical theorem undergo thorough testing? This seems like a lot of work compared to proving it from theorems that are guaranteed to be true.

Almost every new mathematical theorem already has to undergo years if not decades of thorough testing before it is accepted as correct. There is even a pure mathematic project underway that is going to take generations to complete, if it ever gets finished at all. A project to check all the important old theorems to make sure that no-one has made a slip-up somewhere along the way. And even then it’s not really a case of knowing that it’s correct, it’s a case of one or two mathematicians being unable to disprove it.

I would disagree about a wrong theorem not being useful. More than one of Ramanujan’s initial results were wrong. But were still useful because the reasoning behind them, fallacious as it was, led to a generalization.

KJW said:

mollwollfumble said:

Think of the digits of pi for example. “Best so far” suffices until a more accurate result is found.

But what if the digits that have already been given are actually wrong?

Touché, I was hoping you wouldn’t spot that one. There have been many cases in science where digits have been wrong. The Hubble constant for starters, on many occasions. That still hasn’t negated their usefulness. Or to take another couple of cases from science, Newtonian mechanics is known to be wrong, but that hasn’t stopped it from being useful even after it was proved wrong.

My complaint about the necessity for definition to axiom to proof in pure mathematics is that it imposes a speed limit of 0 km/hr on the rate that pure mathematics develops. Take the the Riemann hypothesis. If mathematicians are forbidden from following the scientific method of starting with hypothesis then there would be no Riemann hypothesis.

Have now boght a book with a chapter about this mathematical controversy.

mollwollfumble said:

Have now boght a book with a chapter about this mathematical controversy.

Why not bring Beethoven’s deafness into the equation?