"Define a step and a pace. A step is a step forward and as the other foot arrives under the body the step is finished. Hence we read rise at the end of one."

Actually, there is quite a bit of the rise that happens from the middle of one or earlier. Yes, the most obvious part of the rise begins at the end, and so when simplifying the situation to the point where it can be put in a chart, the book puts it there. But if your read the whole thing, particularly the passage which discusses the different use of the knees in the different dances, you'll see there's more to it. I also recommend watching some videos of dancers - you'll see them still going down after the start of step one, and then going back up again well before it's end. The book's chart is putting some pins in the map, it's up to you to read the whole thing, develop a healthy sense of how the dancing WORKS and then use this to fill in the curves in between those pins.

"A pace is one foot forward as in a heel lead. It will be the same for the Waltz Foxtrot and Quickstep."

WRONG. The action is still very different of a dancer who understands in their body the difference in these dances.

"In the Quickstep the pace is smaller because the music is faster. It goes on to say that there is less flexing of the knees over the step. We are not concerned with that because we are on our pace and haven't arrived yet."

On a skilled dancer who fundamentally understands the dance, there will already be differences.

"Our only concern is the one pace. There will be no flexing of the knees untill thr step is finished. Or if you like the body arriving over the foot."

In reality, there's always some flexing of the knees! The knees will have to accomodate the relatinoship between the step size and the body altitude. Only at certain combinations can the knees be straight, at others they must remain flexed at mid stride. Different dances, and different interpretations of different figures in those dances, will have different situations here.

"In the Waltz. If you swing down half way through the pace. You will have to start rising. As we all know we commemce to rise at the end of the first beat. Not start to rise half way through the first pace."

Actually, the later is much closer to the overall reality. But in terms of initial actions to teach to a beginner - footwork - commence to rise at the end of one sums it up. Beginners don't get the body flight necessary for a greater stride that would create the full underhanded swing of champions.

"From the book. When instructed to rise at the end of the step the dancer should not commence to rise untill the moving foot passes the foot supporting the weight of the body. The heel of the supporting foot will be then released from the floor."

The book is using a very narrow definition of rise, which does not include the loss and regain of altitude which occurs as a result of leg division.

"How much more instruction do you need to convince you that for 10 years you have been doing it wrong."

I've been doing it a lot more close to correclty than you have, for two primary reasons:

1) I actually understand the book - I pay attention to context and scope when reading it.

2) Instead of buying videos of the worlds best ballroom teachers, I take in-person private lessons with them. I get to find out what they think I need to change, and I get to ask them extremely detailed questions about the parts of the technique that I'm having trouble understanding.

3) I put a heck of a lot of thought into reconciling #1 with #2.

"I will say it again. One pace forward on the heel is the same in the three dances that are under question."

Only to someone who does not have the experience to KNOW THAT IT IS DIFFERENT IN EACH CASE.

Because your argument is based not in experience but rather in your ignorance, you simply CANNOT WIN - you will loose every time someone introduces information about differences which you were unaware of.

The flexing of the knees occurs at the end of the step not half way through. The knees at mid stride are straight not flexed. It is impossible to have a knee that is not straight and be on the heel of the front foot and the toe of the back foot.
In the new edition of Alex Moore's technique book it suggests that we get into that position and if neccessary put our hand on a wall so that we can stay there and get used to the feel of it. For those who bend the knee it isn't going to be possible to get into that position.
Of course I am now going to ask how do you propose to get a downward movement or dip, or what ever you care to call it if this is a Waltz and get into the position mentioned above.
They are not going down on that first pace. They are already down. We do not lower twice. I thought you had already agreed to that one. Now you've gone backwards to those bad habits.

"The flexing of the knees occurs at the end of the step not half way through."

OBVIOUSLY WRONG to anyone who takes even a minute to think about it, or tries it in front of a mirror.

The knee will flex as a the body moves onto the foot, which is to say that it will start to flex from the point of midstride, or wherever it is that the body is furthest away from the receiving foot.

"It is impossible to have a knee that is not straight and be on the heel of the front foot and the toe of the back foot."

YOUVE OBVIOUSLY NEVER TRIED TO - or looked at a video for that matter. 99% of the time when your see top professionals at mid stride, the front leg will still be bent, not actually straight. The reason is because they lower enough that straight legs would be impractical; if they did not lower so much, then there legs would be straight... but once again, you ignore the reality of cuase and effect and try to spraypaint the world into a potempkin village with your beloved mindless trivia as its blueprint.

"Of course I am now going to ask how do you propose to get a downward movement or dip, or what ever you care to call it if this is a Waltz and get into the position mentioned above."

By dividing the legs! It's simple geometry. Do a forward back split in your socks, and what happens? Your center lowers.

"They are not going down on that first pace. They are already down. We do not lower twice."

You don't lower "twice", you keep lowering well past the end of the previous step, until you reach your lowest point around midstride (if you are English), or even almost at the arrival on step one (if you are an Italian). As a reminder, the book does not discuss this lowering via leg division; in terms of the mechanisms that the book does discuss, the lowering would not continue. But when you look at the overall body, any skilled dancer will demonstrate that there is plenty of lowering still to occur after the start of a step one action!

"Now you've gone backwards to those bad habits."

Your problem is that you can't tell the difference between various bad habits that beginners exhibit, and the good habits of skilled dancers. You are forever stuck trying to avoid the beginners mistakes, only this PREVENTS YOU FROM ACTUALLY DANCING, or even understanding what it is that those who can dance actually do.

Quote straight from the book. Any leading step forward or backward is followed by a softening of the knee as the weight is taken on that step. The softening of the knee on a leading step to some extent is more important than the following rise which in many cases will occure naturally if the step is done correctly.
Interesting. Too much relaxing of the knee on the first step of a Natural Turn in the Foxtrot will impede the turn. But not so on the first step of the Feather. These are the mans steps.It makes sense doesn' t it.

"Quote straight from the book. Any leading step forward or backward is followed by a softening of the knee as the weight is taken on that step. The softening of the knee on a leading step to some extent is more important than the following rise which in many cases will occure naturally if the step is done correctly.
Interesting. Too much relaxing of the knee on the first step of a Natural Turn in the Foxtrot will impede the turn. But not so on the first step of the Feather. These are the mans steps.It makes sense doesn' t it."

Yes, those are the kinds of application-specific differences between heel leads that we have been trying to point out to you for weeks now.

But they are only the START of the differences. These were just the ones that were so obvious and important that they had to be mentioned in an introductory text. There are many more DIFFERENCES that will become apparent to the advancing dancer, and sadly I would expect remain forever beyond the awareness of others.

No you have got that wrong. What has been said is the very first half of one step in the Waltz. Or half of one step in the Foxtrot there is no appreciable difference between the two in the action untill the suporting foot moves to a position under the body and the knee at this point has already taken over.
This is relevent. Do you remember that I wrote last year some time that the step into a Reverse or Natural for the man is a smaller step.And that the lady at this time has the bigger step. This one can start a real argument. There is less bending of the knee in both of those turns for the man acording to the new book. Yet for years as a man on the outside of the turn we were taught to drive that first step into the turn. Times they are a Changing.

"No you have got that wrong. What has been said is the very first half of one step in the Waltz. Or half of one step in the Foxtrot there is no appreciable difference between the two in the action untill the suporting foot moves to a position under the body and the knee at this point has already taken over."

Such a claim is not only outrageously wrong, it is CONTRARY TO WHAT IT SAYS IN YOUR BELOVED BOOK.

To make my point, I need only recycle your own quote of a few hours ago:

"Quote straight from the book. Any leading step forward or backward is followed by a softening of the knee as the weight is taken on that step. The softening of the knee on a leading step to some extent is more important than the following rise which in many cases will occure naturally if the step is done correctly.
Interesting. Too much relaxing of the knee on the first step of a Natural Turn in the Foxtrot will impede the turn. But not so on the first step of the Feather. These are the mans steps.It makes sense doesn' t it."

There you have it - differences which occur BEFORE the moving foot draws closed. In fact, they begin to occur even as the body is only moving closer to the receiving foot.

And that is just the differences that were obvious enough to make the book. There are many others as well - the more a dancer learns, the more differences they will know of, or at least execute. Because the more they will underststand what is UNIQUE ABOUT EACH DANCE AND FIGURE.

"There is less bending of the knee in both of those turns for the man acording to the new book."

No, you've simply confused yourself. The knee will bend less when LEADING A HEEL TURN than it will when leading a typical waltz-type turn, or dancing a softer action such as a feather. This is because the lady's heel turn is characterized by arriving onto a fairly straight leg, rather than by softening and moving through the arriving leg. To get the lady to do this, the man must do it himself. Find the page in the book where it talks about this, and it's quite clear - this technique is to be used in the foxtrot turns, and in the waltz figures such as the DRS which are functionally similar - which is to say, are lady's heel turns.

You still have this fixation which you find hard to circumnavigate. Read my lips. At the end of the step if this is the Waltz you will flex your knee more than you will if you are going straight on in the Foxtrot. Again after the step is completed there will be a flexing of the knee. which will be flexed even more to get the second drive spoken about and demonstrated by Richard Gleave on his video. If it is the rest of the Feather Step you will rise lifting your left hip and swaying to the right. Don't try to do any of this this before you get there will you.

"You still have this fixation which you find hard to circumnavigate. Read my lips. At the end of the step if this is the Waltz you will flex your knee more than you will if you are going straight on in the Foxtrot."

Your distorted words, not a quote. Sure, it resembles what's in the book, but you've mixed it up and confused the original meaning. Specifically, the original comparison is between the softer knee actions - waltz turns and to a degree feather steps, vs, the more braced leg actions, which are the heel turns (confusingly called 'open turns' in the book).

"Again after the step is completed there will be a flexing of the knee."

After the foot is placed, but long before the "step" is complete!

"Don't try to do any of this this before you get there will you."

What you are missing is that the obvious difference occuring after the foot is placed, will on a skilled DANCER be FORESHADOWED BY A RELATED CHARACTER IN THE MOVEMENT THAT PLACES THE FOOT.

To a novice such as yourself, you simply place the foot in a generic way and then modify the arrival, or maybe even only the rise, to suit the figure. But a true DANCER is moving with the character of the figure in clear intent from a well before the the PREVIOUS FIGURE is completed!

Confusingly called an Open Turn. So how do we work this one out. We know that the lady on a Reverse Turn is Closed and not Open. We also know they were not stupid when the book was written. We also know that the mans steps do pass. So the conclusion is that a heel turn for the lady is part of the open passing steps for the man. So when it is written that the Heel Turn is the backward part of an Open Turn it is correct. Which is confirmed by the step descriptions if they are read correctly. Not bad for a Novice such as myself don't you think.