"You are so stupid it denies belief. How can anything go from one position to another without being at some point half way between the two."
You've just made a dreadful error in logic.
You can't go from one POSITION to another without being halfway in between.
But that isn't what we had been talking about - we had been talking about going form one FOOT to the other.
And therin lies the difference. If you were to mistakenly place both feet into fixed positions, and move the body between them, then yes there would be a point when the body was halfway in between.
But that is just not how foxtrot is danced. Instead, foxtrot moves the body and the foot largely at the same time. The moving foot isn't in a fixed position, instead it is a moving target.
Early in the action, the body is projecting from the standing foot and the feet are still closed. The body is an equal distance in front of both feet.
Soon the moving foot is also moving, but still not caught up to the body. The body is closest to the moving foot.
Then the moving foot is directly under the moving body, and obviously closest.
Next the moving foot is slightly ahead of the body, which has by now project a long way ahead of the standing foot.
Soon thereafter the moving foot stops moving, and the body starts getting closer to it again.
The result? At no point in this process was the body equidistant between the feet - BECAUSE THE MOVING FOOT WAS ALSO MOVING.
"My friend believes that what is written in plain English in the technique books is wrong. It says. At the extent of the stride the heel of the front foot and the ball of the back foot are or off the floor and the body is equally divided between the two."
Wrong - You rephrased the passage in a way that changes it's meaning. The actual reference is to the DIVISION OF WEIGHT rather than the BODY POSITION.
Go get out your book, and recheck and you will see that there is abosolutely no mention of being equidistant between the feet. Indeed, the position described is certainly assymetric, as the front leg with it's heel on the floor and thus ankle low is shorter than the back leg, with it's heel and thus ankle substantially off the floor.
"But because he has been given the idea, by some teacher who should be locked up, that the body travells in front of the foot he doesn't believe there is a mid- point."
Oh, so now you want to lock up Blackpool champions? Really dude, get a clue!
"When he reads or has it read to him that when going Backwards the supporting heel does not lower to the floor untill the moving foot is level with it. This is pointed out to him including the page number and low and behold within no time at all without giving any proof he says the same things all over again."
Please tell me again on what page is says that DURING A LOWERING ACTION the heel will not lower until the moving foot closes. Hint, there is no such page. The only completely detailed description of this action is given for a CASE WITH NEITHER RISE NOR FALL.
Your carelessness with these critical details is your undoing!
"So now tell me where you can find anything from any intelligent source that says anything contrary to the above. Either put up or shut up."
Get yourself some lessons with blackpool champs... they are really wonderful people to work with, and they do know a few things about dancing