Definition of a statistician: Someone with their head in an oven, their feet in a freezer, but on the whole they are doing just fine!
The mathematics you use make a mockery of themselves as soon as you start extrapolating beyond the original 25/75 split. I am 3rd generation which according to your statistics means I am getting 1.56% of learning from O Senseis teaching, I think not.
While the I think the maths part of your post is highly suspect, I agree with much of the rest
Of course teachers can be surpassed by students, it would be ridiculous to think otherwise. if we stuck to the maths then within a few generations the watering down process would make the 'art' almost worthless. Surely a good teacher 'wants' his students to surpass him, if he doesn't then he is ego driven and a lesser teacher for it.
Some western aikido teachers have brought their own skills to the teaching process of aikido and maybe this is an area where things have been surpassed since O Sensei. O Sensei was a man of his time and culture, things were passed on in a particular way. Show - do - little explanation, you just had to get it through repetition. I know there are still fans of this method and I'm sure it has alot going for it. That doesn't mean it can't be improved upon or that it hasn't. My own teacher has done a great deal to create a teaching method that has taken all his learning from his own 1st generation teachers combined with 50 years of aikido teaching, this he is passing onto his own teachers. He knows that some aspects of aikido that he took along time to 'get' he can pass on much quicker now. Improvement from one generation to the next.
It seems in most/much of the world of aikido no matter which country you are in Japanese is heavily used during instruction. Not from where I come from, apart from the names of the thechniques ikkyo, nikkyo, shihonage etc we learn everything in english, a layer of complexity has been removed and learning is perhaps a little easier.
The English invented Cricket, but we ar regularly out done by the India, West Indes, Pakistan.
I would like to think that Aikido has a life of it's own, O Sensei created it and we should all remain thankfull for that. But the cat is out of the bag, no one person or organisation owns or controls it. it is free to become what it becomes, and who knows haow far it can go and in which direction? There is no one type of Aikido that can be called O'Sensei's, as it changed over time, he didn't keep it one way for his own lifetime, so it was evolving even then.
It is up to us to keep the spirit of aikido strong and pure, look backwards to history for guidance, but forward to the foture for where we are going and what we want aikido to mean in the modern world.
Leave the maths out of the dojo it will just get in the way of simple learning.
Good post David, it certainly got me thinking over my morning coffee,