The thing is there is no need to go fast to learn to ski on ice. But is important to ski a slow line fast......(doesnt mean ski fast). ....
I disagree with the parts in red above.
Skiing the slow line fast is a great piece of advice. It's THE advice when talking about recreational carving on very hard snow.
But but but... the "slow line" spends time heading towards the trees, across the hill, between turns. (I am assuming you are skiing groomers below tree line.) When you are carving "a slow line fast," you will indeed be heading towards the trees
FAST between every turn. If something goes wrong during this part of the turn, you may hit the hard snow bodily and continue heading towards the trees
FAST on that icy surface, without the benefit of skis-on-snow to deflect your trajectory. No need to ask me how I know this....
So let's not get effective downhill travel speed confused with the speed you carry while heading towards the trees. (I'm talking below tree-line skiing here). Carving the slow line fast involves A LOT of very fast skiing that's not pointing down the hill. That speed is a major part of the euphoria that carving produces.
Just don't expect to beat your comrades to the lift if they are skiing the fast line fast. You will get there last.