I really don't see your point.

Piketty shows (with data, by the way) that, below a percentage of economic grow, capital returns are bigger than labour returns.

The conclusion is that there is a trend (very important, it is a trend) to bigger inequality inherent to the system.

What do he propose? A communist revolution? The abolition of inequality by the proletariat?

No, just tax capital so we can redistribute it to all the society.

Of course, if you are a billionaire (except maybe Warren Buffet), you are always to be in favour of "laissez faire", that is, in favour of not changing anything. We are just right now like we should be. Everything is perfect, we don't want to kill innovation.

How does one tax capital?

I would guess they calculate some amount of tax that you have to pay based on how much capital you have. And you keep paying it until you go below some magical threshold. Or, you don't pay and they just take it from you.

Of course, a bit trickier if you don't have capital, but rather have plenty of tangible goods. In which case, they'd probably ask you to submit your "profit and losses" for every year, keep track of how much you made in each year, and start taxing you based on anything that means your running total goes above the magical threshold.

How can you pay your tax bill with capital? Do I give the government shares in my corporation? Or, am I forced to sell shares every year to pay the bill? What happens if the corporation is private, and there is no liquid market for my shares? In that case, how can you even determine how much capital I have? What happens if the company I own shares in goes bankrupt at the start of the year? Do I still owe taxes on the capital from the year prior?

I'm guessing they would enforce some sort of standard valuation for things like that. Or only when it is possible. So a fledgling business, or shares that aren't publicly tradeable.

Any who, the point is. They will find a way that they will claim is "fair" and consistent but probably has loop holes, and figure out a way to tax capital.

I'm still not sure how the subjective taxation of risk would work. Nor do I understand how it would be better than the objective taxation of success (i.e., income), especially when it comes to reducing corruption.

I have no idea, ask Piketty. I personally don't agree with any taxation at all, just giving you hypotheticals as to how they'd calculate it.