What's the difference (Present Perfect Progressive/Past Progressive)?

Mister Micawber:

«In the first case, you are finished thinking; in the second case, you are not.»

If to take possible contexts into consideration, I disagree:

Past Simple, but he's still thinking (at the moment of speech):

1. I can't solve this problem! I was thinking yesterday at the lesson, I was thinking in the bus on the way home, I am thinking now. But nothing better than the explanation through the Huygens principle occurs to me.

Perfect Progressive, but he've probably finshed thinking.

2. I have been thinking a lot in the past few weeks, and have come to several solutions: one is to introduce a feedback in order to achieve a negative output resstance at low frequencies, another is...

So, Past Progressive is used to describe what was happening at some past moment (or interval) of time, no matter whether it is still happening or not.

Present Progressive emphasises the importance of the result of a past action for the present, or, is used to indicate an action that has begun but hasn't finished, as in:

«It has been raining since morning.»

In situations, when in focus is a state rather than an action (like the state of being friends), Present Perfect is used:

«We have been friends since childhood»

«My family has owned this castle for ages.»
(the state of owning a castle doesn't imply an active process...)

Though, as I understand, the same can be said by a guy who has just had a _very serious_ quarrel with a friend and doesn't consider him a friend anymore.

The same about the owner, standing before the ruins of his castle, just destroyed by an earthquake.

I'd call them "right-up-to-the-present" actions.

Bokeh wrote:

Mister Micawber wrote: In the first case, you are finished thinking; in the second case, you are not. That's not necessarilly true. I have eaten doesn't mean you are still eating; it just means the residual state prevails. Same with thinking.

Apples and oranges.  You are comparing eaten with thinking -- a past participle with an -ing form.
The question was about the past progressive and the present perfect progressive.  Nobody said anything about the simple present perfect.  To do an accurate comparison with the verb eat, you'll need to talk about these:

I was eating.
I have been eating.

It seems to me that these have the same relationship as the sentences in the original question.  The first is about an activity that was going on the past and has no connection with the present; the second is about an activity that continues right up to the present moment, suggesting that the activity may not yet be finished.  All of this is, in effect, what Mr. M. already said.

CJ

when it comes to day to day conversation, none of that really matters anymore .. how we express ourselves decides what people see from us. what do you think?