Amazing Game Against Medium Computer

This is a game I just played against the medium computer. I lost because the computer made an early bishop sacrifice for positional counterplay. Interested yet? This game seems completely uncharacteristic of a computer. I expected the medium computer to be much more limited and have horizon issues, but that certainly doesn't seem to be the case.

I am interested in what I can learn from this game. I believe neither of us made any tactical mistakes, so my learning really should come on the positional front. 

I have been doing "Tactics, tactics, tactics!" Like a good boy for several months now (I joined the website 7 months ago) and I wonder if this game is a sign that I should be moving onto positional concepts, or if tactical errors led to this defeat. If that's the case, where do I start?

This game isn't in your archive. What is this? The java computer engine?

*mentions medium computer*

*says "Computer - Hard"*

Something is not right here...

Thanks guys >.< I was hoping for some help.

Play -

Play against the computer

Copy the PGN.

I don't know why it says computer-hard. I just copy/pasted the PGN. I selected "Computer - Medium 1200+"

Do I need to take screenshots?

Okay, fine, forget the opponents. Just imagine it's a game between me and some random person.

I'm sorry but 21 Bxc4 was just a bizarre blunder. Black should have just taken it. How it would have given you counterplay is not visible.

"Sacrificing the bishop to get rid of the passed pawn and unpass another pawn is easily compensation, not to mention that blacks king is exposed in the resulting open files."

You would get rid of the passed pawn but you would leave black with a great space for his knight and you would be missing a bishop. Black would be clearly winning afterwards.

You had plenty of chances for counterplay without throwing away your bishop. 21 b4 pushing back his knight would have been a much better move.

And when the computer still refused to take your bishop, you insisted on giving it away for only one pawn.  

You would have done much better if you had tested the computer's ability to play a piece down endgame with its three extra passed pawns.

I don't understand how after move 23 of your proposed line I have counterplay. I calculated this variation, but it looks like I have no way to stop black's d and e pawn and I might as well resign on the spot. What is white's plan for getting rid of the D and E pawn?

(Yes, you may have to spell everything out for me)

It would be a complicated game but certainly it is miles from being resignable.

Okay, here's a different question.

Are there imbalances in the position you can identify for me which give counterplay?

When I look at the position I see two things:

1: Black has connected passed pawns

2: White is a minor piece up.

What else should I be looking for in this position to both find a plan, and to indicate that there is a winning plan to be found?

I can see that there are moves white can make by checking with an engine. I mean more, human to human, what is white's "plan" and what can I look for in any position to indicate that such a plan exists?