Can you talk a bit about how we are connected to this world?

We are connected to the world through our accumulation of energy, the energy we are born with.  We begin assembling this reality as soon as we are born, it's part of our nature to do so.  The problem with our energy is that we have teachers from the moment of birth.  Those teachers force our perception to focus on the world as human beings have learned to perceive it and them especially.  In a real sense our patterns of behavior begin to develop then.  Even though we are born with natural proclivities, the need to "see" the world as others see it often runs against the grain of our natures and begins to create problems for us later.  New born infants are very elastic energetically; the shell that encases their energy is soft and very fluid.  It tends to swell and shrink with their perception.  We assemble a reality from which we never escape.  But it isn't the only reality, or even the best one for us as energetic creatures.

Is it possible to be only partially anchored?

Children of seriously abusive environments usually have problems and are prone to anti social stances, or, they go the other way and become anal retentive.  Take you pick :)  If the basic bonding/teaching isn't going on, at some point you become detached from that learning mode in a way that will stay a feature of your energy.  Often you will find people being either perpetual victims or perpetual abusers.  It shows in their energy at levels that stretch all the way back.  It also depends a great deal on the makeup of energy they are simply born with.  We are all unique within a certain range of energy, no two people are mixed the same.  If you are born with a strong will and sense of self, abuse will not do the damage to you it would someone born with far less of those things.

You said once that  the Recapitulation process can discover how we assembled that 'reality' . . . .

Yes, you can find the moment the world as it is now, first appeared to you.  But the association with the Recapitulation has to do with how we are marshaled into the world and anchored to it.  Or how we're  really chained to that particular perception through the interactions with the people we deal with.  By removing those ties that bind, we also move our ability to see in different ways.  We first must find the places it is chained and loosen the bonds.  This is what the Recapitulation does.