This chapter is a huge trip through the history of modern philosophy.  In it, Arendt pulls together the pieces of what seemed like un-needed romantic views of the Greek world, and places it in a context of the rise of modern science, the concomitant rise of modern doubt, and thus of the 'subjective turn' -- what we might now refer to as the problem of relativism, and combines with this move on the one hand in the world of science and philosophy, the accident of Christian morality (with a view that is explicitly related to Weber's on the Protestant Ethic) which held that LIFE itself, as opposed to LIVING a worthy, 'great', historic life, as Sartre put it 'living a good life and dying a good death'.
    The rise of science lead to the ability of people to first view the world from abstraction -- from nowhere. (As opposed to seeing the world from the very anchored view of their position on the planet).  This abstraction leads to a view of all elements of the world, including our relations with others, from a dis-embodied, 'world-alienated' position.  The only thing left in this world, that we could trust or believe in, were the things we created ourselves. Our models of the universe, our tools, etc, allowed us to encapsulate the vastness of the world into our minds.
     The turn to Homo Feber - the worker was a turn toward the creation of our own hands, and elevated the world of work in the vita activa.  This move was only a start, however, of the fall of action.  For AT THE SAME TIME, there was a change in moral values associated with Christianity that saw Life itself as the key element.  This lead us to a world of utility and a system of valuation that said something was valuable because it added to the greatest good -- the best (read longest) life.  Thus instead of holding actions to 'the standard of greatness' we now look for life itself as the end, not the means.

     [This has heavy Nietzche overtones -- that the Herd mentality is destroying of greatness].

Details.
{35} World Alienation.
     Three events mark the start of the modern age:
     1) The discovery of America
     2) The Reformation.,
     3) The invention of the Telescope, and Galileo's use of it.

All three of these events mark a move away from the 'traditional world'  We now (1) have a new map, and a world that no longer is bound.  We now live in an earth-wide continnous whole.  (2) We are no longer bound to the traditions of the church for spiritual life.  The two strands of the reformation either put salvation into the hands of each individual, or into an uncaring, pre-destination.  And finally (3) we now see the world, our physical world first, from a point outside of ourselves.  The rise of modern science gave us the ability to see the world from the vantage point of the universal.

The Archemidian point:
     The phrase follows from Archemedes - he said that with a level long enough, and the proper placement of the fulcrum, he could move the earth.  The Arechemedian point is where the fulcrum to that lever would be -- somewhere outside the earth itself, a non-place. Arendt uses it as an analogy for modern
science and the move to the universal.

{37 - 38}
     Universal science means we see the world from the standpoint of mathematics -- from a point that is universally valid.  Ironically, the universal truths seen in math help to give rise to the subjective turn in Philosophy.  This turn is best seen in Descartes -- who's Meditations, by the way, should probably be required reading for anyone who wants to think about the social construction of reality.  Descartes started out his meditations by asking what it was he could know with certainty.  The answer was only that he himself was a thinking being.  That everything else was possibly illusion.  His (really unsatisfactory) solution to  the problem of radical doubt was that God was good and wouldn't pull these kind of tricks on us (ok, that's a bit of a simplification, but we don't have time for a full review of the history of modern philosophy.  Please put this book on your summer reading list!).

     Descartes move gave rise to what Arendt calls the 2 nightmares of the modern age:
     1) That reality of the world ad human life is doubted.Nothing can be known for certain.,
     2) Heavily related is that we can't even trust our senses.

Both of these lead to an alienation from the world.

Paradoxically, the uncertainty of the life world has make promises more important -- in some ways, we can't afford to lie anymore.

{39} Introspection and the loss of common sense.
     The internal turn, the look into myself, as all I can know, lead to a decrease in the COMMON sense - that which we could all share.  All men can have in common is not a world of things that we share (which, after all, we can't even know exists), but only the similar structure of their minds.

{41} The consequence of all the above was a reversal of the contemplative and the active life in the order of the vita activa.  The rise of the experiment replaced observation, contemplation, with ACTION, with doing things in the world. Under a world where our senses couldn't be trusted, in order to know, we have to DO.

{42} The victory of Homo Feber.
     This rise of DOING, was key to letting the world of WORK, of DOING to make THINGS in the world rise to the top of the vita activa.  Scientific progress followed from better tool making, i.e. better instruments.  The problem with making as a world view was that it left out the unexpected.
     The move to creation as an end in itself let process take over the product, which further alienated us from thinking and contemplation.

{43} The defeat of Homo Feber and the Rise of Happiness.
     What we need to explain is not why our esteem for homo feber increased, but why laboring was given the highest esteem.  Arendt says this happened very slowly, and followed from the focus on the process nature of making - that the product itself wasn't sufficient, we kept needing to improve the process.

To pull the last parts together:
     The rise of animal laborans came due to the twofold influence of Christianity  and the process of utility maximization.  That what mattered was life itself, and that any process that benefitted the most on this dimension had to be the best.  This is the short version of why homo faber was replaced with animal laborans, with one  who best provides the necessities of life.
     Like Weber, Arendt says we've lost the religious overtones to why we work so hard, but that the result is the same: we are disconnected and alienated from each other. This disconnected, combined with the now almost second nature functioning of jobholding society has left us without the capacity to act (or at least makes it very rare).

     "It is quite conceivable that the modern age - which began with such an unprecedented and promising outburst of human activity - may end in the deadliest, most sterile passivity history has ever known." [p.322].