Paper draft/paragraph ideas

Basic idea: Robinson Crusoe as a proof (in 18th century terms) of ability of European (white) to master savage (land/people).  (the empty boxes are formulas in Microsoft Word).  
Introduction - will explain 18th century concept of proof, focusing on (probably), examples as proof of general by outlining algorithm/procedure for example (exactness/concreteness being valued over abstractness).

In Arithmatick books in the 18^th century, mathematical operations, such as addition, subtraction, multiplication, division, etc. operate by means of an explicitly defined procedure for proving, or solving.  By following this algorithm, one is able to solve any problem of that type (i.e. addition, division, etc.).  Further, this algorithm, in order to arrive at the correct solution, must be done in a certain order, and arrive at only one solution.  That is, up to equalities (i.e. 1 gallon is 4 quarts), the solution is unique.    For subtraction, say 5842 – 2751, as outlined in Spence’s Arithmatick compendiz’d..., “The Operation is thus. Begin at the right Hand, and say, 1 from 2, there remains 1, which set down.  Next 5 from 4, I cannot but from 14 (borrowing 10 as was directed to make it 14) there remains 9.  Then proceed, saying, 1 I borrowed and 7 is 8, from 8 remains nothing, for which set down a Cypher [0].  Lastly, 2 from 5 , remains 3, which set down, and the Work is finished” (12).  This algorithm has two parts.  Let’s say we’re subtracting  If the first number is bigger than the second, “say,  from , there remains ”. If the second is bigger than the first, “say  from , I cannot but from 1 (borrowing 10 as was directed) there remains , and proceed, saying 1 I borrowed and  is , from  is , which set down.”  For each column of numbers, this procedure holds. What is not explained here, or in any other arithmatick treatise in the 18^th century, is why this works.  However, because mathmaticians know that the algorithm works, following it is the ‘reasonable’ approach to arithmatick. 

Similarly, Crusoe knows algorithms work, so, in order to help make sense of his surroundings, solitary existence, and apprehensions of danger, he uses reason, exemplified by this procedural, mathematical approach to his environment, to create an ‘empire’ of his island.  After acquiring supplies from his wrecked ship, Crusoe’s first endeavor is to secure himself from savages or wild beasts. Such a dwelling must have four characteristics,LIST? limiting his options greatly, but, finally, allowing him to find one spot.  Once he finds the appropriate spot, Crusoe explicates his procedure for securing himself against those things which would threaten his livelihood.  “Before I set up my tent, I drew a half circle...[and] in this half circle I pitched two rows of strong stakes ... [which] did not stand above six inches from one another. Then I took the pieces of cable...and laid them in rows one upon another ... between these two rows of stakes ... about two foot and a half high ... so I was completely fenced in, and fortified, as I thought, from the world...” (90-91).  This follows the pattern of the subtraction algorithm, beginning with a half circle, moving next to pitching stakes; then proceeding to lay cables; and ‘there being nothing’ left to do to secure the wall, he, lastly, “lifted over [a short ladder]” (91), ‘and the work is finished’ (for the wall).