mordechai's digibetes for example II jbml thln 35


WHILE
ANCIENT GEOMETERS
VIEWED A TRIANGLE AS AN OBJECT WITH AN INTRINSIC SHAPE,
ALGEBRAISTS DESCRIBE IT AS THREE INDEPENDENT VERTICES DETERMINED BY THREE SETS OF COORDINATES,
AND SO DRAWING LINE SEGMENTS BETWEEN THE VERTICES AND MAKING THE SHAPE OF THE TRIANGLE VISIBLE
BECOMES A SECONDARY MATTER.

SO,
WHILE EUCLID'S
CHARACTERIZATION OF TRIANGLES AND LENGTHS (DISTANCES)
ENCOURAGES THE STUDY OF SIMILARITY BETWEEN TRIANGLES,
THE ALGEBRAIC APPROACH MAKES IT MATHEMATICALLY CONVENIENT
TO STUDY HOW THE SHAPE OF A TRIANGLE CHANGES WHEN JUST ONE OF THE VERTICES (COORDINATES)
IS SHIFTED BY SOME INTERNAL
OR EXTERNAL PROCESS.

IN THIS SPIRIT,
TO EXPLAIN A BALL FALLING FROM OUR HAND
WE ARE PROBABLY MORE INCLINED TO INVOKE A
"force of gravity"
ACTING ON THE COORDINATES OF THE BALL AND PULLING IT TO EARTH,
RATHER THAN DESCRIBE THE EARTH AND THE BALL AS SHARING A GRAVITATIONAL RELATIONSHIP
THAT TENDS TO MINIMIZE THEIR SEPARATION
BY ACCELERATING BOTH OBJECTS.

THE DEVELOPMENT OF PHYSICS IN THE PAST GENERATION
HAS REEMPHASIZED THE INHERENT UNITY OF THE MASSIVE PARTICLES
AND THE RELATIONSHIPS THROUGH WHICH THEY COME INTO EXISTENCE, AND MUCH EFFORT HAS BEEN PUT
INTO METHODS OF SOLVING PROBLEMS THAT AVOID REGARDING THEM
AS APPROXIMATELY INDEPENDENT.
06 mrt 2013 - bewerkt op 07 mrt 2013 - meld ongepast verhaal
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