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Calculus 4E Lsn 1
The Problem of Change (Lsn 1)
| Question | Answer |
|---|---|
| The problem of change asks | "Why do things change?" |
| The problem of change prompted man to embark on a quest to understand _______________ and ____________________. | change (and) motion |
| The problem of motion is simply another way to define the problem of _____________________. | change |
| Orderliness is important aspect of the problem of change, because | while change is frequently TIDY and organized, it is often prone to DISORDER. |
| Example of change that is NOT orderly: | pulling the pin on a grenade |
| Example of change that IS orderly: | planting seeds |
| the philosophy of nature - what we now call SCIENCE | natural philosophy |
| Thales of Miletus | 500s BC, Greek, taught Pythagoras, first mathematician |
| Thales said everything was made of __________________. | WATER |
| Thales put the problem of change "on the table" and first proposed a | SOLUTION (water). |
| "ALL is number" | Pythagorean motto |
| "All is number" means: | 1) ALL is ordered according to mathematical laws 2) DIVINE reason = ORDERER 3) HUMAN reason CAN discern the pattern |
| Pythagoras | 500s BC, student of Thales, Greek, believed everything was made of numbers |
| Pythagoras's discovery that MUSICAL INTERVALS could be represented by _________________ ________________ led to his motto. | WHOLE NUMBERS |
| The "music of the spheres" describes | the idea that the motion of the heavenly bodies produces actual music. |
| When we say that math applies to the world, we mean that math, even though it is _________________, can describe the physical world. | NONphysical |
| God is a ______________________________. | mathematician |
| Two views Plato inherited from the Pythagoreans | 1) The human soul is immortal. 2) The physical world is fundamentally mathematical. |
| Two parts Plato believed comprised humans | a physical body AND a NON-physical soul or mind |
| Two realms into which Plato divided reality | the PHYSICAL realm and the NON-physical realm |
| Plato's NON-physical realm | a mysterious world of Ideas -or- Forms, his heaven |
| Plato's Forms | actual, nonphysical objects that literally exist outside the physical world; absolutely perfect, exist eternally, never change |
| The world is mathematical because | God made it that way. |
| The study of mathematics is important because it trains us to take our minds off of | physical things. |
| Plato's Republic came up with the concept of liberal __________. | arts |
| liberal arts | the TRIVIUM (grammar, logic, & rhetoric) & the QUADRIUM (arithmetic, geometry, astronomy, & music) |
| Plato's version of the problem of change dealt with the MOTION of | the heavenly bodies and the physical world. |
| Plato's problem of change is difficult to solve because heavenly bodies don't really move in an ________________ fashion. | orderly |
Created by:
MrsHough
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