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By Peter Orlowski © 2012 no color no sound no odor no taste no texture no mass no weight no charge no magneticism no thickness no width no length no position.

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Presentation on theme: "By Peter Orlowski © 2012 no color no sound no odor no taste no texture no mass no weight no charge no magneticism no thickness no width no length no position."— Presentation transcript:

1 by Peter Orlowski © 2012 no color no sound no odor no taste no texture no mass no weight no charge no magneticism no thickness no width no length no position no shape

2 ANALYSIS SYNTHESIS PHYSICAL BODY: Known with certitude, but in a confused way, i.e. all the features mixed together PHYSICAL SURFACE: Known thru body, i.e. as the divider and boundary of a body PHYSICAL LINE: Known thru surface i.e. as the divider and boundary of a surface MATHEMATICAL LINE: Conceived through a moving point, as having length without width. MATHEMATICAL POINT: Conceived precisely in itself, as having position without having parts MATHEMATICAL BODY: Conceived through a moving surface, as having length, width, and thickness. PHYSICAL AND CONFUSED KNOWLEDGE MATHEMATICAL AND DISTINCT KNOWLEDGE MATHEMATICAL SURFACE: Conceived through a moving line, as having length and width only. PHYSICAL POINT: Known thru line, i.e. as the divider and boundary of a line.

3 SYNTHESIS A mathematical body has depth, in addition to shape, length, and width. But it has no mass, charge, magnetism, color, odor, etc. A mathematical surface has only length, width, and shape. It has no depth, and also not mass, charge, magnetism, color, odor, etc. The mathematical line has only length and shape. It has no width, or depth, and also no mass, charge, magnetism, color, odor, etc. The mathematical point has nearly nothing, no mass, no charge, no magnetism, no color, no odor, no shape, no parts. All it has is position. MATHEMATICAL LINE: Conceived through a moving point. MATHEMATICAL POINT: Conceived precisely in itself, what has position without parts MATHEMATICAL BODY: Conceived through a moving surface HOW ARE THESE FEATURES GENERATED? MATHEMATICAL AND DISTINCT KNOWLEDGE MATHEMATICAL SURFACE: Conceived through a moving line =

4 A precise understanding of line, surface, and solid can be had by the generation of these from a point. Such a precise understanding adds the complexity of a multitude of features without confusing the various features together.

5 no color no sound no odor no taste no texture no mass no weight no charge no magneticism no thickness no width no length no position no shape And the geometer said, “Let there be a point.” In the beginning the imagination was empty and void And the geometer saw that the point had position and nothing more, and knowing it precisely, he said that it was good. POINT no thickness no width no length no position no shape no color, odor, taste, mass, charge, etc. position

6 no thickness no width or length no position no shape no color, odor, taste, mass, charge, etc. no thickness no width no length noposition no shape no color, odor, taste, mass, charge, etc. HOW ARE THE FEATURES “INHERITED”? MOTION lengthshape POINT position lengthshape position + LINE And the geometer said, “Let there be motion of the point.” The motion added length with shape to the point’s position, and a line was made, the first magnitude.

7 no thickness no width or length no position no shape no color, odor, taste, mass, charge, etc. no thickness or width or length no position no shape no color, odor, taste, mass, charge, etc. no thickness no width no length no position no shape no color, odor, taste, mass, charge, etc. HOW ARE THE FEATURES “INHERITED”? MOTION widthshape MOTION lengthshape POINT position + SURFACE lengthshape position + LINE shape spread position Then the geometer said, “Let the line move in any way, so that it does not move along its length. The motion of the line added width and contour to the line, and a surface was made, the second magnitude.

8 no thickness no width or length no position no shape no color, odor, taste, mass, charge, etc. no thickness no width or length no position no shape no color, odor, taste, mass, charge, etc. no thickness or width or length no position no shape no color, odor, taste, mass, charge, etc. no thickness no width no length no position no shape no color, odor, taste, mass, charge, etc. HOW ARE THE FEATURES “INHERITED”? MOTION shape thickness MOTION widthshape MOTION lengthshape BODY + POINT position + SURFACE lengthshape position + LINE shape spread position shape bulk position Then the geometer said, “Let there be motion in the surface so that it does not move along itself. And it was so. The motion of the surface added thickness and form to the surface and a body was made, the third magnitude.

9 no thickness no width or length no position no shape no color, odor, taste, mass, charge, etc. no thickness no width or length no position no shape no color, odor, taste, mass, charge, etc. no thickness or width or length no position no shape no color, odor, taste, mass, charge, etc. no thickness no width no length no position no shape no color, odor, taste, mass, charge, etc. HOW ARE THE FEATURES “INHERITED”? MOTION shape thickness MOTION widthshape MOTION lengthshape BODY + POINT position + SURFACE lengthshape position + LINE shape spread position shape bulk position And seeing distinctly all that he had made, and how all the features of magnitude came to be, the geometer said that it was very good.

10 no thickness or width or length no position no shape no color, odor, taste, mass, charge, etc. no thickness or width or length no position no shape no color, odor, taste, mass, charge, etc. no thickness or width or length no position no shape no color, odor, taste, mass, charge, etc. no thickness or width or length no position no shape no color, odor, taste, mass, charge, etc. THIS IS THE GENEOLOGY OF MATHEMATICAL MAGNITUDE AND HOW IT WAS MADE IN THE BEGINNING AND HOW ITS FEATURES WHERE INHERITED. MOTION shape thickness MOTION widthshape MOTION lengthshape BODY + POINT position + SURFACE lengthshape position + LINE shape spread position shape bulk position


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