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Merit of meretopology

  1. Aug 23, 2006 #1
    I have a question about mereology and topology. This is a basic question. What is the merit of meretopology.For instance, two parts A and B. What is the meaning of being able to change energy between parts A and B. How about the ability of sharing knowledge. Because I am new in mereotopology and has a great interest on it, please explain to me in a very simple way in term two parts A and B.

    From mereology theorem, for instance x is part of y and y is part of x. How can I create a mathematical relation between it. Let take the example car and tyre. How can I express the relation between car and tyre in term of mereotopology and finally create a mathematical expression of the relation. Is there are any mathematical concept on how to present the part-part relation and part-whole relation?For example,
    Car{width, length, speed,..etc) ===>Tyre(diameter, speed, rpm,..etc)

    In my understanding, for instance two parts car and tyre. Car has it own attributes and same with tyre has it own. How can I connect a group of info/attributes that car have with a group of info/attributes that tyre have
    in term of mereology.

    In term of hierachy, car is built from these parts,{tyre}+{bumper}+{door}+....+{steering} . How about the relation between parts and whole(car).

    :smile:
    Tq
     
  2. jcsd
  3. Aug 28, 2006 #2
    Is a satisfactory answer to your question as simple as the observation that a tire is a part of a car? Whatever is part of a tire is also part of a car: tire parts are a proper subset of car parts. Express this fact in set notation, and you've got your mathematical relationship. There are also relationships between how fast a car travels and how fast its tires travel (provided they are attached to the car and not flying off due to malfunction or accident).
     
  4. Aug 28, 2006 #3
    Not about two parts--but two wholes (A, B) that can change energy without breaking. Thus, think of the shape of your coffee mug (A) when you look at it from above--see the solid walls, the bottom, and the hole ? These are the parts of the whole mug. OK, now look at a donut made of clay (B) from the top--except that walls are thicker--what you see as donut parts, the walls and hole (e.g., the mereology) can be transformed into a coffee mug using molding properties of clay (e.g. a topology transformation, A <---> B). As for the "merit of meretopology" see http://en.wikipedia.org/wiki/Mereotopology
     
    Last edited by a moderator: Aug 28, 2006
  5. Sep 1, 2006 #4
    Thank you for the comments. Just for a corfirmation weather my understanding is right or not about a part-wholes relation. For example a car and a tyre. Tyre is part-of car and the mathematical relation can be expressed between it. We can also describe a topological relation between a car and a tyre e.x speed for both of it. And for a complex hierachy, a set theory is needed to create a relation between a domain/entity/part to anothers and relation about creating a complete wholes.
     
  6. Sep 1, 2006 #5

    HallsofIvy

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    Which sounds like "merotopology" is so fundamental it is mostly useful for notation.

    It's a lot like the statement "Set theory will help get a rocket to Mars": completely true and completely misleading.
     
  7. Sep 5, 2006 #6
    my car doesn't have tires, it has tyres. It also doesn't have a trunk or a hood (it has boot & bonnet).

    Best Regards
     
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