Merit of Mereotopology: Understanding Part-Part & Part-Whole Relationships

[agus]

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).


Tq

 

[NickJ]

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).

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).

 

[Rade]

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...

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

 

[agus]

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.

 

[HallsofIvy]

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.

 

[moving finger]

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).

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