Topology

2015, Aug 15

I hadn’t known Topology until a friend of mine gave me a quiz related to it. Though I still have no idea about the mathematical stuff, it has been drawing my attention due to some of its interesting facts.

What is Topology?

I found a definition on livescience.com (more understandable than on Wiki)

Topology is a branch of mathematics that describes mathematical spaces, in particular the properties that stem from a space’s shape. Many of the shapes topologists deal with are incredibly strange, so much so that practically all everyday objects such as bowls and pets and trees make up a small minority. The word “topology” derives from the Greek words for place (topos) and study (-logy).

For instance, under Topology’s perspective, a donut and a coffee cup are the same since they have a similar shape (a solid object with a hole). Similarly, a rubik’s cube is just a different version of a ball (by somehow, we can mould a cubic object into a sphere).

Another example is the DNA. After a DNA molecule unwinds, it resembles a ladder. So what are the implications here? Well, basically it means: “with the same transformation to a DNA, we may get the same result to a ladder and vice versa”. To be specific, we can shrink a ladder with the same principle a huge DNA molecule winds itself into a smaller one.

For more typical examples, just have a look at the following videos:

We could transform a rubber band to a variety of shapes without cutting or glueing it. There is a sub-branch of Topology studying this kind of homomorphism: “Knot Theory”

Topology - Philosophy

From my point of view, there are 2 pieces of philosophy apparently exposed:

[1] There must be a simple instance of a complex object. Therefore, a complicated problem could be reduced to a simpler one.

[2] Since objects are in analogy under some aspects of consideration, the similar solutions may lead to the similar results.

Why does it draw my attention?

First of all, I love visual objects.
Secondly, I love analogy.
And finally, I love simplicity.

What matters?

I suppose recognizing analogy among objects is not really straightforward. Fortunately, we still have several banches of science on this field, such as Topology, Synectics and so forth.

misc

maths