Understanding Typology and Topology: Exploring Key Ideas for Humanities Scholars

[dementedbear]

Help needed in understanding topology

I am trying to understand basic principles of typology but am having a very hard time. I'm not good at maths at all (last studied it when I was 16) and I'm currently researching a PhD in literature and philosophy. My academic background is firmly situated in the humanities.

The reason I ask about topology is that it seems to play a very important role in the philosophy of Gilles Deleuze, one of the key post-structuralist thinkers I'm writing about. I've looked over the wikipedia entry and got some very basic ideas from it, but I still found it very confusing for a non-mathematician such as myself to understand.

If anyone would be able to explain some of the key ideas to me, or suggest places I can look for more info I would be very grateful!

 

[HallsofIvy]

There are a number of different definitions of typology- even in Wikipedia. Since you refer to literature, I think the one you are referring to is "linguistic typology", http://en.wikipedia.org/wiki/Linguistic_typology
but I don't see what that has to do with mathematics.

 

[g_edgar]

Do you want to ask about "typology" or "topology" ... both are in your message. And they are not at all the same thing.

 

[dementedbear]

Do you want to ask about "typology" or "topology" ... both are in your message. And they are not at all the same thing.

Yes I realized my error after posting and tried to edit the title but it seems to have remained the same.

I'm trying to find out basic ideas of topological spaces and what they are - definitely not typology. That was a late night typo!

 

[rootofunity]

In pure mathematical terms a topological space is a set that satisfies a couple of postulates. Those being:

1) A set X contains the empty set as well as itself.
2) The union of any collection of subsets are also a member of the set.
3) Finite intersections of subsets of the set are contained in the set.

The euclidian plane is a perfect example of a topological space. If I wasn't on my blackberry I'd prove it for you. Perhaps later when I have a moment. Think the x,y axis. Instead of studying the functions that can exist in the space (ie y=mx+b) it studies the structure that y=mx+b exists in.

Anyway, the only word of caution I have for you is if you talk to a topologist, don't ask them about donuts or coffee cups...you'll confuse them :P

 

[andlook]

Hi

I am doing a maths degree and have only just started doing topology after avoiding it for some time. The word around uni was it was very hard. I thought I'd write back to maybe give you an idea of what I see topology to be, as I am new to it but with some maths background.

(As I am new to topology this reply is probably as much for me as it is for dementedbear, so I can get my understanding clear. It would be great if someone with more experience could verify if I have the right, very general, idea.)

I'll try to stick to some general ideas not technical maths.

As I see topology it is a way of defining surfaces and spaces through mathematics. These surfaces/spaces could be geometrical objects like globes or shapes with holes in them, like a doughnut. Because we know how maths works we can then study how these models of spaces can be changed, maybe stretched or made into new ones by sticking two spaces together or by taking parts of the space out.

Also we can use the maths to show that some objects display such similar characteristics that they can thought of as being the same. One way of seperating these classes is how many times the shape is punctured. ie how many holes it has in it. Then we have a way of clasifing all spaces (shapes).

So we can say that a wedding ring is fundementally the same shape as a window frame because both are objects in 3D that have one hole in it. Or a ball can be studied similiarly as the cube because they have no holes. Or a maybe a sink, with the main drainage hole and the overflow hole, and a door, with the hole for the letter box and the hole for the keyhole, both having two holes studied similarly.

It is also then theoretically possible to find a rigorous mathematical method that would deform any similarly numbered punctured shape into the other.

To see the power of this subject consider what I have described:
All 3D shapes can now be described by number of holes and can be represented exactly by mathematics. We can then build new shapes from these by pasting them together. So in theory really complicated structures could be analysed using the powerful tool that is mathematics.

Ok so this is on the geometry side of topology (topology has further implications than just geometry, such as in analysis). Also this is might first attempt at describing topology...

I hope, for a non mathimatically minded person, it gives sense of what topology can be... and I hope I got it close to right...

 

[morphism]

Yes I realized my error after posting and tried to edit the title but it seems to have remained the same.

I'm trying to find out basic ideas of topological spaces and what they are - definitely not typology. That was a late night typo!

I'm very curious about the relevance of topological spaces to philosophy. Would you care to explain?

 

[tiny-tim]

Welcome to PF!

Hi dementedbear! Welcome to PF!

That was a late night typo!

No, it was a late night topo.

Do you ever find yourself confusing doughnuts and coffee-cups?

You're just being Deleuzional. ​

The reason I ask about topology is that it seems to play a very important role in the philosophy of Gilles Deleuze, one of the key post-structuralist thinkers I'm writing about. I've looked over the wikipedia entry …

(there's rather a lot of topology, including algebraic topology and analytic topology … let's try to narrow the field )

The wikipedia entry doesn't help at all …

can you give us some quotes, so we know how Deleuze used topology?

 

[dementedbear]

Thanks for your replies everyone. Well Deleuze basically incorporates topographical thinking into his entire philosophy but never really mentions it singularly or in isolated moments. Andlook's description makes a lot of sense as Deleuze is constantly trying to get away from traditional concepts of space at time which he feels restrict us in the understanding / appreciation of the material world. His philosophy is always changing and evolving but the current of thought that runs throughout his work is that of positive difference between intensities and pressures that allow for immanent potential.

Saying that, I'll try and dig out some quotes that help, although while Deleuze is one of the most thrilling post-structuralist philosophers, he's also one of the most obscure.

 

[quasar987]

Thanks for your replies everyone. Well Deleuze basically incorporates topographical thinking into

You said topographical which refers to topography, which is still not the same as topology (although closer!). Or was that a typographical mistake? :P

I know Deleuze from his interpretations of Spinoza and I'm very curious also in what sense does topology (or topography) enters into his philosophy.