Wednesday, August 24, 2005

Parting the Sea

The Set.

What a wonderful construct a set is, simply a collection of something which only has to be distinct - and nevertheless, “It can be viewed as both the foundation upon which nearly all of mathematics can be built and the source from which nearly all mathematics can be derived.”

You don’t like sets? They remind you of school? Annoying, deadly boring?

Think again, you are grown up now.

Just focus. Forget about native or axiomatic theories, forget about paradoxes, forget about cardinality, unions or intersections: focus on the set.

A collection of something distinguishable.

How can such a simple concept be so important to mathematics? Something put together and voila, it’s a set by the touch of a magic wand?

How about a glass of water? Do the molecules build a set? No, they don’t, just because we can’t distinguish one H20 from the other.

But if?!? Yes, if we could, it would be a set, really.

For nothing more than separating the water from the rest of the world into a special glass and be able to “call them by their names” – we would have created a set.

Imagine that!

Imagine, how much you know about things, if they form a set, because the fact, that the things in a set have to be unique proves you a very, very important point: you have to be able to measure something, some distinctive value like identity to distinguish one set member from the other.

But that’s just a part of the information you got from sets. Because the simple little word “collection” shows you something else: You must be able to decide, whether something belongs to that collection or not.

Again, you must be able to measure something to decide, whether it’s part of the collection.

Look at our water glass of magically distinguishable H20-molecules. “Water in my glass” defines the collection. So air or children or cars don’t fit with the definition – and water? Water has to be in “my glass” to belong to my set. My glass can be defined by its space-time curve or by form or matter, the keys you choose to measure can be anything: They just have to be unique...

and stable.

Remember? It wouldn’t make sense to use changing values as identity, because after the change, how could you track the changes?

That’s the reason, why a set is so important to mathematics – and to each and every information processing system or procedure: it defines identity and properties...

it defines measurability: the precondition for mapping systems.

It’s the “zero-point-information”, the point, where you can stand to structure the whole wide world in two distinct parts: inside the set, outside the set.

And inside the set, you know, there is identity – therefore you can track movings, you can follow events, you can construct relations, you can map and store, retrieve and compare.

A set creates order in a random world.

That’s the magic.

5 Comments:

Blogger Robert said...

Hello my friend. I like the new place. I look forward to many discussions and debates. May I link on me blog?

3:35 PM, August 27, 2005  
Anonymous B said...

I ate this up. Even though I have no education in physics and mathematics, I am fascinated by these subjects and understand on an intuitive level.

I will freely admit I had never heard of a set before now. Set's meaning was always a place where a movie is filmed.:)

Thank you for writing about sets in terms I can understand.

Also, may I also link?

9:18 PM, August 27, 2005  
Anonymous Barnita said...

Congratulations on the beginning of a new blog and thanks for letting MK link up cos that means that all of us ex-warbloggers who now infest MK's have yet another place to crib and moan- hurray!

To new beginnings- Cheers!

2:33 AM, August 28, 2005  
Blogger Again said...

hi, you're welcome - glad to see you here ;-)

and sure i would like to be linked to: to be read is the reason for writing, isn't it?

mk:
I look forward to many discussions

that's what i'm dreaming of

b:
Thank you for writing about sets in terms I can understand.

"If you can't explain it simply, you don't understand it well enough." – A. Einstein

because i love math and physics so much, that i want to share it, i'm glad to be understood - so thank you for that great compliment!

barnita:
Congratulations on the beginning of a new blog

thank you, so i feel free to ask you again: how i could visit your blog - i would like to read stories about a part of the world so far away (note: i'm not curious <blink>)

btw:

now you can see, why i have to begin a blog - it's just because i tend to write too much for comments ;-)

4:31 AM, August 28, 2005  
Anonymous Barnita said...

Hey Again. I'm a shy-blogger I guess. But I've finally worked up the balls to tell you guys where to find me and my blog.

12:49 AM, August 29, 2005  

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