Tuesday, February 08, 2005

 

1+1=3

On the subject of emergence.

Emergent properties (http://en.wikipedia.org/wiki/Emergence) of collections of smaller "things" seem to be very real physical properties. By saying a property is emergent we are saying that its parts cannot fully explain that property. It seems that, as though "by magic" these emergent properties appear when systems get complex, and large enough. The trouble is, even though they are real there is no overall classification system for them (like that of fundamental particles). So why not make one?

Let's have a crack at it. first off we need a model and some rules.

Confused? Me too, here's an example:

First off, pure reductionism (no emergent properties). Let's count the number of particles in this system (we'll try it with a universe containing 5 A) .

1 AAAAA

2 AAAAA

3 AAAAA

4 AAAAA

5 AAAAA

Size does NOT matter in this universe, if you used a microscope to peer down through the scales you would see at size 1 the 5 instances of A. As we get larger (2 and up) the 5 particles still totally describe the universe and nothing new happens (is emergent). No molecules with new properties, no vortexes, no human consciousness, etc. - just cold, hard, boring particles. The number of things in this universe is 5.

Now let's add in some rules of emergence.

1 AAAAA

2 (AA)(AA)A

3 (AAA)AA

4 (AAAA)A

5 (AAAAA)

At size 2 for example, size does matter - we have 2 new B particles (AA) and (AA). Following this logic further you can see we have an (AAA) particle, which could be called C. Then (AAAA) = D and (AAAAA) = E. When we replace sets of A with other letters we get:

1 AAAAA

2 BBA

3 CAA

4 DA

5 E


The list of all things here is (A,A,A,A,A,B,B,C,D,E) which is 10 entities. The number of things can be counted by using a basic formula:

# of things = sum[i=1,...,n] (floor(n/i))

So we can loosely say that 2A = 3 things (an A, another A, and a B) so, roughly speaking, 1+1=3.

So what's this good for?

The classification and categorisation of emergent properties is adhoc. What if there is a pattern in the REAL WORLD by which we can classify and possibly even predict emergent properties?

Something to think about...


Comments:
1+1=4 :)

Check it out!
1 mapping system +1 other mapping system=4 kinds of maps!enjoy… =D
 
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