Tuesday, February 08, 2005
1+1=3
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.
- Our model will be a universe made of a several instances of a single indivisible, fundamental particle, which we'll call A.
- The concept of "size" in our universe will be governed by the amount of A particles we have. E.g. a size of 3 (AAA) is bigger than a size of 2 (AA). Emergent properties will happen at different sizes.
- As with our (real) universe we don't really know what an emergent property is. There may be many more than we can percieve. So we'll assume that emergent properties happen with collections of A. Our rule of collections will be simple, if we have a collection, n of A then the number of emergent properties of a certain size x is the number of times we can fit x into n (rounded down). NOTE - this rule is arbitrary.
- Finally, we'll take it one step further and give each emergent property a name. Better still, we'll call it a new particle (e.g we'll say AA = B). Remember though, we only define these new particles by the number of A they contain, not by each other.
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...
