Saturday, February 4, 2017

What is an Emergent Property?

It seems world of physics is talking about "emergent properties" more and more.
People may ask what is an emergent property?
When any kind of system (physical/computer/game/mathematical) acts with different set of laws/rules at two different scales
then the set of laws/rules of the higher scale are emergent properties of the set of laws/rules of the lower scale.

For example think about the relationship between world of chemistry and world of quantum mechanics.
They seem to be worlds run by completely different rules.
But we know (proven?) that every rule of chemistry can be explained by quantum physics.
That means quantum mechanics creates chemistry.
That means chemistry is emergent property of quantum mechanics.

Similar situation exists between chemistry and biology.
The rules of chemistry is very different than rules of biology.
World of chemical reactions is very different than world of cells, multi-cellular organisms.
And actually when going upwards (in scale) from world of single cells, as the number of cells in an organism increases cell by cell,
each of those species are living in worlds with more and more complicated set of rules.
Each species is an independent emergent property.

Beyond biology there is human psychological world, as another level of emergent property,
beyond psychological world there is social world.
Social world has branches and levels like what happens with species in biology.
For example think of the difference between rules operating in a family, in a school, in a hospital, in a factory/company/store,
town/city/country./inter-country/planetary.

Can we agree that all these emergent properties of existence must be expressible by math?
If so can we always mathematically theoretically predict a higher level emergent property from a lower one?
Can we always predict a lower one from a higher one?

What all these complicated mathematical structure of existence mean?
We are forced to say, if God exists and created and operates all these existence,
God must be an incredible mathematician humans cannot ever hope to match! :-)

2 comments:

  1. If ever there was going to be an example of mathematical truths which can't be predicted, outside of Gödel's specialized examples, it is surely going to be in the field of emergent properties. I'd guess that it's part of what makes them emergent, that they can't be predicted.

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  2. I think one very fascinating example of emergence comes from Stephen Wolframs Automata; where he showed that even the simplest algorithms can form unpredictable structures.
    The only way to find out what they become is to run the algorithm.
    That being said, the only way to see what happens with our physical universe (which is based on at least one algorithm or more we try to describe with natural laws) is probably to let it run its course; for being able to compute it (simulation) mathematically would require more processing power than the whole universe has to offer.
    After all, our universe might be just that, a simulation.

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