Let's take these girls interacting in the schoolyard.
Who is popular or not is a mental notion.
She who has the most expensive clothes, is the funniest, prettiest, most manipulative, most dominant – is considered by most in the class to be the coolest, the tough one.
But then there is another girl who is almost as cool but different.
She is quiet, looks rather ordinary and does little of herself, but she is warm and wise – a good friend, the kind one.
Many in the class think that she is the coolest.
There is an invisible battle between the two girls, the tough one and the kind one, and their followers. They fight in very different ways to attract as many of the students as possible who are still neutral. The one who wins the fellow students takes dominance and will be able to gather even more friends around her.
The two girls are attractors.
They both work on the neutral group, trying to make friends with them. They are competing for mental dominance.
In each recess, the neutrals must decide whether to hang with one or the other of the two – or whether to wander unsystematically around with the neutrals, where no one dominates; everything is «chaos», unclear.
If one of the neutrals chose to join the kind with the fewest friends, it could affect the balance. This one person is then a butterfly. She does something small and seemingly insignificant that has major consequences.
When the other neutral girls see what is happening, it is conceivable that they follow, first one, two, then all at an increasing pace. There is then reinforcement through feedback.
The mental pressure, the attraction from the kind one, can become so strong that even the friends around the tough one have to give in. Feedback loops tend to devour everything.
The opposite development is nevertheless the most probable. The tough one uses the most power, plays more manipulatively, entices and threatens. The tough one already has the most followers and is the most potent attractor.
Most find it a bit unpleasant to follow her, but they have no choice. She is the strongest and takes dominance, even if it should be destructive for the community as a whole.
Then it can also proceed entirely differently.
One day a new girl starts in the class. The tough girl will try to get her on her side. But the new girl is neutral. She does not know the power play between the two girls.
She chooses the kind one because she appears to be nicer and easier to get access to. She moves to where there is an opening, an opportunity.
For her, the kind one is the strongest attractor.
What is attractive is thus not absolute but relative, subjective, mental. The new girl has not yet felt the pressure from the tough one, and she met the kind one by chance first.
The new girl adds to the group around the kind one something they have lacked, namely smartness, gifts of speech, and unassailable common sense. This is lacking in the tough girl.
The new girl says things that expose the tough, revealing her weaknesses. She's like the little boy in the fairy tale about the king without clothes.
H. C. Andersen's fairy tale is about a «butterfly» who overthrew the country's most powerful leader in a few words of truth.
The new girl points out the truth and changes it because she hit a soft spot where the tough one is not dominant.
At this very point – smartness – the new girl was first a butterfly, but soon after, she herself became an attractor.
This suddenly changes the whole dynamic. The system becomes unstable.
Smartness is suddenly in focus for all the girls in the whole class. The rest of the situation between the two groups is locked, but this new element makes everything open, unstable, mobile.
The new girl and the tough one meet.
The new one says something that makes the tough one insecure and weakens her authority. Who will now take dominance? Who allies with whom? Anything can happen.
If the new girl manages to get someone to join her, she can create feedback loops by attracting more people, which in turn attracts even more. The new, insignificant girl can quickly become dominant, the most robust attractor.
In this example, both physical traits (clothes, style) and behaviour (funniest, manipulativeness) determine the degree of popularity – initially.
From there, it Is mostly about a mental power struggle, and it plays out in each individual's subjective experience.
Do you want another example?
Christmas is an attractor. It makes us make choices in our heads, including going out and buying Christmas presents way too late. Or we suddenly get the hunch to start Christmas baking at about the same time as everyone else.
Christmas is an idea with great power.
We have lots of mental notions about what a perfect Christmas is. Traditions – attractors – are created over the years. Most of the population is involved in the rather strange celebration, even if some of us prefer to escape.
One year white Christmas trees were popular. What is it that determines that something comes into fashion? It might have started with an article in a weekly magazine. Then it spread mentally in people's heads through conversations – communication of abstract thoughts.
No one had thought that Christmas trees could be anything other than green. The land was open to a white butterfly.
A small group with defining power, the fashion-conscious, took a stand, created feedback, and inspired ordinary people to join. Every home in the country fell like dominoes. I remember when this actually happened in Norway back in the 1970s.
The physical, mental, emotional and abstract go hand in hand at Christmas, to the delight of some and the frustration of others. The laws of complexity apply to the whole «system».
Are there other explanations for these phenomena?
In my opinion, no.
Mental chaos laws seem to explain complex, hybrid interactions across categories. I interpret this as a strong indication that the world is a mental notion and nothing material.
We have thus observed something interesting.
The laws of complexity have traditionally described physical phenomena. Now it turns out they probably have a more fundamental significance.
What does that mean?
Could it, in fact, be that underneath all of this richness and complexity we see in physics there are just simple rules? I soon realized that if that was going to be the case, we'd in effect have to go underneath space and time and basically everything we know. Our rules would have to operate at some lower level, and all of physics would just have to emerge.
It's worth saying a little about how the derivation works. It's actually somewhat analogous to the derivation of the equations of fluid flow from the limit of the underlying dynamics of lots of discrete molecules. But in this case, it's the structure of space rather than the velocity of a fluid that we're computing.
So what then is time? In effect it's much as we experience it: the inexorable process of things happening and leading to other things. But in our models it's something much more precise: it's the progressive application of rules, that continually modify the abstract structure that defines the contents of the universe.
Stephen Wolfram, British-American
computer scientist and physicist
