Victor MacGill Chaos and Complexity
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A Complexity Perspective on Human Evolution from our Violent Past to a Compassionate Future

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My first book..

When the Dragon Stirs

Healing our Wounded Lives through Fairy Stories, myths and Legends

When the Dragon Stirs Book Cover

The Dragon

Line

My next book...
Gonna Lay Down my Sword
and Shield

A Complexity Perspective on Human Evolution from our Violent Past to a Compassionate Future

Mandelbrot Set

Articles by Victor

Mandelbrot Set   Fairy Stories
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Mandelbrot Set  Complexity
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Mandelbrot Set  Spirituality
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Short previews
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My next book...
Gonna Lay Down my Sword
and Shield

A Complexity Perspective on Human Evolution from our Violent Past to a Compassionate Future

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Small World Networks

A talk given to the Dunedin Spiritualist Centre  March 21 2004

My talk tonight is about the second principle of Spiritualism; the unity of creation. A common idea found in almost all spiritual beliefs is the idea that every part of the universe is pervaded by a single, living spirit. So, although the world seems to be divided between what is living and what is not living, and divided between what is ‘man made’ and what is natural, in fact, spiritual traditions tell us the universe is a single, seamless, living whole. New advances in the science of Complexity Theory are describing our world in surprisingly similar ways to our spiritual traditions. Tonight I want to talk about a part of Complexity Theory called Small World Networks.

Dunedin has a population of around 100,000 people. If we wanted to set up an efficient telephone tree, so information could be relayed to every citizen as quickly and efficiently as possible, how would we set it up?

telephone treeFirst, we would decide how many people each person was to contact. If we decided each person would phone two others then we see from the chart here that we would need 17 layers of phone calls before everyone was contacted. If instead of contacting two people, each person had to telephone 10 others, then only 6 layers would be needed, and if each person had to telephone 25 others, only 5 layers would be needed.

So, what is the best, phoning 2 people, 10 people or 25 people
telephone treeTelephoning only two people is likely to be slow because of the number of levels and with the large number of levels, the likelihood of errors and lost messages increases. Telephoning 25 people is also not likely to be efficient, because each layer would take so long to complete. Adding only one more layer means that each person only has to phone ten people, which is much more manageable.

So, of the options we looked at I think you would agree that 10 is more likely to be the most efficient number for each person to contact.

Another alternative would be to vary the number of people contacted at the various levels. So, we might have people in levels 1-3 phoning 10 people, those from level 4 on phoning 2. I think you can see that we would get a bottle neck that would slow the system down. That would also be the case if 25 people were contact from level 4 on. It would not be as efficient. It turns out to that the most efficient way of getting the message out is to  find the right number of people for each person to contact and to keep that number constant for all levels.

treeA tree has the same basic problem as a person setting up a telephone tree. Instead of sending out a message to all the people in Dunedin, a tree has to send nutrients up the trunk to be distributed to all the leaves. Do you see how it this is the same basic problem? Nature has found the most effective way. It starts with a single large trunk, which then divides into smaller branches, say half the size of the trunk, which in turn divide into branches half the size again, each time reducing be half the size until you get to tiny little twigs. Nature uses the same equal proportions between levels because that is what works best. The size of the branches decreases by the same proportion at each level. If we changed the proportions as we talked about in the telephone tree so there were big branches all a sudden far from the trunk, or had lots of small branches coming straight off the trunk, it would not be as efficient.

Finding the most efficient way of getting a large flow of traffic into a city so each vehicle can quickly reach its home out in the suburbs again uses equal proportions. One or a few large motorways coming into the city on which cars travel very fast branch off to form smaller main roads, which in turn branch off into smaller roads leading to the suburbs, where the traffic moves more slowly. We then turn into yet smaller roads until we come to our own driveway.

Again if we had lots of small roads coming straight off the motorway, or large main roads through the suburbs many traffic accidents would result because of traffic jams caused by cars slowing right down to turn off.

If you think about it there are so many other systems we come across in our daily life that fit this pattern. Our lungs breathe in air down one big tube, which is then distributed through smaller and smaller branches to the tiny alveoli so oxygen can enter our blood stream. Our circulatory system moves blood from the heart to the tiny capillaries so the blood gets to all the parts of the body.

Our telephone system sends voice messages, our power grid sends electricity, the postal system sends mail, our body sends oxygen and blood. We have different systems, but each time equal proportions between levels is the most efficient way of organising them all.

We can see that the same system of proportions also works, when we turn it in reverse. People taking their cars out of the city need roads that have evenly increasing road sizes instead of decreasing ones. Small streams combine into larger and larger rivers until they meet in one main river flowing to the sea. In these systems the proportions increase equally at each level rather than decrease.

Airlines move passengers all around the world. So, what is the most efficient structure linking the airports? The most effective way of setting up an airport system is to have smaller airports feeding into bigger airports which when reversed means bigger airports feeding back out to smaller and smaller airports. If I want to travel to Santa Fe in New Mexico from Dunedin, I fly first from the smaller to the bigger, Dunedin to say Auckland to Los Angeles, then on to smaller airports to Albuquerque and on to Santa Fe. It would not be efficient to have flights direct from Los Angeles to Santa Fe or even Los Angeles to Dunedin. Airport sizes are shown to have equal proportions between levels.

telephone treeThere is another mathematical pattern which you will see is very similar to the equal proportions have just looked at. If you measure the number of earthquakes of every size you get an interesting pattern. Say we get one earthquake at size 8. That is a truly devastating earthquake. If the proportion between layers is ten, we would get 10 earthquakes at size 7 (The proportion is not ten but about 2.7, but using ten makes it much easier to understand the pattern). At 6 we would get 100, 5 1,000 right down to 10 million at size 1. If the line is wiggly it is not equal proportions, but when you do this with real earthquake data you do get a straight line.

If you drop sand onto a pile bit by bit, and then measure the size of the slips that occur as more and more sand is slowly added, you find the same pattern. There is a small number of really big slips, medium number of medium sized slips and very large number of small ones, all in equal proportions between the sizes of slips again.

The same pattern of proportions is found in the nerve cells of our brain. There are literally billions of nerve cells in our brain. A small number of nerve cells are linked to many thousands of other cells, while a large number of others are only linked to a small number of other cells. When you examine the proportions, we find the same equal proportions between the number of connections.

An investigation of our social connections shows that they also exhibits equal proportions between levels.  We have a smaller number of family members or very close friends who know us well. The next layer has more friends we know well and might see every few days or each week. Perhaps it is people we meet regularly at this Centre. As we look at succeeding layers we find more and more people, whom we know less and less. On the outside are a lot of people we know only a little.

You might think it is not important to have a large number of people you know only vaguely. But, imagine that I decided to go and live in Wellington. My friends and family are unlikely to be able to give me the information and advice I seek. It is far more likely that people I met on a training course I went to last year who live in Wellington, will be much more use to me. I don’t know them at all well really, but well enough to phone them up. They will probably also know other people in Wellington to answer questions they do not know. So, having contacts with a wide range of people, who each have their own areas of interest, networks and resources can be extremely important. When you measure social connections, you get equal proportions at each level of closeness because this proves to be the most effective mix to meet all our social needs.

So, we’ve found equal proportions between levels in phone tress, trees, roadways, electricity grids, earthquakes, sand piles, social connections, lungs, hearts, brain cells, rivers, airports and postal systems, but, it doesn’t end there! The very same equal proportions between levels can be found in the shape of clouds, the shape of the coastline, the size of traffic jams, the size of towns and cities people live in, the amount of money in people’s bank accounts, the number of people killed in wars and, can you believe it, the number of sexual partners we have in a lifetime.

So, while we all make our own decisions about our lives, and do our own thing, somehow together we make choices that maintain the same mathematical patterns of equal proportions between levels.

mapoftheinternetNow, tell me what do you think this is. A plant, a brain,  -- well, it is a map of the internet. Why does a map of the internet look so organic. It looks organic because it has the same underlying mathematical proportions as living forms.. That’s is particularly interesting because nobody is in charge of the internet. With literally many millions of people each do their own thing, you would think you would just get an huge chaotic mess, but instead you get this high level of organisation. A few sites have millions of links to them, while the vast majority only have a handful. It probably won’t surprise you by now to find the links form equal proportions between levels. At this point we start to have to ask the question: to what degree can we call the Internet a living being? It is stable, creates and sustains flows of energy as information like a body sustains flows of energy as food, blood, etc. It gets viruses and has an immune system, parts die off while new parts come to life and grow. And it does have exactly the same underlying mathematical blueprint of equal proportions between levels that all life has. Does the internet have a life of it’s own. Is it like they say on Star Trek, “life, Jim but not as we know it? Where exactly is the boundary between what is living and what is not?

And are the city of Dunedin, the road transport system, the postal service, the banking system, the stock market and other things we would clearly call, “man made” in reality just yet more examples of living forms. Maybe our definition of life is a bit restricted.

Now, any scientist who has studied Complexity Theory would say I am making an enormous number of unjustifiable connections. They would say that finding similar mathematical patterns in a wide variety of places does not at all mean that all life is therefore linked and that there are lots of places where equal proportions are not found. Indeed, they would be absolutely right, but looking through the eye of science is not the only valid eye through which to see the world. If we take the learnings of science and see them through the eye of spirit, then wider possibilities are available to us. To my mind the findings of Complexity Theory at least suggest the possibility of that which has been known in spiritual traditions for thousands of years? – and that is that all the universe, from rocks to plants, to animals, to humans, to our social structures, relationships and technology all interconnected by a similar underlying blueprint and that every part of the universe is filled with life. To me equal proportions between the levels suggests the truth of the second principle of Spiritualism, the unity of creation.

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