Chapter 3 – Chaos

A late January paddling of the Okefenokee Swamp, in southeastern Georgia, is an otherworldly experience. It seems miles away from anywhere, because it is. At almost 300,000 football fields in area, there’s nothing around it. No planes fly overhead, no power boats around, only a few people, birds of many species and a number of alligators sunning themselves on the banks. The tannin-stained water flows slowly, almost imperceptibly somewhere. But where? The swamp drains into two rivers, the St. Mary River and the Suwannee River – made famous in the Steve Foster song. The St. Mary empties into the Atlantic Ocean north of Jacksonville, FL. The Suwannee River empties into the Gulf of Mexico north of Tampa, FL. Almost three miles separates these two end points but as we were paddling through the swamp, we came to the Okefenokee divide. This is the “fork in the road,” If you go to the left you travel the St. Mary’s River and end up in the Atlantic Ocean. If you go to the right, you travel the Suwannee River to the Gulf of Mexico. A millimeter difference at this decision point makes a big difference in where you end up – Atlantic Ocean or Gulf of Mexico.

Sounds a lot like some of the decisions you made in your life. Did what seemed like a little deal turned into something very big, bigger than what you imagined? You had more than one of these forks in the road. In fact, anyone who takes the time to look back on their life’s turning points will find that some of them are every bit like the Okefenokee divide. How do life’s decisions end up looking the same as the physical flow of water in a swamp? As we discussed in the last chapter, although there are different ways to interact throughout the hierarchy of life, the end result of interactions is similar. Water can’t think and doesn’t make a decision to go left or right at the divide, a decision is made for it. Doesn’t matter if you decide or someone (or thing) decides for you. At those inflection points in life, a small difference at one point can lead to a big difference later on.

We’ve now talked about hierarchy and how the universe builds up layers of complexity. We followed that with the U-ROC, the only way things change is through an interaction – an exchange with something else that changes both sides of the interaction. We then saw that simple rules for interaction can lead to either simple changes or complex changes. To complicate matters, it wasn’t clear from the rules how the pattern would turn out – simple or complex. The only way to find out what happens is to wait and watch the interactions and see what develops. In fact, it has been proven that for the complex case there is no way to write a mathematical expression that will predict the state after some number of interactions. So mathematics won’t help us predict the future state. However, we do have some things in our favor. Remember, in the examples of Wolfram, out of the 256 possible types of interactions, only 10 of them lead to complex behavior. That’s why patterns dominate the universe. Everywhere we look we see things in a pattern. The sun rises in the east and sets in the west on a regular basis. The moon phases go through a 28 day pattern from new to full and back again. The seasons go from spring to summer to fall to winter and back again.

We need patterns in order to have some type of stability in the universe. As Kasey Kasem said at the end of his American Top 40, “Keep your feet on the ground and keep reaching for the stars.” Of course, if all we had were patterns, we’d live in a world like the movie Groundhog Day. The pattern would get locked in and we’d repeat it over and over again, with little or no change. I believe that if there were only simple interactions, life would have never come into being. We need that complex behavior to drive new levels of hierarchy. Before we get into the emergence of new hierarchies, let’s talk a little more about chaotic behavior. Unfortunately, the term chaos has multiple meanings and the one we initially think of is wild and out of control. In mathematical thought, chaos has a different meaning and is more related to the example at the beginning of the section – a small change can lead to a large difference. Chaos was studied for a while before it was officially called chaos and Edward Lorenz was one of the first people to start a methodical approach to the subject of chaos and the subject of the next part of this section.

I have loved weather all of my life. When I left my first job (an epic failure) out of college, I started on the path to a Masters Degree in Applied Math at the University of Maryland. This degree required three areas of concentration, one of which had to be outside of the mathematics department. It took me only a few seconds to declare Meteorology as my area of application. My Master’s paper was on the work of Edward Lorenz. Lorenz was writing computer simulations of a simplified weather system since the early computers he was working on couldn’t handle the more complex equations. The two most important drivers of the Earth’s weather are the Sun (heat) and the Earth’s rotation. Lorenz has put together a simple apparatus that modeled this behavior. He took a turntable and placed a pan of water (more like a Bundt pan with a hollow part in the middle) on top of it. He put a heater under the pan of water and had himself a simplified weather system. As the turntable rotated, the water spun around and as the heater warmed the water it rose from the bottom of the pan and circulated. The combination of the heated, vertical rotation and the horizontal rotation lead to complex behavior that was similar to how the Earth’s weather works (at least the large High and Low pressure systems we see moving across weather maps). The first thing to note is how two simple behaviors (vertical heat rotation and horizontal rotational motion) can combine to generate complex patterns. And the patterns Lorenz saw in his simplified weather model were fascinating to him.

Lorenz created a computational model that ran on his computer system and printed out results every hour. He compared the results of his computer models with his experimental turntable system to validate the model. On one of his runs, he stopped the computer simulation after a number hours and later on decided to continue the model. He didn’t want to re-run the entire simulation from the beginning so he picked a time near the end of the first run and typed the numbers that were printed out from the first run as starting values for the next simulation run. As the computations continued and he compared the new results with the end of the first run he saw that although they matched closely early on, the results he got diverged pretty quickly. He initially thought he had entered some of the numbers incorrectly but after he verified that he had correctly entered the numbers he had to dig deeper. The only thing he noticed was that the numbers that were printed out had more digits of accuracy than he had entered. (So if the printout said 1.5434 he only typed in 1.54.) It turns out that that a small difference in input caused his model to generate wildly different results.

Lorenz was not the first, but he certainly made a study of what we now know as chaotic behavior. A small change in initial conditions can lead large differences later on. Is everything set of interactions in the world chaotic? No. Although the universe as a whole is chaotic (A recent study has shown chaos effects in the quantum world.) there are times when the chaos is small or non-existent. Something is chaotic depending on the interaction rules for that system. As we saw in the last chapter, some rules of interaction lead to repeating patterns and some lead to complex behavior. It is there complex systems that can exhibit chaotic behavior. If you add in the hierarchical effects you can have a repeating pattern at the highest level of a system but a series of chaotic behavior in the levels below. Combining these things leads to systems that have patterns most of the time, but a small perturbation (or change) leads to radically different results. This has been termed the butterfly effect for the idea that a butterfly’s wings flapping in South America could lead to the formation of a hurricane in the North Atlantic. The Butterfly Effects sounds almost comical, but remember that at the Okeefenokee divide, a difference of a few millimeters leads to a leaf going to either the Atlantic Ocean or the Gulf of Mexico – a difference of hundreds of miles.

I’d like to leave our discussion on chaos with the topic of attractors. Let’s look at two pendulums. One is a standard pendulum, a sting with a weight on the end. If we push it, it swings back and forth and slows down as friction saps its energy until it comes to rest. Having the weight hanging straight down is an attractive state. It is the state that the pendulum will ultimately return to as it swings back and forth. Now let’s look at a pendulum where the weight at the end has a magnet. At the base, right where the weight would hang, let’s place another magnet with a same polarity as the weight. That means that as the weight swings, the magnetic repulsion causes it to “bounce” around crazily. Below is a “video” of the weight when viewed from above and from the side.

Standard Pendulum:

Magnetic Pendulum:

In the standard pendulum, the weight passes through the attractive state (called an attractor) but when we add magnets the repulsion causes the weight to fly away from the attractor. In the magnetic pendulum, this is called a strange attractor since the system approaches the attractor but always misses it. Strange attractors come into being when the high level of the hierarchy is periodic but some of the underlying pieces of the hierarchy are either chaotic or the interactions from the lower level lead to complex interactions between the two levels. In the case of the magnetic pendulum, we have combined a simple, periodic system and a magnet, which is a simple system. Without the pendulum, the two magnets would just repel each other. Without the magnets, the pendulum will swing back and forth. The pendulum constrains the interactions of the magnets (without the pendulum, the magnets would repel each other but the pendulum motion keeps pulling them together) and leads to chaotic behavior.

The image below shows the movement of a slightly more complicated system where there are three magnets on the board that each attracts (rather than repels) the magnet on the pendulum. (In the graph the magnets are colored red, green and blue.) Notice how the pendulum moves between the three magnets in an apparently random manner? Each of the three magnets on the board represent a strange attractor and the pendulum visits each of them, based on the initial position and speed at which the pendulum is launched.

Systems of interactions like the ones I have been discussing come under the heading of discrete events. Discrete is as opposed to continuous. What I’m saying is that the universe is built upon interactions that are discrete and happen in a serial fashion. (That’s at the quantum level.) We see a continuous universe because we far up the hierarchy and the discrete nature is hidden. Ultimately, the force that ultimately yields the continuous world we live in is gravity. We’ll have a lot to say about gravity in the next chapter but for now, suffice it to say that gravity smoothes out the bumps of the discrete quantum world and presents to us a world where change is continuous and smooth. Why do I mention discrete events? It is because it has been mathematically proven that systems built upon interactions are non-computable. That means there is no way to write a mathematical equation to predict the exact state of the system after 100 or 1,000 sets of interactions. You have to run the 100 or 1,000 interactions and then you’ll see the state of the system. Now notice I put the word exact because reality is a little more complicated. I mentioned that gravity smoothed out the discreteness of the universe. That smoothness also allows us make predictions about this smooth system and that is how science works.

As much as scientists talk about understanding the way things work, the reality is that science is built upon the ability to predict the future. I would argue that the main reason science exists today is because of its ability to find patterns in systems and use that pattern to predict the future. How does science work? Science builds models of the system they want to study. They do that by ignoring some of the features that they feel is unimportant and won’t affect the overall pattern of the system. George Box, a statistician of some stature, made the seminal remark on this topic – “All models are wrong, some are useful.” Gravity has done science great service by smoothing things out and making it easier to build models. For example, pretty early on in mankind’s existence we started building models of the solar system and stars. The earliest models were Earth centric, with the sun, planets and stars all followed circular orbits around the earth. A circular orbit was used for religious and philosophical reasons as a circle is a more perfect shape. This model was able to make predictions of a number of events but over time it became harder to get a circular, earth-centric model to predict celestial events. Kepler came up with a different model with the sun at the center of the solar system and planets orbiting in elliptical orbits. The circular model of the solar system worked because a circle is a special case of an ellipse. Specifically, you measure how “oval” an ellipse is by a value called eccentricity. Looking at the three figures below, the one of the far left is a circle with an eccentricity of zero, the one in the middle has a slightly larger eccentricity and the one on the right has a much larger eccentricity.

Figure: Ellipses with increasing eccentricity.

I want to emphasize that Kepler’s model of the universe is wrong but it is much more useful than the earlier models that incorporated circular orbits. It is more useful in that it more accurately predicts the orbits of the planets.

Kepler’s model is indeed quite useful because while it ignores a lot of things, like the quantum behavior of the matter that makes up planets) the gravitational attraction between the sun and the planets is many orders of magnitude more important than any other effect. That means the model can predict the future paths of planets, moons and comets to a great level of detail for a long, long time. The lower levels of this hierarchy are chaotic, but it will take millions upon millions of years before they affect the motion of the planets in any measurable way. At some point in the future, the sun will use up its fuel and start to expand and eventually explode. Or we could have some interstellar object crash into one of the planets and muck up our predictions. At that point, the Kepler model will no longer be useful as the predictions it makes will be way off, But let me state it again for emphasis, Kepler’s model of the solar system has always been wrong.

We can state with conviction that the usefulness of a model in making predictions will decrease as the system being modeled becomes more chaotic. We all have our favorite weather story where the prediction just a few hours ago didn’t pan out. As a child growing up, there was a time when it rained on one half of my block, but not on the other side. No weather prediction model can figure that out. In general, the more chaotic the system, the shorter the time frame where a continuous model will be accurate enough to be useful. But what’s the alternative, do no modeling? That’s not a good way to enhance our survival. Predicting the suture grants the accurate predictor a competitive advantage so it is in our best interest to continue to build models and predict.

Science has made its name finding systems where it can build useful models. Over the past hundreds of years, science has started with the simpler problems (like the solar system) and as time progressed they got better at approximating more and more complicated systems and making more and more useful models. At the quantum level, however, scientists have resorted to statistical modeling in order to gain predictability. They count on the fact that all electrons are alike. (In this day and age, there would only be a single Facebook page that would apply to every electron.) With the assumption that all electrons are alike, you can build statistical models that yield impressive predictions. Any model that took individual electrons into account would be impossible to run in this day and age. Perhaps with time we’ll gain the computer computational power to improve the modeling of quantum systems.

We’re now ready to discuss how the hierarchies develop.

Chapter 2 – How Things Change

Fall of 1973 found me a 16 year old freshman at Guilford College in Greensboro, NC. While I was a science and math geek in high school and I had plans to major in Biology and go to medical school. During orientation, I signed up for classes and got my small stack of computer cards that had my classes listed on them. I thought I had signed up for Introduction to Biology, Freshman English, Being Human in the 20^th Century and Calculus. As I looked at the cards, I noticed that instead of Calculus (MATH 101) I had a class called Foundations of Mathematics (MATH 201) and went to the head of the mathematics department to tell him of the error. J.R. Boyd was like no Texan I had ever known. He was short, bald, never wore boots and smoked unfiltered Camel cigarettes all the time. He was also one of the few non-PhDs at Guilford and had arrived in 1962 to impart mathematical knowledge in a way called the “Moore method.” This is a Socratic teaching style made famous in mathematics by R.L. Moore who taught at the University of Texas. Mr. Boyd told me not to worry about the mistake and he thought MATH 201would be a good fit for me. Only later would I find out that it was Mr. Boyd who had identified me as a math major before I even hit the campus and the “mistaken” MATH 201 class was no mistake at all, He wanted me in that class. MATH 201 was one of the pivotal moments in my academic life and my association with JR Boyd continued until his death, 25 years or so after I was graduated. At a later orientation function I met Dr Rex Adelberger who was new to the school and taking over as the head of (well, actually the only person in) the Physics Department. Between Mr. Boyd and Rex, I forgot about the Biology major, cured myself of medical school and became a math and physics major and lifelong geek. I had no idea that the interactions with JR and Rex would have such a profound effect on my life. It changed so many things about how I thought and put me on a completely different path than what I could have ever imagined.

I bet your could sit down and write your own list of people who have had a great impact on you. These interactions were not something you tried to make happen, but happen they did. Humans interact all the time and if you spent a little time thinking about it you’d figure out that interactions are the most important part of your life. I spoke with someone who had the opportunity to go to the Boca Grande, Florida with her family for the week between Christmas and New Years. Boca Grande is a wonderful island in Southwestern Florida with gorgeous winter weather. What did they think about the trip? They weren’t excited because they didn’t want to spend 5 days with their “dysfunctional” family. It wasn’t the location but the people they were going to interact with that made the biggest impression on them. That’s true for pretty much all of us. Interacting with people can change us. That’s the basis for this chapter; looking at how things change. Here is the only law of the universe that you need to know as everything else derives from it:

Universal Rule of Change (U-ROC):

The only way anything changes is through an interaction.

An interaction is the exchange of something between two (or more) objects.

If the universe was made up of only one thing, there would be no interactions, nothing would ever change and there wouldn’t be a universe. If the things that make up the universe did not interact, there would be no universe. In fact, you can describe the universe is an entity whose sole function is to have things interact. It is through interactions that the entire complicated world we live in today came to exist. It might be hard, initially, to believe that the universe, which seems so complicated, can be expressed in this one simple rule.

This idea is not new and has been expressed by other people throughout the years. In 1714, Gottfried Wilhelm von Liebniz, in his Monadology, said that relation gave rise to substance, not, as Newton had it, the other way around. Because we came to the universe after a lot of the hierarchy had been formed, it appeared that the hierarchy gave rise to the interactions. Scientists spent years peeling back the layers of the universe’s hierarchy to understand how things were put together. Not nearly as much effort was put into trying to figure out how the hierarchy was created. The clearest explanation for this imbalance is that reductionism is much simpler to do so scientist went after problems they could solve. Science was able to find a lot of patterns in the hierarchy, enough to allow them to predict things that were previously unpredictable. Eclipses and the path of projectiles were two early applications of science and predicting the future better than someone else grants a competitive advantage to the predictor. Hence science went down the path of reductionism to figure out how things worked to allow more and better predictions.

We’re not saying that all interactions are equal. Interactions differ depending on where you are in the hierarchy of the universe. At the lowest organizational levels of the universe – elementary particles – the interactions consist of the exchange of a single particle. Electrons interact with other electrons by exchanging a photon. This is the simplest type of interaction in the universe. As you move up the hierarchical levels, the interactions become more complex. Living cells interact by exchanging molecules. Organic molecules form the basis of all living things. Compounds like DNA, RNA and ATP form the basis of all cellular interactions. More complex animals, like dogs, can interact through making sounds. Humans, currently at the top of the organizational hierarchy list, have an almost unlimited number of ways to interact. Our senses form a high level means of interacting. What we call hearing is a series of interactions between the air, the bones in our ear and electrical impulses sent to the brain. We’ve developed forms of interaction based on speech so that talking has nuances to it – irony, parody and sarcasms – which makes human speech a complex and powerful interaction. U-ROC applies at all levels, the only thing that changes are the types of interactions.

Is it “fair” that the universality of U-ROC depends on changing the definition of interaction, based the level of the hierarchy? To some, it seems that there should be one definition of an interaction. In that view, the interactions of the electrons are so different from human interaction that they should be considered entirely different things. Fair enough but consider that it is the universe itself that builds up the hierarchy, which introduces new interactions. With an interaction defined as simply an exchange of something we take advantage of the hierarchy to define what that something actually is. The development of new interactions is at the heart of the universe’s hierarchy and is why the first chapter started with hierarchy. Hierarchy hides the lower levels of interaction which I believes give us free reign to consider the new “higher level” interactions as equivalent to the lower level interactions. It is simply amazing that the universe would take so simple a concept to build up the universe so it makes sense to ask if it can be done this way. We have a ways to go before we can make that claim but first let’s look at how the U-ROC maps onto one of the basic laws of physics.

Since we were mentioning Newton a little while ago, let’s look at Sir Isaac Newton’s laws of motion and how they fit with the universal rule of change:

1. An object at rest remains at rest unless acted upon by a force.

2. An object experiencing a force experiences acceleration.

3. For every action there is an equal and opposite reaction.

Let’s see how this maps into the U-ROC. In physics the terms force and interaction are different words for the same idea.

1. The first law says if an object does not interact, nothing changes – the object remains at rest.

2. The second law says that an interaction between a moving object and something else leads to an acceleration (speeding up, slowing down or changing direction are the three ways a moving body can accelerate) which is a change.

3. The third law says that when two things interact, they are both affected by the interaction, a byproduct of the exchange of something.

Newton’s three laws are just a special case of the U-ROC for objects that move. When it comes to moving objects, the only way an object changes speed or direction is if it interacts and that interaction affects the objects that interact.

In the previous chapter, I discussed how things are organized hierarchically and the fact that moving through different levels of the hierarchy introduces additional ways to interact. Let’s spend a little time discussing the relationship between hierarchy and interactions; starting at the lowest levels – elementary particles.

Electrons are very simple. They have only five things you can say about them:

1. Charge (negative 1)

2. Spin (1/2 - don’t ask one half of what - spin is a scientific term associated with angular momentum which, to us humans feels like spinning)

3. Mass (similar to weight for us humans)

4. Location (where is it)

5. Velocity (where it is going)

The limited organization leads to only one way for elementary particles to interact. Not only do they have no feelings but they don’t have a structure like a rock or even liquid or gaseous water. Lack of structure limits them to interactions that consist of the exchange of a single particle. Electrons (and other particles that have a charge) interact by exchanging photons. In fact, at this quantum level, there are only three ways for elementary particles to interact. These are so fundamental they are described as the three fundamental forces. (Remember that force is the physics term for exchanging particles which is the same as interacting.)

1. Electromagnetic – All charged particles interact through the exchange of photons.

2. Weak Nuclear Force – The exchange of W and Z particles account for the weak nuclear force. There are two types of W particles so a total of three particles are responsible for this force. This force is responsible for the nuclear decay which is, in turn, responsible for nuclear reactions.

3. Strong Nuclear Force – Neutrons and protons exchange gluons (8 different ones) for the strong nuclear force. This is the force that keeps the atomic nucleus together. Since all protons in the nucleus are positively charged and repel each, you can imagine that this is a very strong force (hence the name). It takes a lot of force to keep them in the nucleus.

Why is gravity not on this list? We’ll postpone that discussion but suffice it to say that while gravity is well understood at some levels, trying to unify our knowledge of gravity with our knowledge of how elementary particles interact has been a source of frustration. For now, I believe (as do some others) that the force of gravity does not derive from the interactions of particles (some scientists believe gravitons exist, but no one has ever provided experimental evidence of their existence). Gravity is an essential part of the story but we’ll not deal with it just yet.

We are ready to approach the question of how the U-ROC – things change through interaction – lead to the complex universe we see around us. The short answer is – we don’t know exactly how, but there are some ideas how this could happen and we’ll look into those now. First off, is there any reason to think that a simple set of rules for interaction between something like elementary particles could lead to anything approaching complexity? Yes. Stephen Wolfram’s “New Kind of Science” is an unwieldy, over 1,200 pages, tome that shows how simple rules of interaction can do just that. He starts with a type of program called cellular automata. The great thing about cell automata programs is that their results can be expressed visually so you can see what he’s talking about. In his initial work, a cell is a square that can be either black or white. He starts with a line of white squares with a single black square in the middle. He then studies how many sets of interactions (he calls them rules but the tell us how adjacent squares interact) can there be in this simple systems – black and white squares – and found there were exactly 256 sets of rules. Being a computer literate individual, Wolfram wrote a program to start with the initial configuration (one black and the rest white squares) and apply a specific set of rules. Since I can only interact with my immediate neighbors, each of his rules consists of 8 outcomes. As an example, rule 254 is as follows:

If you are a black square

If your two neighbors are black, remain black.

If your left neighbor is black and your right neighbor is white, remain black.

If your left neighbor is white and your right neighbor is black, remain black.

If your left neighbor is white and your right neighbor is white, remain black.

If you are a white square

If your two neighbors are black, turn black.

If your left neighbor is black and your right neighbor is white, turn black.

If your left neighbor is white and your right neighbor is black, turn black.

If your left neighbor is white and your right neighbor is white, remain white.

I have included the pictures of the rule and the results of 10 sets of interactions below.

It seems that a simple set of rules leads to simple behavior so Wolfram thought it would always be this way. Indeed, almost all of the rules lead to patterns - all black (like number 254 above) or all white or lines or checkerboards. Patterns are very important in the grand scheme of things so it is comforting that patterns are part of the outcome. However 10 of the rules exhibited complex behavior defined by non-repeating patterns. Three of them are shown below. The only difference between rules 254 (which yields all black) and these three are the rules of interactions. It’s not clear at the outset why ten

of these rules of interaction yield such a different outcome. It was a complete surprise to Wolfram. Showing that a simple set of interactions yield complex, non-deterministic behavior doesn’t prove that the U-ROC is the basis of the universe’s structure, it is a necessary condition. If the opposite were true, simple rules always lead to simple patterns of behavior, and then we’d be done with this line of reasoning.

I don’t want to underestimate the power of Wolfram’s work. Using a system that has only one descriptive element (black and white) and a simple set of interactions he generated highly complex systems. We previously discussed how simple elementary particles are - photons only have velocity and spin and electrons and protons add mass and charge but are still pretty simple. So we can imagine that elementary particles interacting in simple ways could lead to a complex set of outcomes. Now the number of particles in the universe is almost impossible to imagine. So if only a few black and white squares can lead to complex behavior, the insanely large number of particles interacting should have no problem generating even more complex behavior.

Can anything in the real world support the idea that a simple set of interactions can lead to a complex result? The clearest example comes from embryology. In humans, a single egg and sperm cell merge to form a single cell that then begins to divide. (This division makes up the interaction.) From a single cell, an entire human being is created in just 9 months. There is no over arching blueprint that governs the emergence of a human from a single egg. At every point, the local cell division determines what happens next. Now, as the cells divide and start to specialize, the interactions get more and more complex. But that is the nature of complex systems, as they grow and organize, they build up more levels of hierarchy that contain different interaction methods, which leads to more hierarchy and more interactions. All of this comes from a single cell with no “grand plan.”

I want to spend a little time discussing what it means for elementary particles to interact and look at one of the corollaries of that behavior. In reality, we really don’t understand elementary particle behavior because they are so different from things in our world. Trying to put elementary particle behavior into what is a called our classical world always fails, or leads to paradoxes. However, experimental data indicates that when two particles interact, the exchange another (different) particle. The elementary particle world is neatly divided into particles that “carry” the force (we called them out above when we talked about the three basic forces) and particles that interact using the force particles (electrons, protons, neutrinos, etc.) When two electrons interact via the electro-magnetic force, one electron emits a photon which is absorbed by the second electron and then the second photon emits a photon. As far as we know, there is no way to tell different photons apart so it makes no sense to ask if it is the same photon that is absorbed and emitted. When the second electron absorbs the photon, it adds energy and so is changed. When it emits the photon, it changes energy levels again and may change position in response to the emission. Since there’s not in the description of an electron, there’s not much change going on here. However, as we move up the level of hierarchy interactions will become much more complex and can lead to massive change. A tornado interacting with a house leads to a lot of change in short amount of time but a tornado is a long ways away (hierarchically speaking) from an electron.

Remember how most interactions lead to patterns and only a few lead to complex, random behavior. If you look around, you’ll see that reflected in the world around you. We have a lot of patterns in the universe and some complex behavior. The universe could have started differently, but you’d find that you need that stability in order to consolidate the change that comes from the random behavior. If everything was random, you could never get anything to “stand still” long enough to be anything other than chaos. If everything was a pattern, nothing new would come into being – things like living beings. The universe is built with just the right balance between chaos and patterns to allow the changes to solidify and then build new changes upon them. Daniel Dennett, in his book, Darwin’s Dangerous Idea, calls this “The Principle of Accumulated Design.” I prefer to describe it as you can always make something better. (It is interesting that you things can only get so bad. We’ll discuss this after we’ve had some time to explore entropy.) As the changes in the universe build up a new level of hierarchy, a stable pattern on interactions forms. From that stable level, new levels of hierarchy can develop, and so one and so on.

East coast white water enthusiasts have a term for this phenomenon, drop and pool. As you go down almost any white water river on the east coast, there are periods where the river runs fast and hard (drop) and periods where the waters deepens and slows (pool). The action is during the drop and the pool (the old saying, still waters run deep comes from this pooling) portion allows you to rest and sort things out for the next drop. While I don’t believe there is any direct connection between the process the river uses to form these drop and pool sections, I am amazed at how much the drop and pool has permeated the universe.

Let’s explore in more detail how this combination of complex interactions and patterns interactions are manifested in the real world.

Chapter 1 – Descriptions and Hierarchy

Around midnight on Dec 15^th, 1973 a Lockheed Super Constellation cargo plane carrying 666 bundles of Canadian Christmas trees, bound for Maiquitia Airport in Caracas, Venezuela, took off from runway 9L, heading east. The weather was clear with visibility of 10 miles and a temperature of 67 degrees. The plane never made it to Caracas. It never made it more than 120 feet in the air and crashed into a parking lot just over a mile from the airport, slid through a number of homes, destroying several of them, destroyed some automobiles and, somewhere along the way, burst into flames. The three crew members were killed along with 6 persons on the ground. (Imagine being awakened from your sleep by a flaming Super Constellation crashing into your house.)

I lived in Hialeah, about 2 miles from the airport, and was home from my first semester of college. Although I suspect the story did not make the national news, it was front page news in the Miami Herald. My buddy Gene (we’ve known each other since 2^nd grade) thought we should do our own crash site investigation. Since I was now partially college educated, it sounded like we had the proper qualifications for crash scene investigators, so off we went. We drove Gene’s Camaro (I didn’t have a car of my own and wouldn’t have one for 4 more years) down to where the police crime scene tape blocked the road. Some folks might have been put off by the yellow tape but we’d never been anywhere near a crash site and we weren’t about to be denied. We turned at the tape, drove down a parallel street and parked on the street. We got out and started walking down the sidewalk, looking for an opening. We didn’t have to go very far before we found a clear path between two houses. Hearts pounding, we walked (we probably thought we were strolling nonchalantly) between them and onto the blocked off street. Trying to look like we were official (or at least as official as two nervous teenagers can look) we surveyed the crash scene.

The plane’s wreckage was gone (it was completely destroyed by impact and fire) but you could see the skid mark of the plane (about 60 feet wide and 500 feet long) and the damage to the houses. (Four were destroyed and several others slightly damaged.) Burnt pieces of paper, part of the flight books the crew carried with them were scattered on the ground. We were a few days past the crash so things were getting back to normal for most of the world - except for the missing people, missing houses, charred papers and skid marks. Birds were singing, people went about their business, the sun was shining (as it usually does in the South Florida winter as that is the dry season) and flights were taking off from the airport. I was still new to flying and to me it was still an adventure. This scene was of adventure gone seriously wrong. What caused this scene? As the plane’s nose left the ground, the 666 unrestrained bundles of Christmas trees were thrown backwards towards the tail, causing the nose to rotate up and the plane to go down. (Restraining straps and cargo nets were generally not used to secure cargo, according to a freelance pilot who had flown this type of airplane.) The crew may have contributed to this problem because of “deficient crew coordination.”

What does it mean to describe something? In the paragraphs above, I tried to describe a crash scene from over 25 years ago. I am still intrigued by the scene and use it as a starting point for a discussion of how we view the world around us. In the case above, I mentioned some of the facts of the event and the scene. I even described a little bit about how I felt. We spend a lot of time as humans describing and categorizing things – both objects and people. We do it so often we don’t even think about it. It seems to come naturally and that’s a pretty good way to describe how we have gone through this learning process. We learned at a young age that nouns stood for things and people, adjectives described color and texture, verbs describe action and adverbs (well some people – seems a minority - learned about adverbs) describe types of actions. Starting when their children are born, parents teach them about the world around them, describing things and helping to associate words with things, actions and feelings. It may take a number of months, but over time most of us learn about the world around us and how to describe it. I want to focus on the descriptions and how they mimic the way the world is organized.

If I was asked to describe myself, how would I start? I could talk about how old I am, how tall I am and other various physical pieces of information. I could talk about where I’m from, where I am going and what I do for a living. In the south, the schools you attended say a lot about you so I might mention my alma mater. I could talk about how I felt – sick or well - and I could talk about how I feel about certain issues – like universal healthcare. In fact, I could go on for a long, long time (too long for anyone else to listen) talking about these things and when I finally bored everyone to tears, I still wouldn’t be anywhere near a full description of myself. Why?

Well I haven’t even begun to tell you about my organs or blood or nerves. Those things that come together to make me who I am. Usually, the only time these parts of me ever come into a discussion is if they aren’t working well. So a description of me when I go to a doctor to review test results yields a much different description of me. And the description doesn’t need to stop there. My organs are made up of cells which are made up of an uncounted number of molecules, the alphabet soup that makes up living things – DNA, RNA, ATP, etc. Those molecules are made up of ever more uncountable elementary particles – electrons, protons, gluons, quarks.

So my description of the events of December 15^th, 1973 doesn’t even begin to account for all of the things that were there or the events that took place. In fact, there was so much going on that on that one day that I could never describe “everything.” From the very start, humans have been interested in this notion of hierarchy and it is such a large part of our existence, we don’t even have to think about it. But while we’re here, I’d like to discuss some notions of hierarchy as we endeavor to explain how it comes about. First off, let me talk at a high level about how the universe’s hierarchy, as shown in the figure below.

____________________________________________________________

\ _____________Quantum particles ____________________________/

\_____________Classical Matter____________________________/

\___________Single Cell Living Matter_____________________/

\___________Multi-cell Living Matter_____________________/

\__________Self Aware Living Matter __________________/

\_________ Intelligent Living Matter__________________/

The picture is drawn as an inverted triangle for a reason. At each level of the hierarchy, there is less matter than the level above it. There are far fewer intelligent things in the universe compared to all living things. (Some might argue there is no intelligent life on earth.) Living matter (by weight) is a tiny fraction of the mass of the entire universe. This is a consequence of the second law of thermodynamics which states that the total organization of the universe decreases over time. It’s worth discussing this a little more.

You experience the consequences of the second law (and see hierarchy in action) if you own a car. Let’s look at how a car comes into existence. First, someone designs the car and decides how the various parts (engine, body, drive train, interior, etc) should fit together. Whole groups of people search the world for the parts and arrange for the parts’ creation and shipment to the assembly line. On the assembly line, people and machines assemble the car from these component parts. If we look at the finished product we see that the car is not just a random assemblage of parts, but the parts have been “organized” into a new hierarchical level. This new organization came into being by using energy from the workers and machines on the assembly line and turned those disparate parts into a car. The second law of thermodynamics says that in order to create a car from the parts, you need to add energy. In this case, the energy came from people and machines that assembled the parts. You not only need to add energy, but the energy has to be applied to specific tasks on the assembly time and in a certain order. The term used for this is “useful” energy. So a car comes into being by applying useful energy to the component parts. Even more amazing, you can do things with a car (drive it) that you can’t do with the individual parts. It’s not too early to note that there is something more going on in the car’s assembly than the traditional notion of hierarchy. Traditionally, we think of hierarchy as a structural notion – like the “Russian Nesting Dolls” – where each doll is a smaller version of the largest one. In the doll hierarchy, each level is the same (only smaller) and the whole group is a play thing for children but doesn’t come close to the hierarchy that we call a car. The car is built up of smaller components but, when complete, exhibits behavior that none of its components exhibited.

Unfortunately, the second law of thermodynamics also comes into play when you drive the shiny new car off of the lot. If you’re lucky, you never experience a collision where “useless” energy is applied to your car and causes things to come apart in an explosive manner. Even without a collision, your car and its components age and stop working. Listen to Car Talk on National Public Radio and you are regaled with people who call to ask why some part of their ancient car no longer works the way it used to. The second law of thermodynamics says that things fall apart over time and you need to put useful energy into fixing them. Going back to Figure 1, the pyramid is inverted because there is a fixed amount of energy in the universe, so in order to organize some part of the universe, some other part must become more disorganized. The sun is a huge nuclear reactor that is becoming increasingly less organized as it burns its fuel to heat the earth. Our gain is due in large part to the sun’s loss.

Just as our car example, the universe is governed by the notion that at each level of the hierarchy in Figure 1 - the whole is greater than the sum of the parts. Unlike the Russian nesting doll, as useful energy is added to create the next level of hierarchy, a new function, or capability, comes into being. This new function did not exist in the previous level but notice that the new level of the hierarchy is made up entirely of things from the previous levels. A living thing is made up completely of non-living matter but it is clear to us living things that we’re not the same as non-living things. Each level of the hierarchy “hides” the complexity of the level below it- for the most part – but that lower, hidden level continues to operate. At the level of intelligent life, I deal with other intelligent beings on a certain level. We talk to each other; write letters, e-mails or texts. I do not text my dogs, but I do interact with them but at a different level. I interact with my body by eating and exercising, but I don’t talk to my kidneys.

The notion of the whole being greater than the sum of its parts is hard to study. You might have noticed that there is no theory or law of the creation of life. You would think that something as important as how did life come into existence would have been subject to such extreme study that we’d have some sort of an answer. We don’t and that’s because the problem is so hard that it is beyond our current abilities to answer. I also believe it is related to how science has evolved to solve problems. Traditional science works on the principle of reductionism; you study the whole by taking it apart and observing the pieces. Since the whole is greater than the sum of its parts, reductionism is flawed. You cannot study a living thing and take it apart to see where the life is located. You end up with a lot of dead pieces! Scientists, the keepers of reductionist thought, cannot agree on a definition of life. There are a lot of things are clearly alive and a lot of things that are clearly not alive. Unfortunately, the line between them is not clearly drawn and will be the topic of the third chapter. Having the whole greater than the sum of its parts leads to a hierarchy of organization shown in Figure 1. Hierarchy has both a structure – I am made up of organs that are made up of cells, etc – and an interaction – my interactions with other people are not at all related to the way my organs interact which is not like the way my cells interact. However, they are related and connected which is why the universe is such a wonderfully complex place. In fact, it is the reason we are here to observe that the universe exists at all.

Hierarchy’s ability to “hide” lower level complexity makes it possible to live as humans. If we had to spend our time and energy thinking about making our heart beat or breathing, we’d have no time left to think. Usually, the only time we think about the lower hierarchy levels are when they don’t do what they’re supposed to do. When our blood chemistry goes awry, we know about it. When your appendix goes sour, we know about it. We stop thinking about the higher level things and drop down the hierarchy to take care of business. When ‘fixed” we resume our focus on the higher levels of the hierarchy and “get on with life.”

It also should be noted that as you move “down” into the levels of hierarchy it takes fewer words to describe them. In short, that is a way to describe where you are in the hierarchy and helps define what we mean by something being more organized. Describing your heart requires fewer attributes than describing yourself (or someone else). You don’t need to discuss your heart’s feelings or what it saw last night. It takes even fewer attributes to describe the cells that make up your heart and fewer still for the molecules that make up the cells and the elementary particles that make up your molecules. In fact, when you get down to the lowest known levels of the universal hierarchy; some of the things are downright simplistic. Physicists use the word state to describe the attributes of the things they study (and describe). For example, a photon (which we view as light or heat) has no mass and always travels at the speed of light. Photons are so simple, the only thing you need to describe them in their frequency (which is related to their energy) which, for humans, is related to their color.

Basic elementary particles have a handful of attributes that describe them – spin, charge, mass, speed and direction – but that’s it. The most basic elementary particle are photons which has only two attributes – wavelength and spin. That’s it! Photons have no mass, only travel at the speed of light and have no electrical charge. At the basic levels of our universe’s hierarchy, it doesn’t take much to describe something. There’s also very little structure in a random collection of elementary particles, such as what existed after the “Big Bang.” The wonder of the universe is how things so simple in structure could possibly turn into something as complicated as the world we live in. We’ve gotten the basic idea of organization and hierarchy so let’s move on to how this hierarchy is built.

Gravity, Big Bang and Dark Matter/Energy Revisited

It sure hurts when you think you've come up with some nifty idea and find out you have it almost totally backwards. My last post fits that description pretty well but as I've reqd and thought some more about it, I'm cautiously optimistic I just got it reversed. As I was reminded (more than once) dark matter ONLY interacts via gravity (that's why it is call dark matter). That means that the Big Bang was the emergence of the three forces of matter (weak nuclear, sting nuclear and electromagnetic) that then organized the visible universe.

I'm thinking more about the best way to characterize these "emergent properties" that evolution creates and will write about that next. In any case, my postulation that evolution is not just an integral part of the universe (as opposed to the traditional sense of biological evolution) but evolution is the process that created the universe. Evolution is an organizing process that builds upon previous "successes" - defined by a more organized - to make even more highly organizaed systems. The Physics of Hope is my way of saying that the world can always get better but it can only get so bad.

The End of the Search for the Grand Unified Theory

I've been thinking about gravity a lot lately. (Perhaps it is because I watched Back to the Future recently and when he goes back to the 1950's Marty says the word heavy a lot prompting Dr. Brown to ask if there's something wrong with the Earth's gravity in the future. In any case, I have been aprticular musing over the failure of science to come up with a Grand unified Theory (or Theory of Everything) that unifies the four basic forces - strong nuclear, weak nuclear, electro-magnetic and gravity. The first three have been unified for quite a while and the fourth has been quite a sticking point.

Today I realized that gravity is not one of the basic forces of the universe. Gravity evolved (I'm not sure exactly how forces evolve yet, but stick with me for a while.) from the other three (or there might have been more, some of which disappeared) some time in the early part of the universe. That makes gravity what some term an emergent property of the universe. other emergent properties are life and intelligence. Life emerged (or evolved) from non-life. We don't completely understand how that happened or how awareness or intelligence evolved. I suspect it is because these are not easily modeled events (not continuous and not linear) so need to be attacked in some other ways.

What evidence is there that gravity evolved? I see three:

1. The amount of dark matter greatly exceeds the amount of matter. Before there was gravity, there was just stuff - elementary particles, I suspect. Through the interactions of elementary particles, gravity evolved as a new "force" and proceeded to "organize" the universe. (I'm struggling with the language here since it isn't clear what gravity did to the stuff to make matter so I refer to it as organize. Similarly, life emerge red on the Earth and started organizing itself.) With emergent properties, the "universe" affected by this new property is a subset of the original universe. For example, the number of living things in the solar system (measured by mass) is a small percentage of the entire mass of the universe. Measurements show that dark matter is much more prevalent than matter that was effected by gravity. We would also see that dark matter would not be effected by gravity, but may have some other properties in common with gravitational matter (like quantum properties).

2. The pace of evolution increases by about an order of magnitude once the emergent property is entrenched. I don't have the data, but I'd bet that the time create galaxies and solar system is an order of magnitude shorter than the previous (non-gravitational) epoch.

3. Some gravitational models approach a singularity as the model gets closer to the "Big Bang." If gravity did not exist at the Big Bang, then the singularity is eliminated.

If there's anything to this evolving gravity model, then we should find evidence of a time in the universe' life where gravity did not exist. I'm not sure yet how to do that, but perhaps someone smarter than me can come up with an experiment or observation to investigate.

The corollary the gravity as an evolved force is that there is no grand unified theory to discover. Gravity is not one of the basic forces but evolved from them so just like there is no grand unified theory of life/non-life, there is no grand unified theory of the three basic forces and gravity. It would be illuminating to understand how gravity could emerge or evolve from the other forces. I certainly see some similarities (like an inverse-square power law) but we're not good at understanding evolutionary processes at this time. That gives me something to think about this week.