Interaction Correction

I mentioned in my Chapter 2 posting that all elementary particle interactions are reversible. While true for almost all, there are a small set of interactions that are not reversible - they are asymmetric. In the early days of the universe (very shortly after the Big Bang) it is thought that the antisymmetric interactions lead to the current matter-anti-matter imbalance in our observed universe. These interactions exhibit CP (Charge Parity) Violation. Recent experiments at the Fermilab Tevatron accelerator have seen more positive muon-muon pairs than negative muons. While initially found many years ago as kaon particle decay, CP violations have all been of the same basic root cause and seemed unable to explain the imbalance of matter and anti-matter. The recent observation of di-muon charge asymmetry gives an additional pathway of CP Violations and may more fully explain the matter-antimatter imbalance.

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.