GESCI 101 Section 1.4

Explore 1.4 Ways to Create Order

Learning Objectives

By the time you have completed the 1.4 Introduction & Exploration Activities, you should be able to:

Understand the meaning of the following terms/concepts and be able to identify examples of each: order, disorder, agent-designed construction, lawful self-assembly, emergent order.
Understand how agent-designed assembly produces order and how lawful self-assembly produces order.
Evaluate examples of ordered systems and identify how the order arose—through agent-designed assembly or through lawfully self-assembly.

Scientific Terms/Concepts

Terms: order, disorder, agent-designed construction, lawful self-assembly, emergent order

Define and give an example of each term:

Term:

Order

Definition:

Example:

Term:

Disorder

Definition:

Example:

Term:

Agent-designed Construction

Definition:

Example:

Term:

Lawful Self-assembly

Definition:

Example:

Term:

Emergent Order

Definition:

Example:

Agent Designed & Lawful Self-Assembly

Watch this video (3.5 minutes) on self-assembly:

How Order Arises

Activity Part 1 (of 3)

Instructions. Take out a blank piece of paper and pencil/pen and reproduce the image below, exactly as it appears. There's no need to take a lot of time.

Multiple triangles inside of a triangle.

Analyze the Order

Now, take a moment to think about what just happened, where the order came from. Your paper was blank before you began drawing, but after you finished there was a pattern on the paper (your drawing of the image above). Analyze the process that produced the pattern by answering the following questions in the box below (number each of your answers):

Was there a designer (agent) involved?
Was there a builder (agent) involved?
How did the builder know what pattern (order) to create?
Was the process involved in creating the order most similar to the process involved in producing the house, the office chair, or the rock candy? Justify your answer.

Activity Part 2 (of 3)

Follow the instructions below:

On a separate sheet of paper, draw a large triangle with equal sides that points up, like this:

Now, draw a small dot on each side of the triangle, halfway between the corners, like this:

Okay, now connect the dots, like this:

Can you see that your original triangle has four new triangles inside it: three that 'point' up and one triangle (with all-black sides) that 'points' down?
Now, repeat steps 2 & 3 in each of the upwards pointing triangles—but not in the downward facing triangle.
Okay, can you see that your drawing now has more upward and downward facing triangles?
Repeat steps 2 & 3 in each of the new upwards pointing triangles—but not in any of the downward facing triangles.
What shape did following these instructions produce? Click on the 'Result' button below to compare your image to the one we created. Our image will be a little more complicated, because we followed steps 2&3 many more times than you did.

Analyze the Order

Now, take a moment to think about what just happened, where the order came from. Your paper was blank before you began drawing, but after you finished there was a pattern on the paper (your drawing). Analyze the process that produced the pattern by answering the following questions in the box below (number each of your answers):

Was there a designer (agent) involved?
Was there a builder (agent) involved?
How did the builder know what pattern (order) to create?
Was the process involved in creating the order most similar to the process involved in producing the house, the office chair, or the rock candy? Justify your answer.

Activity Part 3 (the last one)

This part of the activity is often call The Chaos Game. Enjoy!

Instructions:

On a clean sheet of paper, draw three dots. You can place the dots anywhere, but things get difficult for you if you put the dots near each other. So, spread them out. The image below shows one way to do it. In the example below, we place the dots at the corners of an equilateral triangle, but you don't need to do that. You can place them anywhere, so long as they're spread out. As you do this, note that there is absolutely no way for us to predict where you've placed your three dots. In other words, from our perspective, your placement of the dots is completely random.

OK, label each dot, like this: label one dot "1-2", another dot "3-4", and the last dot "5-6". The image below shows you how we did it. Again, you can select which of your dots is labeled "1-2", etc. in any way you like. Since you'll label your dots however you choose, there is absolutely no way for us to know how you labeled the dots—which makes your labeling completely random, from our perspective.

Now (and this is the final step before you begin playing the game), place an unlabeled 'seed' dot anywhere on your piece of paper ... anywhere! The image below shows you where we placed our seed dot. We were boring and placed our seed dot 'inside' our labeled dots, but you don't have to follow our example. Place your seed dot wherever you please. Obviously, once again, you've placed your dot randomly and there is absolutely no way for us to know where you placed it. We call this a 'seed dot' because you're going to erase it after you place the next dot (in step 5).

Okay, this is where the game begins. Roll your die or click on the 'Generate Random Number' button below. Before proceeding, however, recognize that the die (or button) represents another random part of this processes. There's absolutely no way for us to know which number you'll roll (or generate) each time.
Next, identify the dot labeled with the the number you just rolled (or generated with the button). Now, draw a dot halfway between your seed dot and the dot labeled with the number you rolled (or generated with the button below). The image below shows our example. We rolled a '2', so we placed the new dot halfway between the seed dot and the dot labeled '1-2'. Make sense? Don't draw the green line like we; we drew it to illustrate the concept. Don't draw any lines. Now that you've placed the first 'game' dot, erase the seed dot. You don't need it any more. After erasing the seed dot you won't erase anything else, you'll just keep drawing new dots.

From here on out, you just keep rolling your die (or using the button) and placing a dot halfway between the last dot you drew and the dot labeled with the number you rolled (or generated). As you go, keep a tally of the number of dots you've made. Stop once you've made 40 dots. (Of course, you can do more if you please, but the process becomes rather monotonous.)

Analyze what you've done

Once you've made at least 40 dots, think about the process. Essentially every aspect of the procedure was random: where you placed your original dots, how you labeled them, where you placed your seed dot, and the numbers you rolled using your 6-sided die (or generated with the button). The entire procedure contained only one non-random aspect, this rule: "place the next dot halfway between the last dot and the number you just rolled (or generated)".

With that in mind, make a prediction about what you'd produce if you continued making more dots. In other words, what would you produce if you made a thousand dots? or a million? ...Would you end up with a basically solid triangle, with points defined by your original three dots? Or would you end up with something else? In the box below, record your prediction.

After making your prediction, click on the 'Result' button below to see what our example would look like had we placed 100,000 dots.

The image below shows the pattern our example would have made. It's the same pattern you made in the first to parts of this activity! Had you continued placing dots according to the rules, your pattern would look just like this, except the corners of your pattern would be wherever you placed them and the interior triangle would mimic the outer shape of your triangle.

Sierpinski gasket- triangles within triangles.

Does this result surprise you? For most people, an ordered pattern such as this is the last thing they would have predicted. Many are astounded by the precise order that emerges from a process containing so many random elements. Why are so many so surprised? Most people think random processes produce random results, and that's simply not true! When law (rules) is involved, a pattern (order) can emerge from an otherwise random situation, seemingly from nowhere! ...even when that law is as simple as the one you followed ("place the next dot halfway between the last dot and the number you just rolled (or generated)". Watch this video (2 min) to see the pattern from our example emerge.

Now, reproduce your pattern. Use either GeoGebra's Chaos Game or Shodor's Chaos Game to create the pattern you would have produced had you continued placing dots according to the rules. (We prefer GeoGebra's version because it's easiest to use.) To recreate your patter, follow these instructions:

Open one of the online versions of the Chaos game, but don't change any of the settings (that is, in GeoGebra's version, leave n=3 and proportion=0.5; and in Shodor's version, leave vertices at 'three vertices' and leave all the probabilities at '1'). If you have problems opening one of the websites, try another browser or the other site.
Drag the three points in the simulation to wherever you placed your first three dots. (In GeoGebra's version, you can move the seed dot, but it has no effect on the patter. The exact same pattern is produced no matter where you place the seed dot! The seed dot only controls the order of dots that produce the pattern, not the pattern itself.)
Now, have the program reproduce your pattern. (In GeoGebra's version, select the 'start' button and the 'slow' option—change the speed to medium or fast once you see what's happening. In Shodor's version, select the number of dots you want to add from the drop down list and click the 'add button'—start with a small number and increase it once you see what's happening.)

Kind of freaky, isn't it?! Would you have believed us if we had told you that we could predict the exact pattern you would produce without knowing anything but where you placed your first three dots, and then shown you the pattern? Most people wouldn't have believed us!

Why does it seem so strange to most people for order to emerge from lawful randomness (chaos)? Because most people have either never thought about the origin of the order around them or they incorrectly interpret that order. Why is this? The problem is rooted in the origin of physical intuition. In our everyday lives, we just don't gain very much experience with how processes like this work. Make no mistake, these kinds of patterns are all around you (and in you)! ...everywhere! But you and I mostly just see the results, so we rarely gain any intuition about the processes that produce those results. If order emerging from chaos doesn't 'make sense' to you, not to worry: we're going to give you lots of opportunities to see patterns (ordered states) like this emerge and, in so doing, provide you with many chances to expand your physical intuition for how nature produces order. Our journey From Atoms to Humans will be replete with these examples—in the Universe, in Earth, and in Life.

If you're mind isn't 'reeling' a little right now trying to place what you've just experienced in context, we didn't do our jobs, you knew much more than we anticipated about the emergence of order, or you didn't engage very deeply.

Examples in Nature

This activity is powerful because it allows you to experience creating the same pattern in three different ways. As we mentioned, the first two are great examples of agent-designed assembly—one using a blueprint and the other using instructions—and the the third is an example of lawful self-assembly, which can produce order from chaos. Agent-designed assembly is the way humans create order (patterns). Lawful self-assembly is the way order (a pattern) emerges in natural systems. How do you think Gods create? Is it one of these? Give some thought to how The Creation happened. Was The Creation an event that began and was completed in the past or are we presently living in The Ongoing Creation? Are the processes that we see operating in the world today part of The Creation, or did Creation happen in one way and the world operates differently today? In other words, what's your 'model' for how Creation occurred (occurs?)?

In the last few minutes of this Activity, think about the patterns that self-assemble in two natural systems: a school of fish and a flock of birds.

The Fish. To begin, visualize a group of fish swimming in the shallow ocean, forming no pattern whatsoever. Then, watch this video of the patterns caused when sharks swim through the fish (45 sec). As you observe the patterns, consider the answers to these questions:

What are the individual parts of the system, the pieces that form the pattern? (We'll use the term elements to refer to these parts.)
Can the parts act for themselves or must they be acted upon by an agent?
Is the order self-sustaining?
What is creating the order? Is there a person or other agent somewhere telling each part what to do? If not, what produces the order?

The Birds. To begin, visualize a flock of Canada geese feeding in a field, forming no pattern whatsoever. Then, imagine that something startles the flock and they take flight. Finally, watch this video of the V-shaped pattern that emerges in flight. As you observe the V-shaped pattern emerge from the chaotic distribution of birds in the field, consider the answers to these questions:

What are the individual parts of the system, the pieces that form the pattern? (We'll use the term elements to refer to these parts.)
Can the parts act for themselves or must they be acted upon by an agent?
Is the order self-sustaining?
What is creating the order? Is there a person or other agent somewhere telling each part what to do? If not, what produces the order?

If you'd like to, you could also watch and think about these examples of agent-designed assembly, but you don't have to:

Constructing a house (90 sec)
Making an omelet (90 sec)

A Final Word

We invite you to be on the lookout for ordered systems around you. As you observe the numerous patterns (examples of order) you encounter every day, think about how the order in those systems emerged: was it agent-designed assembly or lawful self-assembly? You encounter many examples of both every day. If you'll thoughtfully consider how order arises in these systems, your mind will be prepared for the ideas we'll explore in our next topic. By the way, we're kind of hoping that you'll become a little obsessed with thinking about this over the next week or twelve. Sorry(ish) in advance, if that happens! ...and happy Explorations!

Ordered Systems

Houses as Ordered Systems

Figure 1.4.2 illustrates the construction of a house, from design & blueprint creation through each construction stage— foundation work, framing, plumbing-electrical-HVAC, and exterior & interior finish work. As part of your analysis, answer the following questions in the “1.4 Analyzing Ordered Systems Questions” ‘quiz’ in iLearn.

Is the system ordered, and what pattern(s) comprises that order?
Can the ordered system be used to accomplish something, i.e., does it have a function or purpose?
What are the component parts that have been arranged into a pattern(s)?
How do the parts interact—can they act for themselves or must they be acted upon?
Is an agent(s)—an individual or entity—responsible for designing and/or building the order or does the order spontaneously self-assemble?
Can the ordered system fulfill its use, function, or purpose at each stage of construction, or can it do so only after the system has been completely assembled?

Chairs as Ordered Systems

Figure 1.4.3 illustrates the assembly of an office chair. Answer the questions below in the “1.4 Analyzing Ordered Systems Questions” ‘quiz’ in iLearn.

Image showing an office chair in assembly

Is the system ordered, and what pattern(s) comprises that order?
Can the ordered system be used to accomplish something, i.e., does it have a function or purpose?
What are the component parts that have been arranged into a pattern(s)?
How do the parts interact—can they act for themselves or must they be acted upon?
Is an agent(s)—an individual or entity—responsible for designing and/or building the order or does the order spontaneously self-assemble?
Can the ordered system fulfill its use, function, or purpose at each stage of construction or can it do so only after the system has been completely assembled?

Rock Candy Crystals as Ordered Systems

Figure 1.4.4 illustrates the kind of rock candy you may have made and enjoyed as a child. If you’ve never done this, you may enjoy doing it sometime soon. It’s interesting, tasty, and simple: 1) Heat water on the stove and dissolve as much sugar into the water as possible, 2) Allow the sugar-water to cool, and pour it into a cup or jar, 3) Place a string (or similar) in the sugar water by suspending it from a pencil (or similar) placed across the mouth of the cup or jar, 4) Wait—as the water evaporates, sugar crystals will form on the string (and sometimes along the edge of the container). Answer the questions below in the “1.4 Analyzing Ordered Systems Questions” ‘quiz’ in iLearn.

Is the system ordered, and what pattern(s) comprises that order?
Can the ordered system be used to accomplish something, i.e., does it have a function or purpose?
What are the component parts that have been arranged into a pattern(s)?
How do the parts interact—can they act for themselves or must they be acted upon?
Is an agent(s)—an individual or entity—responsible for designing and/or building the order or does the order spontaneously self-assemble?
Can the ordered system fulfill its use, function, or purpose at each stage of construction or can it do so only after the system has been completely assembled?

Our Heavenly Father has repeatedly told us in the scriptures that all things must be done in order. D&C 88:119 tells us to “establish a house of order, a house of God.” All that He has created is His house, His domain. We would expect that all of His creations would also follow that things are done in order.