Random Rules: Observations and the Scientific Method

Random Rules is the newest in-browser simulator on the site and the only one that doesn’t currently have a help file. This is in part because the in-browser simulators on the site right now are all ones I plan on using in the fall semester and so my first priority is to have them done so I can use them. Making them usefully available for everyone else has to come second. This post is, partly, a help file. That section will be clearly labeled in a subheading. Just skip straight there if that’s all you need – I’ll repeat a few sentences of material in both places so that if you skip straight to the help file you’ll be fine.

I designed Random Rules to teach the scientific method. The basic idea of Random Rules is that the objects on the left side of the screen interact in a manner determined by rules which you can work out using observations and/or experiments. You can then test yourself to make sure you understood the rules. This certainly isn’t the five-step “scientific method” (observation, question, hypothesis, experiment, conclusion) that makes it’s way into so many science textbooks but there are good reasons for that. First, the five-step method is at best a vast oversimplification of the experimental method (which is NOT the same as the scientific method – certain disciplines are heavily observational rather than experimental, often because experiments are logistically impossible) and at worst a bunch of nonsense that traps students into trying to fit actual science into a method that doesn’t match reality. Second, the five-step method is a specific case of a more general idea of science: to derive patterns from specific cases. This isn’t a universal idea of what science is but a lot of science is this, and a lot more relies on it. So, for instance, one might attempt to generalize from observations of a number of specific ecological communities to a rule about the size relationships between predators and prey (cases to pattern). Another study might try to use these rules to determine what a specific extinct predator ate (pattern to case).

Random Rules also accomplishes a few other things: it forces critical thinking and it demonstrates the power of experiments.

To accomplish all of this I aimed for some fairly specific goals:

  1. The system needed rules. Random Rules is based off of two sets of rules: a set I call the “win rules” and a set I call the “lose rules”. Imagine that the two objects on the screen are playing chicken. The winner is the one that continues on straight. The loser breaks away. A set of rules governs who wins (in the case of a tie both objects “lose”) and a different set of rules determine what direction the losing objects “runs away”.
  2. It needed to be clear when someone figured out the rules. The rules generated by Random Rules are completely deterministic. If I wrote the rules down for you (and the development version of the program printed the rules to the screen for debugging purposes) you would be able to figure out exactly what would happen all the time. All the information you need to make a perfect prediction is available to you once the objects appear on the screen. (The type of objects that appear in each turn is one of the only two actually random processes in the program.) And, since this is a teaching tool, there is a “Test Me” option that allows you to demonstrate that you did actually figure out the rules and displays your results on the screen.
  3. It needed to be hard/impossible to cheat. The rules are random. Each difficulty level has constraints but even at “Dead Simple” there are 30 different options and so knowing what the rules were last time or on your neighbor’s computer is unhelpful. (“Insane” appears to have just over 1.5×1070 possibilities.) The choice of colored, geometrical shapes is also related to this. While it’s not technically cheating for a student to attempt to use external information to solve an exercise like this it does defeat the purpose. I find it much less likely that a student believes that, say, triangles should beat squares than that a wolf icon should beat a squirrel icon.
  4. There should be observations and experiments. There’s a “Run Experiment” button that allows a player to determine which objects will appear next instead of getting a random combination. Since this is a teaching tool there’s also an experiment counter so if you tell students they must try to solve the rules first without experiments you can tell if they cheated. The only way to clear the experiment counter is to reload the page (which re-generates the rules) or click “New Rules”, which negates the value of the experiments.

Help File

Random Rules has two screen sections: a screen where objects can be seen interacting (left) and a control panel (right). When you load the page two options will already be selected for you: “Run” and a difficulty setting. Objects will be appearing in the screen and moving towards each before one or both turn away from the other. The color and shape of the objects are displayed at the top of the control panel in case these are unclear. (I did attempt to accommodate red-green colorblindness but I haven’t actually tested my efforts and obviously I don’t think my efforts would help at all with someone who was completely colorblind.)

On the left side of the screen objects interact according to two sets of rules: the win rules and the lose rules. Essentially the objects are playing chicken. The win rules determine who wins. The winner just keeps going forward. The loser (and in ties both objects lose) consults the lose rules to determine what direction it “flees” given its color and shape. Normally the objects are pulled at random from a set determined by the difficulty setting but there is a control menu option that alters this behavior.

The control panel is set up as follows:

At the very top the color and shape of the objects in the object screen are written out.

In the top control row are controls that alter the speed of the game, “Run”, “Pause”, and “2x Speed”. These do just what they sound like.

The next row down contains difficulty settings. These alter how many options there are for the randomly generated rules and how complex the interactions between various factors can be. I will explain these further in a section below. However, be aware that these rules rapidly get quite difficult. “Insane” really is insane. I know exactly how this program works and I doubt I would have the patience to solve the puzzle on anything above “Medium”.

The third row of control buttons are the really important ones. “New Rules” does just what it sounds like – it generates entirely new rules. “Test Me” initiates test mode. In test mode objects will pause instead of turning aside until the user selects what directions they think the objects will go and hits “Submit” to lock in those answers. Half a point is given for each correct guess and ten rounds are scored in a test. This means two important things: the score for someone who has figured out all the rules will be 10/10 and also it is not that hard to get 5/10 without really having much of a clue. The score will be displayed on the screen. “Run Experiment” allows the user to determine what the next pair of objects will be. It also increments the experiment counter under the control row.

Below the control row are various counters, any selection menus required for test mode or experiments, and an area to take notes.

Difficulty Settings

Here is the detailed breakdown on how difficulty settings work. (At least, the difficulty breakdown that doesn’t go full under-the-hood programming.) The most basic thing to be aware of is that the number of shapes and colors available to the program goes up as the difficulty level increases. However, there are additional rule changes beyond that.

Dead Simple: This difficulty ties both rule sets to only one object characteristic. It is also the same object characteristic for both rule sets. What this means is that you can safely ignore either shape or color entirely once you determine the rules. Example: a blue circle and a red triangle come together and the red triangle goes up. In this example the relevant rules are “circle beats triangle, triangles go up when they lose”.

Simple: This difficulty is like Dead Simple in that both rules are tied to only one characteristic. However, it may not be the same characteristic for both rule sets. The lose directions also now include left and right. Example: a blue circle and a red triangle come together and the red triangle goes up. In this example the relevant rules are “blue beats red, triangle goes right, which is up when the triangle is coming from the right side”.

Medium: In this difficulty every characteristic is assigned a win strength and a lose rule. These combine so that objects effectively have their own unique properties. For the win rules these combinations are simple addition of win strengths. For the lose rules the characteristics have a ranking which determines which rule is in effect for a given object. Medium difficulty can be quite challenging. Example: a blue circle and a red triangle come together and the red triangle goes up. In this example the relevant rules are “circle strength 30, blue strength 80 = blue circle strength 110, triangle strength 50, red strength 10 = red triangle strength 60, blue circle wins, red lose rule = backwards, triangle lose rule = up, triangle outranks red, use triangle lose rule”.

Complex: This difficulty involves one new rule: one side of the object screen is assigned a bonus. This bonus is scaled equivalently to the win/lose strengths of a single characteristic. This means that in the case where two identical objects approach one another one will now lose because it’s one the weaker side. Example: a blue circle and a red triangle come together and the red triangle goes up. In this example the relevant rules are “circle strength 30, blue strength 40, left side bonus 74 = blue circle strength 144, triangle strength 50, red strength 83 = red triangle strength 133, blue circle wins, red lose rule = backwards, triangle lose rule = up, triangle outranks red, use triangle lose rule”.

Insane: This difficulty adds another new rule. I won’t say what it is in such an easily-locatable place since the whole point is that this difficulty requires one to figure out what type of new rule there is but in keeping with the purpose of Random Rules the rule is deterministic. That is, while its parameters are generated randomly the random number generator stays off after that. I will say that this is a great difficulty to use if you need to take a month’s vacation and would like a single assignment that will take your students the entire month to figure out.

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