Jack Alpert SKIL
USGS complex modeling conference Reno Nevada 1/10/03
Human well being on earth results from natural forces, and human behavior. While individuals behave to shape their immediate personal well being, most people believe global long-term conditions result from the behaviors of leaders in powerful religions, governments, and industries.
However, Mark Twain had a different view. He said politicians in Washington were like ants on logs in a flowing river. No matter how much they declared their powers to control the future, they, their institutions, and their constituencies, all were going pretty much where the current took them. Twain ‘s model suggests, that to understand where humanity is going, we have to understand where the currents are going. And we have to understand what creates these currents.
A cellular automata model might suggest these currents are produced by the collected personal acts of billions of individuals. People, living their day-to-day lives produce the currents. What if they choose actions without realizing that action’s contribution to these currents? Then they also would not realize that “to change the global community’s destinations requires six billion sets of behavior to change.” That is change from the behavior that previous generations made.
To change our destination, requires answering the question, “How do individuals choose behavior?” If all human behaviors were hard wired, there would be no opportunity to implement change. Yet, obtaining change is not as simple as just telling each person what behavior to take. Humans use cognitive processes to integrate genetic predisposition, sensed physical environment, and transmitted content to choose their behavior. These cognitive processes, or learning, allow humans to gather, process, and value, experienced, transmitted, and inferred information. Learning determines behavior. Behaving differently begins with different learning.
Learning is both dynamic and recursive. We learn continuously. We learn to learn continuously and recursively. These dynamics make the predictions, of social system conditions, made by cellular automata models using static rules quite limited. To get a model to produce the full range of possible predictions requires the means to allow the rules to change over the time period for which the model is making the prediction. A modeler must identify the existing rules, the future rules, and the processes that change rules. I am referring to two modelers, the one looking at the social system to make policy recommendations, and the individual finding a view that helps him or her choose personal behaviors.
Let me give a simple example of how learning works (or fails to work) in an individual’s efforts to behave to attain a future event. If the example is enlightening, the reader will be able to generalize to other models he or she fashions. I will describe a normal individual’s attempt to understand how his or her behaviors control a system and then use the failure to show how different levels of cognitive process (learning) determine vastly different levels of success in choosing “controlling behavior.”
Three aspects of modeling will guide my presentation. 1) How individuals choose parameters that describe the system. In some circles, this is known as the re-normalization group. 2) How individuals find ways to represent these parameters in a single image. In some groups this is called scaling. 3) Finding the relationships that allow the prediction of change in one parameter given a change in another. In some groups this is called correlation and in others it’s called causal function.
What follows is a short course in how human learning affects how an individual chooses, scales, and relates parameters. It is also a short course in learning to recover from automobile skids.
A car is traveling a lonely dark road. A deer jumps out from the shoulder and blocks the right lane. The driver has just enough time to steer the car to the left of the deer.
Figure 1 Car misses deer then skids
The car is now pointed, and is traveling, straight down the center of the left lane as shown in both the figure above and in the figure below. However, it is rotating clockwise. Within a second, Figure 2, while the center of the vehicle moves neither right nor left in the lane, the rear moves left and the front moves right.
Figure 2 A second after missing the deer
We all know what to do in this situation. It’s the same as normal driving. We turn left to get the car to point down the road.
We also know that if we turn too little – or too late – the clockwise motion will continue. The car will spin clockwise, and will most lightly end up in the right ditch as shown in Figure 3.
Figure 3 Outcomes of steering too much and too little
We also know from experience that if the steering wheel is turned to the left too much – or the correction is held too long – the clockwise rotation will be replaced by an even larger counterclockwise rotation. The car will spin counter clockwise and end up in the left ditch.
Thus, in the skidding condition that immediately follows missing the deer, too much or too little steer – or taking out the steer too early or too late – will cause an accident.
Most drivers have been in skids. Many have gotten out of skids. So many drivers have learned some correct behaviors for some skidding situations. The question is “Is the deer skid, one of those situations.”
Research suggests everyone, except race car drivers, after they miss the deer will go into the ditch. But we need more of an explanation to understand what drivers did (and did not) learn from previous skids. (This need is analogous to: a) knowing that every civilization throughout history moved toward conflict and b) not knowing what to change to prevent that movement toward conflict in the future.)
Practicing skidding in a snow-covered parking lot, in the family car, provides experience that allows the body to subconsciously measure many variables and behaviors -- some of which recover from the car skid. The successful experiences are stored in an N dimensional look up table. In the table, for each set of conditions (car speed, heading deviation, tire squeal, body roll, the force on the shoulder created by the sidewards skidding car, and tens more variables) there is a correct steering wheel behavior.
While the table is compiled subconsciously, we can indirectly inspect its contents by knowing the boundaries of the experience used to fill the table. Then we can ask the question, “Are there correct behaviors stored at intersections defined by the “deer skid.”
Let me draw a picture of this database using only three surrogates for the “N” measured variables. These are car speed (MPH), deviation between the car’s heading and the road heading (q), and road surface –(icy, wet, dry.) An inspection of Figure 4 shows the domain of the three dimensional volume where icy parking lot experience might fill the intersections with appropriate steering behavior.
Figure 4 Volume of Solutions
Since most drivers have only a few emergency experiences outside of the marked volume, it follows that trail and error learning could not have filled in steering behaviors for most of the look up table. For these unfilled intersections, (especially higher speed dry pavement skids) drivers could always guess at the proper steering behavior. However, given how critical timing is in skid recovery, guesses usually result in off road excursions.
The lessons to be learned from Figure 4 are a) the way human beings go about understanding their exposure to loss of control, and b) learning ways to regain control, are not up to their needs. No person has practiced at all the speeds, on all the different roads, in all the different vehicles that they will drive. And thus their future will contain injuries and deaths because their cognitive processes were too underdeveloped to realize their exposure and find other means of control.
The “skidding car control problem” provides a foundation to understand what kind of cognitive process might lead drivers to a better solution. It might also show modelers how to better model complex systems. And it might show that an individual’s contributions to the human destination reflect his or her cognitive abilities.
What thinking does it take to find the behaviors that would work to recover from the full range of car skids to which we are exposed? What does it take to identifying parameters that describe car skids and behaviors in a way that human beings can use them to recover from skids? And in a deeper sense, what cognitive process learns from normal driving experiences, both the limits of the old way of managing skids and motivates a search for new ways?
In this short paper I cannot answer these questions. But I can demonstrate improvements that are available when the effort is made. What follows is an existence proof of the potential gains for complex systems modeling if we do a better job of choosing, scaling, and relating system parameters before we apply brute force computation.
Since a complete solution to skid recovery cannot be accomplished using normal subconscious processes (physiological measurement and computation) the behaviors have to be created from information consciously gathered and consciously manipulated as the skid unfolds. This imposes three constraints on the new solution. First, at a conscious level a driver can dynamically measure little more than one variable. Second, at the conscious level, time-series-computation is similarly limited. And third, the computed behavior must be physiologically performable.
So which skid descriptor is most important? What units should be used to measure it? And finally what is the relationship between this skid measurement and the needed steering behavior?
Often complex control problems can be resolved by breaking them down into component problems that can be solved separately. For example if the car was not rotating but was sliding (moving in the direction of the road but misaligned with it) most drivers could steer gently to the left to realign the car with the road. So let’s make the first problem to stop the “rotation” and thus reduce the skid recovery problem to one most drivers can solve.
Rotation is not the angle with the road. It is the first derivative of the angle, or dq/dt. Rotation is stopped when dq/dt=0. Actually this is when the angle q will be its largest. This will occur when the headlights are pointing away from the road heading the most.
Now if our task is to stop the rotation, we should use a steering behavior that creates the largest torque. That is the largest force opposing the rotation. Which means the driver turns the wheel to the left as much as possible, such that when dq/dt=0 all of this steer, (torque) can be removed. That is the front wheels are parallel to the back wheels. While the car is still sliding down the road, the friction produced by the front and back wheels is the same (that is zero torque).
Even though the car is pointed off the road to the right, its rotation is zero. Then we can begin to execute the remaining portion of recovery, vehicle realignment with the road. Something that we already know how to do.
Table in Figure 5 (which is a working solution for the skidding car problem) shows the N dimensional look up table has been reduced to a two by three look up table.
Figure 5 Controlling skids using the “heading movement”
The sensed data is: is the world moving, “right, “left” or “not moving” in front of the driver. What the eye easily measures is the “sign” of the derivative of “heading deviation.” The steering behavior, required in response to “right, “left” or “not moving” is also easy to implement with a small a mount of training. As a result, this 2x3 table does allow skid recovery for the entire volume defined by a full range of all N parameters. That is, the solution works in any car at any speed, on any road surface. It even works for controlling vehicles like super tankers, and airplanes and space shuttles.
What explains --
|For further information on cognition based solutions to global problems see http://www.skil.org/ For more information on learning and skid recovery see Chapter 1.8 of Time blind --Global problems in terms of human thought processes. For development of temporal inference cognitive abilities see Time Blind - The development of temporal thought processes.|
1/22/03 revised 7/19/2017