Computer simulations offer the possibility of exploring psychological concepts by interacting with the simulator. What follows is a series of simulations which enabled you to experiment with some of theconcepts that were outlined on other pages on this site. Lets start with with exploring some of the relationships between conceptual maps and visual territories. The simulator shown below is an implementation of a Turtle program that was used in the in the computer programming language, Logo. Imagine that the arrowhead cursor is a turtle. The turtle can move in any direction, angle, on the two dimensional screen. You can also tell it what distance to go in the direction that you set. You give it information by clicking on the distance and/or angle fields. Type in the distance and/or angle. Then press move to see the line that you instructed the turtle to draw. In abstract terms you give the turtle a distance and a bearing, angle, and then direct it to execute your move. So you are free to experiment. See if the turtle will do what you think it will do before you make it move.
There are two major ways to approach the turtle world. The first as a direct intuitive interactive trial and error approach. You have a sense of direction, and you follow your intuitive feel of what is going to happen. The second is to construct a conceptual map of the underlying processes which actually draw the lines. These are two very different modes of approaching the task. So see how you approach it. Try to observe your own reactions as you make turtle tracks. It is interesting to see how closely your predictions worked out as you thought they they would. As you work along try to construct a theory of the underlying processes which enable the turtle to move on the screen. This is like trying to analyze the turtles behavior.
Try these exercises. Make a square, a triangle, a pentagon, a hexagon, a five pointed
star. During the exercise try to be conscious of how you
were actually approaching the task.
Now that you have had a chance to do in some experimenting try to move from the territory of your direct experience of crawling around the turtle's territory to a conceptual map of how the turtle converts your instructions into the actual lines that it draws on the computer screen. See if you can construct the underlying procedures which enable the turtle to draw your lines. It was probably easy to draw a square or rectangle. However, it was likely much harder to draw a pentagon or a five pointed star simply by using intuitive methods. In order to draw a pentagon some abstraction is very helpful. Begin by recalling that a full circle is usually divided up into 360 degrees ( there are or other ways), then recall that it pentagon has five sides. If you divided 360 degrees by 5 sides you get 72 degrees per side. So if you gave the turtle a distance of say 50 and an angle of 72, then you could start out in the right direction to construct a pentagon. The next line would be with the same distance, 50 and in angle of 72 plus 72 or 144. Add 72 to the 144 and draw the third line, and so on until you get back to what you started with the fifth line. You may have actually done the same thing with a square but it is less likely that you thought of a general algorithm to draw a polygon with any particular number of sides.
Did you think about how turtle and converted the polar coordinates of the distance and angle to a rectangular coordinates that are actually seen on the computer screen? This is something that is very hard to do intuitively. It takes some trigonometry to make this conversion. The x coordinate is found by multiplying the distance times the sin of the angle. The y coordinate is found my multiplying the distance by the cos of the angle. The computer screen is based on rectangular coordinates of x going across horizontally and of y going up and down vertically. The top left-hand point is x = 0, y =0. The bottom right hand point it x = 400, y = 400. When you reset the simulator the turtle starts at 200. Now try going back and entering some values order to see if you can get a feel of how the conversions work. can do do
Note how we have gone for the computer screen its self to and abstract and essentially arbitrary systems of coordinates. The same actual spot on the screen can be found with either coordinate system. Whether you to use the x, y coordinates or the polar, (distance, angle), coordinates is simply matter of convenience. However, each coordinate system has a very different feel. The reason we find squares and rectangles so much easier than pentagon's is that we all accustomed to living in buildings with rectangular rooms. We are adapted to right angles. Unless we are high-level military officers, we are not used to working in five-sided buildings. So the kind of intuition with which we have been approaching the turtle comes from our everyday experiences. We are thrown to a higher level of abstraction when we leave our common sensible view of the world and enter a mathematical domain.
Above we have noted the map territory distinction. There is another logical level distinction worth considering, mainly the difference between and variable and a value. Distance is a variable. Distance is on a different logical level from any particular value that we assigned to it. The variable distance is not 5 or, 50 or, 200. The variable itself always remains somehow aloof from any specific number that we assign to it. There is great utility in being able to consider variables on the its own level without having to descend to the more concrete level of only thinking about specific values. Considering variables rather than values allows us to conceive whole classes of events rather than specific events.
For some background review the
Servo systems and feedback servo systems and feedback sections of to these pages. Some important psychological concepts can be explored starting with a basic amplifier. first, consider the conceptions of input, processing, and output. There is some kind of input. The input is processed. The result of processing or transformation is the output. In stimulus response psychology, the input is the stimulus and the responses the output. Something goes on inside the organisms that transforms the stimulus into the response. The concept of a basic amplifier is actually metaphor for what happens when we are stimulated externally or internally and how we transform the sensations of the stimuli into a perception. It is easier to start experimenting with a concrete simulator and then try to abstract from your experiences than to struggle with abstract explanations in advance. So consider the basic amplifier shown in the applet which appears below. Start by entering values in the input and gain fields. Then press the feedforward button to see the output. Again, input and gain are variables. The particular numbers that you enter into the input and gain boxes are the specific values that you assign to the variables. To start assign the value, 5 to the input and the value, 6 to the gain. After you press the feedforward button the output becomes 30. Enter different combinations in to the input and gain and observe the output. As you experiment with the amplifier see if you can figure out in, analyze what is going on inside the amplifier to produce the output.
Was at the relationship between the output any output the same under all conditions? A few observations could lead to the hypothesis that the output equals the input times the gain. This is true under most conditioners. However, the basic amplifier like ourselves has its limits. Try making the input 5 and the gain 30. You would expect that the output would be 150, but if you have left the limits set at plus and minus one 100 then the output would be 100 rather than the expected 150. If it were real world physical amplifier the output could never exceed the power supply. That is, if the power supply were plus and minus100 volts, the output could not go beyond 100 volts. Thinking about it another way, I can only lift so much weight. As hard is am I try, I cannot lift 600 pounds. Each of us has limits in other domains. There is just so much frustration that I can tolerate. My attention span is limited, etc. Recognizing that each "truth" functions over limited range is a critically important insight. Knowing the range of which the truth operates, and realizing when you out of the range is essential to wisdom.
Amplifying can be thought of in several ways. One important way is that gain is another way of thinking about sensitivity. Takes very little input to produce a significant output. Sensitivity is good only up to certain point. If one is hyper-sensitive he or she becomes readily overloaded and tends to distort what is happening. In terms of the simulator if you drive the output beyond the limit you produce distortion. This is critically important when we consider what goes in relationships. The situation can escalate very quickly if either member of a relationship is overly sensitive. Conversely, consider what happens if you make the gain 0.1 or less. Now rather than magnifying the amplifier is minimizing. This may be useful or impediment depending upon the situation. In simple human terms, minimizing could be trying to stabilize a situation or maybe one is simply insensitive .
What happens if you give the gain in negative value? Mathematically you are inverting the input. Psychologically it might be thought of as a kind of negativism, or turning it into the opposite. I.e., whatever you I will do the opposite. If you me to agree, I will disagree. These are kinds of psychologically inverting the
Separating figure from ground is fundamental to all psychological
processes. Gregory Bateson made the point that all metal processes start with
being able to distinguish differences. A difference that makes a difference is
the start a mental event. A difference amplifier is the way to begin to model
looking at differences. The different amplifier is different form the basic
amplifier in that the difference amplifier has two inputs. In order for
there to be any output the inputs have to have different values. Try experimenting
with the difference amplifier in the applet below. Enter values into both inputs and
the gain, then press feedforward.
A centrally important observation is that it doesn't matter what the absolute values of the two inputs are. The only thing that is seen at the output is a function of the difference between the inputs. In electronics terms this is known as common mode rejection. For example, make input1 50 and make input2 50. Even if you make the gain 1000 the output will be 0. Only the difference is amplified. The similarity is disregarded. If you think of input2 as the background and input1 as the figure, then output reflects how much the figure is different from the background. We can have very much in common and be more or less sensitive to our differences.
Another way to think about amplifying differences is to ask the questions, where are the stars during the day time? Of course, the stars are still there but the contrast between the bright sky and the faint stars is insufficient for our eyes to see. There is insufficient contrast. Our eyes are unable to sufficiently amplify the difference between the brightness of the stars and a brightness of the sky. So we can not see the faint stars stand out against the background of a bright day.
Some people think in all or nothing, black or white terms. Things are either black or white for them. As one patient so aptly put it, "I think in completelies". He is completely good, or she is completely bad. Implicit in this kind of either or behavior is the amplification of a difference. The difference is between what is seen and some kind of standard of the way one thinks it should be seen. A difference amplifier can be used to simulate this behavior. To see how this operates make input1, 5, input2, 4.5, and the gain 1,000. Push feedforward to see what happens. The output goes to the positive limit. Conversely, set input1 to 4.2. Do not change input2. See what happens when you push the feedforward button. In this case the output jumps to the negative limit A small difference results in the output to moving to an extreme position. It becomes either plus 100 or minus 100. There's no gray area in between the two limits. Thus, essentially the person is acting like a Comparators. A Comparators compares two things. If one is greater than the other the output is high. If one is less than the other the output is low. It is in either or comparison. There are no fuzzy in between states. The comparator is extremely sensitive to tiny differences between what it sees and its reference. It is simply trying to see if something is bigger or smaller than its reference. this is fine for making crisp yes or no decisions, but it can be problem if one is looking for subtleties.
Note that if the gain is not so high, the output will not be driven to a limit so readily. The shades of gray between black and white can be seen.
Feedback can be thought of as some kind of reflection. What you do is turned back on
your self. In the more formal terms of the simulators, some of the output is
turned around and directed back into the input. Feedback comes in two varieties,
positive feedback and negative feedback. In the context in the simulators positive
feedback is not saying good things about a person and negative feedback saying bad things.
Positive feedback is simply turning some of the output back onto the input. Negative
feedback is inverting the signal and then feeding it back to the input. To see how
this works experiment with the simulator below. Fill in the values for the inputs
and the gain. Press feedforward to see the output, and then press feedback to see
what happens when the output is feed back to the input. Cycle through several loops of
feedfoward and feedback to see the output pattern. Notice what happens when
you make the gain plus 1, minus 1, plus 2, minus 2, minus 1.5 and minus.5.
When the gain is positive the output escalates to the limit. A psychological example would be, I am. afraid. I sense my inner agitation which, in turn, gives me the feeling that something what even worse is happening. I become afraid of my fear. I go into a panic. The more intensely I feel something, the more intense my feeling becomes. The situation continues to spiral upward until a limit is reached. Thus, positive feedback tends to destabilize situations.
The situation is different with negative feedback. In order to make he feedback negative it is necessary to invert the gain. Inventing means doing the opposite. If am excited I try to calm down. If I am lethargic, I try to wake myself up. To get an immediate experience of negative feedback try standing on one foot and then close your eyes. Notice when you fall off to the left you regain your balance by moving to the right, and vice versa. Thus, there is a tendency for you to oscillate around your point of balance. This exercise of actually feeling a feedback system in operation will give you an intuitive understanding of negative feedback. Start to by making input1, 4 and input2, 7. Set a gain to -1. press feed forward to see the output, and then press feedback to observe the feedback. Move around the feedback loop several times. The output oscillates between the difference between input1 and input2 (which equals 3), on one cycle, and 0 on the next. Note that on each cycle just the right amount of feedback is given to correct to the difference between inputs. This returns the system to its point of balance (input1 minus input2 equals 0, 0 times the gain, -1 = 0). On the next cycle the zero output is fed back. Since neither of the inputs has changed, the original difference,3 is input on the next feed forward. Once again the result is an output of 3. Now the system is out of balance again. The difference is inverted fed back and balance is restored. The oscillation continues until one of the inputs is changed. In life this is a very common situation. We tend to repeat the same pattern over and over again unless there is a change in how we see things. How often do you feel that you get into the same trouble over and over again? This interesting situation will be discussed more fully in this section on servo systems below.
When the gain is less than minus 1, for example, -1.5 the output oscillates from a negative value to a positive value until it reaches the limit. Try to imagine how these observations could be converted into psychological terms. Positive feedback directly results in a runaway situation. Conversely, if the gain is <-1, the situation runs out of control in a zig zag course. In the situation of negative feedback an effort is made to nullify the difference between the inputs by moving in the direction opposite the difference. However, since the gain is < minus 1 the correction over shoots the desired point, thus generating a difference in the opposite direction. For example, I'm angry (input1) but it is my value to be agreeable ( input2). So there is a difference between my being angry and my conscience telling me that my anger is bad. I try to correct this situation by being overly nice. In terms of the simulator I over correct my anger by being too sweet. My being too sweet generates resentment which eventually results in even more intense anger. Now the discrepancy between my intensified anger and my guilt becomes even greater. A have to become overly sweet to compensate. The situation oscillates back in fourth between sweetness and anger until I reach my limit.
However, it is useful to have a little context for servo systems. Servo systems a widely found in nature and in technical applications. The automatic pilot of an airplane is a servo system. Maintaining body temperature is a servo system. Controlling your balance is a servo system, etc. When thinking of a servo system his useful to think of input1 has some kind of sensory input. what is sensed could come from the external environment or from an internal thought, feeling, or sensation. Input2 is a referent. The referent can be thought of in several ways. First, it is a standard of comparison. The classical example is a thermostatically controlled heating system. You set the temperature let's say it's 70 degrees. 70 degrees is the referent. The thermostat senses the surrounding room temperature and compares it to the referent. If it temperature falls below 70 degrees it turns on the heater. Note the heater reduces the discrepancy between the room temperature and the thermostat setting. This is negative feedback. when it is too cold, it gives heat. It keeps adding heat until the temperature in the room becomes 70 degrees, then the heat is turned off. When the room temperature equals the referent, the system is in balance, and the output falls to 0. This is a very important principal. The system doesn't have to do anything when it is in balance. If the temperature goes above 70 the air conditioner is turned on, cooling the room back down to 70 degrees. Again, reducing the room heat with the air conditioner is negative feedback. In either case, heating or cooling, the servo system tries to reduce the difference between the room temperature and the referent temperature to 0. Just a note in passing, real servo systems have a certain amount of over shoot which has to be corrected. The temperature gets a little above the 70 before the heater the is shut off, and gets cooler than 70 before the air conditioner stops. It tends to cycle around the referent. However, the essential idea is that the servo system tries to make just exactly the correction that is needed.
Experiment with a servo simulator below in much the same way that you approached
the previous simulators. Follow feedfoward and feedback changes that
take place around the loop. Note particularly how much feedback is a and what happens
after the feedback is given on the next round of feedforward.
The servo systems simulation shown above is different from the feedback amplifier given the previous section. The input1 in the feedback amplifier retained its value after the feedback part of the cycle. The feedback system oscillated. When the system was in balance the output dropped to 0. When the 0 was added to value of input on the feedback section of the cycle, the previous difference between the inputs remained. So the discrepancy between the inputs was output once again on the next feedforward. Thus the system oscillated between being in balance, and then as soon as it was in balance the original conditions reasserted themselves. If you consider the difference between me inputs as a measure of dissatisfaction, then the system doesn't stay satisfied. In psychological terms this would be like the situation of my not feeling good about myself. There is a discrepancy in between the way I feel I am, input1, and the way I feel I should be, the referent. We could think of this discrepancy as a motivation for corrective action. I do something, my output, to make myself feel better about myself. For a brief time my dissatisfaction with myself is ameliorated. Unfortunately this fix did not change my original sense of myself, input1. So after doing something to make myself feel better I had a moment of peace, but I could not remain content because I was once again confronted with a difference between the way I saw myself and the way I felt I should be. Essentially, I didn't learn from experience. My successful experiences did not alter the way I see myself.
There is an important difference in the servo system. The value of input1 is changed when the output is feed back to it. The value of input1 is altered by experience. This is a significant distinction. Let us apply these ideas to the servo system model. Think of input1 as how I see myself. In the servo model input2 is called the referent. The referent can the thought of as what you wish for or want want, some kind of ideal, or a needed some sort. Since these are numerical models, it is necessary to assign numbers to the inputs. If input1 is less than the referent then there is some kind of deficiency. This deficiency is transformed into the output. If the gain is plus 1, then something the discrepancy is the output. In psychological terms, I am not as good as I would like to be. To see how this works press reset then make how I see myself, input1, 5, and how I would like to be, the referent 10. You might think of this as being a half as good as I would like to be. So the discrepancy is -5. Press Feedforward. Note that since said the gain is -1, and output becomes +5. This suggests I have to do something positive and to make up for the deficiency. Now press Feedback and see what input1 becomes. The 5 that was fed back was added to input1, which was 5. The value of input1 was then changed to10. I have done something to make myself feel better about myself. Press Feedforward again. Since there is no difference between the inputs, the output is 0. I'm satisfied with myself so I don't have to do anything. The system is how stable because the discrepancy has been corrected. Something would have to change the way I see myself, input1, or the way I feel I should be, the referent for the system to become active again. In the example just given, my way of seeing myself is altered by what I do. It would be a good exercise to think of other situations in which input1 is altered by the feedback and cases in which it is not.
The servo model can be used as a guide to considering where to intervene in psychotherapy. In feedback system there are three parameters that can be altered, input1, input2, and the gain. In the case given above an effort could being made to change how I see myself, input1. Attention could be directed to my expectations of myself, the referent, or, to how much I amplify my discontent, the gain. Note that the servo system itself only sees the difference between the inputs. The system continuously seeks to nullify the difference between in the two inputs. If the therapist speaks about the discrepancy between the way I see things and the way I would like to see things, I experience the therapist is being empathic. The discomfort that I feel comes from tension between the way I think I am and away and think I should be. This difference is what drives me to action. I'm not nearly as aware of what I do as I am of what I see. Recognizing the discrepancy between my referent and/or the way I see myself is probably the safest place to start The therapist's understanding of the difference is felt by me as empathy. If the therapist speaks about what I do, my output, I am likely to see him or her as being critical. I am much more likely to be responsive to criticism if I feel that I am understood.
If you consider a servo system a person, then lets see what happens when
two servo systems interact. In this simulation the output of one servo amplifier
becomes the input1 of the other servo amplifier. Think of this as a situation in which
Helen and Jim are interacting. Try different values of the referents and of the
gains. Have them take turns feeding their output into the others input. Try
several cycles of Helen moving and then Jim moving to see the pattern of their
interaction. Try negative gain and positive gain. As you are doing this try to make
up a story about what is happening in Helen and Jim's relationship.
Here is an example. Helen doesn't feel that she is getting enough attention from Jim. Let us say that she would like5 units of attention but that she is only getting 1. In order to represent this in the simulator make Helen's input1 equal to 1, and her referent equal to 5. Jim, on the other hand, feels he's getting too much attention. So make Jim's input1 equal to 5 and his referent equal to 1. See what happens if both of their gains are plus 1. That is, they reflect to the other their dissatisfaction. Step through few cycles in order to show how their interaction evolves. In order to make the simulation come alive translate what is happening in the simulator into words and say what is happening. Example just given you might say, "Helen sees 1 amount of attention from Jim and she wants 5 amounts of attention". This gives her a discrepancy of -4 amounts of attention. She lets him know it. Jim's sees that she lacks 4 amounts of attention. He compares is with his desire for 1 amount of attention. This leaves him with a difference of -5 units of attention. He in turn withdraws and gives Helen -5 units of attention. She compares his turning away from were even further with her desire for 5 units of attention. Her dissatisfaction grows, and she outputs 10 units of dissatisfaction. Her reaction leaves Jim even more dissatisfied, and he retaliates by withdrawing even further. The situation continues to escalate until it reaches their limits.
The idea of units of attention may seem awkward. It was merely a way of representing intensity of experience. The numbers might be translated into a qualitative sequence such as displeased, disappointed, massively disgruntled, devastated.
Push reset, enter new values for their input1's, and their referents. Make their gains -1. Run the simulator through several cycles until the pattern in the output becomes clear. Reset to the system. Put the same values for the inputs as given above, but make their gains +1. Note that in either case, both having positive or negative gain, their interaction escalates to the limits. What would have to happen in order for the interaction to stabilize? What would you change to enable either Helen or Jim to be satisfied? Jim can be satisfied if Helen makes her output equal to Jim's referent. Conversely, Jim can satisfy Helen by making his output equal her referent. Another way of saying this is that if each gives the other what he or she wants, the other will be satisfied. Either can do this in a variety of ways. The way they see things can be changed, (input1). What they want can change, (referent), and/or their gain can change. As long as the net effect is to see what the other wants ( their referent), and give it to him or her. What would have to happen for them both to be satisfied? I would be very interested to hear your solutions and comments about these simulators
mailto:wd16@columbia.edu.