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finish first pass with chapter 2

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ch_2_visual_modelling.md
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@ -448,89 +448,81 @@ fn s_pipegon! (pipe_rad & <-- note another new name
``` ```
And here is a portrait of `s_pipegon! (60, 30, inv (180), 0, 180)`. And here is a portrait of `s_pipegon! (60, 30, inv (180), 0, 180)`.
********* ##### FIGURE 14: Stripe-pipegon
HERE IS WHERE I STOPPED ON 2025-01-02
*********
Now, imagine an invisible arrow glued to the front of the roller. Now, imagine an invisible arrow glued to the front of the roller.
At the tip, there is a flashing light. At the tip, there is a flashing light.
Here is the new part to fit into our `pipegon!` machine: Here is the new part to fit into our `pipegon!` machine:
TO FLASH:L
; Flashes a light at distance:L from the starting point,; and returns the turtle to where it started.
PU FD:L PD
REPEAT6 [FD 2 BK 2 RT 60]
PU BK:L PD END
To install FLASH into `pipegon!`, we could fix a value for: L, perhaps based on the value for: RR.
Or we could extend `pipegon!`by adding another argument.
<--- FLASH installed.
CNGONremoved
<---
Visual
Modeling
Call the extension L.
`pipegon!`.
TO L.
`pipegon!`: RP: RR: L
: THETA
: CUM
`n`
IF:N < 1 [CNGON 20:RP STOP ] PU FD:RP +:RR
LT:CUM *:RP /:RR
FLASH (***)
: L
RT:CUM *:RP /:RR PU BK:RP +:RR LT: THETA
L.
`pipegon!`: RP
<--- new name and arg
PD
:RR:L:THETA (:CUM+:THETA) <---
(:N-l) new
name and arg
END
51
Chapter 2 Here is the flash portrait of: ```
L.`pipegon!` 60 30 40 2 0 180 fn flash! (len) -> {
~.~*"'*.~- & Flashes a light at distance `len` from the starting point,
*--. & and returns the turtle to where it started.
.- ~~ penup! ()
..* *.. ** forward! (len)
~.,.-~*.... J "'" "'~ pendown! ()
*.* *~.. repeat 6 {
*'**"~".~ forward! (2)
"'*~.*r back! (2)
~ right! (inv (6))
".. }
" tt ~ * ~ o'\W* *"~ '" "".. penup! ()
~ back! (len)
. tt pendown! ()
~ ~ }
-* *- ".~..*,,".~" ```
..""
L.`pipegon!` 60 30 To install `flash` into `pipegon!`, we could fix a value for `len`, perhaps based on the value for `roll_rad`.
- 40 Or we could extend `pipegon!` by adding another argument.
2 0 180 Call the extension `l_pipegon`:
- *-.,.
.. 1 ```
"".. fn l_pipegon! (pipe_rad & <-- new name
.~ ~ roll_rad
~:' t..* *'" ** flash_len & <-- new arg
os- theta
.. * total_angle
~. *'. n) -> {
...~ if lt? (n, 1) then cngon! (90, pipe_rad)
~'" else {
,:.. penup! ()
~.... forward! (add (pipe_rad, roll_rad))
~~... pendown! ()
,... left! (mult (total_angle, div (pipe_rad, roll_rad)))
flash! (flash_len) & <-- call to `cngon!` replaced with `flash!`
rt! (mult (total_angle, div (pipe_rad, roll_rad)))
penup! ()
back! (add (pipe_rad, roll_rad))
left! (theta)
l_pipegon! (pipe_rad & <-- new name
roll_rad
flash_len & <-- new arg
theta
add (total_angle
theta)
dec (n))
}
}
```
Here is the flash portrait of:
```
pipegon! (60, 30, 40, inv (180), 0, 180)
pipegon! (60, 30, -40, inv (180), 0, 180)
```
##### FIGURE 15: Flash `pipegon!`
What happens if we make the radius of the roller negative? What happens if we make the radius of the roller negative?
Right. Right.
The roller is inside the pipe. The roller is inside the pipe.
Some examples are shown on the next page. Some examples are shown on the next page.
Cosure
<!--
The part below will require more careful translation, at least/until we shift Ludus's turtle graphics to use an actor model, and thus be animated.
This is a key difference between Ludus and Logo.
-->
### Cosure
Have you noticed that even the most complex designs we have done so far are drawn quite quickly? Have you noticed that even the most complex designs we have done so far are drawn quite quickly?
Each is complete by the time the roller has made a single 360-degree trip around the pipe. Each is complete by the time the roller has made a single 360-degree trip around the pipe.
If the roller makes a second trip around the pipe, the design repeats exactly. If the roller makes a second trip around the pipe, the design repeats exactly.
@ -540,102 +532,111 @@ Experiments will show that altering the sizes of the roller and pipe leads to di
What determines the number of trips before closure occurs? What determines the number of trips before closure occurs?
Can you calculate the trips until closure if you know the sizes of the roller and pipe? Can you calculate the trips until closure if you know the sizes of the roller and pipe?
Could you "find" a design that never closed? Could you "find" a design that never closed?
52
VisualModeling ### A portfolio of roller-inside-pipe portraits
A portfolio of roller-inside-pipe portraits
53 ##### FIGURES 16-19: Interior pipegons (no code given :|)
Chapter 2
On the next page is a `pipegon!` design that closes only after a number of trips around the pipe. On the next page is a `pipegon!` design that closes only after a number of trips around the pipe.
The individual images show the design at various trip stagesaround the pipe. The individual images show the design at various trip stagesaround the pipe.
Can you guess the pipe and roller sizes I used? Can you guess the pipe and roller sizes I used?
Words elicit images
### Words elicit images
Words that are visually descriptive, like closure, should call up a variety of images in your mind. Words that are visually descriptive, like closure, should call up a variety of images in your mind.
This elicitation of mind-images can be enormously useful in visual modeling. This elicitation of mind-images can be enormously useful in visual modeling.
In each of the following exercises, I will stress the importance of words. In each of the following exercises, I will stress the importance of words.
We must talk a lot in conjunction with sketching a lot. We must talk a lot in conjunction with sketching a lot.
Take a few minutes here to think visually about the word closure. Take a few minutes here to think visually about the word closure.
Say "closure": what images does it bring to mind? Say "closure": what images does it bring to mind?
Tell the turtle to " hurry up and bring a design to a close." Jot down, or sketch, the image ideas elicited in your own mind by the chanting of the word. Tell the turtle to "hurry up and bring a design to a close."
Jot down, or sketch, the image ideas elicited in your own mind by the chanting of the word.
Put it all in your notebook. Put it all in your notebook.
Suppose you needed to find a synonym for closure. Suppose you needed to find a synonym for closure.
What would you suggest? What would you suggest?
Any suggestion must be descriptive of all the image work we have completed. Any suggestion must be descriptive of all the image work we have completed.
By the way, you probably won't find closure in a standard dictionary. By the way, you probably won't find closure in a standard dictionary.
Why is this? Why is this?
At the start of this chapter I mentioned that sometimes we would model machines from the real world- pipes and rollers are very real world- and other times we would model machines that aren 't so real.
### A slowly closing `pipegon!`
##### FIGURE 20.1-7: A slowly closing `pipegon!` (no code)
### Imaginary machines
At the start of this chapter I mentioned that sometimes we would model machines from the real world--pipes and rollers are very real world--and other times we would model machines that aren't so real.
Perhaps we can make one model do both real and imaginary things. Perhaps we can make one model do both real and imaginary things.
For example, can we make our `pipegon!` machine draw some fantastic designs? (By the way, look at that word imaginary. For example, can we make our `pipegon!` machine draw some fantastic designs?
Why does it have image in it? (By the way, look at that word _imaginary_.
Why does it have _image_ in it?
Can you imagine why?) Can you imagine why?)
Let's imagine a striped roller inside a pipe. Let's imagine a striped roller inside a pipe.
The procedure `pipegon!` will generate a composite picture of this roller as it travels around the inside of a pipe. The procedure `pipegon!` will generate a composite picture of this roller as it travels around the inside of a pipe.
So far, this is just like the situations viewed above. So far, this is just like the situations viewed above.
But now, let 's introduce the fantasy feature. But now, let's introduce the _fantasy_ feature.
Make the radius of the roller larger than the Make the radius of the roller larger than the radius of the pipe in which it "rolls." Is this possible?
Imaginary
machines
54
Visual Modeling
A slowly closing pipegon
55
Chapter2
radius of the pipe in which it "rolls." Is this possible?
Can it be done? Can it be done?
I asked PIP E GON to do it, and the results are shown on the next page. I asked `pipegon!` to do it, and the results are shown on the next page.
What is happening? What is happening?
Are these pictures of real or imaginary machines? Are these pictures of real or imaginary machines?
How can you work out your answer? How can you work out your answer?
Can you sketch it? Can you sketch it?
Recapitula lion
### Imaginary `pipegon!`s?
##### FIGURE 21.1-4: `pipegon!`s with larger rollers than pipes
### Recapitulalion
Let's summarize what has happened in the last few pages. Let's summarize what has happened in the last few pages.
We have built a Logo model that can produce a large variety of images, some of them very surprising. We have built a Logo model that can produce a large variety of images, some of them very surprising.
But more important, we have seen how the act of modeling can facilitate the visual exploration of some of the characteristics of a real-world machine. But more important, we have seen how the act of modeling can facilitate the visual exploration of some of the characteristics of a real-world machine.
Once we began to tinker with our model, we wanted to tinker further. Once we began to tinker with our model, we wanted to tinker further.
Some of our designs posed difficult questions whose answers were not at all obvious.Closurewassuchaquestion.Weneededtodomoretinkering andmore experimenting to come to grips with what was going on. Some of our designs posed difficult questions whose answers were not at all obvious.
Closure was such a question.
We needed to do more tinkering and more experimenting to come to grips with what was going on.
Could we have predicted the directions this tinkering and experimentation would take before we started? Could we have predicted the directions this tinkering and experimentation would take before we started?
I don't think so. I don't think so.
Once we begin to model parts of our world, the act of modeling takes on a life of its own. Once we begin to model parts of our world, the act of modeling takes on a life of its own.
I think we have touched what Levi-Strauss said happens when one plays with miniatures. I think we have touched what Levi-Strauss said happens when one plays with miniatures.
Model play Model play "gratifies the intelligence and gives rise to a sense of pleasure which can already be called aesthetic."
"gratifies the intelligence and gives rise to a sense of pleasure which can already be called aesthetic." I hope you would also describe visual modeling as fun. I hope you would also describe visual modeling as fun.
Why pipes and rollers?
### Why pipes and rollers?
I started with this particular machine because I was interested in it. I started with this particular machine because I was interested in it.
I could have used any number of alternative illustrations, but this was my own direction. I could have used any number of alternative illustrations, but this was my own direction.
I will show you, in the chapters to come, dozens of other examples that illustrate the ways in which visual modeling encourages the modeler to look at the world differently. I will show you, in the chapters to come, dozens of other examples that illustrate the ways in which visual modeling encourages the modeler to look at the world differently.
56
Imaginary `pipegon!`s? But please keep the following in mind.
:11,/Ill All of the exercises are based on my own interests and the interests of my students.
S// However, the ordering of these exercises in this book is _not_ arbitrary.
/ I] I have carefully placed my exercises within specific chapters and I have ordered and introduced these chapters in a very structured fashion.
I Recall that the subtitle of the book is _A structured approach to seeing_.
Visual Modeling
57
89 lall AI SES'UE asua's all S PIlOMa ' lO al lO l Ana Aill asalSaSt pJJ It noAUI G J8ldE4~ My intention is to show you, very precisely, one approach to visual modeling and graphics.
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Visual Modeling ### People as scientists: the work of George Kelly
other courses of behavior or inconsistent with them, intellectually reasoned or vegetatively sensed." Having admitted that this book is a very personal document, let me go further by introducing to you the work of an American psychologist who has greatly influenced my own thinking about model builting.
Each person 's scientist aspect encourages him to " improve his constructs by increasing his repertory, by altering them to provide better fits, and by subsuming them with subordinate constructs or systems." For Kelly, human behavior is the application of scientific methodin making sense of a particular environment. George Kelly, born in Kansas in 1905, was trained in mathematics, physics, sociology, and psychology.
Kelly's claim to fame comes from his view that each person tries to make sense of his world using techniques that are similar to those used by scientists.
In fact, Kelly viewed all people as scientists.
"Man looks at his world through transparent patterns or templets which he creates and then attempts to fit over the realities of which the world is composed.
The fit is not always very good.
Yet without such patterns the world appears to be such an undifferentiated homogeneity that man is unable to make any sense of it.
Even a poor fit is more helpful than nothing at all."
Kelly gives the name _constructs_ to the patterns that people try on for size.
He could just as well have called these patterns _models_.
These constructs--or models--"are ways of construing the world.
They are what enables man, and the lower animals too, to chart a course of behavior, explicitly formulated or implicitly acted out, verbally expressed or utterly inarticulate, consisten with other courses of behavior or inconsistent with them, intellectually reasoned or vegetatively sensed."
Each person's scientist aspect encourages him to "improve his constructs by increasing his repertory, by altering them to provide better fits, and by subsuming them with subordinate constructs or systems."
For Kelly, human behavior is the application of scientific methodin making sense of a particular environment.
Rather than merely responding to surroundings, people use an experimental approach to test and extend their system of personal constructs. Rather than merely responding to surroundings, people use an experimental approach to test and extend their system of personal constructs.
Each person's goal, in Kelly's view, is to build explanatory models that effectively explain and predict personal environments. Each person's goal, in Kelly's view, is to build explanatory models that effectively explain and predict personal environments.
Kelly suggested shortcuts for improving construct systems. Kelly suggested shortcuts for improving construct systems.
Kelly's shortcut was to encourage individuals to make their own constructs verbally explicit. Kelly's shortcut was to encourage individuals to make their own constructs verbally explicit.
His most famous method for eliciting and verbalizing personal constructs is known as the repertory grid technique. His most famous method for eliciting and verbalizing personal constructs is known as the repertory grid technique.
@ -643,6 +644,7 @@ Using slightly different words, Kelly 's techniques encouraged individuals to bu
Once built, these verbal models could be analyzed in much the same way as we have analyzed our pipe-and-roller model. Once built, these verbal models could be analyzed in much the same way as we have analyzed our pipe-and-roller model.
Tinkering with constructs would occur naturally, and this would encourage further tinkering. Tinkering with constructs would occur naturally, and this would encourage further tinkering.
And as a result of this play, construct models might become more general and more powerful. And as a result of this play, construct models might become more general and more powerful.
Kelly worked with verbal rather than visual models, but many of his ideas can be extended to the latter. Kelly worked with verbal rather than visual models, but many of his ideas can be extended to the latter.
My interest, as was Kelly's, is to suggest how to describe our inner models. My interest, as was Kelly's, is to suggest how to describe our inner models.
While Kelly was interested in the verbal description of models, I am interested in more graphical descriptions. While Kelly was interested in the verbal description of models, I am interested in more graphical descriptions.
@ -650,29 +652,29 @@ My goal is to encourage you to look at your own visual baggage.
Obviously, I need words, too, to help in my form of elicitation. Obviously, I need words, too, to help in my form of elicitation.
Sometimes, you may think that I rely on words too much. Sometimes, you may think that I rely on words too much.
Too much chat, you might say... Too much chat, you might say...
If you are intrigued by this very brief account of George Kelly 's work, find his book A Theory of Personality: the psychology of personal constructs (W.
If you are intrigued by this very brief account of George Kelly's work, find his book _A Theory of Personality: the psychology of personal constructs_ (W.
W. Norton, New York, 1963). W. Norton, New York, 1963).
All the Kelly quotes were taken from it. All the Kelly quotes were taken from it.
59
Chapter2 Exercises ### Exercises
Exercis2e.1 #### Exercise 2.1
Can you come up with some rules about `pipegon!` closure? Can you come up with some rules about `pipegon!` closure?
Specifically, can you characterize a final pipegon image in terms of the dimensions of its parts? Specifically, can you characterize a final pipegon image in terms of the dimensions of its parts?
Experiment a bit. Experiment a bit.
Try to make some generalizations. Try to make some generalizations.
Do the generalizations hold up after more experimenting? Do the generalizations hold up after more experimenting?
Whether you feel successful in this activity or not, find the following book in your local library: E. Whether you feel successful in this activity or not, find the following book in your local library: E. H. Lockwood, _A Book of Curves_ (Cambridge University Press, Cambridge, 1963).
H. Lockwood, A Book of Curves (Cambridge University Press, Cambridge, 1963).
This book may help you think about closure. This book may help you think about closure.
It may also suggest other image ideas to think about visually. It may also suggest other image ideas to think about visually.
Don't worry too much about the book's math. Don't worry too much about the book's math.
Look at the diagrams, and read the chapter names. Look at the diagrams, and read the chapter names.
Listen to these chapters: cardioids, limac;ons, astroids, right strophoids, tractrices, roulettes, Listen to these chapters: cardioids, limaçons, astroids, right strophoids, tractrices, roulettes, and glissettes.
and glissettes.
What images do these names dredge up? What images do these names dredge up?
Sketch them before you find the book. Sketch them before you find the book.
Exercis2e.2
#### Exercise 2.2
How do you feel about carnivals and amusement parks? How do you feel about carnivals and amusement parks?
Do you enjoy their mechanical rides? Do you enjoy their mechanical rides?
I'm not talking about tame rides, like the merry-go-round or carousel, but wild rides that yank the rider through space. I'm not talking about tame rides, like the merry-go-round or carousel, but wild rides that yank the rider through space.
@ -683,27 +685,24 @@ What pattern will this light trace out as the machine grinds into life?
The pulls and pushes on the rider of this machine change suddenly and unexpectedly. The pulls and pushes on the rider of this machine change suddenly and unexpectedly.
Can you make a picture of this? Can you make a picture of this?
Can you describe visually why this kind of machine is so scary? Can you describe visually why this kind of machine is so scary?
60
Exercis2e.;2 ##### FIGURE 22: A scary amusement ride
Visual Modeling
f"t..~5HUhf 'T Design some _imaginary_ carnival rides and give your machines imaginative names.
,.....~---------...-
Design some imaginary carnival rides and give your machines imaginative names.
Draw big sketches of your ideas; draw them large enough so that others can "read" them. Draw big sketches of your ideas; draw them large enough so that others can "read" them.
Describe the ride in words so that potential travelers will know what to expec,t beforethey climb aboard. Describe the ride in words so that potential travelers will know what to expect _before_ they climb aboard.
You had better show them some picturesofthetrip aswell.WhynotuseLogotogeneratethesescene?s You had better show them some pictures of the trip as well.
Exercis2.e4 Why not use Logo to generate these scenes?
#### Exercise 2.4
Do you know the term "kinetic sculpture"? If not, you can guess what they are, or rather what they do? Do you know the term "kinetic sculpture"? If not, you can guess what they are, or rather what they do?
Kinetic sculptures are mechanical or electronic sculpture-machines that move, clank, or flash. Kinetic sculptures are mechanical or electronic sculpture-machines that move, clank, or flash.
Some even squirt water (for example, the wonderful kinetic fountain designed by Nikki de Saint-Phalle and Jean Tinguely opposite the Pompidou Center in Paris). Some even squirt water (for example, the wonderful kinetic fountain designed by Nikki de Saint-Phalle and Jean Tinguely opposite the Pompidou Center in Paris).
61
Chapter2
Carnival rides are a special class of kinetic sculptures. Carnival rides are a special class of kinetic sculptures.
They may not seem suitable for art gallery installation, but I have seen films of amusement park rides included in exhibitions. They may not seem suitable for art gallery installation, but I have seen films of amusement park rides included in exhibitions.
The French sculptor Jean Tinguely does kinetic sculpture on a more modest scale. The French sculptor Jean Tinguely does kinetic sculpture on a more modest scale.
Below is a reproduction of his " Homage a Marcel Duchamp," done in 1960. It is human scale, about 5 feet high. Below is a reproduction of his "Homage a Marcel Duchamp," done in 1960.
It is human scale, about 5 feet high.
Design and build a kinetic sculpture using Logo. Design and build a kinetic sculpture using Logo.
You might start by trying to model the Tinguely machine. You might start by trying to model the Tinguely machine.
`pipegon!`s are a kind of kinetic sculpture, too. `pipegon!`s are a kind of kinetic sculpture, too.