Of Crab Canons and Turtle Hums
Of Crab Canons and Turtle Hums
A conceptual approach to the teaching of the Logo language
by Liddy Nevile
COM-3 PAGE 25
Whether by quirk or evolution, the humble turtle has a new habitat. His behaviour appears to have altered accordingly. Today, turtles can be found racing across computer screens, zig-zagging their way through a pattern-producing routine. or in a more pedestrian mood, plodding around the outline of a 'house' with its roof either inverted or at least 'slipped' — this is becoming recognized as the 'first turtle house' style.
The turtle family now includes the spearheads of the new dynamic geometry which has been introduced by Logo. This geometry has a new perspective and the student gains access to it by imagining himself into the position of the spearhead which is drawing the shape, the Turtle.
The choice of animal family was not completely random: the British neurophysiologist Grey Walter had a tiny robot which was reminiscent of a tortoise (its namesake), and which inspired the computer-controlled robots which are larger and known as Turtles. The connection between the Turtle robots and the screen spearheads explains the screen Turtle's name.
The attributes of real turtles reinforce the choice of animal family: tortoises move forwards and backwards but not sideways — turning is a different activity; turtles are bald and lack ears (at least obvious ones); and their apparent deafness can cause suspicion that they may be mute too. And turtles seem to have an introspective attitude to life. Their actions often appear to be aimless meanderings through time and space.
It is time to focus attention on some of these characteristics of the turtle family.
First, the turtle's deaf-muteness. To the newcomer, computer languages and the programmes written in them are incomprehensible concepts. However, if it is explained that as the Turtle cannot hear or speak it will be necessary to communicate with him with written messages, the keyboard can be given a positive role. For children particularly, the learning of a language is familiar, as is the learning of the decoding and encoding skills called reading and writing. So it is logical to them that a new Turtle would have a small vocabulary but that he should be able to increase it with careful teaching. It is logical too, that a Turtle might choose to communicate with pictures rather than written words, and more so when it is remembered that he is to be seen as both mute and semi-literate. Thus the Turtle's handicaps are put to benefit in the explanation of the concepts of languages and programmes.
There is then the next attribute of Turtles to be considered. The puzzle of "What is it like to be a bat?"
has long entertained the minds of the students of artificial intelligence. The inner life of this curious deaf-mute seems dark and lonely. Not so the life of the Turtle: his meanderings are reminiscent of the musings of that familiar fellow Pooh. Yet we appear deaf to the Turtle's music_ For nearly a decade, many have been admiring the visual displays of Turtle trips but their form has been ignored.
Cynthia Solomon has written articles urging teachers of Logo to invite their children to re-call Turtle hums, either as they are if they are not complete (closed displays), or turning the Turtle a little and then re-calling them if they were complete. The visual representation, on the screen, of a Turtle trip has received great attention. Re-calling it, as Cynthia Solomon says, is a powerful idea.
It is as if the difference between what is being communicated by the Turtle and what is understood, or received, by the user, is being forgotten. If there is perfect communication it must be the first ever — a powerful idea. It is more likely that there is some gap. Familiarity with the Turtle suggests that what is to him a hum (in the style of Pooh) is received as a line drawing by the viewer. All the discussion has focussed on what is received, and the value of what is communicated is being missed.
Harold Abelson and Andrea diSessa have produced a most erudite work on Turtle geometry. In the book they have written at length about the important Total Turtle Trip Theorem, and earned it a place among the respected geometric theorems. The Total Turtle Trip Theorem is all about Turtle hums but the authors don't mention them anywhere. The focus is on the visual display — it is, after all, recognizable as geometry.
What then is the elusive hum?
Its origins lie with the computer user. As a result of a user entering a message such as ED 25 RT 37 FD 26 LT 74, the screen Turtle sets off on what is seen by the user as a trip but to the Turtle is a hum. The 'trip' creates a visual display which may be a recognizable shape, a fancy squiggle, or merely a line. It may be long or short.
So the hum is user-generated (or called). It is not a procedure (or programme).
Several different hums can be called consecutively and the results may be visually exciting. And as suggested by Cynthia Solomon, the hums can be recalled to establish the TTT Theorem, thus producing fascinating polygons and other interesting patterns.
Hums can be successfully called without careful planning and without any understanding of the likely outcome in visual form. All that is needed is the simplest vocabulary (RT, LT, and FD), and the most elementary keyboard skills. The point is that a line of commands can be made one at a time and purely arbitrarily, e.g. FD 21 RT 67 FD 34 LT 92 FD 51 RT 46 FD 32 ...
Once a hum has been called, it is very easy to repeat it with the screen split so that the hum-call being copied can still be seen while it is being re-typed (this is true of hum-calls which are three or fewer lines long). Here is another special teaching aid. That long hums can be called by young children, and so easily re-called by these children, makes them available to young users. In fact often the hum-call is too long for even an adult to remember it.
When the hum-call message is sent to the Turtle, he hums and trips without error. It is easy to show a child how he cannot remember more than a few different instructions given at one time and so draw attention to the amazing memory of the Turtle. The Turtle's memory capacity becomes very important as the user's programming abilities develop, and so an early understanding of this feature of computers is essential.
The Turtle's hum is closely allied to other musical forms. Full-scale musical works are frequently developed from simple melodies. These melodies may be found throughout a piece of music in a range of recognizable forms — the melody may have changed key, speed, or been inverted or contorted, and yet still be the cohesive element throughout the musical work. The visual form of the hum will vary with each change in the hum, and therefore with each hum-call. The benefit here is that a hum which has been called without any particular purpose can be varied bit by bit and the results can suggest techniques for further change, e.g.
Here then is a way of introducing the use of variables. By changing one part only of the hum, the common features of the new hums can be made obvious and also the differences can be highlighted, e.g.
image
"The length of the sides is being changed!" This discovery is available to primary school children, as are its effects. Children who could not write a procedure (programme) can copy hum-calls from immediately above on the screen and vary one part as they do so. They can see the result. They can identify what is being changed in the hum-call and what becomes different in the display. They soon see that a change in length may result in a bigger version of the original shape.
In Logo, variables are given names by the user so that as soon as the element to be varied is identified, it can be named as the variable. For example, if it is the size of the angle which is to be changed, then it can be named ":angle" and the different sizes can be thereafter fed in as required. (This is actually not done until the user is writing procedures but the basic concept can be developed at the hum stage.) With this naming of variables, there is no need to tackle the mysterious x's and y's — in fact the belief that all variables are either x's or y's will be avoided.
The hum lends itself easily to the teaching of the concepts of rotation and reflection. Just as a hum-call can be repeated by simply re-typing what is still written on the screen, the hum-call can be repeated with an extra turn first and, if this is done several times, the visual display will be rotated about the starting point. Rotation is "an extra bit- before the hum-call. Reflection is just changing all lefts for rights and all rights for lefts. This is easy for even a young child.
Inverses are one further skill: if rights and lefts are interchanged, and forward and backwards are too, the result is the inverse of the original. Where the user may get muddled, the steps can be taken separately with the pen up for the incompletely changed hum-call.
Finally, the Turtle's top-down approach to movement: he can go forwards or backwards, or he can turn on the spot. Thus a movement in any direction must be broken into the two components and executed one at a time, and the order is likely to be important. The user who hum-calls randomly will need only to remember to leave spaces when typing the hum-call — the Turtle will respond to mixed calls such as: FD 34 FD 12 RT 90 RT 90 ... For the user who has planned the display, however, the hum-call must be in terms of turns and motion and those must be in the correct order to achieve the desired result. Here is a lesson in identifying the parts of a problem before solving it, and in logical ordering. Again the lesson is within the reach of young children.
This consideration of the Turtle's handicaps has been undertaken in an attempt to give a conceptual explanation of the vocabulary and syntax used by those operating in Logo. The notion of the Turtle hum has been adopted as a pre-programming tool with connotations which are familiar to children. The concepts which are made available to children by Logo are not in question, rather the need to be able to help children assimilate the new language they are meeting with the computer. For children who have no trouble learning Logo and are intuitively motivated, this is unnecessary, but there are still many children who do not relish the idea of time at the keyboard, and for whom the props mentioned may be the missing link.