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LC1bT02 Protocol 2

Included Text Pages (2)

RAL Discussion before Protocol 2

Protocol 2.1
RAL Protocol 2.1

Included Materials (3)

RAL 2-A1 Terminal Log

RAL 2-A2 Terminal Log with Notes

RAL 2-A3 Terminal Log


LC1bT15 Protocol 15

Included Text Pages

RAL protocol 15

Included Materials



Vn103.1 Reprise 10/15/77

As we have attempted reducing Miriam’s cortisone dosage, she has
again begun wheezing severely. Her problem was especially unfortunate
today, for she had asked a friend to come visit. Lizzie is an energetic
red-haired colleen of 6. At lunch she disclosed to Miriam and Robby all
the problems they could expect with a younger sibling. (Her sister
Katie, at 14 months, not only keeps her awake but also tackles Lizzie
every time she strolls by). The weather was so bad no one could play
outside. Miriam, hoping for some relief in the better air of the Logo
lab, agreed to Robby’s suggestion that we all go over there to play.

Once at Logo, Miriam showed Lizzie around — through the Learning
Lab, the Music Room; the toilets out here and the coke machine across
the hall. Lizzie said she wanted a picture of a flower and then explained:
earlier in the year Miriam had made copies of the image made
by a FLOWER procedure and took one for each member of her kindergarten
class; the children colored them and some took them home. Miriam was
still feeling low, so I helped Lizzie get what she wanted. First, a
FLOWER picture. Next, looking at Miriam’s work hung on the walls of my
office, she declared she wanted a copy of PF (for PRETTYFLOWER). As we
waited for her picture to come from the printer, Lizzie saw a 6-fold
near triangular polyspiral which Robby had printed from a different
terminal. “Wow! I want one of those. Show me how to do it.”

I started the SHAPES (or MPOLY) procedure. Miriam showed some signs
of improvement and the two girls worked together creating designs which
they would color in later (cf. Addenda 103 – 1 and 103 – 2). Whenever
they got in trouble, I was available to help them get started again.
This play of making computer designs, then printing pictures of them for
later coloring, occupied both girls for about two hours. Both girls
made some very pretty novel designs. For example, the design of Addendum
103 – 2 was one I had never seen before and judge pretty (more so
with the drawing in light on the cathode ray tube). When Robby and I
tried to show SHOOT to Lizzie, she could not get interested in it and
returned to MPOLY.

As the day wore on, Miriam’s apparent improvement faded. We drove
home by way of a playground on St. Paul Street. (Miriam and I stayed
in the car while Robby and Lizzie ran around). As we continued on to
her home, Lizzie revealed that her daddy had a computer too where he
worked, but ours sure was different from his.

These notes record the children’s continuing engagement at Logo
though our project be over, and provide a glimpse of the reaction of
one of Miriam’s peers.

Addendum 103-1

Colored Polyspiral at 155 degreesVn103-1 Colored Polyspiral

Addendum 103-2

Six-fold MPOLY with a person in the middle

Vn 103-2 Six-fold MPOLY with person


Vn104.1 Back to School 10/14/77

During the last days of our project experiments, I promised Miriam
to visit her first grade class as I had visited in kindergarten. I had
the mistaken impression that Miriam had arranged my visit with Ms.
Fieman. The oversight proved to be no problem, for despite my beard
and over-size frame I blended in well with the group of children.

It was “Read me this, read me that. Do you know my name?” David
B. said, “I remember you. Last year you came and we set up that thing
from the ceiling.” His reference was to a 3 string pulley I rigged in
the spring which enable the children to hoist heavy weights, their
desks (!) and each other (!!) a few feet off the floor. One of the
other boys (was it John?) asked if I still had that machine for making
electricity. Curtis brought over a soma cube and the children squabbled
over it. Miriam did not have a chance to work on the puzzle for any time
with 5 classmates each wanting a turn. Meg and Laurie Ann sat with me
and Miriam before the class split into two groups — one headed for the
library, the other for an introduction to the class’ activities for the

The librarian attempted to introduce to the children the distinction
between factual and fictional writing. It is possible my presence, my
sitting on the floor with the children, caused her some unusual confusion.
Nonetheless, it appeared that she neither had articulated for herself
any consistent set of criteria nor had any good language for communicating
her ideas to the children.

Once again in class, Miriam took up the writing activity. Curtis
and I joined her. The task was one of sentence completion: e.g. “With
my eyes I can see ________.” The children’s task is to write a description
and draw a picture of some appropriate object. Miriam chose to spell
and draw flowers. Her other senses led her to taste corn on the cob and
ice cream; to feel fuzzy things (here Scurry was the exemplar); and to
hear a song — which she represented by a person singing the complete
text of “Drive, drive, drive your car, gently down the street” as sung
by Don Music on Sesame Street.

After Miriam’s work was approved, we had a few minutes to play
before I left. She suggested checkers. Lately we have been playing
variations of the standard game. We tried a 4×4 board (played with 2
checkers on each side) and a 6×6 board (played with 6 checkers on each
side). The board fell to the floor while still folded but with squares
showing. I suggested we play ‘half a game’ of checkers. (The board
was thus 4×8 and played with 6 checkers on each side). We played 3
games. Miriam’s friends came crowding around and all wanted their turns.
But I did have to leave and suggested Miriam could play ‘half a game’
with them.

These notes try to capture both the continuity and change of Miriam’s
kindergarten and first grade. There is more structure in that the children
cycle through a set of selected activities (of such a sort that they
could be interesting). The children can get some play time by finishing
their work quickly. Ms. Fieman is good with the children and flexible
enough to let a parent visit with insufficient notice. Miriam seems
comfortable in the situation and enjoys school to the extent that she
chooses to attend even if she feels unwell.


Vn105.1 Hotel Magee; Two Microworlds; Decadal Computation 10/20 & 27/77

10/20 With Robby’s introduction of WUMPUS to Miriam yesterday, the
mechanically recorded sessions at Logo cease. Vignettes continue to
round out and close off at natural stops various themes of the project.
The sense of closing off the mechanical recording is that the project
has REALLY ended. Thus our trip to witness my cousin’s wedding in
western Pennsylvania is both a vacation, an obligation, and a celebration.

After 7 and more hours of driving, nightfall found us in Bloomsburg,
on the east fork of the Susquehanna. We passed motel after motel with
NO VACANCY signs. After dark, we came to the Hotel Magee. (Their bill
board advertisements along the road declared ‘children stay free’; I
thought staying in a hotel (their first time) would offer them an interesting
contrast with the motel room we knew awaited us the next night at
our journey’s end.) We piled into the hotel, and while Gretchen and the
children freshened up after a day on the road, I sought a table at the

A grandmotherly hostess first informed me there was no room now and
no empty tables were expected till 8 in the evening. When I asked for
recommendations to other dining places about town — for my two hungry
children would not peacefully wait another hour for service — the woman
scratched a reservation from her list, making room for us.

Soon we were at table; the food was good and the variety quite
surprising. So even though Miriam was tired and refused to eat, the
meal had a festive sense for all of us for our various reasons. During
the evening we talked about the children’s sense of the project and some
of the amazing things they had done. I told Miriam how her addition of
96 plus 96 impressed me (cf. Vignette 100) and contrasted that with her
attempt to sum 89 plus 41 by counting hash marks 5 months earlier (cf.
Miriam at 6: Arithmetic). When I recalled that detail, Robby convulsed
with laughter. How could anyone attempt so absurd a procedure? I
asked Robby to think back, reminding him of the night he showed the same
response when I asked him to add 75 and 26 (Robby recalled having a late
pizza at the European Restaurant with our friend Howard Austin — Cf.
ADDVISOR, Logo W.P. #4). This reflection sobered him some. Miriam
piped up: “That’s a hundred and one.” “And how did you get that result?”
Miriam replied (to my surprise), “It’s like 70 [sic] and 20 is 95 and then you
add 6. 75 and 20 is 95 plus 6.” I was surprised because with those
particular numbers I thought Miriam might compute the result using a
money analogy. After assuring her of the correctness of her result, I
posed a different problem. “Miriam, suppose you had 75 cents and I gave
you 26 cents — say a quarter and a penny — how many cents would you
have?” When she responded “A dollar ten,” I asked where the extra 9
cents came from. Miriam computed for me in explanatory mode: “75 cents
is like 3 quarters and another quarter is a dollar. That’s a hundred
cents and one more is a hundred and one.” She denied her first answer
was a hundred and ten cents.

Note first that Miriam did not carry the result from one computation
to the second. Note further that although she applied directly her
decadal then unary algorithm for the numbers (75 plus 26), the same
numbers applied to money engage with a most minor variation the
well-known result that 4 quarters make a dollar. I can not confidently
explain the penny-dime confounding. I speculate that when not central,
they are not well distinguished. A dime won’t buy a 5-pack of bubble
gum and you can’t use pennies for anything but paying food taxes (cf.
Vignettes 54 and 55).

10/27 While waiting for the school bus this morning, I asked Robby if he
were doing anything interesting. He was enthusiastic about certain games
and said he liked especially the play time when the first graders come to
play with his class (3rd grade). I asked if they ever did any academic
stuff — TIMES problems and so forth.

Miriam informed us both she knew how to do TIMES. She argued her
point concretely: “Four twenties are eighty.” I laughed and reminded
her that I was driving the car yesterday while she and Robby discussed
that sum in the back seat. She protested, “I can do it.” “You can do
4 times 20. Can you do 4 times 90?” I challenged her. Robby knew and
said the answer. Miriam complained to him and walked down the driveway
kicking leaves. She returned. “The answer’s 3 hundred and 60.” Robby
claimed credit: “I told you first.” I argued that having the first
result was not so important, that what matters most is having an answer
you can understand yourself. Miriam said, “Can I tell you how I figured
it out?” and proceeded to do so: “I had a hundred eighty and a hundred
eighty. I took the two hundreds and one of the eighties. That’s 2 hundred
eighty. Then I took away 20 from the other 80 and I had 300
with 60 left over. 3 hundred 60.” I congratulated Miriam on good execution
of a very complicated computation and wished both children a good
day as the school bus came to rest where we waited.

These notes close off my informal observations on Miriam’s computational
development. Miriam shows herself clearly in command of com-
plicated procedures for mental arithmetic, as witness her computation
of 4 times 90 with her decadal additive procedures and their integration
with unary adding. The contrast of computation performed on numbers and
money document the interaction of computation and microworld well-known


Vn106.1 Tic Tac Toe and Nim 10/22/77


Miriam’s Tic Tac Toe play shows an opening game played only with Glenn before and some surprising rigidity. When we play a subtraction arithmetic form of Nim, Miriam adduces “going second” as the efficient cause of her winning game 2. This appears to be as a consequence of our playing with hexapawn; this idea — I call it a vanguard issue — appears to be one Miriam has become sensitized to and is trying to fit into other microworlds.

Vignette 106, page 1 Scanned from Original Fair Copy

(click to enlarge scanned image; back-arrow to return here)
Vn106-1 scanned; no digital source available

Vignette 106, page 2 Scanned from Original Fair Copy

Vn106-2 scanned; no digital source available


Vn107.1 Self-Understanding 10/22/77

My cousin’s wedding has been a day of reconciliations, of growing
closer to family from whom I had been long and much estranged. After a
late breakfast, we attended the wedding. I felt proud of Robby later
when he told me the nicest part of the wedding was a piano-organ duet
(‘Jesu, Joy of Man’s Desiring’) even though my engagement was other.
As I later told my cousin, the groom, in a scene reminiscent of the end
of The Madwoman of Chaillot wherein I stuttered several times
then spoke clearly, I came to bear witness that marriage and paternity were
the two great blessings of my life.

At the reception, as we arrived early I took a table for 8 and then
asked my brother, his family, and my father to join us four. There, and
at a later party for the immediate family, we spoke much with Dave (my
brother) and his wife. As their daughter has gone through school they
have become appalled at the quality of the “education” to which she has
been subject and indignant at the pretense of knowledge ignorant
teachers make. (We spoke freely because I told them my difficulty in
foreseeing an academic future was that I could not endure the pretense
of knowledge with its implicit deceit and manipulation of other people
that the professorial stance systematically demands.) I explained to
them parts of our newly completed project: one of our goals was to render
a child more articulate, to give a child better control of his own
mental procedures and knowledges.

Miriam was playing chase outside with Robby and Peter (a second
cousin, her junior by nine months). When Peter last tagged her, he hit
her in the back of the neck and pulled her hair (thus her story goes).
I found Miriam outside, sobbing and very much out of breath. I would
have judged she needed a dose of her wheeze-suppression medicine at
that time. I loaned Miriam my handkerchief and speculated that his
unkindness had been an accident, or perhaps a thoughtless act, but
surely not a mean one directed at her as a person. Inside, my brother
sat down with Miriam, who was still wheezing heavily, in an out-of-the-
way place. As he subsequently related their conversation to me, Dave
told her of his severe childhood asthma, a difficulty he suffered when
the practice was less sophisticated and medications fewer than today’s:
he had found that through conscious effort, he could stop an impending
asthma attack, bring his breathing and his emotions under sufficient
control that his bronchi could recover from the particular assault they
suffered in a given incident. Miriam tells me they made friends. Dave
said if Miriam comes to visit him, she can play in the large playhouse
he made for his daughter (almost 7 years Miriam’s senior) and could
watch for the deer which visit at his four apple trees.

Later in the evening I accosted Miriam outside. She was again
breathing heavily, engaged once more in a game of chase with the two
boys. “Come walk around slowly with me.” When Miriam refused, I
pointed out how she was breathing so heavily and that I didn’t want her
to end up wheezing. She explained to me, “Daddy, I have a very good
trick, to stop it when I have trouble breathing.” “How’s that?” I asked.
“I just think about it [pointing to her head], and after 5 minutes, or
maybe even 15, I won’t be breathing so hard.” I left Miriam playing tag.

I reported Miriam’s reply to my brother, who said this was
substantially the advice he had given her and filled in the information
I noted previously. Dave remarked further that he didn’t really under-
stand my description of our project’s work at Logo but volunteered the
judgment that he had never met so young a child so well able to under-
stand the idea of controlling her own processes.

This incident reports one example of how Miriam’s work on this
project has developed a perspective on self-control which may be
profoundly valuable for her in an entirely separate area of her life —
controlling her allergic reactions.

Some more detailed notes. My brother is an engineer, not an
educator nor a psychologist, so his exposure to young children is limited
to his daughter and her friends. His daughter is in her school’s pro-
gram for ‘gifted’ children, which fact I cite as witness that he is used
to having a bright girl child around. Further, he is a design engineer
for microcomputer-based milling machine control systems; by this I imply
that he is used to thinking in terms of procedures and control.

I would not claim that Miriam understands herself in the profound
sense of placing herself coherently in her world. It is clear she can
talk with and comprehend the ideas of a mechanistically-oriented but
sophisticated 40-year-old engineer in his attempt to explain what he
views as a milestone of self-understanding. It is very likely that her
ideas of herself in this respect are influenced by our work at Logo (cf.
Vignettes 87, Turtle Tactics, and 88, One or Many Minds). It might be
more direct to say that Miriam can establish a theory of herself as an
object. (For a discussion of whether that is a good thing, see Vignette 81,
Imitating Machines.) If one criticizes a culture or subculture for
leading people to think mechanistically about themselves, one criticizes
an approximation to the actual human condition — and are not approximate,
wrong theories a first step toward the truth? Contrast a theory I might
impute to Miriam, wherein she sees herself partially as a coughing robot
who can be commanded to stop (by another agent’s insistent
will), with an alternative conception — that of a small creature wakened
in the dark of her bedroom at midnight by coughings which fall her way
through ill luck, whom nothing can help. The wrong, mechanical theory
may be the lesser evil.


Vn108.1 Miriam Doesn’t Stop 11/1/77

I have ceased collecting data for this project, have focused my
attention on the data reduction problem, but Miriam keeps growing, making
breakthrough after breakthrough. This afternoon, for example, I sat
transcribing videotapes in the reading alcove. Miriam, waiting in place
the ten minutes till Sesame Street should appear on TV (we don’t turn on
the TV till the scheduled time for a chosen program arises), was musing
on the couch. She mentioned something about 10 sixties. I could see
her, in her half-reclining position, lifting fingers up and down. A
short time later she exploded; “Hey, Dad! 10 sixties is 6 hundred 20.”
“Wow! How did you ever get an answer like that?”

She explained and demonstrated so quickly I had trouble keeping
pace while I wrote down her computation. She used her finger counting
to control her decadal arithmetic addition procedures thus:

first result -- 620
recapitulation --

Finger count   intermediate computation
       1               60 + 60          120
       2              120 + 60          180
       3              180 + 60          240
       4              240 + 60          300
       5              300 + 60          360
       6              360 + 60          420
       7              420 + 60          480
       8              480 + 60          520     [an error]
       9              520 + 60          580
      10              580 + 60          6. . . .

At this point Miriam hesitated. . . . “Wait. . . . 560 plus 60 is. . . no. . . 580
plus 60 is 640. 640 is the answer.”

This performance of Miriam’s is noteworthy several ways. Contrast
this “product” with 4 x 90 of Vignette 106. Notice that the computation
of Vignette 106 is assembled AD HOC. The intermediate results, as numbers,
are manipulated with legitimate and varied operations (addition
and subtraction) to give other especially good intermediate results
which simplify the computation, e.g. 20 is taken from 80 and added to
280 to produce the ‘better quality’ intermediate sum 300; 60 is tacked
on as a simply addable residuum (confer here Seymour Papert’s article
on ‘The Mathematical Unconscious’). This computation is different. The
addition procedure itself is manipulated by controlling its iterations
through counting; the control is independent of the intermediate results.
Counting by non-unary increments (Miriam’s method of multiplying single-
digit numbers) has been replaced in a hierarchical control structure by
the general addition operation. (Confer here the data of Protocol 21,
Multiplying, from the series on Robby’s development.)

This is a further incident giving evidence that “you can’t schedule
learning” (cf. Vignette 91, Squirming and Thinking). Although Miriam
lives in a micro-culture wherein computational issues easily surface,
this particular problem of 10 times 60 is one she posed herself, one
clearly at the expanding periphery of her competence. I claim that, for
whatever reasons (including but not limited to sibling competition),
multiplication has become a vanguard issue of Miriam’s concerns; that
one sees the natural surfacing of such concerns and real intellectual
growth occurring in the interstices of other activity. This claim does
not argue Miriam learns no other way — but this incident shows how
engaging and powerful such learning is. It also argues again that to
study learning, you have to go where the person does it and be there
when it happens.


Vn109.1 Tic Tac Toe 10/4/77

These 5 games are revealing of Miriam’s knowledge and ignorance both. Game 2 reveals more of my failings than I am happy to admit, but its contrast with game 3 permits a central revelation of her thinking about tic-tac-toe. These two together show by how much good fortune (when it occurs) is preferable to good planning. Throughout this session I prompted Miriam to think out loud and make predictions, hoping that she would thereby illuminate her representation of the game. The consequence is evidence how well articulated is her knowledge of what she does in specific cases.

Game 1: Miriam moves first (letters)

         A | 3 | C    
           | 2 | D    
         1 |   | B 

[after Miriam’s opening] I’m going to ask you some questions. Will you answer them?


[placing 1] Can you beat me?

Think so.

Go ahead.

[moves B]

Do you have me beat already?


Can you show me how?

If I put one here [at ‘C’], I’ll get two ways to win. . . 3 ways to win. One [B – C], two [A – C], three [A – B].

Can I go anywhere to stop you from getting those?

I don’t know.

Suppose I go up here [at’C’]; could you still beat me?



[places her index finger on 2]

Ah, yes. The way things are [gesturing from A to B], do I have a forced move? . . . So I have to go here [moves 2], and you still get two ways to win.

[moves C] C. Go!

Go, huh? Hum. All right [moving 3], all right.

[moving D] D! [pointing to C] You know why I went there?


If I went here [pointing to 3], you would put yours down there [pointing to C].

That’s right. I guess you had a forced move too.

Yeah [agreeing that such was her reason]. Yay! I win!

Game 2: Bob moves first (numbers)

After Miriam’s center response, I realized I was myself so unfamiliar with games of this opening I didn’t have any specific plan to follow. I was confused and not wanting to keep Miriam waiting, moved aimlessly at 2. The game thus becomes pointless but does exhibit Miriam’s defensive play without confusion by any aggressive objective (hers or mine).

         c  | 2 | b    
         1  | a | 5    
         3  | d | 4  

Game 3: Miriam moves first in the center

         3 | D1 | 2    
         1 | A  |
         B | D2 | C  

If I move here (1), can you beat me?

It will be sort of like the same game.

Same game as what?

The last game. Go!

You think it will?



[moves B — after hesitating and moving her hand between corners B and 2; laughs]

Let’s see. I have a forced move now [moves 2]. How do you figure out where to go next?

I just pick a space [moves C].

Why is that a good space?

I don’t know.

You have no idea?

I just pick a space.

Why don’t you move here [pointing to side opposite 1]. I think that would be a good place.

Nahh. I want to move there [pointing to C].

Is there any reason?


You just don’t want to tell me. Here. . . . I’ll stop you [places 3] along your way to win there.

[quickly moves D1 between 2 and 3]

Did you block me?


‘Cause you thought I had a way to win?

Yeah [it’s obvious] 3 and 2.

That’s right. I had a way to win. Do you think it’s better to block somebody who’s got a way to win or do you think it’s better to win yourself?


Do you think you have a way to win?


May I call your attention, Miriam, to a way to win you could have had? [points to D2]

[moves D1 to D2]

That’s why I asked so many questions. I wanted to know if you knew you had two ways to win.

No, I didn’t. . . . Tic-tac-toe, three in a row.

Miriam became angry when I argued her victory ‘didn’t count’ since I had to show it to her.

Game 4: Bob moves first

This game shows Miriam’s confusion of move 2 in a game of form VII-B (the only safe response to a corner opening) with move 1 of game form IV (cf. Learning: Tic-tac-toe ). This is an explicit example of configuration dominating to the exclusion of serial information.

         1 |    |     
         b | a2 |     
         2 | a1 |   

Can you go any place at all so I won’t beat you? If I move in the corner [moves 1].

One place.

Is there a safe place? Where is it?

[moves a1]

You believe that’s a safe place?


Well. . . shall I prove you wrong?


[moves 2] What now?

[making forced move b] Hold it. I want to have him. [cheats: she moves a1 to a2]

That’s not fair. You moved here [removes a2 to a1].

No [replaces a2 in the center].

Let’s back off, then, if you don’t want to play that game.

Game 5: Bob moves first (restarting game 4 with his opening marker at 1 and Miriam’s at a1)
RESET the figure in a sensible fashion

         1 |   | b3          1 |   | b3   
           | a1|               | 3 |  
         b2| b1| 2           a2|   | 2 

Let’s say you moved there [a1] right off. If I move here [2] what do you do? Can you move any place?

[removes a1 to b1]

Miriam! That’s just not fair.

[reluctantly replaces a1]

Now, where can you move?

I know [moves b1].

[pointing to b2] Why didn’t you move there?

Good idea! [moves b1 to b2]

O. K.? You want to do that?

What? [moves b2 back to b1]

Go ahead and move here. I’ll show you what I’ll do.

[moves b1 to b2] Win?

Take a look at my chances to win.


Do my chances to win come together?


[gesturing to the fourth corner] No?

[grabbing Bob’s hand] No! [moves b2 to b3]

You think that’s a good defense?

[laughing, points to the empty space b2] Here.

Yes, they do.

[moves a1 to a2 as in the second frame] No. I didn’t want you to go there.

When I move 3 in the space just vacated, Miriam sulks and we give up tic-tac-toe for another game.

Miriam exhibits her extensive and flexible command of games of the form of game 1. Her comment, after the opening two moves of game 3, that it will probably be the same as game 2 renders explicit the absence from her thinking of the concept of move order variations as significant in tic-tac-toe. I consider it staggering that anyone could play so well as Miriam does and yet not have a well formulated idea of opening advantage. Game 3 also appears to show a game whose play has (may be interpreted as having) degenerated to a serial procedure with loss of an original, configuration-oriented forking objective. Game 4 shows strong confusion between the 2 move of game VII-B and 1 of game IV. These games permitted no show of table-turning because Bob never clearly won any games.


Vn110.1 Tic TacToe 10/30/77 & 11/12/77

10/30 When Robby and Miriam agreed to play tic-tac-toe together (intending to use Miriam’s ‘magic slate’ which would have left no record of their play), I suggested they play on the chalkboard in the reading alcove. Miriam was granted first move (letters).

Game 1

	    | D  | 2    
	 3  | A  | C    
	 B  | 4  | 1 

Game 2: When Robby moved first (numbers), he chose the corner opening

	 1  |    | a   
	 c  | b  |    	 
	 3  | 4  | 2   

At his move 2 Miriam said, “Oh oh,” apparently sensing the fork’s distant threat, and attempted to circumvent it by moving twice. Her attempt was met by Robby’s loud and justifiable complaint. The game proceeded to Miriam’s defeat.

Game 3: Miriam moves first

	 A  | D  | C    
	 2  | 3  |      
	 B  |    | 1 

In her turn as aggressor, Miriam first complained “Wah!” when Robby moved 1, then went on to defeat him with an expert win. Her conversation highlights her sense of the situation. While Robby, still confident that he had blocked the corner offensive, walked away, Miriam said somewhat gleefully, “Robby, you’re gonna kill me for this,” and then moved B. She then went on to promise him a million dollars in reparations if she should move between A and B. Robby then moved 2; with his move in place, she added, “I wasn’t going there anyway.” When I asked Miriam if she could beat Robby now, she replied, “Yeah, I think so,” and then she did. Robby was not accustomed to being beaten fairly by Miriam, and he was angry. Miriam offered to let him turn the table on her.

Game 4: Robby first

	  c  |   | a    
	  4  | 1 | 3   
	  2  |   | b  

After this game, Miriam was surprised that Robby didn’t know how to turn the tables. I agreed that he did not have so specific an idea as we did of what we meant by “turning the tables.” I interpret Miriam’s failure to block row 3 – 1 – 4 as a gift to Robby, so he wouldn’t “kill her” for her prior victory. Although she also achieved her preferred three-corner configuration, Miriam appeared not very interested in winning the game.

At this point, I was called outside the house on peripheral matters. I told the children I would return shortly and asked them not to play with each other while I was gone. Miriam, true to her word, played a game against herself on her magic slate (game 5).

	 A | D | C    
	   | a | g    
	 b |   | B  

Miriam explained on my return that she had been playing tic-tac-toe against herself, making “smart moves” for both herself and “the other guy.”

11/12 This evening, when I stopped videotape transcription, a quiz show override signal from channel 4 displayed a tic-tac-toe board with this configuration:

	 X |   |      
	   | O |      
	   |   | X 

I shut off theTV, then called Miriam and asked if she had figured out yet how to block a corner opening. She said, “Give me some chalk,” thus volunteering to show me. I reached to the chalk supply, drew a game frame, and placed the corner opening. Once she controlled the chalk, Miriam made moves for both players.

Game 6

	 1 | D | C    
	 b | g |      
	 B |   | a 

Miriam claimed she could block the corner opening thus: “Go in the opposite corner.” After response a, Miriam knew the next move would be B. She made that move, the forced b, and moved C — at which point she realized she was forked! Miriam then claimed “he” would not go there. I replied, “Yes, he would.” Miriam responded, “Yes, he would try hard to win. So I block him there [moving g] and he wins there [moving D].

Two points stand out in these data. As aggressor, Miriam is unquestionably able to defeat an opponent with an opening game (first two moves) as in game 3. The last two games show a major new capability as the culmination of Miriam’s development: she can now play both sides of the game simultaneously. I consider such an accomplishment the ultimate decentration in any domain, which, when achieved, renders competition-engaged analysis possible.


Vn111.1 Swears 11/30/77

A few days ago I sat at a terminal with Miriam at the Children’s
Learning Lab. In response to the “login” request, Miriam typed “FUCK”
then turned to me and said, “Look, Daddy, I typed a swear.” I responded
non-committally, “Oh yeah. Why don’t you hit new line and see if it
works?” The response came back, “No such user.” I found it amusing to
think back a few months when I overheard Robby making fun of Miriam
because she spelled the word ‘FUKC’. I continued: “You say that’s a
swear. Can you tell me what a swear is?” Miriam didn’t answer.

This evening Miriam demonstrated for me how good she had become at
doing “Miss Lucy.” This is a chanting game for two with partner hand
clapping a la “Patty-cake, patty-cake.” I had earlier seen some third
grade girls playing this game when I rode on the school bus to visit
with the children. With most of her attention focussed on the quite
complex clapping patterns, Miriam began singing:

Miss Lucy had a steamboat, 
   The steamboat had a bell. 
The steamboat went to Heaven, 
   Miss Lucy went to --
Hello, operator, 
   Give me number nine, 
If you disconnect me, 
   I'll cut off your -- 
Behind the 'frigerator 
   There is some broken glass. 
Miss Lucy sat upon it 
   And cut her big fat -- 
Ask me no more questions, 
   I'll tell you no more lies. 
The boys are in the bathroom 
   Pulling down their -- 
Flies are in the meadow, 
   Bees are in the grass. . .

She then called out, “Robby, what comes next?” I was tempted to tell
her myself. The sense of deja vue was very strong, for the tune was one
I knew as a child with these words:

Lulu had a baby, 
   She named him Tiny Tim.
Put him in the piss pot 
   And learned him how to swim. 
He swam to the bottom, 
   Swam to the top. 
Lulu got excited 
   And grabbed him by his -- 
Cocktail, ginger ale, 
   Five cents a glass. 
If you don't like it, 
   Stuff it up your --
Ask me no questions, 
   I'll tell you no lies. 
If you ever get hit with a bucket of shit, 
   Be sure to close your eyes.

When Robby did not respond to her question, Miriam turned to me and said,
“That song sure has a lot of swears in it, doesn’t it, Daddy?” I agreed.
“Michelle taught you the hand clapping, you said. Is she the only one
who knows all the swears?” Miriam confided to me that really everyone
knew them. I admitted I knew many, possibly some she didn’t know.
Miriam’s curiosity rose. I established my claim by running past her some
gutter Italian I had learned in grade school and a few Spanish phrases
I picked up in the Army. Miriam was impressed. I remember being similarly
impressed myself recently when a friend indulged in some exemplary
Afrikaans. I couldn’t understand or mimic his performance, but it
appeared he was mouthing a string of unimaginably vulgar and insulting

Songs such as those of Lulu and Miss Lucy obviously are broadly
dispersed and endure in the child culture we all pass through and no
longer attend to. Beyond the fun implicit in violating the petty taboos
against vulgarity, these rhymes engage the children in memorizing chants,
the crucial humor of which is found in the punning of the terminal rhyme.
Children learn the puns first and realize their double meaning after.
For example, Miriam did not appear to understand the pun on ‘BEHIND’ in
the Miss Lucy song.


Vn112.1 How Her Teacher Sees Miriam 12/7/77

Miriam’s teacher, Sue, sees her as a special child in several ways.
Her surprise at Miriam’s easy solution of class inclusion problems (cf.
Vignette 90, Meeting Miriam’s Teacher) shows she had reason outside of
anything I told her in our first meeting. She learned of Miriam’s continuing
work at the Logo project and was favorably impressed by our links
with the now-respectable scientist Piaget. Thus Miriam appears special
by developmental progress for her age and by the experience of her ongoing
engagement in a serious study.

As The Intimate Study concluded, the children asked if they could
bring their classmates over to visit Logo. I agreed to help them work
that out if they wanted to, on condition that a few children came at one
time and that Robby and Miriam be the ones who ran the show. Both accepted
this scenario as the best one. Robby suggested that their teachers
be first to visit (I don’t know why). Miriam was not keen on the idea
but didn’t argue enough to undermine Robby’s support of the plan. About
the middle of November, the two teachers spent approximately 2 hours at
Logo. The children showed off their computer pictures and their desks,
then explained their work to the teachers. I stayed in the background
as much as possible. Both wanted to play Wumpus, but because this was
confusing to their teachers, they showed them SHOOT and its variations,
explaining the primitives and exhibiting the arithmetic tasks the game
involved them in. Otherwork included the use of POLYSPI and INSPI,
drawings, and a text manipulation work. I believe the teachers were
impressed by the work and the children’s command of it. Sue’s note (see
Addendum 112 – 1) witnesses her response.

Yesterday Gretchen met with Sue for an evaluation conference. (The
report is attached as Addendum 112 – 2, 3, and 4). I was unable to attend
the meeting, but Gretchen recalls these comments:

- Miriam gets a great deal of pleasure from seeing and playing with 
     her school friends.
- Miriam always did her work with a great deal of attention to detail, even
     if she was merely drawing to fill in time between organizeed activities.
- Miriam didn't copy from other people, either to get directions 
     for what she should be doing or to get an idea.
- Miriam cooperated and worked well with her classmates, but not 
     merely that. She tried to help them and was able to do so.
- Miriam seemed to enjoy solving problems. Her focus was not on getting 
     the answer; she seemed to enjoy the process of working out problems, 
     to take pleasure in the process more than in the result.

These notes record a view of Miriam independent from mine.

Addendum 112-1

Note from Miriam’s Teacher

Vn 112-1 Teacher note

Addendum 112-2

Conference Report, page 1

Vn 112-2 Conference report, pg 1

Addendum 112-3

Conference Report, page 2

Vn 112-3 Conference report, pg 2

Addendum 112-4

Conference Report, page 3

Vn 112-4 Conference report, pg 3


Vn113.1 Steady State 12/8/77

A few nights ago, Miriam approached me: “Dad, why do we have to
spend 6 hours in school every day?” “Why do you ask?” I countered.
Miriam continued, “It sure is a long time.” When I first asked what
was the problem, the answer came back that the work was too hard, there
were so many math papers to do, and so forth (but note that Miriam’s
work of choice at school is doing math papers; Cf. Addenda 112 – 2, 3).
Finally Miriam said, “It’s just boring.” And then, “Do I have to go to

Two years back, I recall Robby asking if he could quit school at
the end of 3 months in the first grade. He argued that he knew how to
add and had learned how to read and that there was little more the schools
could teach him. Miriam’s position is the same. I told her she can stay
home from school any time she wants except on certain days when Gretchen
and I might both have to be out of the house — and that this would be
the case especially when the baby is due. Beyond giving that permission,
I offered a little advice of this sort. “School may be boring, but you
will have friends to play with there. It can be boring at home as well;
while I’m working I won’t be able to play with you as much as you might
like, nor will I be going over to Logo too frequently.” I offered to
take Miriam to Logo whenever I go there, either going over after school
or telling her in the morning of my plans.

Since that conversation, Miriam has several times declared she was
not going to school. She stayed in bed, and I didn’t argue or disapprove
at all. All those times she subsequently changed her mind, got dressed
in a rush, and hurried out to await the school bus.

Recently Miriam has learned two things at school she values. The
‘academic’ learning is that there are 2 sounds for the A vowel. She
knows one is long A and the other short A and that the first is
distinguished by its spelling with a terminal silent E. Her example of the
distinction was the couple HAT/HATE. She was not too interested when
I suggested we play with the voice box at the lab to make it talk with
long and short vowels. Miriam comments that she can’t remember learning
anything else besides the spelling of a few words — and one important

The student teacher of her class taught Miriam how to twirl a baton.
Baton twirling first engaged Miriam’s interest in kindergarten when her
friend Michelle brought hers to school. At Miriam’s request, I bought
her one which she has played with discontentedly since then. After her
one day’s instruction, Miriam has marched, posed, and practiced before
the glass doors of our china closet, declaring herself a “batonist” (a
word she is conscious of having made up.)

At Logo, too, Miriam’s current interests are primarily physical
skills. She plays with the computer (Wumpus, and lately some new facil-
ities I’ve shown her) but her first choices are the hula hoop or jump
rope. An incident occurring last night gives evidence of what may be
the outstanding consequence of her learning during The Intimate Study —
what I refer to is her sensitivity to instruction and advice couched in
procedure-oriented terms:

Miriam had convinced Margaret Minsky to turn a long rope for
Miriam’s jumping (the other end being tied to doorknob). Miriam tried
hard and long to jump into an already turning rope. She attended
carefully to the rope and at the right time moved toward the center —
but only a short distance in that direction. In consequence, she got
her head inside the space, but the turning rope regularly caught on her
arm. Miriam had no good answer when I asked if she could recognize the
specific problem. I asked if she could take some advice and said she
should jump onto a line between Margaret and the doorknob. Miriam could
not. I put a paper napkin on that line — but the turning rope picked
it up and away. José Valente drew a chalk line. Miriam took the chalk
and drew a box to jump into. Now she was ready.

Miriam’s first attempt failed because she jumped into her box with-
out attending to the rope. Then she regressed to watching the rope and
moving only a little. Finally, “Miriam,” I said, “you’ve got a bug in
your SETUP procedure. You’re doing only one thing at a time. You have
to do both things at once.” On her next try, Miriam jumped into the
turning rope successfully. I did not see her thereafter exhibit either
of her two earlier bugs (too little movement or not watching the rope).
This incident occupied about 3 minutes.

Miriam finds school boring, but not depressing. Though allowed to
stay home, she goes to play with her friends. Of most immediate and
spontaneous interest to her are physical skills. She shows herself
very capable of using advice formulated in concrete terms focused on
separate procedures.


Vn114.1 The Game Goes Ever On 12/28 & 29/77


In the first incident, Miriam invents the idea of opening advantage for “Tic Tac Toe two in a row.” I believe this is connected to her introduction to Hexapawn (a pawn capture gain played on a 3×3 board) as a reduced form of chess, and my invention of “half a game” of checkers as a reduced form. This invention of Miriam’s is a significant advance whose development I will follow in its application to Tic Tac Toe Three in a Row (cf. Home Session 20, Tic Tac Toe Finale).

Miriam’s defeating the Children’s Museum computer brings her back as master to her point of engagement with the game.

Vignette 114, page 1, scanned from Original Fair Copy

(click on the image to englarge it; back arrow to return here.)
Vn 114-1 Scanned Original Fair Copy

Vignette 114, page 2, scanned from Original Fair Copy

Vn 114-2 Scanned Original Fair Copy


Vn116.1 Transferring a Good Trick 1/3/78

Miriam, not imagining yet that she will one way or another make
a living, sees her best hope of getting a lot of money as inheriting my
money. Thus my impending demise is a subject on her mind and one that
involves her in computations. At lunch today:


Daddy, if you die in another 37 years — no, if you die in another 30 years you will be 67.

Right. But suppose I live those 37 years. How old will I be then?

(After a short pause, wherein she raised and lowered a few fingers) 74.

That’s absolutely correct. How did you ever figure that out?

I know a good trick. See, you have the 67. And you know the other 7?

(Nodding assent here)

Well, that’s like a 3 and a 4. So I took the 3 with the 67 and that’s 70 and then the 4 left over made 74.

That’s beautiful, sweetheart.

This is the first time I have witnessed Miriam doing a sum with
a decade crossing without the use of a counting-up procedure to sum the
secondary units addend with the intermediate result.

What I find most striking in this decomposition of a single
units digit is that the trick (though similar to her reduction to nines
technique for carrying) was first explicitly applied as a procedure for
mental addition in decadal arithmetic (cf. Vignette 105, Decadal Compu-
tation). Thus here we witness a procedure developed for summing large
numbers being retrofitted to addition of small numbers, and in that
microworld supplanting (in this case) the serial counting-up procedure.