Excerpts, Part IX (Pearls & Sacks)

Excerpts from Must Read Books & Articles on Mental Health Topics
Books, Part IX

Gestalt Therapy Verbatim- Frederick Pearls
Part II- Dreamwork Seminar, pp. 73-89

    Basically I am doing a kind of individual therapy in a group setting, but it's not limited to this; very often a group happening happens to happen. Usually I only interfere if the group happening comes merely to mind-fucking. Most group therapy is nothing but mind-fucking. Ping-pong games, "who's right?," opinion exchanges, interpretations, all that crap. If people do this, I interfere. If they are giving their experience, if they are honest in their expression-wonderful. Often the group is very supportive, but if they are merely, "helpful," I cut them out. Helpers are con men, interfering. People have to grow by frustration--by skillful frustration. Otherwise, they have no incentive to develop their own means and ways of coping with the world. But sometimes very beautiful things do happen and basically there are not too many conflicts, everybody who is in the group participates. Sometimes I have people who don't say a single word through the whole five-week workshop and they go away and say that they have changed tremendously, that they did their own private therapy work or whatever you want to call it. So anything can happen. As long as you don't structure it, as long as you work with your intuition, your eyes and ears, then something is bound to happen.
    Two years ago I read a paper at the American Psychological Association. I claimed all individual therapy to be obsolete and I pointed out the advantages of the workshop. I believe that in the workshop, you learn so much by understanding what's going on in this other person, and realize that so much of' his conflicts are your own, and by identification you learn. Learning equals discovery. You discover yourself, and awareness is the means of discovery.
    Now I'm slowly coming to the insight that workshops and group therapy also are obsolete, and we are going to start our first Gestalt kibbutz next year. A Gestalt kibbutz is so far the following fantasy, though we have already some actual materials available. I expect to have a permanent number of people, about 30. The division between staff and seminarians will be obsolete. The main thing is, the community spirit enhanced by--let's call it for the time being, for lack of a better expression, therapy. The whole thing is meant to be growth experience and we hope that in this time we can produce real people, people who are willing to take a stand, people who are willing to take responsibility for their lives.
    In our work here, with Gestalt Therapy, we distinguish two types of work. One is the seminar, and one is the workshop. The workshop is a very limited number of people, up to fifteen, and there we work. The large week-end seminar has another purpose--to get you acquainted with what we are doing, and in spite of this, I hope you still will learn something. Now these lecture-demonstration seminars are not therapeutic workshops. They're a kind of sampling situation, and any growth experience or therapeutic experience is purely coincidental.
    In order to give some idea of what Gestalt Therapy is, there are always a number of people who volunteer to work with me, and I want to clarify my position. I am responsible only for myself and for nobody else. I am not taking responsibility for any of you--you are responsible for yourselves. Fortunately or unfortunately, I've lately gotten such a reputation as a therapist that I can't possibly live up to it. It was about three years ago when I finally could accept what people always told me, that I was a genius. This lasted only three months, and I discovered that I didn't have it in me to be a genius any more. It really doesn't matter one way or another.
    I am not God, I am a catalyst. I am well enough versed in understanding projections and so on, to be able to differentiate when it's observation, or whether I have to take a role in this person's life--they make me a wailing wall, or a papa, or a scoundrel, or the wise man. My function as a therapist is to help you to the awareness of the here and now, and to frustrate you in any attempt to break out of this. This is my existence as a therapist, in the therapy role. I haven't managed it yet for many other segments of my life. You see, like every other psychologist or psychiatrist, I solve my problems to quite an extent outside. The fact that I'm so happy in integration means that my own integration is incomplete.
    So if you want to go crazy, commit suicide, improve, get "turned on," or get an experience that will change your life, that's up to you. I do my thing and you do your thing. Anybody who does not want to take the responsibility for this, please do not attend this seminar. You came here out of your own free will. I don't know how grown up you are, but the essence of a grown-up person is to be able to take responsibility for himself--his thoughts, feelings, and so on. Any objections?... Okeh.
    Basically, I would say that we encounter two types of clients or patients, and roughly speaking there are the ones who come with goodwill, and the others, those who are clever. The clever people are usually recognized by a specific kind of smile, a kind of smirk, a smirk that says, "Oh, you're an idiot! I know better. I can outwit you and control you." And whatever one tries to do will run off, like the water off the famous duck's back, and nothing will penetrate. These people need quite a bit of work. Very many people do not want to work. Anybody who goes to a therapist has something up his sleeve. I would say roughly 90% don't go to a therapist to be cured, but to be more adequate in their neurosis. If they are power mad, they want to get more power. If they are intellectual, they want to have more elephant shit. If they are ridiculers, they want to have a sharper wit to ridicule, and so on.
    Now we are going to have some of these here, and in the short time we have at our disposal, I will very often throw them out from this hot seat. But when you find somebody who is really suffering and is bothered by the aridness of his existence, then with his cooperation we can do a relatively quick job.
    Two weeks ago I had a wonderful experience--not that it was a cure, but at least it was an opening up. This man was a stammerer, and I asked him to increase his stammer. As he stammered, I asked him what he feels in his throat, and he said, "I feet like choking myself." So, I gave him my arm, and said, "Now, choke me." "God damn, I could kill you!" he said. He got really in touch with his anger and spoke loudly, without any difficulties. So, I showed him he had an existential choice, to be an angry man or be a stutterer. And you know how a stutterer can torture you, and keep you on tenterhooks. Any anger that is not coming out, flowing freely, will turn into sadism, power drive, and other means of torturing.
    So we don't need any more the year-long therapies. On the other hand, I am often very much over-estimated in what I am doing. I am not perfect, I am a son-of-a-bitch, I am sometimes very nice, I am not omnipotent, I cannot produce any magic, so I have got very much my limitations and very often I find somebody coming forth who has no other aim than to show what a nincompoop I am. I know this anyhow, that in certain situations I am impotent, I am helpless, and I don't have to win.
    So, apart from this limitation, that I reserve the right to break off whatever we do--in some cases I even throw people out--but within this limitation I am available, and please, I am available only within these working hours. Outside these working hours, I am not available. I know some people have the compulsion to interfere with other people's lives, and have to act out their very interesting life, have to run about broadcasting of their tragedies, and so on. They have to choose other victims for that purpose. Apart from this, I am open for work, and I especially prefer to work with dreams. I believe that in a dream, we have a clear existential message of what's missing in our lives, what we avoid doing and living, and we have plenty of material to re-assimilate and re-own the alienated parts of ourselves. In Gestalt Therapy we write the "self" with lower case s, not capital S. Capital S is a relic from the time when we had a soul, or an ego, or something extra special; "self" means just yourself --for better, for worse, in sickness, in health, and nothing else.
    I use six implements to be able to function. One is my skill, one is kleenex. Then there is the hot seat. This is where you are invited if you want to work with me. And there is the empty chair which will implement quite a lot of your personality and other--let's call it for the time being--intrapersonal encounters. Finally, I need someone who is willing to work with me--someone who is willing to stay in the now and do some work with dreams. So, I'm available. Who really wants to work with me and not just make a fool of me?

SAM

Sam: (speaks rapidly) My name is Sam.
Fritz: I have met Sam before. We met before.
Sam: A-across the table, eating.
Fritz: Yah. But you never worked with me.
Sam: No. . .
Fritz: Now please don't change your posture. What do you notice about his posture?
X: He's up pretty tight.
Fritz: He's a closed system. And not only is he a closed system, but the right side goes to the left and the left side to the right. So, how mixed up can you get? He hasn't said anything yet but you can see how much he expresses with the posture. . .
Sam: Yeah, I feet very secure. (laughter)
Fritz: Will you do me a favor? See how you feel when you open up. Yah. . .
Sam: I feel my heart pounding.
Fritz: Ahah. Now we get stage fright. Not quite so secure. And--you see I will often give you some remarks in between--anxiety, as it's called in psychiatry, is considered a very difficult problem. It's actually nothing but stage fright. If you are in the now, you have security. As soon as you jump out of the now, for instance into the future, the gap between the now and the then is filled with pent-up excitement and it's experienced as anxiety...
Sam: I still feel my heart pounding.
Fritz: Yah. Close your eyes and enter the now, namely the experience of your heart pounding and so on. Stay with your body. What do you experience now?
Sam: A very... My whole body, I can feel my heart pound... I feel myself breathing...
Fritz: Yah? What are you experiencing?
Sam: Let's move on.
Fritz: What's your objection to staying in the now? "Let's move on" means, again, towards the future. What's your objection to sitting there?... Do you have any experience like being stuck or feeling impatient or bored or anything?
Sam: I feel like this will be my only chance with you and I better make the most of it, and not spend time on anxiety.
Fritz: Ahah. Will you put Sam in the empty chair and talk to Sam. "Sam, that's your only chance. Make the best out of it." (laughter)...
Sam: Yeah... You're sitting there looking pretty stiff... What did you go up there for?
Fritz: Change seats. Now the term I have for this is "write your script." You invent a script or dialogue between two opponents. This is part of integrating the fragmented parts of your personality, and these usually go in opposites--for instance, topdog and underdog. So talk back to him. Is it a he or she who sits there?
Sam: ( defensively) It's a he.
F: You don't know how many people have a she as topdog where there's a "Jewish mother."
Sam: Well, I'm not so sure any more. (laughter) I don't know why I came up here. just to see if--see if he could get at me, I guess. . . " "That's a hell of an attitude. (laughter) You think you're up here to fight with Fritz?...
No. No, I don't want to fight with Fritz... I don't know why I'm up here... Who are you, anyway?... What's it to you... What's it to you?... (sigh)...
Fritz: You notice I always let the "patient" do all the work. What's your right hand doing?
Sam: Playing with my left hand.
Fritz: Okeh. Can you invent a dialogue between your right hand and your left hand? have them talk to each other.
Sam: I'm going to hold onto you, left hand. It makes me feel good. I wanna hold on to you, too.
Well don't let go….O. K…I just--hey look, left hand. I just saw my left foot move. (laughter) I wonder what that means….hey ah, right thumb, look at my left thumb. I'm gonna touch you. And I love you….That feels very comforting…You know left--left hand, ah, I'm gonna hold you….That's very nice…I don't feel like holding you any more. Now look what you're doing. You're pressing your thumb against your fingers. Looks like eyes. Doesn't it, left hand?..Yeah. You look more like an eye than I do….Yeah.
Fritz: Can you play the eyes now? Go to the audience. Do you have eyes, or has the audience eyes? Do you feel that you're being looked at, or do you have your own eyes and can do some seeing? Or as I call this type, many people are mirror-draggers. They always drag their mirrors around with them and use other people for reflection. They usually have no eyes themselves...
Sam: Hmm... I don't feel ah, governed by all your eyes.
Fritz: What do you see?
Sam: But I'm really not looking at you either. Kind of a-just comfortable to look out and see everybody. But I'm not really looking at you. Scanning... There's my wife... I think you all are kind of curious... Yeah, and yet you care... But not too much.
Fritz: Now play them. Take this chair. "I'm curious but I don't care too much about you."
Sam: I'm curious but I don't care too much about you. Really what I'm doing is waiting for my turn up there. You are kind of an interesting looking fellow, though. A bit closed. You don't look like you let go very much... Probably have a hard time getting any work done the way you're acting. But I suppose you don't know any other way to act.
Fritz: Change seats again.
Sam: I wouldn't exactly call that a caring comment.
Fritz: What would you call it?
Sam: (quietly) I don't think you're on my side, the way I feel. You're just taking care of number one. I'd call that a selfish contentment….(impatiently) Well, you are using up a lot of time. Nothing's happening. Let's get on with the--pretty soon he'll come to me. I'm number 20 or so. How long you gonna sit up there?
just, just lay off! /Fritz: Say this again./
Lay off. /Fritz: louder./
Lay off! /Fritz: louder!/
Lay off! /Fritz: Louder./
LAY OFF!...
What are you getting so excited about? (laughter) No one's trying to get you. Relax...
Fritz: How do you feel now?...
Sam: (sighs) Hmm. I'm holding my breath.
Fritz: How does the world appear to you? The audience...
Sam: Curious, interested, caring, attentive.
Fritz: Do you see anything?...
Sam: Some smiling faces...
Fritz: Anything else? Do you see any colors?
Sam: Now, I do. /Fritz: After I-/After you mentioned it.
Fritz: Ahah. Do you see any lights?
Sam: Now I do.
Fritz: But not before.
Sam: No. Before, I saw a lot of interesting people.
Fritz: I think you saw your mirror again. You used them for mirroring you. They exist only as far as they are of interest to you.
Sam: Yeah. Could be.
Fritz: Okeh. You noticed already something here in Sam--something very interesting--that he has no eyes. In the course of our development we put up a game, a role, instead of actualizing ourselves, and during this process most people develop holes in their personality. Most people have no ears. At best they only listen to the abstractions, to the meaning of the sentences. Usually they don't even hear that. Many have no eyes. They have their eyes projected. They always feel they are being looked at. Other persons have no heart. Many people have no genitals. And very many people have no center, and without a center you wobble in life. Now these are a bit more complicated to investigate but I'm sure that we'll come across these holes in the personality during our work here.

LINDA

Linda: I dreamed that I watch... a lake... drying up), and there is a small island in the middle of the lake, and a circle of... porpoises--they're like porpoises except that they can stand up, so they're like porpoises that are like people, and they're in a circle, sort of like a religious ceremony, and it's very sad--I feel very sad because they can breathe, they are sort of dancing around the circle, but the water, their element, is drying up. So it's like a dying--like watching a race of people, or a race of creatures, dying. And they are mostly females, but a few of them have a small male organ, so there are a few males there, but they won't live long enough to reproduce, and their element is drying up. And there is one that is sitting over here near me and I'm talking to this porpoise and he has prickles on his tummy, sort of like a porcupine, and they don't seem to be a part of him. And I think that there's one good point about the water drying up, I think--well, at least at the bottom, when all the water dries up, there will probably be some sort of treasure there, because at the bottom of the lake there should be things that have fallen in, like coins or something, but I look carefully and all that I can find is an old license plate... That's the dream.
Fritz: Will you please play the license plate.
Linda: I am an old license plate, thrown in the bottom of a lake. I have no use because I'm no value--although I'm not rusted --I'm outdated, so I can't be used as a license plate... and I'm just thrown on the rubbish heap. That's what I did with a license plate, I threw it on a rubbish heap.
Fritz: Well, how do you feel about this?
Linda: (quietly) I don't like it. I don't like being a license plate--useless.
Fritz: Could you talk about this. That was such a long dream until you come to find the license plate, I'm sure this must be of great importance.
Linda: (sighs) Useless. Outdated... The use of a license plate is to allow--give a car permission to go... and I can't give anyone permission to do anything because I'm outdated... In California, they just paste a little--you buy a sticker--and stick it on the car, on the old license plate. (faint attempt at humor) So maybe someone could put me on their car and stick this sticker on me, I don't know.
Fritz: Okeh, now play the lake.
Linda: I'm a lake... I'm drying up, and disappearing, soaking into the earth... (with a touch of surprise) dying... But when I soak into the earth, I become a part of the earth--so maybe I water the surrounding area, so... even in the lake, even in my bed, flowers can grow (sighs)... New life can grow... from me (cries)...
Fritz: You get the existential message?
Linda: Yes. (sadly, but with conviction) I can paint--I can create--I can create beauty. I can no longer reproduce, I'm like the porpoise. . . but I... I'm... I... keep wanting to say I'm food... I... as water becomes... I water the earth, and give life-growing things, the water--they need both the earth and water, and the... and the air and the sun, but as the water from the lake, I can play a part in something, and producing-feeding.
Fritz: You see the contrast: On the surface, you find something, some artifact--the license plate, the artificial you--but then when you go deeper, you find the apparent death of the lake is actually fertility...
Linda: And I don't need a license plate, or a permission, a license in order to...
Fritz: (gently) Nature doesn't need a license plate to grow. You don't have to be useless, if you are organismically creative, which means if you are involved.
Linda: And I don't need permission to be creative. . . Thank you.

LIZ

Liz: I dream of tarantulas and spiders crawling on me. And it's pretty consistent.
Fritz: Okeh. Can you imagine I am Liz and you are the spider? Can you crawl on me now? How would you do this?
Liz: Up your leg and...
Fritz: Do it, do it... (laughter)
Liz: I don't like spiders.
Fritz: You are a spider now. It's your dream. You produced this dream...
Liz: (very quietly) All these people, they're covering me up.
Fritz: Yah. Now, is there anybody here who you would like to take the role of a spider?
X: You mean to be a spider on her? /Fritz: Yah./...
Liz: I don't see anyone that reminds me of a spider. (laughter)
Fritz: In that case let's be satisfied with the dialogue. Put the spider in that chair and talk to the spider...
Liz: (signs) I don't know what to say except to get it off of me.
Fritz: Now be the spider...
Liz: I wanna get somewhere and you're in my way and so I'll crawl over you... That was very symbolic. (chuckles)...
Fritz: What do you say?...
Liz: I feel as though you're inanimate and it doesn't matter if I crawl all over you. /F: Again./ I feel as though you are inanimate and it doesn't matter if I crawl all over you.
Fritz: Say this to the group. . .
Liz: I don't feel that way toward the group.
Fritz: You feel this towards Liz?... Towards whom do you feel this?...
Liz: I don't feel that way. I think the spider feels that way.
Fritz: Oh, you're not the spider.
Liz: No.
Fritz: Can you say this again, "I am not the spider?"
Liz: I'm not a spider.
Fritz: Go on. "I am not a spider."
Liz: I am not a spider.
Fritz: Which means you're not what?
Liz: Aggressive.
Fritz: Go on.
Liz: I'm not aggressive.
Fritz: Give us all the negations; all of what you're not. "I'm not a spider, I'm not aggressive-"
Liz: I'm not... ugly, I'm not black and shiny, I don't have any more than two legs.
Fritz: Now say all of this to Liz. . .
Liz: You're not black and shiny, you only have two legs, you're not aggressive, you're not ugly.
Fritz: Change seats. Talk back.
Liz: Why do you crawl on me?
Fritz: Go on, change seats on your own and write a dialogue.
Liz: Because you're not important.
But that's not true. I am important.
Fritz: Now keep going. Now something begins to develop.
Liz: Who says you're important?
(quietly) Everybody tells me I'm important and so therefore I must be... It's healthy to be important and feel worthy. It's mentally healthy to be--feel self-important and worthy.
Fritz: Sounds like a program, not like a conviction. (laughter)
Liz: (chuckling) It is a program.
Fritz: Change seats again.
Liz: When are you going to believe that you are beautiful and healthy and all these things?
Fritz: Now let the spider say the same-"I am ugly and I want to be beautiful." Let the spider say the same.
Liz: I am ugly and I want to be beautiful. To a spider-lover I probably am... But a lot of people don't appreciate spiders.
Fritz: Okeh, go back and give the spider some appreciation.
Liz: Spiders are necessary because they keep the insect--the flying insect population down. (laughter) Spiders are fantastic because of the webs that they can build.
Fritz: Talk to the spider directly in terms of you. "You are important because you-"
Liz: You are important because you keep the insect population down and you are important because you build beautiful webs... and you're important because you're alive.
Fritz: Now change seats again. . . I would like you to try and let the spider return the appreciation.
Liz:You're important because you're a human being, and there are fifty zillion of you and so what makes you so important? (laughter)
Fritz: Now you notice already the hole here in her personality--self-appreciation; lack of self-confidence. Other people have feelingsof worthiness or something. She's got a hole...
Liz: But it's up to her to fill the hole.
Fritz: No, it's up to the spider.
Liz: What can the spider do about it?
Fritz: Well, find out. Let the spider give her some appreciation...
Liz: Spiders can't think of anything.
Fritz: The spider plays stupid. Yah?
Liz: No. No. She does some neat things but they aren't--she doesn't do them as well as almost anybody she can think of.
Fritz: Are you by any chance suffering from the curse of perfectionism?
Liz: Oh! Yes. (chuckles)
Fritz: So whatever you do is never good enough.
Liz: Right.
Fritz: Say this to her...
Liz: You do things adequately but never right, never perfectly.
Fritz: Tell her what she should do, what she should be like.
Liz: She should...
Fritz: "You should--" Never gossip about anybody who is present, especially when it's about yourself. (laughter) Always make it into an encounter. Talk to her.
Liz: You should be able to do anything and everything and do it perfectly. You're a very capable person, you've got the native intelligence to do it and you're too lazy.
Fritz: Ah! You got the first appreciation--you are capable. At least she admits that much.
Liz: Well she was born with that. She didn't-(laughter)
Fritz: Immediately you say something good about you, here comes the spider and shits on you. Do you see this?
Liz: Well I think that's true.
Fritz: Yah. Now we have got here the typical topdog, underdog situation. The topdog is always righteous--sometimes right, but not too often--and always righteous. And the underdog is willing to believe the topdog. Now the topdog is a judge, is a bully. The underdog usually is very canny and controls the topdog with other means like manana or "You're right," or "I try my best," or "I tried so hard," or "I forgot," things like that. You know that gimmick?
Liz: Oh yeah.
Fritz: Okeh, now play the topdog-underdog game. The topdog sits here and the underdog there.
Liz: Why don't you ever do, ever-anything perfectly?
Because I try to do too many things. (laughter) I don't have enough time to spread myself around, and I like to read
Why do you like to read? To escape?
Fritz: What a mean topdog. (laughter)
Liz: Yes, but it's also to improve my mind. (laughter) get some enjoyment out of life, besides being perfect.
Fritz: Say this again. Say this again. . . Say this again you...
Liz: I have to get some enjoyment out of life besides being perfect.
Fritz: This time I want to introduce a new element. Let the topdog go on talking to her, and I want her each time to answer back "fuck you" and see what happens.
Liz: You have a responsibility to yourself to fulfill yourself and get the most out of life and experience the most things and so on... Fuck you... But the topdog's right. . .
Fritz: Say this to-
Liz: But you're right.
Fritz: Who is it? Papa, or Mama, or both together?
Liz: Grandma.
Fritz: Grandma. Ahah. So put Grandma in that chair...
Liz: Everything you say is true. . . but I don't want them...
Fritz: I'd like to try to work on a hunch and I might be completely wrong. Say "Grandma, you're a spider. . ."
Liz: (convincingly) Grandma, you're a spider...
Fritz: Change seats. . .
Liz: (grandmotherishly) No I'm not, dear. I just want what's best for you. (laughter)
Fritz: That is a stock phrase of the topdog as you probably recognize. . . Change seats again. Now I would like you to close your eves and enter your self. What do you experience right now? Begin to feel something?
Liz: Feels like a spider.
Fritz: What do you feel? What do you experience personally?
Liz: Do you mean physically?
Fritz: Physically, emotionally, so far we have mostly think-think, talk-talk, things...
Liz: I feel like I'm--there's a spider sitting on me and I want to go do something.
Fritz: What do you experience when the spider sits on you?
Liz: It feels like black up here.
Fritz: No reactions to the spider?... If a spider really would crawl over you now what would you experience?
Liz: Adrenalin and jump and scream.
Fritz: How? (Liz halfheartedly brushes away spider) Again. Spider's still there. . .
Liz: (monotonously) I'd jump up and down and scream for Walter to come and get it off of me.
Fritz: Can you hear your dead voice? Are you aware that you are talking literature? Say this again and see whether we can believe you...
Liz: I'd scream and-
Fritz: How?... How would you scream?
Liz: I c--I don't know if I could do it. I can hear it though when I do it. It just comes out.
Fritz: How?...
Liz: (sighs) I feel too structured to scream.
Fritz: Say this to your grandmother now.
Liz: I feel too structured to scream.
Fritz: Okeh, apparently we would have to do quite a bit of work to get through this block of yours, through this armor. But I would like to spend a few minutes on a phony game. Are you willing to cooperate? I want you to write a script, a good girl and a bad girl talking to each other. "I'm a good girl, I do everything my grandmother wants me to do," and so forth. The bad girl says "fuck you" or whatever your bad girl would say.
Liz: I'm a good girl and I use all my potentials to the greatest degree: all my--as my grandmother would say--God-given creative abilities, my God-given intelligence and appearance and whatever. And I'm just a very nice person and I get along well with everybody...
That's very nice for you but you're not gonna get any kicks out of life because I have a very good time and you can go fuck yourself. (to Fritz) All I can think of is things that bad girls are supposed to do to have fun. But I don't-
Fritz: Tell her that. Don't tell me.
Liz: See what you've done to me?... You don't enjoy yourself and I don't enjoy myself and we wallow around in it. I can't be bad and you can't be good...
Fritz: Now this is a point which we would call the impasse. This is where she's stuck. Okeh, be the good girl again.
Liz: Well, if you'd listen to me we'd at least get some kicks being good. You have no self-discipline whatsoever and the greatest joys in fife are productive ones...
The greatest joys in life should just be in experiencing it...Live a little here and now. . .
Fritz: May I have a private consultation with you? Your bad girl--is she really so bad?
Liz: I think other people would think so.
Fritz: Yah? Ask them...
Liz: Walter, would you think my bad girl so bad?
Walter: Ask them. Don't ask me. (laughter)
Liz: Chicken.
X: I want to know which way you feel best up there now.
Liz: Neither one.
Fritz: Yah. This is the impasse. You're stuck...
X: Your bad girl isn't bad enough.
Liz: That's because she's only speaking in generalities. (laughter)
P: I think she's fine.
Q: I do, too.
R: Her bad girl's pretty great.
S: I think the good girl's a god-awful bore.
T: She's awfully self-righteous. The bad girl would be easier to get along with.
U: The bad girl would be much more fun.
V: The bad girl is almost unable to be bad. She's really too good to be called bad.
W: I was hoping you'd feet better being the bad girl after you got up there.
Liz: Well, the bad girl really doesn't feel too self-righteous which is one of the things that the good girl would like to give up.
X: What is bad?
Y: Or good, for you?
Liz: Being unproductive and using your greatest potential-
Fritz: Ahnh-ah. Bad is what Grandmother disapproves of, and good is what Grandmother approves of. When Grandmother feels bad she calls you bad, and when Grandmother feels good she calls you good. She simply killed your soul, and the whole potential of your soul is missing. It's all mind.
Liz: My soul?
Fritz: No, there is only mind. So there's just a little bit of your potential used. I don't see any usage of your emotions, of your femininity, of your joy, joie de vivre. All that is waste-land so far. You are a "good girl." And behind the good girl there is always the spiteful brat. It's the worst possible diagnosis, because in order to be "good" you have to be a hypocrite--to be the good child, the obedient child--and all the opposition goes into spiting yourself. Life always works in polarities like this. On the surface you're open and compliant, while underneath you're sabotaging me, spiting me. A good girl is the girl that pleases poppa, momma, society. A bad girl is the girl who displeases. So, the only way a good child can assert itself is through spite. Spite, in this case, is identity--identical with being somebody, being something. So this is where you are stuck, between compliance and spite. Okeh.
Liz: Thank you, Fritz.
Fritz: You notice that everything deals with the present. All talking about is out, all interpretation, all mind-fucking is discouraged. What is, is. A rose is a rose is a rose. Very strictly, phenomenologicillv, is she in touch with herself, is she in touch with her environment, is sll(., in touch with tier fantasy? And then you notice something else, this change of seats. I believe we are all fractionalized. We are divided. are split up in many parts, and the beautv of working with a dream is that in a dream every part-not only every person, but every part is yourself.

The Man Who Mistook His Wife for a Hat- Oliver Sacks
Chapter 23- "The Twins", pp. 195-213

When I first met the twins, John and Michael, in 1966 in a state hospital, they were already well known. They had been on radio and television, and made the subject of detailed scientific and popular reports. They had even, I suspected, found their way into science fiction, a little 'fictionalized', but essentially as portrayed in the accounts that had been published. The twins, who were then twenty-six years old, had been in institutions since the age of seven, variously diagnosed as autistic, psychotic or severely retarded. Most of the accounts concluded that, as idiots savants go, there was 'nothing much to them' except for their remarkable 'documentary' memories of the tiniest visual details of their own experience, and their use of an unconscious, calendrical algorithm that enabled them to say at once on what day of the week a date far in the past or future would fall. This is the view taken by Steven Smith, in his comprehensive and imaginative book, The Great Mental Calculators (1983). There have been, to my knowledge, no further studies of the twins since the mid-Sixties, the brief interest they aroused being quenched by the apparent 'solution' of the problems they presented.
    But this, I believe, is a misapprehension, perhaps a natural enough one in view of the stereotyped approach, the fixed format of questions, the concentration on one 'task' or another, with which the original investigators approached the twins, and by which they reduced them--their psychology, their methods, their lives--almost to nothing.
    The reality is far stranger, far more complex, far less explicable, than any of these studies suggest, but it is not even to be glimpsed by aggressive formal 'testing', or the usual 60 Minutes-like interviewing of the twins. Not that any of these studies, or TV performances, is 'wrong'. They are quite reasonable, often informative, as far as they go, but they confine themselves to the obvious and testable 'surface,' and do not go to the depths--do not even hint, or perhaps guess, that there are depths below.
    One indeed gets no hint of any depths unless one ceases to test the twins, to regard them as 'subjects'. One must lay aside the urge to limit and test, and get to know the twins--observe them, openly, quietly, without presuppositions, but with a full and sympathetic phenomenological openness, as they live and think and interact quietly, pursuing their own lives, spontaneously, in their singular way. Then one finds there is something exceedingly mysterious at work, powers and depths of a perhaps fundamental sort, which I have not been able to 'solve' in the eighteen years that I have known them.
    They are, indeed, unprepossessing at first encounter--a sort of grotesque Tweedledum and Tweedledee, indistinguishable, mirror images, identical in face, in body movements, in personality, in mind, identical too in their stigmata of brain and tissue damage. They are undersized, with disturbing disproportions in head and hands, high-arched palates, high-arched feet, monotonous squeaky voices, a variety of peculiar tics and mannerisms, and a very high, degenerative myopia, requiring glasses so thick that their eyes seem distorted, giving them the appearance of absurd little professors, peering and pointing, with a misplaced, obsessed, and absurd concentration. And this impression is fortified as soon as one quizzes them--or allows them, as they are apt to do, like pantomime puppets, to start spontaneously on one of their 'routines'.
    This is the picture that has been presented in published articles, and on stage--they tend to be 'featured' in the annual show in the hospital I work in--and in their not infrequent, and rather embarrassing, appearances on TV. The 'facts', 'Under these circumstances, are established to monotony. The twins say, 'Give us a date-any time in the last or next forty thousand years.' You give them a date, and, almost instantly, they tell you what day of the week it would be. 'Another date!' they cry, and the performance is repeated. They will also tell you the date of Easter during the same period of 80,000 years. One may observe, though this is not usually mentioned in the reports, that their eyes move and fix in a peculiar way as they do this--as if they were unrolling, or scrutinizing, an inner landscape, a mental calendar. They have the look of 'seeing', of intense visualization, although it has been concluded that what is involved is pure calculation.
    Their memory for digits is remarkable--and possibly unlimited. They will repeat a number of three digits, of thirty digits, of three hundred digits, with equal ease. This too has been attributed to a 'method'. But when one comes to test their ability to calculate--the typical forte of arithmetical prodigies and 'mental calculators'--they do astonishingly badly, as badly as their IQs of sixty might lead one to think. They cannot do simple addition or subtraction with any accuracy, and cannot even comprehend what multiplication or division means. What is this: 'calculators' who cannot calculate, and lack even the most rudimentary powers of arithmetic?
    And yet they are called 'calendar calculators'--and it has been inferred and accepted, on next to no grounds, that what is involved is not memory at all, but the use of an unconscious algorithm for calendar calculations. When one recollects how even Carl Friedrich Gauss, at once one of the greatest of mathematicians, and of calculators too, had the utmost difficulty in working out an algorithm for the date of Easter, it is scarcely credible that these twins, incapable of even the simplest arithmetical methods, could have inferred, worked out, and be using such an algorithm. A great many calculators, it is true, do have a larger repertoire of methods and algorithms they have worked out for themselves, and perhaps this predisposed W.A. Horwitz et al. to conclude this was true of the twins too. Steven Smith, taking these early studies at face value, comments:

"Something mysterious, though commonplace, is operating here--the mysterious human ability to form unconscious algorithms on the basis of examples."

    If this were the beginning and end of it, they might indeed be seen as commonplace, and not mysterious at all--for the computing of algorithms, which can be done well by machine, is essentially mechanical, and comes into the spheres of 'problems', but not 'mysteries'. And yet, even in some of their performances, their 'tricks', there is a quality that takes one aback. They can tell one the weather, and the events, of any day in their lives--any day from about their fourth year on. Their way of talking--well conveyed by Robert Silverberg in his portrayal of the character Melangio--is at once childlike, detailed, without emotion. Give them a date, and their eyes roll for a moment, and then fixate, and in a flat, monotonous voice they tell you of the weather, the bare political events they would have heard of, and the events of their own lives--this last often including the painful or poignant anguish of childhood, the contempt, the jeers, the mortifications they endured, but all delivered in an even and unvarying tone, without the least hint of any personal inflection or emotion. Here, clearly, one is dealing with memories that seem of a 'documentary' kind, in which there is no personal reference, no personal relation, no living center whatever.
    It might be said that personal involvement, emotion, has been edited out of these memories, in the sort of defensive way, one may observe in obsessive or schizoid types (and the twins must certainly be considered obsessive and schizoid). But it could be said, equally, and indeed more plausibly, that memories of this kind never had any personal character, for this indeed is a cardinal characteristic of eidetic memory such as this.
    But what needs to be stressed--and this is insufficiently remarked on by their studiers, though perfectly obvious to a naive listener prepared to be amazed--is the magnitude of the twins' memory, its apparently limitless (if childish and commonplace) extent, and with this the way in which memories are retrieved. And if you ask them how they can hold so much in their minds--a three-hundred-figure digit, or the trillion events of four decades--they say, very simply, 'We see it.' And 'seeing'--'visualizing'--of extraordinary intensity, limitless range, and perfect fidelity, seems to be the key to this. It seems a native physiological capacity of their minds, in a way which has some analogies to that by which A. R. Luria's famous patient, described in The Mind of a Mnemonist, 'saw', though perhaps the twins lack the rich synesthesia and conscious organization of the Mnemonist's memories. But there is no doubt, in my mind at least, that there is available to the twins a prodigious panorama, a sort of landscape or physiognomy, of all they have ever heard, or seen, or thought, or done, and that in the blink of an eye, externally obvious as a brief rolling and fixation of the eyes, they are able (with the 'mind's eye') to retrieve and 'see' nearly anything that lies in this vast landscape.
    Such powers of memory are most uncommon, but they are hardly unique. We know little or nothing about why the twins or anyone else have them. Is there then anything in the twins that is of deeper interest, as I have been hinting? I believe there is. It is recorded of Sir Herbert Oakley, the nineteenth-century Edinburgh professor of music, that once, taken to a farm, he heard a pig squeak and instantly cried 'G sharp!' Someone ran to the piano, and G sharp it was. My own first sight of the 'natural' powers, and 'natural' mode, of the twins came in a similar, spontaneous, and (I could not help feeling) rather comic, manner.
    A box of matches on their table fell, and discharged its contents on the floor: '111,' they both cried simultaneously; and then, in a murmur, John said '37'. Michael repeated this, John said it a third time and stopped. I counted the matches--it took me some time--and there were 111. 'How could you count the matches so quickly?' I asked. 'We didn't count,' they said. 'We saw the 111.' Similar tales are told of Zacharias Dase, the number prodigy, who would instantly call out '183' or '79' if a pile of peas was poured out, and indicate as best he could--he was also a dullard--that he did not count the peas, but just 'saw' their number, as a whole, in a flash. 'And why did you murmur "37," and repeat it three times?' I asked the twins. They said in unison, '37, 37, 37, 111.'
    And this, if possible, I found even more puzzling. That they should see 111--111--ness in a flash was extraordinary, but perhaps no more extraordinary than Oakley's 'G sharp'--a sort of absolute pitch, so to speak, for numbers. But they had then gone on to 'factor' the number 111--without having any method, without even 'knowing' (in the ordinary way) what factors meant. Had I not already observed that they were incapable of the simplest calculations, and didn't 'understand' (or seem to understand) what multiplication or division was? Yet now, spontaneously, they had divided a compound number into three equal parts.
    'How did you work that out?' I said, rather hotly. They indicated, as best they could, in poor, insufficient terms--but perhaps there are no words to correspond to such things--that they did not 'work it out', but just 'saw' it, in a flash. John made a gesture with two outstretched fingers and his thumb, which seemed to suggest that they had spontaneously trisected the number, or that it 'came apart' of its own accord, into these three equal parts, by a sort of spontaneous, numerical 'fission'. They seemed surprised at my surprise--as if I were somehow blind; and John's gesture conveyed an extraordinary sense of immediate, felt reality. Is it possible, I said to myself, that they can somehow 'see' the properties, not in a conceptual, abstract way, but as qualities, felt, sensuous, in some immediate, concrete way? And not simply isolated qualities-like '111-ness--but qualities of relationship? Perhaps in somewhat the same way as Sir Herbert Oakley might have said 'a third,' or 'a fifth'.
    I had already come to feel, through their 'seeing' events and dates, that they could hold in their minds, did hold, an immense mnemonic tapestry, a vast (or possibly infinite) landscape in which everything could be seen, either isolated or in relation. It was isolation, rather than a sense of relation, that was chiefly exhibited when they unfurled their implacable, haphazard 'documentary'. But might not such prodigious powers of visualization--powers essentially concrete, and quite distinct from conceptualization might not such powers give them the potential of seeing relations, formal relations, relations of form, arbitrary or significant? If they could see '111-ness' at a glance (if they could see an entire 'constellation' of numbers), might they not also 'see', at a glance--see, recognize, relate and compare, in an entirely sensual and nonintellectual way--enormously complex formations and constellations of numbers? A ridiculous, even disabling power. I thought of Borges's 'Funes':

We, at one glance, can perceive three glasses on a table; Funes, all the leaves and tendrils and fruit that make up a grape vine A circle drawn on a blackboard, a right angle, a lozenge--all these are forms we can fully and intuitively grasp; Ireneo could do the same with the stormy mane of a pony, with a herd of cattle on a hill . . . I don't know how many stars he could see in the sky.

Could the twins, who seemed to have a peculiar passion and grasp of numbers--could these twins, who had seen '111-ness' at a glance, perhaps see in their minds a numerical 'vine', with all the number-leaves, number-tendrils, number-fruit, that made it up? A strange, perhaps absurd, almost impossible thought--but what they had already shown me was so strange as to be almost beyond comprehension. And it was, for all I knew, the merest hint of what they might do.
    I thought about the matter, but it hardly bore thinking about. And then I forgot it. Forgot it until a second, spontaneous scene, a magical scene, which I blundered into, completely by chance. This second time they were seated in a corner together, with a mysterious, secret smile on their faces, a smile I had never seen before, enjoying the strange pleasure and peace they now seemed to have. I crept up quietly, so as not to disturb them. They seemed to be locked in a singular, purely numerical, conversation. John would say a number--a six-figure number. Michael would catch the number, nod, smile and seem to savor it. Then he, in turn, would say another six-figure number, and now it was John who received, and appreciated it richly. They looked, at first, like two connoisseurs wine-tasting, sharing rare tastes, rare appreciations. I sat still, unseen by them, mesmerized, bewildered.
    What were they doing? What on earth was going on? I could make nothing of it. It was perhaps a sort of game, but it had a gravity and an intensity, a sort of serene and meditative and almost holy intensity, which I had never seen in any ordinary game before, and which I certainly had never seen before in the usually agitated and distracted twins. I contented myself with noting down the numbers they uttered--the numbers that manifestly gave them such delight, and which they contemplated, savored, shared, in communion.
    Had the numbers any meaning, I wondered on the way home, had they any 'real' or universal sense, or (if any at all) a merely whimsical or private sense, like the secret and silly 'languages' brothers and sisters sometimes work out for themselves? And, as I drove home, I thought of Luria's twins-Liosha and Yura--brain damaged, speech-damaged identical twins, and how they would play and prattle with each other, in a primitive, babble-like language of their own (Luria and Yudovich, 1959). John and Michael were not even using words or half-words--simply throwing numbers at each other. Were these 'Borgesian' or 'Funesian' numbers, mere numeric vines, or pony manes, or constellations, private number-forms--a sort of number argot--known to the twins alone?
    As soon as I got home I pulled out tables of powers, factors, logarithms and primes--mementos and relics of an odd, isolated period in my own childhood, when I too was something of a number brooder, a number 'see-er', and had a peculiar passion for numbers. I already had a hunch and now I confirmed it. All the numbers, the six-figure numbers, which the twins had exchanged were primes--i.e., numbers that could be evenly divided by no other whole number than itself or one. Had they somehow seen or possessed such a book as mine--or were they, in some unimaginable way, themselves 'seeing' primes, in somewhat the same way as they had 'seen' 111-ness, or triple 37-ness? Certainly they could not be calculating them--they could calculate nothing.
    I returned to the ward the next day, carrying the precious book of primes with me. I again found them closeted in their numerical communion, but this time, without saying anything, I quietly joined them. They were taken aback at first, but when I made no interruption, they resumed their 'game' of six-figure primes. After a few minutes I decided to join in, and ventured a number, an eight-figure prime. They both turned towards me, then suddenly became still, with a look of intense concentration and perhaps wonder on their faces. There was a long pause--the longest I had ever known them to make, it must have lasted a half-minute or more--and then suddenly, simultaneously, they both broke into smiles.
    They had, after some unimaginable internal process of testing, suddenly seen my own eight-digit number as a prime--and this was manifestly a great joy, a double joy, to them; first because I had introduced a delightful new plaything, a prime of an order they had never previously encountered; and, secondly, because it was evident that I had seen what they were doing, that I liked it, that I admired it, and that I could join in myself.
    They drew apart slightly, making room for me, a new number playmate, a third in their world. Then John, who always took the lead, thought for a very long time--it must have been at least five minutes, though I dared not move, and scarcely breathed--and brought out a nine-figure number; and after a similar time his twin, Michael, responded with a similar one. And then 1, in my turn, after a surreptitious look in my book, added my own rather dishonest contribution, a ten-figure prime I found in my book.
    There was again, and for even longer, a wondering, still silence; and then John, after a prodigious internal contemplation, brought out a twelve-figure number. I had no way of checking this, and could not respond, because my own book--which, as far as I knew, was unique of its kind--did not go beyond ten-figure primes. But Michael was up to it, though it took him five minutes--and an hour later the twins were swapping twenty-figure primes, at least I assume this was so, for I had no way of checking it. Nor was there any easy way, in 1966, unless one had the use of a sophisticated computer. And even then, it would have been difficult, for whether one uses Eratosthenes' sieve, or any other algorithm, there is no simple method of calculating primes. There is no simple method, for primes of this order--and yet the twins were doing it.
    Again I thought of Dase, whom I had read of years before, in F.W.H. Myers's enchanting book Human Personality (1903).

We know that Dase (perhaps the most successful of such prodigies) was singularly devoid of mathematical grasp . . . Yet he in twelve years made tables of factors and prime numbers for the seventh and nearly the whole of the eighth million-a task which few men could have accomplished, without mechanical aid, in an ordinary lifetime.

He may thus be ranked, Myers concludes, as the only man who has ever done valuable service to Mathematics without being able to cross the Ass's Bridge.
    What is not made clear, by Myers, and perhaps was not clear, is whether Dase had any method for the tables he made up, or whether, as hinted in his simple 'number-seeing' experiments, he somehow 'saw' these great primes, as apparently the twins did. As I observed them, quietly--this was easy to do, because I had an office on the ward where the twins were housed--I observed them in countless other sorts of number games or number communion, the nature of which I could not ascertain or even guess at.
    But it seems likely, or certain, that they are dealing with 'real' properties or qualities--for the arbitrary, such as random numbers, gives them no pleasure, or scarcely any, at all. It is clear that they must have 'sense' in their numbers--in the same way, perhaps, as a musician must have harmony. Indeed I find myself comparing them to musicians--or to Martin (Chapter Twenty-two), also retarded, who found in the serene and magnificent architectonics of Bach a sensible manifestation of the ultimate harmony and order of the world, wholly inaccessible to him conceptually because of his intellectual limitations.
    'Whoever is harmonically composed,' writes Sir Thomas Browne, 'delights in harmony . . . and a profound contemplation of the First Composer. There is something in it of Divinity more than the ear discovers; it is an Hieroglyphical and shadowed Lesson of the whole World . . . a sensible fit of that harmony which intellectually sounds in the ears of God . . . The soul . . . is harmonical, and hath its nearest sympathy unto Musick.'
    Richard Wollheim in The Thread of Life (1984) makes an absolute distinction between calculations and what he calls 'iconic' mental states, and he anticipates a possible objection to this distinction.

Someone might dispute the fact that all calculations are noniconic on the grounds that, when he calculates, sometimes, he does so by visualizing the calculation on a page. But this is not a counter-example. For what is represented in such cases is not the calculation itself, but a representation of it; it is numbers that are calculated, but what is visualized are numerals, which represent numbers.

Leibniz, on the other hand, makes a tantalizing analogy between numbers and music: 'The pleasure we obtain from music comes from counting, but counting unconsciously. Music is nothing but unconscious arithmetic.'
    What, so far as we can ascertain, is the situation with the twins, and perhaps others? Ernst Toch, the composer--his grandson Lawrence Weschler tells me--could readily hold in his mind after a single hearing a very long string of numbers; but he did this by 'converting' the string of numbers to a tune (a melody he himself shaped 'corresponding' to the numbers). Jedediah Buxton, one of the most ponderous but tenacious calculators of all time, and a man who had a veritable, even pathological, passion for calculation and counting (he would become, in his own words, 'drunk with reckoning'), would 'convert' music and drama to numbers. 'During the dance,' a contemporary account of him recorded in 1754, 'he fixed his attention upon the number of steps; he declared after a fine piece of musick, that the innumerable sounds produced by the music had perplexed him beyond measure, and he attended even to Mr. Garrick only to count the words that he uttered, in which he said he perfectly succeeded.'
    Here is a pretty, if extreme, pair of examples--the musician who turns numbers into music, and the counter who turns music into numbers. One could scarcely have, one feels, more opposite sorts of mind, or, at least, more opposite modes of mind. I believe the twins, who have an extraordinary 'feeling' for numbers, without being able to calculate at all, are allied not to Buxton but to Toch in this matter. Except--and this we ordinary people find so difficult to imagine--except that they do not 'convert' numbers into music, but actually feel them, in themselves, as 'forms', as 'tones', like the multitudinous forms that compose nature itself. They are not calculators, and their numeracy is 'iconic'. They summon up, they dwell among, strange scenes of numbers; they wander freely in great landscapes of numbers; they create, dramaturgically, a whole world made of numbers. They have, I believe, a most singular imagination--and not the least of its singularities is that it can imagine only numbers. They do not seem to 'operate' with numbers, non-iconically, like a calculator; they 'see' them, directly, as a vast natural scene.
    And if one asks, are there analogies, at least, to such an 'iconicity', one would find this, I think, in certain scientific minds. Dmitri Mendeleev, for example, carried around with him, written on cards, the numerical properties of elements, until they became utterly 'familiar' to him--so familiar that he no longer thought of them as aggregates of properties, but (so he tells us) 'as familiar faces'. He now saw the elements, iconically, physiognomically, as 'faces--faces that related, like members of a family, and that made up, in toto, periodically arranged, the whole formal face of the universe. Such a scientific mind is essentially 'iconic', and 'sees' all nature as faces and scenes, perhaps as music as well. This 'vision', this inner vision, suffused with the phenomenal, none the less has an integral relation with the physical, and returning it, from the psychical to the physical, constitutes the secondary, or external, work of such science. ('The philosopher seeks to hear within himself the echoes of the world symphony,' writes Nietzsche, 'and to re-project them in the form of concepts.') The twins, though morons, hear the world symphony, I conjecture, but hear it entirely in the form of numbers.
    The soul is 'harmonical' whatever one's IQ and for some, like physical scientists and mathematicians, the sense of harmony, perhaps, is chiefly intellectual. And yet I cannot think of anything intellectual that is not, in some way, also sensible--indeed the very word 'sense' always has this double connotation. Sensible and in some sense 'personal' as well, for one cannot feel anything: find anything 'sensible', unless it is, in some way, related or relatable to oneself. Thus the mighty architectonics of Bach provide, as they did for Martin A., 'an Hieroglyphical and shadowed Lesson of the whole World', but they are also, recognizably, uniquely, dearly, Bach; and this too was felt, poignantly, by Martin A., and related by him to the love he bore his father.
    The twins, I believe, have not just a strange 'faculty'--but a sensibility, a harmonic sensibility, perhaps allied to that of music. One might speak of it, very naturally, as a 'Pythagorean' sensibility--and what is odd is not its existence, but that it is apparently so rare. One's soul is 'harmonical' whatever one's IQ, and perhaps the need to find or feel some ultimate harmony or order is a universal of the mind, whatever its powers, and whatever form it takes. Mathematics has always been called the 'queen of sciences', and mathematicians have always felt number as the great mystery, and the world as organized, mysteriously, by the power of number. This is beautifully expressed in the prologue to Bertrand Russell's Autobiography:

With equal passion I have sought knowledge. I have wished to understand the hearts of men. I have wished to know why the stars shine. And I have tried to apprehend the Pythagorean power by which number holds sway above the flux.

    It is strange to compare these moron twins to an intellect, a spirit, like that of Bertrand Russell. And yet it is not, I think, so far-fetched. The twins live exclusively in a thought-world of numbers. They have no interest in the stars shining, or the hearts of men. And yet numbers for them, I believe, are not 'just' numbers, but significances, signifiers whose 'significand' is the world. They do not approach numbers lightly, as most calculators do. They are not interested in, have no capacity for, cannot comprehend, calculations. They are, rather, serene contemplators of number--and approach numbers with a sense of reverence and awe. Numbers for them are holy, fraught with significance. This is their way--as music is Martin's way--of apprehending the First Composer.
    But numbers are not just awesome for them, they are friends too--perhaps the only friends they have known in their isolated, autistic lives. This is a rather common sentiment among people who have a talent for numbers--and Steven Smith, while seeing 'method' as all-important, gives many delightful examples of it: George Parker Bidder, who wrote of his early number-childhood, 'I became perfectly familiar with numbers up to 100; they became as it were my friends, and I knew all their relations and acquaintances'; or the contemporary Shyam Marathe, from India--'When I say that numbers are my friends, I mean that I have some time in the past dealt with that particular number in a variety of ways, and on many occasions have found new and fascinating qualities hidden in it . . . So, if in a calculation I come across a known number, I immediately look to him as a friend.'
    Hermann von Helmholtz, speaking of musical perception, says that though compound tones can be analyzed, and broken down into their components, they are normally heard as qualities, unique qualities of tone, indivisible wholes. He speaks here of a 'synthetic perception' which transcends analysis, and is the unanalyzable essence of all musical sense. He compares such tones to faces, and speculates that we may recognize them in somewhat the same, personal way. In brief, he half suggests that musical tones,' and certainly tunes, are, in fact, 'faces' for the ear, and are recognized, felt, immediately as 'persons' (or 'personalities'), a recognition involving warmth, emotion, personal relation.
    So it seems to be with those who love numbers. These too become recognizable as such--in a single, intuitive, personal 'I know you!' The mathematician Wim Klein has put this well: 'Numbers are friends for me, more or less. It doesn't mean the same for you, does it--3,844? For you it's just a three and an eight and a four and a four. But I say, "Hi! 62 squared." ' I believe the twins, seemingly so isolated, live in a world full of friends, that they have millions, billions, of numbers to which they say 'Hi!' and which, I am sure, say 'Hi!' back. But none of the numbers is arbitrary--like 62 squared--nor (and this is the mystery) is it arrived at by any of the usual methods, or any method so far as I can make out. The twins seem to employ a direct cognition--like angels. They see, directly, a universe and heaven of numbers. And this, however singular, however bizarre--but what right have we to call it 'pathological'?--provides a singular self-sufficiency and serenity to their lives, and one which it might be tragic to interfere with, or break.
    This serenity was, in fact, interrupted and broken up ten years later, when it was felt that the twins should be separated--'for their own good', to prevent their 'unhealthy communication together', and in order that they could 'come out and face the world . . . in an appropriate, socially acceptable way' (as the medical and sociological jargon had it). They were separated, then, in 1977, with results that might be considered as either gratifying or dire. Both have been moved now into 'halfway houses', and do menial jobs, for pocket money, under close supervision. They are able to take buses, if carefully directed and given a token, and to keep themselves moderately presentable and clean, though their moronic and psychotic character is still recognizable at a glance.
    This is the positive side--but there is a negative side too (not mentioned in their charts, because it was never recognized in the first place). Deprived of their numerical 'communion' with each other, and of time and opportunity for any 'contemplation' or 'communion' at all--they are always being hurried and jostled from one job to another--they seem to have lost their strange numerical power, and with this the chief joy and sense of their lives. But this is considered a small price to pay, no doubt, for their having become quasi-independent and 'socially acceptable'.
    One is reminded somewhat of the treatment meted out to Nadia--an autistic child with a phenomenal gift for drawing. Nadia too was subjected to a therapeutic regime 'to find ways in which her potentialities in other directions could be maximized'. The net effect was that she started talking--and stopped drawing. Nigel Dennis comments: 'We are left with a genius who has had her genius removed, leaving nothing behind but a general defectiveness. What are we supposed to think about such a curious cure?'
    It should be added--this is a point dwelt on by F. W. H. Myers, whose consideration of number prodigies opens his chapter on 'Genius'--that the faculty is 'strange', and may disappear spontaneously, though it is, as often, lifelong. In the case of the twins, of course, it was not just a 'faculty', but the personal and emotional centre of their lives. And now they are separated, now it is gone, there is no longer any sense or center to their lives.

Postscript

When he was shown the manuscript of this paper, Israel Rosenfield pointed out that there are other arithmetics, higher and simpler than the 'conventional' arithmetic of operations, and wondered whether the twins' singular powers (and limitations) might not reflect their use of such a 'modular' arithmetic. In a note to me, he has speculated that modular algorithms, of the sort described by Ian Stewart in Concepts of Modern Mathematics (1975) may explain the twins' calendrical abilities. Their ability to determine the days of the week within an eighty-thousand-year period suggests a rather simple algorithm. One divides the total number of days between 'now' and 'then' by seven. If there is no remainder, then that date falls on the same day as 'now'; if the remainder is one, then that date is one day later; and so on. Notice that modular arithmetic is cyclic: it consists of repetitive patterns. Perhaps the twins were visualizing these patterns, either in the form of easily constructed charts, or some kind of 'landscape' like the spiral of integers shown on page 30 of Stewart's book.
    This leaves unanswered why the twins communicate in primes. But calendar arithmetic requires the prime of seven. And if one is thinking of modular arithmetic in general, modular division will produce neat cyclic patterns only if one uses prime numbers. Since the prime number seven helps the twins to retrieve dates, and consequently the events of particular days in their lives, other primes, they may have found, produce similar patterns to those that are so important for their acts of recollection. (When they say about the matchsticks '111--37 three times', note they are taking the prime 37, and multiplying by three.) In fact, only the prime patterns could be 'visualized'. The different patterns produced by the different prime numbers (for example, multiplication tables) may be the pieces of visual information that they are communicating to each other when they repeat a given prime number. In short, modular arithmetic may help them to retrieve their past, and consequently the patterns created in using these calculations (which only occur with primes) may take on a particular significance for the twins. By the use of such a modular arithmetic, Ian Stewart points out, one may rapidly arrive at a unique solution in situations that defeat any 'ordinary' arithmetic--in particular homing in (by the so-called 'pigeon-hole principle') on extremely large and (by conventional methods) incomputable primes.
    If such methods, such visualizations, are regarded as algorithms, they are algorithms of a very peculiar sort-organised, not algebraically, but spatially, as trees, spirals, architectures, 'thoughtscapes'--configurations in a formal yet quasi-sensory mental space. I have been excited by Israel Rosenfield's comments, and Ian Stewart's expositions of 'higher' (and especially modular) arithmetics, for these seem to promise, if not a 'solution', at least a powerful illumination of otherwise inexplicable powers, like those of the twins.
    Such higher or deeper arithmetics were conceived, in principle, by Gauss in his Disquisitiones Arithmeticae, in 1801, but they have only been turned to practical realities in recent years. One has to wonder whether there may not be a 'conventional' arithmetic (that is, an arithmetic of operations)-often irritating to teacher and student, 'unnatural', and hard to learn--and also a deep arithmetic of the kind described by Gauss, which may be truly innate to the brain, as innate as Chomsky's 'deep' syntax and generative grammars. Such an arithmetic, in minds like the twins', could be dynamic and almost alive--globular clusters and nebulae of numbers whorling and evolving in an ever-expanding mental sky.
    As already mentioned, after publication of 'The Twins' I received a great deal of communication both personal and scientific. Some dealt with the specific themes of 'seeing' or apprehending numbers, some with the sense or significance which might attach to this phenomenon, some with the general character of autistic dispositions and sensibilities and how they might be fostered or inhibited, and some with the question of identical twins. Especially interesting were the letters from parents of such children, the rarest and most remarkable from parents who had themselves been forced into reflection and research and who had succeeded in combining the deepest feeling and involvement with a profound objectivity. In this category were the Parks, highly gifted parents of a highly gifted, but autistic, child (see C. C. Park, 1967, and D. Park, 1974, pp. 313-23). The Parks' child 'Ella' was a talented drawer and was also highly gifted with numbers, especially in her earlier years. She was fascinated by the 'order' of numbers, especially primes. This peculiar feel for primes is evidently not uncommon. C.C. Park wrote to me of another autistic child she knew, who covered sheets of paper with numbers written down 'compulsively'. 'All were primes,' she noted, and added: 'They are windows into another world.' Later she mentioned a recent experience with a young autistic man who was also fascinated by factors and primes, and how he instantly perceived these as 'special'. Indeed the word special' must be used to elicit a reaction:

'Anything special, Joe, about that number (4875)?' Joe: 'It's just divisible by 13 and 25.' Of another (7241): 'It's divisible by 13 and 557.' And of 8741: 'It's a prime number.'

Park comments: 'No one in his family reinforces his primes; they are a solitary pleasure.'
It is not clear, in these cases, how the answers are arrived at almost instantaneously: whether they are 'worked out', 'known' (remembered), or--somehow--just 'seen'. What is clear is the peculiar sense of pleasure and significance attaching to primes. Some of this seems to go with a sense of formal beauty and symmetry, but some with a peculiar associational 'meaning' or 'potency'. This was often called 'magical' in Ella's case: numbers, especially primes, called up special thoughts, images, feelings, relationships--some almost too 'special' or 'magical' to be mentioned. This is well described in David Park's paper (op. cit.).
Kurt G6del, in a wholly general way, has discussed how numbers, especially primes, can serve as 'markers'--for ideas, people, places, whatever; and such a G6delian marking would pave the way for an 'arithmetization' or 'numeralization' of the world (see E. Nagel and J. R. Newman, 1958). If this does occur, it is possible that the twins, and others like them, do not merely live in a world of numbers, but in a world, in the world, as numbers, their number-meditation or play being a sort of existential meditation--and, if one can understand it, or find the key (as David Park sometimes does), a strange and precise communication too.