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INTRODUCTION (written by Catherine Gold, PhD, clinical psychologist):

Since the following story is going to turn on a well-known but imperfectly-understood psychological phenomenon, a short popular introduction is in order. The story begins with Dr. Joseph Jastrow, who received the first American PhD in psychology in 1886, and went on to found the Department of Psychology at the University of Wisconsin, Madison, where he taught most of his life. Besides his scientific work, Prof. Jastrow was a prolific popularizer of psychology, who wrote articles in nonscientific journals and, for many years, hosted a radio show, “Keeping Mentally Fit” which introduced psychological concepts to the general public. He was also one of the founders of the American Association of University Professors

One of Prof. Jastrow’s many research interests involved illusions (he was a friend of the magician Harry Houdini, who frequently lectured to his classes about illusions and how to create them) and what are now called bistable figures, namely figures which can be seen in one of two possible ways. Among Jastrow’s more famous illusions is the one used to illustrate this story - a figure which can be seen either as a duck or as a rabbit - which plays a key role in the tale. Jastrow’s cartoon first appeared in a popular article published in Harper’s Weekly in November, 1892. It has been studied by hundreds of researchers since, including the philosopher Ludwig Wittgenstein. Recent studies involving it (by Toppino in 2004) show, for example, that children tested near Easter Sunday are more likely to see a rabbit while if those tested in October are more likely to see a duck. Go figure.

TO BECOME AN ILLUSION

Gene Dowling came across Joseph Jastrow’s duck/rabbit illusion in a book which he had received for his 14th birthday from his Uncle Henry. Gene didn’t like his uncle very much, but he did like the book and especially this illusion. Gene also didn’t like being referred to as “he” because, even though there was no doubt that his body was male, he usually felt himself to be female, who should have been named Jean. This was rather confusing to a kid and he had trouble understanding it, let alone putting it in words. Suddenly, everything became clear. He was a bistable person, the same as Jastrow’s figure. Look at it one way, and you see Jean; look at it another way, and you see Gene. Miss Duck and Mr. Rabbit!

This - as Gene/Jean found out later after reading up on the subject - is not the same as being a male crossdresser (who knows he is male at all times though he likes, on occasion, to appear and act female) or being a male-to-female transsexual (who knows she is female at all times even though she was born in a male body). Nor was it a case of dissociative identity disorder (“split personality”) in which a person displays several distinct identities, each of which prevails for various periods of time. No, Gene/Jean wanted to be both male and female simultaneously and to let others perceive him/her whichever way they wish and act accordingly. Such perceptions need not be permanent, either. One minute one should be able to see, and interact with, Gene and the next one could see, and interact with, Jean. It should be possible for two people to perceive and interact with Gene and Jean simultaneously.

(AUTHOR’s NOTE: In order to, imperfectly, realize this concept, I will, from now on, write “Gene” or “Jean” depending on which of these bistable identities I am perceiving at the moment of writing.)

Gene’s parents didn’t understand all of this when he tried to explain it to them. They were simple people and, though they loved him dearly, were more apt to dismiss all of this as “going through a teenage phase”. So long as Gene did not drink or take drugs, or in any other way get in trouble with the law, and so long as he maintained reasonably good grades in school, they pretty much allowed him a free hand. After all, that is the course of action recommended by well-known experts on “parenting” in articles in Readers’ Digest and in People Magazine, which is all that Jean’s mother ever read.

As he passed his 16th year, Gene first tried to explain this theory to his classmate Marina Markov. Marina was a good choice since she, herself, had a slight problem of dual perceptions - on one hand, she was by far the smartest student in her class and was considered by her teachers and some of her friends as the class “brain”, on the other she was also the prettiest and sexiest girl in the class, and was the object of wet dreams by many, if not all, of the boys. Marina and Jean were good friends - girlfriends that is. They liked talking about boys and about fashion. But Gene also felt that Marina was the only person with sufficient brains to understand what he was still trying to formulate.

Marina understood the concept easily enough, but pointed out one basic problem. “Gene” was perceived visually, whereas “Jean” could only be perceived subjectively. She suggested to Gene that he have to change his external appearance to make some room for Jean as well, and at the same time, Jean’s very feminine identity had to allow for some of Gene to be there too. In other words, bistability had to be achieved on the physical and emotional levels separately.

On the physical level, bistability would have to translate into ambiguity in dress and mannerisms. Gene began wearing skinny jeans and tighter tops, as well as gender-ambiguous shoes. (His parents never noticed.) Marina taught him how to apply makeup subtly so that nobody would notice but which would give him the look of a teenage girl, if one wanted to see her. Jean grew her hair longer, but not too long. She could easily pass for a boy, or for a girl, depending on what one wanted to see. The lipstick was there, but maybe it was just a balm for chapped lips. Within several months, Gene had reached the situation where half of the cashiers he encountered in stores would call him “ma’am” and half would call him “sir” - often with the same girl calling him one and then the other on successive days.

Introducing bistability into his emotional and identity levels was harder. Marina and Jean practiced hard. When they would go to the mall or the park, or even in school, Marina would switch her attention from Gene to Jean and force the appropriate reaction, often in mid-sentence or mid-action. They got so good at it that, after a while, Jean could sit at a table in the mall flirting with a boy while, at the same time, Marina was busy flirting with Gene, without the boy noticing. The game got more and more complex and Gene was better and better at it. Jean felt that she had become truly bistable at all levels.

It ended, however, when Gene and Marina graduated from high school. Marina accepted a full scholarship to Cal Tech to study nanophysics, while Gene, whose GPA was much lower, had to make do with a low-interest loan to attend the state university, the campus of which was about 100 miles from his home. In order to save money, he decided to live in the dorms.

CASE NOTES (written by Catherine Gold, PhD, clinical psychologist):

I first met Gene during his sophomore year in college. He had not been coping very well and was referred to the Mental Health Clinic of the University Hospital by the housemaster of his dorm, after he seemed to have fallen into what seemed to be a deep depression and had stayed away from classes for two weeks. The resident who interviewed him was a participant in a special short course on gender psychology which I was delivering at the university while spending a month on research leave. After one of our sessions, she came up to me and told me enough about Gene to pique my interest and so, when she asked me to give my evaluation of Gene, I readily agreed.

I must admit that it was hard for me to decide at first glance whether it was Gene or Jean who walked into the room for our first interview. She was wearing very short shorts (which showed off her pretty and shaven legs), green sandals, and a t-shirt showing the image of a rock singer who was all the rage among teenage girls that year. She was wearing subtle makeup, but no nail polish on her manicured fingers or toes. She smiled when she sat down (and crossed her legs) and did not offer a handshake. I opted for Jean.

I introduced myself and told her that I had read a summary of her file, but would like to hear her story as she tells it. Patiently (she had obviously been through this several times), Gene led me from Jastrow to bistability to Marina’s theory that bistability had to be both external and internal. As the story unfolded, I admit that I saw more of Gene than of Jean. It was too abstract and impersonal to be a girl’s story. When she finished, I asked her if she had any close friends at the university. She told me that she had nobody who was as close to her as Marina was, but six weeks ago she had met a very wonderful boy named Walter, whom she really liked. I asked if Walter knew about her bistability, and she admitted that he didn’t, he had never seen her name written out, and had just assumed that she was Jean. They had been on several dates, until she started feeling depressed and staying in her dorm room.

I asked her if she felt she loved Walter, and she said she did.

Seeming to change the subject, I took out a copy of Jastrow's famous illustration.

“Well,” I asked, “is it a duck or a rabbit?”

“It is what you want it to be,” Jean replied.

“What does it consider itself to be?”

“It is whatever it wants to be at any given moment.”

“In other words, it has no fixed identity, even to itself.”

“Of course not, it is bistable.”

“Don’t you really mean unstable in that case?”

“No.”

“Do you think that it is capable of making up its mind once and for all?”

“Why should it?”

“Having one identity is better than having none.”

“It doesn’t have none, it has two.”

“Maybe interaction with others can force it to make a decision, like Schroedinger’s cat.”

Jean didn’t know what Schroedinger’s cat was, so I had to tell her the story which lies at the heart of quantum physics. A sealed box containing a cat is passed through a radiation field which will kill the cat with a probability of exactly 50%. Is the cat alive or dead? Well, until we are capable of observing what is inside the box, it is essentially bistable. It can either contain a live cat or a dead cat, and we must assume that both of these possibilities exist simultaneously. However, once we do observe what is inside the box, one of these possibilities disappears forever and the other becomes reality from now on.

She didn’t quite understand. “Look,” I said, "external ambiguity is like the sealed box. When I look at you, I simultaneously see both Jean and Gene. Even if I were to see your genitals, I must still consider the equal probabilities that your gender identity is that of a girl or a boy. I have no clue as to which it is, since your external appearance is truly bistable. Marina chose not to observe what is inside the box. On the contrary, she encouraged you to deepen the bistability of your emotions and your responses to others, so as to make observing what is inside the box all that more difficult. But somewhere inside is your true identity, what you really are. I think that you are afraid that Walter will manage to open the box - since love opens all locks - and in doing so force you to become one or the other for good.”

“But why do I have to make a choice? Why cannot I be bistable?”

“Oh, you can, and probably will, continue to be bistable externally and emotionally. Or, for that matter, you can present more than two faces to the world - there are an unlimited number of choices. But, deep underneath it all is your own identity, what you are, and that is unique. You are you, not a multiple of you’s. Your parents never made you ask yourself who you really are, and your friend Marina didn’t either. But your love for Walter has penetrated deeper than they have. It is forcing the box open, and forcing a decision.”

“Think about this, and we will talk again.”

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AUTHOR’S NOTE: I want to make it clear that I am not advocating either Gene’s or Dr. Gold’s position. I am just trying to set up a basis for a dialogue on the question of whether one should necessarily talk about gender identity only in the singular.

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CASE FILE #2 (written by Catherine Gold, PhD, clinical psychologist): Gene came to see me for a second time two days later. This time, I sensed Gene and not Jean. He was wearing jeans, trainers, and a t-shirt and baseball cap with the university logo. On the other hand, he also sported bright pink lipstick and nail polish, and thus maintained the ambiguity which would allow people to react to him/her as they wished. Nonetheless, the overall sense was of Gene.

I asked him if he had resumed going to class, and he said that he didn’t feel he could yet. I asked him if he was afraid of running into Walter, and he nodded shyly. I asked him what he was afraid of, and he whispered “just afraid”. I asked him if he was afraid Walter would, all of a sudden, sense Gene and not Jean. He thought about it for a moment and shook his head. I asked him if he were more afraid that Walter would not sense Gene, thus using the (admittedly forced) analogy of Schroedinger’s cat, forcing him into being Jean permanently.

Jean disagreed (her body language changed subtly but noticeably at this point, as Jean came to the fore, taking over from Gene - or so it seemed to me) and, in fact, said that she disagreed with my whole analogy to Schroedinger’s cat.

“Life is not quantum physics,” she said. Let us look at a more humanistic discipline - say history.

What is the psychological identity of Napoleon? Every historian sees a different Napoleon. Was he the savior of France, a bloodthirsty tyrant, an egomaniac, a genius, a charlatan, a base opportunist? Each one of them writes a book or books thinking that he or she has opened the sealed box to reveal the “real” Bonaparte. But does that make all of the other perceptions go away? Does it make them less valid? And, of course, it is not just a matter of historians writing after Napoleon was safely dead. Every person who came in contact with Napoleon had his or her own version of what Bonaparte really was. But did that mean that the “real” Napoleon was determined by whether Josephine or Joseph managed to open some sort of quantum box and peek inside? Did Napoleon’s identity depend on what Sieyes or Talleyrand considered him to be? Nor can we ask what Napoleon considered himself to be. True, he was a very introspective person, who liked to analyze himself, but his analyses changed with his moods. Like most people, he probably knew himself less than others knew him, or at least thought they knew him.”

I replied that this was an interesting point, but - as I mentioned in our previous session - from a psychological point of view, we are talking about something much deeper. Gender identity is very basic. It is about whether you see yourself as a female or a male, not about what sort of a woman you are or what sort of a man you are. There are only two possibilities.

“I suppose that I could argue with you about whether there are only two possibilities: male or female,” Jean replied, “but I am willing to concede that point, at least for the moment. However, just as a two-element set has four subsets, we actually have four alternative gender identities: male, female, both, and neither. Obviously the vast majority of people opt for a gender identity which is clearly male or clearly female. That is the simplest thing to do. However, I am sure that in your professional experience you have also encountered, or at least have read about, people with no gender identity at all. So why is it so hard to accept the fourth alternative: that someone can be both male and female simultaneously?”

I admitted that there have been documented cases of individuals, who seemed to have no gender identity at all, but those were considered pathological and the individuals involved were invariably mentally disturbed on several levels. As for the fourth alternative - simultaneous male and female gender identities, there is no documented case as far as I recall. I told Jean that I found the argument unconvincing.

“Well,” said Gene, “let me try another mathematical argument. After our first session, I talked to my friend Marina over the phone, and she suggested an interesting mathematical model. Have you ever heard of George Banchoff?”

I admitted that I hadn’t.

“George Banchoff is a mathematician at Brown University, who was one of the pioneers of the use of computer animation to explain mathematical concepts. In the 1970’s, when computer animation was still relatively primitive, he wrote a computer program to illustrate the graph of the complex-valued function of a complex variable z --> exp(z). Now the complex numbers form a plane, which is two-dimensional over the real numbers, and so the graph of this function would be in a vector space of four real dimensions, which is obviously impossible to visualize directly. What Banchoff’s computer program did was to allow us to see any projection of this graph onto a three-dimensional hyperplane of this four-dimensional space, and move continuously from any one projection to any other.

The complex exponential function is very difficult to visualize. If we restrict our consideration to the X-axis (i.e. the real numbers) then the function r --> exp(r) is an unbounded rapidly-increasing function. On the other hand, if we restrict our consideration to the Y-axis (i.e. the purely imaginary numbers) then we know that exp(ai) = sin(a) + icos(a) for each imaginary number ai and so is both bounded and periodic. Banchoff’s animation allows us to see how a function can appear to be rapidly growing from one point of view and periodic from another. I am told that seeing it for the first time is an amazing experience.

Maybe this can help us understand bistability. The function has clearly only one “underlying identity”, namely as the exp function, but can be simultaneously seen as unbounded and rapidly-increasing or bounded and periodic, depending on how one looks at it. It is not like Schroedinger’s cat; people who look at it see different things, but they don’t force it to make a choice of what it has to be.”

We talked some more about this analogy, and then our time came to an end. We would continue in our next session. However, after Jean left, I admit that I was much disturbed by her comments. Perhaps I was wrong after all. I decided to consult with my boss Dr. Jayne Mautner and ask her if, in her long experience as a plastic surgeon specializing in gender problems, she had ever come across a phenomenon similar to Jean. After I explained the entire situation - and my problem in admitting the notion of a bistable gender identity - Dr. Mautner was quite unsympathetic. “You seem to have forgotten the tale of Ellen Caine.” she said. (AUTHOR’S NOTE: this case was discussed in detail in my story “The Doctor, II”.) “More importantly, you forgot the moral of the tale - we deal with individuals, not with scientific theories. If you come across a patient who does not fit your theory, concentrate on treating the person, not trying to squeeze him or her into the appropriate mold.

Gender identity, like legal identity, is something that most people want to be clear and unambiguous and so it seems to us that that is what must happen. But of course, there are a few people out there who choose to be ambiguous about their legal identity, simultaneously living two or three or more independent lives until they themselves are no longer sure who they really are. I am not surprised then there are those who choose to be ambiguous about their gender, even to themselves.

But that isn’t what you should be worried about. Jean has been severely depressed for the past two weeks. Concentrate on finding the root of that.”

Jayne was right, of course. The common failing of any scientist is to consider theory as a form of super-reality - a platonic ideal if your wish. Doctors have to look at individual cases, not at instances of theory.

At the onset of my next meeting with Jean (for it was clearly she who walked through the door, wearing sandals and a very short and sexy dress), I told her that she had obviously decided to forego her gender bistability for the meeting - one can hardly be ambiguous wearing such obviously feminine clothes. I was glad for that, I said, for I did not want to talk about theories of gender identity; I wanted to talk about Walter. “So do I,” said Jean, “which is the reason I dressed this way.”

I asked what had happened, and Jean said that they had met two days ago. “And …,” I said. “And,” he replied, “let us just say that Schrá¶dinger’s cat is out of the bag. He kissed me, and told me he loves me. I kissed him back. Then I told him everything.”

“Everything?”

“Yes, everything.”

“And what did he say?”

“He said he envied me. He is a biology student and so thinks in those terms - he called me an identity chameleon and said that he always envied chameleons for their ability to physically match their environment. He thinks that is a wonderful trait.”

“But whom does he love, Gene or Jean?”

“He said he wants and loves both, and hopes that he never has to make a choice between Gene and Jean.”

“Won’t that be confusing?”

“Well, he hopes I can teach him to become bistable too, but I frankly doubt that it is possible. I think that being bistable is something you are born with, or are blessed with. It is not something one can learn.”

“You may have a point there,” I replied. “I am sorry to say that my sabbatical ends tomorrow, so I won't be able to continue seeing you. I would appreciate it very much if you keep in touch with me and let me know how you are doing.”

Jean got up, came over to me, and air-kissed me. She then stepped back and gave me a very masculine handshake. With that, she/he turned and left the room.