Sex, Sin and Buddhism

A supplement to Sex, Sin and Zen by Brad Warner

Bhikkhu Cintita Dinsmore

 

Brad Warner writes near the beginning of his recent book, Sex Sin and Zen: “I only really know Zen, myself, so that’s all I’m going to be addressing here,” which appears to be accurate, but then, “… we Zen Buddhists tend to be so arrogant that we just call what we believe ‘Buddhism’ without specifying the sect. I’ll be doing a little of that, too. Deal with it.” What follows is my attempt to deal with it.

I am concerned Sensei Warner makes a number of statements explicitly about general or “early” Buddhism that are misleading or simply wrong, and other statements that are true specifically of Japanese Soto Zen but which the reader can easily falsely assume applies to every tradition in every Buddhist country. I don’t think he appreciates how peculiarly unique modern Japanese Buddhism has become within the mix of Asian Buddhism, even with respect to, say, Chinese or Vietnamese Zen. I used to be a Zen priest myself and was confused about this for many years, so I know Sensi Warner is in good company in this. The important distinction to be made here is between Modern Japanese Buddhism and the Rest of Buddhism, modern and premodern. When I write “Buddhism,” without further qualification, I mean ” almost all Buddhism outside of modern Japan.”

My purpose here is to clarify what is true of Buddhism. This has a bonus; in a real sense sexuality is a much more interesting topic in Buddhism than in modern Japanese Buddhism, because of a seeming paradox: On the one hand Buddhism—and this is shared with modern Japanese Buddhism—has a very liberal attitude about sexuality. As Sensei Warner observes, there is no Sin in Buddhism! Many Westerners find that very refreshing and that is an important theme of Sensei Warner’s book. On the other hand, Buddhism—but this is not shared with modern Japanese Buddhism—has this strong tradition of monastic celibacy, which has persisted from the time of the Buddha to the present day. So the really interesting question is: Why would Buddhism be so liberal about sexuality for lay folks, yet deny it altogether for monks and nuns? Almost all Western Buddhists are baffled by this, yet in Asia it is accepted as part of the nature of Buddhism. The answer tells us not only a lot about Buddhism, but about the Buddhist understanding of human sexuality. Unfortunately this fascinating question falls pretty much outside of the scope of Sensei Warner’s book or of his experience.

There is no Sin in Buddhism. Sensei Warner makes this point accurately. Sin is generally considered in the Abrahamic religions (Judaism, Christianity and Islam) to be a kind of insult to God, a violation of what God demands of us. As such a Sin carries much more gravity than simply doing something that harms someone else or something which we might regret doing. In fact Sins may or may not correspond to actions that are harmful to humans at all. Murder, theft, bearing false witness, adultery are actions that are generally harmful in themselves. Homosexual acts, masturbation, making for yourself an idol, or not keeping the Sabbath are actions that are generally not harmful to others, but sometimes regarded as Sins anyway. Even some thoughts are Sins, such as coveting your neighbor’s house, cow or wife. Buddhism does not have a remotely similar concept of Sin; it can’t since it makes no reference to a God whose demands we could violate. Yet Buddhism does have a basis in strong, clear ethical principles and these need to be clarified to understand Buddhism and Sex.

Buddhist ethics, in a nutshell, is based on two key concepts along with their opposites: Non-harm and Skill. Some actions are harmful in that they cause suffering or disharmony, some are non-harmful, or beneficial, in that they bring good things like joy and peace. Skill is fixed at the intentional level, at the level of our thoughts. For instance, rage is considered unskillful, while equanimity is considered skillful. While non-harming is an outer view, skill is the inner view. Yes, Buddhist ethics also extends to what we are thinking, in fact that is mostly what Buddhist ethics is about. This might seem invasive, and evoke images of goose-stepping Thought Police, but bear with me and you will see why this is important.

A third, auxiliary, concept should also be mentioned: Precepts are rules of thumb to help us help us recognize what is harmful or unskillful, even when we are drawing a blank and cannot work out the harm or skill of a proposed action. The following is the most commonly observed short list of Precepts, recognizable in probably all Buddhist countries:

1. To refrain from killing living beings. (This means bugs, etc., as well as humans.)
2. To refrain from taking what is not given.
3. To refrain from sexual misconduct.
4. To refrain from false speech.
5. To refrain from consuming alcohol and drugs that cause heedlessness.

In the Dhammapada the Buddha tells us,:

Avoid all evil,
Do good,
Purify the mind,
That is the teaching of all buddhas.

Avoiding all evil refers to following the precepts, doing good to creating benefit and purifying the mind to learning to be skillful in your thinking. This little verse reminds us of these three aspects of Buddhist ethics.

One immediate consequence of this very grounded way of thinking about ethics is that Buddhism does not have arbitrary prohibitions, what we would call “Victimless Crimes,” like handling leather from a pig, like homosexuality, or like performing an “unnatural” sexual act, because these in themselves do no harm and are not necessarily unskillful. Sexual misconduct in rule #3 here, for instance, refers to things like acts of adultery and sex with a child in which the harmony of standing human relations is violated, that is, to circumstances in which sexuality almost always leads to harmful results. It does not refer to aspects of the sex itself, such as societal norms about the proper way to engage in sex, insofar as these are victimless. The sexual act in itself is never regarded as harmful or unskillful in Buddhism; the problem is rather that we do have ways of using sex harmfully and also of wrapping sex in many layers of unskillful thoughts, as you, the reader, are almost certainly already painfully aware if you’ve ever been around the block. Buddhism helps us understand where the real problems arise so that we may avoid them in the future. This is what Buddhist ethics is about.

Buddhist Ethics is Grounded in Personal Choice. Many people in the Abrahamic faiths assume that without God there can no morality. If there is no God watching, they argue, what incentive would we have to observe ethics at all? In contrast, it has been observed that Buddhist countries in Asia, where God is largely unknown, tend to have the lowest rates of crime in the world! I certainly observed that Burma, which is a strongly Buddhist country, impoverished by years of military rule to boot, and with little everyday police presence, is nevertheless a country with remarkably little crime, quite unlike my own USA.

The fact is that people everywhere have an innate desire to Do Good!. In teaching Buddhism and meditation in prisons I have discovered the urge to Do Good in the most ignoble ruffians; their problem is that their thinking has gotten side-tracked, almost always in predictable ways given circumstances in which they grew up. Buddhism lays out the wisdom, it doesn’t have to provide the motivation. Ethical behavior in Buddhism comes from personal choice, that is, from personal vow. As a Buddhist, you vow to follow precepts, or not; you vow to make benefiting others a cornerstone of your life, or not; you vow to development skillfulness in thought and action, or not. The degree of vow, it turns out, depends largely on your wisdom, aided by the Buddhist teachings or other sources, but also on conflicting obligations in your life and on some very human personal values. To the extent people understand, they invariably want to do the Right Thing, that is to benefit, not to harm.

Also the idea that there are Good People vs. Evil People is foreign to Buddhism. If there is a battle between Good and Evil it is only in our own hearts, where the Skillful and the Unskillful compete. We vary in how much harm or benefit we do, in how skillful our thinking is, and how how much effort we put toward the perfection of character, including the strength of our vows, but everybody in the end is on the same path, we all are doing the best we can, and as in everything some of us are ahead of others because of talent or opportunity. That guy behind me on the path probably does more harm in the world than I do, but for me the skillful thing to do is not to turn around and fight this sleazeball but to help this fellow traveler along the path. That guy ahead of me on the path probably does more benefit than I do, but for me the skillful thing is not to undermine this goody-goody, who is without doubt trying to win for himself the Nobel Peace Prize, but to rejoice in the success of someone who can be an inspiration to myself.

Because not all people are not alike in the vows they are willing to take on, there are options. For instance, some people follow the five precepts above most of the time, and a larger set of eight or nine or ten precepts at other times, sometimes one day a week. I am a Theravada monk, and Theravada monks take on a set to 227 precepts, all the time, forever! Likewise some people, in order to develop skillfulness in their lives, may meditate religiously and study Buddhist teachings, while others will simply try to be more deliberate and mindful in their everyday activities. This is why there are monks and nuns in Buddhism; they are the ones whose choice is to go completely off the deep end of practice, still a rare choice in Western Buddhism, but very common indeed in some countries like Burma.

In short, Buddhism is not a cookie-cutter religion in which everyone is expected to have the same behavior, understanding or practice. It provides choices, but most importantly the means for fully investigating those choices, so that they are made with due deliberation on the basis of Buddhist wisdom.

Skillful and Unskillful Thoughts and Actions. I have not yet written much about what Skill is. Buddhism is in the end about the Perfection of Character. The perfect human character is, briefly, virtuous to a fault, joyfully imperturbable, and penetratingly wise with no sense of being anyone at all, yet confident in all activities. Not many of us feel like this yet, but Buddhism manages at least to steer people in that direction, in fact decisively and increasingly as their conviction in the wisdom of Buddhism grows. All of these features of the perfected human character come together from mastering the Skill of life, in one’s thoughts, and thereby in one’s actions. This is why Buddhism likes to talk so much about what is Skillful and what is Unskillful, and about Karma, which in Buddhism means “Intentional Action” (really the opposite of fate).

It is easy to recognize the need for Skill in our lives. If we have the habit of drinking ourselves under the table and waking up with a hangover day after day, we probably are not being very skillful. If we eat junk food routinely and weight 300 pounds, we probably are not being very skillful. If we find ourselves engaged to marry four different people, we probably are not being very skillful, unless maybe if we are Mormons. If we have tempers that are always on a hair trigger, scare people away when we get red in the face and have had two heart attacks, we are probably not being very skillful. If we support a distant war for an abstract ideological reason, a war that has no clear benefit but is causing the loss of hundreds of thousands of innocent lives, we are probably not being very skillful. Buddhism takes this idea of Skill and refines it to the point that it can in principle advise almost all of our thoughts and activities, even the smallest, if we choose to let it.

Unskillful thoughts, in brief, are recognizable as follows:

1. They are stressful. (This is the famous dukkha, or suffering.)
2. They distort reality.
3. They are grounded either in greed, in aversion or in delusion.
4. When they give rise to actions, those actions usually cause some degree of harm.
5. They subvert the development of perfected character

A skillful thought has none of these properties. As you can see, skill (and therefore ethics) is understood in a very refined and psychological way. It is not a matter of imposing arbitrary judgments or even societal norms on yours or other people’s behaviors. It is also not a matter of making you feel guilty about your unskillful thoughts and actions; in fact Guilt is itself recognized in Buddhism as a kind of unskillful thought, as a form of aversion. Get rid of it. It is rather a basis for understanding our own mind and how it goes awry, and with this understanding to make more rational choices for the benefit of all.

In fact much of what it means to practice Buddhism is to become acutely and continuously aware of when each of these five properties is present and when it is absent. Meditation practice is enormously valuable in helping you to do this. It settles your mind like a clear forest pool in which you see every ripple, every little fish or pebble. As your practice, and thereby your wisdom, deepens, you will begin to appreciate that what ties these seemingly diverse factors of unskillful thoughts together is the Ego, the abiding delusion that you are a separate self. Our self-centeredness underlies our stress, the way we misperceive in our search for personal advantage and become confused, the arising of greed and aversion in service to the self, the harmful actions that we thereby let loose, and our reinforcement of all of these factors in our character as we entertain such thoughts and act on them over and over.

Seeing into your own mind is like taking a new roommate into your apartment, who may initially present himself as a nice guy but who turns out to be a jerk. After a month you can list all of his faults in detail, which he is invariably totally clueless about. After two months you are ready to throw him out. The difference is that when you see into your own mind, the roommate is you! You just hadn’t noticed your faults before, even though you had already been living with you all your life. You will now understand why you have always been so miserable and why everyone else seems to think you are a jerk: You have been just living with a jerky roommate, you. So you kick you out. That is the heart of Buddhist practice: kicking you out of your apartment.

So, which specific thoughts are skillful and which are unskillful? There are long lists of each that you can glean from Buddhist literature, for instance, among the unskillful are restlessness, agitation, conceit, jealousy, guilt, pride, greed, miserliness, thoughts of revenge, envy, grumpiness, anger, hatred, rage, sorrow, fear, bias, delusion, stubbornness, narrow-mindedness, torpor, complacency, affection, lust, and so on. Skills are pretty much the opposite: generosity, renunciation, loving-kindness, compassion, equanimity, pliancy, stillness of mind, mindfulness, and so on. However, your job is not to memorize lists, but to learn to recognize skill and non-skill in your own experience. These are testable, in fact they must be tested, otherwise you will never thoroughly understand the role of skill and non-skill in your own mind, you will be driven by forces you do not understand, and you will not find satisfaction in your life. So these things are important.

Sex and Buddhism. We have discussed Sin and how Buddhism provides an ethics without Sin. We have discussed Non-Harming and Skill. In fact I’ve laid out the fundamentals of Buddhist ethics in just a few pages so we could get here as fast as possible. Whew. Now we can begin to discuss Sex, which is why most of you are reading this.

If you have read through the list of unskillful thoughts at least two of the items will probably surprise you: affection and lust. “What gives?,” you ask, “Aren’t those Good Things? I wouldn’t want to live without affection and lust, how dull!”

The dilemma arises because we have a variety of standards of Good and Bad inside and outside of Buddhism. For instance, we have personal preferences, such as Excitement is Good, Stillness and Quiet are Bad, or the exact opposite. We have societal norms: Getting Rich is Good, Working Hard is Good, Being a Nobody is Bad, Quiz Shows that evoke greed for stuff and money are Good, Pornography that evokes lust is Bad. Our standards often shift if we think about them. at all. For instance, is it really Good to be beautiful, talented and famous? It certainly did not work out so well for Marilyn Monroe or Elvis Presley in the end. Skillful and Unskillful are indeed Buddhist standards for Good and Bad, and are endorsed by the Buddha, but remember they are not divinely ordained. These must compete in your set of values with other standards. It’s your choice.

So let’s consider Affection and Lust with regard to the five marks of Unskillfulness listed above, then consider your competing standards.

Affection, for instance, toward a sexual partner, a child or a friend, is just a little unkillful.

Affection.

1. Stressful. Affection is a source of stress as you cannot get enough of it or feel a sense of loss when you can no longer express it.
2. Distorts Reality. Affection has a self-centered dimension, it is granted to those who will return your affection, or who will benefit you in some way, even though we commonly think of affection as selfless.
3. Grounded in: Greed.
4. Harmful. Affection extends the range of self-interest. Just as you may be willing to harm others for your own benefit, you may harm others for the benefit of those with whom you share affection or friendship.
5. Subverts development. Affection is easily confused with loving-kindness, which in Buddhism is like sunshine: It applies universally and equally to all, without bias, friend or foe, and does not cause stress. Affection is biased and that bias can inhibit the development of loving-kindness, or be a stepping-stone in developing loving-kindness.

Lust is greed for sensual pleasure, for instance, for sex, for snacks, for massages, long showers, or sleep, for dancing, music, alcohol, smoking, drugs, action movies, dangerous sports, or video games, for chatter and gossip, and so on. It is important to distinguish lust from pleasure, which is the object of lust.

Lust:

1. Stressful. Lust is painful, sometimes so painful you can hardly stand it. It is like a fever. Relief is possible if the object of lust is realized but otherwise typically leads to bitter disappointment, a kind of aversion..
2. Distorts Reality. “Love will find a way,” we say. Likewise, “cookies will find a way,””beer will find a way,” and so on. We interpret lust as a need and often abandon all wisdom to attain the object of our lust. Careers, marriages and health have been overlooked and discarded through lust.
3. Grounded in: Greed.
4. Harmful. Of course, stealing is often a result of lust, including stealing someone’s man or someone’s woman. One of the surprising features of lust is how consciously self-destructive it can be. People sacrifice physical health out of lust for food, drink, cigarettes and so on, and mental health out of lust for electronic entertainment, drugs and so on. People are often propelled by lust from one unhealthy and unhappy sexual relationship to another. When the object of lust is not attained or is lost, depression, suicide and murder can result.
5. Subverts development. Lust agitates the mind, obstructing stillness and other skillful factors. It easily spins out other unskillful thoughts such as anger, jealousy, and greed for various instruments needed for satisfying lust such as those sporty clothes or that sexy sports car. It easily becomes ingrained as unskillful habit patterns, that is, addictions.

Pleasure, what lust seeks, is actually not problematic in itself. However, lust and pleasure tend to condition each other. Lust seeks pleasure. Pleasure often evokes lust for more of the same, or for an escalation of pleasure, or for some other kind of pleasure altogether. Together they often form a cycle. Because of their intimate association in that cycle they are confused with one another. However lust is painful, pleasure is, uh, pleasurable. Addiction is when this cycle spins out of control. The failure to properly understand the cycle of lust and pleasure, and to recognize which is which, has miswritten many lives, and even the histories of nations.

Most people are actually not very good at experiencing pleasure, even when it is there for the taking. If I cannot be present, I will miss a pleasurable moment altogether. Treated to a magnificent sunset over a sparkling ocean, I will instead be worrying about business, or lusting for magnificent woman in a sparkling dress. In this way pleasure easily becomes an abstraction, something I think I remember experiencing in the past and that intend to experience in the future. Yet the lust for this abstraction of pleasure will continue unabated. The result is simply misguided lust, a life of more pain than pleasure.

Lust leads to great plans. Lusting after nature, longing for the sun casting shadows through rustling leaves, I might decide to move to the country, thereby burdening my life with a long commute. However, in the end I never bring forth the stillness of mind, or the time, to ever actually enjoy the sun casting shadows through rustling leaves. I’ve been spending my time and energy chasing imaginary pleasures. But what will I do next? Probably I will decide I need to move further into the country where I can really enjoy these things. In fact we typically experience lust, that is, pain, much more than pleasure, but we confuse the two. No wonder we are so miserable. However, Buddhist practice enhances both the ability to experience pleasure and the wisdom to moderate lust.

Identifying what is skillful and what is unskillful provides one standard of Good and Bad. Competing, non-Buddhist standards are at hand. For instance, we tend to think in our society that Being in Love is Good. It is certainly a mind-bending experience, alive, uplifting. It is in fact a unique and particularly potent blend of pleasure and pain, or rather bliss and anguish, volatile in composition, easily spun out into despair, anger, depression or worse, yet if nursed along able to settle down into a solid lifelong partnership and the foundation of a happy, harmonious family, until other unskillful thoughts intervene. We also tend to think in our society that Fun and Excitement are Good. More often then not we can tease these apart into the same runaway cycle of lust and pleasure, to discover that there is actually a lot of stress, sometimes even despair, underneath most Fun and Excitement; we just fail to notice.

Certainly we think in our society that the affection within a harmonious family or among friends is Good. I am myself a father of twenty-somethings (a pre-monastic attainment) and can report that fatherhood has been and remains one of the most meaningful parts of my life. I was, however, enmeshed in years of financial pressure; concerns about health, academic achievement and other developmental issues; responsibilities as caregiver and breadwinner, and so on. It was my choice at the time, and I have no regrets. What you value as Good for you is your choice.

Celibacy. and Monasticism To recap, Buddhism is not a one-size-fits-all religion; it sorts out the ethical issues for you in a way that relates your values and motivations, choices, likelihood of harm and the path toward perfection of character, then allows you to make an informed decision based on your personal values, existing commitments and motivation concerning the shape of your life. It embraces a wide variety of life choices, even allowing as an option that most perverse and unnatural of deviant sexual behaviors: … celibacy.

A nun or monk, at least an ideal nun or monk, is someone who attempts to be skillful in all things, that is to renounce self-interest, greed, aversion and delusion altogether, overriding any other personal value which might conflict with this resolve, thereby entering the most direct path to the perfection of character. This means giving up what are what for others are normally compelling values and behaviors, whenever these encourage unskillful thoughts and acts. This is often called the Path of Renunciation. Let Dogen, the Thirteeth Century founder of Soto Zen in Japan, describe it for us:

If you have a home, leave your home. If you have beloved ones, leave them. If you have fame, abandon it. If you have gain, escape from it. If you have fields, get rid of them. If you have relatives, separate from them.

The idea is that anything in your life that threatens to evoke or entangle one in greed, lust, aversion, fear, anxiety, is simply let go of. A nun or monk simply does not participate in in the world on his or her own behalf, has no stake in the world that could evoke the unskillful. Sex, although pure in and of itself, inevitably gets entangled in lust, jealousy, attachment, possessiveness, loss, anger and pregnancy. That makes it a key object of renunciation, in fact its renunciation is the hallmark of the monastic life. Physical renunciation, for instance, not engaging in sex, is the easy part. Mental renunciation, for instance, not obsessing about Sex constantly in spite of one’s vows, is the hard part, but necessary to remain in the path of renunciation without going crazy.

How does this work out for the nun or monk? It sounds pretty austere. One of the functions of the nun or monk in the wider Buddhist community, one of the main ways that they serve laypeople, is to be a kind of Robed Walking Science Experiment. You put this combination of ingredients into the human test tube and what happens? If the experiment is a success, then laypeople, short of becoming nuns or monks themselves, will start looking at their own lives and asking how they can make them simpler. They might want to keep sex and family, but might question whether they need the weekend cabin, the latest gizmo, the latest styles? If the experiment is a failure then laypeople will continue, reassured, in their hedonism. Monks and nuns are a reality check, the presence of which has kept the flame of Buddhism burning all these years.

The fact is that monks and nuns are generally the most uplifted and uplifting people you will ever meet. Modern examples are the Dalai Lama, Thich Nhat Hanh, Cheng Yen, Bhikkhu Bodhi and Pema Chrodron, oh, and me, along with a few million other people. The experiment is in general a huge success, as common sense would not predict, but as Buddhist psychology would. Things are not as they seem; we live in a Looking Glass world. As embodiments of Buddhist principles the traditional presence of nuns and monks in the larger Buddhist community have served throughout history to incline everyone steadily toward seeking greater purity of mind, an invaluable teaching prior to words. Also, skillful factors based in generosity, kindness and wisdom displace unskillful thoughts of greed, hatred and delusion. Freed of self-concern, freed of personal problems, monks and nuns have a valuable reserve of energy available for benefiting others, traditionally bringing them into education and social welfare as well as teaching the Dharma.

On the other hand, monastic life requires resolve. If the mind does not fall into accord it is very easy to lapse and fall back into the attractions of the world. Not surprisingly, the quickest point of monastic lapse is in sex, a testament to the primacy of sexual impulses. For this reason remaining in monastic life requires a lot of community support, just as remaining sober generally requires to support of a community like Alcoholics Anonymous, as well as clarity about boundaries, over which the nun or monk can easily slip into a thicket of unskillful impulses, and which lay people should also be aware of. It is also important that a monastic be a renunciate first and foremost, not as a condition for some other role. This is the difference between the Buddhist monastic Sangha and the Catholic Priesthood: Monastics are not priests; if they no longer want to practice renunciation, they simply return to lay life. Catholic priests are often priests, but not not renunciates, at heart.

It sounds like a lot of work, however, if the resolve is there, it is a condition with no personal problems, a selfless condition, of complete ease. It is a state of utter freedom, clear blue sky, nothing to clutter the mind, just stillness, having nothing to do but practice the Buddhist path and find ways to benefit the world. These dwarf all other values.

Japanese Buddhism. Let me conclude with a few words about Japanese Zen, since I began with the contrast between modern Japanese Buddhism and all other forms of Buddhism. The monastic Sangha, which had developed Zen as we know it in China then carried it to Japan, Korea and Vietnam, began to collapse in Japan in 1872, not because Japanese Buddhists had found a better way, but by decree from a government hostile to Buddhism and eager to Westernize. The Meiji government decided to reform Buddhism to look like Western Protestant churches, and so by forcibly ended the requirements of celibacy, abstention from alcohol and wearing robes in public for Buddhist clergy, transformed the monastic Sangha over time substantially into a priesthood. This begin to alter the tradition in Korea as well during the Japanese colonial occupation (1910-1945). I speculate that this shift to an institutional form more recognizable in the West, was inadvertently responsible for the relatively rapid growth of Zen here. There is however a small movement in Japan and in the West intent on restoring the monastic order in Soto Zen, in the West most notably represented by Shasta Abbey in California.

Japanese Soto Zen, in which Sensei Warner has been extensively trained and has had the opportunity to observe at its source, remains, in spite of these changes, a powerful tradition. Its 13th Century founder in Japan, Dogen, is undoubtedly one of the greatest thinkers in the history of Buddhism. I hope it continues to flourish here, and I think teachers like Sensei Warner have a critical role in making sure it is correctly understood, which I think is a sincere concern of his. Zen is subtle but has a sharp edge, it has traditionally been taught by example more than by words. For this reason I want to apologize to Zen readers of this essay for my rather analytical language, which is more in the spirit of Indian Buddhism than Zen. (I should also apologize if you were looking here for racier passages. However you do have Sensei Warner’s book to fall back on, and if that is what you were hoping for here, you probably have not read as far as this apology in any case.) The fact is that people tend to understand monasticism quite readily when they see it, simply by example, but for most readers without that opportunity its logic needs to be described. I hope this account has served to do that.