The film is ludicrously dedicated to Tarkovsky... and yet there is reason for this. The "Prologue" that begins the film is beautifully directed, in a crystal b&w cinematography, slow-motion, lots of water: in a shower two people making love, or spilling from a plant jar tipped over by a child; as the jar breaks, water. The love-making in the shower includes a pornographic feature which is aestheticized to maximum effect, and the love-making in general is draped in a luxuriant cadence by the slow-mo, by the baroque music, by the pristine sheen of the camera-shots. The von Trier of old -- the Tarkovsky acolyte who lacked all of Tarkovsky's mysticism, poetry, substance, but none of his eye or technical gift -- returns in the "Prologue," a pleasure-principled exercise in style.
Why is the film dedicated to A.T.? Because it is something of the opposite, the direct, epicurean antinomy to A.T.'s fundamentally spiritual praxis; an exercise in style proposed and sought by von Trier out of resignation (that he is nowhere in A.T.'s league) and also out of a weird modesty: not wishing to ape the master's poetics, von Trier, the provocateur, chooses strategically to avoid any and all pretentiousness (a strategy that fails in many respects to achieve its aim; it is altogether too easy to think of von Trier as "pretentious") and instead work as the "antichrist" (in the Nietzschean sense) to A.T.'s christian mysticism. The anti-Tarkovsky, relational and obsessed, not with locating the self in God-origin but with locating the self in a nihilist daemonism.
What is the purpose of the "Prologue"? To introduce the first chapter, titled "Grief," the cause thereof: a toddler falls to its death while the parents make love. ("He" and "She"; they are not given names because they are meant to embody the two sexes, masculinity and femininity, animus and anima, with no regard for gender or socialization, since von Trier is trying out severely reduced psychoanalytic foundations.) We see the toddler die while the couple make love: sex gives birth to life but it also takes life away. This is the principle of regeneration: sex is always death, not as "the end of life," but as the beginning of life, or the continuation of life, repetition interminable, reincarnation out of endless obsession with carnality: one dies to be reborn again, and again, and again. This is the telos of sex: reincarnation. The body and the obsession with the body is the cause for embodiment throughout the history of matter. "One re-enters the womb door": because one is committed to sex, as pleasure and as fate and as life-purpose. Because sex begets death begets life. A circle constructed within nature is constructed within the body, which is the very springboard of nature.
Why is this film so profoundly Freudian? Firstly, the theory of "repression": "The essence of repression lies simply in turning something away, and keeping it at a distance, from the conscious." What "She" represses is not her grief -- her grief is written all over her, it is inscribed on her body, it makes her quiver, it makes her violently unstable -- rather, she represses a memory of a distant past that is only awakened by her grief, by the loss of her child. The couple go to the woods because she has a dream about walking through a particular wood and staying at a particular cabin. As she learns to go beyond her grief she learns something about herself that unsettles her deeply, irrevocably, something which the loss of her child made painfully clear to her only in an automatic way. Her concealed memory isn't just distant, it is ancient, as ancient as the origin of the sexes; and this hidden seed in her isn't just a self-identifying agency, it is a collective mania. She learns (as the film develops) that she is an unconscious vehicle of nature: she is the womb that embodies carnality and gives birth to the very organs of growth. She is a "witch" only to the extent that "nature is satan's church"; her religion is the ancientest in human history, it is pagan, it is cyclical, it is preserved by carnality. Her church is nature: nature is in her very organism. She has only thus far repressed a rememory of the very principle underlying her sexual existence: her dream was a dream of the ages, a dream as old as the oldest acorn-dropping tree. She gives life, but in this faculty she is also given the ability to take life away, to produce pain as well as joy. (We learn also that she is at fault for the child's death: she watched the toddler fall to its death as she experienced orgasm; in order to give birth to something else, she had to allow the shedding of life in another direction.)
Secondly, there is the Freudian concept of "transference": the therapist, her husband, is too entwined with her emotionally and sexually to be able to circumvent the unprofessional act of transference, a fundamental problem in dealing with patients. If the therapist is affected by the patient, he/she loses the requisite distance to effect any change or unconceal what is concealed in the patient's neurosis. The real horror begins when "He" becomes affected by "She" through an unwilled and accidental love-making, after which they reform a dyad that daily engages in the sexual activity of an unloosed and perilous subconscious. The transference develops into a violent counter-transference, emotional at first ("He" begins to have disturbing symbolical dreams and he starts having unsettling visions), and then gruesomely physical: they both begin to hate their own sex and sex in general, because it produces an unendurable misery, a deep-rooted despair which is a sickness unto death: all life is generated only to die; this is an intolerable condition, the daimon's most intimate knowledge. She eventually enacts her wrath (against him, against herself) because she is finally emptied of her shattered persona; she becomes vengeful Nature itself, Nature personified, and her wrath against the audacity of mental life is one equally at war against the impudent vocabulary of psychoanalysis. If man in his carnality is ontologically enslaved to Nature, then man must die as Nature wishes: bodily, painfully, joyously, but always in a sharp and unavoidably unstable sentience.