Psychotherapeutic processes deal with psychological problems, ranging from mild ones like a depressed mood, to more subtle ones like interpretation of dreams to more controversial problems like dissociative identity disorder. Denied emotions (not admitting or voicing one's emotions to the therapist) is a root cause of many psychological problems as honest communication is the numero uno factor for the psychotherapeutic process to work. Emotional honesty can be a difficult task for the client or patient.
Psychotherapists make analysis of dreams a significant part of their work. It is tempting to wish petulantly that the unconscious would speak to us more clearly as significance of many dreams eludes us. But dreams that can be interpreted provide helpful information like warnings of personal pitfalls; solutions to problems; sources of necessary information and judgement; as direction-finders when we feel lost; as pointers to the way we proceed when we are floundering and the message always seems to be one designed to nurture spiritual growth.
The unconscious may communicate to us when we are awake with as much elegance and beneficence as when we are asleep, although in a slightly different form of 'idle thoughts' or even fragments of thought. As with dreams, we pay these idle thoughts no attention and cast them aside as insignificant. Hence patients in psychoanalysis are instructed to say everything, however insignificant, that comes in their minds. Idle thoughts provide us with insight into ourselves and others.
The seemingly alien and unwanted quality is characteristic of unconscious material and its manner of presentation to the conscious mind. This and the associated resistance of the conscious mind led Freud to perceive the unconscious as a repository of the primitive, the antisocial and the evil within us. He tended to assume that mental illness somehow resided in the unconscious as a demon in the subterranean depths of our mind. To Carl Jung fell the responsibility of correcting this which he did through his work The Wisdom of the Unconscious. As he concluded, mental illness is not a product of the unconscious but a phenomenon of consciousness or a disordered relationship between conscious and unconscious. Consider the matter of repression. Freud discovered in his patients sexual desires and hostile feelings of which they were unaware but which were making them ill. Because these desires and feelings resided in the unconscious, the notion arose that it was the unconscious that caused the mental illness. But why were these desires and feelings in the unconscious in the first place? Why were they repressed? The answer is that the conscious mind did not want them. And it is in this not wanting, this disowning, that the problem lies.


When people who are talking don’t share the same culture, knowledge, values, and assumptions, mutual understanding can be especially difficult. Such understanding is possible through the negotiation of meaning. To negotiate meaning with someone, you have to become aware of and respect both the differences in your backgrounds and when these differences are important. You need enough diversity of cultural and personal experience to be aware that divergent world views exist and what they might be like. You also need the flexibility in world view, and a generous tolerance for mistakes, as well as a talent for finding the right metaphor to communicate the relevant parts of unshared experiences or to highlight the shared experiences while demphasizing the others. Metaphorical imagination is a crucial skill in creating rapport and in communicating the nature of unshared experience. This skill consists, in large measure, of the ability to bend your world view and adjust the way you categorize your experiences. Problems of mutual understanding are not exotic; they arise in all extended conversations where understanding is important.
When it really counts, meaning is almost never communicated according to the CONDUIT metaphor, that is, where one person transmits a fixed, clear proposition to another by means of expressions in a common language, where both parties have all the relevant common knowledge, assumptions, values, etc. When the chips are down, meaning is negotiated: you slowly figure out what you have in common, what it is safe to talk about, how you can communicate unshared experience or create a shared vision. With enough flexibility in bending your world view and with luck and charity, you may achieve some mutual understanding.
Communication theories based on the CONDUIT metaphor turn from the pathetic to the evil when they are applied indiscriminately on a large scale, say, in government surveillance or computerized files. There, what is most crucial for real understanding is almost never included, and it is assumed that the words in the file have meaning in themselves—disembodied, objective, understandable meaning. When a society lives by the CONDUITmetaphor on a large scale, misunderstanding, persecution, and much worse are the likely products.
Later, I realized that reviewing the history of nuclear physics served another purpose as well: It gave the lie to the naive belief that the physicists could have come together when nuclear fission was discovered (in Nazi Germany!) and agreed to keep the discovery a secret, thereby sparing humanity such a burden. No. Given the development of nuclear physics up to 1938, development that physicists throughout the world pursued in all innocence of any intention of finding the engine of a new weapon of mass destruction—only one of them, the remarkable Hungarian physicist Leo Szilard, took that possibility seriously—the discovery of nuclear fission was inevitable. To stop it, you would have had to stop physics. If German scientists hadn’t made the discovery when they did, French, American, Russian, Italian, or Danish scientists would have done so, almost certainly within days or weeks. They were all working at the same cutting edge, trying to understand the strange results of a simple experiment bombarding uranium with neutrons. Here was no Faustian bargain, as movie directors and other naifs still find it intellectually challenging to imagine. Here was no evil machinery that the noble scientists might hide from the problems and the generals. To the contrary, there was a high insight into how the world works, an energetic reaction, older than the earth, that science had finally devised the instruments and arrangements to coart forth. “Make it seem inevitable,” Louis Pasteur used to advise his students when they prepared to write up their discoveries. But it was. To wish that it might have been ignored or suppressed is barbarous. “Knowledge,” Niels Bohr once noted, “is itself the basis for civilization.” You cannot have the one without the other; the one depends upon the other. Nor can you have only benevolent knowledge; the scientific method doesn’t filter for benevolence. Knowledge has consequences, not always intended, not always comfortable, but always welcome. The earth revolves around the sun, not the sun around the earth. “It is a profound and necessary truth,” Robert Oppenheimer would say, “that the deep things in science are not found because they are useful; they are found because it was possible to find them.”
...Bohr proposed once that the goal of science is not universal truth. Rather, he argued, the modest but relentless goal of science is “the gradual removal of prejudices.” The discovery that the earth revolves around the sun has gradually removed the prejudice that the earth is the center of the universe. The discovery of microbes is gradually removing the prejudice that disease is a punishment from God. The discovery of evolution is gradually removing the prejudice that Homo sapiens is a separate and special creation.
For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is: