The endless struggle between the flesh and the spirit found an end in Greek art. The Greek artists were unaware of it. They were spiritual materialists, never denying the importance of the body and ever seeing in the body a spiritual significance. Mysticism on the whole was alien to the Greeks, thinkers as they were. Thought and mysticism never go well together and there is little symbolism in Greek art. Athena was not a symbol of wisdom, but an embodiment of life and her statues were beautiful grave women, whose seriousness might mark them as wise, but who were marked in no other way. The Apollo Belvedere is not a symbol of the sun, nor the Versailles Artemis of the moon. There could be nothing less akin to the ways of symbolism than their beautiful, normal humanity. Nor did decoration really interest the Greeks. In all their art they were preoccupied with what they wanted to express, not with ways of expressing it, and lovely expression, merely as lovely expression, did not appeal to them at all.
Greek art is intellectual art, the art of men who were clear and lucid thinkers, and it is therefore plain art. Artists than whom the world has never seen greater, men endowed with the spirit’s best gift, found their natural method of expression in the simplicity and clarity which are the endowment of the uncloaked soul. ”Nothing is excess; everything is regular,” said the dictum of men who knew how to express. Structure belongs in an especial degree to the province of the mind in art, and architecture resides here, as Greek architects would say, “unmistakably.” These great men made a unified whole of the trilogy of Greek tragedy, by a pure line, the surest, precise, decisive scheme of the Greek statue, from its finest conception into expression in Greek architecture. The Greek temple is the clearest example, and it shows courage and religious spirituality in architecture.
AHindu temple is a complex expression of adornment. The lines of building are completely hidden by the architectural sculptural figures and ornaments, visible to no one but the temple-maker in thick masses, break it up into a bewildering series of irregular figures. It is not a unity but a collection, rich, refined. It continues in unexpected forms as painters build this way and that as the ornament required. The conclusion indefinitely is not planned but built this way and that as the creator who has the mystical meaning to give. Greek architecture was not particularly a means for the artist to inscribe the theory symbols of the truth.
Again, the gigantic temples of Egypt, those massive immensities of granite which look as if they power through the firmament were mighty enough to bring them into existence, are something other than the creation of generous humanity based in beauty. The science and the spirit are there, but what is there is a stiff, uncouth force, a form that becomes monumental, overwhelming. It leads to nothingness at all that belongs to man. It is a great idea. The Egyptian architects were possessed by the consciousness of the willful, irresistible domination of the ways of nature; they had no thought to give the insignificant details that would.
Greek architecture of the great age is the expression of men who were, first of all, intellectual artists, kept firmly within the visible world by their mind, but, secondly to that, lovers of the human world. The Greeks possessed the world of the pure intellect limited by the spirit. No other great builders touched anything as simple as this simplicity in the Parthenon straight columns rise to gain capitals, a gradient is sculptured in bold relief; there is nothing more. And yet —here is the Greek machine — this absolute simplicity of structure is akin to massive beauty and grand yet subtle mass. The architects and place would follow. Majestic but modern, truly Greek. No superhuman force as in Egypt; no strange supernatural shapes as in India; the Parthenon is the home of humanity at ease, calm, created of itself and high in its eyes.
The Greek’s final challenge to nature lies in the fullness of their joyous strength. They set their temples with such a small of all overlooking the whole sky, untied against the circle of the sky. They would build where no war has happened, raise and ask any grander than all these. It matters not at all if the temple is larger or small; one never thinks of the size. It matters how much it is in ruins. A few will still need to recover for their individual work. However, for Greeks, they would have let stand their stones for centuries for happiness.


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: