Atmospheric jet streams were discovered towards the end of World War II by U.S. bomber pilots over Japan and by German reconnaissance aircraft over the Mediterranean. The World Meteorological Organization defines a jet stream as a strong, narrow air current that is concentrated along nearly horizontal axis in the upper troposphere or stratosphere (10 to 50 kmaltitude), characterized by wind motions that produce strong vertical lateral shearing action and featuring one or more velocity maximum. Normally a jet stream is thousands of kilometers long, hundreds of kilometers wide and several kilometers deep. The vertical wind shear is of the order of 5 to 10 m/sec per kilometer, and the lateral shear is of the order of 5 m/sec per 100 km. An arbitrary lower limit of 30m/sec is assigned to the speed of the wind along the axis of a jet stream.
With abundant radio-sonic data now available over the Northern Hemisphere it is possible to map the jet streams in the upper troposphere (near 10 to 12 km) in their daily occurrence and variation and to forecast them reasonably well with numerical prediction techniques.
Upper-air information from the Southern Hemisphere is still sparse. Constant-level balloons (the so-called GHOST balloons) and satellite information on temperature structure and characteristic cloud formations in the atmosphere are serving to close the data on the global jet stream distribution.
The strongest winds known in jet streams have been encountered over Japan, where speeds up to 500 km/hr (close to 300 knots) occur. A persistent band of strong winds occurs during the winter season over this region, flowing from the southwest and leading tropical air northern India into juxtaposition with polar and arctic air from Siberia. A similar region of confluence of air masses with vastly different temperatures exists over the central and eastern United States, leading to a maximum frequency of occurrence of jet streams during winter and spring.
The main impact on weather and climate comes from two distinct jet stream systems: the Polar- Front Jet Stream, which is associated with the air mass contracts (the fronts) of middle latitudes and which gives rise to the formation of squalls, storms, and cyclones in this latitude belt; and the Subtropical Jet Stream, which lies over the subtropical high-pressure belt, and which is characterized by predominant subsidence motions and, hence, with fair weather. During summer, a belt of strong easterly winds is found over Southeast Asia, India, the Arabian Sea, and tropical Africa, this tropical, easterly jet stream is linked with the weather disturbances of the Indian and African summer monsoons and their heavy rainfalls. Because jet streams have a great effect on aircraft flights, they are of considerable importance to aviation. On eastbound transoceanic flights, extra fuel, which takes up useful cargo space. Clear air turbulence (CAT) is often found in jet streams, and this turbulence, which leads to irregular aircraft motion, can be a hazard to passengers


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: