ee20-hw04-f09 - EECS 20N: Structure and Interpretation of...

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Unformatted text preview: EECS 20N: Structure and Interpretation of Signals and Systems Department of EECS University of California Berkeley Problem Set 4 Issued: 18 November 2009 Due: 24 November 2009, 6pm Circumstances Favorable and Unfavorable to Original Ideas It will be fairly clear to the reader that the really fundamental and seminal idea is to a large extent a lucky and unpredictable accident. There was no absolute necessity for Euclid to develop the axiomatic theory of geometry, nor for Gibbs to insist so strongly on the notion of probability in thermodynamics. These innovations might easily have occurred somewhat earlier or considerably later, and are no more satisfactorily subject to betting about them, say, than about the particular house in the village which would next be struck by lightning. For all that, though lightning is a sporadic phenomenon even for good betting, we do have a general idea of what circumstances are favorable for lightning and what are unfavorable. We do not build a house on top of a high and isolated hill without being particularly attentive to our lightning rods. So too in matters of invention, occasional and sporadic as the phenomenon is, we may look to certain circumstances to favor it, just as we may look to other circumstances to cut down the risk of lightning. There are certain procedures which are undoubtedly favorable for invention and discovery. One of the most potent tools in reanimating a science is mathematics. To some extent, a mathematical treatment of a science consists in writing down its data and its questions in a nu- merical or a quantitative form, but it is perhaps better to consider that here number and quantity are secondary to a logically precise language. If a certain question is to be asked in biology, and if we are to ask it in biological language, then we ourselves and whoever reads our work are likely to be strongly conditioned to think of what we have done as the answer to a biological question. However, if we express our ideas in a mathematical form, we are using what is much more likely to be...
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This note was uploaded on 12/24/2011 for the course ELECTRICAL 20 taught by Professor Babak during the Spring '11 term at University of California, Berkeley.

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ee20-hw04-f09 - EECS 20N: Structure and Interpretation of...

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