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Equations as icons

Comments We welcome your comments! Our full comment policy can be found here. Learn more about Disqus on rabble. Please keep in mind:. Do Tell the truth and avoid rumours. Add context and background. For some people this expression, named after the 18th-century Swiss mathematician Leonhard Euler, even seems to have become an icon, having special significance apart from its mathematical context.

It once even served as a piece of evidence in a criminal trial. In August an eco-terrorist assault on several car dealerships in the Los Angeles area resulted in millions of dollars worth of damage when a building was set alight and over vehicles were destroyed or defaced. Using this as a clue and later as evidence, the FBI arrested William Cottrell, a graduate student in theoretical physics at the California Institute of Technology, who was later tried and convicted.

The Equations: Icons of Knowledge - AbeBooks - Sander Bais:

Icons can have a dark side, when they call more attention to their image than to what they stand for. The spell cast by equations can tempt us to think that all knowledge can and ought to be couched in the form of equations, with neat packages, balanced amounts and simple units. Equations have, for example, been composed for making perfect sandwiches, workable relationships and successful sitcoms. These are, however, illegitimate attempts to create algorithms for things that cannot be quantified.

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The spell of equations that I want to discuss is something different, that of genuine equations that enthral authentic scientists. But how can an equation become an icon? After all, an equation is merely one step in the ongoing process of scientific inquiry.

Exact Differential Equation - Numerical - M2 - Lecture 2

If equations are only a means to an end, of less intrinsic value and interest than the tasks they were developed to help us with, why do some of them seem to possess an inherent value or significance beyond the process of inquiry to which they belong? Why can an abstract object like an equation literally stand alongside a pair of boots or a car? The answer is that some steps in an inquiry acquire, and deserve, special status. Certain expressions serve as landmarks in the vital and bustling metropolis of science, a city that is continually undergoing construction and renovation. They preserve the work of the past, orient the present, and point to the future.

Theories, equipment and people may change, but formulas and equations remain pretty much the same. They are guides for getting things done, tools for letting us design new instruments, and repositories for specialists to report and describe new discoveries. They summarize and store, anticipate and open up.

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But there is still more to equations. They serve as clear and concise examples of what equations and formulas do: they show how seemingly disparate elements are implicated in a unity, and do so concisely, with few moving parts, so to speak. They bring what equations do out into the open. They are like a really good joke the economy of which reveals the structure of a joke, or a proof so concise that it demonstrates what a proof is.

If equations have a dark side, it is that they can also lead us to think that knowledge resides in the equation itself, rather than in the ongoing processes of construction and renovation.