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It is because of these Greeks that we can tell a child, “If you build it out of triangles it will not collapse the way it does when you build it out of rectangles.” The Rhind Papyrus from Egypt (c.
These early surveyors laid the foundation for the development of geometry (“earth measurement” in Greek) by Pythagoras and Euclid and their colleagues around 350 BC.
Geometry is a precise language for talking about space. (Euclid’s has been used in this way for more than 2000 years.) It makes the children smarter, by giving them ways of expressing knowledge about arrangements in space and time.
Similar discoveries were made in many places in the world.
Holders of this practical knowledge were held in high esteem, and the knowledge was transferred to future generations through secret cults.
The practice of computation arose from military, scientific, business, and accounting applications. The computer revolution is a revolution in the way we think and in the way we express what we think.
Just as the early Egyptian surveyors probably thought of themselves as experts in the development and application of surveying instruments, so have we developed a priestly cult of “computer scientists.” But, as I have pointed out (H. The essence of this change is the emergence of what might best be called the study of the structure of knowledge from an imperative point of view, as opposed to the more declarative point of view taken by classical mathematical subjects.In a reprinted letter first published in 1967, Newell, Perlis, and Simon characterize computer science broadly as the study of the phenomena surrounding computers.We have witnessed and participated in great advances, in transportation, in computation, in communication, and in biotechnology.We close with some reflections by computer scientists on the nature of the field and the sources of their passion in their own work.Sussman identifies a distinctive characteristic of computer science as “procedural epistemology”—the representation of imperative knowledge that allows us to treat a symbolic expression as data for purposes of analysis and as procedure for purposes of dynamic interpretation.In each of these cases there was an advance in human intelligence, ultimately available to ordinary children, that was precipitated by an advance in mathematics, the precise means of expression.Such advances are preceded by a long history of informal development of practical technique.Traditional mathematics provides a framework for dealing precisely with notions of “what is.” Computation provides a framework for dealing precisely with notions of “how to.” Computation provides us with new tools to express ourselves.This has already had an impact on the way we teach other engineering subjects.But the advances that look like giant steps to us will pale into insignificance by contrast with the even bigger steps in the future.Sometimes I try to imagine what we, the technologists of the second half of the 20th century, will be remembered for, if anything, hundreds of years from now.