By James Bailey
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Additional info for After Thought: The Computer Challenge To Human Intelligence
This Renaissance-era view of the world is still wired into modern multiuser electronic computers at the hardware level. Such computers have two memory-address spaces. One is for program instructions (sometimes called I-space) and is shared by many users because, of course, instructions never change. The other (D-space) is for data, which is allowed to be different for each user. The success of Newton's Principia Mathematica focused scientists on behaviors that could be successfully predicted within the constraints of fixed formulations.
The vocabulary 0/ the mathematical/iction inexorably becomes the vocabulary with which we describe the reality. This is the reason that a change from sequential equations to parallel matings and breedings is so seminal. It affects all of us, not just scientists. It will literally change heaven and earth because it will change the way we conceive of them. It was, for example, precisely this kind of intellectual-computational transition that brought Galileo into conflict with the Renaissance Church.
Today, this book is best known as the one in which Fermat wrote the marginal reference to his Last Theorem. It was, however, also the vehicle by which the ideas of "algebra," including the concept of an "unknown," entered Christian Europe. As is clear from the purely geometric work of Copernicus half a century later, the impact of the new algebraic technology was not immediate. It was integrated in halting and tentative steps. For example, at the time Regiomontanus was absorbing Diophantus, he was preparing his own treatise on triangles.
After Thought: The Computer Challenge To Human Intelligence by James Bailey