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Why Software Is Abstract

Oct 10, 2010, 19:02 (15 Talkback[s])

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"Following the ruling of the Supreme Court in Bilski, the USPTO asked, in substance, how to tell an abstract idea from an application of the idea. In this article I propose an answer to the question of what makes software abstract. It is a follow up to the previous article, Physical Aspects of Mathematics.

"The logic is to look at why a mathematical calculation is abstract and then see if the same logic applies to software. It happens that it does. It is possible to show that software is abstract with references to the underlying mathematical aspects. This is not, however, the topic for this article. The argument is presented without any assumption as to whether or not software is mathematics. I work from the observation that a mathematical calculation solving a mathematical problem is abstract. Then I look at what makes it abstract. Then I observe that the exact same logic is applicable to all software whether or not the law sees it as an algorithm as defined by Benson. This is not surprising. Software is mathematics and this makes it abstract, but I don't use or rely on this fact in making the arguments in this article.

"Abstraction Is Self-Containment

"Let's start with experts, who can define for us what makes mathematics abstract, in some writings on the psychology of learning. See Mitchelmore, Michael and White, Paul — Abstraction in Mathematics and Mathematical Learning (where you can download the article as PDF)

"We claim that the essence of abstraction in mathematics is that mathematics is self-contained: An abstract mathematical object takes its meaning only from the system within which it is defined. Certainly abstraction in mathematics at all levels includes ignoring certain features and highlighting others, as Sierpinska emphasises. But it is crucial that the new objects be related to each other in a consistent system which can be operated on without reference to their previous meaning. Thus, self-containment is paramount."

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