Computer Software and Copyright
Appendix 2. Why Mathematical Formulas and Computer Algorithms Cannot Be
Copyrighted
By way of example here is yet another somewhat philosophical explanation.
The great Hellenic Greek mathematician Archimedes had an idea which almost
resulted in the development of Calculus almost two millennia before Newton's
achievements. At the time of Newton, the German mathematician Lebiniz also
had an idea which led to Calculus. Although Newton and Lebiniz argued about
which one of them came up with Calculus, neither of them could successfully
argue that the idea belonged to one or the other. There can be no copyright
ownership of ideas.
The mathematical expressions of the ideas of Archimedes, Newton, and
Lebiniz are examples of ideas that are inseparable from their expression.
To express these ideas one must use the language of mathematics. As mentioned
in the
example in §5, mathematical
equations are considered works of nature. They represent abstract truths.
When a scientist characterizes an observation via a mathematical equation,
she is expressing an abstract truth of nature. Her idea to express the
truth is inseparable from the truth itself. Likewise, the means of expressing
the idea, or abstract truth, are inseparable from the truth itself.
The key for an equation is "abstract." Recall that if the equation is
incorporated into an article that describes a method, then the whole article
is subject to copyright protection. The equation, however, cannot be copyrighted.
One may theoretically use it to solve an entirely different problem expressed
in an entirely different manner.
Likewise, a computer algorithm by itself cannot be copyright-protected.
A mathematical algorithm is a "procedure for solving a given type of mathematical
problem." It is basically a particular way to write an abstract mathematical
truth. This algorithm is inseparable from the mathematical truth it represents.
* Written by John E. Wehrli, formerly of the Patent Department, Lawrence Berkeley
National Laboratory. Available as LBL Report No. 38995.
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