A new science
Applying higher mathematics to established technologies could certainly generate a slew of new patents and inventions.
by Andy Wilson
Recently, I received a question via e-mail on whether a "flux capacitor" had ever been invented. For the fans of the classic movie series "Back to the Future," this device needs no explanation. Doc and Marty traveled back in time using a "flux capacitor" embedded in a time machine designed into an inventive automobile, the DeLorean.
Intrigued by this somewhat fanciful idea, I proceeded to consult the Google oracle to discover such a device. Numerous mentions revealed a rock group from Entrea, a spiritualist sect from Tulsa, OK, and a man trying to contact aliens from Omsk, Russia. Obviously, these were irrelevant.
After several days of further research, the answer was revealed. The Lateral Flux Capacitor has been patented by researchers at Stanford University (Stanford, CA; www. stanford.edu). The researchers found a way of applying fractal geometry to the design of capacitors.
According to the patent (#6,084,285; July 4, 2000), Arvin Shahani and others have used the Koch Islands and Minkowski Sausage families of fractals for generating capacitor-conductive component perimeter shapes. Using such methods, they created linear integrated-circuit capacitors with greater capacitance per unit area.
No doubt, this invention will provide a boon to developers of capacitors for such markets as cellular telephones and personal digital assistants. By extrapolating this invention, one can envision the possibility of other inventions based around the idea of taking an established technology—such as a capacitor—and applying higher mathematics to it.
Imagine, for example, taking a typical power-supply heat sink and applying the Minkowski Sausage family of fractals to generate a more-effective means of heat dissipation. Or, for that matter, taking the established photolithographic means of collecting light at CCD photosites and applying fractal geometry. Maybe a fractal-based photosite could store charges more effectively than one based on linear photolithographic techniques.
Although no one has yet developed products based around this technology, the concept of applying higher mathematics to established technologies could certainly generate a slew of new patents and inventions. The idea is simple. Apply a new form of mathematics to an old product, apply for a patent, and make lots of money.
Getting the idea
But where can you look for the next big advances in mathematics that you can apply to established problems. For a start, you could turn to Stephen Wolfram's excellent book, A New Kind of Science, containing more than 1000 pages of easy-to-read mathematics. Published by Wolfram Media (Champaign, IL; www.wolfram-media.com), this seminal work has been called "an important work of ontology" by famed technologist Ray Kurzweil (www.kurzweilai.net/articles/.art0464.html?printable=1).
In the book, Wolfram states that phenomena do not always require complex models, and models based on simple programs can produce behaviors that are arbitrarily complex. To illustrate, Wolfram uses simple programs called Cellular Automata in numerous examples of physics, chemistry, biology, and mathematics. At the same time, the author questions the existing methods of characterizing systems, such as the Second Law of Thermodynamics, and the relationship between space, time, and relativity.
Mathematicians from all over the world are praising, criticizing, and commenting on the book. But this book offers more than mathematics. Were Friedrich Nietzsche and Immanuel Kant alive today, they probably would have spent hours discussing the philosophical implications of Wolfram's work.
A quiet revolution
A New Kind of Science works on a number of design levels. And it will be especially interesting to see how inventors use the mathematics presented to improve on today's established products. Like the application of fractal geometry to build more efficient capacitors, Wolfram's new science could start a quiet revolution in new-product development.