A Cyberneticist, or cybernetician, is a person practicing Cybernetics: a transdisciplinary approach for exploring regulatory systems; their structures, constraints, and possibilities. Professor Eduardo Bayro-Corrochano is one such leading academic who uses Geometric Algebra to handle the diverse fields of theoretical knowledge and practical application he needs. Such fields include Robotics, Neural Computing, Computer Vision, and Lie Algebras. In this post, I interview Prof. Eduardo Bayro who tells us about how using GA in his work can simplify dealing with such diverse fields, and how can GA relate, generalize, and unify ideas from these fields together in his mind and the minds of his students.
I discovered Geometric Algebra (GA) back in 2003 and it caught my attention immediately. In my whole life as a student, engineer, researcher, and teacher I’ve never met a symbolic mathematical system so beautifully close to geometric abstractions. In this post, I try to explain how Geometric Algebra can express, unify, and generalize many geometric abstractions we use as engineers and computer scientists.
In part one of this functional history of numbers we saw the development of various number systems we are mostly familiar with. In this part, we will see the development of many number systems that are important for our modern scientific needs, geometrically and computationally. The sad fact about these developments is that we are using and teaching less effective number systems today because of a “series of unfortunate events” that took place during the grand drama of human development of modern mathematics.
The main goal of this post is to link Geometric Algebra to mathematics on the fundamental level of numbers. Here I briefly describe the history of numbers with emphasis on their functional role in mathematics, science, and engineering to put the computational role GA can play into perspective.