GA Explorer Updates - January 2017
Geometric Algebra: Ascension of the Mind
New Blog Posts:
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.
Elements of Geometric Algebra
In my view as a software engineer, I could identify 10 main elements of the mathematical structure of GA. The integration of the 10 elements produces a rich mathematical language capable of expressing much more than the mere sum of its parts. In this post, I will describe each component and talk a little about its significance and varieties without delving into any mathematical details. The information in this post can be useful for someone starting to study GA and wanting a clear roadmap for understanding and relating its main concepts and algebraic tools.
The GA Interviews Series
A series of interviews with key researchers developing and applying GA in their work, and sharing their valuable insights and experiences. New posts in this series:
- Knowing About the World via GIS: Dr. Yu Zhaoyuan explains the importance of Geographical Information Science (GIS) and the potential of Geometric Algebra as a mathematical modeling tool in this fascinating field of study.
- Founders of Geometric Calculus: Dr. Garret Sobczyk tells us about his fascinating life journey with Prof. David Hestenes. Their journey eventually inspired many researchers to follow their lead in learning, developing, and applying Geometric Algebra and Geometric Calculus to many fields of science.
- Geometric Algebra in Computer Science: Dr. Leo Dorst, Dr. Dietmar Hildenbrand, and Dr. Eckhard Hitzer are 3 key researchers who apply Geometric Algebra in their work to share their valuable experience and insights. Their applied research spans many applications in computer science including Computer Graphics, Robotics, Computer Vision, Image Processing, Neural Computing, and more.
- Cybernetics with Transdisciplinary Geometric Algebra: Professor Eduardo Bayro-Corrochano is a leading cyberneticist 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. Prof. Eduardo Bayro 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.
New and Updated Pages:
If you think this new content is useful, please support the GA Explorer website efforts to make GA a popular mathematical tool by sharing this email with your friends and colleagues.
- Updated the GA Explorer website to use secure SSL (https://gacomputing.info). Now you can enter your information safely and register in the GA Explorer website securely.
- Updated the GA Software page: On this page, you can find a list of software related to Geometric Algebra. The list is ordered alphabetically with descriptions and links to each software web page. The GA Explorer website welcomes all GA software designers to send or update a description of their GA software to be added to this list.
- Updated the GA Community page: This page lists some information, up to the best of my limited knowledge, on the people involved in research related to Applied Geometric Algebra in computer science and engineering in alphabetical order by last name. The GA Explorer website welcomes members of the GA community to send information about their GA-related work to update this list.
- Updated the GMacDSL Affine Geometry Sample page: The samples described on this page illustrate how to use GMacDSL for encoding 3D affine primitives and transformations using the simplest of all geometric algebras: the 3D Euclidean GA having 8-dimenstional multivectors. We will explore using GMacDSL for this task, and see how the selection of our algebra can seriously limit our ability to write geometric computing code regardless of the selected programming language.