SEMF | Taliesin Beynon | Geometry of Computation | SPACIOUS SPATIALITY 2022 @SEMF | Uploaded May 2022 | Updated October 2024, 18 hours ago.
Plenary session kindly contributed by Taliesin Beynon in SEMF's 2022 Spacious Spatiality
semf.org.es/spatiality
SESSION ABSTRACT
Continuous geometry has served as a substrate for a deeper understanding of many topics in science and engineering: organizing families of objects or actions into abstract spaces unlocks both familiar geometric intuitions and powerful new mathematical tools. Phase spaces of physical and chemical systems, shape spaces of 2D and 3D forms, representation and parameter spaces of neural networks, state spaces of control systems, probability distributions in information geometry, and configuration spaces of mechanical robots serve as diverse examples. But finite computational processes provide a wellspring of discrete spaces with connections to language, reasoning, logic, and information. How might we adapt tools devised for continuous geometry to these fundamentally discrete settings? What are the digital forms of familiar constructions like continuous maps, quotients, curvature, product spaces, and fiber bundles, and what role do they play in understanding the computations that generate them?
SESSION MATERIALS
· Discrete Geometry and Quivers Website: quivergeometry.net
TALIESIN BEYNON
Wolfram Physics Project: wolframphysics.org
Profile in Wolfram Research: wolframphysics.org/people/tali-beynon
Personal website: tali.link/about
GitHub: github.com/taliesinb
Twitter: twitter.com/taliesinb
LinkedIn: linkedin.com/in/taliesinb
SEMF NETWORKS
Website: semf.org.es
Twitter: twitter.com/semf_nexus
LinkedIn: linkedin.com/company/semf-nexus
Instagram: instagram.com/semf.nexus
Facebook: facebook.com/semf.nexus
MUSIC
youtube.com/user/Baroquenoise
Plenary session kindly contributed by Taliesin Beynon in SEMF's 2022 Spacious Spatiality
semf.org.es/spatiality
SESSION ABSTRACT
Continuous geometry has served as a substrate for a deeper understanding of many topics in science and engineering: organizing families of objects or actions into abstract spaces unlocks both familiar geometric intuitions and powerful new mathematical tools. Phase spaces of physical and chemical systems, shape spaces of 2D and 3D forms, representation and parameter spaces of neural networks, state spaces of control systems, probability distributions in information geometry, and configuration spaces of mechanical robots serve as diverse examples. But finite computational processes provide a wellspring of discrete spaces with connections to language, reasoning, logic, and information. How might we adapt tools devised for continuous geometry to these fundamentally discrete settings? What are the digital forms of familiar constructions like continuous maps, quotients, curvature, product spaces, and fiber bundles, and what role do they play in understanding the computations that generate them?
SESSION MATERIALS
· Discrete Geometry and Quivers Website: quivergeometry.net
TALIESIN BEYNON
Wolfram Physics Project: wolframphysics.org
Profile in Wolfram Research: wolframphysics.org/people/tali-beynon
Personal website: tali.link/about
GitHub: github.com/taliesinb
Twitter: twitter.com/taliesinb
LinkedIn: linkedin.com/in/taliesinb
SEMF NETWORKS
Website: semf.org.es
Twitter: twitter.com/semf_nexus
LinkedIn: linkedin.com/company/semf-nexus
Instagram: instagram.com/semf.nexus
Facebook: facebook.com/semf.nexus
MUSIC
youtube.com/user/Baroquenoise
