Difference between revisions of "Holonomy Project"

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== Title ==
{{InfoboxProject
Holonomy Project
|project=Holonomy Project
|image=[[File:Holonomy.png]]
|topic=[[Graph, Wall, Tome]]
|leader=EricRWeinstein#6876<br>[https://twitter.com/Tim_Melon Tim (TimFH#7940)]
|startdate=
|customlabel1=
|customdata1=
|customlabel2=
|customdata2=
|customlabel3=
|customdata3=
|customlabel4=
|customdata4=
|link1title=GitHub Repo
|link1=[https://github.com/serenedesiree/Models Repo (private)]
|link2title=Documentation
|link2=[https://github.com/serenedesiree/Models/blob/master/README.md Documentation (Private)]
|link3title=
|link3=
|link4title=
|link4=
}}


== Project Manager ==
<span class="highlight">Wait for Further News from Eric</span>
serenedesiree#0956


== Team Members ==
A visualization of the effect known as "holonomy", whereby parallel transporting a vector around a loop in a curved space leads to the vector changing upon returning to the start of the loop. How/how much the vector changes orientation/position in space is the holonomy of that loop in that space. This effect reveals deep information about the [https://en.wikipedia.org/wiki/Curvature curvature] of the space itself.
* serenedesiree#0956 - Project Lead
* Tim FH#7940 - Mathematics Lead
* Ben C#7492 - Programming Lead


== Prod URL ==
Please send any enquiries to TimFH in the Portal discord.
TBD


== Dev URL ==
== Goals ==
TBD
* Visualize holonomy to develop public intuition of the concept.
 
== GitHub URL ==
https://github.com/serenedesiree/Models (private)
 
== Documentation URL ==
https://github.com/serenedesiree/Models/blob/master/README.md (private)
 
== Description ==
[Programming Lead's Best Attempt Effort] Interactive demos highlighting the concept of [https://en.wikipedia.org/wiki/Holonomy holonomy]: where a calm ("[https://en.wikipedia.org/wiki/Parallel_transport parallel transport]"), round trip path traveled following "straightest" paths ([https://en.wikipedia.org/wiki/Geodesic geodesics]) reveals deep information about the [https://en.wikipedia.org/wiki/Curvature curvature] of the space itself.
 
== Long Description ==
[Programming Lead's Best Stab]
 
Gauge theory allows us to map from one space to another, essentially allowing exploration in the second space via traversing the original space. The position in the original space sets the foundations and assumptions of the second space, and by allowing that position to vary, we can move beyond fixed assumptions (such as, preferences are fixed in computing the consumer price index in Economics) to a mathematics that expresses the true underlying richness available across all of Physics, Economics, and other fields.
 
This project provides a suite of interactive visualizations, aiming to share intuitions about the core concepts that are gatekeepers to understanding Gauge theory: multi-variable calculus, curvature, fiber bundles, and fibration. Intuition is built by implementing these concepts in things we can see and manipulate: 2D and 3D objects.
 
Currently, we have a Python demo that shows how we can map from a 2D space into 5D: a 3D space with 2D vectors at each point. The visualization follows the  2D original space (x and y plane) as it varies in time, and shows the total amount of curvature (holonomy; z plane) experienced by a special kind of round-trip in the mapped space. Attached at each point, it also shows the curvature of the output space (otherwise, not visualized) associated with that point, to give a sense of how curvature is generating the holonomy measured at each point along the original space.


== Demo ==
== Demo ==
https://theportal.wiki/etc/holonomy/2r-4s.gif
https://theportal.wiki/etc/holonomy/2r-4s.gif
<div class="max-width">
https://theportal.wiki/images/7/7b/Holonomy_Example_-1.png
</div>


== Screenshots ==
== Members ==
[[File:Holonomy Example -1.png|thumb]]
* Lex Fridman#3057
 
* Tim FH#7940
== Cover Image ==
* serenedesiree#0956
https://theportal.wiki/images/f/f5/Holonomy.png
* Ben C#7492
* BeefSandwich27#0143


__NOTOC__
[[Category:Archive]]
[[Category:Stalled]]
[[Category:Projects]]
[[Category:Projects]]
__NOTOC__
[[Category:Graph, Wall, Tome]]

Latest revision as of 18:24, 7 March 2021

Holonomy Project
Holonomy.png
Information
Topic Graph, Wall, Tome
Leader EricRWeinstein#6876
Tim (TimFH#7940)
Links
GitHub Repo Repo (private)
Documentation Documentation (Private)
All Projects

Wait for Further News from Eric

A visualization of the effect known as "holonomy", whereby parallel transporting a vector around a loop in a curved space leads to the vector changing upon returning to the start of the loop. How/how much the vector changes orientation/position in space is the holonomy of that loop in that space. This effect reveals deep information about the curvature of the space itself.

Please send any enquiries to TimFH in the Portal discord.

Goals

  • Visualize holonomy to develop public intuition of the concept.

Demo

2r-4s.gif

Holonomy_Example_-1.png

Members

  • Lex Fridman#3057
  • Tim FH#7940
  • serenedesiree#0956
  • Ben C#7492
  • BeefSandwich27#0143
Retrieved from ‘https://old.theportal.wiki/wiki?title=Holonomy_Project&oldid=9646’