Discovering Group Theory, Day 2

Topics:

  • Rotational symmetry
  • Identity
  • Inverse
  • Formal definition of a group
  • Group product

On Day 2, we considered only rotations of various polygons around their geometric centers. After a systematic hands-on investigation and cataloguing of rotations which leave a polygon unchanged, we identified the identity transformations and the inverse of each rotation. The class concluded we the formal definition of a group.

A white board with drawn polygons and lists of the rotations which leave it looking the same.
Cataloguing rotations of various polygons which leave them unchanged.

 

Physics of Color @Hampshire, Day 2

Topics: Physical and neurological mechanisms for perception of color

  • We began the class by discussing students’ responses to a short assignment asking them to paint something and investigate how its appearance changes when it is illuminated by different types of light. Examples of interesting and insightful experimentations pictured were done by Madeleine Perreault and Lindsey Appleyard. (The effects of taking a cellphone photograph to be discussed later!)
    The difference in appearance of a watercolor composition illuminated by a desk lamp and by sunlight, by Madeleine Perreault

 

A painting illuminated by full spectrum light and pink light, by Lindsey Appleyard.

 

 

  • We discussed the physical processes necessary for the perception of color to take place, including everything from the generation of light by a source to the neural processing of the light signals by the brain, and identified those which can be explained by fundamental physics.
  • Students investigated and made qualitative observations of the color spectrum of various sources of light using hand-held spectrometers.

Resources:

  • B. Conway, “Color consilience: color through the lens of art practice, history, philosophy, and neuroscience.” Annals of the New York Academy of Sciences, vol. 1251, The Year in Cognitive Neuroscience, 2012, pp. 77–94.