It’s been quite a while since our last post, what with vacation and tests and all, but I think you’re really going to like this next one. I’m going to try to keep my own comments and questions brief to let the videos speak for themselves and give you all some real creative freedom in the discussion of the topic which is: spatial dimensions (2D, 3D and even 4D)!
You’ll be happy to know that the two videos to watch have English audio but are subtitled in Spanish. As I’ve said before, the questions I pose are not required answering. You can address as many (or as few) of them as you’d like, so long as you post a thoughtful and substantial comment related to the topic. I don’t want to see any lists of answering questions 1,2,3. Try to pick out an idea or two from the videos and the questions and focus your energy on responding analytically to those few concepts that capture your interest. In other words, responding to fewer questions with more depth is better than responding to all the questions with simple, one-sentence responses.
The first video asks you to imagine the confrontation between a 2 dimensional world and a 3 dimensional being (such as ourselves). After watching the video, considering the following:
The narrator speaks of the dots’ “fear of the unknown” and the forbidden “a” word (above). In your knowledge of the history of mathematics and science, what were some important moments and concepts that forced people to confront this basic human fear? Who were some of the important scientists and mathematicians that worked to explain and publicize their unsettling discoveries? (hint: think Galileo etc.)
Imagine yourself as the dot, confronting a being (like the white haired superhero from the video) that exists in a dimension completely beyond your experience and comprehension. How might you react in such a situation? Would you be scared? Curious? Angry? Try to think of real world examples of human reactions to scientific discoveries that threaten the comfort of existing circumstances (eg. the theory of a world that is round rather than flat). In what ways do people try to explain or justify that which they cannot understand (eg. superstitions, denial, investigation etc.)?
Food for thought: The difficulty (and frustration) that results from trying to explain something that is outside someone’s experience. Think about trying to explain the color red to a person who was born blind, and has never seen any color at all.
OJO! Optional, secondary topic for those who prefer: If you would rather address the following questions you have that option. It isn’t necessary to answer both sets of questions unless you feel compelled to do so or wish to integrate them. If the concept of various dimensions really interests you, take a look at this video with Carl Sagan (who is really an incredible person—I highly recommend his TV series, “Cosmos: A Personal Voyage”).
In this video, Carl Sagan gives us an explanation of spatial dimensions very similar to the one we saw in the previous video, but he includes an introduction to the concept of a 4th spatial dimension and the four dimensional analog of the cube, called the tesseract. If you’d like to see a brief video that represents the rotation of the tesseract click here.
Sagan explains the tesseract as a “projection” of the shadow of a 4 dimensional shape that he calls a hypercube. Explain what he means by this.
The tesseract forms part of a theory of a 4th spatial dimention, as opposed to theories that speak of the “space-time continuum” in which time forms the 4th dimension and even more dimensions beyond that are considered possible. Do you have any ideas about what other dimensions could be like? Use your imagination. Science fiction proposals are warmly welcome!