Peas in a Pod
"As alike as peas in a pod" is a familiar saying. Is it true? Today was the beginning of pea harvest in our garden, so I set out to test that hypothesis. A peapod and a camera were all the equipment needed.
You can see some photos at http://kensview.mirror1.org/post/2011/07/04/Peas-in-a-Pod with some pedestrian comments. Here I'm going to blue-sky the topic!
The first two photos show the pod before opening, and the pod after opening. Notice that the peas are attached to opposite sides of the pod. Perhaps one side has negative charges and the other has positive charges? And, by the way, how many peas are in a pod? Is it always an odd number?
The next two photos, snaps A and B, show hexagonal arrangements of the seven peas. What happened to the central pea in snap A? Did it remain the central pea in snap B, or is it on the periphery?
I cannot tell, at least not within my presumed ability to resolve pea-sized objects, which might be no larger than dust particles with a few excess or deficit electrons. One might consider the number of different arrangements of identical peas, with various charges, all of which would produce the same charge distribution. With all charge-X peas indistinguishable.
And of course to consider the arrangements in 3-space, not just in the plane.
Well ... I hope you may have fun thinking about that! I am enjoying it!
A book I recently read, "Symmetry" by Hermann Weyl, relates to this topic, ie conclusions that might be drawn from the variety of possible rearrangements of similar objects. Weyl's book is an odd combination of artistic commentary and mathematical musings. I think it is worth a read for the good artistic content. The mathematical musings, I believe, are no more than thought provoking. Weyl made numerous compromises in writing his book, and thereby lost the meaningful math within the arm-waving. Promoting the formation of intuition in math is good, but if done carelessly it may cause the reader to turn away, and miss both the insight and the opportunity to develop intuition. An intuitive presentation should be balanced with clear linkages to more careful explorations. Archimedes vs Euclid, perhaps, but Archimedes still leaves one with a clear logic accompanying his insights.
Nonetheless, one particular comment by Weyl may be useful for me. He mentions a pentagonal bit of architectural design, in Venice, on the island of San Michele: a passageway to the Capella Emiliana. I expect to visit Venice sometime and hope to be able to look for that passageway. It's great to have an objective when one visits a new place; so much else is learned along the way to a specific goal.
I've now started another book by Weyl, "The Theory of Groups and Quantum Mechanics", which appears to be a more careful treatment of topics such as symmetry. We'll see. Weyl is a very gradual writer, and takes a long time to set the stage before presenting his promised entertainment. His stage setting is itself interesting; one can notice "Ah-ha, sofa in that corner! Maybe villain will fall over it in the dark, in act 3?" But still, an investment in reading Weyl is not trivial, and one wants to attain some substantial insight as the outcome.
You can see some photos at http://kensview.mirror1.org/post/2011/07/04/Peas-in-a-Pod with some pedestrian comments. Here I'm going to blue-sky the topic!
The first two photos show the pod before opening, and the pod after opening. Notice that the peas are attached to opposite sides of the pod. Perhaps one side has negative charges and the other has positive charges? And, by the way, how many peas are in a pod? Is it always an odd number?
The next two photos, snaps A and B, show hexagonal arrangements of the seven peas. What happened to the central pea in snap A? Did it remain the central pea in snap B, or is it on the periphery?
I cannot tell, at least not within my presumed ability to resolve pea-sized objects, which might be no larger than dust particles with a few excess or deficit electrons. One might consider the number of different arrangements of identical peas, with various charges, all of which would produce the same charge distribution. With all charge-X peas indistinguishable.
And of course to consider the arrangements in 3-space, not just in the plane.
Well ... I hope you may have fun thinking about that! I am enjoying it!
A book I recently read, "Symmetry" by Hermann Weyl, relates to this topic, ie conclusions that might be drawn from the variety of possible rearrangements of similar objects. Weyl's book is an odd combination of artistic commentary and mathematical musings. I think it is worth a read for the good artistic content. The mathematical musings, I believe, are no more than thought provoking. Weyl made numerous compromises in writing his book, and thereby lost the meaningful math within the arm-waving. Promoting the formation of intuition in math is good, but if done carelessly it may cause the reader to turn away, and miss both the insight and the opportunity to develop intuition. An intuitive presentation should be balanced with clear linkages to more careful explorations. Archimedes vs Euclid, perhaps, but Archimedes still leaves one with a clear logic accompanying his insights.
Nonetheless, one particular comment by Weyl may be useful for me. He mentions a pentagonal bit of architectural design, in Venice, on the island of San Michele: a passageway to the Capella Emiliana. I expect to visit Venice sometime and hope to be able to look for that passageway. It's great to have an objective when one visits a new place; so much else is learned along the way to a specific goal.
I've now started another book by Weyl, "The Theory of Groups and Quantum Mechanics", which appears to be a more careful treatment of topics such as symmetry. We'll see. Weyl is a very gradual writer, and takes a long time to set the stage before presenting his promised entertainment. His stage setting is itself interesting; one can notice "Ah-ha, sofa in that corner! Maybe villain will fall over it in the dark, in act 3?" But still, an investment in reading Weyl is not trivial, and one wants to attain some substantial insight as the outcome.