I usually begin with a story about lying on a cot looking up at the stars on a dark night in the mountains, seeing countless stars and the hazy Milky Way stretching across the sky. I talk about how they seem to be part of a celestial dome rising very high above me, and I note that I do not have any way to know, as I am looking at the stars above me, how far they are away from me. I talk about how ancient people used and envisioned the stars. I mention the experiment with the Hubble Space Telescope in which the "darkest" and most empty part of space was imaged, and found to contain countless distant galaxies (search on "Hubble deep field" or go to http://www.stsci.edu/ftp/science/hdf/hdf.html). I mention that this often leads people to consider how insignificant they are in the scheme of things. My feeling is that you are only as significant (or insignificant) as your actions make you. I then talk a bit about how we now know that "visible" matter is organized into atoms, which are very, very small. In a way, they are like the stars in that they seem to be incomprehensibly small, while stars seem to be incomprehensibly large and distant. I then pose the question, "How does the part of this world that we observe and experience on a daily basis fit into a physical reality that spans from the incomprehensibly small to the incomprehensibly large?" I pass-out the blank worksheet "Comparison of Lengths Relevant to Our Universe" to every student, and have them organize into groups of 2-3. The task is to fill-in the exponents corresponding to 9 distances listed in a box on the page, and to locate those distances on the logarithmic scale. I give them a couple of minutes to start working with the page, and then interrupt to ask what they need help with. This usually involves determining one of the lengths involving light years on the board. I let them complete the tasks in their small groups, then I ask group representatives to call-out their results. Working from a set of correct answers, we then discuss the scale. For example, we note that there is a greater difference (in orders of magnitude) between the size of a proton or electron versus the size of a hydrogen atom, and the height of a person and the peak elevation of Mt. Everest. It is usually noted that humans fall near the middle of the length spectrum of the universe, which was also noted by Primack and Abrams (2006). Some students place great importance on this. I tend to note that there is a practical limitation to the size of individual cells that will have predictable functions (they need to be larger than the length scale governed by quantum mechanics) and constraints on the upper size limit of organisms made of cells, which determines where we are on the scale.


  • Mathematics > General

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Vocational/Professional Development Education,Higher Education,NSDL_SetSpec_380601,oai:nsdl.org:2200/20100502195218142T,Undergraduate (Lower Division),Space Science,Lunar and Planetary Science,Mathematics,NSDL



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