September 25, 2017

Explore Particle Physics

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dimensions of particle physics

I, Dr. Rob, am a particle physicist. While theoretical physics is an amazing topic, it can be difficult to discuss with non-physicists. For that matter it can be difficult to discuss with physicists from other fields. I am thrilled to tell my friends about Symmetry Magazine. The articles are short, well written, and the photos and other graphics are incredible. If you wish you may subscribe for e-mail updates that contain links to the feature stories.


Symmetry Magazine -- Annus Mirabilis

One article that is especially interesting concerns Einstein’s most famous equation, E=mc2. The article is Einstein’s most famous equation, and it contains a fabulous video that is only two and one-half minutes long. It discusses how mass may be converted into energy, such as fusion or fission energy. It also discusses how new particles are created in particle accelerators like the LHC. Just click on the Annus Miarbilis figure shown, or go to the article link above. The visuals are very powerful, and the discussion is surprisingly easy to follow.

I choose to teach!

apple web size copyOur culture is the exponentially growing collection of knowledge and invention that we pass from one generation to the next.  Science and mathematics are especially rich components of our culture with millenia of contributions from many cultures and all regions of the globe.  Unlike other forms of inheritance which must be subdivided and are often distributed with inequity, this inheritance is the birthright of every person, and every person may consume as large a share as he or she would wish. Our world is one of science, mathematics and technology; literacy in these areas is essential for any individual who is to be engaged with and empowered in our world.  The curriculum is a subset of this inheritance which is distilled down and shared with students in the environment we call school.

The America that we know today was built by those who left their homelands because they were not first-born sons  and therefore had very limited birthrights.  Others came from situations where even first-born sons had few if any prospects.  With an education in America a person has prospects to not only survive but to thrive and to provide for children.  But if we measure the value of an education solely in terms of economic benefit, then we ignore the greater part of its value.Owl Box

In times past you might have been a  carpenter because  your father was a carpenter whether or not you were well suited for that occupation.  You might have been a mother and a housekeeper because it was expected,  but even learning to read was not a possibility.  Perhaps you would have been a field hand because that was the only option available.  Carpentry, parenthood  and farm work  are all important roles, and they bring joy to those who choose them.  However, with education you may choose to be a nurse, or a doctor or a software engineer because  the work suits you well.  And along the way you may sculpt your own identity;  you need not accept the identity that others force upon you.

Students do not always appreciate the awesome value of this cultural inheritance, so  a primary function of the teacher is to help the student understand the meaning of the curriculum with respect to the life of the student.  Once the student is engaged the teacher serves as  a guide.  Success is  achieved when the student is  able to function as the most important person in his or her own education.  A successful education system produces graduates who are life-long learners that are able to learn and grow with or without formal schooling.   I teach as a matter of social justice. I teach to empower students. I teach so that students may understand their world, be part of it, contribute to it and reap its rewards.  I teach because the rewards of working with students greatly outweigh the economic remuneration that comes with teaching.

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Group Theory and Indigenous People

The mathematics of Group Theory arises in so many contexts!  Not all of them are expected.  The kinship relations of the Warlpiri people of Australia are seemingly very complex, and one must wonder how the scheme was ever devised.  This is rather nicely covered in the book Ethnomathematics, A Multicultural View of Mathematical Ideas, by Marcia Ascher.  In my article at Warlpiri Groups I build upon the presentation from that book.  I work out a concrete representation of the group in terms of states and operators in an eight-dimensional real space.  This is a fairly advanced topic, but it is a great opportunity to deal with Group Theory in a pragmatic example.

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Why Lissajous Figures?


Lissajous figures may be drawn by moving some type of marking tool back and forth in one direction with one frequency while simultaneously moving it in a perpendicular direction at a second frequency.  The resulting curve will be closed when the frequencies are in an integer ratio.  The results can be somewhat amusing, like a child’s Spirograph toy.  At the same time, these curves are rich with mathematical content interesting to mathematicians, physicists and engineers.  For a more in depth discussion visit my Lissajous Figures article.  The curve you see plotted here was generated by a Matlab program with a Graphical User Interface which is available for free download to users of Matlab.  The program is useful for investigating the properties of Lissajous curves and their derivatives.  The discussion is rich with the periodic functions sine and cosine with various parametrizations.  The curves are parametric curves, and the derivative of a Lissajous curve is another Lissajous curve.  Jules Antoine Lissajous was inspired by these curves to create a mechanical device for projecting them on a screen, and others improved upon the concept in the form of the harmonograph.

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