Next meeting:
6:30PM Friday, May 11, 2012 in ST301
ST is the Charlene Nunley, Student Service Center, 7625 Fenton Street,
Silver Spring, MD 20912, USA on the Takoma Park/Silver Spring Campus of
Montgomery College
Old humans, at the moment only old men, but we are not adverse to old
women joining us: Alan Bromborsky, Michael Brabanski, Jack Gaffey,
Walter Faust, and Harold Williams (host) and now joined by Wayne
Warren. The core group are all NCA, National Capital
Astronomers, members, but this is not about astronomy. The core
group could be described vocationally as engineers, mathematicians, and
physicist. As of March 5, 2010 jointed by Tecola, Phineas St.
Clair and Haliu Bantu. They are all interested in the way the universe
works and how it might be modeled mathematically. Paul Barrett
joined us for the first time on May 7, 2010. On May 28,
2010 T.J. O'Malley joined us for the first time. On June 18, 2010
Juan Carlos Godefroy joined us for the first time. On October 29, 2010
Randy Bryant from Fort Walton Beach, Florida joined us regularly now
via Chat using Google and the Google Chrome browser. He had
occasionally joined us earlier, but we regularly lost him, now the
Internet and its tools seem to be stable enough to support this without
dropping him. Montgomery College's internet and Cox Net on
Randy's end seem to be improved now, too. Joined on May 20, 2011
by Allen Dayton.
Younger humans, Montgomery College students who have attended some of
these meetings: Alpha Bada, Ian McIntire, Lorena Aries, Georgio
Mori-Block, Ahadu Tilahun, Daman Camara, Leah Gold, Tony Johnson, Chris Leeney, Cassidy Farrel, Brian
McDermont, Eban Coleman, and on 11-4-2011 joined by Edelweiss Calcagno.
These
very bright students continue to move forward in their studies
now mostly at other illustrious institutions (we have been doing this
since 2007) with only the newer students still with us, we are a
2 year institution, but some of our bright students are with us more
than 2 years, especially if they have to work full or part-time to
support their studies or have three young children and a husband and
household to manage.
Rules: We eat together on some Friday evening; this is a supper
discussion group. Old humans (people with good jobs or retirees with
good incomes) pay for their meals that we order to be delivered to the
meeting room, younger humans (college students, who are obviously poor
by definition, remember what it was like when you were young) eat for
free. Older humans contribute a small amount of money so
that the younger humans may eat for free. Coffee and tea and sometimes
cake or cookies, a white board, computer with Internet link, and
computer video projector are in the room that we meet
in. We generally start by listen to a
little music while eating and then start studying and asking
questions. We often listen to music while eating; or occasionally
watch a short video. The music generally has words and is some times
folk music and is quite satirical and often irreverent and sometimes
political. We have members who have voted for both
Democrats and Republicans and a few who have voted for both parties at
different times; and religiously we have members who are Unitarians
through Baptist Deacons with at least one militant Atheist; so it helps
to be a tolerant person with an open mind and a strong sense of
yourself in this group; everyone is welcome regardless of political
party, religious faith or lack there of, ethnic group or groups, or
gender definition. All sentient life forms are welcome, though as
far as we have been able to determine so far only humans have attended,
but extra-terrestrials who are non-violent would be most welcome by the
group. For instance we have listened to Utah Phillips, a
labor organizer, folk singer, storyteller, poet and self-described
"Golden Voice of the Great Southwest". We are clearly corrupters
of the youth just as Socrates was. Anyone who is free when we
meet and is interested in our study of Geometric Algebra is
welcome. Many more people have been invited by a factor of
several than have ever showed up, mostly mathematics and physics
faculty from all of the campuses of Montgomery College and students
from the "Science Adventure Club" that Harold Williams is the
adviser. Dragon City Menu that we often order from is here.
Previously we have learning to multiply Multivectors (vectors) in a
Linear Space (sometimes called a vector space)
over a scalar Fields
a Clifford Algebra. This has great application in engineering,
computer science (vision), and physics. We are now slogging
through the fundamental theorem of geometric calculus and it is not
easy, but it includes all of the vector, tensor, multivector integral
and derivative theorems all at once. It is very powerful and very
general and somewhat abstract.
A group of files on Geometric
Algebra collected by Alan Bromborsky most written by others, but
some written by Alan is here. Our study guide for now is the "An
introduction to Geometric Algebra and Calculus" by Alan Bromborsky now
book format bookGA.pdf. Another file
written by Alan Bromborsky with just the Geometric Algebra part with
out the Calculus part is at file and is
titled "An Introduction to Geometric Algebra." It is very similar
to the first part of the previous document but it does have one diagram
that is some what different on page 23 and may help some people
understand the geometry in the Euclidean case. We have been
applying Geometric Algebra to solve some problems, we used the document
GAexamples.pdf. A file in the
GA-SIG directory is GA&GC.pdf
and its title is "A Survey of Geometric Algebra and Geometric Calculus"
by Alan Macdonald of Luther College, Decorah, Iowa so you can see these
idea have even spread to Iowa. So it is time we caught up with
the dark side of the moon, if they know it in Iowa, where the corn
grows, then Arkansas and Mississippi, where the cotton grows, can not
be far behind! What is it that we grow in Maryland besides
brilliant students? This document is only 26 pages long with
another 4 pages of web links and other references. It also says
on the first page:
“The principal argument for the
adoption of geometric algebra is that it provides
a single, simple mathematical framework which eliminates the plethora
of diverse
mathematical descriptions and techniques it would otherwise be
necessary to learn.”
[9] McRobie, F. A. and J. Lasenby (1999). Simo-Vu Quoc Rods using
Clifford Algebra,
Int. J. Numer. Meth. Eng. 45, 377–398.
Furthermore this is true. Another excellent review of some of
these ideas is in "Using Geometric Algebra for
Navigation in Riemannian and Hard Disc Space" which even explains
how to store these mathematical structures on a computer in HDF5, Hierarchical
Data
Format. A new lecture "Clifford algebra: use and abuse
in physics and engineering" by Peter Renaud of the Department of
Mathematics and Statistics, University of Canterbury, Christchurch, New
Zealand, (dated 11 January 2011) that is a PDF version of a PowerPoint
can be found here. The Moral page here is particularly
important.
Some interesting articles using Clifford Algebra in elementary particle
physics
Meetings in the 2007-2008 Academic year:
Year One
5:30PM Friday, September 14, 2007 at Mayorga Coffee Factory
6PM Friday, October 5, 2007 at ST301
6PM Friday, October 26, 2007 at ST301
6PM Friday, November 16, 2007 at ST301 directory
of
pictures from my crummy cell phone camera during this meeting,
but very informative about what we do.
Tuesday, December 4, 2007 University of MD at College Park Physics
Colloquia attended by old humans given by Sean Carroll notes.
6PM Friday, December 7, 2007 at ST301 directory
of
pictures from my crummy cell phone camera during this meeting,
but very informative about what we do.
Noon Friday, January 4, 2008 at ST256, classes have not restarted
6PM Friday, January 11, 2008 at ST256, classes have not restarted
6:30PM Friday, February 15, 2008 at ST256
6:30PM Friday, February 22, 2008 at ST256
6:30PM Friday, March 21, 2008 at ST256
6:30PM Friday, March 28, 2008 at ST256 a directory
of
pictures taken on this date with my wife's digital camera.
6:30PM Friday, April 18, 2008 at ST256
6:30PM Friday, April 25, 2008 at ST256
6:30PM Friday, May 16, 2008 at ST256 after college commencement!
We will decide on future dates this summer.
6:30PM Friday, May 30, 2008 at ST256
6:30PM Friday, June 13, 2008 at ST256
6:30PM Friday, June 27, 2008 at ST256
6:30PM Friday, July 25, 2008 at ST256
18 meeting completed the first academic year studying Geometric
(Clifford) Algebra!
Meeting in the 2008-2009 Academic year:
Year Two
6:30PM Friday, September 5, 2008 at ST256 We started on
Geometrical Calculus, we only got the first two pages done so you can
catch up we spent a lot of time reviewing with a new MC student Cassidy
Ferrel, who is also in the US Army. Wayne Warren and Walter Faust
were absent so being Faustless we also did not cover as much material
as carefully as when we have Walter Faust! We had two MC students
as Chris Leeney was also with us. Our leader Alan Bromborsky and
our host Harold Williams is always there and Michael Brabanski and Jack
Gaffey were also in attendance.
6:30PM Friday, September 19, 2008 at ST256 We shall continue
Geometrical Calculus!
6:30PM Friday, September 26, 2008 at ST256
6:30PM Friday, November 7, 2008 at ST256
6:30PM Friday, November 21, 2008 at ST256
6:30PM Friday, December 12, 2008 at ST256
6:30PM Friday, January 9, 2009 at ST256 a directory
of
pictures taken on this date.
6:30PM Friday, January 30, 2009 at ST256 canceled on account of two
essential members feeling poorly.
6:30PM Friday, February 20, 2009 at ST256
6:30PM Friday, March 27, 2009 at ST256
6:30PM Friday, April 10 (Good Friday), 2009 at ST256
6:30PM Friday, April 24, 2009 at ST256
6:30PM Friday, May 22, 2009 at ST256
6:30PM Friday, July 10, 2009 at ST256
14 meetings completed the second academic year studying Geometric
(Clifford) Algebra!
Meetings in the 2009-2010 Academic year:
Year Three
6:30PM
Friday, August 21, 2009 at ST256 watched 1996 version of "O Brother,
Where Art Thou?" and then did Geometric Algebra,
6:30PM Friday, September 11, 2009 at ST256
6:30PM Friday, September 18, 2009 at ST256
6:30PM Friday, October 16, 2009 at ST256
6:30PM Friday, November 13, 2009 at ST256
6:30PM Friday, January 29, 2010 at ST256
6:30PM Friday, February 5, 2010 at ST301 canceled College closed on
account of snow.
6:30PM Friday, February 12, 2010 at ST301 canceled College closed on
account of snow clearing.
6:30PM Friday, March 5, 2010 at ST301 finished through page 125! Cassidy Farrel back with us and joined by
Tecola, Phineas St. Clair and Haliu Bantu.
6:30PM Friday, April 2, 2010 at ST301 a directory
of pictures taken on this date.
6:30PM Friday, April 9, 2010 at ST301 a directory
of pictures taken on this date.
6:30PM Friday, April 16, 2010 at ST301 a directory
of pictures taken on this date.
6:30PM Friday, May 7, 2010 at ST301
6:30PM Friday, May 21, 2010 at ST301 a directory
of pictures taken on this date.
6:30PM Friday, May 28, 2010 at ST301 we are really getting serious
about this stuff, I know I am. Directory
of pictures taken on this date.
6:30PM Friday, June 11, 2010 at ST301
6:30PM Friday, June 18, 2010 at ST301 a directory
of pictures taken on this date.
6:30PM Friday, June 25, 2010 at ST301
6:30PM Friday, July 2, 2010 at ST301
6:30PM Friday, August 20, 2010 at ST301 we are taking a summer break,
it is getting very hot and the room we use has the sun coming in at the
wrong direction in the early evening putting glare on the computer
video projectors and LCD screen in June, July, and early August.
We understand projection and the obliquity of the ecliptic which caused
seasons on planet earth. Full blackout curtains should have been
installed in this room. We watched the first half of the silent
movie Metropolis by Fritz Lang in German with Michael Brabanski
translating.
20 meetings completed the third academic year studying Geometric
(Clifford) Algebra!
Meetings in the 2010-2011 Academic year:
Year Four
6:30PM Friday, September 3, 2010 at ST301we will watch the second half
of Metropolis. A directory of
pictures taken on this date.
6:30PM Friday, September 17, 2010 at ST301 we are going to start
consolidation of our knowledge on Geometric Algebra.
6:30PM Friday, October 29, 2010 at ST301 we are going to continue our
consolidation of our knowledge on Geometric Algebra. A directory of pictures taken on this
date.
6:30PM Friday, December 3, 2010 at ST301.
6:30PM Friday, December 17, 2010 at ST301.
6:30PM Friday, January 7, 2011 at ST301.
6:30PM Friday, February 4, 2011 at ST301.
6:30PM Friday, February 25, 2011 at ST301. The Fundamental
Theorem of Geometric Calculus on a manifold
6:30PM Friday, March 25, 2011 at ST301. Stokes theorem on a manifold.
6:30PM Friday, April 1, 2011 at ST301. A directory
of pcitures taken on this date.
6:30PM Friday, April 15, 2011 at ST301.
6:30PM Friday, May 6, 2011 at ST301.
6:30PM Friday, May 13, 2011 at ST301.
6:30PM Friday, May 20, 2011 at ST301.
14 meetings completed the fourth academic year studying Geometric
(Clifford) Algebra!
Meetings in the 2011-2012 Academic
year: Year Five
6:30PM Friday, August 26, 2011 at ST301.
6:30PM Friday, September 23, 2011 at ST301.
6:30PM Friday, September 30, 2011 at ST301.
6:30PM Friday, October 14, 2011 at ST301.
6:30PM Friday, November 4, 2011 at ST301. Started recycling
through the basics to make sure we understand everything. A directory
of pictures taken on this date.
6:30PM Friday, December 9, 2011 at ST301 we covers some new stuff
including new notation evidently invented by our leader Alan
Brombosky. We did find some errors and before December 16, 2011
we are hopeful of a new bookGA.pdf. with some
changes.
6:30PM Friday, December 16, 2011 at ST301 we had a new MC TPSS
mathematics faculty member show up.
6:30PM Friday, January 6, 2012 at ST301 Wayne Warren returned to us for
taking care of his mother in Florida.
6:30PM Friday, January 20, 2012 at ST301
6:30PM Friday, February 3, 2012 at ST301
6:30PM Friday, February 17, 2012 at ST301
6:30PM Friday, March 2, 2012 at ST301
6:30PM Friday, March 23, 2012 at ST301
6:30PM Friday, April 13, 2012 at ST301
Future
dates God willing (believers in God, Gods, agnostics and atheist are
welcome at our meeting)!
6:30PM Friday, May 11, 2012 at ST301
We will continue recycling through the basics when ever a new member
shows up or an old member ask a basic questions. This happens
about one meeting in three.
Sometime after that we are going to explore the at least three
different ways of defining "Covariants Derivatives" in general
coordinate transforms leading to different "General Relativities" all
of the ECSKs, Einstein-Cartan-Sciama-Kibble, theories. We many
even explore the case where coordinates do not commute or are small,
but finite around 10^-35meters (abandoning real numbers and using finite, but large Fields, many elements in the
set.). Some of us want to understand quantum gravity!
Doesn't every thinking creature want to understand the origin of mass
and the creation of intrinsic quantum mechanical spin in fermonic
matter? I know, I do! But I also know I can't do it by
myself, besides it is more fun if you do it with others. Right!!!
Links:
Linear and
Geometric Algebra first undergraduate linear and
geometric algebra textbook, affordable, too by Alan Macdonald.
Geometric Algebra Net at
University of Amsterdam, Computer Scientist; support for the excellent
book Geometric
Algebra for Computer Science, an object oriented approach to
Geometry
Geometric Calculus: David
Hestenes and Group at the University of Arizona, Physicist
Geometric
Algebra for Physicist a book by Chris Doran and
Anthony Lasenby at Cambridge University
Geometric
Algebra and Applications to Physics a book by VENZO DE
SABBATA and BIDYUT KUMAR DATTA see URL: http://ebookee.org/Geometric-Algebra-and-Applications-to-Physics-Taylor-and-Francis-_273120.html
.
Scientific Python recommended by
Alan Bromborsky
Python(x,y):
Free scientific and engineering
development software, recommended by Alan Bromborsky
Some Video Mathematics Resources some
of us have found useful
Applied
Geometric Algebra by László Tisza is Professor
of
Physics
Emeritus at MIT, where he began teaching in 1941. This
online publication is a reproduction the original lecture notes for the
course "Applied Geometric Algebra" taught by Professor Tisza in the
Spring of 1976 in MITOpenCourseware. This was found by Cassidy
Ferrel, MC student participant in our Geometric Algebra Study group.
MATH
E-222 Abstract Algebra by Benedict Gross, PhD, George Vasmer
Leverett Professor of Mathematics, Harvard University, found by Randy
Bryant.
Norman J. Wildberger's
home page, Divine
Proportions:
Rational Trigonometry to Universal Geometry or same
from
Amazon.com.
Lagrangian and
Symplectic Techniques in Discrete Mathematics a Ph.D. dissertation
by James William Gilliam at University of California at Riverside.
Montgomery
College's
Planetarium
home
page.
web page by Dr. Harold Williams, last modified Sunday 5:59PM,
April 22, 2012.