Next
meeting: 6:30PM Friday, May 31, 2013 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 and Andrew Secord. 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. 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.
Steve Bray joined us in year five.
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
6:30PM Friday, May 11, 2012 at ST301
6:30PM Friday, June 15, 2012 at ST301
6:30PM Friday, July 6, 2012 at ST301 postponed again!
6:30PM Friday, August 10, 2012 at ST301
6:30PM Friday, August 31, 2012 at ST301
18 meetings completed the fifth academic year studying Geometric
(Clifford) Algebra!
Meetings in the 2012-2013 Academic
year: Year Six
6:30PM Friday, September 14, 2012 at ST301
6:30PM Friday, October 5, 2012 at ST301
6:30PM Friday, October 12, 2012 at ST301
6:30PM Friday, November 9, 2012 at ST301 we actual started
using Lecture Notes Quantum Mechanics
Quantum Mechanics from Walter Faust
6:30PM Friday, December 7, 2012 at ST301
6:30PM Friday, January 4, 2013 at ST301
6:30PM Friday, February 1, 2013 at ST301
6:30PM Friday, February 8, 2013 at ST301
6:30PM Friday, February 15, 2013 at ST301 we shall omit our usual
entertainment, but not study on this date because of the asteroid
2012 DA14.
6:30PM Friday, March 1, 2013 at ST301
6:30PM Friday, March 8, 2013 at ST301
6:30PM Friday, March 29, 2013 at ST301 Steve Bravy We
Are those For Whom Bell Toiled.
6:30PM Friday, April 19, 2013 at ST301 Steve Bravy We
Are those For Whom Bell Toiled.
6:30PM Friday, April 26, 2013 at ST301back to Quantum Mechanics with
Walter Faust!
6:30PM Friday, May 3, 2013 at ST301
6:30PM Friday, May 10, 2013 at ST301 Quantum Mechanics with Walter
Faust
Future
dates
God willing (believers in God, Gods, agnostics and atheist are
welcome at our meeting)!
6:30PM Friday, May 31, 2013 at ST301 Quantum Mechanics with Walter
Faust
And eventually maybe General Relativity, actually the
Einstein-Cartan-Scima-Kibble Theory or really General general
Relativity with Harold Williams! New
Gauge Symmetry in Gravity and the Evanescent Role of Torsion by H.
Kleinert and Kerr Geometry
as Space-Time Structure of the Dirac Electron by A.Burinskii
and Time-Space Invariance and Quantum
Gravity: or how c, G, and h created the fabric of the universe.
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 "Covariant 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.
Vector and
Geometric Calculus first undergraduate multivariable
calculus textbook, also 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 at 7:07PM, Friday,
May 10, 2013.