A Mathematica Add-On for Quantum Computing in Dirac Notation: Dreamming with Charles Babbage and Ada Lovelace

Charles Babbage designed in the XIX century a "mechanical computer" (he called it the "Analytical Engine"). This "mechanical computer" was never built. It was a challenge to build such a machine for the XIX century engineers. Ada Lovelace (Ada Byron) wrote with him the first computer program (they called it "calculation method") for this computer that never existed. Nowadays computers and computer programs are far more powerful than any wild dream Babbage and Lovelace could have had.

Scientists and Engineers nowadays write programs (algorithms) for "quantum computers". A general purpose quantum computer has not been built yet. It is a challenge to build such a quantum computer for the XXI century engineers. Therefore, the quantum algorithms have to be tested (simulated) in our "normal" computers. There are many simulators to do that. We have written such a simulator for doing Quantum Computing calculations in Mathematica. This simulator is special because it uses Dirac Notation and it can plot (graph) Quantum Circuits. It brings the power of Mathematica to the Dirac Notation, and the power of Dirac Notation to Mathematica. I invite anyone interested in Quantum Mechanics and Quantum Computing to use this new Mathematica Add-On. It can be downloaded at: http://homepage.cem.itesm.mx/lgomez/quantum/
And let us dream, just the way Charles Babbage and Ada Lovelace did.

Internet collaborations of Jose Luis Gomez-Munoz

I made application examples of Finite Element Method (FEM) applied to the Asymptotic Homogenization Method (AHM) to obtain effective coefficients of composite materials for the Imtek Mathematica Supplement (IMS). Those examples are included in IMS documentation http://www.imtek.de/simulation/mathematica/IMSweb/
I developed an improved installation procedure and documentation for QDensity, a Quantum Computer Simulator in Mathematica: http://www.pitt.edu/~tabakin/QDENSITY/index.htm, see the section "New" in QDensity download page.
I made a tutorial in Spanish for LiveGraphics3D http://wwwvis.informatik.uni-stuttgart.de/~kraus/LiveGraphics3D/index.html the tutorial is listed in the links page of LiveGraphics3D http://www.vis.uni-stuttgart.de/~kraus/LiveGraphics3D/links.html
My Mathematica tutorials in Spanish are included in the Wolfram Library Archive (a.k.a. Wolfram Information Center) http://library.wolfram.com/infocenter/Courseware/5707/
Rubén Dario and I created a tutorial to transform a Mathematica package into an Add-on with the following characteristics: 1. It will be loaded using the Needs[] command, just like the built-in Mathematica Add-ons 2. Its documentation will appear in Mathematica's Help Browser 3. It will have a Palette in the Palettes menu of Mathematica. The tutorial is included in the Wolfram Library Archive (a.k.a. Wolfram Information Center) http://library.wolfram.com/infocenter/MathSource/6709/
I extended the "Murder Mystery Method" (MMM) to the solution of exact differential equations. The original MMM was developed by the "Bridging the Vector Calculus Gap" project http://www.math.oregonstate.edu/bridge/ and my version of MMM is included in their links page http://www.math.oregonstate.edu/bridge/links/
I created an activity based on an article of "SimponsMath.com" http://www.simpsonsmath.com. You can see the activity here: http://homepage.cem.itesm.mx/lgomez/activity_simpsons/di_texto.htm

Why does the Divine Proportion (Phi, golden section) appear in nature?

If you like Math and Art, or Math and Natural Sciences, it is very likely that you have heard about the Divine Proportion (Golden Section) http://goldennumber.net/ ,
http://homepage.cem.itesm.mx/lgomez/audio03/index.htm
The fact that the Divine Proportion (the number Phi=1.618…) is present in Art might not be so surprising, we could argue that is only a convention of western art, coming directly from the ancient Greeks.
However the number Phi=1.618… is also present in nature http://www.bbc.co.uk/radio4/science/5numbers3.shtml
Why? Why does this specific number appear everywhere in Nature? Is there something really “divine” about it?
The answer seems to be, at least in some cases, evolution: survival of the fittest. The geometrical structures that contain the number Phi=1.618… are usually the best structures in terms of “use of available space”, therefore plants and animals have evolved to have that kind of structures in their bodies, shells, seeds, etc.
Dr Ron Knott has written a very interesting page http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat2.html, go and search in that page the section with title “Why does Phi appear in plants?”. This page includes very interesting computer-generated animations explaining why Phi=1.618… is the best number for packing seeds. For those of you that like the computer program Mathematica, I think it would be great to recreate some of those animations in Mathematica, with the Manipulate command, and then send them to the “Wolfram Demonstrations Project” http://demonstrations.wolfram.com/, please let me know if someone does it.

Welcome

Welcome to my blog in English. I am a mexican mathematics teacher. I will use this blog to share some of the things I learn about Mathematics, Physics, Mathematica, Excel, Education, etc. I hope you will find here something interesting and useful.
Jose Luis Gomez-Munoz