Bad in Berlin, Perfect in Paris

Barack Obama passed the critical commander in chief test in France, but got a bad case of cold-war blues in Germany.

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Invert

The phrase 'Invert, always invert,' is associated with Jacobi for he believed that it is in the nature of things that many hard problems are best solved when they are addressed backwards.

This quote of Jacobi comes from Wikipedia.

I believe that inverse and direct may have something of an artificial aspect. Maybe one learns one way or the other by some kind of spontaneous symmetry breaking situation. The first teacher of Arithmetic emphasized sums over subtractions, and therefore multiplications over divisions. Maybe she could have chosen differently.

How could we know?

Design some didactic sequences, i.e., some lesson plans, at the most elementary level possible. Do students become imprinted by the didactical approach?

Real Coaching Radio's Shows - Real Coaching Radio Network

Real Coaching Radio's Shows are about the 7 areas of life. Come join us.

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Google Index Reaches 1 Trillion URLs

Three years after Google (NSDQ: GOOG) declared that its index was three times larger than any other search engine and then declined to cite a specific number to support that claim, it was widely believed that Google had tired of index one-upmanship and that it would no longer be measuring its index. Well, Google has its yardstick in hand once...

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A New Era In Search For 'Sister Earths'

Research presented at a recent astronomical conference is being hailed as ushering in a new era in the search for Earth-like planets by showing that they are more numerous than previously thought and that scientists can now analyze their atmospheres for elements that might be conducive to life

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Gustavo Gordillo

I had Gordillo's Blog in my previous Blogger template. When I changed templates it just went poof. I chose to put links back as I saw fit. I just read Gordillo's piece in La Jornada today, and chose to put him back. He is an even handed political analyst, as a student he fought against the Government forty years ago. By the way today, forty years ago the police attacked students downtown Mexico City. A long summer of struggle began, more than five hundred people were killed. Many of those students have changed the political life of Mexico. Tomorrow we vote on oil policy. I believe the government of Felipe Calderón will go ahead with his plans to give the oil to foreigners; but in the future I hope, we Mexicans can direct our destiny better. More struggles lie ahead.

URGENT BREAKING:2 More Banks Failed tonight!!! DIGG IT!!

On July 25, 2008, First National Bank of Nevada, Reno, NV, was closed by the Office of the Comptroller of the Currency (OCC). Subsequently, the Federal Deposit Insurance Corporation (FDIC) was named Receiver. No advance notice is given to the public when a financial institution is closed.

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Failing Banks?

I just read in Digg (above), and heard on KCRW about two American banks failing on a Friday. What is going on?

The world is definitely changing. Here down in Mexico we are voting tomorrow on whether or not oil profits should go to foreigners. The argument is that Mexicans do not know how to profit from oil. I will vote for Mexico.

Oil prices are not really going down in the near future.

I hope more money comes to Mexico and less to failing banks in the US.

Perelman

I am finally reading "Grisha" Perelman's ideas, as explained by Huai-Dong Cao and Xi-Ping Zhu.

The man is a genius.

He introduced ideas form Physics in Differential Geometry and Topology. It is sad that he chooses to be alone. It will be great to meet him.

Classical Music Inspired by Jerry Garcia

With my iTunes portal I found KCRW, and right now I am listening to a classical music composer inspired by Jerry Garcia.

You can go to the Santa Monica Public Radio website mentioned in the note below.

KCRW 89.9 FM | Next Generation Internet Radio

KCRW, a community service of Santa Monica College, is Southern California's leading National Public Radio (NPR) affiliate, featuring an eclectic mix of music, news and arts programming. Broadcasting at 89.9 FM and online at KCRW.com, the station boasts one of the nation's largest arrays of locally-produced and nationally-distributed content.

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Improving HTML Skills

Now some of my widgets are showing something. I understand the reason is that I did not exist in the iTunes world. I never have bought music online. That will do. My family is more savvy in that respect. I believe my problems were less caused by knowing too little HTML, than by being such a cheapskate!

Maybe if I spend a buck, I will exist in iTunes.

HTML Adventures

I did do some basic HTML way back then. Then I was doing something else, like teaching high school math. Back at the university environment, now I am supposed to be more knowledgeable.

First I tried to put my Amazon PayPage link to this Blog. OK, I know how to do that I thought. Then I remember that I had changed my template. It turned out I did not know how to put it in that template; so I put it in a test page I render only in my computer at the office. Even there the silly picture never came up.

I went to iTunes then to set a myiTunes webpage. Same problem, I did not know how to position those widgets in my Blogger account. So again I went to my workbench. Now I did get the pictures, but the content never came up. I went back to iTunes to have some presence there. Now I am listening to some radio station in the US; but still nothing coming out of my widgets in my workbench.

I hope to report something more up beat next time.

One good thing though, I got my AOL webpage going, even a Journal.

0Lalo.

That is me. Lalo is nickname for Eduardo in Spanish, I figure there were many Lalos, so I stole an idea from a friend, just put a number IN FRONT, and very likely nobody has chosen that. So there it goes.

Quaternions

Today I started my Quaternion Project in Mathematica. This area has fascinated me since I was in Graduate School. Prof. Plebanski was a world star in the area. Unfortunately we didn't cross as student and mentor at CINVESTAV (Centro de Investigación y de Estudios Avanzados, Instituto Politécnico Nacional, México). Nevertheless I could ask him once his opinion on writing General Relativity in this language. He said that he did not make much progress. Then I read Stephen L. Adler's papers on Quaternionic Quantum Mechanics in the seventies. He has a book now: Quaternionic Quantum Mechanics

Now I have an academic position and my love affair with quaternions starts today!

MyAOL

I do have an account an AOL. My wife started this service at least since 1996. She opened it and I used it. I was in Mexico, she in the US. That was great to be in touch with my family while I was working in Mexico. Then we were together for several years until the beginning of this year when I returned to Mexico. Now I also have a Google mail account. I refuse to collect accounts, as I refuse to add credit card accounts to my worries. I never used the AOL homepage I was entitled to. Now I started to poke around, and all of a sudden I was asked for the last four numbers of my Social Security number (SS#). Dutifully I wrote it down and I was bumped out!

I had to use the master account SS#.

If I were in the US, I could´ve just shouted to the next room, and problem solved. Here I had to write an email, through AOL, and I am still waiting for the information.

One can imagine living in a virtual world, but we are in the real world. I guess this is a minor inconvenience.

Happy blogging!

US Dollar Steadily Crashing Against Mexican Peso

"Buttressed by rising interest rates and a surprisingly strong economy, the peso has been surging against the dollar in the last few weeks, continuing a run-up that began early in the year." The policy of fiscal responsibility started by Vicente Fox administration and the profligate US central banking policies begin to bear fruit!

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Poincaré's Conjecture Proven in 2003

H.-D. CAO AND X.-P. ZHU; state Poincare's Conjecture this way:

"A closed three-manifold with trivial fundamental group is necessarily homeomorphic to the 3-sphere S³"

This result was established more than a hundred years after it was conjectured by Henri Poincaré.

In the end the proof depends on ideas close to what is called the Renormalization Group; the language is Differential Geometry, the arena is Topology.

I was always impressed by the ideas of the seventies in the last century, from Statistical Mechanics, that led to the revolution in phase transition theory. Near the critical point, classes of interactions were equivalent, the correlation lengths become infinite, and after the transition point a new world awaits us.

It is very intriguing to me how does this relate to Poincaré's conjecture.

Now I am beginning to study this deep connection.

Girls' math skills now equal boys'

Sixteen years after Barbie dolls declared, "Math class is tough!" girls are proving that when it comes to math they are just as tough as boys. In the largest study of its kind, girls measured up to boys in every grade, from second through 11th. The research was released Thursday in the journal Science.

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First PDF

I finished today my first LaTeX exercise in Chilpancingo. I took:

MathPages/kmath434.htm

and wrote it in LaTeX to produce a PDF file.

If you are interested, I can give you access to my GoogleDocs site where I posted it.

I believe the author of this work has a tendency to show up when his material is posted online. He is a very good thinker, I will like to exchange ideas with him.

Continued Fractions & Rational Approximations

“Continued fractions can be thought of as an alternative to digit sequences for representing numbers, based on division rather than multiplication by a base. Studied occasionally for at least half a millennium, continued fractions have become increasingly important through their applications to dynamical systems theory and number theoretic algorithms. Mathematica has highly efficient original algorithms for finding large numbers of terms in continued fractions, as well as for handling exact continued fractions for quadratic irrationals.”

The above comes from Wolfram´s Research. Stephen Wolfram himself has written at least one program to calculate the continued fraction expansion of roots of integers. One can download this as a demo. For instance one can learn from this that:

4^1/3 = [1;1,1,2,2,1,3,2,3,1,3,1,30,1,4,1,2,9,6,4,1,1,2,7,2,....]

This is equivalent to:

4^1/3 = 1.587401052...

The second is based on multiplication, and the first on division.

The question of which is more natural seems more and more artificial to me.

Both can have periods, and maybe quasiperiods. There are more irrational numbers than rationals, maybe there are more quasiperiodic numbers than periodic. By the same token, there may be more without periods, than with quasiperiods.

What is interesting to me is persistence. Phenomena described by periodic mathematics seem persistent, somehow in presence of quasiperiodic mathematical objects I get surprised when after a long period of chaos, suddenly some order appears. With complete periodic praedicere, information is zero, with quasiperidicity, information arrives.

We live to get surprised. As Freman Dyson wrote, “The Universe is as interesting as it can be”. Lately Lee Smolin has looked into an evolving Universe, according to him, the great amount of black holes is a clue to understand the World we live in.

If Smolin is right, there must be tests, maybe finding Kaon Condensates inside stars. In 1973 Ray Sawyer from UCSB told me that maybe there were condensed pions in astrophysical objects, it will be really surprising to find out that not only there are condensed pion, but also kaons. Strange stars really.