Monday, July 28, 2008

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.

read more | digg story

Saturday, July 26, 2008

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.

read more | digg story

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.

read more | digg story

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.

Friday, July 25, 2008

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!

read more | digg story

Thursday, July 24, 2008

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.

read more | digg story

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:

41/3 = [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:

41/3 = 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.

Schweiger amd Wolfram

I am curious: Why didn´t Prof. Schweiger know about Stephen Wolfram?

Wolfram has worked in continued fraction expansions. I guess it will take a long time and new people to get "A New Kind of Science" accepted.

Mexican Workers

Next door a new building is going up here on campus. Big iron rods are bent almost by hand; they use levers, but still it is amazing how they are making that structure. Rolling and rolling iron rods, day in and day out. After some days there will be a new Engineering building next door, just like the one I am sitting in right now.

Made by hand, amazing!

Big LED Breakthrough at Purdue Could Change the World

They found a way to make LED using standard silicon wafers, cutting prices A LOT. They also have a bunch of other techniques to make LEDs better and longer-lasting.

read more | digg story

Wednesday, July 23, 2008

Thanks Math Department at UConn!

I did it!

Thanks from the Math Department at UAGro!

I have my first PDF produced at Chilpancingo.

Installing MikTeX

The University of Connecticut dudes came through, they did not sleep on the wheel. I am installing MikTeX right now. I hope I can report back with my first PDF on this blog.

Charlie Rose

I am watching Charlie Rose interview Larry Wright on April of last year. The issue is: How does the Arab world sees the US? The conversation sounds eerie from down here in Chilpancingo. We have a population as disenfranchised here as the Arabs are in the world community. The original inhabitants of this land have been abused beyond belief. I hope I can contribute a little bit to bring some sanity around here.

LaTex

I am installing ProTeXt.exe in my Windows machine.

I went to the CTAN site:

TUG page.

Automatically they connected me with UNAM. I waited almost two hours and poof, there goes my connection. I know it is summer and my friends at UNAM must have other things to do than support their site. So I went to:

The University of Connecticut

and here I am happily waiting for my toy. I hope the LaTex dudes at Connecticut have more of a work ethic, than my buddies at UNAM.

I love choices.

Philosophy

I decided to go to a math and physics high school because I could handle the humanities alone. As it turned out I only read Kant´s Critique of Pure Reason. Later I got Sartre´s Critique de la raison dialectique. I am afraid that I did not read these works thouroghly. Now I am reading Leibniz´s La Monadologie. This has to stop, I cannot go to High School again. I have to read carefully what these people had to say.

It is important also to state why I do this. My concern is with Physics. I know Quantum Field Theory, but I am working in Quantum Gravity now. I find old conceptions lacking in my quest to understand the physical world.

This is my first note on Philosophy on this Blog. I hope it is not the last one.

Tuesday, July 22, 2008

All Hail ‘McBama’

The right position on Iraq today is probably “McBama” — stick to a clear withdrawal timetable, but leave yourself some wiggle room.

read more | digg story

x3 - x2 -1



Simple equation. Only one real root.

Quasiperiodicity

Tompaidis studies the symplectic map. This map codifies dynamics as we understand it now. He studies quasiperiodicity, which was initially discovered in number theory. When Prof. Schweiger presented Jacobi´s periodicity discovery in the nineteenth century, my internal voices were telling me that this was important. All I could gather immediately in my mind was to ask if Prof. Schweiger knew about cellular automata, as presented in Wolfram´s book, "A New Kind of Science". He did not. At the end of the lecture Prof. Glen Van Brummelen from Quest University in Canada, told me that he had just heard Wolfram give a talk the previous week, on cellular automata. The word is slowly getting around that these mathematical objects are important. I did not pursue the issue with either scientist; only now it is downing on me that there is something deep here.

I am reading papers now on these topics and my ideas are coming together. I write here where I am right now.

Number Theory may likely be the oldest branch of mathematics where periods were found. Astronomy also gave our ancestors the sense of repetition. Every day the Sun is up there, this led us to think of day, month and year; when the other astronomical objects showed us their periods.

Then the crisis in Greek Mathematics with Pythagoras Academy presented to our minds the possibility of something else. Non-periodicity.

Jacobi pursued more periodicity in mathematics, and did seem to get confused when he did not find it. Now though, he was closer to the concerns of modern dynamicists. That was the bell that rang in my head very lightly, in Mexico City last week.

I will say now that Jacobi suffered a mild case of Aristotelean shock. Instead of pursuing the study of quasiperiodicity scientifically, as Tompaidis is doing. He just could not finish his thoughts.

Even last century Leon Bernstein at the Illinois Institute of Technology, kept on trying to get more and more periodicity, and did not focus instead on quasiperiodicity.

Penrose was one of the first mathematicians to recognize the deep importance of this mathematical phenomenon, when he invented his period five Tiling.

Now there are technical applications of this new branch of mathematics; the study of quasiperiodicity.

Quasiperiodic Perturbation of a Symplectic Map

Stathis Tompaidis from the University of Texas at Austin, writes

Numerical Study of Invariant Sets of a
Quasiperiodic Perturbation of a Symplectic Map


We study the behavior of invariant sets of a volume­-preserving
map that is a quasiperiodic perturbation of a symplectic map,
using approximation by periodic orbits. We present numerical
results for analyticity domains of invariant surfaces, behavior
after breakdown, and a critical function describing breakdown
of invariant surfaces as a function of their rotation vectors. We
discuss implications of our results to the existence of a renor-­
malization group operator describing breakdown of invariant
surfaces.

The quasiperiodicity of mathematics, may describe physical systems. I studied a mapping with symmetry five for the harmonic oscillator, periodically kicked. By no means do we know all there is to know on quasiperiodicity.

JACOBI'S LAST THEOREM The history of Jacobi-Perron algorithm

Prof. Schweiger states the following in his Mexico City presentation last week:

We take an integer and two numbers of the form:

α + βx + γx2; α; β; γ ∈ ℤ; x3 = n; n ∈ ℕ

With more specifications that I´ll go over in another note, he states that the algorithm he presents produces a unit of the cubic number field.

Physicists Shed Light On Key Superconductivity Riddle

MIT physicists believe they have identified a mysterious state of matter that has been linked to the phenomenon of high-temperature superconductivity.The researchers are exploring materials that conduct electricity with no resistance at temperatures around 30 degrees Kelvin above absolute zero. Such materials could have limitless applications..

read more | digg story

Constant Width Bodies

One knows a sphere when one sees one.

Problem is, how do you define a sphere? A simple answer might seem to be, if the diameter is constant from every direction, then it is a sphere.

Many years ago a friend told me that it is not so. There are many bodies with this property and they are not spheres.

Just think of a two dimensional projection, my circlesquare from previous notes may qualify for a constant width curve. If you take the square part, due to symmetry, any line through the center has the same size. There you have it; but the size should be maximum from every direction. So this is not a constant width curve.

Monday, July 21, 2008

Madness and Shame

When the constraints of the law are unlocked by people at the pinnacle of power, terrible things happen in the real world.

read more | digg story

Yet Another Cubic



Above you see the cubic:

y = (x -1)(x - 41/3)(x - 42/3)

These three roots: 1, 41/3, 42/3

do not have a periodic continued fraction expansion.

I Found Part of the Answer

I asked a question in the note below. Here I have part of the answer. I work in Guerrero, today I read the following:

96% of Guerrero Indians do not get medical service.

There you have it.

If you cannot read Spanish to read both news items you have to believe me, we are so backward because we do not value our own people.

Why Do Mexican Students Fail?

This is a hard question. I am responsible to understand why. I do research in Mathematics Education in Mexico. I hear little children around me right now. Are they different than children everywhere else? Absolutely not.

What is going on then? As you can read below more than 90% of the students applying to the most prestigious public university in Mexico City were rejected.

This is a good news, bad news story. The good news is that UNAM (Universidad Nacional Autónoma de México) professors will have the best students the public education system of the city offers. The bad news is that many intelligent young people won´t be given a chance to prove that they can perform at the highests levels. In the past only one student became a Mine Engineer after eight years of study, with very few others in his cohort. This might have been acceptable then to keep these valued professionals well paid; but Mexico and the world have entered into a new era. China is graduating many more professionals than Mexico. This is my concern. Mexico is staying behind in these difficult times we are going through.

I can report one good note though.

A friend of mine assures me that the Universidad Autónoma de Puebla is graduating around two hundred computer scientists with a bachelor´s degree every year, and he assures me that they have high standards there.

I have to understand what is my friend in Puebla doing well, and why UNAM is so backward.


Jacobi´s Last Theorem

This distinguished German mathematician contributed to physics with the Hamilton-Jacobi equation, important in classical and quantum mechanics. Nevertheless my interest here is to highlight his contributions to number theory.

Last week Professor Fritz Schweiger from the University of Salzburg presented in the History and Pedagogy of Mathematics (HPM 2008) in Mexico City a paper on Jacobi´s Last Theorem, as he calls it. It is actually a conjecture, but paraphrasing Fermat´s Last Theorem, he chooses to call it this way. To this day nobody knows if Jacobi´s conjecture is true. He claimed that the trio:

(1, 41/3, 42/3) when expressed as infinite continued fractions, produce periodic values for the three fractions.

It is an interesting and apparently simple question, that so far has eluded mathematicians.

These problems appear in integer relation formulae:

Integer Relation Algorithm.

Thank you Professor Schweiger for teaching us these questions.

Mexican Tragedy

Here you can read in Spanish about a Mexican tragedy.

The news today in Mexico City were sad. Ninety one per cent, 91%; of all students applying for college were rejected.

A tragedy is a Greek word. According to Aristotle: "The change to bad fortune which he undergoes is not due to any moral defect or flaw, but a mistake of some kind."

There is a mistake of some kind when 91% of students are not ready to pass a college entrance examination.

I am thinking how to help all those willing students to be ready for professional lives.

Blogging Despite Bureaucrats

I tried to download ScribeFire inside a firewall maintained by the State of Guerrero in Mexico. After failing several times, wrongly assumed that my hardware was at fault. Now I am outside that WebSense protected connection and installed this add-on easily.

There it goes, the Internet wants to be free!

Sunday, July 20, 2008

Sobriety, Herr Obama

The Obamania in Europe needs to be kept in check. There’s work to be done.

read more | digg story

Gore Sets Alternative Energy Challenge

Just as John F. Kennedy set his sights on the moon, Al Gore is challenging the nation to produce every kilowatt of electricity through wind, sun and other Earth-friendly energy sources within 10 years, an audacious goal he hopes the next president will embrace.

read more | digg story

Saturday, July 19, 2008

"Hot" Mexican Musical Genre Picks Up Steam In U.S.

MIAMI (Billboard) - Mexico's music from the hotlands -- better-known by its Spanish term, "musica de tierra caliente" -- has long played second fiddle to its more popular cousin, duranguense.

read more | digg story

9/11 and 4/11

We are addicted to dirty fossil fuels, and this addiction is driving a whole set of toxic trends that are harming our nation and world in many different ways.

read more | digg story

It’s the Economic Stupidity, Stupid

Were voters forced to actually focus on John McCain’s response to our economic crisis, the prospect of his ascension to the Oval Office could set off panic.

read more | digg story

Wednesday, July 16, 2008

Do a Circle and a Square Measure Up?


Lately I have been thinking the following. How are a circle and a square related? It all started with a simple question: Do the areas representing integration by parts add up? Here I explain this question, and write how that question leads to the one heading this note.

If you draw v(u) on a v-u graph, the area from u(1), v(1) to u(2), v(2) using straight lines perpendicular to the axes can be calculated in two ways, one multiplying base times height of the square that ends in the second point, and subtracting the area of the square determined by the axes and the first point, i.e., u(2)v(2)-u(1)v(1), or drawing rectangles with base Δu (Δu is the difference between two u values)and height v, adding these up from point 1 to point 2; then doing the same with u and v exchanged. Graphically it is clear that they add up to the same area.

Algebraically one has Leibniz´s rule and the fundamental theorem of calculus, to prove the same result.

Now we come to the circle and the square.

Using the construction described above, one ends up with a very crooked line. The lines of the rectangles for constant u and v values are the steps and the heights of the steps of a ladder.

There is no problem for the area calculation, but if one choses to calculate the length of the crooked line (you can see the crooked line in Is it a Fractal?) one gets in trouble. The line gets close to a line that joins the bents in the crooked line into a line of different length than the crooked line.

The squarecircle above is an example, the length of the square is different than the length of the line defining the circle. One is 2πr, and the other 4 √2 r.

The circle radius is r.

Obviously these two numbers are different, and there lies the problem.

Sunday, July 13, 2008

My Plan for Iraq

On my first day in office, I would give the military a new mission: ending this war.

read more | digg story

Mexico movement against high iPhone3G plans

More than 13,000 persons have signed, what are u waiting for? Ayudanos a que Telcel baje los precios y abra planes ilimitados en mas rangos de precios.

read more | digg story

Saturday, July 12, 2008

Something Good This Way Comes

Jacob Dylan

read more | digg story

My Photo

 
Volcanic Activity

Is It A Fractal?


This drawing, made with Star Office and converted to bmp format with a trial version of PDF Image Magic, is described on my note, What Kind of Line is This?, represents a Fractal indeed.

Another Bureaucrat Story

I live across the street from the General Coordination of Finances and Administration of the Education Department of the Guerrero State Government, at Chilpancingo.

I had written two notes on my encounters with bureaucrats. This is a good news bad news story. The good news is that they are providing me, free of charge, wireless internet connection for my Toshiba Satellite Pro 4300 laptop. The bad news is that some gorvernment official, or maybe just an overconscientious IT person, has decided that chats and blogs, are out of the question. Maybe some state secrets about the poor performance of teachers.

I could not post my blog last night from home. Here you have it now. I am working from my workstation, MicroStar or some such. The Autonomous University of Guerrero in its infinite wisdom has decided that college professors have more sense than mere bureaucrats; at least I want to conceptualize it that way.

To finish this off, I can report that I went to the only telephone office in Chilpancingo where you could buy the new 3G iPhone. No crowd, no nothing, but free cookies and cofee, and nobody starting their iPhone service. The man in charge, should I call him a bureaucrat? looked at me like "I don´t want to waste my time with you". He did answer some questions, though. I can have mine if besides the two hundred bucks the iPhone costs, I give the sometimes richest man in the world, Carlos Slim, six hundred extra dollars for a "contract". If I want double the memory, 16 Gb, then I just give an extra hundred dollars.

That is why nobody was in a hurry to give their money away. What I saw though, were some worried people paying their dues to this new King of Mexico, for the more mundane "contracts" they already have with him . This is how fortunes and legends are made.

Friday, July 11, 2008

A Virginal Goth Girl

How a series of novels starring a hunky vampire boyfriend reveals a rift between the sexes.

read more | digg story

Feeling No Pain

Neither party in this presidential campaign has been forthright with the public about the true extent of the crises facing the country.

read more | digg story

DNA Study Traces Human Origins Across the Continents

Scientists trace the path of human migrations by using bones, artifacts and DNA. Ancient objects, however, are hard to find. DNA from contemporary humans can be compared to determine how long an indigenous population has lived in a region.

read more | digg story

What Kind of Line is This?


This broken line is used to calculate areas. Riemann used it many years ago to define integrals. Calculus concerns itself with change. Small changes when combined are noticeable. Each step may be as little as to be lost to the eye staring on a page. Nevertheless many of them, one after the other, can be indistinguishable to the eye from a straight line that crosses each one symmetrically at half a right angle. It turns out that taking very many steps and looking from afar, the straight line that crosses all of them half way from a right angle, is shorter than taking the steps as shown. If the length of the inclined line is 1.4 units, the sum of all the steps to go from beginning to end, along the crooked line is 2.

What kind of line is this?

I am a Gutemalan Also

Mr. Camayd-Freixas is a good man, as you can read in the story below.

An Interpreter Speaking Up for Migrants

A Spanish interpreter says that hundreds of illegal immigrants arrested at a meatpacking plant did not fully understand the criminal proceedings against them.

read more | digg story

My Grand Nephew is a Spaniard

The little one is hardly over a year old. I can claim my guatemalan citizenship. Nevertheless I cannot prove that I live in Chilpancingo. What am I going to make of all this nonsense?

I understand that not everybody is welcome in my house, I have the right to say who is in and who is out, but I feel that we humans, overdo this citizenship bit.

Let Spaniards be Spaniards, congratulations little one!

Thursday, July 10, 2008

Seagate Unveils World's First 1.5TB Hard Drive

Seagate today announced their new Barracuda 7200.11 1.5TB hard drive which marks the largest single jump in capacity for hard drives in 50 years. The drive uses perpendicular magnetic recording technology to achieve the breakthrough.

read more | digg story

Back in Chilpancingo

Today I have another bureaucrat story. I guess this is more of an eccentric story, dealing with the regular problems everybody else takes on stride.

Today I went to open a bank account. First I did not have my passport with me. I returned with it, and the nice lady in charge asked me for a proof of residency. Telephone, electric, or any other proof that I am a legal resident in Chilpancingo. I immediately had the feeling of, "here we go again". Read my bureaucrats piece here.

I decided then and there, after nicely informing the lady that I rather get my bank account in Mexico City, where I have one of my two legal residences in Mexico; the other one is in Puebla City.

You gotta lov´em.

Wednesday, July 09, 2008

How To Convert Website URL into PDF

Pdfonfly.com is a website, where in you can convert any webpage into pdf. Just enter the URL of the website and fill the captcha code, within five seconds the entire webpage will be converted into pdf and will be ready for download.

read more | digg story

Back

Last week I did not write in this Blog; I try to keep it current, but somehow when back in the city where I grew up, I did not find the time. Particularly touching for me was to be back at my Alma Mater. The National Polytechnic Institute; north of the City, it is the major higher learning institution. When I was a student there, the total area was already big, but it was not built, nor, I am afraid to say, was it well kept.

Now it is beautiful. Many workers keep it like a big garden. Mexico City does not lack fresh water, it rains profusely, especially this part of the year, then it is no wonder how green the place is.

The scientific meeting I attended was equally impressive. It was the twenty second version of the Latin American Meeting of Mathematics Education (RELIME). This happens every year. Next year it will be in the Dominican Republic.

All in all, a very gratifying experience. It didn´t hurt that I stayed with my beloved mother.

Ride the Turibus to See the Sights of Mexico City

Visiting Mexico City isn't complete without a tour of the major museums, parks, historical sites and centers. If your time is limited, but you still want to experience some of the great sights and places Mexico City has to offer, The Turibus - Circuito Turistico is the best way to see it all in a day. And, you can do it without leaving your seat.

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