Monday, June 30, 2008

Chilapa

Sunday, June 29, 2008

Chilapa

Today was the Party of the Democratic Revolution (PRD) primary in the State of Guerrero. I went to Chilapa, a beautiful town near the capital of Chilpancingo. There is an old Catholic Seminary there. The Cathedral has been “repaired”; where a traditional building use to stand, now we see a cement construction that made me wonder how the original one looked. What I was impressed more with though, were the long lines of the inhabitants of this region, patiently waiting in the main plaza of this town; some with babies in their arms, for more than an hour, to cast their vote in a primary.

This people have been living here, as a people, longer than most of my readers have been in this continent. They came through the Bering Strait more than ten thousand years ago, carrying babies in a similar way as I saw today. I was deeply touched.

A Democratic Revolution is happening in Mexico right now.

I could sense the presence of the Mayas from Chiapas, and Central America, the Incas from Bolivia, together with the Nahuas, Tlapanecos, Amusgos, and Mixtecs from Guerrero I was fortunate enough to witness.

Nobody knows, least of all this writer; what is the next stage of human evolution in this part of the world, I hope that what I saw, is what is coming: A people that finally wakes up from a five hundred year slumber, to claim what is rightfully theirs.

If you want to learn more about Chilapa, read this.

Saturday, June 28, 2008

AOL

In the early 2000s, I bought AOL stock. What went wrong?
First I was a novice, I lost my shirt, and second many people were wrong, like in: Nobody knew that Saddam did not have weapons of mass destruction.

With hindsight I write this.

AOL LLC formerly America Online Inc. had a nice ring to it. American Telephone & Telegraph, also had that important adjective, American or America. AOL was the first American company to enter the Internet age with the full support of the American United States.

My mistake was to assume that the Twenty First Century, was going to be the American Century. After Vietnam and Iraq. I do not think that anymore. Mr. Bush is letting America burn while playing the violin, as Nero did with Rome.

The King is dead, long live the King (Hu Jintao).

In any case I lost my money and the dollar is getting close to ten Mexican pesos. Big empires come down. It hurts though, when one loses money.

What's to Be Done with AOL?

Jon Fine: It's always been easy to hate on AOL. It's a New Media property with Old Media problems, dependent on outmoded businesses — hello, dial-up subscribers! — and in need of reinvention. It's a technology company based on lousy technology. But in an ongoing mystery of modern media, it persists.

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Human Suffering

“No sorrow can be compared to my torture experience in jail. That is the reason for my sadness.”

These are the words of a survivor of American caused torture. You can read Bob Herbert piece below.

All Too Human: The Agony of Innocent Victims of US Torture

Once the green light is given to torture, the guaranteed result is an ever-widening landscape of broken bodies, ruined lives and profound shame to all involved.

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Friday, June 27, 2008

700 California Wildfires: Where the Hell Are the Resources?

Right now, there are 700 wildfires burning in California -- many unattended. Fire departments are working with skeleton crews. Residents are literally being told they're on their own. Where are the resources to save homes and lives?

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Quantum Coherence as a Source of Selection

I listen to myself talking to my friend here in Chilpancingo. The most astounding aspect of Quantum Mechanics is non-locality. Then I remember the Generalized Selection Principle I have been writing about recently. I put two and two together and Bingo!

Correctly many thinkers have questioned random change as the source of the Endless Forms Most Beautiful, that Darwin wrote about.

Here I propose that Quantum Entanglement is at the source of this Generalized Selection Principle. Some form of quantum correlation ties All Matter, in a harmonious universal dance.

More to come.

Selection 2

"That synthesis holds that mutations to DNA create new variants of existing genes within a species. Natural selection, driven by competition for resources, allows the best-adapted individuals to produce the most surviving offspring. So adaptive variants of genes become more common. Although selection is often seen, even by biologists who should know better, as primarily negative, removing poorly adapted individuals, Charles Darwin understood that it was a powerful creative tool."

I am not the only one looking for a Generalized Selection Principle. The paragraph above was taken from the NYT article by Douglas H. Erwin, that you can read below.

Douglas H. Erwin is a senior scientist at the National Museum of Natural History at the Smithsonian Institution and a research professor at the Santa Fe Institute.

Darwin 2.0 - The Evolving Theory Of Evolution

Is Darwin due for an upgrade? There are growing calls among some evolutionary biologists for just such a revision, although they differ about what form this might take.

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1968, 1988, 2008


I still remember forty years ago, October 2, 1968, looking out the balcony in the apartment I lived in Mexico City with my family: Military tanks headed towards the site of the peaceful student demonstration I was planning to go to. I decided then and there, not to go. That decision might´ve spared my life. Some five hundred other people were not so lucky, and the Mexican Government of Gustavo Díaz Ordaz, committed one of the worst political crimes of Modern Political History.You can see above a picture of a group of my friends in Puebla requesting City Hall to take away the name of President Gustavo Díaz Ordaz, from an important street in Puebla City.

In 1988, twenty years later Prof. James Hansen went to the US Congress to testify on Global Warming. He was right, and the politicians did not do what was necessary. Now you can read in the note below that Prof. Hansen thinks it may be too late.

Now in 2008, something is going to give. Tell people that you read it here.

"Flooded London" and a NASA Scientists Prophetic Warning

Last Friday the Medcalf Gallery in London debuted the "Flooded London" series, a photographic depiction of the future of London as it is overtaken by the rising sea. On Monday, exactly 20 years after warning us about global warming, NASA scientist James Hansen told congress that time's up and he warned of such apocalyptic consequences.

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Stephen Hawking's Explosive New Theory on the Universe

Prof Stephen Hawking has come up with a new idea to explain why the Big Bang of creation led to the vast cosmos that we can see today. Astronomers can deduce that the early universe expanded at a mind-boggling rate because regions separated by vast distances have similar background temperatures.

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Bureaucrats

I will write here about a few of my encounters with these human beings, the bureaucrats. When I first applied for a US visa as a student, the agent denied it. I had the acceptance letter from the University of California at Santa Barbara (UCSB). A document number, granting the University of California the right to invite foreign students, was missing. After a few phone calls more, and a few dollars less, the nice lady at the other side of the line, at the UCSB Foreign Students Office could not figure out what I meant. Many foreign students from all over the world had gone through with the same document, without the alleged required number, apparently without problems. The lady at the consulate in Mexico City, granted me a tourist visa. When I was in California, for a fine of $75 US Cy., for entering the country on a tourist visa, instead of a student visa, I was finally granted the visa.

I married in the US to a woman I met at UCSB. We came to Mexico to live. As a foreigner she did not have permission to leave Mexico for extended periods of time. I was accepted to the Massachusetts Institute of Technology (MIT). My plan was to stay two years in Cambridge. We went to the Justice Department in Mexico to request a waiver on the stay requirement in Mexico. The director of my department wrote a nice memo expressing the interest of the University in my work abroad. He believed, he wrote, that the academic activities of the department will greatly benefit from my stay at MIT. After several trips to the Justice Department, the government agent finnaly gave us a document in legalese. I thought we had succeeded. Unfortunatley I could only stay one year at MIT. Great was my surprise when on my birthday, back in the Mexico City airport, I was informed that my wife never received any such permit, and they kept her immigration papers, after keepeing us for more than an hour in their offices, while my Mexican family waited outside. Eventually we went to the Justice Department, actually the office in charge of foreigners is called, Secretaría de Gobernación, which corresponds to the Interior Departement in the US. At "Gobernación" they told us that we were a few days short of the days she could use with no consequences. I went to the office of the nice gentleman that did not give us permission to go and asked why he did not agree with my boss on the benefit to Mexico, and the school, of my experience abroad. He answered that he only saw benefit to my reputation, but not to Mexico.

Now I come to the interaction with this group of our brothers and sisters, in charge of procedures and proper paper work, today. The University of Guerrero, where I want to work, does not recognize the Ph.D. Diploma from UCSB that I showed them. They need the "stamp of approval" of the Secretary of the State of California. This procedure entails the physical handling of my Diploma by US officials in California. I decided over two months ago, to hire a company to do this for me. I paid their services already, and I haven´t received my "Certified Diploma" yet. My email inquire was answerd today. The agent in charge of my case, told me that the number they sent me more than ten days ago for the FedExp delivery is correct. I have been using that number to request information on my package, and all I get is the automatic response that the information about my Diploma was sent to them more than ten days ago. There is no information on: Where is the Diploma, at FedEx, or at the Company in charge of the case?. Obviously it is not in my hands.

You got to love them, we are in their hands. Their good will is essential to a successful case!

Today I received my Diploma. At the end bureaucrats come through. As I said, you gotta lov´em.

Oil Prices Jump to $141.50 a Barrel

Crude oil prices climbed to $141.50 a barrel Friday morning on the New York Mercantile Exchange, setting a record for a second consecutive day.

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Thursday, June 26, 2008

Mathematica


Same cubic with Mathematica

Sage



Nice cubic made with Sage.

Wednesday, June 25, 2008

How did the universe begin?

One of the most interesting questions considered by astrophysicists deals with the start of our universe. Indeed, there is a great deal of speculation on the subject, with different theories about how the universe began, and what may have existed before the universe came into being.

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Abraham Robinson

This mathematician followed in the steps of Leibniz. You can read about him here.

I believe that Leibniz and Robinson will be remembered by future generations.

Prophets are born, sometimes indifference is what they get. Future men and women find them again to enrich everybodies´ lives.

Leibniz

" * Identity/contradiction. If a proposition is true, then its negation is false and vice versa.

* Identity of indiscernibles. Two things are identical if and only if they share the same properties. Frequently invoked in modern logic and philosophy.

* Sufficient reason. "There must be a sufficient reason [often known only to God] for anything to exist, for any event to occur, for any truth to obtain." (LL 717).

* Pre-established harmony. See Jolley (1995: 129–31), Woolhouse and Francks (1998), and Mercer (2001). "[T]he appropriate nature of each substance brings it about that what happens to one corresponds to what happens to all the others, without, however, their acting upon one another directly." (Discourse on Metaphysics, XIV) A dropped glass shatters because it "knows" it has hit the ground, and not because the impact with the ground "compels" the glass to split.

* Continuity. Natura non saltum facit. A mathematical analog to this principle would go as follows. If a function describes a transformation of something to which continuity applies, then its domain and range are both dense sets.

* Optimism. "God assuredly always chooses the best." (LL 311).

* Plenitude. "Leibniz believed that the best of all possible worlds would actualize every genuine possibility, and argued in Théodicée that this best of all possible worlds will contain all possibilities, with our finite experience of eternity giving no reason to dispute nature's perfection." (From Plenitude.)"

This is taken from:

Gottfried Leibniz.

This German Philosopher is taken more serioulsy now than in his time. Newton´s Absolute Conception of Time, was preferred for many years over the relationist view of Leibniz, which seems to be better for The Theory of Quantum Gravity".

One simple observation on the modern importance of this thinker, is the size of the Liebniz article in Wikipedia linked above.

Two more things, Leibniz writes:

"1. All our ideas are compounded from a very small number of simple ideas, which form the alphabet of human thought.
2. Complex ideas proceed from these simple ideas by a uniform and symmetrical combination, analogous to arithmetical multiplication."

This rings true.

Mexico, an Oil Producer, Hasn’t Benefited From Soaring Price

MEXICO CITY — Mexico is the world’s sixth-largest oil producer, and the steady climb in the price of oil has reached record highs. The soaring prices should have generated $3 billion above budget estimates for the state oil monopoly, Pemex. But now the government says that windfall just is not there.

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Rogelio Gasca Neri

This Mexican engineer was my professor. I studied Solid State Physics, under him. Now he is an expert on energy. There is a debate going on in Mexico on the next steps in the Mexican oil industry. Professor´s Gasca discourse is made out of basic facts hard to swalow. Politicians hate this kind of talk. They are everywhere, like Mr. George W. Bush. Whatever gets me elected, and my buddies also, that is what I am for. Bush is telling Americans: Don´t worry, give me your money and I will give you oil forever.
How different discourses. I prefer Rogelio Gasca Neri´s, my Professor, over George Bush´s, my children´s President.
I hope the world listens to reason before it is too late.

Mixtecs

Like the Kurds in the Middle East, this people is divided in three states in Mexico. Guerrero, Puebla, and Oaxaca. Today these peoples are collecting money working in the US. What will happen when they collect enough?

Tuesday, June 24, 2008

Auger 1

"1 Introduction

The identification of the sources of the cosmic rays with the highest energies so far detected has been a great challenge ever since the first event with energy around 1020 eV was reported [2]. If the highest-energy cosmic rays are predominantly protons and nuclei, only sources which are less than about 200 Mpc from Earth could contribute signifi cantly to the observed flux above 6x1019 eV. Protons with higher energies interact with cosmic microwave background photons to produce pions [3,4], which leads to a signifi cant attenuation of their flux from more distant sources. The energy of light nuclei is damped over an even shorter length scale due to photo-disintegration processes [5,6]. If the relatively nearby sources are not uniformly distributed then we expect that the arrival directions of the most energetic cosmic rays should be anisotropic, as long as deflections imprinted by intervening magnetic fields upon their trajectories are small enough that they point back to their place of origin."

I couldn´t resist placing here this first paragraph of the paper published by over four hundred people. I wonder who wrote that part?

I want to write here that Alberto Cordero Dávila proposed the Schmidt camera optical architecture used for this historical discovery.

Auger

The correlations discovered by the group which made the third most important discovery last year according to Science magazine, is published today in:

Auger.

These results were published in Astroparticle Physics 29 (2008), 188. Now the online varsion in Los Alamos matches the published results.

Bolometric Bound for AGN-UHECR Correlation

According to Zaw et al., AGNs luminosity has to satisfy:

Lbol≥1045E202 erg s-1

to produce UHECRs.

They conclude:

"If the AGN-UHECR correlation is a real one, these results provide evidence in favor of the new mechanism of UHECR acceleration by giant AGN flares proposed by Farrar & Gruzinov (2008), in which a modest AGN has an intense flare producing a jet of the required luminosity (initiated for instance by a stellar tidal disruption rapidly heating the accretion disk) and then reverts to a mild-mannered existence."

Smolin, Farrar, and Black Holes

Glennys Farrar et al. from the Auger Observatory report today the correlation between AGNs and the UHECR (below, Galaxies Correlating with Ultra High Energy Cosmic Rays). Lee Smolin has been proposing since the early nineties of last century a correlation between the number of black holes and the parameters of the standard model of elementary particles.

To the extent that these ideas are scientific, there must be a way to corrleate this set of ideas.

Farrar argues that the AGNs in the Virgo cluster are not energetic enough to send our way the particles of highest energies ever detected on Earth.

What changes in the parameters of the standard model could produce less black holes and less cosmic rays from the Virgo cluster?

Utopia or Oblivion

Many years ago Buckminster Fuller wrote a book with the title of this note. He saw then what is clear to more and more people now. Humanity is getting close to a critical point or singularity. Ray Kurzweil, together with other thinkers, foresees a near future of great promise. Around 2025, according to his calculations, the rate of technological change will increase to such a point that we will be surprised. I just found out that the iPhone in Mexico will sell for half the price as in the US. Both markets are different and I can see the need of such a move, but it still surprises me nevertheless.

At the same time the deterioration of the environment is even clearer here in the Third World, than in Illinois, where I was just a few months ago. Is there a signal in all this?

I believe so. The moment predicted by Fuller is with us. We have to get ready; may you live in interesting times.

Why There Are Not UHECR Coming from Virgo?

Ultra High Energy Cosmic Rays (UHECR) have been detected by the Auger Collaboration. There is a deficit in the direction of the Virgo galaxy. Zaw et al. propose an explanation in:

Galaxies Correlating with UHECR.

They argue that this source has less energy overall, maybe not enough to produce UHECR.

Thomas L. Friedman: Mr. Bush, Lead or Leave!

Bush declared that America was “addicted to oil,” and, by gosh, he was going to do something about it. Well, now he has. The new Bush energy plan: “Get more addicted to oil.” It’s as if our addict-in-chief is saying to us: “C’mon guys, you know you want a little more of the good stuff. One more hit, baby. Just one more toke on the ole oil pipe."

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Darwin in the Sky?

Prof. Lin has this insight (note below from the NYT):

"In Dr. Lin’s view, planetary evolution is a kind of Darwinian affair,
as embryonic planets compete to enlarge themselves with heavy metal “food” from the disk, while struggling not to be consumed by a sibling or pulled into the mother star."


Does it support my view of a Generalized Selection Principle?

You bet, it does!

For Alien Life-Seekers, New Reason to Hope

With your Earths, Neptunes and Mars. I sing hello across the void To your Pluto, O.K., plutoid. Whatever the name, the laws demand it You’re a star. Show me your planet. For those of us who still mourn the demise of the “Star Trek” franchise and its vision of the cosmos as a thrillingly multicultural if occasionally lethal nightclub, the announceme

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Monday, June 23, 2008

One Laptop Per Child Project Extends to American Students

OLPC America plans to combat digital divide by distributing low-cost laptops to needy students in the U.S.

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Americans save on gas in Mexico, but costs may hit later

TIJUANA, Mexico (CNN) -- More Americans, tired of skyrocketing gas prices, are crossing the border to Mexico, where fueling up costs a great deal less.

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Spore is Spreading All Over YouTube

YouTube is in the middle of a creature invasion, courtesy of our creative community of video gamers and "Spore", the much-anticipated new game

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Acatempan´s Hug

In Acatempan, near Teloloapan and Iguala, two Mexican chiefs agreed not to fight with a hug. Vicente Guerrero, and Agustín de Iturbide, fought together from then on. Independence from Spain, got a big boost, and as they say, the rest is History.

Friday, June 20, 2008

Gromoll

The Poincaré conjecture stood for a hundred years as a challange for the human mind.

"The conjecture essentially says that any shape that does not have any
holes and that fits within a finite space can be stretched and deformed
into a sphere — although Henri Poincaré was conjecturing about shapes
and spheres of a higher dimension."

Dr. Gromoll helped to solve it, Perelman solved it. Now this 70 year old man is dead. Are there successors? I hope his work stays with us as he goes away.

Detlef Gromoll, Known for Math ‘Soul’ Idea, Dies

Dr. Gromoll was a mathematician who helped lay the foundations for studying the abstract distortions of shapes in three or more dimensions.

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Ice in Mars

My son found this before me. I knew that the evidence was strong, but he knew first, real water in Mars!

Now what?

The atmosphere is dead, as James Lovelock told us many years ago. The planet very likely is dead. There is a desert on Earth, Atacama in Chile, it is so dry that NASA has been testing instruments there. If they can find life in Atacama, there may be life in Mars.

I have been writing about selection, the system selects. System as I think of it, is inside other system, and contains smaller system inside. Somehow there is a level of interaction with which some levels do not depend for certain choices on the other systems. I do not need to know if tomorrow I´ll be productive to wake up. It could be determined at some level what my performance will be tomorrow, but I don´t know that. All I know is that I feel well. Very likely I´ll wake up tomorrow, and I will be as effective as it is determined, and as I make it on the spot. But in hindsight, I could know that I should not have gone to that date. Today I don´t know that.

Mars selects, it is as much a system as the Earth is. Earth is alive, Mars may be dead, we will find out as more data comes to us from our robots there.

"We have ICE!!!!! Yes, ICE, *WATER ICE* on Mars! w00t!!!"

There is water ice on Mars within reach of the Mars Phoenix Lander, NASA scientists announced.

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The Next Einstein? This is Amazing

His revolutionary ideas about the way the universe works will finally be put to the test this year at Switzerland's Large Hadron Collider, which will be the world's most powerful particle accelerator.The accelerator, estimated to cost between $5 billion and $10 billion, could provide answers to questions physicists have had for decades.

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Method

In general I do not like methods. Free association is my thing. I guess method is everywhere even in free association. Method is a scaffold for actions and thoughts. Everything is inside some scaffold, whether or not we are aware. I guess my new method is to sense the scaffold. Selection is the keyword for me now. What am I selcting and why? I chose to depend on other people, the intelligence embedded in the world, and it seemed to have worked, two people helped me get out of a jam. Now I have to look forward to the new challenges ahead. Build a network of smart people around and hope for the best.

Can I Apply my Method?

I am in a jam. From a rich country I moved to a poor country. Sure, things have improved since I was here last; but still this is the Third World. I am not going to describe the "issues" I face. I do not like to be that specific. I want to keep it useful for me, and maybe interesting for others. I liked the Truman Show, but I do not want to be Truman. Life is as interesting as it can be, therefore there is no way I will solve the problem and move ahead.

My Method states that I have to follow Polya´s four steps. Understand, Strategize (like in the Flinstone´s Movie), Execute, and Review. But my Method states more. Selection is the key word. I propose a Generalized Selection Principle. Darwin´s Natural Selection, states that copies that have copies are good, the more copies the better. This principle can be seen not only in finches in the Galápagos Islands, but also in all the versions of the "Indiana Jones" movies. My Method does not tell you what to select. You will know if it was good by the number of clones of your original choice you encounter in your future. Also it is important that you engage your environment, there is a distributed "intelligence" around us. This is easy to see in the internet, you can find information "out there". At the end of the day, the choices are yours, and you live with the consequences. The heuristic character of the method is necessary, nobody knows the future.

Are We in This Together?

Budweiser and Corona would be one!

I do not drink that much beer, but I could not pass this piece of news. The others, Beligians, Brazilians, and who knows who else, want to buy Corona´s company Modelo. Mr. Fernández does not want to sell. The point here, is he does not want to belong to Anheuser-Busch either. I guess the Americans want to sell and he doesn´t.

Maybe if Mr. Fernández reads my method (below) he can get direction for his selection. I doubt it, though.

These are tough times when not even Coronas would be Mexican!

Modelo CEO Resigns From Anheuser - Busch Board

NEW YORK (Reuters) - Anheuser-Busch Cos Inc said on Friday that Carlos Fernandez, chairman and chief executive of Mexican brewer Grupo Modelo , has resigned from the U.S. brewer's board of directors.

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Thursday, June 19, 2008

How Far Can Theory Take Us?

Yesterday I wrote a note (below) with a method. The Mexican peasant I was thinking of, does take her people far. If our western civilization collapses globally, those Mexican Indians may be able to keep going. Modern Science has taken us this far. Both examples answer the question of this note affirmatively. Theory can take us far.

Nevertheless not any theory can take us far. Theory that reflects observations, like the Mexican peasant constant comparison of this year´s corn head size with last year´s; is bound to be successful. On the other hand my selection method (note below) may be worthless.

Can we know beforehand which case is which?

I have to use the method and report results. At this point all I can do, is a little more theory.

Given a situation requiring a selection, we take one. That is our life in a nutshell. Here I write an analogy with Natural Selection, to strengthen my proposal.

Selection as I have been referring to in these recent notes, is human selection. Natural Selection is different. Unless I want to give Nature human qualities as the people from some places now do, and all places long ago did. Then what I write here is useless. I assume though, that even if Nature surprises us often, humans are different. I will introduce an idea due to Stephen Wolfram in this Natural Selection. It is not Darwin´s version then, maybe I can call it Darwin-Wolfram Natural Selection.

Principle of Computational Equivalence.

My understanding of this Principle is that above a complexity threshold; complex systems are computationally equivalent. A simple cellular automaton rule, was proven by Wolfram, to be a universal computer.

One lemma for me then, is that human selection and Natural Selection, are not all that different.

With this perspective a statement of Natural Selection, may be useful for my Generalized Selection Principle.

Natural Selection: A system produces more copies of one type than other types.

The fitness property is used to distinguish permanent parts from transitory ones. We say that those permanent parts are more fit for that system. The system is contained in other systems. As scientists we may be aware of the other systems or not, still the principle is applied locally.

I suspect that the system is fractal. As the Poet put it:

So, naturalists observe, a flea
    Has smaller fleas that on him prey;
     And these have smaller still to bite 'em,
      And so proceed ad infinitum.
       Thus every poet in his kind
        Is bit by him that comes behind.
- Jonathan Swift, Poetry--A Rhapsody

We only know a few fleas, but that is enough, and that is the power of thought.

Darwin only had to see finches, what prey on finches? That was not necessary. Gauss could tell a flea if its world was spherical, without the flea leaving the surface of the sphere. That insect only had to go around, holding a flag leaving its twin behind, if the flag pointed to the same direction as the flea left behind, there was no sphere, there was curvature otherwise. Locally Gauss tells us, we can leave the curved surface, at least in our mind´s eye.

Kenneth Wilson taught us to use the phase transition to know about the system almost without knowing much about its Hamiltonian, or dynamical generator. Whole classes of Hamiltonians, universality, led to the same type of phase transition. That is good and it is bad. At the point of transition we do not need to know much about the system, by the same token at the transition point, we won´t know much about the system.

I believe that these different thinkers, Smolin, Wilson, Wolfram, and Darwin, are telling us something very deep.

I want to encompass all that in the Generalized Selection Principle.

In conclusion:

A simple method is needed to know which step to take in all cases. It is known from the Travelling Salesman Problem, that the trivial solution is not a solution. It is easy to convince oneself, that this person cannot just go to the nearest client and expect to get the shortest path when all the clients are visited, you can try it with three points judiciously located, it is easy to construct a counterexample. Some hindsight is needed, the next move needs some depth of vision in the game to be a good move. I feel that there is no universal strategy to always win, my Principle, at most is heuristic, as the great George Polya understood so well, so many years ago.

With Wolfram I believe that I have to respect and negociate even with a sufficiently complicated cellular automata. There are some around, for instance that virus that put you down with a cold the other day.

The Principle then is only a guide to take informed decisions.

In any case as Smolin still has to convince me that something of value will come out by changing parameters to produce universes worse than ours. I still have to convince myself that my theoretical game is worth anything. At least Smolin has a way to test, I still have not given a test for my Principle. Remembering Renè Descartes, I feel that maybe I will be the only one using this Method. I hope I am at least as successful with this kind of game as he was.

Conclusion

Natural selection is different than human selection. Given Wolfram´s result, now I believe they are not different, therefore for a first try on my Generalized Principle, I will assume they are the same. In a future revison of the Principle I may introduce the differences I feel may be necessary.

Wednesday, June 18, 2008

Generalized Selection Principle

There is human work that remains, and some that is lost. What to do? is a frequent question we answer to keep our lives meaningful. I joined Sugar Labs. Since I speak Spanish I tried to write a proper translation, when I finished it was not saved. I am a member of Wikipedia also; likewise my contributions there are very small. I propose here for myself a method, like Descartes many years ago in France. Here it goes.

Selection is a process we engage in. I choose when to stop writing, and when to continue. Tendency is where I want to end up after some work is finished. I select where I want to end up. I believe that Charles Darwin, just found the tip of the iceberg. Lee Smolin has a specific proposal for Quantum Gravity. The right theory is that one that leads to the maximum number of black holes. He expects to get some, maybe all, the values of the Standard Cosmological Model, that way. Varying these parameters within small ranges, the production of black holes should go down. There are some unknown actors, selecting big corn heads (read note below), at play behind this beautiful Universe of ours.

This proposal is for my work only, if some reader finds it useful, I´ll be grateful if she lets me know.

The Generlized Selection Process consists of a method to choose, the goal of this method is the production of members of a class. Say scientific ideas. One idea is chosen, if it produces more ideas that in their turn, produce even more ideas, then the idea is selected. These ideas have to be interesting to the author and others that know them. A set of ideas is not chosen if varying one of them just a little, produces less ideas. There has to be some wholeness to the final set of ideas. Some consistency; as Smolin is trying to do with his proposal of maximum production of black holes.

The method consists at least of four items:

  • Understand the situation in need of choice
  • Imagine an strategy to go from beginning to end
  • Execute the strategy
  • Check that the goal was achieved
This is clearly George Polya´s method to solve a math problem. Other thinkers have reached similar proposals, and I believe that even the Mexican plant breeder I write about in the Selection note below, uses a variation on this theme.

This Generilized Selection Principle produces coherent response systems for my actions, and those that choose to use it. It can be recursive, if this first version of the Principle does not work, applying the method a better one could be found. Eventually like that ancestor of mine, bigger corn heads will be produced.

Selection

Plant domestication is one of the oldest practices of civilized people. Only in few places on Earth has this taken place. One is Mexico. To this day this process continues. I believe that the people of Mexico has insight on the ways of Nature.

Norman Borlaug, started the modern era of this in Mexico.What I write about here is: What to expect of concepts on central tendency?

I expect that Mexicans without western school education have conceptions of central tendency.

To select corn with bigger heads the experts on hand had to select the proper seed to get, during a future harvest bigger corn heads.

It must be possible to engage the descendents of these experts to teach us: How do they select?

Natural Selection for Everything?

A few years back, Lee Smolin proposed to go past the impasse in the quest for Quantum Gravity using a modified Darwin principle of Natural Selection. I myself toyed with that idea in the eighties, I did not pursue it and Smolin did. Now he has predictions and a few of us are waiting to see if he is right.

I was wondering what else can we do with this. My friend Alan Boss from the Carnegie Institution in Washington DC, claims that so many parameters allow sceintists to fit anything. I am afraid he is right. How could we keep ourselves out of trouble in problems with so many parameters?

Maybe a generalized Natural Selection Principle can help. But I will write about that in another post.

Ida and Lin 1

These scientists conclude:

"Many planetesimals and embryos migrate to the proximity of their host stars, especially in the limit of relatively efficient type I migration. Many cohesive collisions may also occur among these planetesimals and embryos in the proximity of their host stars. Provided most of these planets are retained (despite the effect of their interaction with the magnetosphere and tide of their host stars), we anticipate the fraction of solar type stars with short-period earthmass objects to be several times that of short-period gas giants. The physical composition of these close-in planets is most likely to be rocky to icy. Their observed mass distribution will enable us to calibrate the magnitude of the type I migration (the magnitude of C1). The next step is to extrapolate and to calibrate the fraction of low-mass M-dwarfs and high-mass G sub-giant stars which may bear potentially habitable planets."

We may soon find Earth twins, if they are right.

Are There Planets Out There for Us?

It is difficult to know which Physics problems will be solved soon. String theory has many solutions, but not a single chosen one agreeing with most data. Planetary formation models can give little planets, big planets, some in between, but can they find and explain one just like ours? It seems that more data is needed, and more money and time spent. I hope they finish before we are through with this Earth of ours.

Ida and Lin

These two scientists have predicted many small planets in the Universe. Read:

Toward a Deterministic Model of Planetary Formation V. Accumulation Near the Ice Line.

Now, as noted below, Major et al. just announced the existence of planets smaller than Jupiter. Prof. Guillermo González from Iowa State University has this to say:

"These are certainly exciting news. It does confirm the expectation (from Lin and Ida's planet formation models) that there should be far more low mass planets than giants. I'm interested to see what the orbital parameters are like. For instance, are the high eccentricities prevalent among the giants also common among lower mass planets?"

Should I Join Open Source Teams?

I have been a user for more than 14 years of Open Source products. I even hosted Eric Raymond at Naperville, when I worked at Lucent Technologies. But so far there is nothing I have given back to the community. My son is more responsible, when he uses BitTorrent, he leaves the connection open for others to use. I have been stinky.

I plan to change that, I am starting Sugar Labs., Chilpancingo.

Weather Pattern Changes: Jet Stream Shifting

One of the main drivers of world’s weather is moving due to climate change. Scientists are finding that the jet stream, that river of air that pushes storms across the country, is moving towards the north and south poles.

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A Field Guide to Firefox 3: A Full Inventory of the Goodness

Deb, long time mozillian, gives a hefty outline of all the juicy new goodness in Firefox 3 in preparation for the final release next Tuesday.

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Web Applications

I am doing research on Mathematics Education. My emphasis is on digital instruments for education. Yesterday I was trying to figure out why divisions are so hard for kids. My first answer is that they memorize multiplication facts, not division facts, and then they have to learn complicated multiplication rules to do long divisions.

Under closer inspection I convinced myself that it is going to be hard if I want to make billions of grammar school teachers to change.

Then I read today about the Bill Gates - Marc Andreessen saga. Marc did not change the many Gates clients using Microsoft browsers in the nineties, but his children, Google-FireFox, are winning.

Is there a lesson here?

I think so. Good ideas win out, everything else being equal.

My goal is to imagine good ideas, they will take care of themselves.

FireFox

I am using version 3.0!
So far so good. You can read about this baby of Marc Andreessen in the note below. I wonder how much he is involved with this descendant of Mosaic.

Forbes: Why Firefox Matters

But don't be fooled. Firefox has become one of the most important pieces of software around today as consumers shift from using their PCs to run applications living on their hard drives to a communications device able to connect with applications living on distant servers. The new browser has plenty of these soon-to-be-ubiquitous features...

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Shabaa Farms

Finally the Arab and the Jewish people are talking about something I can understand, they are fighting over the "Shabaa Farms". Everybody needs land and water, if they had said that in 1945 when this whole mess started maybe by now there would have been an arrangement; everything can be negociated by the best negociators the world has ever known, the children of Abraham: Isaac and Ismael.

Are Lebanese Leaving Puebla?

Peace talk goes around in the Middle East right now, as you can see in the note below. Maybe those Arab-Pueblans are considering a return home. Maybe; I don´t know.

Israel Offers to Talk Peace With Lebanon

JERUSALEM — Israel offered on Wednesday to start direct peace talks with Lebanon, saying all issues would be negotiable including a tiny piece of Israeli-held land on the countries’ mutual border that Israel has long argued does not belong to Lebanon but that the Lebanese say is theirs.

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Iraq: Still Inscrutable By THOMAS L. FRIEDMAN

When I was in Cairo last week, Osama Ghazali Harb, an Egyptian political analyst, told me about a speech that he had recently given at the main Coptic Cathedral there. It was a discussion about the state of Arab politics. After he had finished, he said, an Iraqi man who had come with some Egyptian friends, got up to ask a question and along the ..

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Tuesday, June 17, 2008

Astronomers Identify 45 New Planets

At a meeting in Nantes, France, Michel Mayor of the Geneva Observatory and his group presented a list of 45 new planets, ranging in mass from slightly bigger than Earth to about twice as massive as Neptune, from a continuing survey of some 200 stars.

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Are Lebanese Moving to Puebla?

This past weekend I went to Puebla City in Mexico, after 10 years. The south east part of town is changed. Tall buildings and new business all over the place. That is good for my house because I guess its price went up. Where is the money coming from? Then I put two ant two together, and I think I have a solution. Lebanese are not as welcome to the US as they were before 9/11. There was a thriving Lebanese community already, the war in Palestine does not seem to be coming to an end anytime soon. I guess they are moving with millions of dollars, and invest with relatives in Puebla.

This hypothesis can be checked, I just leave it like that.

Friday, June 13, 2008

Even More Cubics

Even More cubics

Super Black Holes: NASA mission seeks new laws of physics

The Gamma Ray Large Area Telescope (GLAST) is an astounding mission to explore the most extreme environments in the universe, search for signs of new laws of physics, what composes the mysterious dark matter, and secrets found in gamma ray explosions.

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Super Black Holes: NASA mission seeks new laws of physics

The Gamma Ray Large Area Telescope (GLAST) is an astounding mission to explore the most extreme environments in the universe, search for signs of new laws of physics, what composes the mysterious dark matter, and secrets found in gamma ray explosions.

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The Mini-Laptops of Summer

You're not the only one losing weight for beach season. The latest and least expensive breed of slimmed-down mobile PC--the mini-laptop--is ready for summer travel.

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Thursday, June 12, 2008

Curious 'Quasiparticles' Baffle Physicists

Israeli physicists have discovered bizarre 'quasiparticles' which have one quarter the charge of an electron, and may be useful in quantum computing.

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8 Steps

1. Gather data
2. Diagnose data
3. Select and prioritize your objectives
4. Create and analyze alternatives
5. Select one of them (make a decision)
6. Plan the action steps to carry out that decision
7. Implement the plan
8. Study the results against the objectives

Professor Polya many years ago proposed:

First principle: Understand the problem

Second principle: Devise a plan

Third principle: Carry out the plan

Fourth principle: Review/extend

Now James Rick, as you can read in the note below proposes the 8 steps I wrote here.

Method, can solve some problems.

8 Surefire ways to Problem Solving

If you find yourself dealing with a problem or challenge use these surefire 8 Step Problem Solving Method to clarify your thinking in a systematic approach.

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Wednesday, June 11, 2008

Apple and Lucent

Today I saw Steve Jobs presenting his 3G iPhone. Lucent was not capable of doing something like this. Why?

This seems a classic case of The King is dead. Long live the King! A new generation is in charge of communication companies in the US, and very likely the world.

More Cubics

Now I changed the coefficient values, we have three graphs in:

x3 - 27x - 54, x3 - 30x - 50, and x3 - 24x - 56.

One sees how we could have three real roots, two repeted, all different, or one real root and two complex roots.

Sums and Subtractions

Is it easier to calculate sums than subtractions? Why?

It may be that we memorize addition facts and need to apply an algorithm for subtractions. By the same token it seems that multipplications are easier than divisions.

You can read lesson plans for children in:

The Math Lesson.

Children start counting. Could they start subtracting?

It may be natural, whatever that means, to count than to subtract. Could we start by asking small children to take away, before we worked on counting?

I suspect that society chose sums over subtractions and adults taught children that way. It could have been the other way around. If the child has a few things, adding seems natural, but if she already has more than she uses, she could see subtraction as relevant. More and less are concepts we learn from a young age. Which is more "natural", whatever that means?


Tuesday, June 10, 2008

Physicists in Congress Calculate Their Influence

WASHINGTON — According to the Congressional Research Service, there are only about 30 scientists among the 535 senators and representatives in the 110th Congress, and that is counting the psychologist, the psychiatrist, a dozen other M.D.’s, three nurses, an engineer, two veterinarians, a pharmacist and an optometrist.

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Monday, June 09, 2008

It’s a Different Country : By Paul Krugman

Fervent supporters of Barack Obama like to say that putting him in the White House would transform America. With all due respect to the candidate, that gets it backward. Mr. Obama is an impressive speaker who has run a brilliant campaign — but if he wins in November, it will be because our country has already been transformed.

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Saturday, June 07, 2008

Google Docs

Obviously I am not the best user of Google Docs. But there it is. I graphed a cubic with OpenOffice, I uploaded it, published the graph independently, and voilà.


By the way the formula is:

x3 - 27x - 54

Cubic 1

Cubic

Click here to get a Cubic

Savor the Moment By BOB HERBERT

Friday was the 40th anniversary of the death of Robert F. Kennedy. Had he lived, he would be 82 now.

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Friday, June 06, 2008

Gauss´Less Constraint Principle and Covariation

Dr. Carlson has developed ideas around mental processes associated to function graphing in mathematics. She stresses the ability of the person doing the graph, to coordinate two variables as they vary. On the other hand Gauss, many years ago developed the idea that objects move minimizing force constraints, as if free.

Is there a connection?

The actual process of doing the graph can be with straight lines between the points considered for one interval. The more points, the more faithful the graph is. In Gauss´method the particle moves as if free, between points also.

One basic difference between the two sets of ideas is that Gauss does get exactly Newton´s force law, and Carlson gets a graph without physical motivation.

It may be interesting to ask if Gauss was considering the best way to do a graph with mental processeses similar to those Carlson has drawn our attention to.

User Scripts

At Lucent Technologies I worked with a Script Guru. He build a whole structure to automatize software construction tasks. I was even included in one of his patents. Now I want to us this technique to automatize teaching activities. I really don´t know how good they´ll turn out to be. But I will try.

The Gmail extension I added to my FireFox browser, Better Gmail, is an example of user scripts.

My Role in OLPC

I recently met Carla Gómez Monroy. She belongs to the One Laptop Per Child foundation. She accepted my offer to help in that endevour. I want to write some scripts to mimic what my colleagues do here in Chilpancingo. They break up, in detailed pieces, lesson plans and other practical products teachers do to help students do mathematics.
I want to add digital instruments to this box of tricks.
I expect good things from these efforts.

Gina Trapani

I am reading something written by this software creator. She writes so well that in my new life as a Math Education Professor I feel envious. I hope my writing and speech improve in this new stage in my life. She directed the production of the Gmail tools I installed today.

Math Education

I am starting to read long papers. They go on and on, and seem to never end. These people know more words than I do, and even make up some more, say construct. That word is supposed to mean something else from construction. It is used as a noun.

I am having fun. I cannot change the collegues a bit, I guess that will come with time.

Better Gmail?

I just installed Better Gmail to my Firefox browser. I really don´t know yet what this will do for me. I am happy with the ScribeFire add on so far. It gets somethings done faster.

Gmail Gets 13 Experimental New Features Tonight

Starting at 6 PM Pacific Time tonight, Google will start rolling out Gmail Labs, an experimental area of new Gmail features that will be familiar to Better Gmail users...

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Complexity

As a physicist I try to simplify everything. Now that I am working on Math Education, whatever that means, I am trying to simplify everything. I need a more nuanced approach. This is an effort to state a more useful methodology.

I hear my colleagues belaboring what for me seem like simple situations. What is the Social Representation (SR) of grammar school mathematics? Hour after hour I hear the many, many nuances, this question has. My colleagues even debate whether a conjunction for or on should be used in a paragraph. Grammar is not my forte; they were really arguing not about a conjunction, but about a coordinating conjunction. I am in trouble.

Are SRs that important? Yes. Do I know one when I see one? No.

Is it really true that the Theory of Quantum Cosmolgy is simpler? Maybe not, and that is why theoretical physicsts are stuck. I do want to contribute to Quantum Cosmolgy as I do to Math Education, but in any case I have to confront the intrinsic complexity of our lives.

I assume that the place to start is the Principle of Computational Equivalence (PCE), discovered by Stephen Wolfram.

Once one reaches a threshold of complexity, all complex systems are equivalent. The good news is that the threshold is low, a Cellular Automata is enough, the bad news is that it is complicated once the automata is run long enough.

I had the same feeling, I guess most people do, when I run my first "simple" iterated equation:

xn+1 = λ xn(1 - xn)

Now I have to search for an equivalent guide in Math Education, whatever that means.

Thursday, June 05, 2008

Bright Children

I was reading today the ideas of David Dalrymple, since he was thirteen, grown ups were interested in him. He is set to fix computer architecture from serial to parallel. Also today I heard about children in Mexico City ready to get into science programs. I ask myself: What can a child do and when?

My son is also sixteen and bright. Can they go ahead without our help?

I don´t think so, at least we have to provide social references, What and why is important? We adults sometimes have trouble knowing this, Then how can we help?

Our role is to provide a useful common sense. Einstein said that common sense is what we believe before 18. Science has to go beyond common sense, but first we have to develop a new improved common sense we can share with our children.

Yes David Dalrymple can improve computers, and most bright children deserve the opportunity to make their mark in this world.

Ray Kurzweil and Neil Gershenfeld: Two Paths to the Singul..

MIT professor Neil Gershenfeld and technology futurist Ray Kurzweil have long worked at the leading edges of physical science and computer science. Today, in their own ways, both believe that we are on the event horizon of a technological singularity. But they arrived at this conclusion from two very different directions, discovered one child ..

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The Future Is Now? Pretty Soon, at Least

Ray Kurzweil is a futurist with a track record who makes his predictions using what he calls the Law of Accelerating Returns.

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Scientists Have Solved The Mystery of Levitation

The University of St Andrews team has created an 'incredible levitation effects’ by engineering the force of nature which normally causes objects to stick together and reversing a phenomenon known as 'Casimir force'.

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Acer bets big on Linux

Acer has stated that it will be pushing Linux aggressively on its laptops and netbooks. The company is already heavily promoting Linux for its low cost ultra-portable netbook range out later this year, but senior staff have said that Acer will also push Linux on its laptops.

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Roger Cohen: Energy lessons

Time to start thinking about energy abundance, not about energy conservation.

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Wednesday, June 04, 2008

Mathematics Education in the US

I have been reluctant to write about my experience in US high schools. For one thing I may not be as objective as I would like. For another thing I am not knowledgeable since I only taught two years in that system.

Be it as it may, here is my first installment.

I did not succeed. I know more physics and mathematics than most of my colleagues in those schools. Nevertheless I did not satisfy the expectations of my bosses.

In one occasion I did not present the material in the expected way. In another occasion I did not keep the discipline as was expected of me.

My first assessment of my US experience, is that what I knew was not as important as what the hiring authorities expected of me.

I am disappointed because in one occasion my students were minorities, and my knowledge could have helped them. Now I am back in Mexico, I feel appreciated.

Mathematics Education

You can read in Wikipedia about this field of Mathematics.

This could become a strategic area in the world at large. In the past, the need to produce and know mathematics was satisfied with a small number of practitioners. In Greece, only small groups of people were involved in these activities. It is clear that the need is more extensive nowadays.

There are countries which took this activity as very important for the long time survival of the way of life of its people. I can think at least of three countries that recognize this situation: The United States of America, Russia, and China.

I mention these three because two of them were in a fierce competition propelled by the so-called Cold War. The third is a newcomer to the competition for markets and sources of raw materials.

Mexico, the country where I reside now,is mainly in the sphere of influence of the US, but this influence is less now than during the last decade say. China has a plan to build efficient cars in the Mexican state of Michoacan. The current Governor of that state is the grandson of the Mexican President that confronted the US when oil workers went on strike in 1938. As a result of the political decision of that President, now Mexico is responsible for the best use of Mexican oil; at close to one hundred dollars a barrel, this resource is more valuable than ever.

It is not chance then, that his grandson, now in a nation building measure, agrees with the Chinese leaders to build these cars using Mexican resources. The state of Michoacan has plenty of iron, an important resource for this enterprise. Furthermore there is a deep water port in the Pacific strategically located for this factory in the same state.

Here in Chilpancingo we are ready to educate our young in this very important area of Mathematics Education. We need hundreds of new teachers, and thousands of new students to produce a viable society in this part of the world, which has had human habitation for ten thousand years at least.

We are ready for the coming world based on mathematics, science, and technology.

Mexico at the Brink

The War on Drugs may be fading from memory north of the Rio Grande, but south of the river, bloody battles are threatening to overwhelm Mexico’s democratically elected government. The timid assistance package proposed by the Bush administration and pared down by Congress suggests that Washington doesn’t grasp either the scale of the danger or its..

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Escuela de Chilpancingo

Plan de Trabajo de Eduardo Cantoral en el Centro de Investigación de Matemática Educativa de la Unidad Académica de Matemáticas de la Universidad Autónoma de Guerrero en Chilpancingo.

04/06/08

Sumas y Restas en Matemáticas

Introducción


El objeto de investigación aquí propuesto es la
dificultad de los algoritmos matemáticos. En la antigüedad
las operaciones aritméticas sin el uso del concepto de cero
provocaron la siguiente situación en Europa. Se sabía
de la existencia del cero a través de los Árabes, que
obtuvieron este concepto de los Hindúes. La Filosofía
Europea estaba sustentada en la Griega como había sido
incorporada por la Iglesia Cristiana Europea. En esta religión,
la idea de la nada se consideraba errónea y extranjera, Árabe
e Hindú.



Los hombres de negocio, sin embargo, eran pragmáticos. Si
alguién pudiera llevar sus cuentas eficientemente, no les
importaba que se usara el cero.


El resultado de esta situación fué el uso ilegal de los
algoritmos árabes. En una especie de contrabando, se usaban
estos algoritmos sin informar a las autoridades eclesiásticas.
Los números oficiales, o romanos, no eran adecuados para
llevar las cuentas de la mejor manera posible en esa época.


Aquí se propone el uso de instrumentos digitales para la
matemática.


Ahora no es un dogma religioso el causante de las dificultades, es
una situación histórica. En particular se considera
aquí el estudio del cálculo diferencial e integral.
Existe un obstáculo epistemológcio con la concepción
del infinito. Entre parentésis, es el mismo concepto medieval
del cero, pero ahora al intentar la división con su uso sin
atención del usuario del algoritmo. Los creadores del cálculo,
Newton y Leibniz, probablemente hubieran inventado otros algoritmos 
de haber tenido en ese tiempo instrumentos digitales como los modernos 
para realizar sumas y restas.


No se propone aquí revisar la historia, ni siquiera entender
cómo hubiera sido la historia si los actuales instrumentos
digitales hubieran existido. Simplemente se propone retomar los
desarrollos del siglo diecisiete antes de Newton y Leibniz, y
proseguir, ahora con instrumentos digitales, el estudio y la
enseñanza de las diferencias finitas.


Desarrollo


La primera parte de esta propuesta de trabajo es la recopilación
del conocimiento, tanto actual como del siglo diecisiete, de los
algoritmos de sumas y restas para obtener razones de cambio
y la suma de estas razones de cambio. El enfoque metodológico
será el de la Mecánica Clásica, tanto porque el autor de esta
propuesta es Físico, como por que se argumentará que la
matemática surge en contextos históricos que sirven para su mejor comprensión.


Posteriormente se revisará la literatura en el área de
la Matemática Educativa, de trabajos previos relevantes a la
presente investigación.


Después se implementarán las propuestas en salones de
clase, principalmente en el nivel medio superior y superior.


Finalmente se presentarán los resultados en medios y foros
adecuados que le den continuidad a este esfuerzo y que permitan a
otros investigadores y profesores activos, usar lo descubierto y
construido como resultado de este trabajo, en las escuelas y lugares
donde sean útiles.

Conclusión


Se propone el estudio de los algoritmos de cálculo para su implementación en
instrumentos digitales para el estudio y la enseñanza de las matemáticas en los
lugares donde suceda este estudio. Ahora es posible construir un objeto de
estudio en un lugar y usarlo en otro. Por ejemplo el Tecnológico de
Massachusetts, ya le da a los profesores de esa institución la oportunidad de
poner sus notas de clase en la Internet, para que sean usados por sus
estudiantes, y cualquier otro estudiante en el mundo que tenga una conexión de Internet.


El objeto de este estudio es la dificultad de los algoritmos
matemáticos. Didácticamente se intenta presentar ideas,
como el teorema fundamental del cálculo de diferencias
finitas, de la manera más simple. Se presenta la hipótesis
de que este esfuerzo por parte del profesor llevará a mejores
resultados de aprendizaje de los estudiantes.


Finalmente se propone aquí que este es el momento histórico
adecuado para este estudio. El autor está involucrado en el
Proyecto, Una Computadora Portátil Para Cada Niño (OLPC
por sus siglas en inglés), del Profesor Nicholas Negroponte
del Instituto Tecnológico de Massachusetts. Las contribuciones
de la Escuela de Chilpancingo serán consideradas y en su caso
incorporadas a este esfuerzo de alcance mundial.

Absolutely Stunning: Magnetic Fields Visible For First Time

Natural magnetic fields are revealed as chaotic, ever-changing geometries as scientists from NASA’s Space Sciences Laboratory excitedly describe their discoveries.

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René Descartes

"For myself, I have never fancied my mind to be in any respect more perfect than those of the generality; on the contrary, I have often wished that I were equal to some others in promptitude of thought, or in clearness and distinctness of imagination, or in fullness and readiness of memory. And besides these, I know of no other qualities that contribute to the perfection of the mind; for as to the reason or sense, inasmuch as it is that alone which constitutes us men, and distinguishes us from the brutes, I am disposed to believe that it is to be found complete in each individual; and on this point to adopt the common opinion of philosophers, who say that the difference of greater and less holds only among the accidents, and not among the forms or natures of individuals of the same species."

This quote taken from the French thinker, René Descartes, allows me to think that all children can learn mathematics.

Time for Radical Pragmatism

When I reported from Israel in the mid-1980s, the big debate here was whether Israel’s settlement-building in the West Bank had passed a point of no return — a point where any serious withdrawal became virtually impossible to imagine. The question was often framed as: “Is it five minutes to midnight or five minutes after midnight?” Well, having ..

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Sunday, June 01, 2008

What the Mexicans Might Learn From the Italians

The headline in The New York Times that morning in 1984 was macabre, if unintentionally hilarious: “Unknown Arm of Sicilian Mafia Is Uncovered in the United States.”

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