Revising the state of science in Mexico – Quantum Tunnel Podcast

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Science in Mexico

A focus editorial about science in Mexico appears in the most recent issue of Nature Materials. The editorial content was  prepared, commissioned and edited by Joerg Heber and myself. It includes a commentary by Arturo Menchaca Rocha, President of the Mexican Academy of Sciences, and an interview with Juan Ramón de la Fuente, President of the International Association of Uniersities and former Rector of the Universidad Nacional Autónoma de México.

In terms of population, Mexico is the largest Spanish-speaking country in the world and the second most-populous country in Latin America after Brazil. Mexico boasts an abundance of natural resources, all of which are important to its economy and oil being a very important one of them. According to the U.S. Energy Information Administration in 2009 Mexico was the world’s seventh-largest producer of crude oil, and the second-largest supplier of oil to the United States. In contrast, although the country has substantial natural gas reserves, Mexico is a net importer of this resource. This is of course a very brief assessment of the energy situation in the country, but one that can be extended to other areas, including education, science and technology.

There is no doubt that Mexico has improved access to education and literacy over the past few decades. According to a 2007 World Bank report, enrolment at the primary level is nearly universal (97.9% net), and more children are completing primary education. However, this is not the case at higher education levels.

Achieving a strong economic growth and a high level of human development requires increasing the investment in science, technology and innovation, as well as a close collaboration between government, private sector and higher education and research institutions. In the case of Mexico, in order to solve the current lag in the areas mentioned above there are three issues that need to be addressed, and which are analysed in the recent editorial inthe Nature Materials.

The first thing to tackle is to compensate the slow development in basic science, manifested for instance in the in the rates of Research and Development personnel and researchers which are among the lowest in those ranked by the Organisation for Economic Cooperation and Development (OECD) which places Mexico in a low position compared to other OECD countries. This situation can be partly explained bu the lack of investment in infrastructure and the inefficiencies in human resource management, as pointed out by the commentary of Menchaca Rocha for Nature Materials.

A second point to address is to counter the enormous asymmetries between federal states, institutions and social sectors, as highlighted by Juan Ramón de la Fuente Ramírez. For instance, in terms of institutions for example, in 2009 UNAM received a budget of 1.6 billion US dollars from the Federal Government, which is larger than the budget of some states in Mexico. However, other publicly funded Universities around the country do not have access to similar resources, producing an acute imbalance. Nonetheless, these other institutions make important contributions to the research output of the country, although their visibility might be reduced.

The third issue is to improve technological transfer. In Mexico the business sector plays a much smaller role in the innovation process than the higher education sector. As a result Mexico has an enormous dependence on foreign technology and a very low rate of registration patents from Mexican nationals.

In order to tackle these issues it is necessary to bring together researchers, academics, directors and managers of higher education institutions, research centres and legislators in order to harness the potential of science and technology more effectively. Juan Ramón de la Fuente brings up the urgency for a strong state policy for science and technology and hints at the need for legislators to take up the responsibility to make this a reality.

Two hundred years ago, Mexico embraced the idea of political independence and in the last hundred years of Mexican history, the country has seen the creation of the vast majority of its higher education institutions, as well as the systematisation of research as a professional activity. It is time now for Mexico to take the necessary steps to provide its scientific and technological development with a strong basis in order to allow the country to be fully engaged in an ever more competitive world.

The editorial is available to be seen freely to registered users, whereas the Commentary by Arturo Menchaca Rocha and the interview with Juan Ramón de la Fuente can only be accessed bu subscribers.


Testing Relativity on Earth

Einstein’s theory of relativity tells us that relative speed and gravity affect the passing of time. Relativistic effects have been measured using synchronised atomic clocks on jumbo jets back in the 70s. However, more recently researchers at the National Institute of Standards and Technology have tested relativity at a more everyday-life scale, as reported in the journal Science. Chin-wen Chou and colleagues have shown that time speeds up if you raise your height for instance by going a rung up a ladder, and it slows down if you travel at just 36 kilometres per hour.

Daisy Fossil

A 47 million year old fossil of a daisy has been identified in the Argentinean city of Bariloche. The Argentinean and Swedish scientists also found traces of pollen and their findings have been reported in the journal Science. According to the scientists the Asteraceae family, to which daisies belong to, are originally from the Patagonian region and from here it aprese to the rest of the world. This discovery is quite interesting as usually flowers do not leave fossil records, they usually desintegrate.

Heart stopping surgery

Heart surgeons use extreme cooling to allow them to stop a patient’s heart long enough to carry out surgery and then revive them. Sounds a bit like science fiction, but it is not.

The technique induces hypothermia on the patient, whose body is cooled to 18 degrees centigrades. This provides the surgeons with a brief but important window to perform surgery, which has to be completed before any brain damage is caused to the patient. Once the surgery is finished, the patient is warmed up and their heart restarted with a defibrillator.

The secret of a good dancer

Not everoine has the dance moves of Tony Manero in Saturday Night Fever, but what is the secret if a good dancer? Scientists from Northumbria University have carried out a rigorous analysis of dance moves that make men attractive to women and their findings have been published in the Royal Society journal Biology Letters.

The scientists captured the best moves of young men using 12 cameras. These movements were then converted into a computer-generated cartoon which women rated on a scale of one to seven. They found that women paid more attention to the torso, neck and head and that it was not just the speed of the movements, it was also the variability of the movement. Movements that went down terribly were twitchy and repetitive – so called “Dad dancing”.

Keep your desktop desktop tidy Mendeley style – Quantum Tunnel Podcast

You can download this podcast in iTunes o Feedburner.

A couple of weeks ago I had the opportunity to visit the headquarters of Mendeley in London for a social event which they call “Open Office Friday”. It was a very causal evening with very enthusiastic and interesting people and surrounded by pizza, beer and table football. The ideal combination, and indeed a very good way for Mendeley to hear directly from their users and take suggestions and comments. But what exactly is Mendeley?

Well, let us start with an example that I’d like to think is a very common situation. As a researcher, not only are you interested in generating knowledge, but also in what other people in your field (or related fields) are doing. Therefore it is not unusual to have your own bibliographic collection. Dealing with a handful of papers (even physically printed) is a perfectly manageable situation, however, when you start gathering more and more of this precious sources of information, the task can become a big challenge. Well Mendeley is a tool that can help you with that and more.

Mendeley is a combination of a desktop software and a web based social tool. The desktop part of the combo is a free academic software for managing and sharing research papers. The web part provides you with online backup for your papers and can be used to see research trends in your chosen discipline.

I have often heard it being described as a Last.Fm or Groove Shark for research papers. In you can build a profile based on your musical tastes and the website automatically recommends music that you might like, based on your profile and you can in principle get in touch with people that share your musical tastes. Mendeley does pretty much the same.

Uploading PDF files to the desktop application is very easy, all you have to do is drag an drop the document to the Mendeley library and voilá. The software will extract the appropriate metadata from the file and will prompt you to check if things are OK, if for whatever reason that is not the case, you can manually edit the information for the paper. In my experience the automatic recognition works pretty well and if has not been a hassle to fix those entries that went a bit wonky. Once the paper is in the library you can run full-text searches and even annotate the papers. They also have plugins to generate bibliographic entries in Word, OpenOffice and for the geeks out there BibTeX as well.

But, the fun does not stop there. We have the on-line side of things remember? From the desktop application you can set up sharing and synchronisation settings for your entire library or for part of it, which might be a great idea for creating your own paper repositories. The site can also provide you with some useful statistics such as how often your papers are downloaded, who reads them and where, trending topics in your area, etc. The website also has a bit of a social network flavour, where you can discover people with similar interests to yours and track colleagues publications. I personally have not used this service as much, and as I put it to some of Mendeley’s people during the Open Office event, is because I do not necessarily go to the website all the time.

In any case, I was very pleased to have had the opportunity to interact with some of the developers, designers and in general the people behind Mendeley, as well as fellow users. They ended up putting up a board where people could write what they liked and disliked about Mendeley, as well as suggestions. In my case, as I mentioned earlier on, I have not used the social tools provided by the website. Victor Henning told me that they have been working on bringing to the desktop version more of these social elements, so that you don’t have to go to the website to actively look for this kind of information. I also had the opportunity to have a preview to the new logo, thanks to Steve Dennis. Carles Pina, a developer at Mendeley, introduced me to some new tools that are available in the latest version of the desktop application, for instance he mentioned that the setting page in the desktop is actually a webpage, which implies that they are already giving some steps towards bringing the web side of things closer to the desktop. I also had a chat with Ian Mulvany, vice president of new product development regarding the future of scientific publishing and the daunting task of dealing with data.

For those interested, Mendeley has recently released an API. I wish I had talked to Rosario Garcia de Zuñiga a bit more about that, but there you go, maybe next time. All in all, Mendeley as a company seems to me to be an enthusiastic and creative enterprise. As a product, it is great tool and one that I wholeheartedly recommend. Give it a go and let me know what you think.

Mendeley 1 Mendeley 2 Mendeley 3

Amphibian skin
It has long been know that the skin of some frogs contain a great number of substances that are capable of killing germs. Making antibiotics with these chemicals is a challenge because they tend to be toxic to human cells too. However, a team in the United Arab Emirates University have come up with a method to modify the chemicals obtained from our amphibian friends and remove these harmful side-effects.

Double-blow to dinosaurs
We probably have all heard about the dinosaurs being wiped out of the face of the Earth 65 million years ago. A theory that explains this massive extinction event tells us that the impact of a giant asteroid on the Earth’s surface killed off the dinosaurs and may other species. In 1991 a crater that backs up the theory was discovered in Chixulub, Yucatan, Mexico. Recently, evidence of a second impact in Ukraine has been discovered. Prof David Jolley of Aberdeen University in the UK has announced the discovery in the journal Geology. The study suggests that the Boltyish crater in Ukraine was not created at the same time as the Chixulub, but several thousand years apart.

Artificial corneas
Light is allowed to enter our eyes through a transparent covering called the cornea. The cornea is also responsible for refracting light onto the retina to allow us to see. Damaged corneas are the second highest cause of blindness in the World and although transplant can reverse this condition, there is a shortage of donors.
Scientists from Canada and Sweden have tackled this problem but developing artificial corneas which have been experimentally transplanted to 10 patients. The patients all recovered their sight and were followed for two years in order to assess their development.

Planetary discovery
The richest system of plants, outside our own Solar system has been discovered by scientists working at the European Southern Observatory in Chile. The system contains five exoplantes orbiting around the star HD 10180 and are said to be similar to Neptune. There is evidence of other candidate planets.

Quantum Tunnel Podcast – What makes laser light so special?

You can download and listen to this episode here.

What makes laser light so special?
When we look at a light source, we can immediately tell whether the source is a laser or not, but what are the main properties that a laser has that distinguish it from any other “normal” source of light.

Oscar Price and Adam Bekele have spent a week at the Photonics Group at Imperial College London working on some theoretical aspects to describe laser behaviour. In this episode, Adam and Oscar will tell us something about properties such as monochromaticity, directionality and coherence, that make of the laser a very special form of light.

Cloned cows
Meteor shower
Gamers help out science: FoldIt
A million dollar question: Is N equal to NP?

I’m a Scientist… interview with Paula Salgado – Quantum Tunnel Podcast

You can download and listed to this episode here.

Have you ever heard about “I’m a scientists, get me out of here?”… Yes you read it correctly, SCIENTIST!

If you follow some pop culture you might be familiar with “I’m a celebrity…”, the drama of reality TV is now available in the classroom thanks to a group of people that adapted the idea and created a truly innovative way to bring science and scientists to the classroom.

In this episode, the Quantum Tunnel Podcast talked to Paula Salgado, a structural biologist at Imperial College London. She took part in the most recent edition of “I’m a scientist…” and she tells us all about the great experience she had.

If you want to find out more about the scheme, please visit the I’m a scientist website.


The proton could be smaller than previously thought
Scientists from the Max Plank Institute for Quantum Optics in Germany have recently revealed that the proton might be smaller than previously thought. According to the results of the experiment reported in the journal Nature, the proton is 4% smaller.

The Earth could be younger than we thought
A new geological study published in the journal Nature Geosciences has provided us with a more precise age for our planet. The international team involved in the study estimated that the Earth is about 70 million years younger than previously thought.

Solar plane flies overnight
Its name is Dolar Impulse HB-SIA and it is a prototype for a solar plane which recently accomplished the challenge of flying about 26 hours using only solar energy. The aircraft has the same length of an Airbus A340, a wing span of 64 metres and a weight of 600 kilos.

Eclipse in Chile y Argentina
People in southern Chile and Argentina, as well some islands in the southern hemisphere were among the few fortunate to have witnessed a total solar eclipse on Sunday, July 11th. A solar eclipse occurs when the Moon passes between the Earth and the Sun, and thus blocking the light from the Sun, projecting a shadow on the Earth.

Plastic that degrades in a matter of seconds
Students form the Instituto Politécnico Nacional in México have invented a plastic made out of maize, which is non toxic, it can be consumed and it degrades in water or soil in a matter of seconds. In general, other plastics are manufactured using toxic materials and it takes years for them to be degrades.

The Bernoulli Family – Quantum Tunnel Podcast

The podcast can be downloaded here.

The Bernoulli Family

The Bernoullis were truly a prolific scientific family, in three generations this remarkable Swiss family produced eight mathematicians – three of them outstanding – who in turn had a swarm of descendants who distinguished themselves in many fields.
Jakob Bernoulli (1654-1705) studied theology at the insistence of his father, but abandoned it as soon as possible for science. He taught himself the calculus and became professor of mathematics at Basel. He wrote on infinite series, studied many special curves, invented polar coordinates and introduced the Bernoulli numbers that appear in the power series expansion of the tangent function. In his book Ars Conjectandi he formulated the basic principle in the theory of probability known as Bernoulli’s theorem: if the probability of a certain event is p, and we run n independent trials out of which we get k successes, then the ratio of the successes to the trials k/n tends to the probability p as the number of trials n tends to infinity.
Jakob’s younger brother Johann Bernoulli also made a false start in his career, by studying medicine but he also became fascinated by calculus and applied it to many problems in geometry, differential equations, and mechanics. In 1695 he was appointed professor of mathematics and physics at Groningen in the Netherlands, and on Jakob’s death he succeeded his brother in the professorship in Basel.

The Bernoulli brothers sometimes worked on the same problems, which was unfortunate in view of their jealous and touchy dispositions. On occasion the friction between them flared up into a bitter and abusive fight, as it did over the brachistochrone problem. In 1696 Johann proposed the problem as a challenge to the mathematicians of Europe. It aroused great interest , and was solved by Newton and Leibnitz as well as by the two Bernoullis. Johann’s solution turned out to be more elegant, while Jakob’s one although rather clumsy and labourious was more general.

Johann’s son was Daniel Bernoulli (1700-1782), who also studied medicine like his father and who also gave way to his talent and became a professor of mathematics at St Petersburg. In 1733 he returned to Basel and was successively professor of botany, anatomy and physics. In his famous book Hydrodynamica he discussed fluid mechanics and gave the earliest treatment of he kinetic theory of gases. He is considered by many to have been the first genuine mathematical physicist.


On June 13th 2020 the Japanese unmanned spacecraft Hayabusa landed over southern Australia. Hayabusa or Falcon in Japanese, was launched on May 2003 to visit the near-Earth asteroid Itokawa. Hayabusa was meant to take a sample from the asteroid and bring it home. However, it seems that the capture mechanism malfunctioned and scientists expect that some material might have found its way inside the probe.
Prehistoric Hair
Palaeontologists from the University of Rennes, France have discovered two mammal hairs encapsulated in a piece of amber 100 million years old. Analysis of the hairs revealed that they have similar structure to fur of modern mammals but the identity of the animal is not known.

Entangled Photon Source
A group of researchers from Toshiba Research Europe and the University of Cambridge produced a new way to generate entangled photons, a key ingredient for quantum computing. The electonicdevice, called an entangled light-emitting diode is produced in a similar way to existing LEDs in combination with a quantum dot.

Radiation Law in San Francisco
San Francisco will become the first city in the United States to require all mobile phone retailers to quote radiation levels in the handsets they sell. Although some studies have suggested that mobile phone radiation is not harmful to people, the bill defines an amount of radio waves that people can safely absorb when using the devices.

Flower power
According to researchers from the University of Chicago, the world is a cooler, wetter place because of flowering plants. The researchers carried out simulations that demonstrate the importance of flowering-plant physiology in climate regulation in the ever-wet forest. Flowering plants are highly efficient at transpiring water from the soil back into their surroundings. This recycling process depends on transpiration and it would have been much slower in the absence of flowering plants.

Quantum Tunnel Podcast – the laser at 50

Listen to the podcast here

The laser at 50
When people mention the year 1960, what are some of the things that come to mind? The Beatles perhaps? Or may be is it the mini-skirt and hippies? But would the laser come to mind? Well, it certainly should.

Fifty years ago, on 16 May 1960, the first laser was demonstrated at Hughes Research Laboratories by Theodore Maiman. It is often said that the laser was a solution in search of a problem and if we were to believe that, fifty years after its demonstration, it is clear that it has found a great number of problems to solve. We obviously use them quite a bit but what is a laser? I think that the 50th birthday of the laser is a great opportunity to answer that question.

Laser stands for Light Amplification by Stimulated Emission of Radiation. Strictly speaking laser devices not really amplify the light, they are better described as oscillators, however you might understand that the acronym LOSER would not be the best to market around.

Some of the key words in the acronym take us back to 1917, when Einstein, following his successes with relativity and the theory of the photon, established the idea of stimulated emission. In order to understand this, one must understand a bit about the light emission and absorption properties of atoms, as well as their electronic structure. Every atom has a nucleus surrounded by electrons, which are bound to the nucleus by electrical attraction between the positively charged protons in the nucleus and the negatively charged electrons around it.

We can think of the atoms as existing in different energy levels depending on the configuration in which the electrons are arranged. We can visualise these energy levels as steps on a ladder in which the steps are not equally spaced. Each higher step on the energy ladder has higher energy than the one below. The first step on this energy ladder is the ground state of the atom and all the next ones are ‘excited energy’ states. An electron can gain some energy when it absorbs a photon and as a result it moves up to a higher excited state. When an electron jumps from an energy level, to a lower energy level, it loses energy and emits a photon. It is possible therefore that an electron makes a spontaneous transition from a higher to a lower energy state and this is what is known as spontaneous emission.

Let us now consider the case in which we force a number of electrons to be in an excited state by bombarding the atoms with photons, this process is known as pumping. As a result of pumping we end up with more electrons in the higher energy states than when we started, this is what we call population inversion.

Now that we have achieved population inversion, an interesting process can take place. If we bombard the atom with a photon with the right energy, the electron can  be stimulated to jump into a lower energy level by emitting a photon identical to the one that was used to start with. This is what is called stimulated emission and a very important feature is that now we have two identical photons at the end of the process. If this is repeated with a bunch of atoms then we have a great number of identical photons. The light output is monochromatic or single wavelength, as all the atoms emit photons of same energy and it’s coherent as the photon emissions occur in unison! That is what we call a laser.

The laser is thus a great application of quantum mechanics and one that has permeated many areas of modern life from telecommunications to medicine and even popular culture: just think of that famous Goldfinger scene where James Bond is  expected to die under the power of a laser or the battles in Star Wars. So next time you use a laser later today, do not forget to wish it a very happy 50th birthday.


Laser Survey uncovers ancient Mayan City of Caracol
Researchers from the University of Central Florida using NASA laser technology have discoverednew ancient structures at the Mayan city of Caracol, Belize. Using a technique called Light Detection and Ranging or LiDAR made the process much easier and faster.

Laser to combat flesh-eating bugs
Strathclyde University has been awarded £65,000 by Microsoft billionaire Bill Gates’ charity to combat a potentially-fatal flesh-eating infection.

The parasitic disease is spread by the bite of infected sand flies and Strathclyde team aims to develop a laser-targeted system to vaccinate against the infection.

Laser technology to strip paint
Researchers at Concurrent Technologies Corp. are proving that a robotic laser system for removing paint and other coatings can do the same job in less time without creating hazardous waste. Teaming with Carnegie Mellon University’s National Robotics Engineering Center, the Richland-based company has shown the laser system’s effectiveness with handheld devices and robotic units taking the paint off of aircraft.

Extreme Light Infrastructure
The Extreme Light Infrastructure (ELI) is a european project which will provide by 2015 a new infrastructure for an ultra-high intensity laser to investigate laser-matter interactions in the unexplored ultra-relativistic regime.

From 13 european countries, more than 50 institutes are involved and cooperating for this project. The project will have 4 facilities located in Hungary, Czech Republic and Romania. The last location will be decided in 2012.

Separate English and Spanish Podcasts…

Hello everyone!

As you may have noticed, I have been playing with podcasting and it has come to my attention that the fact of having episodes in English and Spanish in the same server was a bit confusing.

It certainly did not help the fact that the episodes did not have the same content. In other words, they were not translations of each other. In order to address this, I have split the streams into two different podcasts, one in English and the other one in Spanish. As soon iTunes approves the second podcast I will let you know.

In the mean time, you can find the episodes in English here.

The episodes in Spanish can be found here.


¡Hola a todos!

Como muchos de ustedes sabrán, he estado jugando un poco con esto de los podcasts. Recientemente he notado que ha habido cierta confusión al tener episodios tanto en Inglés como en Español en el mismo servidor.

Ciertamente no ayudo el hecho de que los episodios no tuvieran el mismo contenido, es decir, no son traducciones uno del otro. Para mejorar esta situación he decidido separar los podcasts en dos, uno en Inglés y el otro en Español. Tan pronto como iTunes apruebe el nuevo podcast se los haré saber.

Mientras tanto pueden encontrar el podcast en Inglés aquí.

El podcast en Español está aquí.

Quantum Tunnel Podcast – Episode 2

The podcast can be downloaded here.

Bletcheley Park

Should you be in the UK and want to visit a very special place, I would suggest to visit Bletchley Park where ciphers and codes of countries such as Germany, Japan and Italy were decrypted during the Second World War.

Bletchley Park is located in the town of Bletchley in Buckinghamshire, England and the estate houses a museum where Enigma and Lorenz machines can be seen. The present mansion became the home of Sir Herbert Samuel Leon in 1883 and with its quirky mixture of Tudor, Dutch Baroque and Victorian Gothic styles it truly has become a symbol for the museum itself.

In 1938, with the threat of Hitler’s movements in Europe, the UK government needed a safer location for the Government Code and Cypher School, which at the time was based in London. The position of Bletchley Park at a junction of a major road,  rail and teleprinter connections, while being in the middle of a rural landscape, made it an irresistible option. Being the tenth station acquired by MI6 for its wartime operations, Bletchley Park was given the cover name Station X.

We visited Bletchley Park on a chilly spring Sunday morning and despite the cold it was pleasant to see many visitors around the site. Bletchley Park can easily be reached by train, bus or car. There are frequent services from London Euston or Birmingham New Street. From Milton Keynes there are several buses arriving at Bletchley Bus Station.  The park is open every day except for Christmas Eve, Christmas Day, Boxing Day and New Years Day. Your ticket is an annual pass and secures admission to the site for twelve months, which really is a bargain.

Bletcheley Park is owned by the Bletchley Park Trust, a registered charity. It is very surprising that despite the importance of this place, it receives no public funding and thus the trust relies upon donations to help preserve and revitalise the Park. If you are interested in helping you can indeed pay a visit and maybe even make a donation. For more information visit their website and you can also follow their tweeter feed @bletchelypark.


Novel Material mimics muscles
Scientists of the University of British Columbia have created an artificial material that mimics the tough, stretchy properties of muscle.

Bonobos say no
Researchers form the Max Plank Institute for Evolutionary Anthropology in Leipzig, Germany have reported the observation and filming of bonobos shaking their heads to say “no” in order to prevent unwanted behaviour in another animal

Dengue fever
The search for a dengue fever vaccine has been boosted by recent research that explains why people that recover from the disease have much worse symptoms if they catch it again.

Light harvesting with bacteria
The cellular arrangement of purple bacteria could be adapted for use in solar panels and similar energy conversion devices according to Neil Johnson from the University of Miami.

Transylvanian Dwarf Dinosaur
A horse-sized dinosaur named Magyarosaurous dacus lived in what is now Transylvania, Romania some 75 million to 70 million years ago.


Quantum Tunnel Podcast – E1

This episode is in English.

Pierre de Fermat

Pierre de Fermat who is said to be the greatest mathematician of the seventeenth Century.

In 1629 he invented analytic geometry, but most of the credit went to Descartes, who did publish his own similar ideas in 1637. At this time – 13 years before Newton was born – Fermat discovered a method for drawing tangents to curves and finding maxima and minima, which amounted to the elements of differential calculus.


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His discovery of the principle of least time and its connection with the refraction of light was the first step in the development of a coherent theory of optics. It was however in the theory of numbers that Fermat’s genius shone most brilliantly. Among his discoveries in this field, the most famous are:

  • Fermat’s two square theorem: Every prime number of the form 4n+1 can be written as the sum of two squares in one and only one way.
  • Fermat’s theorem : If p is any prime number and n is any positive integer, then p divides np-n.
  • Fermat’s last theorem: If n>2, then the equation x^n+y^n=z^n cannot be satisfied by any positive integers x, y and z.


Brain training
According to a recent scientific study launched by the BBC, brain training games do not improve overall brain power.

MEMS design in Mexico
On april 19th the National Institute of Astrophysics, Optics and Electronics in Mexico opened up the new Micro Electromechanical System Innovation Laboratory in  Tonanzintla, Puebla, Mexico.

20 years of the Hubble Space Telescope
The Hubble Space Telescope is celebrating its 20th anniversary this week.

Commercial whaling
The International Whaling Commision has proposed allowing whales to be hunted under strict quotas. This measure will bring the World closer to the first legal commercial whaling in nearly 25 years.

Quantum Tunnel Podcast

Very pleased to announce that the Quantum Tunnel Podcast has finally been approved by the iTunes store.

The podcast can be reached using the links provided at the top of this page.

The Quantum Tunnel Podcast is a pet project of mine as a way to communicate science. Emphasis will be given to physics and mathematics, but that might change over time.

The posts will appear in English and in Spanish, but the episodes will not necessarily have the same content.

I will announce here whenever a new episode is posted.

Extra information regarding the subjects discussed in the podcast will be posted in this site.