In order to like mathematics…

… you need a good math teacher!

I was talking to my daughter the other day and she told me how her impression about mathematics improved after she entered the school here in Texas, compared with the school in Brazil. I asked her the reason and she told me that here in the USA the teacher has time to dedicate to the particular needs of the student, while in Brazil the teaching is automatic, rapid and unpersonalized, the teacher explains the subject, to the student remains to understand the subject or simply to skip understanding and focusing in the next subject.

Then I remembered what happened with myself at the school. I was blessed (or cursed) with an analytic mind. An example is the image I chose to illustrate this article. This is the so called Euler’s identity. The first time I saw it (probably at the Physics course) I could not understand why Euler bothered to express it.

If fact its proof is trivial (in my opinion), we have the identity


where x is read in radians. By simple inspection one observes that the value of this quantity at 180° is real and corresponds to +1, then, for me, the identity was equivalent to stating the 1 – 1 = 0, and if you state this to any person, he or she will say it is obvious. It took me about twenty years to appreciate what is considered an expression of the beauty of mathematics.

At the fundamental school, you will probably find it strange, I initially didn’t like mathematics. The reason, now I recognize, was because I was bored. Teaching mathematics in the fundamental school is a repetition process. Fact is that most persons don’t learn so easily the mechanistic ways of mathematics and this is achieved by solving a lot of identical exercises until this mechanistic process enters the kid’s brain by brute force.

This changed some time in the seventh grade by two fortuitous events.

First, during the winter pause (in Brazil our school winter pause corresponds roughly to the month of July), for some miracle, I decided to take a look at the math textbook to see in advance what would be the subject when the lecture resumed after the pause. I remember it was the solution to quadratic roots (the quadratic formula). I remember it contained a simple deduction (in one page) of the formula (it is the same found in the Wikipedia article), and I read that and understood. I found that marvelous, to understand why a formula was the way it was, and not only to learn the formula. Of course, I went happy to the first mathematics lecture after the pause, to show what I did learn by myself, only for the teacher (an Asian lady, I don’t recall her name) to say she would skip that part because it was unnecessary.

The next fortuitous event was a test for some school Olympiad we had in that year in Sao Paulo. As I told, I was bored with mathematics, as a consequence I rarely did my homework, and, of course, this resulted in bad grades at the tests, in particular I never got a 10 (maximum note) in any math tests ever. I was considered back then an “expert” in Geography. Then this test came, and we had to do it in all subjects, since this would be considered for the school grades. To my surprise, and to the surprise of anybody else in the classroom (and the teachers included) I scored a 10 in that test.

The two events taught me I could like mathematics. I didn’t recognize back then that the reason I disliked math before was because I had very bad teachers, or at least, access to very bad teaching methods. Today I realize this is the reason why so many peoples hate Mathematics. We should have more empathy with our children.


How to write (bad) science fiction

You may find strange that I decided to write an article about science fiction in a Science & Technology Blog. Fact is that, according to my experience, all scientists enjoy science fiction. Granted, not everyone of them like Star Wars or Start Trek, but authors like Phillip K. Dick, Ray Bradbury and Stanislaw Lem are widely appreciated. And, why not, we scientists are also humane, we also need entertainment once in a while.

One of the reasons why science fiction appeals to me is that it allows me to dream. The kind of book allows us to answer the question: What if?

Naturally a good science fiction book (or film)  establishes a set of presumptions about future things, and then the author allow him(her)self to probe what would happen if those presumptions are valid.

Of course, the reality must stretch a bit, if you want to allow interstellar travel, you must somehow overcome the barrier of the speed of light, you must assume there is something like a hyperdrive, or a warp drive, or simply something called FTL (Faster-than-light) engine.

You have to allow people to manipulate the huge amounts of energy required to operate these machines, you may postulate something called dilithium crystals which can safely combine matter and anti-matter (and magically not “fry” everyone around, since a simple event of positron-electron recombination results in two gamma photons with the minimal energy of 0.511 MeV).

I tried already to write some limited science fiction and I know that in order to get your story going forward you have to take some liberties with physics. Even the movie Interstellar, highly appraised for the correct depiction of the relativistic time dilation effects due to the gravity of a black hole overcome the obvious fact that any accretion disk  would produce so much X-ray and gamma radiation which would make the existence of that planet with exposed water unlikely (and forget about the nonsense of entering, and principally, leaving a black hole).

Even though you have to assume some unknown physics to allow your plot to move forward, you have to remain as close as possible to the known physics (and chemistry, and biology) to write good science fiction.

Science fiction allows also some “foretelling”. Authors like Jules Verne or H. G. Wells correctly predicted many of the things we have in our modern world. You don’t need to go so back in time, however, to find science fiction influences you our modern world. It is obvious that our smartphones are a direct adaptation of the communicators in Star Trek (more precisely, they are a crossing between the Tricorder and the communicator). Sometimes science fiction provides us with an idea, which becomes relevant in the future. What to say about the famous prediction by Arthur C. Clarke that in the future all long-range calls would cost the same as a local telephone call? What is the internet, if not the possibility to call someone on the other side of the globe at the price of a local call?

Of course, the predictions do not need to be exact. Since a long time Internet is not related with the telephone line, and any submarine commander would surely laugh at the description of the luxurious interior of the Nautilus (the fiction one). Our smartphones cannot provide data to proceed with a medical diagnosis (yet) and, for sure, they will not work in another planet.

The problem is that in the search for entertainment, some authors end up violating the known laws of physics (and chemistry and biology), therefore producing bad science fiction.

Recently I watched a movie called Cloverfield Paradox. It was advertised as related with the excellent movie Cloverfield, this one really good (and low budget). In particular, the advertisement promised to give some answers about the monster in the first film.

The setting was really interesting, but the film already fails in the premises. We learn right in the beginning of the movie that Earth is facing an energy crisis (obviously caused by the end of our fossil fuel reserves). Anyone with the slightest knowledge of the modern world would ask: “What happened with the solar and wind technologies?”. The worst is that a single line of text in the script could solve this inconsistency, one of the the characters would simply “remind” that these alternative forms of energy are totally dedicated to keeping industries and hospitals working, or that their growth (especially in the case of solar energy) depends of rare raw materials. In my case, the funniest part was watching the characters sitting in a long line before a gas station to get fuel for their cars. It is funny because everyone would ask, why are they using their cars, really? If fuel is so rare, why bother driving around? Are there no mass transport vehicles in the future?

Then we learn that the female protagonist has to go to a space station to operate a particle accelerator which would solve the energy crisis, providing infinite energy. She is referred as vital for the project, and yet, due to careless use of a technology she caused the death of her two kids (this is the vital scientist needed for the project?). We learn that this particle accelerator can only be operated in orbit. OK.

The space stations has even some realistic architecture. A set of rotating rings linked by a tower-like structure. You see that and think, OK, they will provide gravity by inertial forces. The problem is that the characters act like there was real gravity going on. A rotating ring, even if it has a diameter of hundreds of meters, would produce measurable Coriolis forces depending on the height. It would be funny seeing the characters playing with this, for example, throwing a ball to the air and seeing it making a curve, but nobody thought about this (it would be very easy to fake this effect). Another problem related to this is that in no place inside this stations there is absence of gravity (and the characters must migrate between the rings, evidently, using the tower structure, which is not spinning). Would it to be too much to ask for the actors to fake absence of gravity once and a while?

Then they operate (after more than 600 days in space) the so called particle accelerator. Before, obviously, we learn what is the connection with Cloverfield. A conspiracy theorist suggests that operating that particle accelerator could open portals to another dimension allowing monsters to invade Earth. Really? Why? How does the guy knows this? (obviously, he read the script for Cloverfield).

The operation obviously goes awkward, and suddenly, Earth is no longer where it was. Whaaat? Even thought the connection with other dimensions and other universes, how could you justify the disappearance of an entire planet? With the progress of the story we discover that this happened because a fancy gyroscope went missing. Really, one gyroscope? A space station like that would have lots of gyroscopes (not to mention that the rotating rings are some sort of gyroscope themselves).

There are other inconsistencies like these, in one scene the rotating rings are in attrition with the structure and they produce sparks. I think nobody told them that oxygen is necessary to produce sparks.

When I was at the Physics course, in the 1980’s, the most interesting book at that time was the first Portuguese translation of A brief history of time, by Stephen Hawking. Not because of the content, but because the translation was so full of errors, that the the fun was to try to understand what the English version told, based on the faulty translation. At that time one of my professors told that the publisher contacted a physicist in Rio de Janeiro to do this translation, and the guy asked for some payment to do this, the publisher was not satisfied with this, and, obviously, hired an English-literature student to do this (obviously, but much less money). My feeling with Cloverfield Paradox is this, they decided not to hire the physics professor to be consultant. A pity is that the general plot is actually good (if you disregard this bullshit of parallel universes), but these inconsistencies destroy the film (or, maybe you want to watch the film to spot these inconsistencies, as my colleagues in Brazil did with the book).

To end, just about the last scene of the film. The main female protagonist is finally returning to Earth, fleeing a crumbling and disintegrating space station, besides her only one colleague, hurt, survived (the others died with horrible deaths, I will not talk about the complete violation of the second law of thermodynamics in the middle of the film), and the mission control manages to call her husband on Earth to tell the good news. The reaction of the guy is to say, “tell them not to come”! Really? What does he expect them to do? It is better to die in the cold of the space or burned in the uncontrolled reentry of the wreck of the space station? And finally, the monster appears.






Michael Marder’s Fracking Physics

Yesterday I was able to attend the seminar given by Michael Marder (UT Austin) about “hydrofracture as a materials problem” at the Materials Science and Engineering Department of the Texas A&M University. I didn’t know Prof. Marder, but learned he is author of a popular textbook on condensed matter physics.

It was a pleasure hearing him, he showed complete control of the audience, in the majority composed of graduate students. He started by telling how he got involved with the theme, and clearly stating what were the science difficulties involved in the research. These were the necessity to bridge wide gaps in scale (processes taking place in the nanometer scale for structures hundred of kilometers wide) and the highly interdisciplinary character of the subject.

Hydrofracture is the official name of the the activity popularly called “fracking”: the extraction of hydrocarbon gases impregnated in shale rock (in Portuguese, shale in known as “Xisto betuminoso”). This extraction is difficult, because the medium is impermeable. Another source of difficulty is the distribution of the rock, which is very wide in area, but very thin in thickness.

The solution to this problem is the application of high pressure fluids to opened wells, which fracture the rock, releasing the entrapped gas. The talk was centered in the modeling of this fracture process and gas extraction and the achievements were really impressive.

The interesting aspect of his talk, however, were the economic driven parts of his talk. First he showed that shale gas played a prominent role in adverting the worst effects of the 2008 economic crisis in the USA, by decreasing the energy costs. Second, the own results show that the activity will be short -lived. The estimate is that the shale gas extraction has the potential to deliver energy for 30 year, but not much more, therefore Prof. Marder defends, as it is the opinion of the present author too, that all energy sources must be researched and developed.




The physical chemistry of brewing a decent coffee

I am brazilian, therefore I am addicted to coffee. OK, not all brazilians drink coffee, as not all US Americans play baseball. This does not change the fact that I feel miserable if I have to go out my home in the morning without drinking a large mug of the dark brew (which I drink without additions, including sugar).

I also travel a lot, occasionaly going to places in which coffee is decisively horrible. Recently a former student went through the same problem, and this reminded me of the period in which I lived in Germany.

Not that German coffee is that bad, at least there are places in the world in which coffee is even worse. The problem with German coffee is that if you drink it using a glass, you can see through! For me, this was something like an heresy.

Being myself a scientist, I decided to make experiments. Soon I discovered that the amount of powder didn’t matter. Neither did the roasting level. I tried powders of various provenances, but this didn’t help either. 

Then, one day, I was buying coffee powder at a specialized shop called Tschibo (I had already partially solved my problem, noticing that freshly ground coffee produced better results) when the vendor asked me wether I wanted my powder fein  gemahlen (finely ground) or grob gemahlen (coarsely ground). I asked her what was the difference and she explained to me that the finely ground particles were designed for expresso machines and that if I used it with normal filter, I would get particles going through.

Imediately I realized the solution to my problem, I asked my powder finely ground and confirmed the next day that I was able to brew Brazilian  quality coffee in Germany.

My explanation is the following: in Brazil the griding machines are old, the filters are bad, so many fine particles pass, giving the excellent taste we are used to. In Germany the machines are brand new, the filters are perfect, and hence, only liquid passes. Naturally, having solid particles in suspension the Brazilian coffee becomes opaque.

Of course, according to the scientific method, I would need to further test my hypothesis. I would need to perform a granulometric analysis of the different powders, or verify the solid residues left from evaporation. As my good friend, Eng. Alberto Imoto thaught me, however, in the case of performance-driven research you are entitled to stop the action once you get the desired effect.

Benjamin Thompson (a.k.a Count Rumford), Julius Robert Meyer

The title reminds of two early heroes of what we know today as thermodynamics. More precisely, the first law of thermodynamics. First I must acknowledge that I only heard about them due to the excellent formation in physics I had at the Instituto de Física da Universidade de Sao Paulo.

Benjamin Thompson was a curious fellow. Born in the United States (better said, in the Massachussets colony), he fought in the American Independence War (at the side of the British), made career in the British Empire (was raised to knighthood) and later went to work for the King of Bavaria (from where his noble title stems, apparently). In other words, he was a sort of a mercenary.

220px-Benjamin_Thompson Benjamin Thompson, 1753 – 1814 (source: wikipedia)

His famous discovery was made while drilling holes in bronze to produce cannons. Everyone who already did this (drill holes in any metal) will agree that the metal piece becomes quite hot. At that time people believed heat was a kind of fluid (a liquid called caloricum) which could be shared by different bodies by flowing.

Thomson devised an experiment to disprove this notion. He placed the drill and the cannon inside water and showed that the water could be brought to boil just by the drilling activity. More than this, he showed that the amount of available heat was practically infinite, depending only on the work done by the drilling activity, and showed that no transformation happened in the material, by comparing the specific heat of the removed material (metal chips) with that of the bronze piece.

He correctly stated, based on this experiment, that mechanical work could be transformed into heat by friction, and it seems that he had the notion that their sum must be conserved, but this was not stated in his work.

Robert Meyer, on the other hand, was a German. He is described in the modern texts as a physician (meaning medic), but one has to remind that at this time all of them were polymaths, so these distinctions we have today made no sense.

GW163H219Robert Meyer, 1814 – 1878 (source: Hmolpedia)

His key experiment was an observation. Working as ship physician in the coast of Java, he noticed that the venous blood of the sailors was less dark than the color he was used to in Germany. This blood was mostly red and only slightly darker than the arterial blood. He correctly assumed that this was a consequence of the different average temperatures in both places, arguing that the body heat is generated by combustion and that more combustion is needed in the cold Germany compared with the hot Java. He also observed (or better, was told by the sailors), that the sea water heated after a storm, and that this was due to agitation (mechanical work). Later he did experiments and came out with a value for the R constant (the mechanical equivalent to heat), and correctly stated the conservation of the sum of heat and mechanical work (the first law). He also published a small brochure in 1851 correctly stating that mechanical work and  heat could be transformed into each other.

He tried to publish his findings in the Ann. Chem. Phys.  in 1841 (two years before Joule) but was ignored. With help of friends he managed to publish a work in the Annals of Chemistry and Pharmacy in 1842. It seems that the problem was that he used philosophical ideas (principally by Immanuel Kant) to justify his physics, bordering metaphysics. His role in thermodynamics was acknowledged only after Helmholtz lectured about him to a group of physicist.

Both characters were complicated persons. Thompson is remembered for his correct interpretation of the drilling experiment, but he also defended very weird theories which were later proven wrong. Meyer was an adept of philosophical thought and obviously designed and interpreted his experiments in the light of these theories (i.e. by preconception), what is today considered frontally wrong in the scientific method. Meyer was also one of Boltzmann’s antagonists, equating his ideas with alchemy (an intended insult, of course).

The important is to realize, however, that both characters relied on observation of physical phenomena to reach their conclusions, something which was very alive in the birth years of thermodynamics, but has been forgotten since then. We should recovery this tradition, experimenting more.

I always remind my students not to judge past characters using present day’s moral compass. Thompson and Meyer are products of their respective times and what is contradictory today made perfect sense to them at that time. Their role in the development of thermodynamics, in particular, of the first law, cannot and should not be overlooked.


On Thompson:

On Meyer:



How to Lead in a Losing Cause – Lessons from the Real Robert E. Lee

Nice article of Cory Galbraith, showing we should not judge past characters using our present moral standards.

Cory Galbraith


He lost the Civil War but is respected to this day, could control his emotions like nobody else, and kept a pet chicken for companionship.

Robert Edward Lee, the commander of the Confederate army in the U.S. Civil War is said to have never fired a single shot, but was responsible for the deaths of hundreds of thousands of people.

This elusive and misunderstood figure of history, despite being flawed, displayed both humility and a deep appreciation for the unexpected benefits of losing.

Today, these qualities possessed by Lee have much to teach us about leading ourselves, and others, in a world turned upside down.

“We must expect reverses, even defeats. They are sent to teach us wisdom and prudence.”

Lee won the vast majority of his battles, losing ground towards the end of the war. But he understood that with loss comes learning, greater determination, and the ability to…

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How to get rid of pseudoscience?

This post is the English translation of my post “Como se livrar da pseudociência”, published in Portuguese here.

Some months ago I read a post which started like this “Studies show that any post which starts with studies show will be taken seriously by the reader”. This is, of course, a joke (or better, a metajoke), but it is, in some sense also true.

We are flooded with information from multiple sources. Only in Facebook there is a multitude of “so said” science channels. Due to the anarchist nature of internet, anyone can create one of these pages or even a science blog (no pun intended). Worse than that, everyone competes for attention.

Dealing with science one should expect honesty and knowledge of the subject by the ones who create these channels. Unfortunately this is not always the case. In the nonsense search for audience these channels share questionable posts, either by ignorance (in the sense of lack of knowledge) or by ill intention. This is one of the sources of pseudoscience.

There is, however, another source of pseudoscience: ideology driven channels. Fundamentalist religious groups and adepts of conspiracy theories use the internet to gather followers. Ideology and science never worked well together, the ability to question the results is an integral part of the scientific method and this kind of fanatic is unable to proceed with this questioning, so what they generate is always pseudoscience.

But what about the reader? How can he (or she) protect from (or even recognize) pseudoscience? After all, not everybody interested in science has the capability to understand the details and particularities of the scientific method. Also, many of my colleagues refuse to educate the general population and, particularly n Brazil, the poorness of science teaching in the fundamental and intermediate education levels create the proper ground for spreading pseudoscience.

Here are some clues to recognize pseudoscience:

  1. Be suspicious of bombastic contents. Once I read a post which claimed the disk of planet Mars would appear in the sky with the same size as the Moon, this is obviously ridiculously impossible.
  2. Due scientific results are usually published in trustworthy sources: scientific magazines and pages maintained by important universities and research institutes. Published articles usually go through the peer reviewing, a process in which other scientists (usually anonymous) evaluate the work before publishing (but attention, really revolutionary results are usually published in repositories first, therefore before peer reviewing, this does not mean they are less trustworthy). It is always important to read the original source (if possible), the authors of the articles not always understand what they read.
  3. Trust in the science you learned. It is true that really revolutionary results may challenge the view we have from reality at any moment, but Newton’s third law, mass and energy conservation, and the basic chemical reactions in biological organisms will not cease to exist from one day to the other.
  4. True science admits the contradictory, so, get suspicious of any post which claims to defend the absolute truth, without questioning the own result.

I hope this helps.