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Profession and academia

How to write a recommendation letter?

First, to put things in perspective, the identity of the person signing the recommendation letter is more important than the contents of it. However, writing a letter of recommendation can be quite hard, so the person recommending you may ask you to write a draft of the letter yourself.

I have written and received several recommendation letters, and while I am not particularly good in English writing, I think I know how a good recommendation letter should look like.

A good recommendation letter includes: identification, context, recommendation and closing. In one or two pages, it must contain:

  • The name of the recommender and the applicant.

  • A description of the circumstances in which both met.

  • Something positive about the work developed together.

  • Something positive about the recommended person.

  • The phone number or other personal contact information of the recommender.

It may help to think before writing the letter about 1 or 2 characteristics that you want to highlight, and without insisting too much have these characteristics in your mind while writing the letter. It can be characteristics such as responsibility, care for the details, global vision, capacity to work under pressure, technical competence, intelligence, knowledge, leadership, enthusiasm, commitment, etc. These 1-2 characteristics must really represent how the applicant is (honesty is the best policy) and should be skills that are required by the position for which the application is being written.

Identification

A recommendation letter can be addressed to the chair of the selection or search committee (being careful about writing correctly the name and the position) or to the whole committee.

Typically call for applications include a contact address, in that case, that information should be used. The next paragraph should contain the identification of the person issuing the recommendation, showing the credentials of the recommender clearly but without pomposity:

My name is XXX, currently XXX (charge) at XXX (department/organization). I am writing in support of the application of XXX ...

I am XXX, currently XXX at XXX. This letter is to recommend XXX for ...

The best recommendation letters are usually written by people who has worked or collaborated in a close relationship with the organization to which the applicant is applying, and/or by people who are well known in their field..

Context

The next paragraphs indicate which was the work that the recommender and the applicant developed together:

I worked with XXX in the year YYYY, developing the project "XXX" (project name or short description) in the context of XXX (context) for XXX (company/organization).

Now it is the right moment to write about something positive about the work done together, here you have a lot of freedom, as you are speaking about a project, not about a specific person. You must be truthful and specific. You can include several ideas:

The resulting XXX (software/building/project/book/etc.) allowed that 400 people benefit directly from ... (immediate impact).

The project was finished 1 month before the projected deadline / on time / without problems ...

The resulting XXX is still in use ....

The project received the XXX award from XXX because of XXX....

It is better to pick a high-visibility project, or a project that is well known by the selection committee, or that is similar to some activity that the applicant will have to develop if hired for the position.

Recommendation

Here the letter speaks directly about the applicant in positive terms, without exaggerating and being specific. It is ideal that the characteristics being highlighted be related to the position to which the applicant is applying.

Mr./Dr. XXX was important in the team because XXX

His/her characteristics allowed to achieve XXX ...

Working with XXX was particularly good because XXX (something specific!) ...

In more than one ocasion, XXX (if it was something small, but that was consistent)

Here it is important to mix the skills of the applicant for the job with his/her skills to work in a team, because it is very important, when hiring someone new, to believe that you will be able to work with this new person easily. The recommendation should include something like:

It was good to work with XXX because of XXX ...

XXX fitted very well in our team because of XXX ...

The team still maintains a friendly relationship with XXX ...

Closing

First the most obvious, state the recommendation:

Because of all this, I recommend XXX for XXX ...

In my opinion, XXX will perform very well as XXX in XXX ...

XXX meets / meets and exceeds the qualifications and experience required for XXX

Finally it is good to include the phone number of the recommender. This gives more credibility and a more personal tone to the recommendation letter:

If you need further details, you can call me to XXXX ...

If you need me to elaborate on some aspect of this recommendation letter, do not hesitate to call me to XXX ...

Good luck!


Contratando gente: Lago Wobegon

Tuve la gran suerte de ir a una charla de Michael Mitzenmacher sobre estrategias para contratar personal en una organización.

A modo preliminar, existe un problema más simple que se conoce como "el problema de la secretaria". Tienes un puesto de trabajo y entrevistas candidatos, y al final de cada entrevista debes decidir si contratas o no a la persona. Si no la contratas, el entrevistado se irá a otra empresa. El asunto es que si contratas muy pronto, puedes no entrevistar a un buen candidato, y si contratas muy tarde, puedes perderte de contratar a un buen candidato.

El problema general es tomar una decisión sin conocer el futuro. El caso particular del problema de la secretaria puede ser analizado matemáticamente, y la solución óptima es la siguiente.

La hipótesis es que despues de cada entrevista el entrevistador sabe qué tan bueno es el candidato con exactitud, lo que puede no ser exactamente cierto pero es una aproximación.

Si tienes N candidatos, debes entrevistar a los primeros 1/e = 0.38 N candidatos, sin contratar a ninguno, y luego elegir al primer candidato que sea mejor que los que haz visto hasta ahora. Por ejemplo, si tienes que entrevistar a 100 personas, entrevistas a las primeras 38, sin contratar a ninguna independientemente de qué tan bueno sea el candidato, y luego continúas entrevistando y contratas cuando encuentras a alguien que es mejor que todos los que haz visto antes. El análisis está en Wikipedia: Secretary Problem.

Contratando y Creciendo

Ahora, el problema de contratación que analizó Mitzenmacher en su charla es distinto. Supongamos que tienes una organización que quiere contratar gente. Tiene dos objetivos en mente: uno es crecer, y el otro es tener gente de buen nivel. Si es demasiado estricta al momento de contratar, no crecerá, pero si es demasiado relajada con el estándar, el nivel tenderá a decrecer. La organización está permanentemente entrevistando candidatos, y debe al final de cada entrevista decidir si hacer una oferta o no. ¿Cómo debe contratar?.

Una primera solución es contratar a alguien si es mejor que el empleado más malo que tenga en la empresa. Esto permite contratar rápido pero la calidad promedio disminuye con el tiempo.

Otra solución es contratar a alguien si es mejor que el mejor empleado que tenga la empresa. Esto aumenta la calidad promedio pero es muy lento para crecer, de hecho la cantidad de entrevistas necesarias para cada contratación aumenta exponencialmente, dado que el umbral crece con cada entrevista y la probabilidad de encontrar alguien aún mejor se hace más baja.

Las estrategias de tipo Lake Wobegon consisten en contratar a el entrevistado si es mejor que el promedio de la gente que ya está contratada en la organización. Hay sutilezas dependiendo si usamos promedio o mediana, pero básicamente estas estrategias logran un buen compromiso entre crecer rápido y contratar gente buena.

¿Por qué Lago Wobegon?

A modo de anécdota, explicó también de donde proviene el nombre. El Lago Wobegon es un lugar ficticio donde:

... todos las mujeres son fuertes,
todos los hombres se ven bien,
y todos los niños están por sobre el promedio ...

Y se refiere a una observación hecha por sicólogos, que es que tendemos a sobreestimar nuestras propias habilidades. Por ejemplo, el 80% de los conductores considera que conduce mucho mejor que el promedio, y el 25% de los estudiantes de secundaria se considera parte de el mejor 1% de los alumnos [*].

Fuente foto: SectionZ.

La historia de Lenna

En 1972, la modelo sueca Lena Söderberg, residente en ese entonces en la ciudad de Chicago, USA, fue elegida para las páginas centrales de la revista Playboy de Noviembre. La revista Playboy decidió que era mejor escribir su nombre como Lenna, puesto que de esa forma sería pronunciado adecuadamente por los lectores de habla inglesa de la revista. El por qué la pronunciación del nombre de la modelo era importante para el editor de la revista escapa a mi comprensión. En todo caso, ese número de la revista vendió más de 7 millones de copias, convirtiéndose lejos en el número más vendido de la revista.

En Julio de 1973, en la University of Southern California (USC), Alexander Sawshuck, un profesor del departamento de ingeniería eléctrica, junto a uno de sus estudiantes de postgrado, buscaban una imagen para probar unos algoritmos de compresión. Querían una foto de la cara de una persona, y la querían sobre papel brillante y a color. Lo mejor que pudieron encontrar en el laboratorio fue una revista Playboy (!), y realizaron un scan de la imágen de la modelo de las páginas centrales a la resolución de 512x512 pixeles, pero sólo del rostro y hombro de la modelo. La imagen de prueba resultante está ligeramente distorsionada, y los colores son ligeramente incorrectos, producto del proceso de escaneo. Con un scanner más moderno se obtiene la imagen de la derecha, a página completa, digitalizada por Chuck Rosenberg.

Despues de la publicación del paper, otros investigadores solicitaron el archivo con la imágen digitalizada para comparar sus algoritmos y programas sobre la misma base, de forma de poder visualmente comparar el resultado de cada operación. Por ejemplo, la siguiente es la imagen a de Lenna a distintas resoluciones:


Desde la publicación de la primera foto de Lenna, prácticamente todos los artículos científicos sobre compresión de imagenes y muchos de los relacionados con algoritmos incluyen en sus páginas finales una prueba de las ideas sobre esta imagen. David Munson, quien fuera editor de la IEEE Transactions on Image Processing, explica el motivo: "La imagen de Lenna contiene una buena mezcla de detalle, regiones planas, sombras y texturas que hacen un buen trabajo para probar varios algoritmos de procesamiento de imagenes. ¡Es una buena imagen de prueba!. Segundo, la imagen de Lenna es la foto de una mujer atractiva. No es sorprendente que la comunidad (predominantemente masculina) de investigadores en procesamiento de imagenes hayan gravitado hacia una imagen que encuentran atractiva."

A principios de los '90 la imagen se distribuyó a través de varios servidores en Internet como parte de un set de fotos para pruebas en procesamiento de imagenes. Otro ejemplo: esta es la imagen usando distintos valores de compresión JPEG:


Por supuesto, los autores del paper original no escribieron a la revista Playboy para pedirles su autorización, pero aunque los editores de la revista sí se preocupaban de la pronunciación del nombre de sus modelos extranjeras, al parecer no tenían ningún interés en el procesamiento de imagenes. PERO en Julio de 1991 la revista Optical Engineering incluyó en su portada la foto. En ese momento recibieron una carta de los abogados de Playboy, quienes tras una explicación sobre la historia de la imagen, accedieron a conceder permiso para su uso para fines educacionales y científicos. La imágen de Lenna de 512x512 pixeles es prácticamente un estándar de la industria, aunque algunos critican su uso, no porque sea un rostro femenino sino porque proviene de una revista (Playboy) que representa una relación entre hombre y mujer que refleja una sociedad más machista que la actual. En todo caso hay muchas otras imagenes de prueba disponibles, pero Lenna sigue siendo lejos la foto que se usa con más frecuencia.

La importancia de la imagen de Lenna ha trascendido incluso las fronteras de la computación. Woody Allen en su película Sleeper, representa a una persona que es congelada en un tanque criogénico hasta el año 2173. Al despertar, le piden que identifique una serie de artefactos del siglo XX. Uno de ellos es la edición de Noviembre de 1972 de la revista Playboy, y en la película se muestra claramente a Lenna en las páginas centrales.

Para la conferencia anual de la Society for Imaging Science and Technology (IS&T) de 1997, el presidente de esta sociedad invitó a Lenna a la conferencia, donde firmó autógrafos y conversó con los presentes, como parte de un encuentro sobre la historia de la computación y el procesamiento de imágenes.


A la fecha de la conferencia se encontraba trabajando en Suecia, y su trabajo consistía, casualmente, en ayudar a discapacitados a trabajar con computadores. No tenía idea de que era así tan famosa y uno de sus comentarios fue "deben estar tan cansados de mí ... ¡mirando la misma foto por todos estos años!.

Más información: www.lenna.org

Relativity, Uncertainty, Incompleteness and Undecidability

These principles were studied by, respectively, Albert Einstein, Werner Heisenberg, Kurt Gödel and Alan Turing. This is a very simple explanation without the technical details, but which tries to show at least the general idea behind each principle.

Note: there is a spanish version, and also a Thai version.

Relativity


This section explains the general principle of relativity of motion, which is older than Einstein's theory of relativity, and tries to state at the end just one of Einstein's contributions. Relativity says that there is no privileged, "objective" viewpoint for certain observations. Let's imagine that two ships are in the sea in a very dark night, and that each of them only has a positioning light at the tip of the mast. The night is so dark that neither points at the horizon nor the waves in the water can be seen to check on which direction each ship is moving. Under these conditions, any of the captains could say that his ship is the one that is "still", while the other ship is moving, or vice versa.

Similarly, let's ask: at what speed does the sun move? We need a reference view point to measure speed. We can measure the speed of the sun related to a distant object, like another star, the center of the Milky Way, the center of our star cluster, but there is nothing we could call "the absolute speed of the sun". Surely, we could measure the speed of the sun relative to the space surrounding it, which is not exactly empty but has some particles, but those particles are also moving. Any attempt to determine an absolute speed is useless, as there is always an alternative view point that is equally valid and that produces a speed that is completely different. Speed is relative.

Now, if things move relative to each other, then obviously their positions at a given time are also measured relative to each other. The universe, as we know it, has no "center" with special characteristics, and even if it had it, clearly it would be completely arbitrary to say that something is "up", "down", "to the left" or "to the right". In space, these things have no meaning. Position and direction are relative. Any measurement of them requires a frame of reference.

So far, so good, but things get a bit more complicated. Let's think for a moment, how do we measure time? We measure it with changes of position and speed: the time a certain thing takes to fall to the ground, the time a ray of light takes to move between two points, etc. A direct consequence of the fact that position and speed are relative, is that time is also relative. There is no "now" that is simultaneous to the whole universe. There is no big clock ticking for the entire universe at the same time. The following experiment has been repeatedly made: if we synchronize two very precise clocks, and then we move them, for instance, by taking one of them in a plane and making a trip around the world, while the other remains in the ground, when they are together again we can see that one of the clocks has measured a longer time than the other. If we let more time pass and we increase the speed, we obtain the typical image of an astronaut on a space trip that takes a few years for him, but that returns to earth and notices that hundreds of years have passed. While relativity of motion itself is a very old concept, Albert Einstein first showed that, as the velocity of light is absolute, time is relative.

Do not confuse this with subjectivity: in a movie I once heard a dialog like "for Einstein, everything was relative, for instance, half an hour with a person you love or half an hour waiting for the metro are not the same". This is not relativity, it is called subjectivity and it's a different story. Relativity says that different view points can produce different observations. This does not mean there is no objective truth, but rather that there are no privileged view points.

Uncertainty


Baseball could be played with a smaller ball, the size of a ping-pong ball, or with a larger ball, the size of a volley ball; it would look weird but the game would still be playable. The rules of the game at our scale, are the same for a small, medium or large ball. We could even figure out how to play a table version of a mini-baseball with small balls of 1 millimeter of diameter. The dynamics of the game would be the same: the ball is thrown, the ball describes a curve, the ball is hit.

However, on the scale of the very small, if we continue reducing the size of the ball until it is the size of an atom or the size of an electron, the scenario is radically changed. At atomic scale, all sort of things that would look very weird at our scale happen. An example of how different things are, when we see them at atomic scale, is the following: if we have in our living room a lamp with a dimmer to make the light brighter or darker, we can fine-tune how much light there is in the room. If the lamp has a certain luminosity, we have the impression that we can always continously lower a bit the luminosity without turning off the lamp completely. This is just an illusion, because if we look closely and take a very precise source of light, then we could see that there is a point in which if we lower a little more the light, we start having a light with "bursts": sometimes on, sometimes off; there is a limit under which there are no more continuity. This happens because light has a minimal unit, indivisible: it is called a "photon". All subatomic particles have an indivisible unit called a "quantum", and a "photon" is a quantum of light. Because of this phenomenon, the theory that tries to explain how everything works at a very small scale is called quantum mechanics.

Now, let's get back to the baseball game. Now we no longer throw a rubber and leather ball but a very small particle, let's say an electron. This electron goes on its way to a miniaturized baseball bat with which we want to hit it. We need to know where is the electron, but to see it, we need light. The only problem is that light is made of photons, and the electron is so small that a photon hitting it will move it from its trajectory. We aim a miniature lamp to the electron to see it and we receive the photons back, but once we have received the photons we have altered the trajectory of the electron. We could try to use just a single photon but that would be enough to move the electron. We can try to make this photon less capable of moving the electron, by having less momentum, but the problem is that for doing that we should have to generate light with longer waves and that would not allow us to see the electron precisely.

Werner Heisenberg showed that if we built a machine to tell us with high precision were an electron is, this machine could not also tell us the speed of the electron. If we want to measure its speed without altering it we can use a different light but then we wouldn't know where it is. At atomic scale, no instrument can tell us at the same time exactly where a particle is and exactly at what speed it is moving. Clearly, we could try to stop the electron with a wall and in that way we would know exactly where the electron is and we would know that it is still in relation to the wall, but that has no predictive value and doesn't help us in our baseball game. When measuring, we create a distortion and we are always bound by a trade-off in the measurement of certain quantities.

Heisenberg's uncertainty principle goes deeper than this, as the particle itself has an indeterminate position or velocity, so the principle not just related to the measurements we can do and even "ideal" measurements will show indeterminacy. Several characteristics of subatomic particles are just a probability of making certain observations, they are not absolute quantities but rather probabilities.

Incompleteness


In our normal life, there are many situations that have only two states. If you have to take a train at 8 o'clock in the morning, then there are two possibilities: either you catch the train, or you miss it; if you switch a light, it will either go on or off; the accused of a trial is declared guilty or not guilty, and so on. This type of logic of true or false, which is called boolean logic, is central in mathematics. One plus one equals two? True. Two plus two equals five? False. True or false - there are no other options.

There are many natural phenomena that have intermediate states, but boolean logic only cares about phenomena with two possibilities: true or false, black or white, zero or one, on or off, etc. This is not a weakness of it, but rather a definition of its scope, as for instance, botany works with plants or geology with rocks, boolean logic works with anything that has two states.

Propositional logic, which also deals with truth values, is an old discipline whose fundamental tool is deduction or logical deduction. Let A=Mary was murdered with a knife, B=John was at Mary's place at 23:00, C=Mary died at 23:01, D=John knew Mary, E=a hair from John was found in Mary's hands, F=a knife was found with Mary's blood and John's fingerprint. A and B and C and D and E and F could imply: John is guilty. If we take G=John is left-handed and the stabs are right-handed, then A and B and C and D and E and F and G could imply: John is not guilty. Several premises are composed to reach a conclusion.

This deductive, "Sherlock Holmes"-type logic, provides the rules to compose certain facts and reach certain conclusions. For instance, if for something to be true it is necessary that other two things are true, and one of the latter is false, then the former has to be false. If to get snow we need rain and low temperatures, and the weather is warm, then there will not be snow. It's logic. There are several rules in propositional logic that build a deductive system.

There are systems based in propositional logic that include more expressive power, and the classical system used for analyzing natural numbers is an example that includes deductions plus other mathematical tools. If this system is complete, then anything that is true is provable. Similarly, anything false is provable false. Kurt Gödel got the intuition that this system was not complete, and devoted several years to try to find one thing, a single thing that was inside the mathematics but outside the reach of logic. Gödel searched, inside the rigidness of the laws of number theory in mathematics, a valid theorem that could not neither be proven to be true nor to be false insite the system.

Let's consider this expression: "this sentence is false" (which is not well defined, but is just an example). If "this sentence is false" is false, then it is twice false, hence true ... and if "this sentence is false" is true, then we only need to read it to see it's false. In number theory, Gödel found a way of writing a statement p that is similar to "p cannot be proved", using numbers and mathematical formulas, something that is possible to handle using number theory, but that can neither be proved nor disproved within this system. To do it, he had to express many ideas as numbers and weave step by step a very long proof, but he was finally able to prove that the system is incomplete, this is, that there are true things that we could never prove that are true, and false things that we could never prove that are false within the system.

Gödel's incompleteness states that for any formal theory in which basic arithmetical facts are provable, it is possible to construct an arithmetical statement which, if the theory is consistent, is true but not provable or refutable in the theory. This is not only related to apparent paradoxes involving self-references, but goes deeper and means that certain important theorems cannot be proved.

Undecidability


Alan Turing is considered as one of the fathers of computer science. He designed a model of how a computer works that is fundamental to computer science and showed that, for instance, a pocket calculator or a sophisticated video game console work in the same way: they read some data, check a table of rules and a memory and write some data back.

In a calculator, what is read is a key stroke, the table of rules are mathematical operations, memory is the partial result and what is written back is the final result. In a video game console what is read is the controller or joystick status, the rule table are the rules of the game, the memory is the game status and what is written back are the drawings on the screen. Memory, even when it can be very large, is never infinite and the behavior of the machine is completely determined by rules that are always obeyed, so this model is known as a "finite deterministic Turing machine".

Turing wrote many programs, and he worked in deciphering codes for the Allies during the Second World War. He quickly become aware that some programs "hang" and stayed working forever without going anywhere. This happened often when there was something strange given as input. For instance, it is possible to write a program to decipher codes made of numbers that represent the coordinates where an attack will take place, but if this program is accidentally fed with letters instead of numbers, then the program fails, as it is not prepared to this type of input. Even after solving the trivial problem of accepting only numbers, a new problem appears and it is that the coordinates could be inconsistent, for instance, they could represent a place that is farther to the north than the north pole, and so on. Every new problem solved can create new problems in the program.

If we want to write a "perfect" program, that never hangs, then one way is to test it to try all different inputs, but this is often impractical as there are too many combinations; besides this, there is a deeper problem and that's that even if a long time has passed, we can never know for certain if the program is still doing something useful or if it has "hung". Turing thought that this problem could be solved with the help of another program, and he tried to write a "superprogram" that would be able of examining another program and check if it was correct, in the sense that it would terminate at some point, instead of running forever. After several attempts, he started to suspect that it might be impossible to write such a superprogram, and finally he was able to prove that in general it is not possible to check if a program in general will halt. Certainly, trivial examples of programs that can be checked can be writen, such as a program with a single "halt" instruction at the beginning, but the idea is that a machine for verifying a program in general cannot be built.

Turing's halting problem is one of the problems that fall in to the category of undecidable problems. It says that it is not possible to write a program to receive a program (unknown beforehand) and check if it is correctly written, in the sense that it will never hang. This creates an important limit to the verification programs, as all the attempts of building actual computers, usable in practice and different from Turing machines have been proved to be equivalent in power and limitations to the basic Turing machine. It is impossible to build a "superprogram" for checking all programs, and modern programming techniques try to minimize the probability of this occurring, as well as ensuring a smooth recovery and avoiding data loss, but for non-trivial programs, there are usually no guarantees of correctness.

A "Blind Spot"?

These fundamental principles should not be taken as limitations to science, and they do not exclude the existence of an objective reality. They are rather limitations to some operations, such as making a measurement or working with formal logic, that have to be taken into account to understand natural phenomena.

There is a certain relationship between these principles. Both relativity and uncertainty arise from physics and are related to observations, while incompleteness and undecidability arise from mathematics and are related to the limitations of formalisms. Uncertainty and undecidability govern our capacity of making predictions, while relativity and incompleteness are related to the fact that references are necessary, but prevent us from doing certain operations. I would not like to try to take these relationships too far, instead, I would like to state another analogy.

The retinal nerves of a mammal's eye converge at a single spot, the optic nerve, which transmits impulses to the brain. This design has a disadvantage and that is that right in the point where the nerves meet, there is no sensitivity to light. This produces a "blind spot", a zone of the visual field where we cannot see. At the same time, it is curious that we usually cannot see that we cannot see. First, the blind spot is rather small; second, the brain compensates the image so we don't see a black disc floating in the air, and third, we have two eyes and their blind spots do not fall in the same visual area. We could use the fact that we know about the blind spot in the design of certain things, such as in the design of the instruments board of an aircraft, but besides that in daily life and for 99.9% of the population the existence of a blind spot has little practical implications.

Something similar happens with the laws we have discussed here. They certainly restrict observations and formalisms, but they do not mean we cannot make observations or formalizations. Even with relativity, if we are caught driving at 80 miles per hour in a 65 miles per hour zone, we will have to pay, even if relative to us the car was not moving, because we have agreed in a certain frame of reference. Even with uncertainty we can still play baseball as the uncertainty in the position of an object the size of a base ball is far smaller than what we can see with our naked eyes. Even when deductive systems are incomplete, incompleteness is not a problem to most mathematicians, and every year very complex and difficult proofs are shown without problems. Even with undecidability, high quality programs control high availability systems and most of the errors do not arise from arcane halting conditions, but rather from simple and avoidable programming mistakes.

The rules of the scientific game include relativity, uncertainty, incompleteness and undecidability. From the point of view of science, understanding these laws can lead us to new discoveries on how the universe works. Through this particular "blind spot", we can see.

Acknowledgments

Pepe Flores, computing engineer, entrepreneur, and also my professor, boss, partner and friend, in that chronological order, was the person from whom I first heard that these are the four most important laws in science. Ingmar Weber and several Kuro5hin readers also provided valuable feedback and comments.

Errata

These are corrections from the article published in Kuro5hin that were suggested after the article left the editing queue.

Relativity

  • I have removed references to earth vs sun (thanks Morosoph)
  • I insisted more in that I explain a principle that is older than Einstein's theory of relativity (thanks bml)
  • I clarified at the end that this does not exclude the possibility of an objective reality (thanks benna)

Uncertainty

  • I emphasized more that Heisenberg's uncertainty goes further (thanks benna, bml, Morosoph and others)
  • I clarified the example about the dimmer because light gets intermitent, is not switched off completely (thanks Eustace Cranch)

Incompleteness

  • I added that there are several types of logic (thanks several readers)
  • I clarified that Gödel's incompleteness is not just about the self-referencing paradox (thanks several readers)
  • I corrected the final sentence to change "logically" by "provable" (thanks bml)
  • I corrected the difference between boolean logic, propositional logic and the classical formal system for dealing with natural numbers (thanks city lights)
  • Corrected 'botanics' to 'botany' (thanks kevhito)

Undecidability

  • I emphasized more that some specific programs can be checked (thanks bml and Morosoph)

Thanks all the readers for their suggestions.

¿Cómo escribir una carta de recomendación?

Ver también: Profesión y Academia en ChaTo.cl.

Para ponerlo en su justa medida, lo que más importa no es qué dice una carta de recomendación, sino más bien quién la firma; sin embargo, redactarla puede ser muy difícil, por eso no es raro que quien te recomiende te pida un borrador de la carta.

Una buena carta de recomendación tiene cuatro partes: identificación, contexto, recomendación y cierre. En una o dos páginas, debe contener:

  • El nombre de quien recomienda y del postulante.

  • Una descripción de dónde se conocieron.

  • Algo positivo sobre el trabajo que desarrollaron juntos.

  • Algo positivo sobre la persona recomendada.

  • El teléfono o información de contacto de quién recomienda.

Puede ayudar el pensar antes de escribir la carta en 1 o 2 características que son las que se quiere destacar, y sin ser demasiado insistente, tenerlas en mente durante toda la carta, por ejemplo, responsabilidad, cuidado por los detalles, visión global, capacidad para rendir bien bajo presión, competencias técnicas, inteligencia, conocimientos, habilidad para dirigir y liderazgo, entusiasmo y compromiso, etc. Estas dos características debe tenerlas el postulante (ser honesto es la mejor política) y deberían ser cosas que el cargo al cuál se postula requiera.


Contratando Gente | Venderse o Hundirse | La Paradoja de la Elección

Identificación

Una carta de recomendación se puede dirigir al presidente del comité de selección o de búsqueda (teniendo mucho cuidado de escribir bien el nombre y el cargo) o al comité completo:

Señores
Comité/Comisión de XXX
Departamento de XXX
XXX

O bien:

Señor
XXX
Director/Presidente de Comité/Comisión de XXX
Departamento de XXX
XXX

La forma más segura es simplemente tomar la dirección a la que hay que enviar los antecedentes, y usar esa como dirección de contacto. El párrafo siguiente, debe contener la identificación de quien hace la recomendación, cuidando de dejar en claro las credenciales de quien recomienda, pero sin sonar pedante:

Mi nombre es XXX, en la actualidad me desempeño como XXX (cargo) en XXX (departamento, organización). Le escribo para apoyar la postulación de XXX ...

Soy XXX, actualmente XXX en XXX. El motivo de la presente es apoyar la postulación de XX ...

Las mejores recomendaciones provienen de gente que haya trabajado o colaborado en una relación estrecha con la organización a la que se está postulando, o que sean conocidos en el área de trabajo en que se desempeñan.

Contexto

Los siguientes párrafos indican cuál fue el trabajo por el cual se conoce al recomendado:

Trabajé junto a XXX en el año 2000, desarrollando el proyecto de "XXX" (nombre del proyecto o descripción corta) en el marco de XXX (contexto), para la empresa XXX (destinatarios).

Ahora es el momento de elaborar sobre algo positivo sobre el trabajo desarrollado, aquí se pueden usar muchos adjetivos con cierta seguridad porque se está hablando de un trabajo, no de una persona. Lo importante es ser veraz y sobre todo específico, evitar generalidades. Se pueden combinar ideas:

El proyecto resultante permitió que 400 personas se beneficiaran de ... (hablar del impacto inmediato).

El trabajo realizado fue entregado 1 mes antes de lo proyectado ... (hablar de las condiciones del trabajo).

Lo construído es usado actualmente en XXX para XXX ... (hablar del impacto a futuro).

El programa recibió un premio de XXX por XXX ... (hablar de los reconocimientos).

Ojalá sea algún proyecto con cierta visibilidad que haya sido conocido por quién recibe la carta, o alguna actividad similar al que deberá desarrollar el postulante en la organización que lo recibirá.

Recomendación

Acá se habla directamente del postulante en términos positivos, sin exagerar la nota y siendo específicos. Lo ideal es que las características que se destacan sean comprobables, estén en consonancia con el trabajo realizado y con las características del puesto al que se postula.

El Sr./Sra./Srta./Ing./Dr./etc. XXX se destacó en el equipo por ... XXX

Estas características permitieron lograr XXX ...

Trabajar con XXX fue muy positivo porque XXX

En más de una ocasión, XXX (si es algo interesante y se repitió más de una vez)

Hay que matizar estas características personales con las características del postulante para trabajar en equipo, que es muy importante cuando se contrata a alguien nuevo, porque un temor importante de quien abre la postulación puede ser que el postulante sea muy bueno pero no se integre bien con el resto. Por ello la recomendación debería incluir algo de:

Fue un agrado trabajar con XXX porque XXX ...

XXX se integró muy bien a nuestro equipo porque XXX ...

El equipo de trabajo mantiene aún una relación cordial con XXX ...

Cierre

Lo primero del cierre es lo más obvio, una llamada a la acción, directamente recomendando al postulante:

Por lo anteriormente expuesto, recomiendo sin reservas a XXX para XXX

Por lo anterior, es mi opinión que XXX reune las características necesarias para XXX

En mi opinión y según lo expuesto, XXX reúne/reúne y excede las calificaciones y experiencia requeridas para XXX

Finalmente, la carta indica el teléfono de quién recomienda. Esto le da más credibilidad y un tono más personal a la carta:

Si necesita más detalles sobre XXX, puede llamarme al teléfono XXX ...

Quedo a su disposición, para más detalles, puede llamarme al teléfono XXX ...

¡Mucha suerte!


Ver también


Ver también: Profesión y Academia en ChaTo.cl.

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