A Mathematical Theory of Meetings

Aquí tenemos una modela matemática para una reunión por Hans Freudenthal:


A meeting is an ordered set \begin{aligned} consisting of a bounded part \(M\) of Euclidean space; a finite set \(P\), that of the participants; two elements \(c\) and \(s\) of \(P\) called chairman and secretary; a finite set \(C_1\), called the chairs; a finite set \(C_2\), called the cups of coffee; an element \(b\), called bell; an injection \(i_1\) of \(P\) into \(C_1\); a mapping \(i_2\) of \(C_2\) into \(P\); an ordered set \(S\), the speeches; a mapping \(i_3\) of \(S\) into \(P\) with the property that c belongs to the image of \(i_3\) \end{aligned} If \(i_3\) is a surjection, it is usual to say that everybody has had the floor.
Encontré lo anterior mientras estaba leyendo el libro "The Mathematical Experience" y pensaba que está bastante  interesante compartir.

La Pistola y El Corazón de Los Lobos

In English:

The Gun and The Heart
by Los Lobos

I don't know how to tell you
I don't know how to explain
That here there's no remedy
For what I feel
For what I feel

The moon tells me one thing
The stars tell me another
And the light of day sings to me
This sad song
This sad song

The kisses that you gave me, my love
Are what is killing me
Already my tears are drying
With my gun and my heart
And here I always spend my life with
my gun and my heart

I don't know how to love you
I don't know how to hold you
Why won't [it] leave me
Pain that I have
The pain that I have

This night so dark with your
Shadows so calm
And the wind continues singing to me
This humble song
This humble song

The kisses that you gave me, my love
Are what is killing me
Already my tears are drying
With my gun and my heart
And here I always spend my life with
my gun and my heart


En Español:

La Pistola y El Corazón
de Los Lobos

No se como decirte
No se como explicarte
Que aqui no hay remedio
De lo que siento yo
De lo que siento yo

La luna me dice una cosa
Las estrellas me dicen otra
Y la luz del dia me canta
Esta triste cancion
Esta triste cancion

Los besos que me diste mi amor
Son los que me estan matando
Ya las lagrimas me estan secando
Con mi pistola y mi corazon
Y aqui siempre paso la vida con
La pistola y el corazon

No se como amarte
No se como abrazarte
Porque no se me deja
Dolor que tengo yo
El dolor que tengo yo

Esta noche tan oscura con sus
Sombras tan tranquilos
Y el viento me sige cantando
Este humilde cancion
Este humilde cancion

Los besos que me diste mi amor
Son los que me estan matando
Ya las lagrimas me estan secando
Con mi pistola y mi corazon
Y aqui siempre paso la vida con
La pistola y el corazon

El Otro Yo de Mario Benedetti

The Other Me
by Mario Benedetti

He was a normal boy: his pants were baggy, he read comics, ate noisily, picked his nose, snored during naps, he was called Armando Normal in all except for one thing: he had Other Me.

The Other Me had poetry in his eyes, fell in love with actresses, lied cautiously, loved evenings.  The boy worried about his Other Me greatly and felt uncomfortable around his friends.  For his part the Other Me was melancholy, and because of this, Armando couldn’t be as ordinary as he wanted.

One evening Armando came home from work tired, slipped off his shoes, moved his toes slowly and turned on the radio.  Mozart was on the radio, but the boy slept.  When the Other Me woke he cried inconsolably.  At first, the boy didn’t know what to do, but soon he composed himself and thoroughly reprimanded the Other Me.  The Other Me said nothing, but the next morning he had committed suicide.

At first the death of the Other Me was a shock for poor Armando, but right away he thought that now he could be completely ordinary.  This thought comforted him.

There had been only five days of mourning, when he took to the street to show off his new and complete ordinariness.  From far off he saw his friends approaching.  This filled him with joy and immediately he broke into laughter.

But when they passed close to him, they didn’t notice his presence.  To make things worse, the boy could hear what they said: “Poor Armando.  And to think that he seemed so strong and healthy”.

The boy didn’t have any more desire to continue laughing and, at the same time, he felt a lump in his throat that seemed slightly nostalgic.  But he couldn’t feel truly sad, because all of his melancholy had died with the Other Me.

[[ TODO: add in mp3 of John speaking the above in English ]]


En Español

El Otro Yo
de Mario Benedetti

Se trataba de un muchacho corriente: en los pantalones se le formaban rodilleras, leía historietas, hacía ruido cuando comía, se metía los dedos a la naríz, roncaba en la siesta, se llamaba Armando Corriente en todo menos en una cosa: tenía Otro Yo.

El Otro Yo usaba cierta poesía en la mirada, se enamoraba de las actrices, mentía cautelosamente , se emocionaba en los atardeceres. Al muchacho le preocupaba mucho su Otro Yo y le hacía sentirse imcómodo frente a sus amigos. Por otra parte el Otro Yo era melancólico, y debido a ello, Armando no podía ser tan vulgar como era su deseo.

Una tarde Armando llegó cansado del trabajo, se quitó los zapatos, movió lentamente los dedos de los pies y encendió la radio. En la radio estaba Mozart, pero el muchacho se durmió. Cuando despertó el Otro Yo lloraba con desconsuelo. En el primer momento, el muchacho no supo que hacer, pero después se rehizo e insultó concienzudamente al Otro Yo. Este no dijo nada, pero a la mañama siguiente se habia suicidado.

Al principio la muerte del Otro Yo fue un rudo golpe para el pobre Armando, pero enseguida pensó que ahora sí podría ser enteramente vulgar. Ese pensamiento lo reconfortó.

Sólo llevaba cinco días de luto, cuando salió a la calle con el propósito de lucir su nueva y completa vulgaridad. Desde lejos vio que se acercaban sus amigos. Eso le lleno de felicidad e inmediatamente estalló en risotadas.

Sin embargo, cuando pasaron junto a él, ellos no notaron su presencia. Para peor de males, el muchacho alcanzó a escuchar que comentaban: «Pobre Armando. Y pensar que parecía tan fuerte y saludable».

El muchacho no tuvo más remedio que dejar de reír y, al mismo tiempo, sintió a la altura del esternón un ahogo que se parecía bastante a la nostalgia. Pero no pudo sentir auténtica melancolía, porque toda la melancolía se la había llevado el Otro Yo.

[[ TODO: add in mp3 of John speaking the above in Spanish ]]

Soneto XXX de Garcilaso de la Vega

En Español:

Soneto XXX
de Garcilaso de la Vega

Sospechas, que en mi triste fantasía
puestas, hacéis la guerra a mi sentido,
volviendo y revolviendo el afligido
pecho, con dura mano noche y día;

ya se acabó la resistencia mía
y la fuerza del alma; ya rendido
vencer de vos me dejo, arrepentido
de haberos contrastado en tal porfía.

Llevadme a aquel lugar tan espantable,
que, por no ver mi muerte allí esculpida,
cerrados hasta aquí tuve los ojos.

Las armas pongo ya, que concedida
no es tan larga defensa al miserable;
colgad en vuestro carro mis despojos.


In English:

Sonnet XXX
by Garcilaso de la Vega

Suspicions, that in my sad fantasy
put, making war with my sanity,
coming and stirring my stricken
chest, with a hard hand night and day;

already my resistance is gone
and the strength of my soul; already spent
to win you left me, regretted
having checked each insistence

take me somewhere so frightening,
that, not to see my death sculpted there,
I close my eyes until I have. (?)

I place weapons, given that
it isn’t too long a defense of the miserable;
hang my remains in your car. (?)

¿Vale la pena estudiar? (2) Datos básicos

Is going to university worth it? (2) Basic facts
by Samuel Bentolila

Apparently, many youths in this country think that “studying is a scam”, according to an article in El Confidencial. True or not, if young people believe it, we would be facing a serious problem. So, today I address once again last week’s question answered by Florentino Felgueroso, Luis Garicano and Sergi Jimenéz, bringing some basic additional facts about the economic viability of studying in Spain.

A simple form of calculating the (financial) return of studying is to see how salary changes when the level of education is increased , defined as follows:

Expected income = [Probability of employment * Salary] + 
[Probability of unemployment * Compensation in unemployment]

(Compensation in unemployment would be unemployment benefits, if they’re available.)

As changing the level of study affects not only income but also future income, the decision to continue studying or not will depend on this variable: the difference between (a) the present value of the sum of expected discounted future income flows for someone with a higher level of education (level 1) and (b) this value for someone with a lower level of education (level 0).

The idea is to add present and future income, discounting them – that is, weighting them less – for what happens in the future instead of today for distinct educational levels, and find the difference between these sums. It is also necessary to subtract the cost of attaining a level 1 education. If the difference is positive the person will decide to continue studying and otherwise not.

Given the importance of future income flows, I’m going to focus on workers older than 20 (for those between 16 and 19 years the revelations that follow are even more significant).

We will approximate the probability of being unemployed by the unemployment rate. This varies greatly with the level of education. Chart 1 shows the average unemployment rates by education level for the population of 20-24 years and of 30-44 years in the period 2005-2010 in Spain.

Chart 1 – Rate of unemployment by level of education and age, 2005-2010 (%)


We see that the rate of unemployment is much greater for the youngest (on average, 22% versus 11%). Later, workers from 20 to 24 years old that finish mandatory secondary education (ESO, 1st stage) have an unemployment rate 5.6 percentage points less than those that only achieved primary school education and for those from 30 to 44 years old, 5.1 points less. The failure to complete secondary school in the ESO is apparently very costly.

In the third place, compared with having finished ESO, having upper-level secondary education (Bachelor’s and FP, 2nd stage) reduces the rate of unemployment by almost 4 percentage points and having higher education (pre-doctoral) by 5 points. In the 30 to 44 year age group the respective advantages are of 3.4 and 7.2 points. The economic incentive to study past ESO is not, in principle, insignificant.

Additionally, the increase in the employment rate for having studied more is also significant, although less so than in other countries. Graph A7.1, taken from Education Review. OECD Indicators 2010, shows that the income derived from secondary education of the 2nd stage is 19% greater than that of a lesser educational level, compared to 22% on average in OECD countries. Still, for workers from 25 to 34 years old, the difference is only 7% in Spain, compared to 18% in OECD countries.

Chart A7.1 (from Table A7.1)
Relative incomes from labor (2008 or indicated reference year)
By level of training of the population from 25 to 64 years (second stage of Secondary Education = 100)


The difference is greatest for tertiary education or better. With respect to post-mandatory secondary education, performance is 38% compared to 53% in OECD countries. Only in Sweden and Norway is the difference less (probably because of the wage compression resulting from collective bargaining, which is very centralized). Some of this lower level of income can be ascribed to the fact that, as Florention, Luis and Sergei noted in their post, many workers can only get jobs they are overqualified for. (Here are the facts.)

We could now calculate changes in expected incomes derived from an increase in the level of education. But, although it is interesting, this measure is limited. For one thing, these data do not take into account other characteristics like gender, experience, cohort, etc. and are merely measures that don’t capture causal effects: as Antonio Cabrales has been explaining, for example here, evaluating the causal effects of education is not trivial.

In addition, the well-being of an individual does not only depend on salary, but also other working conditions, like the length and composition of a work day. Only the probability of employment is not of little importance either, but also the stability of employment. As we have noted often on this blog (for example, here and here), the temporary employment rate is very high, especially among youths (data from 2005-2010): 58% of those from 20 to 24 years old compared to 42% of the workers from 30 to 39% and 22% of those from 40 to 49 years old.

More concretely, the distribution of educational level by type of work, for example in 2009:3, is as follows (thanks to J. Ignacio García-Pérez who gave me the figures):



We see that temporary workers have a level of education much lower than the permanent workers. This could be due to the fact that having a level of study much higher reduces the probability that the worker is offered a temporary contract or other reasons.

In total, the facts suggest that reaching a higher educational level helps to obtain better salaries, realizes a lower unemployment rate, and provides more stable employment. Without doubt, these favorable effects don’t seem to induce sufficient demand for education (except in crises). In the next entries, various collaborators will present results from analysis of the decision to pursue further study and some implications for public policy.

Medicare I

Medicare I
by Juan Rubio-Ramírez on 1 October 2010

One of the most important consequences of the recent crisis is that markets and rating agencies have shown themselves to be very sensitive to public deficits of western economies.  Spanish debt has been downgraded from its highest rating and the same thing has happened with many economies in southern europe.

For this reason, in a bid to calm the markets, political leaders have announced and launched adjustment plans and tighter budgets everywhere (see, for example, the latest out of France).

As I've pointed out more than once on this blog, western economies' fiscal problems are more structural than crisis-related.  The aging population, on one hand, and the increase in public health spending per person, on the other, pose long-term fiscal problems related to pensions and health -- much more important than those related to the current economic situation.

At Nada es Gratis we're going to dedicate Saturdays to the subject of pensions, so I would like to dedicate this post (and those following) to healthcare spending.  In particular, I'd like to address healthcare spending in the United States.  This federal program pays healthcare costs for older citizens.  In 1970 medicare spending was less than one percent of GDP.  In 2009 it was 3.5%.  A significant increase.

As we can see in the following chart, and as I mentioned above, the majority of the increase in healthcare spending (as a percentage of GDP) on medicare in the United States is due to the per-person spending increase rather than the increase in older people (the chart was created by the CBO for their report on the deficit and long-term debt from December 2005).



As Jesús has said before, this is normal for two reasons.  First, new technologies are being developed that are much more effective but at a much greater cost.  Second, as our income increases we want to consume more health in relative terms.  As has also been mentioned on this blog, medicare spending will become even greater in terms of GDP as the "baby boomer" generation ages.

The problem is that, for reasons Jesús has outlined many times, medicare poses a spending/financing problem for the american government.  In the coming week we'll talk about how this will be solved.  We hold that the proposed cuts on the spending side don't seem to be sufficient to square the national accounts and that tax increases are inevitable if there are no radical changes to the proposed solution.

Control Remoto de Alejandro Romualdo

Remote Control
by Alejandro Romualdo

In English:

Remote Control

Anonymous, social and belligerent,
my silent body rises.
Eat with me.  Smoke.  Whistle.  Sing.
Fall in love.  Suffer and live.

Always correct everything I write.
Always feel my pain.  And make it worse.
Quick, run away: I'll get there first.
Brutal, deny myself all pleasure.

From animal nature, breathe.
From animal nature, I look
at the poor: quiet, human.

Ah, my kind, angelic body.
Paid in metal and covered in nonmetal (?)
its right to live in chains.


En Español:

Control Remoto

Anónimo, social y combativo,
mi tácito antropoide se levanta.
Come conmigo.  Fuma.  Silba.  Canta.
Enamoro con él.  Padezco y vivo.

Siempre corrije todo lo que escribo.
Siempre intuye el dolor.  Y se agiganta.
Veloz, fuga de mí: se me adelanta.
Brutal, me empuja todo lo lascivo.

Desde su límite animal, suspira.
Desde su límite animal, me mira
el pobre: taciturno, humanizado.

¡Ah, mi civil, angélico antropoide,
paga en metal y cobra en metaloide
su derecho a vivir encarcelado!