Math's Everywhere

Latin Polytopes

Latin squares are well studied combinatorial objects. In this paper the concept is generalized and new designs are proposed (Latin triangles, Latin tetrahedra, etc.) that feature similar properties.

The paper starts with a classic definition of Latin squares followed by one based on concepts of modern design theory. A Latin square appears then as a combinatorial design whose points are geometric. Its rows and columns are now symmetric lines that intersect in specific ways, while its “labelled lines” intersect the former also in a particular manner.

The generalization that follows proceeds by 1. broadening the inherent symmetry of the Latin square 2. considering more general configurations of points and 3. admitting symmetric and labelled lines that intersect more freely. The resulting concept is the Latin board. Finally, this object is particularized to define Latin polytopes, Latin polygons and Latin polyhedra.

A Latin tetrahedron. Fold the picture along the black lines to create a tetrahedron.
Now each band between lines of the same color contains all numbers from 1 to 16.

The Sudoku Ripeto & Custom Sudoku Puzzles

Sudoku Ripeto and Custom Sudoku are the first Sudoku variants with repeated numbers and letters  respectively.

Presentation at the 13th Gathering 4 Gardner Conference in Atlanta, 2018

Sudoku Ripeto

Custom Sudoku

 

Más allá del bien y del mal

Una clara mañana de invierno
Que podría ser de verano
Un tiempo cualquiera, eterno
Un lugar que no figura en el plano

Hombres y seres que sin nombres nacen
Sin nombres ni ninguna otra etiqueta
Hombres que extralimitándose hacen
Del nombrar muy importante meta:

Bien, mal, regular, grande, pequeño...
Festival de la clasificación
Feria de las mil formas derivadas

Promesa de porvenir halagüeño

Si no fuera por la aprehensión
De haber perdido con ello la nada

Death

It's a curious fact: it is not easy for me to ponder over this topic without noticing the bearing of theories proposed by open religions or by disguised forms of religion like atheism.

However, once this influence has been detected and overcome, the answer to questions like: What is death? Why we die? What happens after death? appears to be surprisingly simple: I don’t know.

At our last gathering we mentioned our inner desire to draw conclusions about everything, to “reason our way through” in order to produce a “solution-in-a-phrase” to the issue being raised. This impulse, like many others, has its origin in a more primordial one: survival, although expressed this time through cognitive abilities that appeared in the course of evolution.

Nevertheless, while recognising its usefulness in many cases, we see that it might not be universal. In the same way that the need to eat is at the root of eating disorders such as bulimia or anorexia, the need to reach conclusions can be a major obstacle to certain issues, today’s for example. I remember the time when we discussed that life could be a joke, a solid hypothesis when one notices the stark contrast between the strong desire to live and the truth of death. It involved also some sort of conclusion though.

There is thus ground to make a couple of personal experiments. The first one has both the idea of death and “I don’t know” as a basis, and it involves a conscious and disciplined avoidance to draw conclusions other than incontrovertible ones: “I will die some day”, “The people I see every day will die someday”, “In the course of recorded history, 100,000 million humans have lost their lives”, “Life is the leading cause of death in people” and the likes.

What happens to a mind that feeds on facts about death instead of on speculation? To a mind kept silent when confronted to non-facts?

Even if there is no response in the short term, this first experiment brings about something surprising: a truly appreciation of the sensation of being alive. Once past the anguish caused by the instinct of survival, the presence of death and its mystery make life more intense. Knowing that I am going to die makes every day special and unique. By recognising the certainty of death, every event, just by pure contrast, acquires an unheard of character. Respect for life is thus naturally enhanced. For this alone is worth the try.

The second experiment is the generation of respect towards death. This may need some effort given the accumulated apprehension towards the issue. One can get help from the idea that death has always been there, that it has the quality of being immutable amidst universal change, that it partakes of the beauty inherent to natural processes.

Respect for both life and death curbs the polarisation between the two, and helps seeing more clearly what is happening here. Then the answers to the questions arrive, not as conclusions but as deep intuitions.

Lo Familiar

Con qué gran sutileza me engañas
Haciéndome ver viejo lo que es nuevo
"como lo nombro conocerlo debo"
Me digo yo sin sospechar tus mañas

Voy así viendo sólo lo que pienso
Sin pensar cómo ver sin pensamiento
Yo y sólo yo de esta forma me miento
Y más que su olor quiero el término "incienso"

Si por un breve momento pudiera
Rasgar del verbo el espeso velo
Para asomarme al mundo sin nombres

Vería que nosotros los hombres
Si por la familiaridad no fuera
Estaríamos cerquita del cielo

Reseña musical de Antonio Navarrete

Reseña del guitarrista y compositor Antonio Navarrete: Las canciones de Miguel Palomo tienen detalles muy originales. You are the one viene de la conexión del artista con la cultura asiática, en la cual se sumergió de pleno durante unos años. Amour à nous es un tema acústico en francés con un ritardando peculiar, un pequeño homenaje al país que lo acogió en su época de estudiante. Hay dos etapas claramente diferenciadas en su música. En la más actual la tecnología le ha permitido producir canciones tan sorprendentes como Rocket boy (mi favorita de esta etapa), aunque tambien Darky, Going Home y Catalina se han beneficiado de las posibilidades del home studio. De su etapa en db Producción Musical, con los medios técnicos y los músicos que allí colaboraban, nos dejó maravillas como Ella te quiere, Vocación -canción sencilla pero con fuerte significado-, o Capitale della moda. La música brasileña, tan elaborada pero tan fácil de escuchar, se convirtió para él en su momento en referente imprescindible, de ahí vienen los arreglos de esta evocación a la Garota de Ipanema que es Rebajas de verano. Todas merecen la pena.