The Role of Phidippides

Phidippides a professional runner of the Athen's army is the one whose tale was immortalized by the Olympic Marathon.
The Athens were fighting the Persas and they were outnumbered, so the Athenian generals send Phidippides to call for Sparta's help. He run 140 miles and another 140 miles back with the disappointing news that the Sparta agreed to help but said they would not take the field until the moon was full due to religious laws. They fought in disadvantage, but they launched a surprise offensive thrust which at the time appeared suicidal and won the battle. Phidippides was again called upon to run from the battlefield in Marathon to Athens (26 miles away) to carry the news of victory and warning about the approaching Persians ships. He reached Athens in 3 hours delivering the message and died thereafter from exhaustion.
When the modern Olympics began in 1896, the tale of Pheidippides' feat was immortalized: A 24.8-mile race would serve as the final event of the Games, covering the route from Marathon Bridge to the Olympic Stadium in Athens.

Critique of Practical Reason

Zwei Dinge erfüllen das Gemüt mit immer neuer und zunehmender Bewunderung und Ehrfurcht, je öfter und anhaltender sich das Nachdenken damit beschäftigt: Der bestirnte Himmel über mir und das moralische Gesetz in mir.
[Two things fill the mind with ever new and increasing wonder and awe, the more often and the more seriously reflection concentrates upon them: the starry heaven above me and the moral law within me.]
-- Immanuel Kant --

words, thoughts and reality

As words miss when they want to express any thought, thoughts also miss when they want to express any reality.
-- Fernando Pessoa --

night and silence

Il ne voit que la nuit, n'entend que le silence.
[He sees only night, and hears only silence.]
-- Jacques Delille --

Conversation between Achilles and Tortoise

"Tortoise: (...) But it is beautiful anyway, is it not?
Achilles: Oh, yes, there is no doubt of its beauty.
Tortoise: I wonder if its beauty is related to its impossibility. (...)"

Introduction - Gödel, Escher, Bach - Douglas Hofstadter - pq. 29

Juana's Dream

Juana's Dream - Eduardo Galeano

She strolled through the market of dreams. The saleswomen settled various dreams over big clothes on the ground.

There arrives Juana's grandfather, deeply sad as it's a long time he doesn't dream. Juana takes him by the hand and helps him to choose dreams, dreams of marzipan or cotton, wings to fly while sleeping, and they go away, both, so full of dreams that there won't be enough night.

(translated by me)

Justice

A personification of the four cardinal virtues (Justice, Prudence, Fortitude and Temperance) represented usually by the scale, the sword, the blindfold and the law books. She symbolizes the fair and equal administration of the law, without corruption, greed, prejudice, or favor.
This figure dates back to the ancient history. The Ancient Egyptians referred to Ma'at, a woman carrying a sword with an ostrich feather in her hair to symbolize truth and justice. The Ancient Greeks believed in Themis, the goddess of divine justice and law. She held a pair of scales upon which she weighs the claims of disputing parties. She was daughter to Uranus and Gaia and was a partner and advisor to Zeus. Themis was a Titan who believed in and taught obedience to laws and peace. "She became known as a goddess of divine justice." The Roman goddess of justice was called Justitia. She’s represented by the constellation Libra, shaped like a heavenly pair of scales.

mortals

"We are all mortal until the first kiss and the second glass of wine."
-- Eduardo Galeano --

Measure

"Measure what is measurable, and make measurable what is not so."
-- Galileo Galilei --

Fourier

"Fourier is a mathematical poem."
-- Lord kelvin --

Möbius Strip

In the eighteenth century, Euler observed that for polyhedra the number of vertices minus the number of edges plus the number of faces equals two. But this relations does not states for all polyhedra, as for example, for a polyhedron with a hole. The astronomer and mathematician August Ferdinand Möbius (1790-1868) studied the geometrical theory of polyhedra and identified surfaces in terms of flat polygonal joined pieces. The Möbius strip, a continuous surface named after him, has only one side and one edge. Starting in any point in its surface, one can reach every point on the strip without even crossing an edge. The Möbius strip is a mathematical construction that shows an evolution from a two-dimensional space into a three-dimensional one, by merging inner and outer spaces it creates a single continuously curved surface. The Möbius strip is also a non oriented surface. In order to be an oriented surface it should, for any point on the surface, have normal vectors with opposite directions.

The torus has a parametric equation:
1. x = (R + L*Cos(Alpha)) * Cos(Theta)
2. y = (R + L*Cos(Alpha)) * Sin(Theta)
3. z = L*Sin(Alpha)
Alpha and Theta ranging from 0 to 360 degrees

The strip of Möbius has a very similar parametric equation:
1. x = (R + L*Cos(Alpha/2)) * Cos(Alpha)
2. y = (R + L*Cos(Alpha/2)) * Sin(Alpha)
3. z = L*Sin(Alpha/2)
Alpha ranging from 0 to 360 degrees, L ranging from -Lmax to +Lmax

The Möbius strip has provided inspiration both for sculptures and for graphical art. Maurits C. Escher is one of the artists who was especially fond of it and based several of his lithographs on this mathematical object. It is also a recurrent feature in science fiction stories, such as Arthur C. Clarke's The Wall of Darkness. Science fiction stories sometimes suggest that our universe might be some kind of generalised Möbius strip.
In the short story "A Subway Named Moebius", by A.J. Deutsch, the Boston subway authority builds a new line; the system becomes so tangled that it turns into a Möbius strip, and trains start to disappear.
There have been technical applications; giant Möbius strips have been used as conveyor belts that last longer because the entire surface area of the belt gets the same amount of wear, and as continuous-loop recording tapes (to double the playing time).