Las matemáticas y la didáctica

Bachelard ends his Poétique de l'espace with a chapter called "La phénoménologie du rond." It concludes this inquiry into the image of the house and the inhabited space, because it in essence is the ultimate inhabited space, the space of the concentrated habitat. Bachelard begins this chapter by citing writers and artists who claim that "life is round," that "intimate truth" that dwells within all beings. This roundness is a new way of living inside. He cites three main characteristics of le rond. Images of roundness "nous aident à nous rassembler sur nous-même, à nous donner à nous-même une premiere constitution, à affirmer notre être intimement, par le dedans."³⁷⁴ Roundness is also "undivided" there is no separation from observer and observed. It is not a state of seeing but of being, and as such there are few exterior descriptions. This is concentrated being, lived from the inside.

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Bachelard also defines roundness by what it is not; it is not a sphere, nor is it merely geometrical. A sphere is empty, described only by its outside limits. Roundness is "rondeur pleine," or plenitude, like the difference between a basketball that is full of air and a billiard ball that is heavy and solid inside the round exterior shape. Roundness is also not Bachelard's nest from the beginning chapters of La poétique de l'espace, but it is like Michelet’s bird instead,

"l’oiseau (est) presque tout sphérique."³⁷⁵ While Bachelard has discouraged us from connecting the sphere and the round, he uses Michelet's description to illuminate roundness’s "cosmic situation."³⁷⁶ Like the bird, roundness is characterized by a certain isolation and "extreme individuality."³⁷⁷ The bird pulls away from the earth as it flies through the sky putting large amounts of space between it and the rest of the world. Roundness and the bird are the "une centralisation de la vie gardée de toute part," or life "enclose dans une boule vivante."³⁷⁸ It is a totally enveloped life "au maximum par consequent de son unité."³⁷⁹ Bachelard mentions nut and the tree, in addition to the image of the bird ,as examples of images of roundness. All of these shapes are full, solid, isolated, and thus the physical expression of "le rassemblement de l'être en son centre."³⁸⁰

Roundness does not depend solely on exterior descriptions; it is not, as Bachelard states, only geometry. It surpasses geometry; it is an interior quality with an exterior result. Roundness of an exterior does not necessarily imply that the image is a round image, though a concentrated life form (tree, human, bird...) will often be a round image even if it lacks exterior roundness for the unimaginative reader. A sphere is not considered round in Bachelard's sense of the term, for

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it lacks an interior "fullness" or solidity; however, a tree is a round image because it is a concentrated life form, solid from the inside and isolated and round if viewed from above.

Bachelard believes that it is essential to imagine, to regress a little, to withdraw from philosophy, to dream and be inside the image in order to understand and imagine le rond. "Ces images, elles effacent le monde et elles n’ont pas de passé. […] Il faut un instant, les prendre pour soi seul. Si on les prend en leur soudaineté, on s’aperçoit qu’on ne pense qu’à ça, qu’on est tout entier dans l’être de cette expression."³⁸¹

Finally Bachelard brings us to the conclusion that this "being is subject to no dispersion;"

there exists a "permanence de l’être," it is watertight, like the skin of a blueberry. It is the ultimate place of "Bonheur," which he says is the place that houses our subconscious. It is the state of being that calls upon the essence of the human being or what we see as our self, that concentrated me. The ultimate habitat for the human being is the self that houses all experiences and potential across time.

So how does this relate to my discovery of the petite madeleine? The petite madeleine is perhaps the most famous image of Proust’s Combray section; it is round not only because of its geometry but because images of roundness are of “rondeur pleine,” and ""nous aident à nous rassembler sur nous-mêmes, à nous donner à nous-mêmes une première constitution, à affirmer notre être intimement, par le dedans."³⁸² In other words, the madeleine on a very concrete level is a solid piece of cake that is not very big, no bigger than your palm, and the madeleine made in Combray is that of a nearly spherical shell. The madeleine is full in one way because it is solid;

it is more billiard ball than basketball. It also looks as if it took the form of the shell, as if it grew inside of a shell filling up the shell. Explaining the roundness of life forms Bachelard writes,

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“On vit dans la rondeur de la vie comme la noix qui s’arrondit dans sa coquille.”³⁸³ The madeleine is solid life and looks as if it formed inside of a shell, like Bachelard's example of the nut here, and the rest of Proust's tome will now take shape from this round cake.

And, yet it is not just from this little cake that the entire novel springs forth, which leads me to the next characteristic of images of roundness, that images of roundness “confirm our being intimately inside.” Proust describes the madeleine’s exterior in only a few sentences because he says the outside really had no meaning for him. “La vue de la petite madeleine ne m’avait rien rappelé avant que je n’y eusse goûté; peut-être parce que, en ayant souvent aperçu depuis, sans en manger, sur les tablettes des pâtissiers, leur image avait quitté ces jours de Combray pour se lier à d’autres plus récents […]” ³⁸⁴ The madeleine’s exterior no longer possessed meaning for the narrator, but the experience from within was where he found the meaning and his meaning for the rest of the story. It is that only once he had eaten the cake, ingested it, that he could remember what it was like to be inside again.

5.4 Proust's definition of roundness: explicit description of the circle, the ovale and the