Infinitesimals and the Self

In my immediate-moment theory of animal behavior, the physical center-of-gravity of an animals’ body is how an animal becomes aware of its Self. I believe this is substantiated by the discovery that animals have an inherent sense of calculus, which is how they compute an efficient manner of movement. This is also substantiated by Dr. Wolter’s work that movement is the fundamental principle of neurological evolution. And nothing could be more fundamental to locomotion than the body symmetrically configured around its physical center-of-gravity. This is why in the NDT model emotion is a calculus of motion. From here it follows that the mind processes emotion the same way as the body processes motion, configuring around the center-of-gravity.

Central to calculus is the notion of the infinitesimal and it’s interesting to read how this concept was once considered to be a heresy. It’s an age old struggle, the intellect versus the intuition. Consider the following page from the book: “Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World.”

“Destroy or be destroyed— such were the stakes when it came to infinitesimals, according to Tacquet. Strong words indeed, but to the Fleming’s contemporaries, they were not particularly surprising. Tacquet was, after all, a Jesuit, and the Jesuits were then engaged in a sustained and uncompromising campaign to accomplish precisely what Tacquet was advocating : to eliminate the doctrine that the continuum is composed of indivisibles from the face of the earth. Should indivisibles prevail, they feared, the casualty would be not just mathematics, but the ideal that animated the entire Jesuit enterprise. When Jesuits spoke of mathematics, they meant Euclidean geometry. For, as Father Clavius had taught, Euclidean geometry was the embodiment of order. Its demonstrations begin with universal self-evident assumptions, and then proceed step by logical step to describe fixed and necessary relations between geometrical objects: the sum of the angles in a triangle is always equal to two right angles; the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the long side; and so on. These relations are absolute, and cannot be denied by any rational being. And so, beginning with Clavius and for the next two hundred years, geometry formed the core of Jesuit mathematical practice . Even in the eighteenth century, when the direction of higher mathematics turned decisively away from geometry and toward the newer fields of algebra and analysis, Jesuit mathematicians held firm to their geometrical practice. It was the unmistakable hallmark of the Jesuit mathematical school. If only theology and other fields of knowledge could replicate the certainty of Euclidean geometry, they believed, then surely all strife would be at an end. The Reformation and all the chaos and subversion that flowed from it would never have taken root in such a world. This vision of eternal order was, to the Jesuits, the only reason mathematics should be studied at all. Indeed, as Clavius never tired of arguing to his skeptical colleagues, mathematics embodied the Society’s highest ideals, and thanks to his efforts the doors were opened at Jesuit institutions for the study and cultivation of the field. By the late sixteenth century , mathematics had become one of the most prestigious fields of study at the Collegio Romano and other Jesuit schools. Just as Euclidean geometry was, for the Jesuits, the highest and best of what mathematics could be, so the new “method of indivisibles” advocated by Galileo and his circle was its exact opposite. Where geometry began with unassailable universal principles, the new approach began with an unreliable intuition of base matter. Where geometry proceeded step by irrevocable step from general principles to their particular manifestations in the world, the new methods of the infinitely small went the opposite way: they began with an intuition of what the physical world was like and proceeded to generalize from there, reaching for general mathematical principles. In other words, if geometry was top-down mathematics, the method of indivisibles was bottom-up mathematics. Most damaging of all, whereas Euclidean geometry was rigorous , pure, and unassailably true, the new methods were riddled with paradoxes and contradictions, and as likely to lead one to error as to truth. If infinitesimals were to prevail, it seemed to the Jesuits, the eternal and unchallengeable edifice of Euclidean geometry would be replaced by a veritable tower of Babel, a place of strife and discord built on teetering foundations, likely to topple at any moment. If Euclidean geometry was, for Clavius, the foundation of universal hierarchy and order, then the new mathematics was the exact opposite, undermining the very possibility of universal order, leading to subversion and strife. Tacquet was not exaggerating when he wrote that in the struggle between geometry and indivisibles, one must destroy the other or “must itself be destroyed.” And so the Jesuits proceeded to do just that.”

Alexander, Amir (2014-04-08). Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World (p. 120). Farrar, Straus and Giroux. Kindle Edition.

So the question for us in Dogdom is which side of history do we intend to be on, dogma, or the dogs’?

Published October 27, 2014 by Kevin Behan
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2 responses to “Infinitesimals and the Self”

  1. wetnosewarmhearts says:

    Perhaps, old ideas whose time has arrived: “Heart, guts, and brain communicate intimately via the ‘pneumogastric’ nerve involved in the expression and management of emotions in both humans and animals. When the mind is strongly excited, it instantly affects the state of the viscera; so under that excitement there will be much mutual action and reaction between these, the two most important organs of the body.” C. Darwin in “The Expression of the Emotions in Man and Animals” (1872) “Darwin goes on to observe that the fundamental purpose of emotions is to INITIATE MOVEMENT that will restore the organism to safety and physical equilibrium.” (Bessel van der Kolk, 2014) S. Porges developed the pneumogastric nerve into the “Polyvagal Nerve Theory” but the intent of the original Latin’emovere, “to move out-act and flesh out” remains. Movement, especially, social engaging ones are central. Porges explains that the first line of returning to normalcy after trauma (N.B. Trauma is not the same as PTSD, a diagnostic category meant for human beings with a fully developed frontal cortex.] is to socially re-engage, move toward other animals. Porges places social interaction as foundational for healing while competition remains in other arenas. Simple rhythmically attuned movements that re-engages the animal is enormously beneficial. It is that type of movement that I see you do in rehabilitating dogs. It is your rhythmic steps, rather than the more dramatic, that re-involve, critical engagement returns. The dance of re-engagement that modern and some old affective neuroscience truly supports. You convey vital information via tone of voice, posture, gesture, facial expression, body tension etc. You become safe and interested albeit provocative. The dog no longer has the option of being frozen in its trauma. “Human beings [animals-emphasis mine] are astoundingly attuned to the subtle emotional shifts in the people (and animals) around them. Slight changes in the tension of the brow, wrinkles around the eyes, curvature of the lips, and angle of the neck quickly signal to us how comfortable, suspicious, relaxed, or frightened some is. Our mirror neurons register their inner experience, and our own bodies make make internal adjustments to whatever we notice….at a deeper level we barely exist as individual organisms. Our brains [and bodies-emphasis mine] are built to help us function as members of a tribe.’ (Bessel van der Kolk, 2014) Reading the dog and how to communicate bodily back to the dog via voice, body movement, and re-sensualizing touch is the gift sought in November 2014.

  2. Kevin Behan says:

    Greatly appreciate such a helpful synthesis of so much science. Looking forward to putting all this in action next week. Thank you.

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