Poincaré and Geometry of Curvature. Thought of the Day 60.0

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It is not clear that Poincaré regarded Riemannian, variably curved, “geometry” as a bona fide geometry. On the one hand, his insistence on generality and the iterability of mathematical operations leads him to dismiss geometries of variable curvature as merely “analytic”. Distinctive of mathematics, he argues, is generality and the fact that induction applies to its processes. For geometry to be genuinely mathematical, its constructions must be everywhere iterable, so everywhere possible. If geometry is in some sense about rigid motion, then a manifold of variable curvature, especially where the degree of curvature depends on something contingent like the distribution of matter, would not allow a thoroughly mathematical, idealized treatment. Yet Poincaré also writes favorably about Riemannian geometries, defending them as mathematically coherent. Furthermore, he admits that geometries of constant curvature rest on a hypothesis – that of rigid body motion – that “is not a self evident truth”. In short, he seems ambivalent. Whether his conception of geometry includes or rules out variable curvature is unclear. We can surmise that he recognized Riemannian geometry as mathematical, and interesting, but as very different and more abstract than geometries of constant curvature, which are based on the further limitations discussed above (those motivated by a world satisfying certain empirical preconditions). These limitations enable key idealizations, which in turn allow constructions and synthetic proofs that we recognize as “geometric”.

Nihilism Now! Monsters of Energy by Keith Ansell Pearson and Diane Morgan

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Blurb: Have we had enough? But enough of what exactly? Of our mourning and melancholia? Of postmodern narcissism? Of our depressive illness and anxieties of not ‘being there’ any longer? Enough of enough! We now ask: what of the future of the human and of the future of the future? Is it now possible to produce revitalised ways of thinking and modes of existing that have digested the demand for transhuman overcomings and so are able to navi- gate new horizons of virtual becoming? Is it possible to save thought from its current degenerative and vegetative state at the hands of a smug and cosy postmodern academicism? Can we still invent new concepts?

If one follows certain influential contemporary accounts, it would appear as if the experience and question of nihilism have become passé. Is not the urgency informing the question of the `now’ of nihilism redundant and otiose? For Jean Baudrillard, for example, there is now only the simulation of a realised nihilism and little remains of a possible nihilism (a nihilism of the possible) in theory. In relation to previous forms of nihilism ± romanticism, surrealism and dadaism ± we find ourselves in an ‘insoluble position’. Our nihilism today is neither aesthetic nor political. The apocalypse is over, its time has gone and lies behind us:

The apocalypse is finished, today it is the precession of the neutral, of the forms of the neutral and of indifference. (Baudrillard)

Baudrillard goes on to make the claim, terrifying in its full import, that all that remains is a ‘fascination’ for these indifferent forms and for the operation of the system that annihilates us.

Surely, Baudrillard is being ironic when he claims that this mode of nihilism is our current ‘passion’? How can one be passionate about indifference and one’s own annihilation? As Baudrillard acknowledges, this is the nihilism of the observer and accepter. It is the nihilism of the passive nihilist who no longer aspires towards a transcendence or overcoming of the human (condition), but who simply announces and enjoys its disappearance, the spectator watching the spectacle of his own demise. History, politics, metaphysics, have all reached their terminal point, and willing nothingness appears to be the only desire of the will available to the post-modern mind:

The dialectic stage, the critical stage is empty. There is no more stage . . . The masses themselves are caught up in a gigantic process of inertia through acceleration. They are this excrescent, devouring, process that annihilates all growth and all surplus meaning. They are this circuit short- circuited by a monstrous finality. (Baudrillard)

Diane Morgan and Keith Ansell Pearson Nihilism Now Monsters of Energy