Intuitionnisme

Résumé

L'intuitionnisme est une philosophie des mathématiques que L. E. J. Brouwer a élaborée au début du . Pour Brouwer, les mathématiques sont une libre création de l'esprit humain et tous les objets qu'elles manipulent doivent être accessibles à l'intuition. L'intuitionnisme a pour conséquence une profonde remise en cause des mathématiques, notamment en refusant l'infini actuel : un nombre réel ne peut être représenté comme une suite infinie de décimales qu'à la condition de disposer d'un moyen effectif de calculer chacune de ces décimales ; on parle alors de réel constructif. Sur le plan logique l'intuitionnisme n'accepte pas le raisonnement par l'absurde ou le tiers exclu pour la raison que ces principes permettent de démontrer des propriétés de façon non constructive : par exemple si on veut démontrer l'existence d'un nombre réel satisfaisant une certaine propriété, on peut raisonner par l'absurde, supposer qu'aucun réel ne satisfait la proposition, en déduire une contradiction et co

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https://fr.wikipedia.org/wiki/Intuitionnisme

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On Sphere-Filling Ropes

Henryk Gerlach

What is the longest rope on the unit sphere? Intuition tells us that the answer to this packing problem depends on the rope's thickness. For a countably infinite number of prescribed thickness values we construct and classify all solution curves. The simplest ones are similar to the seam lines of a tennis ball; others exhibit a striking resemblance to Turing patterns in chemistry, or to ordered phases of long elastic rods stuffed into spherical shells.

2011

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AlloHaptic: Robot-Mediated Haptic Collaboration for Learning Linear Functions*

Wafa Monia Benkaouar Johal, Barbara Bruno, Pierre Dillenbourg, Hala Khodr, Soheil Kianzad, Aditi Kothiyal

Collaborative learning appears in a joint intellectual efforts of individuals to understand an object of knowledge collectively. In their search for understanding the problems, meanings, and solutions, learners employ different multi-modal strategies. In this work, we explore the role of force feedback in learners interaction with tangible hand-held robots. We designed a collaborative learning environment to provide embodied intuitions on linear mathematical functions combined with graphical representations and ran a first study involving 24 participants. Our analysis shows a positive learning gain for our learning activity. Moreover, to explore the link between different types of force feedback and learners’ collaboration, we designed a focus group study with 12 participants. Our results suggest that the haptic communication channel affects the collaboration dynamic differently according to the nature of the learning task. We finish by proposing design insights for future exploration of haptic in collaborative learning.

IEEE2020

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Black hole bound on the number of species and quantum gravity at CERN LHC

Michele Redi

In theories with a large number N of particle species, black hole physics imposes an upper bound on the mass of the species equal to M-Planck/root N. This bound suggests a novel solution to the hierarchy problem in which there are N approximate to 10(32) gravitationally coupled species, for example 10(32) copies of the standard model. The black hole bound forces them to be at the weak scale, hence providing a stable hierarchy. We present various arguments, that in such theories the effective gravitational cutoff is reduced to Lambda(G)approximate to M-Planck/root N and a new description is needed around this scale. In particular, black holes smaller than Lambda(-1)(G) are already no longer semiclassical. The nature of the completion is model dependent. One natural possibility is that Lambda(G) is the quantum gravity scale. We provide evidence that within this type of scenarios, contrary to the standard intuition, micro-black-holes have a (slowly fading) memory of the species of origin. Consequently, the black holes produced at LHC will predominantly decay into the standard model particles, and negligibly into the other species.

2008

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