Introduction to the Tangent Grupoid

We present some plausible definitions for the tangent grupoid of a manifold M, as well as some of the known applications of the structure. This is a kind of introductory note.Comment: 8 pages, late

Lessons from Numerical Analysis

It is reviewed how Renormalization Group, species doubling and CKM mixing are known to appear in numerical analysis: Butcher group, parasitic solutions and higher order methodsComment: 3 pages Late

Dream of a Christmas lecture

We recall the origins of differential calculus from a modern perspective. This lecture should be a victory song, but the pain makes it to sound more as an oath for vendetta, coming from Syracuse two milenia before.Comment: 7 pages LaTe

Some conjectures looking for a NCG theory

It is pointed out that ambiguities in the regularization of actions with second derivatives seem to happen with the same multiplicity that the standard model of elementary particlesComment: 7 pages, LaTe

A new Koide tuple: strange-charm-bottom

With the negative sign for $\sqrt m_s$, the quarks strange, charm and bottom make a Koide tuple. It continues the c-b-t tuple previously found by Rodejohann and Zhang and, more peculiar, it is quasi-orthogonal to the original lepton triplet.Comment: 6 page

Some bounds extracted from a quantum of area

Asking very elementary relativistic quantum mechanics to meet quantums of area and time, it is possible to observe at a general level: a) the seesaw bound for the mass of neutrinos, and b) the need of a gauge group at energies below Planck mass.Comment: 10 pages, no figure

Flashes of noncommutativity

Noncommutativity lays hidden in the proofs of classical dynamics. Modern frameworks can be used to bring it to light: *-products, groupoids, q-deformed calculus, etc.Comment: 4 pages Latex, 1 figure ep

Some minor examples on discrete geometry

Assuming a minimum value for area measurement, the emergence of quantum mechanics can be easily motivated from naive consideration of gravitational force. Here we provide some pedagogical examples and extensions. At the same time, the role of Planck mass is shown to be of some theoretical influence even at low energies.Comment: 4 pages, added a remark on classical orbits and space time dimensionalit

Democritus as Taoist

While similarities do naturally exist between tao and other philosophical systems, for the specific case of Democritus we can argue also the chronological parallels, the parallels in the posterior development (alchemy and mathematics) and the textual parallelism.Comment: 4 pages, LaTe

Standard Model Masses and Models of Nuclei

We note an intriguing coincidence in nuclear levels, that the subshells responsible for doubly magic numbers happen to bracket nuclei at the energies of the Standard Model bosons. This could show that these bosons actually contribute to the effective mesons of nuclear models.Comment: 8 Pages, 9 figures. New plots added, mainly to check the neutron drip lin