1/2 #Engineering, #Comedy, #NoeticSpectrum Dept : Yesterday found myself outlining current work in #Precognition to a non #Science person using the example of a self driving car to introduce the concept of #boundedness ; there are not infinitely many ways to get where your going etc...
This in spite of the fact that I would never own a self driving car, let alone let one drive me anywhere, so irony and hypocrisy for 500 please...
The tangent aside to this is that #Precognition, #Telepathy...

Long ago I had learnt that continuity and boundedness guarantee a unique solution to a real initial value problem for a linear ode. Does this work for the complex domain-codomain ?

#maths #ode #boundedness #uniqueness

1/2 It truly frightens people that on some level our #Universe being a simulation might not be a completely insane notion . Then perhaps having acquired a few necessary tools comes confrontation with the fact that ,at least *computationally*, the #SimulationHypothesis by itself is not falsifiable.It either all goes south from there or the drive to know more lands one on the doorstep of the question- what do notions of #boundedness refer to wrt physical systems?A first good conflict to entertain-

`To prove #boundedness on Lp spaces, Calderón and Zygmund introduced a method of decomposing L1 functions, generalising the rising sun lemma of F. Riesz. This method showed that the operator defined a continuous #operator from L1 to the space of #functions of weak L1. The Marcinkiewicz interpolation theorem and duality then implies that the #singular #integral operator is bounded on all Lp for 1 < p < ∞.`

https://en.wikipedia.org/wiki/Singular_integral_operators_of_convolution_type#General_theory

#functionalAnalysis #mathematics #math

Singular integral operators of convolution type - Wikipedia