On Feb 20, 2016, at 8:00 AM, Fel Reb <email@example.com> wrote:I don't have access to respond to the posthaven blog, so I'm sending it directly to you....Your questions made me think of meta-stability and Simondon... I don't know if if I'm off in left field but here are my two cents' worth... Gotta say though that f is not just any (differentiable) scalar function… it's a nice way at "inducing" continuity where the underlying may not have it..
Yes, right — in fact distribution theory : representing a function by convolving against approximations to the identity with a kernel that converges to the Dirac delta function is a well known and beautiful way to densely approximate any integrable function — a much vaster set of functions, which includes wildly non-differentiable and even discontinuous functions — by infinitely differentiable functions.
If the second time-derivative is going to zero, one would be approaching a steady state of no change, i.e. no new energy entering or leaving the system.
The second time-derivative of what, prices of Apple stock, immigrant flows through Ellis Island ? That is only the case when we’re talking about position (potential energy mass * dx).
If the second time-derivative is positive, why would that induce flickering? If the second derivative is positive at a point, are not you not only providing half the story? Wouldn’t you need to see how the change is changing over time rather than tending?
Yes exactly, that’s why I speak of second time-derivative f’’: change is f’ and change of change is f’’.
If the potential is locally a quadratic with nonzero second derivative, then it looks like a parabola (in potential space). The classic dynamic (solution) subject to that sort of potential (differential equation) is harmonic oscillation.
For the thing to flicker, one would need discontinuities in the system or very tight oscillations to the changing system... tending-positive to infinity, finding another “plateau” of zero (or near zero) and then another tending-negative to infinity and repeat
This flickering effect feels like a cycling of meta-stability where contributing factors within the system impede the system from acquiring a one way or the other... or exit that meta-stable state... the correlation lengths would depend on the energy dynamics of the system, how rough the cycling is, i.e. how much energy is required to get out of the troughs of the meta-stability yet not enough to break away from the cycling and revert to the meta-stable trough. Experimentally, to break the spell one needs to introduce ever larger amounts of energy, heighten the amplitude of the energy dynamics as roughness into the cycling so one overwhelms the threshold boundary and break free from the prevalent dynamic onto another regime. You gotta introduce some rough stuff into the system, i.e. introduce difference or change, to mix it up and break free from the toxic stability....Does this make sense?
Not clear what you mean by all this. Are we speaking of the base space, or the state space of configurations, or the space of potential energy (functional on configurations)?
I hope this doesn’t land like a hair in the soup, like they say in Qc French.
hahaha , what’s that in quebecois?
Best, FelixP.S. I found this reference on my way to somewhere else... thought it might be an interesting comment to the death scenario of the .From NatureUniversal resilience patterns in complex networksJianxi Gao, Baruch Barzel & Albert-László BarabásiNature 530, 307–312 (18 February 2016) doi:10.1038/nature16948Received 13 July 2015 Accepted 14 December 2015 Published online 17 February 2016