Free will 4 - or soft wiring

Exercise from QMC

In the last post I talked of the controls of Captain Mekon's submersible not being hard wired to the inbound visual stimuli.

This morning I woke to thoughts of soft wiring and asked Bing about 'chains of pendulums connected by springs', a subject which he seemed to know all about, with his offerings including the learned paper at reference 1 and a university exercise, the start of which is illustrated left.

Without having done more than turn the pages of reference 1, my recollection is that your fiddlings with the pendulum on the far left do transmit, after a fashion, to the pendulum on the far right. But it is only after a fashion and you might have some bother computing the effect given just the cause, never mind vice versa.

Nevertheless, my 'not being hard wired' means even softer wired than these chains of pendulums. Most likely you could not even compute the effect from the cause, never mind the cause from the effect, this last being what is necessary to have any control over the behaviour of our Captain.

PS: two of the three authors of reference 1 come from an Italian university department of civil engineering. Perhaps this morning they are busy with collapsing bridges rather than with swinging springs.

Reference 1: On the synchronization of chains of nonlinear pendulums connected by linear springs - L. Marcheggiani, R. Chacón, and S. Lenci - 2014. I commend the introduction for its call to scientific arms and from which I take the quote: '... Complex multidimensional systems, consisting of chains of identical coupled chaotic pendulums, present a non-trivial dynamics which has attracted, in the last decades, the attention of the scientific community and which is still under study; in particular there is a growing interest in understanding and controlling the synchronization and de-synchronization phenomena in networks of coupled chaotic oscillators; this topic is currently under investigation in physics, biology and technology for the wide area of practical applications including laser systems, fluid mixing, secure information processing, plasma systems, neuronal stimuli transmissions, and pedestrians-structure interaction, to cite just a few. The lack of a theoretical approach to chaos control in this type of multidimensional chain system is an open issue. Also the lack of a universal theory able to provide an analytical synchronization criterion is worthy of investigation...'.