Saturday, August 7, 2010

as i was saying..

it has been a moment or two..

news at work

work on the circuit has slowed for the moment, until we build the mechanism which will allow us to couple multiple circuits together. right now, there is a setup which allows the circuits to be coupled "uni-directionally", where one circuit influences the behavior of another, but not vice versa. this generally synchronizes the behaviors of the circuits. in this setup, the primary circuit is called a "master", while the circuit being synchronized by it is called the "slave". this is an awkward yet standard terminology. we will use it here, as you will see.

with this uni-directional synchronizing setup, all behavior is dictated by the master, whether it is periodic or chaotic. all that can be built is a system of circuits that are all controlled by, and thus exhibit, the behavior of the master. this is true except for in the case where they make a loop, so that the master ends up influencing itself through a chain of slaves... in which case the synchronization becomes unstable (more on this later). the point is, i intuit that studying a (loopfree) uni-directionally synchronized system will not be much more interesting (from our perspective) than studying a single circuit. so i will attempt to pursue a "bi-directional" coupling scheme, as i have previously mentioned. i have ordered the remaining necessary electronic components, and they should arrive within a few days.

of course, until then, there are a few things to look into. for instance, my intuition that the master slave setup is not so rich. there are some questions that did strike me about such a system, mostly regarding the degree to which the slave is, well, enslaved by the master. each circuit has parameters that we can change. for different parameter values, the circuits behave differently. what happens if one changes the slave's parameters while it was being driven by a master? can the slave overcome the influence, and revolt? if so, what effect might the revolt have on the master, if any?
-first, i observed which values of the slave's parameters corresponded to its different behaviors when it is not being influenced by a master.
-then, i turned on the master, and allowed the connected the synchronization, and synchronized the slave to the master.
-i then changed the slave's parameters and looked for any indication of a change in its behavior.

there was none.
there was also no change in the master's behavior.
(this second fact turned out to be trivial, since the synchronization circuit has a diode in it. a diode allows current to flow one way, and not the other. so, the setup does not allow any influence to travel backwards from the slave to the master. )

but, i found one thing curious. the place where the master signal comes into the slave is the same place where we were measuring the slave. this is a problem because, in effect, we are just remeasuring the master. the measurements were being taken to close to the source of influence, and they were not a fair representation of the effect of the influence. (it was actually fine, since we were measuring the slave at other points as well). this is just a fairly trivial issue of methodology, and experimental/measurement design... and would normally not be mentionworthy, other than as an account of a sort of "aha! slight/potential folly!"... but it immediately struck me as beautifully analogous to instances of media acquiring bias by measuring at the cause of a situation, as opposed to measuring at the effect.
easy examples are fluttering around us daily... especially vivid are the "scientific" claims released by bp, formerly "brittish petroleum", about the effects of the oil and dispersant in the gulf. in fact, the u.s. federal government and bp (the two conductors of this spill) have demonstrated that they are the least reliable sources of information about the event itself...
sorry.. that may have been a long walk to a not so compelling well... but i find myself trying to forge a general perspective on what a "power system" might just be, in the most general terms, and i keep thinking that systems of governance and perpetuation can generally be systems which contain components that have or produce a resource for the system, and also dynamically allocate that resource to parts of the system. this allocation requires very specific organization in order to be effective and efficient. pathologies vary as the systems do. in power systems, the generator (allocator) is completely devoted to serving its "constituents", although in the event of a constituent component malfunctioning, or becoming damaged, the generator can "shed" that load (disconnect from that component). the system reconfigures, re-routing power around the malfunctioning part. in social governance, the government (allocator) is faced with an everchanging multiscale system to which it supplies (for instance) federal funding. this is quite different from the power system, where the loads do not necessarily change, though their needs change. for social allocators (gov.), there is a vast and fast evolving ecosystems of interdependent entities, all with different motivations, and histories.. all asking for a piece of the federal resource. in the power system, the loads have relationships with each other as well, and they compete at times...but generally it is known before hand which loads have priority (vital loads) over others.
the situation with the social system is interesting, since humans can play multiple roles at different stages of their lives, and are capable of discovering clever indirect ways to create benefit for themselves.
so, for instance, suppose a policy maker (resource allocator) is in a position to influence the benefit of some entity,.. let us say a corporation. if that corporation is able to influence the policy maker's decision (by allocating private resources to say.. an election campaign), then the entity is effectively controlling the allocation it receives, and creating a feedback loop.. whereby one of the components that the allocator is influencing is, itself, influencing the allocator. well... we know that when this happens to coupled chua circuits.. the order (synchronization) throughout the system becomes unstable (in that system, the resource being allocated is really just behavior. that is what is coming from the master to the slave.. information in the form of behavior...being provided and distributed by the master to all the slaves). [addendum: in the chua system, we thought of instability as arising when the master circuit gained an avenue to influence itself through the slaves. in the governance scenario, we speak of it more as the component gaining an avenue to influence itself through the master. it turns out that these are one in the same.] so, what is there to see in the general picture from all of this...well... that is not clear yet.
when a new feedback loop emerges in an evolving dynamical system, the stability should be expected to change.. since the system has essentially gained new influence over an aspect of itself.. for instance, an oven gaining a heat-controlled knob, or workers gaining control over production... or some other such scenario where a system becomes dependent on itself or its environment in a new way. such a thing could be as simple and treacherous as the arrival of a positive/negative feedback loop, sending some aspect of the system off in one direction...

of course, speculations like those above are (hopefully) excusably nebulous, as the nature of such thought is relatively new...
alright.. i will relent for the moment, and leave you with a visual reward for reading so far..

below are two bifurcation diagrams from the circuit here.
essentially, what you are seeing is the over all behavior of the voltage at a point in the circuit as a parameter changes (left to right). in the beginning (far left), the voltage stays constant, and as the parameter increases (moving rightward) the single voltage splits into two which the voltage alternates between. the behavior is periodic (repeating), and as the parameter changes further, the oscillations become larger (alternating between points which are moving away from each other). this is the first pitchfork looking split, opening to the right. then, as the parameter increases further, the oscillations bifurcate (as in the july 7 and the june 22 entry), alternating between four values, as marked by the secondary pitchfork looking openings. further increase leads to more bifurcations, but increasingly quickly, so that we do not actually see them as clearly as the first two.. . leading eventually briefly into chaos (the fuzzy end of the structure in the top left corner of figure 1). as the parameter continues to increase, the dynamics drop back into being periodic, alternating between two values, as seen by the lower pitchfork, to the right of the upper one. more bifurcations are seen..(still going left to right) and another transition into chaos. these dynamics are the same as in the video in the previous entry... this is just a compact way of keeping track of the specific structure of the bifurcation. figure 2 is an visually explained version of what was just stated above. figure 3 is a bifurcation diagram acquired while the parameter was being changed by the pc 104 microcontroller. it turned out that the way that it changes the parameter was very far from "continuously", and so did not make the best bifurcation diagram. on the other hand, figure 1 was made while i adjusted the parameter by hand, as closely as possible to "continuously". i was literally turning the knob with my hand, trying to turn as consistently and continuously as possible. it took quite a few tries to get a good one.. but we got one.

figure 1 (click on these figures to see them larger)

figure 2 (parameter increases from left to right)

figure 3. bifurcation diagram with less control (pc 104)

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