Abstract
Have you ever noticed that when "we need more time", we can increase the number of things we do in a second, but when "we need more space", we don't use a magnifying glass ? Principle of Self organizationRedundancy:
by increasing H_max by decreasing HIncreasing H_max:
Increasing 'brightness' (intensity) exposes more available states but increases the system energy. The system is no longer closed so, increasing H_max alters a "closed" system's behaviour.Decreasing H:
Increasing the systems 'contrast' by decreasing H, reduces the number of distinguishable[2] states, but does not necessarily increase the potential energy in the system[1].Spatio-temporal redundancy:
Increasing H_max is analogous to increasing the number of 'spatial' states. Increasing H_max, increases the number of possible parallel or simultaneous observations 'spatially' by increasing the number of available states; thus, H is in a sense 'virtually' reduced relative to H_max. More intuitively, this can be modelled as increasing the number of relative parallel observers, without affecting their individual sample-rates (times). Each observer can be treated as a distinct path within phase space. It is not necessary that each path confer with the same language. This action has side effects: State Tunneling Linguistic Indeterminacy Decreasing H is analogous to increasing the number of temporal states. Decreasing H, decreases the number of possible states. This is more of an absolute reduction of H and not a relative one as in terms of increasing H_max. Decreasing H reduces the state space to a more sequential path through a phase sub-space which limits the possible state transitions. We can say that "the former states were possible states and that now they are not". That they 'were' possible admits that the phase space is inclusive of them even though they are not used 'now'. This action has side effects: Wave-function collapse Semantic UncertaintyLinguistic Discrimination and Semantic Uncertainty
'Linguistic indeterminacy' is the admission of many possible languages or protocols in the transmission of information. Whereas in serial communication, this can only be done if each observer along a single observational path can speak the same languages as its nearest neighbors, multiple paths through phase space allow each path to represent one observer with its own peculiar language and only at some point of convergence is it required that these languages be translatable. Because a single path through phase space is sequential and causative, 'linguistic discrimination' is minimized but the 'telephone effect' leads to 'semantic uncertainty' within in smaller set of languages.
[1] In the reduction of entropy of a battery cell, the potential energy of the battery is increased reducing the number of possible states of the system Mixed oil and vinegar separate in much the same sense that we attribute to charging a battery, and yet this does not increase the potential energy of the oil-vinegar "battery": Oil and Vinegar In this case it appears that a closed system's potential energy was expended in the process of separation. The oil and vinegar system winds up in what appears to be a "highly organized" binary set of states at max-entropy. This seems quite contrary to the popularized notion of "entropy" as being a measure of disorder. Here, max-entropy is thermodynamically disordered, yet in some sense it is highly ordered. Can we say the oil-vinegar max-entropy is of low Shannon entropy and high thermodynamic entropy ? Janus and Entropy: "In the latter part of the nineteenth century, the eminent physicist Maxwell defined entropy as a measure of of the disorder or ``randomness'' in matter." http://www.cs.auckland.ac.nz/~cthombor/Pubs/Entropy/node2.html "Entropy, the thermodynamic state function that drives reactions to equilibrium, was defined by Rudolf Clausius in the early 1860's." http://www.madsci.org/posts/archives/may98/894567622.Ch.r.html "Entropy can be defined as the measure of dissorder a system contains. One way to calculate entropy is to use a formula Ludwig Boltzman came up with:" http://inst.augie.edu/~dedeneva/entropy.htm "The information theory concept of entropy in its present form was introduced by Shannon in 1948" http://www.nmia.com/~monsmith/diss/node21.html "Around 1850, German scientist Rudolf Clausius first introduced the idea of entropy" http://www.aip.org/physnews/preview/1997/qinfo/sidebar2.htm "In all processes in closed systems entropy never decreases (Clausius-Boltzmann)." http://www.plmsc.psu.edu/%7Ewww/matsc597c-1997/introduction/Lecture3/node1.html "Of course, you already know that thermodynamic entropy ONLY applies to chemicals and matter, atoms and molecules, not to economics or information or pollution or human problems, unless they are directly connected to atomic and molecular behavior, right?" http://www.2ndlaw.com/entropy.html "...there are both classical and quantum statistical mechanical definitions of physical entropy..." http://www.math.washington.edu/~hillman/entropy.html "Entropy is a peer-refereed scientific journal." http://www.mdpi.org/entropy/ http://www.mdpi.org/entropy/entropyweb/defineentropy.htm "So what is the problem between entropy and evolution?" http://www.mdpi.org/entropy/entropyweb/prigogine.htm "Entropy has a bad taste..." http://www.cpm.mmu.ac.uk/~majordom/entropy/ "The work of Prigogine in drawing attention to non-linear thermodynamics" http://www-diotima.math.upatras.gr/mirror/autopoiesis/0158.html "Prigogine called systems which continuously export entropy in order to maintain their organization dissipative structures." http://pespmc1.vub.ac.be/SELFORG.html "K Denbigh (1981) How subjective is entropy?" http://www.ph.ed.ac.uk/%7Eviv/maxwells-demon.html "Since Shannon (1945), Jaynes (1957) and Kullback (1959), the notion of entropy has widely been used in communication theory and data and signal processing." http://www.maxent99.idbsu.edu/ "Where do we stand on maximum entropy?" http://bayes.wustl.edu/etj/node1.html#stand
[2] Here, 'distinguishment' is in terms of 'resolution', and not necessarily in terms of the actual number of physically available system states (relative entropy). Increasing contrast on a television screen reduces it's information entropy, but not necessarily its physical entropy. Such a distinction between Shannon and Thermodynamic entropy becomes less apparent as finer resolutions approach the quasiatomic limit where information and energy are almost synonymous.
[4] Information here means "new information". Information which is redundant is useless as "new information" but not useless for conveying information.