Date: Tue 20 Jul 2004 - 09:43:55 CEST
Replying to Stan:
> I will try to express the idea... Originally Zipf and recently
>Ramon Ferrer i Cancho, Richard V. Sole (2003) both attribute Zipf's law to
>the principle of "least effort".
>SS: So, do you mean the physical principle of least action?
>V.: No. It is from Cybernetics. The principle of the least effort says: "a
system will try to adapt to its environment or will try to change the
environment to suit its needs, whichever is easier" (dictionary of
Cybernetics and Systems at http://pespmc1.vub.ac.be/ASC/INDEXASC.html).
>Now let me translate your question 'how does "data to being plotted as a
>power laws suggest systematicity" ?' to 'how can the principle of the
>least effort relate with systematicity in terms of structure of a system
>?' Possible answer... Systems evolve or grow,
>SS: Not by least effort! They strive mightily to grow.
V.: Let me disagree. Let's compare for example life and an explosion of a
mixture of hydrogen and oxygen, both from a chemical point of view are
oxidation processes. Life is an example of oxidation processes controlled by
a complex well organized system. Meanwhile the explosive oxidation of free
hydrogen is much more mighty...
>they respond to changes in their environment, they have to optimize their
>structure and performance for optimal functioning (being a structural part
>of other systems), or in other words systems communicate with their
>environment. Something that is 'not a system' does not 'care' about
>optimization of it's performance, growth, development, adaptation, or any
>sort of evolution, energy saving (principle of least efforts)
>SS: I would like to hear this principle stated in words explicitly.
>In general there is no "energy saving" in natural systems. They dissipate
>energy gradients as fast as possible.
V.: I would not agree again... The definition of the principle of least
effort and the comparison of controlled vs. uncontrolled oxidation look like
saying the opposite. The later dissipate energy gradients much faster
comparing with much more complex living systems. One could also think of
difference between controlled nuclear breakdown in power-stations vs.
uncontrolled blast if to remember our own creations.
>or structural change simply because of the absence of any internal
>organization or structure or feedback loop between the 'non-system' or
>'random system' and it's environment. Its history should be uniform: no
>changes in structure, no development, no growth, no evolution, no
>function, no communication - no need for the least effort... As a
>consequence a structure of any system facing the entropy should be
>organized in such a way as to oppose the II-nd law and optimize its
>performance against energy losses - e.g. the principle of least effort
>that is true for language also works elsewhere (any other communication).
> SS: I disagree with this supposed "least effort" Least action would
> have nothing to do with it. It is the smallest integral over velocity,
mass
> and path length. From that you cannot derive energy efficiency.
V.: May principles of Cybernetics be incompatible with laws of Physics or
vice versa ? I would not like to think this is an unsolvable "conflict"
between those two domains of science. On the other hand I would doubt that
physics alone is capable or has all means to explain what is system,
complexity, information, communication, life...
>How does it look like ? Design features of a communication system are the
>result of interaction between the constraints and demands of the job
>required (Hauser, M.D., 1996. The evolution of communication). Probably
>differentiation of parts according to their functioning scales is the
>right answer. So we have several large elements performing some specific
>functions, and much larger amounts of smaller elements that do 'finer and
>more precise functionality'. And it is likely that aranging systems
>internals (elements, design features, communication system) according to
>Zipf's law is the optimal solution.
>SS: Well, how can that explain the power functions of earthquake
>magnitudes?
V.: They represent structural properties of Earth's crust. There are
different sorts of rocks, other large geological formations (systems again..
). So how that system breaks into parts should depend on and therefore
reflect its internal structure and different properties of composing
elements. I would think energy quantities released through disintegration of
any system is proportional to strength of links (between the elements)
broken. So energy released communicates out what was broken down there...
This should not look too weird if to remember "popular methods of
communication" among larger social groups - wars, riots, revolutions,
terrorism.
>Thus my speculative (as always :) ) conclusion would be that zipf's law is
>observed in systems trying to compensate entropy related energy or
>information loss. If it is 'not a system' - it will not try to optimize
>anything...
>SS: Is a fault line a system?
V.: It is, at least a part of a larger geological system.
>And it's elements will not follow the Zipf's law. The same as a dice or a
>coinwill not attempt to optimize themselves (and the random result they
>produce) according to environmental conditions...
>SS But, again, how will you tell by looking at ranked magnitudes only
>whether or not the population of data come from a system?
V.: By estimating how well it fits selected power (Zipf's) law. Of course
there are downsides and various concerns - for example how well observation
represent the real world (data quality). However we have statistical means
to estimate nearly any "how well". By the way, Ramon Ferer in his article
gives a log-log plot with compared human language, artificial languages and
animal languages. There are noticeable differences among those different
systems...
With best regards
Viktoras
