Re: [Fis] probability versus power laws

From: Stanley N. Salthe <[email protected]>
Date: Sun 25 Jul 2004 - 21:33:12 CEST

Commenting upon Guy's posting:

>Commenting on the apparent conflict between the principles of "least
>effort" and "least action":
>On Jul 20, 2004, at 12:43 AM, Viktoras Didziulis wrote:
>
>>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...

>I suspect that Stan and Viktoras are looking at systems from different
>viewpoints, which is generating the apparent conflict. Stan is focusing
>on the striving of self-organization driven by opportunity to channel
>flows across gradients, while Viktoras is focusing on the structural
>solutions adopted by systems to the challenge of flows.
     SS: Yes, I think you have it.

>In this light, I find myself agreeing with both views. Systems do indeed
>strive "mightily" to self-organize and break down gradients, but they do
>so given the constraints of their circumstances. Flows, and dynamical
>systems themselves, are always searching for and pushing up against
>sources of resistance. Resistance is either gradually overcome, or
>adapted to. Explosions are like potential systems that tear through
>frictional resistance as they grow; but failing to sense and respond to
>sources of resistance in the process dooms an explosion to a rapid
>extinction.
     SS: A very neat summing up!

>The principle of least effort makes good sense to me because flows always
>tend to take the path of least resistance. This makes natural machines
>relatively efficient.
     SS: Here I'm not so sure I follow. The path of least resistance
dissipates a gradient more rapidly. Rapid dissipation is not coordinate
with energy efficiency (of work), which is better served by slow, careful
dissipation.

>On the other hand, these same systems are under constant pressure to serve
>the thermodynamic imperative ("final cause" sensu Stan) by breaking down
>external gradients. I see plenty of room to balance these demands. A
>system only needs to break down external gradients fast enough to pay the
>thermodynamic cost of its continued existence (maintenance, growth,
>reproduction, ...). Any extra gradient-breaking would be thermodynamic
>"icing on the cake." I could build a fire tonight, but it won't help with
>my survival or functioning one bit. It's like tipping the black jack
>dealer in a casino (note that I live in Reno).
     SS: Ah, well, Reno is ALMOST the center of our civilization. Las
Vegas is the real center. On this score we see in blazing colors the
"wasting" of energy from the environmentalist point of view. BUT, here we
show how well we serve our true mistress, the Second Law. I do agree
however, that actual dissipative structures do "balance" the urgings of the
Second against the need for their own survival. Gradient dissipation is
moderated to the extent required to develop, grow and endure.

>Systems also only need to be efficient enough to make sure that the rate
>of fuel input is adequate to pay the costs of existence. Excess fuel
>intake allows a system to generate internal resistances to flow that can
>be used for the extraction of free energy (I am thinking of highly complex
>biological organisms here). Even then, however, flows will take the path
>of least resistance, given the obstacles erected by the system.
>
>In sum, it seems to me that systems evolve to be as efficient as they can
>be, given both external and internal (engineered) sources of resistance.
>This is the principle of least effort. At the same time, the efforts they
>do make are ultimately aimed at channeling flows across gradients. This
>often does not look like effort directed at achieving an externally driven
>goal because they are paid for their efforts in the form of free energy
>with which they express constrained striving.
     SS: Good summary

STAN
>
>My 2 cents,
>
>Guy
>
>Department of Biology
>University of Nevada Reno
>Reno, NV 89557
>
>Phone: 775-784-4860
>Fax: 775-784-1302
>

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Received on Sun Jul 25 21:17:02 2004

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