Friday, June 28, 2013

Part 09 of 29. THE DIALECTICA MANIFESTO. 'The Nonlinearity Breakthrough' and 'The Fusion Breakthrough'.




Part 09 of 29 --

The Dialectica Manifesto

 

 

 

 

Dialectical Ideography 

 

and the Mission of F.E.D.

 

 

 

 

The Nonlinearity Breakthrough

 

and

 

The Fusion Breakthrough

 




Dear Readers,


I am, together with F.E.D. Secretary-General Hermes de Nemores, and F.E.D. Public Liaison Officer Aoristos Dyosphainthos, organizing to develop a new, expanded edition of the F.E.D. introductory documents, for publication in book form, under a new title --
The Dialectica Manifesto:  Dialectical Ideography and the Mission of Foundation Encyclopedia Dialectica [F.E.D.]
 

-- and under the authorship of the entire Foundation collective.
Below is the ninth installment of a 29-part presentation of this introductory material, which the F.E.D. General Council has authorized for serialization via this blog over the coming months, as we develop the material.


I plan to inter-mix these installments with other blog-entries, including the planned additional F.E.D. Vignettes, other F.E.D.  news, my own blog-essays, etc.


Links to the earlier versions of these introductory documents are given below.





Unlike the typical blog-entry, this series will attempt to deliver an introduction to [in this case, to the Foundation worldview as a totality], in a connected account, making explicit many of the interconnexions among the parts.


Enjoy!!!



Regards,

Miguel










 

 

The Nonlinearity Breakthrough

and the Fusion Breakthrough.


The prospect of fusion power epitomizes the vast scientific, industrial-technological, and social benefits — potentially human-social progress re-igniting, and human-species-continuation-enabling — of a Nonlinearity Breakthrough.


Hypothesis.  A “closed-form”’, global solution of the “highly-nonlinear” Maxwell-Boltzmann-Vlasov plasma equation should enable direct computation of control-parameter-values corresponding to self-sustaining nuclear fusion reaction regimes, while also providing other physical / engineering insights, all leading rapidly to the design and construction of commercially super-competitive fusion power reactors, utilizing low-radioactivity or ‘no-radioactivity’, virtually pollution-less fuel cycles [e.g., the Hydrogen-1/Boron fuel-regime].


Consider the intensely auto-kinesic, nonlinear character of a “plasma” --

“A plasma is a gas of charged particles, in which the potential  energy of a typical particle due to its nearest neighbor is much smaller than its kinetic energy.”

“The plasma state [also termed plasma phaseF.E.D.] is the fourth state of matter:  heating a solid makes a liquid, heating a liquid makes a gas, heating a gas makes a plasma. (Compare the ancient Greeks’ earth, water, air, and fire).”

“The word plasma comes from the Greek plásma, meaning “something formed or molded. 

It was introduced to describe ionized gases by Tonks and Langmuir [in a 1929 paper — F.E.D.].

More than 99% of the known [M.D.:  visible, e.g., excluding "Dark Matter", and "Dark Energy"] universe is in the plasma state.”

[Dwight R. Nicholson, Introduction to Plasma Theory, Wiley (NY:  1983), p. 1].



The motion of the non-neutral, electrically-charged «plásma» “particles” just described continually, dynamically generates a changing magnetic field — a magneto-dynamical field of forces.
The locations and concentrations of the electric charges of these “particles”, changing moment by moment, due to that same motion, also continually change the «plásma»’s electric field of forces, sustaining an electro-dynamical field.


A «plásma» thus generates, by the continual motions of its electrically-charged constituents, an overall or collective electro-magneto-dynamic field of forces.

That field of forces, in addition to acting on anything external to the «plásma», to a degree dependent upon the physical-spatial proximity of such an “anything” to the «plásma», also acts  self-reflexively and self-refluxively  — on the «plásma» itself, also because its constituent “particles” are electrically-charged, rather than being mostly electrically neutral[ized], as in typical gas-phase matter.


The «plásma»’s field continually changes the motions of its constituent “particles”, and thus changes the electric/magnetic fields that they are generating.


Those “particles” changing positions/motions thus change their collective field, which changes their collective motions, which again changes their field, which again changes their motion. ... 


Nonlinear self-consistent motions are thereby possible, whereby the «plásma»-internal, self-generated field also guides the «plásma»’s “particles” to reproduce their very pattern of flow by which they generate that «plásma» field which, in turn, generates that «plásma» flow . . .  viz. --

“The field. . .is termed ads “self-consistent”.”

“It is determined by the distribution of particles and in turn influences their motion . . ..”
[N. N. Kalitkin, D. P. Kostomarov, Mathematical Model of Plasma Physics, http://www.eolss.net/Sample-Chapters/C02/E6-03A-03-03.pdf ].

-- and --

“This thesis investigates self-consistent electrostatic structures in plasmas and related collective systems. “

“They are coherent structures in which particles become trapped in the wave potential.”

“These phenomena require a kinetic description i.e. a description in which the velocity distribution of the particles is taken into account.”

“Trapping structures extend the areas in configuration space in which a plasma is unstable.”

“The main argument and result of this work is that there exist certain kinds of perturbations of an equilibrium that can destabilize the plasma, even if linear theory predicts stability.”

“The usual procedure in plasma theory of analyzing the stability of a plasma by means of a linearization of the equations is therefore questioned.”
[Alejandro Luque Estepa, Ph.D. Thesis, Notes, “Electrostatic Trapping as a Self-Consistent Phenomenon in Plasmas and other Collective Systems”, http://trove.nla.gov.au/work/5306782?q=subject%3A%22plasma+instability%22&c=book&versionId=6172546 ].


This dialectical process thus foments a sustained self-re-iteration; a self-consistent state [or dynate] of motion; a consistent-with-self [consistent-with-continuation-of-self] /- consisting-of-self’, self-reproducing motion of the «plásma».


Indeed, the ‘“asymptotically stable”’ solutions of the «plásma» equations, corresponding to actual long-maintainable flows [to spatio-temporal attractors, as contrasted with fleeting, “measure zero”, virtually unobservable transients], must typically have this dynamically self-consistent, self-reproducing character.


Along with any additional influences, acting upon it from its outside, from its ‘externity’, the «plásma»’s ‘internity’ thus interacts with itself, self-reflexively and self-refluxively driving its own internal motion, hence, its auto-morpho-genesis, and its auto-meta-morphosis, as a subject-verb-object-identical eventity


The «plásma» phase of atomic / pre-atomic matter-energy, thus, at least in part, exemplifies a self-forming content — a partially ‘self-shaping’, ‘self-molding’ phase of matter-energy, characterized by ‘self-[induced-]plasticity’ as well as by ‘other-[induced-]plasticity’.


The text Dialectical Ideography, in its Section 1. b., entitled Why Dialectical?, glosses a hypothetical fusion reactor design, which F.E.D. has dubbed the Cyclonetron design [link:  http://www.dialectics.org/dialectics/Dialectic_Ideography_files/5_Dialectics-Part1b-WhyDI_OCR.pdf ].

This design hypothesis is based upon, not a "magnetic bottle" equilibrium, imposed upon the «plásma» by external magnetic fields, but a plásma» bottle', a bottle "made of «plásma»", such that the «plásma» is confined by its own, internal -- internally-generated -- fields, that is, the «plásma» is confined by means of a dynamical, non-equilibrium 'self-confinement'.

A «plásma» can potentially generate and contain and anchor fields which are far stronger -- and far more effective at confining that plasma -- than the fields that any external, solid-phase magnets and/or electrodes can sustain, and still remain in the solid phase.
This design hypothesis is based upon the propensity or proneness of ‘‘‘flowing media’’’, or ‘‘‘rheids’’’  — whether they be the » electro-neutral liquid or gaseous ‘‘rheids’’’ described by the [nonlinear] Navier-Stokes system of equations, or the electrically-charged, ‘electro-magneto-active’ and ‘electro-magneto-self-active’ «plásma» ‘‘rheids’’’ described by the [nonlinear] Maxwell-Boltzmann-Vlasov [vector-]equation(s), by the Klimontovich equation, and by the Liouville equation — to “spontaneously” generate, i.e., to self-generate’, ‘‘‘cyclonic’’’ [and ‘‘‘anti-cyclonic’’’], or ‘‘‘self-re-entering’’’, vortices‘‘‘toroidal vortices’’’.


This ‘‘‘genericity’’’, by ‘‘‘rheids’’’, with respect to ‘‘‘toroidal-vortical flow-forms’’’, may be related to the ubiquitous, ‘‘‘particle-like’’’, ‘‘‘solitary wave’’’, or ‘‘‘soliton’’’, solutions that have been derived, in closed-form, for a very large and diverse variety of one-dimensional, nonlinear, partial-differential wave-equations. 

‘Neo-closed-form’ ‘‘‘toroidal vortex’’’ solutions, or ‘‘‘cyclonic vortex’’’ solutions, may be the true three-dimensional generalization of those closed-form, one-dimensional, ‘‘‘solitonic’’’, nonlinear wave solutions


We conjecture that non-pulsed, continuously-“burning” fusion reaction may be maintainable at the ‘‘‘heart’’’ of the ‘“eye”’ of a «plásma» toroidal vortex, or «plásma» micro-hurricane, induced into ‘‘‘self-precipitation’’’ in a «plásma» control-chamber whose parameter-vector of control-parameter-value set-points is appropriately tuned, e.g., via engineering guidance received from the ‘neo-closed-form’ solution of the «plásma» equations.

This conjecture is depicted below.




In the above-depicted hypothesized nonlinear self-consistent motion of the «plásma», fresh fusion fuel is injected at the base of the ‘«plásma» cyclone’, then ‘vortically’ conveyed up the ‘eye chimney’ of that ‘cyclonic «plásma» vortex’, and concentrated maximally, umbilicoid-like, at the ‘‘‘heart’’’ of that ‘eye chimney’ -- approximately half-way up that ‘eye chimney’ -- by «plásma»-borne ‘electro-magneto-dynamic’ fields, stronger than any solid-state -- e.g., metal -- magnetic field coils and/or electrodes, could source, without themselves being converted to a molten liquid phase, to a vaporized gaseous phase, or even to an ionized «plásma» phase, thus with sufficient field-strength to overcome the Coulomb mutual repulsion of the fusion fuel nuclei, thereby bringing these nuclei into a proximity sufficient to ignite, and to continuously sustain the ignition of, the fusion reaction, thence continually, ‘vortically’ conveying the fusion reaction products up and out of the top of the ‘eye chimney’ for removal, in a continuous toroidal motion, the motion of a «plásma»-constituted torus ‘rolling upon itself’.











Monday, June 24, 2013

Marxian, Dialectical Social Science: The Way Forward for Humanity -- in Brief.

Dear Readers,

Sometimes brevity is of value, even with respect to extraordinarily complex issues.

Below, I have provided an extremely brief summary description of what I hold to be the way forward, for humanity, out of the present death-spiral of the capitalist system, and out of the human species extinction to which that death-spiral leads if that way forward is not taken.

Of course, to be so brief, it must eschew explaining the "why" and the "how" of the way forward that it summarizes.

Hopefully, the previous posts to this blog, for their readers, and the posts to this blog that are to come, will adequately address those more detailed questions and explanations.


Regards,

Miguel









 
THE WAY FORWARD FOR HUMANITY, OUT OF THE DEATH-SPIRAL OF THE PRESENT, 'DESCENDANCE-PHASE' CAPITALIST SYSTEM --


In Practice, in Law [Constitutional and Statutory], and in Social Principle, 

Expand Social Equity from Capital Equity only -- from Equity for Capital-owners only; from Stockholders-only Stockholder Economic Democracy -- to encompass Universal, Citizens' Equity, with checks and balances against BOTH concentrated state/political power and concentrated private/economic power:  institute Stakeholder Democracy; Political-ECONOMIC DEMOCRACY, by means of the constitutional establishment of (1) Citizens Externality Equity, (2) Citizen Birthright Equity, and (3) Citizen Stewardship Equity.

Restart the socio-ecological negentropic growth of the social forces of production:  overthrow the fetters of the Petroleum/Finance Plutocracy and deploy Fusion Power globally.

Marxian, Dialectical Social Science: Capitalism's Fatal Flaw -- in Brief.

Dear Readers,

Sometimes brevity is of value, even with respect to extraordinarily complex issues.

Below, I have provided an extremely brief summary description of the fatal flaw of the capitalist system.

Of course, to be so brief, it must eschew explaining the "why" and the "how" of the fatal flaw that it summarizes.

Hopefully, the previous posts to this blog, for their readers, and the posts to this blog that are to come, will adequately address those more detailed questions and explanations.


Regards,

Miguel










THE FATAL FLAW OF THE CAPITALIST SYSTEM --

The growth of the social forces of production -- of social productivity -- which capital initially fosters, is net profitable for Capital, initially, but, later on, it begins to literally destroy Capital itself, as that growth continues and deepens.

Hence, Capital then turns against, and begins to attack and to destroy, the very prosperity, the very freedom, the very growth of the social forces of production, and the very working population, which Capital initially promoted, as a by-product of its quest for net profitability, for self-financing re-investment of profit, and for its own expansion/accumulation/growth.










Part 08 of 29. THE DIALECTICA MANIFESTO. Nonlinearity, Autokinesis, and Dialectic.

Full Title:  Part 08 of 29 --

The Dialectica Manifesto

 

 

Dialectical Ideography 

 

and 

 

the Mission of F.E.D.




Nonlinearity,
<<Autokinesis>>,
and
Dialectic.







Dear Readers,

I am, together with F.E.D. Secretary-General Hermes de Nemores, and F.E.D. Public Liaison Officer Aoristos Dyosphainthos, organizing to develop a new, expanded edition of the F.E.D. introductory documents, for publication in book form, under a new title --

The Dialectica Manifesto:  Dialectical Ideography and the Mission of Foundation Encyclopedia Dialectica [F.E.D.]
 

-- and under the authorship of the entire Foundation collective.
Below is the eighth installment of a 29-part presentation of this introductory material, which the F.E.D. General Council has authorized for serialization via this blog over the coming months, as we develop the material.

I plan to inter-mix these installments with other blog-entries, including the planned additional F.E.D. Vignettes, other F.E.D.  news, my own blog-essays, etc.


Links to the earlier versions of these introductory documents are given below.





Unlike the typical blog-entry, this series will attempt to deliver an introduction to the Foundation worldview as a totality, in a connected account, making explicit many of the interconnexions among the parts.



Enjoy!!!



Regards,

Miguel









Nonlinearity, «Auto-Kinesis», and Dialectic.

If nonlinearity is the root cause of this mathematical difficulty and “intractability”, and if nonlinearity is the root cause of this present “closed-form unsolvability”, then what doesnonlinearity signify?


In its deepest meaning, nonlinearity signifies what Plato called «autokinesis» [see below].


¡Differential-equation nonlinearity is the mathematical name for mathematical, ideographical, ‘equational’, ‘purely-quantitative’ modeling of self-motion, of self-motion, of self-[induced] movement’; of self-induced change-of-state; of self-reflexiveness [cf. Russell], that is, of self-reflexive, self-referential action; of self-refluxiveness and of self-refluxive action, that is, of action which flows back to and changes its source, its agent, its subject -- and, thus, of self-developing process, or of developmentally self-propelling, self-developing eventity!


These equations -- equations that the presently absent, presently-unformulated ‘‘‘closed-form’’’ function-formulae solve -- are called nonlinear because, in them, the unknowns [which, for integro-differential equations, are function-unknowns, not single number-values as are the solutions of algebraic, diophantine equations], the so far unfathomed solving-functions, appear, with their function-values, or with the values of their derivative-functions, and/or with the values of their integrals, operating upon themselves, and/or operating upon one another.

  
Conjecture:  Such signifies the dynamical, i.e., the time-like [indeed, the chronogenic], interaction and self-interaction of the underlying actualities that these unknown solving-functions must mime.


Linear integro-differential equations, the kind that have for so long been so easily solved by Terran mathematicians, are characterized, in contrast, by function-unknowns which occur in “isolation”, singly, independently, without interaction, operating upon / multiplying neither self nor any other unknown / to-be-solved-for function(s).


A typical nonlinear “ordinary” or “total” differential equation is an ideographical state-ment’, that asserts -- that “states”, in effect -- that the instantaneous velocity of evolution of the generic, pure-quantitative value of the state of the system modeled by that equation for any, generic time-value, t — the state represented by x(t), thus denoting the generic state-function-value of the dynamical function-unknown to be solved for — is proportional to a higher power of that unknown, generic state-value itself, denoted x(t)n, n > 1, i.e., to a multiplicative self-application / self-operation / self-flexion or self-re-flexion; to a self-multiplication, of that state-value.


Such a purely-quantitativeself-multiplication signifies:  either (1) a [purely-quantitative’]self-magnification, or; (2) a [purely-quantitative’] self-diminution’, of one or more of the values of the state-variable(s) of x(t), for every [‘non-Boolean’] value of the state-variable-value components of that state-“vector” function, x(t)  =  x1(t) + . . . + xm(t)


That state-“vector” function is, in effect, a ‘“list”’, or, more precisely, a “non-amalgamative sum”, of m “state-variables”, x1(t) through xm(t), each one reflecting a model-predicted value of a different prime “vital sign” measurement of the system modeled by that state-“vector” function, x(t), as of a given value of t.  Let us herein call that system as a whole by the name X.


Such an equation describes a system’s “evolution” as an at least partially self-induced, or autokinesic’, self-driven, self-propelling motion in a state-space, or ‘space of states.


“State Space” an imagined space, or conceptually-constructed space, in which every point denotes a different possible state of that system, as a ‘“list”’ of that system’s vital signs.


For example, nonlinear differential equation models of predator-prey population-count dynamics, or bio-mass dynamics, within an ecological system, often contain a population-size, or bio-mass, self-limiting Verhulst term -- a ‘“self-interaction term”’. 


This term involves adding in, e.g., a self-multiplication of Ni(t), where Ni(t) denotes the population-count-as-state of the ith species as a function of time, t, such that a minus sign is applied to that self-product[ion], thus registering as a negative contribution to the momentary, “instantaneous” rate of growth of that species’ population-count — where that rate of growth is here defined as the metric for the rate of evolution, or velocity of evolution, of that species’ statewith respect to time, as the [“continuous”] time ‘‘‘count’’’ advances

The nonlinear correction term is referred to as a self-interaction . . . term [which term we also term self[-re]-flexive [‘‘‘bent back upon itself’’’] or self[-re]-fluxive[‘‘‘flowing [from self] back to self’’’] —  F.E.D.], of the form Ni(t)2 . . . where the terms of the form Ni(t)Nj(t), i ~= j, also quadratically nonlinear, are referred to as mutual interaction terms [which terms we also term hetero-flexive’ or ‘allo-flexive’, meaning ‘‘‘other-bent’’’, or ‘‘‘bent by other-than-self’’’F.E.D.].
 
[R. Dutt, P. K. Ghosh, “Nonlinear Correction to the Lotka-Volterra Oscillation in a Predator-Prey System”, in Mathematical Biosciences [27: 1975], pp. 9-16].




The equations of Einstein’s mathematical model of the ‘“universal gravitational field”’, that is, the equations of his General Theory of Relativity, are nonlinear  precisely because they must model the non-a-tom-istic, self-reflexive, auto-kinesic, self-changing self-interactivity of the cosmos-encompassing gravitic ‘‘‘field’’’ --
 
...an interaction is non-linear if the total force exerted by several bodies is not the sum of the forces each would exert if acting alone.”

Why is the gravitational-inertial interaction non-linear?”

“The reason is a fundamental one.”

“We saw at the end of the preceding chapter that all forms of energy have mass and so act as a source of gravitation and inertia.”

“This is true, not only of matter and of light, but also of gravitational potential energy.”

“We know that this form of energy has a real physical significance; it has to be included in a total energy balance . . ..”

This means that when two bodies act together as a source, in addition to their individual masses we must take their mutual gravitational potential energy as a source.”

“The total force is then not the sum of the individual forces.”

“... It follows that the exact interaction between [better, amongF.E.D.] an arbitrary number of bodies is going to have a complicated form.”

“Indeed, as we shall see, it has not been possible to formulate this interaction in an explicit way.”

In consequence, our previous calculation of the total inertial force due to all the matter in the universe is neither strictly correct nor easily correctable.”

“We can only hope that our linear approximation gives an answer that has the correct order of magnitude . . ..”

“In view of all these difficulties, how was Einstein able to write down a law general enough to specify all the properties of the non-linear gravitational-inertial interaction?”

“The answer is that he wrote down the local properties of the interaction, using the field point of view.”

“From this the global properties of the interaction between [better, amongF.E.D.]  distant bodies can be calculated in principle, although in practice no one has been able to do this exactly even for just two bodies, except in the limit when one of them has a mass negligible compared with the other . . ..”

“It is instructive to look at this self-interaction of the gravitational field from a slightly different point of view . . . inertial forces act on gravitational waves and, if the Principle of Equivalence is correct, so must gravitational forces. ...”

“This shows how essential is the self-interaction of gravitation. . ..”

“It is one manifestation of the fact that gravitation acts on everything . . ..”

“We then have a self-interacting gravitational field satisfying a non-linear field law.

[D. W. Sciama, The Physical Foundations of General Relativity; Doubleday [New York: 1969]; pp. 55-62].




Thus, for the past 300+ years human knowledge and industry have been partially paralyzed and vitiated by a perennial failure to “solve” general nonlinear integro-differential equations, that is, to attain the means by which the vast potential knowledge that especially the laws of nature equations among them encode can be explicitly extracted and practically applied.
Key instances of this incapacity include --

·         the Newton gravity-equations for more than two mutually-gravitating bodies, the Einstein universal gravitational field equations of General Relativity just addressed in the quotation above;

·         the Navier-Stokes equations for electro~neutral liquid / gaseous hydrodynamics, and;

·          the ‘‘‘electro-magneto-hydrodynamics’’’ of the Maxwell-Boltzmann-Vlasov equation for electro-dynamically non-neutral, ‘‘‘magneto-hydro-dynamical’’’ “plasmas”, e.g., for superheated, ionized gases — that is, for the very media in which nuclear fusion reactions, self-sustaining over ‘mega-macroscopic’ spatial and temporal scales, are observed to occur in extra-human nature, e.g., in the central core-regions of stars.