handedness

26.I.1430

Drawing what they wrote on chirality and helicity.

"a standard clock, tossed with its face directed forwards, has Left-handed helicity." (wp>Chirality_(physics))

This is only a reaction note, without benefit of a fuller image yet.

The discussion of chirality and helicity ought to cover the notion of handedness and particularly parity. More importantly and as with other properties of matter (observables) it should also cover the group structure of these properties - understanding which is alas in progress.

An object has chirality if it is not identical to its mirror image. Chirality coming from the greek Chir for hand thus literally means handedness.

A chiral object will not superimpose with its mirror image. The term mirror image misleads a bit. For when I thought about this I visualized placing my left palm over a mirror which superimposed perfectly with its mirror image. Instead, what is meant is rather better described as a reflection about a basis axis.

More precisely a chiral object is not identical to itself when reflected about one axis or the other.

This reflection, an isometry transformation corresponds to a reversal of orientation.

Mathematically this is expressed by applying an orthogonal matrix to the particle's vector. The determinant of such a matrix is either 1 for a chiral object or -1 for an achiral object.

It thus that the left hand (or foot or glove or coffee mug with handle on the left) is the reflection of the right counterpart.

The electric field of a charged particle is achiral, invariant under reflection. But the magnetic field of a moving charge is revered under the reflection.

As an aside, This transformation is called an isometry because it preserves the norm (or metric) of the vector. Such reflections that either preserve or reverse orientation keep the coordinate origin fixed (it is only a reflection about a given axis). Such transformations are thus also considered Lorentz transformations, a subset of linear transformations.

The symmetry or asymmetry properties of chirality and helicity are studied through the representations of Poincare groups and their subgroup the Lorentz group, and their decomposition into further group representations. But detail on this hopefully comes later.

In the case of a Dirac-fermion that has mass such as a quark or an electron , Helicity is the projection of the spin vector S onto the momentum vector p. i.e., a dot product
h = S.p .

In the "massive" case, whereas helicity deals with whether the object transforms in an right-handed or left-handed way, chirality is the property that an object is not identical to its mirror image. Switching between an object and its mirror image is called leaves some properties unchanged such as mass. This transformation is thus a symmetry on mass (among other things) called parity.

But if there is no mass, there is also parity of spin. Ie the spin appears to be in the same direction as its axis of motion regardless of perspective (direct or mirror image). I could be wrong on this however.

When there is no mass, (and consequently no momentum) Helicity is the product of the chirality operator (which takes values -1 or 1) multiplied by

Consequently helicity has one of two values and .

So if we imagine that the two clocks shown above as (massless?) fermions or particles with half-spin ,
the clock on the left is
a lefthanded clock with
chirality =-1
helicity h=
the clock on the right is
a righthanded clock with
chirality =1
helicity h=

Nonetheless another page at wp (wp:Chirality_(physics)) makes an apparently contradictory statement: for a massless fermion (with spin 1/2) such as gluons, photons and gravitons, chirality is said to be the same as helicity.

Because helicity depends as it were on the state of motion of the body (massless or not), viz. the direction of its axis of motion , then it appears it is not an intrinsic property of a particle.

On the other hand, chirality which is a simple yes/no case, seems to be an intrinsic property - indpendent of the quantity or direction of motion , and likewise independent of the point of view of observer (or coordinate transformation).
- more -

acknowledgement: the image of the clock itself comes originally from a google image search thumbnail of the clock image at www-math.cudenver.edu. The thumb has been sheared vertically by 15 degrees and reflected horizontally.

... Read more

what is pneumatics?

25.I.1430

Pneumatics is a certain outlook on knowledge that will take it seriously when it is told things like God blows a life giving breath into living things , and other things which to a "pure reason" scientist are fantastical.

It is a believer's "science" or rather epistemology. For its aim or pretension, it seeks to integrate religious beliefs and scientific knowledge, putting either in the context of the other.

Effectively, pneumatics replaces the a priori assumption of atheism or materialism - alias "pure reason" to some - with the a priori assumption/choice of theism and axioms of religious belief.

Returning to the example pneumatics would accept the notions of a spirit in living organisms and even try to account for it in as empirical or analytical a way as possible.

Thus it will note much like scientists - or indeed elementary school pupils - the things that set "life" apart from inanimate things even though both classes are constituted of the same matter. Namely that they are endowed with complexes of autonomous self-regulating mechanisms. It would note this is the most-physical description possible yet of a soul, a sort of ordering or organizing principle endowed by the Divine.

Unlike modern "science", instead of saying spirit cannot be seen therefore it does not exist until proven otherwise, pneumatology (or pneumatics) having accepted its existence as a given , would say that the closest we've come to seeing "soul" is in that it is closely associated with those homeostatic processes unique to life.

In a further sweep we could even say the "fast" homeostatic mechanisms of life - which must be the result of spirit, also belong to a spectrum or processes that also includes those subitted by inanimate matter - paving the way to rationalising another religious belief - that inanimate matter is not so inanimate after all and that it too is endowed with such things as consciousness comfort and discomfort and so on.


We can recall the italicized greek word "biota" indicates a duality perhaps precisely that of the presence of matter and of something else, the soul in living organisms.

In other words, pneumatics is much ado about how and what religion-believing scientists really think, in the privacy of their thoughts, or the security of their home countries' campuses - not in international symposia or western academic campuses.

It would thus have to admit that it is not "science" in the modern academic sense of the word of hard or natural science. Nor it is necessary to call it "pseudoscience". It simply is a paradigm of knowledge , or better, an epistemology (ie, a set of knowledge-defining and knowledge-ordering principles).

Attempting to express religious beliefs and scientific knowledge in terms of each other, and reconcile both in a coherent body of knowledge also leads to such endeavours as reasoned apologetics, eg for ritual and other things, much like the ancient practice of "kalam", but hopefully i ways that are a lot more careful, and knowledgeable.












... Read more

control theory not good for social theory

12.I.1430

Elements of control theory are often tempting as metaphors in the context of social organization. But treating such analogies as readily mappable to the social subject is a mistake.

As an example , here's an ostensible pearl of wisdom that : "A first-order control mechanism is any mechanism that is controlled by direct motion in a single direction. Similarly, in social theory, a single direct action producing a social change is a first-order control system." (wikipedia) .

This example in itself is innocuous enough. But just a question why would such a taxonomy be useful to social scientists? Why try to be social engineers? Haven't they all watched Adam Curtis' movies? By this question I mean, haven't they learned the disasterous effects of treating society as a machine (it's not) and making atrocious assumptions about human motivation?

tirade segment: haven't the bolsheviks miscalculated human motivation? didn't Hitler miscalculate the anglosaxons' motivations? Weren't both the cold war and the economic restructuring of the post-revolutionary quarter century a result of a very paranoid and a most cynical interpretation of history and economics?

I cite the Adam Curtis movies because they readily convey how a lot of the international politics (eg, the cold war) of the past half-century have evolved out of attempts at mathematical modeling stemming from game theorists who played games called "fuck you buddy", that sought to highlight the utility of betrayal and mistrust. I was left with the impression that such theory encoded the personal paranoia of its authors - particularly after watching John Nash and other supporters admitting as much !

Likewise it seems economic theory is at best based on stupid assumptions. But it's useless to debate them because they are discredited by the practitioners of those theories. For instance, they seem to take natural self-regulation as a guiding principle for the market and "the invisible hand". Yet in practice, the choir and agressive imposers of the theory's policy implications have been practicing selective protectionism (selecting that which protects their voters' interests), anti-labor violence, tying aid to "freer" markets, and interest rate manipulation all along. This is to say nothing of chronic and endemic cheating on the balance sheets by all the biggest players - as the past nine years have repeatedly shown us.

So we could criticize the notion of self-regulation, that it is not so instantaneous. Self-regulation is a long winded process, taking much longer in nature than the flashing intervals of market cycles. But it would be useless.

Another fact that undermines economic theory is its acceptance of the banking model of monetary supply as a given. Nonetheless, it should not be a given. it is a swindle. and should be thoroughly replaced with someone reflecting true value, and given the sovereignty of the state not the investor.

So when I see the terminology of control theory being applied so cavalierly and needlessly in social science, I worry. Because this translates into blind and ruthless policies under which millions get crushed figuratively or literally.


P.S.

Disclaimer: i've written before about social organization as well as information transfer, not in engineering terms, but in a formal framework. This was within the computational context of artificial multi-agent systems.

The idea was to apply the obvious social analogies for the sake of designing interesting schemes of social organization for artificial agents, in the vein of bio-mimetics. Not the other way around.

The study of information transfer has for its intent only the study of human communication, and not the control or tailoring of communication.

... Read more

quotations dept: surplus value

12.I.1430

"Every day I watched how a bare metal frame, rolling down the line, would come off the other end, a spanking brand new car [Lincoln-Mercury automobile factory, Detroit]. What a great idea! Maybe, I could do the same thing with my music." -- Berry Gordy Jr. Motown founder. ... Read more

candles in the dark شموع فى الظلام

 

In the course of the past week while a terrorist bloodbath (human political and cultural) unfolded next door a few events gleamed in the gloom.

Now to sample a few without further ado:

1- Greece - a longtime supporter of justice for Palestine - sends aid. This is despite its recent civil woes. This was a Greek government action in perfect consonance with the will of the Greek people, even though the two have been at loggerheads and youth demonstrating against them. It was a moment where all Greece, Ellas, spontaneously came into unison to sound a harmonious note ; aid to Gaza. Gia'sou. (btw, did Egypt let it through?)



2- people across the near east and as far as the sind, the EU and the transatlantic protest in large numbers.
Except in our "near east", the protestors are not overly opressed (fallout of the financial meltdown which is a Madoff-like swindle but multiplied a hundred-fold?)
Also indicative of this laissez-faire is the notable absence of agents provocateurs. This, despite the agitations in Ellas anfd Fce coupled with the associated whirled bank head's warning of civil unrest all of which could have been played up here.
But there was apparently no will to do so.
Everybody, even the PDs' agents-provocateurs are impoverished , clipped by practically the same financiers of the psychotic mayhem in Gaza. Perhaps the police's agents provocateurs stood in the demos and remained peaceful this time in order not to undermine their own cause.

3- Louder voices have come also from the very nation that injected the zionism into our oriental and arab midst. justice'n'peace fixtures Ken Livingston, George Galloway the Respect MP; from the novel quarter of the brit-music universe, music past master Annie Lennox and UN activist Bianca Jagger called on Obama the PE to cut the chicken-dove and "but he'th thtill the prethiden'" weasel act s and say or do something.
Reference: (in arabic) Brit activists call on Obama to break his silence.



4- Also from the brit-music universe, electronic/ambient music guru Brian Eno wrote a piece on Gaza.
OK. These statements, in the persons of Eno and Lennox make up a bit for when McCartney took that whiz in the Jordan. Macca are you listening to them? Do you regret your misplaced whiz?

5- This quote by Jonathan Cook: "In a country such as Israel, with a citizen army, the public has become positively phobic of a war in which large numbers of its sons will be placed in the firing line. That fear is only heightened by reports in the Israeli media that Hamas is praying for the chance to engage Israel’s army in serious combat. The decision to sacrifice many soldiers in Gaza is not one ... the Labor Party will take lightly with an election in six weeks."

6- The very candid report by UN special rapporteur Richard Falk in which he detailed the humanitarian catastrophes visited upon Palestinians in Gaza by the zionists, in spite of his being both jewish and American. In his words there was none of the serpentine zigzagging and fudging of crucial context and detail we are accustomed from the so-called "zionist doves" like Avnery, the oh-so-Gushing shalom and the other fakes.
His uncompromising reports can be read here and here.

7- In contrast to the Mr-Obama-chicken-dove-goes-to-washington roadshow, Cynthia McKinney and a group of remarkable human beings (including Mr. Sami al-Haj)


Mr. Sami al-Haj, wrongfully detained at Guantanamera guajira guantanamera camp for seven years and recently released.

have risked their own lives (yet again) boarding a relief boat that headed for Gaza from Cyprus despite the air bombing campaign. The civilian boat, Dignity, was rammed in its larboard (port, ie left side) bow , a clear proof of intent, and a crime of international maritime law. The Dignity was rammed two more times by Israeli patrol boats.

The Atlanta Journal Constitution , the newspaper of record for the bible belt state of Georgia , actually used this misleading headline "McKinney relief ship, Israeli vessel collide ". OneNewsNow's headline went for the jugular: "McKinney seeks publicity, endangers crew in Gaza."


Photograph: Ali Hashisho/Reuters

The damaged ship which had set out from and with blessings of the Cypriots, as one of their parliamentarians Dr. Elena Theoharous was also among those on board, putt-putted to safe harbor to Soor in Lebanon, licking its wounds from the gaping hole on its larboard. It was thus that Cynthia thankfully lived to tell the tale.

8- from the churchillian and often antagonistic Fisk:
of all people, he managed to sound a consonnant note for once in a blue moon in his article, "The rotten state of Egypt is too powerless and corrupt to act" , Thursday, 1 January 2009. In it he managed to take up issues that go to the heart of Egypt's struggle under its valetudinarian government. Though he did not spare the easy target his usual robust denigrations and race-tinged sneers. He faintly echoed the thoughtful arab op-ed وجهات نظر - مصر.. العدو في الداخل by `Atef Mu`tamad (Atef Mutamad) (as did I echo him, in previous posts ("resign already") and future ones ("on egypt and lebanon part 1 - egypt") ).

9- Throughout all this was the near omnipresence of aljazeera. i am not and would not intentionally plug it. This is simply an empirical observation. It was always there: in Gaza, on the boat the Dignity, at Rafah, in London, at the worldwide demonstrations, reprinting and commenting on Fisk and on Egypt and so on. Unlike most the rest of the world's news media.

Cependant, Egypt's antidandruff shampoo appear to act, rather conspicuously, the way turncoats feigning indignation do. Whether it is an act of egyptian cryptography is anybody's guess. Then there are Lebanese (and likely israeli agents provocateurs posing as lebanese) lobbing shame grenades not just at Egypt's head and shoulders, but at the entire population - which for the latter is a rather tenuous proposition. Qatar patronizes the cause , though its aid did get turned back , rerouted to the incommunicado israeli gates instead. Qatar , if only through aljazeera, plays up the complacency of Egyptians as if they thesmelves haven't been hosting US terrorist forces as well as the ooze-spurting conference of the WTO. Abu Mazen vowed to kick back in NYC until the security council forces a cease-fire (it might as well be until Sharon levitates 100 feet in the air and glides gleefully past high-rise windows) or realistically until the us and israel decide it's time to stop. This while "our man in Ankara" Mubarak kicks back and takes in some of that lingering whiff of High-Porte gravitas from Mr. Erdoğan.

The 9 items above were like candles. But the vaudeville numbers in the preceding paragraph remain a part of the gloom.

(An unabridged unproofed vulgar version is at the alter-blog)

- 30 -

P.S.

The doubt lingers whether I am not falling for elaborate strategems of opinion forming. As though one is supposed to think Israel is bad, the PA is a bad, hamas is bad , iran bad, al jazeera good, egypt bad, or hamas good, all arab leaders bad ; bad bad good ; good good bad. bad good bad. good bad good.

Such guessing at the actual hands of cards that state and media players are clutching is pointless, miring one in mirrored irrealities.
Only the spontaneous reactions of people around the world provide a concrete indication of reality.

 

... Read more

Last Call: Save Gaza

Save Gaza for the sake of Jesus' memory at least.

When Mary and Jesus alayhim a'salaam took refuge in Egypt, they couldn't have done so by crossing the Nejef dessert. It must have been close by the shoreline , though not directly on the coastline of course to escape jewish persecution. So it was via Gaza that their refuge was accomplished.

And no Jesus was not a jew, anymore than Mohamed was a polytheist or Moses was a Horus worshiper .

Save Gaza, the holy land from the same hands that choked it and the truth for so many decades. Save them from the same hands that bankrupted world economy for the n-th time. From the same hands that brought us the bolshevik massacres and brought on the fascist massacres of the 20th century. Fro the same hands that used the crown jewel of physical theory to build atomic weapons. From the same hands that impoverished the world and spread guns alcohol and pornography in it.

Save Gaza. This is the last call ! ... Read more

Genetically modified lies

examples of uninformed apathetic design extend above & beyond the domain of software. GM crops with their tons of fertilizers and insecticides apparently do not match the crop yields of Akkadian farmers of 40 centuries ago - and we're not even talking the unusually rich egyptian soil - without any of the disasters attendant on GM agro. ... Read more

information waves - two further notes

- As pulses, sequences of local (one-to-one) information transfer among autonomous agents are better conceived as solitons rather than continuous waves.

- the medium of information transfer which is comprised of constituent agents has a further property of latency (as well as a delay effect in the case of messages incoming from different sources). The latency is not only caused by processing but also by routing decisions - whether and when to pass a message on.

earlier notes on information waves:

informatic notions applied to us macroscopically ... Read more

wormhole problematics

Image: Corvin Zahn, physics education group (Kraus), Theoretische Astrophysik Tübingen, Space Time Travel (http://www.spacetimetravel.org/)
click on image to go to article

1. Would require negative energy density
   * don't know yet why this requirement, 
   * but it is done via Riemann tensor in spacetimetravel.org
   * also mentioned in Motion Mountain - adventures in Physics
     by Christoph Schiller
    * nature asserts limits on energy, mass and length-to-mass ratio: 
      * energy cannot be negative
      * mass cannot be negative
      * limits on Length to mass ratio
2. Would require an infinite horizon
   * I don't know if this refers to the Minkowsky space plane
     that is involved with spherical topology
   * or whether this refers to the gravitational horizon, 
     as in event horizon, the Schwarzchild limit.
   * a general horizon equation is derived from the principle 
     of maximum force in Schiller, p. 445 eq. (238), III ch. 6.
3. Would require enormous radial tension 
   * radial tension, if i'm not mistaken is known in english
    (wikipedia) as radial stress which refers to the pressure
    on matter such as iron rings around a barrel. 
   * weirdly, it is measured in (unit mass x unit Area) per 
     unit length - don't know why yet.
   * requirement is said to be for the material of the wormhole. BUT !
     * why would we need a material per se, is not the wormhole 
     a matter of bending space, or connecting space, or otherwise
     acting on the space topology? Why would a material be needed,
     other than for gravitational mass requirements?
     * unless the radial tension refers to that to which objects transiting
       via the wormhole are subjected. But isn't the idea of wormholing
       to remove amount of time in transit? ie, with a wormhole, 
       there should be no transit! that's the whole point.
       the displacement through the wormhole should be indistinguishable
       from "local" displacement.
4. Question on the behavior of light in or through the wormhole
   * namely the inability of light exterior to the wormhole 
     to interact with its interior , or vice versa.

... Read more

Confucius says

47. 困 K'ouen:
Six at the third place:
This shows a man who is restless and indecisive in times of adversity. At first he wants to push ahead, then he encounters obstructions that, it is true, mean oppression only when recklessly dealt with. He butts his head against a wall and in consequence feels himself oppressed by the wall. Then he leans on things that have in themselves no stability and that are merely a hazard for him who leans on them. Thereupon he turns back irresolutely and retires into his house, only to find, as a fresh disappointment, that his wife is not there. Confucius says about this line:

"If a man permits himself to be oppressed by something that ought not to oppress him, his name will certainly be disgraced. If he leans on things upon which one cannot lean, his life will certainly be endangered. For him who is in disgrace and danger, the hour of death draws near; how can he then still see his wife?" ... Read more

the great natural compressors

the great natural compressors are mathematical formalisms that serve to describe a generalized physical perspective or theory.

For example, there is the group theoretic description of different particles of physics that encapsulates and catalogs their different properties. It is not the only possible way to describe and classify the fundamental particles or fields of nature, but one that happens to be for the moment convenient and popular.

There is also the Hamiltonian formalism to describe the motion of a rigid body , or a chain of them. A system of differential equations can be used to describe completely the thermodynamic behavior and state of an arbitrary physical system. And so on.

The phrase "mathematical formalism" thus refers not merely to a bunch of theorems, but to a distinct coherent scheme of description or model; often one among other possible ones. They encapsulate a great deal of information in terms of two important things. Namely:

(A) the laws and theorems themselves that go into the description or the model.
The formalism usually boils down to (ie, is expressed as / takes the form of a formula of) a single quantity or object
( eg,
the Hamiltonian is the value of the total energy of a system;
the Lagrangian is the action of some segment of a time dependent path (of motion / or in configuration space) defined in terms of some local property of the path ;
the group description is a "representation" (think of it as a set function) of groups of invariant/symmetric and skew/hermitean transformations on observables
).
Despite this, the laws of physics that enter into play in the system being modeled are all derivable from the formalism. For instance, the Lorenz-Maxwell equations of electro-magnetism are all derivable from the Lagrangian formulation. (see [Shankar] ch. 2 for an explicit example of how ; I don't yet know how particle field equations are derivable from group representations).

(B) The formalism readily gives "solutions" that are empirically verifiable when input data is plugged into it.

This is why mathematical formalisms in physics (as in other fields) appear like compression dictionaries (or they are compression schemes). Both functions served by the formalism seem like obvious acts of compression, giving rather fine-detailed and formal descriptions of nature (or whatever the domain of study which is also ultimately a natural subset). These formalisms are a number of conceptual layers up from the underlying "physical theory" (ie the set of proven laws).

They represent a creative act in physical conceptualization / or theoretical thinking, not merely a deductive act. For useful though they are they are interchangeable , not unique. One gaining favor over another by accomplishing a better feat of compression (what is often refered as simplicity, brevity, conciseness, and gaining more generality by separating the field of application from the formal description and manipulation - very much the same way we like to separate content and presentation on computers).

mathematics - ؟ -

These formalisms are even more conceptual layers up from the basic alphabets of literals and idioms and formal patterns we call mathematics. For this seems to be if not the most immediate , than a reasonably good definition of mathematics. It is a set of conventions of linguistic manipulations. Again the spectre of an isomorhpism can be raised between the process of formal reasoning and mathematical expression.

That those conventions have as their by-product the ability to compute, to induct, deduce, the ability to calculate - ie the aspect of calcul or calculus or حساب in mathematics - is the reason we employ them. It's what's great about them.

The quaint thing is, formal though they are, they must be considered part of natural language.


natural vs. formal languages

I do not know why this notion is often ignored (or maybe it isn't) but whatever formal dialects and languages we concoct that are utterly human-readable are to me reasonably considered a subset of natural languages. For two reasons:
1. "we concoct"ed them
2. they are utterly "human-readable".

The arbitrary languages we figuratively feed into state machines in automata theory classes are reasonably formal. Those are the sets of strings acceptable to or generated by FSA ; such as for instance AB*A.

Likewise the programming languages that people develop which are utterly defined , geared to the constraints of a computer architecture are reasonably formal - but frankly the higher-level they are , the more human-readable they become.

But again computer architectures are natural systems.

nature

When we look at what differences there are between the myriad ecological systems that have developed through this planet's history, and the systems that we humans have built ("artificially"), one is tempted to view as a major difference the notion that our artificial systems were consciously developed - rather than emerged.

But nature does not care for conscious acts. although we can study it, bend it to our will, damage it , and hopefully fix it, nature is oblivious to our "will" and our "conscious" efforts.

Our artificial systems are artificial only to ourselves. To any reasonably distant perspective they remain natural systems, as natural as the next quark pair or the next asteroid.

Even within the bowels of human design and architecture, emergence is a common feature and patterns and architectures grow and develop in spite of us.

References

... ... Read more

complex vector algebra must be taught in pre-college curricula

Complex vector algebra (with the generalization of dot product, the inner or scalar product) should be taught in preparatory school curricula , following vector algebra.

This is addition to other absolute necessities in science such as affine geometry, topology , group theory (feasibly one step up from set theory which also are already in pre-college curricula), conditional probability and so on.

It is true not everyone will set out to work in the theoretical physics of fields. Significant patterns in information processing however involve analogues of physical measures (i don't know why they don't call them metaphors) taken in abstract spaces such as data spaces, search spaces, associated weight spaces, etc.

So thus far, complex vector algebra is seen in first in modern physics then in informatics with the myriad applications of its methods in nearly every field.

Sociological research for instance needs to resort to population sampling methods less and less as more comprehensive data is generated state and citizens (societies).

The more creative a researcher can get with what information to induct from and what to search for in the data would depend on how well they can study the input data space. Even though such skills are largely taken up by the software tools they use, the emphasis is on "creative", as in what more information is hidden and not revealed by the classical battery of statistical tools.

In any case, whether all pupils grow up to enter science or not, we all learned real vector algebra in preparatory and secondary grades, and the same should be affored for complex algebra and topology.

So why in prep. grades rather than freshman year at college? Because as is known, the earlier the intake of a technical dialect the more solid its foundation becomes. ... Read more

note on notation and choice of indices

examples of Poisson-Bracket notation: 
  *  [(d)]
  *  [(f)]
  * note how version (f) opts for supercripted indices for one set of canonical
  coords. and subscripted for the other, while the (d) equivalent chooses 
  the simpler notation with all indices subscripted.
  * In [Siegel] [Srednicki] [Aitchison] and others there are discussions on the 
  importance of the choice of indexing scheme used in the QFT commutator formalism 
  - which is already so complicated (;;) .
  * Notation in another version (r) uses square brackets for the PB on the LHS,
  eg. [f,g] , thus making it indistinguishable from the notation used to designate
  the related quantum commutator, the Lie Bracket [a,b]. (Cf. introduction of the 
  commutator in [Shankar])
  * Indeed in __Fields__, Siegel devotes §§A,B in the Symmetry chapter to 
  "Coordinates" and "Indices" resp. [Siegel]
  * [Sussman] calls the superscript indices "traditional"
  * Indexing is usually (almost universally) zero-based. 


-- 24.xi.2008

refs: (of the better/more detailed discussions on indices)

[Aitchison] Gauge theories in particle physics volume 1, 3rd ed.
[Shankar] R. Shankar, Principles of quantum mechanics, 2ed., Yale UP 1992/4.
[Siegel] Warren Siegel, Fields.
[Srednicki] Srednicki, Quantum Field Theory, (c) 2006 , \\ [[http://www.physics.ucsb.edu/~mark/qft.html|book website]]
[Sussman] [Sussman 2001] Gerald Jay Sussman and Jack Wisdom with Meinhard E. Mayer, Structure and Interpretation of Classical Mechanics, The MIT Press Cambridge, Massachusetts, 2001,
http://www-swiss.ai.mit.edu/~gjs/6946/sicm-html/book.html , retrieved 08 aug 2006, 20 nov 2007 and nov/dec 2008. ... Read more

linearity ≅ whole=∑parts?

In general, the main condition or step in proving a set to be a linear space is to show that for any two members f, g of the set under consideration, and for any two reals α,β

a. the linear combination αf + βg is in the set
b. this satisfies closure, from whence follow the remaining axioms 
  if applicable.

As an illusration, consider an operator qcq , L: D → ℝ^ℝ , where D is some set of functions , and ℝ^ℝ is the set of all real valued functions of a real variable.

L is linear, ie, is a linear space if , ∀y∈D, ∀z∈D, ∀α∈ℝ , ∀β∈ℝ

L(αy+βz)= αL(y)+βL(z)

This suggests some meaning. Viz., that operations on / properties of the whole are equal to sums of operations on / props of the parts.

This property appears to be akin to that of self-similarity, suggesting a rather profound meaning for the character of natural organization.

The ubiquity of linearity in the abstract algebra by which we represent natural systems^** (as noted earlier) has such consequences as the integrable character of physical law (discussed elsewhere).

^** if theory were complete then one could say up to an isomorphism, ie, the mathematical formalism is in a one-to-one, onto and domain-covering image of the fields of the physical system being described. ... Read more

Next big wave of jazz: South Korea?

South Korea probably has the best music education in the world this decade. Some of the most elaborate orchestration and scores I've heard this decade was on South Korean movies.

This tells me to set my eyes on what *is* going on in their modern music scene - that is jazz , fusion and electronica.

I think digging through some of that music may be worth its while.

As an optimist, I keep hoping for new directions both for jazz and for popular music (e.g., rock).

Something tells me the language barrier is just not going to afford us the spectacle of a rock revival emanating from the far east - except maybe in terms of hardcore and thrash metal - though these need no revival - they thrive.

But things may be a lot easier going for pop music and jazz. ... Read more