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
27 December 2008
26 December 2008
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
18 December 2008
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
- 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
17 December 2008
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
... Read more
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.
13 December 2008
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
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
10 December 2008
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
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
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
06 December 2008
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
As an illusration, consider an operator qcq , L: D → ℝℝ , where D is some set of functions , and ℝℝ is the set of all real valued functions of a real variable.
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
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 → ℝℝ , where D is some set of functions , and ℝℝ 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
03 December 2008
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
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
28 November 2008
baby group
Part of the skill of the craftsmen behind familiar patterns such as this one snipped from Schiller's sprawling FREE book Motion Mountain,
is that the pattern of interwoven (wicker-like) white lines hides the much simpler structure of the underlying patches of color that have well defined shapes. But already by reducing the size of the figure, the color regions become clearer, and so does the simpler underlying design.
To facilitate identifying the color patches , we simplify the pattern by removing the white lines (roughly) and exposing the pattern that was hidden under their clutter.
The colored patches now become clear:
Now we can consider the transformations on this figure that Schiller talks about, and which were unclear before.
The following is largely a distillation of Schiller's discussion .
One of the symmetry transformations that leave the pattern unchanged is rotations in its plane about the origin.
The pattern is unchanged under rotations of pi/2.
It has only four positions in which it appears identical.
In general transformations on a square that leave it looking the same form a group, called dihedral.
Any transformation or bunch of transformations that leave an object appearing unchanged is called a symmetry.
Any collection of symmetries forms a group, a symmetry group.
For a square we can enumerate the possible such symmtery transformations:
rotations and reflections (flips).
We can rotate a square by &plusminus; 90 180 and 270 degrees , leaving it unchanged.
We reflect a square about either diagonal (flip it diagonally)
or reflect the sq. horizontally or vertically (flip it hor. or vertically) and it remains unchanged.
Along with counting the rotation by 0 degree, which is the equivalent of no rotation, which is called an Identity transformation (meaning no-op or do-nothing transformation) , we thus have 8 possible transformations.
To repeat, These form a group called dihedral, hence Schiller refers to it by its symbol as group D4.
Though Schiller says there is only one transformation - rotation about pi - I don't see it . What i see is that
we have rotations about pi/2 not pi. in other words , yes the figure looks the same when you rotate it 180 degrees,
but it will also look the same when you rotate it ninety degrees. So here either I misunderstand Schiller (more likely)
or something gives.
Apparently he's considering a reflection about pi. yet his group representations use cos n pi/2 and sin n p/2 .
also weirdly he cites a reflection matrix rather than a rotation matrix, unless on (p. 202) he uses a rotation matrix.
With every rotation transformation applied to the figure,
we can see that there are sets of shapes that get transformed into each other with every transformation.
Each set of these identical shapes that get transformed into one another with each transformation is called a multiplet.
To see this, we have the same figure with the multiplet sets enumerated. Again these are the sets of similarly shaped objects that transform into each other under all symmetry transformations (those that leave the properties of the object invariant - here it is the pattern, or the shape - ) such as rotation.
the numbered areas belong each to a multiplet indicated by the number.
Some of the multiplet sets are numbered, with the elements of each set given the number of that set.
Some multiplets are not numbered, but have arrows pointing at them.
Each multiplet as a whole (its entire set of elements) has the same symmetry as the overall figure.
For some of the colored shapes, the multiplet needs four objects to make up a whole multiplet (e.g.,
in the case of multiplet numbered 1 , we have identified its four elements).
Another multiplet, number 5, looks like it has 8 elements, but I am guessing since the symmetry degree of the multiplets is the same as that of the group.
Schiller points out another multiplet that has only one member, the central star. It is a one-element multiplet.
In any symmetry system such as this arabesque pattern, each part or component of the system is "classified" by the type of multiplet it belongs to.
Multiplets are also known as group representations.
More formally than the kindergarten chitchat above,
the representation of a group (aka symmetry group) is
an assignment of linear transformation matrix A(g) to each group element s.t.
A(g ∘ h) = A(g) ∘ A(h)
More formally still it is a homomorphism from the space of linear transformations onto the elements of the symmetry group.
Representations of unitary transformations are called unitary. Unitary transformations are matrices s.t. A*=A-1.
These have eigenvalues of norm (value?) 1 (perhaps leading to principle of gauge invariance? - afterall a gauge is a seminorm, and since norm is always one, gauge is invariant?) and mappings of unitary matrix are one-to-one.
If a matrix is not 121 it is singular, its determinant is zero, and it has no inverse transformation.
Almost all representations appearing in physics are unitary.
time evolution of physical systems is always described by the always one-to-one unitary mappings because these
map from time t-1 to t in a one-to-one fashion.
All unitary representations correspond to transformations that are one-to-one and invertible (both properties ,
equivalent to saying that determinant of the matrix is not zero and the matrix is thus non-singular.
A matrix whose det is zero is called singular as it has no inverse matrix. It cannot thus belong to a group.
Schiller then discusses reducibility of representations , identifying submultiplets , and giving rise to a classification of representations.
E.g., the pattern's symmetry group (called approximate) "has eight elements.
It has the general faithful unitary and irreducible group representations." and is an octet
Giving rise to the notation D4(The so-called "approximate symmetry group") in the given figure, denoted D_4 , has eight elemnts.)
In any case it is from the symmetry that the deduction of the "list of multiplets or representations" that describe the symmetry's "building blocks" is possible.
Apparently other symmetry groups are given for other multipets? ie the representations are reducible to singlets doublets and quartets? This is what Schiller seems to say.
Schiller notes how unlike the transformations of the tiling pattern , which were discrete, the viewpoint transformations under which the world demeures unchanged are continuous and unbounded.
Siegel's Fields also states that continuous symmetry "is one of the most fundamental and important concepts of physics."
Continuity of the xforms means their representations are continually variable, without bounds and notably are magnitudes. In other words, scalars - as opposed to vectors. They can only be scalars.
Schiller notes ominously that in contrast vectors and tensors "only scalars may take discrete values", "may be discrete observables." (p. 204)
But weren't representations just made continually variable b/c nature's symmetry transformations are continuous? sounds a bit coucou .
To make things worse Schiller states that most representations also possess direction.
So they're not scalars anymore ?
Also it is states that symmetry under change of observ. pos inst or orientation => all observables are scalars, vectors, tensors or spinors (in asc. ord. of generality).
BTW rotations form (i.e., are) an Abelian group because g ∘ h = h ∘ g.
And generally it seems that a group has higher symmetry than its subgroups; iow, a group is a "larger symmetry group" than its subgroups. Makeosa della sensa.
* * *
The b&w lines thrown on top of the layer of multiplets (the color patches or geometrically shaped regions) (that get mapped to each other when undergoing transformations like rotation) are not mere spaghetti thrown on top of the rotation group representations.
That is to say, the layer of interlocking b&w lines is not trivial. the new layer is describable - i guess - by a greater number of representations for the transformation group of this pattern. (not sure this is correct though)
... Read more
is that the pattern of interwoven (wicker-like) white lines hides the much simpler structure of the underlying patches of color that have well defined shapes. But already by reducing the size of the figure, the color regions become clearer, and so does the simpler underlying design.
To facilitate identifying the color patches , we simplify the pattern by removing the white lines (roughly) and exposing the pattern that was hidden under their clutter.
The colored patches now become clear:
Now we can consider the transformations on this figure that Schiller talks about, and which were unclear before.
The following is largely a distillation of Schiller's discussion .
One of the symmetry transformations that leave the pattern unchanged is rotations in its plane about the origin.
The pattern is unchanged under rotations of pi/2.
It has only four positions in which it appears identical.
In general transformations on a square that leave it looking the same form a group, called dihedral.
Any transformation or bunch of transformations that leave an object appearing unchanged is called a symmetry.
Any collection of symmetries forms a group, a symmetry group.
For a square we can enumerate the possible such symmtery transformations:
rotations and reflections (flips).
We can rotate a square by &plusminus; 90 180 and 270 degrees , leaving it unchanged.
We reflect a square about either diagonal (flip it diagonally)
or reflect the sq. horizontally or vertically (flip it hor. or vertically) and it remains unchanged.
Along with counting the rotation by 0 degree, which is the equivalent of no rotation, which is called an Identity transformation (meaning no-op or do-nothing transformation) , we thus have 8 possible transformations.
To repeat, These form a group called dihedral, hence Schiller refers to it by its symbol as group D4.
Though Schiller says there is only one transformation - rotation about pi - I don't see it . What i see is that
we have rotations about pi/2 not pi. in other words , yes the figure looks the same when you rotate it 180 degrees,
but it will also look the same when you rotate it ninety degrees. So here either I misunderstand Schiller (more likely)
or something gives.
Apparently he's considering a reflection about pi. yet his group representations use cos n pi/2 and sin n p/2 .
also weirdly he cites a reflection matrix rather than a rotation matrix, unless on (p. 202) he uses a rotation matrix.
With every rotation transformation applied to the figure,
we can see that there are sets of shapes that get transformed into each other with every transformation.
Each set of these identical shapes that get transformed into one another with each transformation is called a multiplet.
To see this, we have the same figure with the multiplet sets enumerated. Again these are the sets of similarly shaped objects that transform into each other under all symmetry transformations (those that leave the properties of the object invariant - here it is the pattern, or the shape - ) such as rotation.
Some of the multiplet sets are numbered, with the elements of each set given the number of that set.
Some multiplets are not numbered, but have arrows pointing at them.
Each multiplet as a whole (its entire set of elements) has the same symmetry as the overall figure.
For some of the colored shapes, the multiplet needs four objects to make up a whole multiplet (e.g.,
in the case of multiplet numbered 1 , we have identified its four elements).
Another multiplet, number 5, looks like it has 8 elements, but I am guessing since the symmetry degree of the multiplets is the same as that of the group.
Schiller points out another multiplet that has only one member, the central star. It is a one-element multiplet.
In any symmetry system such as this arabesque pattern, each part or component of the system is "classified" by the type of multiplet it belongs to.
Multiplets are also known as group representations.
More formally than the kindergarten chitchat above,
the representation of a group (aka symmetry group) is
an assignment of linear transformation matrix A(g) to each group element s.t.
A(g ∘ h) = A(g) ∘ A(h)
More formally still it is a homomorphism from the space of linear transformations onto the elements of the symmetry group.
Representations of unitary transformations are called unitary. Unitary transformations are matrices s.t. A*=A-1.
These have eigenvalues of norm (value?) 1 (perhaps leading to principle of gauge invariance? - afterall a gauge is a seminorm, and since norm is always one, gauge is invariant?) and mappings of unitary matrix are one-to-one.
If a matrix is not 121 it is singular, its determinant is zero, and it has no inverse transformation.
Almost all representations appearing in physics are unitary.
time evolution of physical systems is always described by the always one-to-one unitary mappings because these
map from time t-1 to t in a one-to-one fashion.
All unitary representations correspond to transformations that are one-to-one and invertible (both properties ,
equivalent to saying that determinant of the matrix is not zero and the matrix is thus non-singular.
A matrix whose det is zero is called singular as it has no inverse matrix. It cannot thus belong to a group.
Schiller then discusses reducibility of representations , identifying submultiplets , and giving rise to a classification of representations.
E.g., the pattern's symmetry group (called approximate) "has eight elements.
It has the general faithful unitary and irreducible group representations." and is an octet
Giving rise to the notation D4(The so-called "approximate symmetry group") in the given figure, denoted D_4 , has eight elemnts.)
In any case it is from the symmetry that the deduction of the "list of multiplets or representations" that describe the symmetry's "building blocks" is possible.
Apparently other symmetry groups are given for other multipets? ie the representations are reducible to singlets doublets and quartets? This is what Schiller seems to say.
Schiller notes how unlike the transformations of the tiling pattern , which were discrete, the viewpoint transformations under which the world demeures unchanged are continuous and unbounded.
Siegel's Fields also states that continuous symmetry "is one of the most fundamental and important concepts of physics."
Continuity of the xforms means their representations are continually variable, without bounds and notably are magnitudes. In other words, scalars - as opposed to vectors. They can only be scalars.
Schiller notes ominously that in contrast vectors and tensors "only scalars may take discrete values", "may be discrete observables." (p. 204)
But weren't representations just made continually variable b/c nature's symmetry transformations are continuous? sounds a bit coucou .
To make things worse Schiller states that most representations also possess direction.
So they're not scalars anymore ?
Also it is states that symmetry under change of observ. pos inst or orientation => all observables are scalars, vectors, tensors or spinors (in asc. ord. of generality).
BTW rotations form (i.e., are) an Abelian group because g ∘ h = h ∘ g.
And generally it seems that a group has higher symmetry than its subgroups; iow, a group is a "larger symmetry group" than its subgroups. Makeosa della sensa.
* * *
The b&w lines thrown on top of the layer of multiplets (the color patches or geometrically shaped regions) (that get mapped to each other when undergoing transformations like rotation) are not mere spaghetti thrown on top of the rotation group representations.
That is to say, the layer of interlocking b&w lines is not trivial. the new layer is describable - i guess - by a greater number of representations for the transformation group of this pattern. (not sure this is correct though)
... Read more
27 November 2008
quote of the interval dept.: patience svp
"Patience is a kind of confidence or trust."
src: Waiting.
Also patience w/out work seems like hypocrisy. ... Read more
src: Waiting.
Also patience w/out work seems like hypocrisy. ... Read more
Vexillological deconstructionism dept.:
from arabo-american coincidences,
Cf. pan-arab colors
src: pan-arab colors, uae.
and the flag of the independent republic of rio grande (1840).
src: Image:Flag_of_the_Republic_of_Rio_Grande, public domain.
This flag also adds to the collection of the American/panamerican motif of stripes and its use throughout the offshoots of the Spanish empire; and particularly stripes with cantons or other divisions as shown in this flag. this collection is still unfinished.
This is not to imply the coincidence lies much deeper. For unlike their arab counterparts, the present-day occupants of the Rio Grande are far more likely to shoot in situations of misunderstanding "do not dial 911" first.
This kind of antagonism or misantrhopy perhaps borne of centuries of lawlessness and abuse (?) exists in arab society only , and not very informatively (as in not surprisingly,) in those arab (and other) areas occupied largely by Rio Grandian motivation.
The other antiparallelism b/w the two is that while this kind of pathology occurs in the occupied arab cases out of dispossession, it flourishes in the rio grandian ethos, even though they are the dispossessors (be they spanish with all sorts of habsbourg monarchs or anglosaxon)
Although the collection of American colonial striped flags is still in a process of selection and compilation, these arms of Charles I Habsburg of Spain (1516 - 1556; Charles V, HRE 1519) should provide enough appetizer as to the evolution of the striped motif in modern american colonies:
... Read more
Cf. pan-arab colors
 |  |
src: pan-arab colors, uae.
and the flag of the independent republic of rio grande (1840).
src: Image:Flag_of_the_Republic_of_Rio_Grande, public domain.
This flag also adds to the collection of the American/panamerican motif of stripes and its use throughout the offshoots of the Spanish empire; and particularly stripes with cantons or other divisions as shown in this flag. this collection is still unfinished.
This is not to imply the coincidence lies much deeper. For unlike their arab counterparts, the present-day occupants of the Rio Grande are far more likely to shoot in situations of misunderstanding "do not dial 911" first.
This kind of antagonism or misantrhopy perhaps borne of centuries of lawlessness and abuse (?) exists in arab society only , and not very informatively (as in not surprisingly,) in those arab (and other) areas occupied largely by Rio Grandian motivation.
The other antiparallelism b/w the two is that while this kind of pathology occurs in the occupied arab cases out of dispossession, it flourishes in the rio grandian ethos, even though they are the dispossessors (be they spanish with all sorts of habsbourg monarchs or anglosaxon)
Although the collection of American colonial striped flags is still in a process of selection and compilation, these arms of Charles I Habsburg of Spain (1516 - 1556; Charles V, HRE 1519) should provide enough appetizer as to the evolution of the striped motif in modern american colonies:
... Read more
26 November 2008
etymo note: ψυχή , روح
the greek ancestor of psyche is ψυχή , ps-u-kh-é (we deliberately maintain the latin grapheme u for the greek υ which otherwise is expressed in latin with grapheme y and phoneme i)
I wonder if sukh is not derived from rukh , they differ in only one letter.
as an aside there is a symbolic - or rather shambolic - linkage: i wonder also whether there is a link between the spirit , pneuma, and the fish . though the general agreement is that the salted fish (fisikh) of Paque -> Pasc and pisces -> Pesakh = فصح in arabic (sham el nesim feast has roots in the christian miracle of the fishes. This is an unecessary line of imagination ,since the goal is to link sukh to ru[h|kh] not link ruh to fsooh. the possible linked is noted however.
it is called to mind because it resembles the weird greek cognate .Sukh of Ru.h
are there are any other instances where psi, ψ , replaces R in cognates. i would have thought it was cognate of the .Sad . ... Read more
I wonder if sukh is not derived from rukh , they differ in only one letter.
as an aside there is a symbolic - or rather shambolic - linkage: i wonder also whether there is a link between the spirit , pneuma, and the fish . though the general agreement is that the salted fish (fisikh) of Paque -> Pasc and pisces -> Pesakh = فصح in arabic (sham el nesim feast has roots in the christian miracle of the fishes. This is an unecessary line of imagination ,since the goal is to link sukh to ru[h|kh] not link ruh to fsooh. the possible linked is noted however.
it is called to mind because it resembles the weird greek cognate .Sukh of Ru.h
are there are any other instances where psi, ψ , replaces R in cognates. i would have thought it was cognate of the .Sad . ... Read more
etymo note: chlor- خضر + other H/ηemial elements
1. Chlorine , Chloros
Chloros is greek for pale green.
whereas the arabic trilit. root for green (akhdar) is Kh-D-R
if we line it up with an hypothetical greek trilit. root for khloros (xloros),
we get X-L-R , Kh-L-R (greek) and Kh-D-R (arabic)
which suggests a possible connection between the two names of the same color.
What is needed is to check whether the L in XLOR is a phonological transformation of the D in KhDR and whether there are other examples of a D to L transformation from semitic / afroasiatic to Greek.
If this is the case than Chloros and Khadar could be cognates.
2. Sodium (Na), comes from lat. Natrium , with symbol thus Na, from greek Natrios , comes from Arabic / egyptian Natron
eg, the huge Wadi al Natron , natron valley , south of Alexandria in Egypt.
Natra has come to be synonymous with salts in ancient chemical nomenclature.
3. Potassium (K), comes from lat. Kalium, thus symbol is Ka , from the Arabic Qalja , which is the ash of plants. ... Read more
Chloros is greek for pale green.
whereas the arabic trilit. root for green (akhdar) is Kh-D-R
if we line it up with an hypothetical greek trilit. root for khloros (xloros),
we get X-L-R , Kh-L-R (greek) and Kh-D-R (arabic)
which suggests a possible connection between the two names of the same color.
What is needed is to check whether the L in XLOR is a phonological transformation of the D in KhDR and whether there are other examples of a D to L transformation from semitic / afroasiatic to Greek.
If this is the case than Chloros and Khadar could be cognates.
2. Sodium (Na), comes from lat. Natrium , with symbol thus Na, from greek Natrios , comes from Arabic / egyptian Natron
eg, the huge Wadi al Natron , natron valley , south of Alexandria in Egypt.
Natra has come to be synonymous with salts in ancient chemical nomenclature.
3. Potassium (K), comes from lat. Kalium, thus symbol is Ka , from the Arabic Qalja , which is the ash of plants. ... Read more
