KRNN FM is one of the most famous online radio station on Alaska. KRNN is a non-commercial (NPR) music radio station broadcasting from Juneau, Alaska. It is broadcasting on 102.7 FM. KRNN airs a variety of music genres which include, jazz, classical, and adult album alternative. Capital Community Broadcasting purchased KSRJ and KFMG from White Oak Broadcasting of Alaska in 2006.


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Graded on a Curve: Motörhead,
No sleep 'til Hammersmith
By Michael H. Little | Published: March 28, 2018
On which the late metal minimalist/ genius/ proud-to-be-a-lummox Lemmy Kilmister delivers the hard rock goods live in a couple of halls not including London's Hammersmith Odeon. No sleep 'til Hammersmith features Motörhead at their ferocious and pummeling best, and is the perfect corrective to the lyrical excesses, grand themes, and emphasis on musical virtuosity that characterized much of the metal then popular. Call them the anti-Rush.
With the able assistance of "Fast" Eddie Clarke on guitar and backing vocals and Phil "Philthy Animal" Taylor on drums, Lemmy bangs out some tunes (most of them of unfashionably short length and unfashionably fast tempos), announces in DIY fashion that Motörhead is its own damn road crew, and demonstrates that his very hoarse bark has real bite.
Kilmister possessed not a whit of glamor and about as much charm, but that's exactly what made him so lovable; he wasn't good looking, his tonsils hardly made the little girls swoon, and when push came to shove he was the perfect antithesis of, say, Robert Plant. "No Class" is addressed to (or so I suspect) some anonymous groupie hanger-on, but Lemmy would no doubt have agreed it applied to him as well; he had about as much class as your average lorry driver, and never pretended to have better manners than your average lorry driver.
In short, you could relate to Lemmy Kilmister. He sang about all of the things you cared about, and said fuck it to the darkest depths of Mordor. He was a creature of the road and of the tedium and excesses that entailed, didn't give a shit about Xanadu or hobbits, and didn't want to write the next "Stairway to Heaven" either. He was down to earth, didn't look like he placed a very high premium on personal hygiene, and probably would have come in handy in a bar fight. He's as close as English music has ever come to producing an outlaw country musician.
I love Motörhead for the same reason I love AC/DC; both bands kept it as simple as a kick to the bullocks. But I like Motörhead more because (1) they played 'em faster and (2) Lemmy's grizzled roar was the perfect delivery mechanism for Motörhead's raw sewage swagger. The guy sounds like he swallowed a couple of razor blades before he the curtain went up, then washed 'em down with whisky, cigarettes, and some very biblical nestles. If a battered Triumph motorcycle engine could sing, it would sound like Lemmy.
And No sleep 'til Hammersmith was recorded at the most opportune of times, capturing Motörhead at their peak. I may be alone on this one, but their later LPs possess a sheen and polish where I prefer grit. Robert Christgau may have liked the "fierce clarity" that later producer Bill Laswell' brought to their sound, but I'm a mud and grit guy myself. Remember all those SST records people accused poor Spot (the Phil Spector of Murk) of ruining? I liked 'em all!
And speaking of punks, England's greatest power trio (Cream? Bah!) did more to bring punk and heavy metal together than anybody this side of Kix. They did it by means of tempo, mainly, but mood had a lot to do with it as well; Lemmy may have been too much the grizzled road warrior to be a gob young punk, but his sense of humor and fuck it all attitude are the hallmarks of a guy taking the piss, and if taking the piss ain't punk, what is?
The songs on this great live document can be separated into fast and faster, and I'll let you guess which I like better. The best of the faster ones is "Ace of Spades," which is speed metal at its most stripped down and proof positive that Lemmy's taste in illicit chemicals didn't run to downers. "The Hammer" is less hammer than nail gun, and "Philthy Animal" Taylor is the guy operating the damn thing. On "No Class" the din even overwhelms even Lemmy; you can literally hear him going hoarse trying to sing above the mayhem.
"Overkill" is just that; it's faster, harder and meaner than the competition, right down to Taylor's twin bass drum bash. "Bomber" is the sound of the London Blitz making its way back to London for a second go round; "It's a bomber, it's a bomber, it's a bomber" croaks Lemmy, before Clarke launches into one of his patented back-to-basics guitar turns. And I love both Lemmy's "Na na na na" and the 19th nervous breakdown at the end. Which leads us, of course, to "Motörhead," the last song Lemmy ever wrote for his old band Hawkwind.
My faves amongst the slower fast ones include "Stay Clean," on which Lemmy declares he can't abide little white lies and comes out front on bass as well. Then there's "(We Are) The Roadcrew," on which Lemmy speed raps about the travails of life on the road only to conclude, "But I just love the life I lead/Another beer is what I need/Another gig my ears bleed/We are the road crew." Junk food, groupies, super glue, and a new set of scars; it's a helluva life Lemmy leads, having to memorize the capitols of Europe and all, but it's the only life he knows.
As for "Metropolis" it's heavier than heaven, and Clarke's wah-wah guitar is heavenly indeed. On "Iron Horse/Born to Lose" Lemmy rides the "motorcycle as iron horse" meme to the grave; "Loaded forever and ferociously stoned," he sings, while Clarke goes totally blotter acid on guitar. "This one is a slow one," announces Lemmy before going into "Capricorn," but Lemmy's slow is another man's fast just as Lemmy's week is another man's year, and Black Sabbath rarely moved so nimbly. And once again Taylor proves he has the biggest and baddest backbeat in the biz.
To paraphrase The Most Interesting Man in the World, I don't always listen to heavy metal, but when I do it's Motörhead. They're leaner, meaner, and yes funnier than the competition, and a wonderful cure for a headache (the remedy has to be worse than the disease). Toss in the fact that they owe nothing to the blues and you positively cannot dance to them, and what you have is the greatest heavy metal band in the history of the world. The sleaziest one too. And unlike fleeting joy, sleaze is forever.

redpajama_set_name: RedPajamaCommonCrawl


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Home » Capacitors Materials Technology
Storing electricity in paper
source: Linkoping University article
Researchers at Linköping University's Laboratory of Organic Electronics, Sweden, have developed power paper – a new material with an outstanding ability to store energy. The material consists of nanocellulose and a conductive polymer. The results have been published in Advanced Science.
One sheet, 15 centimetres in diameter and a few tenths of a millimetre thick can store as much as 1 F, which is similar to the supercapacitors currently on the market. The material can be recharged hundreds of times and each charge only takes a few seconds.
It's a dream product in a world where the increased use of renewable energy requires new methods for energy storage – from summer to winter, from a windy day to a calm one, from a sunny day to one with heavy cloud cover.
"Thin films that function as capacitors have existed for some time. What we have done is to produce the material in three dimensions. We can produce thick sheets," says Xavier Crispin, professor of organic electronics and co-author to the article just published in Advanced Science.
Other co-authors are researchers from KTH Royal Institute of Technology, Innventia, Technical University of Denmark and the University of Kentucky.
The material, power paper, looks and feels like a slightly plasticky paper and the researchers have amused themselves by using one piece to make an origami swan – which gives an indication of its strength.
The structural foundation of the material is nanocellulose, which is cellulose fibres which, using high-pressure water, are broken down into fibres as thin as 20 nm in diameter. With the cellulose fibres in a solution of water, an electrically charged polymer (PEDOT:PSS), also in a water solution, is added. The polymer then forms a thin coating around the fibres.
"The covered fibres are in tangles, where the liquid in the spaces between them functions as an electrolyte," explains Jesper Edberg, doctoral student, who conducted the experiments together with Abdellah Malti, who recently completed his doctorate.
The new cellulose-polymer material has set a new world record in simultaneous conductivity for ions and electrons, which explains its exceptional capacity for energy storage. It also opens the door to continued development toward even higher capacity. Unlike the batteries and capacitors currently on the market, power paper is produced from simple materials – renewable cellulose and an easily available polymer. It is light in weight, it requires no dangerous chemicals or heavy metals and it is waterproof.
The Power Papers project has been financed by the Knut and Alice Wallenberg Foundation since 2012.
"They leave us to our research, without demanding lengthy reports, and they trust us. We have a lot of pressure on us to deliver, but it's ok if it takes time, and we're grateful for that," says Professor Magnus Berggren, director of the Laboratory of Organic Electronics at Linköping University.
The new power paper is just like regular pulp, which has to be dehydrated when making paper. The challenge is to develop an industrial-scale process for this.
"Together with KTH, Acreo and Innventia we just received SEK 34 million from the Swedish Foundation for Strategic Research to continue our efforts to develop a rational production method, a paper machine for power paper," says Professor Berggren.
Power paper – Four world records
Highest charge and capacitance in organic electronics, 1 C and 2 F (Coulomb and Farad).
Highest measured current in an organic conductor, 1 A (Ampere).
Highest capacity to simultaneously conduct ions and electrons.
Highest transconductance in a transistor, 1 S (Siemens)
The mixture consists of nanocellulose and a conductive polymer.
Photo: Thor Balkhed and Abdellah Malti
Stability Prognosis of Components During Dry Heat & Biased Humidity Testing & Application


Looking for a way to add a touch of naturalistic elegance to your pool? Or perhaps you're seeking a luxurious oasis that resembles that which can be found on the properties of 5-star resorts. If either is what you crave, then an infinity pool is sure to hit the mark.
Also referred to a zero edge, negative edge or a vanishing edge style of pool, an infinity pool is one which is able to produce a stunning effect of a pool's waters extending forever towards the horizon for a limitless amount of time, thus the "infinity" term that comes with this design. The term is also often used to describe any perimeter overflow pools.
But infinity pools are actually far more diverse than most realize. Most homeowners may not have the most picturesque backdrop apart from their very own backyard or garden. Having an infinity pool which extends to a very beautiful or scenic part of the yard can be extremely complimentary to your landscaping. The infinity pool design can act like a giant mirror, reflecting the most beautiful parts of your backyard and surrounding area.
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\section{Introduction}
At this stage (see \cite{dahm:MRST5} and references), we've
established the ties from our original Lie group based approach
of hadronic (and quantum) degrees of freedom in terms of SU(4)
and SU$*$(4), respectively, to (classical and advanced) projective
geometry of real 3-space. Now, in parts VII and VIII of this
series, we want to focus more detailed on two of the included
major aspects or building blocks -- spin and relativity. So
departing from a description common to both parts and based
on elementary line geometry, we are going to present a more
detailed treatment of each spin and relativity related to
classical line and projective geometry. This, however, at
the same time almost immediately and inherently comprises
a necessary branch of the two topics here and in upcoming
papers.

It is the task of this paper to recall briefly some (very)
elementary geometrical properties and features, and to
relate this approach to spin and associated algebraical
concepts and physical background. As such, we'll rearrange
coordinates and relate this rep\footnote{As in the papers
before, we use the shorthand notation 'rep' to denote both
representations or realizations as long as the respective
context is unambiguous. 'PG' subsequently denotes 'projective
geometry'.} to nowadays common spin (and 'quantum') aspects
and some of their reps. Moreover, we use this approach
to discuss further aspects as mentioned in the abstract
so that inherently we obtain a relation between the various
reps and, moreover, between their respective interpretations
and related concepts. Here, the crucial point with respect
to spin discussions is the application of Lie's transfer
principle \cite{lie:1872} and a special complexification
of the real (inhomogeneous) coordinates.
On the other hand, this is also the branching point mentioned
above so that, based on the same Ansatz but on real coordinates,
in part VIII we'll concentrate on the original real (and the line
geometric) aspects, and there we'll continue this second branch
to discuss special linear Complexe and relativity.
We feel that the next few pages grant to state the relation
of the usually disconnected 'quantum' world to classical
geometrical concepts, however, the wealth of possibilities
comprised in Lie's mechanism \cite{lie:1872}, e.g.~with
respect to higher order (or class) objects or using further
choices of the transfer functions $f_{i}$, are still far
from being applied or even exhausted. The 'degenerate cases'
mentioned in Lie's paper are related to very special choices
and cannot serve to comprise the full power of this Ansatz
based on \PLu's algebraic concept of a general (higher
dimensional) description of ordinary space and Lie's extension
thereof (see \cite{lie:1872}, especially page 151 above/end
of \S 2 with respect to Lie's understanding of \PLu's original
algebraical Ansatz \cite{pluecker:1846}).

So although at this time we'll include general aspects only,
we feel it is the time to split our original series on a
microscopic rep of space-time at this point into a spin (using
complex numbers and elliptic geometry) and a relativistic
(hyperbolic) part. On one hand, it is worth to investigate
Lie transfer in more detail and to relate Clifford's and
Study's work on elliptic geometry as well as especially
Study's further work on (different) line geometries and on
kinematics (see e.g.~\cite{study:1903} and later publications).
To our opinion, in conjunction with (quaternary) invariant
and form theory, this should be sufficient to exhaust and
comprise what is nowadays called 'quantum theory'. On the
other hand, it is worth to separate a discussion focussing
on real aspects and hyperbolic geometry in order to keep
in parallel the track to relativity - special relativity
using (special) linear Complexe as well as the full geometry
of regular linear Complexe in $P^{5}$ and/or higher order
Complexe and nonlinear
transformations. Stepping back to line and Complex geometry
as the basic and underlying framework of Lie's approach
\cite{lie:TransfGruppen}, we feel to escape the various
restrictions of early use of (linear) rep theory of groups
and algebras as well as concepts of differential geometry,
and we think it's sufficient when asking for integral and/or
nonlinear representations only afterwards.

As such, in the upcoming sections, we use \PLu's line rep
(in inhomogeneous coordinates) and feel free to rearrange
and reinterpret this rep in a special form so that we can
write the coordinates and transformations in matrix notation.
This helps to identify elements and relate them to quantum reps,
e.g.~in Lagrangean or current algebra notation, and to ongoing
discussions. Please note, too, that the next section is useful
both for spin and relativity, especially after switching to
homogeneous coordinates and departing from affine to non-euclidean
geometry, and that it includes nothing but elementary PG.
Afterwards, in section \ref{sec:lietransfer}, we branch from
real projective geometry by Lie's transfer principle \cite{lie:1872}
to the derivation of (complex) spin reps and the known algebraic
formalism. Throughout this section, we feel free to recall some
historic contexts and include them in the text, not to write
some science-history related paper\footnote{According to current
discussions and the attribution of achievements, we feel the
urgent necessity to reconsider the real historical development,
however, personally, we neither have the competency nor the
time to evaluate and honor those achievements scientifically
and relate them in detail to the original authors. So we focus
here on few spin-related aspects only which to our opinion need
(among other authors) to be attributed mainly to S. Lie and
especially E. Study already back in the late $19^{th}$ and
first decade of $20^{th}$ century instead of E. Cartan in 1938
\cite{cartan:1938} (or even 1913, as he claimed there, see
his introduction). However, we cannot rise a fundamental and
historically complete priority discussion here.} but to put
some known facts in an understandable context right from the
original development. The last section is devoted to a brief
outlook in order to sketch the wealth of opening possibilities
which appear by Lie transfer and sphere geometry.

\section{Line representation and coordinates}
The reason to cite some (very elementary) issues from
\cite{plueckerNG:1868} is mainly to connect the reasoning
of the $19^{th}$ century view of projective geometry to
the dynamic picture used nowadays in terms of 'time' and
'velocity' coordinates which emerge only after we tag
points in the respective geometry and 'observe' them moving
around\footnote{We want to emphasize the difference of the
'pictures' because there are alternative reps of points
e.g.~by considering points in terms of (inter-)sections
of lines in 3-space. This leads almost immediately to a
discussion of Congruences when including (moving) observers
into the physical description, see also our preparatory
discussions in \cite{dahm:MRST4}, \cite{dahm:MRST5}. We
have to remark as well the {\it dependent} relation of
velocities to the respective time coordinates of the
individual lines, or axes, or of the (local) coordinate
systems which in its simplest form of (linear) motion
with uniform velocity read as $s=v\cdot t$ in those
coordinates. Note also, that \PLL (as well as Lie in
his approach) uses (inhomogeneous) euclidean coordinates
$x, y, z$ and not fourfold/quaternary point coordinates,
neither homogeneous nor (affine) Hesse coordinates by
introducing the additional $t$-coordinate common at that
time to denote the fourth (affine) point coordinate. This
reduces the anharmonic ratio using point reps to a simple
quotient of point distances or 'coordinate' projections.}.
So in choosing \cite{plueckerNG:1868} the (euclidean) rep
\begin{equation}
\label{eq:basicline}
x\,=\,r\,z+\rho\,,\quad y\,=\,s\,z+\sigma\,,
\end{equation}
we obtain first of all a (cartesian) line rep of 3-space
which is 'globally' defined by two linear functions in terms
of the third cartesian coordinate $z$. In each of the planes
$(x,z)$, i.e.~$y=0$, and $(y,z)$, i.e.~$x=0$, we find linear
line projections, too, which we may map to separate line reps
as well. So far, we do not have tagged special points on the
line like the origin as a reference or a unit point or two
(fundamental) points to declare anharmonic ratios or three
points to declare a coordinate (or measure) on the line itself.
Moreover, in the same picture, we do {\it not yet} apply the
vector calculus of real 3-space common today by pointing with
a vector to the line and defining a 'time' parameter and a
velocity on the line (or at least its direction).

\subsection{Coordinates}

So the following arguments are concerned with the (real)
parameters $r, \rho, s$ and $\sigma$ from eq.~(\ref{eq:basicline}),
i.e.~what enters these equations are position and orientation
(i.e.~'the geometry') of the line itself and as a 'whole'
object in the 3-dim euclidean\footnote{We are going to extend
this approach by homogeneous coordinates mainly in part VIII
and postpone the more general discussion, also with respect
to anharmonic ratios and projective transformations of the
lines, to upcoming parts.} coordinate system $x,y,z$. Now
\PLL founds his definition of (4-dim) line coordinates and
their necessary extension\footnote{This ensures to preserve
the grade during transformations whereas a sixth coordinate
is necessary to linearize the transformations of the line
coordinates.} by a fifth line coordinate $\eta=r\sigma-s\rho$
on this basis, and in \cite{plueckerNG:1868} he shows how
to define and use sets of lines in terms of Complexe,
Congruences and Configurations as foundation of a space
description, his so-called 'new geometry', in distinction
to standard (projective) geometry which uses the point
as base element and planes to complete the point-based
framework with respect to duality (see e.g.~his contemporary
summary \cite{pluecker:1846} or later text books on PG
also by other authors).

Suppressing PG details here, we want to prepare our discussion
of both parts VII and VIII, i.e.~spin and relativity, by
rearranging the (euclidean) coordinates $x,y$, still as a
function of $z$ only, with respect to the line projection
onto the $(x,y)$-plane at $z=0$. Our main concern and driving
force having been inclusion and understanding of special
Lorentz transformations, however, it turned out that if we
transform (in the point picture) along the $z$-axis, and if
we require as usual the $x$- and $y$-coordinates to remain
invariant, we have remarkable freedom in that this transform
concerns only $z\sim\tfrac{x_{3}}{x_{0}}$ as (euclidean)
normal to $(x,y)$. Moreover, weakening the invariance
requirement(s), we can rearrange the variables in the
projection plane\footnote{We discuss more details related
to relativity in part VIII.} $(x,y)$ as needed to investigate
invariances of products, quotients, etc., too.

So if we arrange e.g.~the ratio of the two (cartesian)
coordinate projections $x$ and $y$ of the line into a
new coordinate $\zeta$ by $\zeta=\tfrac{x}{y}$, using
eq.~(\ref{eq:basicline}) we obtain the relation
$\tfrac{x}{y}=\zeta=\tfrac{r\,z+\rho}{s\,z+\sigma}$.
Now we can interpret the rhs as projective transformation\footnote{The
three (cartesian) projections of the original line onto
each of the planes $(x,z)$, $(y,z)$ and $(x,y)$ in the
general case are, of course, related to the line by
perspective.} and, of course, map the parameters to
a (real) matrix formalism by
\begin{equation}
\label{eq:euclideanProjTransf}
\frac{x}{y}=\zeta\longrightarrow
\left(
\begin{array}{c} x\\ y\end{array}
\right)\,=\,
\left(
\begin{array}{cc} r & \rho\\ s & \sigma\end{array}
\right)
\left(
\begin{array}{c} z\\ 1\end{array}
\right)\,.
\end{equation}

\subsection{Homogeneous Coordinates}
Moreover, by formally\footnote{Here, we may only use
the affine (linear) coordinate extension by an absolute
plane $x_{0}=0$ (better by $\pm\sqrt{x_{0}^{2}}$) in
the denominator.} introducing homogeneous coordinates
for $\zeta\longrightarrow\tfrac{\zeta_{1}}{\zeta_{2}}$
and $z\longrightarrow\tfrac{x_{3}}{x_{0}}$, we can
rewrite eq.~(\ref{eq:euclideanProjTransf}) according
to
\begin{equation}
\label{eq:homogeneousProjTransf}
\left(
\begin{array}{c} \zeta_{1}\\ \zeta_{2}\end{array}
\right)
=
\left(
\begin{array}{cc} r & \rho\\ s & \sigma\end{array}
\right)
\left(
\begin{array}{c} x_{3}\\ x_{0}\end{array}
\right)
\end{equation}
and apply the usual $2\times 2$ matrix formalism.

Now, dependent on whether we focus on the rhs of
eqns.~(\ref{eq:euclideanProjTransf}) and (\ref{eq:homogeneousProjTransf}),
or on the lhs of these equations, we steer towards a
discussion of spin for the rhs or (special) relativity
for the lhs as we'll discuss soon. Note, however, that
throughout our approach $\tfrac{x}{y}$ remains 'invariant'
if we replace the cartesian coordinates $x$ and $y$
homogeneously by $x\longrightarrow\tfrac{x_{1}}{x_{0}}$
and $y\longrightarrow\tfrac{x_{2}}{x_{0}}$,
i.e.~$\tfrac{x}{y}=\tfrac{x_{1}}{x_{2}}$, following the
affine interpretation by tagging a certain plane within PG.

\PLu's fifth line coordinate $\eta=r\sigma-s\rho$ then turns
out to represent the determinant of the transformation matrix
above, i.e.~via the line rep in eq.~(\ref{eq:basicline}), we
have as\-so\-ciated (formally) a projective transformation of
the (euclidean) $z$-axis to a (projective) transformation of
the coordinate $\zeta$. Accordingly, we can relate this 'new'
coordinate axis of $\zeta$ to $z$ by associated projective
transformations $\zeta=f(z)$. More general, the projective
relation of $z$ and $\zeta$ allows to apply the full framework
of point transformations on first order (projective) elements
and to investigate binary forms (and the related invariant
theory) in terms of mappings of point sets on lines to each
other. In addition, our approach suggests the discussion of
involutions on projective elements of first kind, so that
we may include complex numbers via von Staudt's or L\"{u}roth's
geometric interpretation of complex numbers naturally. By
considering this approach from a more general viewpoint,
we have now set up the very foundation of the complete
framework of PG, here in terms of point geometry on two
lines coordinated by $z$ and $\zeta$.

\section{Lie Transfer and Spin}
\label{sec:lietransfer}
Following Lie's approach here, we are going to discuss
the rhs of eq.~(\ref{eq:euclideanProjTransf}) only. Also,
we require the matrix determinant (or \PLL coordinate
$\eta$) here as nonzero, i.e.~the original line doesn't
hit the $z$-axis, and the line of the respective projections
in the $(x,y)$-plane is skew versus the $z$-axis. In other
words, $(0,0)$ being the (cartesian) projection of the
$z$-axis in the $(x,y)$-plane (and all its parallel planes,
i.e.~planes hitting the same 'absolute line' within the
spatial affine picture), the non-vanishing determinant
ensures considering the case of two skew lines, and
moreover eases the introduction of homogeneous coordinates
by avoiding singular/special cases. Some aspects related
to the general case, including $\eta=0$, will be discussed
in part VIII, also in the context of using homogeneous
coordinates.

\subsection{Lie's Mapping -- aka 'Lie Transfer'}
Lie restricted the general cases of his mapping at first by
considering lines instead of general curves (\cite{lie:1872},
\#5 and \#21), and further by choosing special constants
in that the second Complex in the degenerate case (\cite{lie:1872},
\#21) hits the conic section in the absolute plane of the
{\it affine} geometry. Note, that it is this linear extension
of euclidean geometry\footnote{\ldots which also forces
the switch to homogeneous coordinates to describe absolute
elements. We refer to Study's remarks \cite{study:1907}
and some of his further work cited here. See also our few
remarks in section \ref{sec:studyswork}.} which introduces
the isotropy discussion (and as such the 'spinor' rep),
whereas with respect to relativistic (or non-euclidean)
transformations, leaving a general second order
(i.e.~quadratic) surface invariant, we have to switch to
3-space instead of (linear) planar discussions. There will
remain the connecting link that 2$^{nd}$ order surfaces
can be generated by two families of lines, i.e.~in each
point of the surface, we can find appropriate members of
the two generating families, however, in order to handle
spin and (special) relativity from the viewpoint of the
degeneracies discussed here and in the upcoming part VIII
with respect to special linear Complexe, it is obvious
that one should switch to Complexe in general as geometrical
base elements as we have worked out and proposed throughout
this paper sequence (see \cite{dahm:MRST5} and references
there). A strongly supporting, direct argument for switching
to line and Complex geometry of $P^{5}$ would be to refer
back to Lie's original investigations \cite{lie:1872} and
by noting that the general theory underlying Lie's approach
and reasoning is Complex geometry. Indeed, Lie obtained
this (bilinear) approach given in eq.~(\ref{eq:lietransfer})
only by further specializing his originally more general
mapping to a line Complex hitting the absolute circle of
affine geometry\footnote{It is obvious from the Cayley-Klein
construction of a metric that this construction is relevant
to metrical properties, too. However, we do not want to
discuss general lengths, 'masses' or 'charges' here as this
approach is, first of all, connected to absolute elements
of an affine Ansatz only.}, or isotropic lines, respectively.
For now, we think that Lie's Ansatz in general establishes
sphere geometry in a separate space besides the line (and
the represented Complex) geometry of ordinary 3-space,
whereas concerning 'spin', here we treat only simple/linear
and (multiply) degenerate cases of Lie's general mapping
which 'overlap' or relate in certain aspects due to the
(linear) cases and/or the degeneracies considered.

\subsection{Matrix Reps and Spin}
\label{sec:matrixreps}
Nevertheless, we depart from Lie's restricted (bilinear) Ansatz
(see \cite{lie:1872}, p.~146, or \cite{lie:1872}, \S 8, \#24 (1)),
\begin{equation}
\label{eq:lietransfer}
-Zz=x -(X+iY)\,,\quad (X-iY)z=y-Z
\end{equation}
to relate the (cartesian) coordinates of the spaces $r$ and $R$,
which we rearrange into
\begin{equation}
\label{eq:lietransferrearranged}
x=-Zz+(X+iY) \,,\quad y=(X-iY)z+Z\,,
\end{equation}
and according to our choice\footnote{For detailed analytic
consideration and calculations one should recall that at the
time of \PLu's and Lie's writing, the authors were used to
coordinate systems with different handedness, especially to
a different sign of the $y$-coordinate, which sometimes leads
to signs especially in linear equations involving $y$ or
$\sigma$.} of the line representation in eq.~(\ref{eq:basicline})
and the matrix definition in (\ref{eq:euclideanProjTransf}),
this allows to identify the transformation matrix directly
by
\begin{equation}
\label{eq:matrixrep}
\left(
\begin{array}{cc} r & \rho\\ s & \sigma\end{array}
\right)
\,\sim\,
\left(
\begin{array}{cc} -Z & X+iY\\ X-iY & +Z\end{array}
\right)
\,.
\end{equation}
Note here, that on the lhs, we originally describe a {\it linear}
transformation of {\it cartesian} coordinate projections which
yields the context for discussion of \cite{clebsch:1872} later
on. So the original line coordinates of space $r$ are represented
(or 'replaced') by (complexified point) coordinate combinations
of the space $R$, where the rhs of eq.~(\ref{eq:matrixrep}),
however, may be re-expressed in nowadays common notation according
to
\begin{equation}
\label{eq:spin}
\left(
\begin{array}{cc} -Z & X+iY\\ X-iY & +Z\end{array}
\right)\,=\,
X\sigma_{1}-Y\sigma_{2}-Z\sigma_{3}
\end{equation}
when introducing standard 'Pauli matrices' $\sigma_{i}$. So
the important point here -- derived from the background of
Complex geometry -- is the identification of real (point)
coordinates of $R$ in the Pauli/spin basis by eq.~(\ref{eq:spin})
with (inhomogeneous) line coordinates\footnote{This is especially
noteworthy facing the current discussions on non-local aspects
of quantum theories if we depart from real parametrizations
of Pauli matrices. Note in this contexts, that already special
linear Complexe are {\it sets} of lines in 3-space, and that
using Complexe, we also have to take into account regular and
higher order Complexe, i.e.~the geometry of P$^5$ as well as
quadratic manifolds. Here, we are discussing linear mappings
and degenerate cases only, so these are only the very beginnings
of a potentially relevant description of observations in nature.}
of real 3-space, and it is the su(2) (Lie) algebra which maps
the geometries and the respective coordinate interpretation.
However, for the general environment and the context of our
current discussion, it is necessary to mention and cite three
more important aspects given by Lie in his paper \cite{lie:1872}.

\subsection{Geometry in $R$-space}
\label{sec:geom-r-space}
Casting the equations above in a form to identify coordinates in
$R$-space, Lie shows (\cite{lie:1872}, p.~168) that those (still
inhomogeneous) coordinates fulfil the equation $R^{2}+S^{2}+1=0$,
or when cast in differential form\footnote{We cite the expression
as given, not discussing partial derivatives. Please note, that
this replacement of coordinates by derivatives is attached to \PLu's
original line rep and to a {\it linear} choice of the coordinates.
So this Ansatz yields the very foundation of Lie's contact transformations
based on line elements (or five-parameter space reps $(x,y,z,p,q)$)
later on. However, due to the intrinsically linear rep, we may also
switch directly to the point rep on lines in terms of binary forms
\cite{clebsch:1872} and the related symbolism.}, based on
\cite{lie:1872}, \S 8, eq.~(3), by\footnote{We want to mention the
relation to three homogeneous (planar) coordinates only.}
$R=\tfrac{\mathrm{d}X}{\mathrm{d}Z}$
,
$S=\tfrac{\mathrm{d}Y}{\mathrm{d}Z}$
, which yields $\mathrm{d}X^{2}+\mathrm{d}Y^{2}+\mathrm{d}Z^{2}=0$
and suggests the considerations of isotropic elements.
This led Lie to the statement that the line Complex in $R$-space
is being built of imaginary lines of zero length\footnote{Isotropic
lines.}. We want to address those aspects later and separately.

Here, to connect to 'Cartan's' spin rep, we want to recall Lie's
equations (\cite{lie:1872}, p.~168) of the line coordinates $R$
and $S$,
\begin{equation}
\label{eq:lie2cartan}
R=\frac{1}{2}\left(z-\frac{1}{z}\right)\,,\quad
S=\frac{1}{2i}\left(z+\frac{1}{z}\right)\,,
\end{equation}
and the quadratic equation $R^{2}+S^{2}+1=0$ from above. We can
now start from either 'side' -- using the quadratic equation and
introducing homogeneous coordinates, or recalling the inhomogeneous
character of $z$ and introducing homogeneous quaternary coordinates
of 3-space in (\ref{eq:lie2cartan}). By the second approach, we
obtain from eq.~(\ref{eq:lie2cartan})
\begin{equation}
\label{eq:lie2cartan2}
R=\left(\frac{z^{2}-1}{2z}\right)=\left(\frac{x_{3}^{2}-x_{0}^{2}}{2x_{0}x_{3}}\right)\,,\quad
S=\left(\frac{z^{2}+1}{2iz}\right)=\left(\frac{x_{3}^{2}+x_{0}^{2}}{2ix_{0}x_{3}}\right)\,.
\end{equation}
By introducing primed 'homogeneous' variables $R=:\tfrac{R'}{T'}$,
$S=:\tfrac{S'}{T'}$, we can extract the identifications
\begin{equation}
\label{eq:lie2cartanhomog}
R'=x_{0}^{2}-x_{3}^{2}\,,\,
S'=i\left(x_{0}^{2}+x_{3}^{2}\right)\,,\,
T'=-2x_{0}x_{3}\,,
\end{equation}
where we've used the standard relation $z=\tfrac{x_{3}}{x_{0}}$
from affine geometry with respect to the $z$-axis in all places.
The equation $R^{2}+S^{2}+1=0$ converts to $R'^{2}+S'^{2}+T'^{2}=0$,
thus featuring (finite) line coordinates and 4$^{th}$ order
surfaces in the original (point) coordinates. Eq.~(\ref{eq:lie2cartanhomog})
yields Cartan's coordinate and 'spinor' 'definition' in
\cite{cartan:1938}, \#52.

\subsection{Lie Transfer and 'Spinors'}
Now regarding eqns.~(\ref{eq:lie2cartan2}) and (\ref{eq:lie2cartanhomog}),
it is easy to trace back Cartan's miraculous 'definition' of
'a spinor' emerging in \cite{cartan:1938}, \#52 by recalling
the relation of inhomogeneous and homogeneous coordinates of
(real) 3-space, the definition of the absolute element of
affine geometry. What enters in addition, are the absolute
circle, by $x_{1}^{2}+x_{2}^{2}+x_{3}^{2}=0$, $x_{0}=0$ in
{\it homogeneous} spatial coordinates, and an identification
$x_{0}^{2}-x_{3}^{2}$ here with $\xi_{0}^{2}-\xi_{1}^{2}$
in Cartan's notation. Accordingly, his 'spinor' coordinates
$\xi_{0}$ and $\xi_{1}$ map to two homogeneous point
coordinates $x_{0}$ and $x_{3}$ of real 3-space, whereas by
eqns.~(\ref{eq:lie2cartan2}) or (\ref{eq:lie2cartanhomog})
the three linear coordinates $x_{i}$ of Cartan map to Lie's
'line coordinates' $R$ and $S$, or $R', S'$ and $T'$ from
above and from the 'inverse' Lie mapping, obeying
$R^{2}+S^{2}+1=0$ or $R'^{2}+S'^{2}+T'^{2}=0$, respectively.

There is, however, a much easier way to establish the 'spinor'
interpretation versus Lie's mapping by starting from
\cite{cartan:1938}, \#55, eq.~(1), and by recalling
$z=\tfrac{x_{3}}{x_{0}}\sim\tfrac{\xi_{1}}{\xi_{0}}$
from above, i.e.
\begin{equation}
\xi_{0}x_{3}+\xi_{1}(x_{1}-ix_{2})=0\,,\,
\xi_{0}(x_{1}+ix_{2})-\xi_{1}x_{3}=0\,,
\end{equation}
Here, we can at first change the order of the equations
and divide by $x_{0}$, thus switching back to inhomogeneous,
cartesian coordinates $X$, $Y$ and $Z$. We obtain
\begin{equation}
-\xi_{1}Z+\xi_{0}(X+iY)=0\,,\,
\xi_{0}Z+\xi_{1}(X-iY)=0\,,
\quad\mathrm{or}
\end{equation}
\begin{equation}
\label{eq:help2}
0=-Z\xi_{1}+(X+iY)\xi_{0}\,,\,
0=(X-iY)\xi_{1}+Z\xi_{0}\,.
\end{equation}
We may put these equations in matrix form, too, by
extracting a 'spinor' $(\xi_{1}, \xi_{0})^{T}$ to
the right, and celebrating the su(2) (Lie) algebra
in terms of Pauli matrices. What is more important,
however, is the comparison with eq.~(\ref{eq:lietransferrearranged})
if we introduce an inhomogeneous coordinate
$\xi:=\tfrac{\xi_{1}}{\xi_{0}}$ (which, as we see
above, is Lie's original $z$). Dividing eq.~(\ref{eq:help2})
by $\xi_{0}$, we obtain
\begin{equation}
\label{eq:cartanrewritten}
0=-Zz+(X+iY)\,,\,
0=(X-iY)z+Z\,,
\end{equation}
which recovers a special case of Lie transfer, i.e.~instead
of Lie's general coordinate projections $x$ and $y$, Cartan's
definition is obviously fixed to the $z$-axis at $(0,0)$
in the $(x,y)$-plane, which from Lie's approach is related
to vanishing $\eta$ (or determinant).

More important is the missing dependence of $x$ and $y$
at all, or according to (\ref{eq:cartanrewritten}) $x=0$
and $y=0$. So in addition to the restrictions and the
resulting degeneracies/singularities applied by Lie, there
is {\it a priori no suitable coordinate dependence} besides
the 'spinor' itself describing a line in terms of two
homogeneous coordinates $\xi_{i}$, or a simple 1-dim projective
transformation of the quotient. The quotient may be reversed
by the exchange $\xi_{1}\longleftrightarrow\xi_{0}$, in
'spinor' notation induced by $\sigma_{1}$ or $i\sigma_{2}$,
which correspond to reciprocal transformations\footnote{By
a suitable setup of the system, arranging a (metric) radius
along $\hat{z}$, we have $r\longleftrightarrow\pm\tfrac{1}{r}$,
and planar duality as well. Conjugation of eq.~(\ref{eq:cartanrewritten})
in $R$-space is invariant if, at the same time, we perform
$z\longleftrightarrow-\tfrac{1}{z}$, etc. Note also sign
behaviour of $R$ and $S$ in eq.~(\ref{eq:lie2cartan}) in
the $\pm$-cases. Such methods can be applied throughout
Cartan's 'spinor' formalism, however, it should at least
be founded on Lie's approach. The more general treatment
has to include and respect polar systems.} $z\longleftrightarrow\pm\tfrac{1}{z}$.
Due to the remarkable situation that (in the usual point
picture) special relativity doesn't transform $x$ and $y$
when we choose the transformation along $z$, Cartan's
approach -- being independent of $x$ and $y$ -- survives
and reflects those transformations. One should, however,
place question marks to general space-dependent SU(2)
spinors like $\psi(x)$ or $\psi(x^{\mu})$ founding on
Cartan's definition.

\subsection{Further Linear Aspects}
The second aspect covers a more general case. Here, Lie's
equations (\ref{eq:lietransfer}) mapping the two spaces
$r$ and $R$, relate both spaces in a manner that points
in $r$ map to isotropic lines in $R$, and points in $R$
map to the linear Complex $r+s=0$ in $r$. In upcoming
papers, we hope to have the possibility to discuss more
geometrical details, especially with respect to further
details and geometrical relations mentioned by Lie in
\cite{lie:1872}. For now, we want to close this subsection
by reference to Lie's remarks in \S 9, p.~171 with respect
to the second unnumbered equation (see also eq.~(\ref{eq:Rsphere}))
holding a quadratic relation. Tracing this back with
our matrix rep, it is obvious that the variable $H$ in
$R$ corresponds to the {\it unit matrix} $\sigma_{0}$,
and it thus relates the unit matrix of the $R$ matrix
rep with the linear Complex $r+\sigma$ of $r$-space and
it's special r\^{o}le. In Lie's original work \cite{lie:1872},
p.~171, the spheres in $R$-space (i.e.~using \PLu's inhomogeneous
coordinates\footnote{Generalizing the coordinates via
affine homogeneous coordinate extensions, note that
$\rho$ and $\sigma$ are related to the 'new' affine
coordinate $t$ or $x_{0}$ and as such to the absolute
plane in $r$-space. Recall also, that transformations
of the inhomogeneous \PLL coordinates $r,s,\rho,\sigma$
do not preserve grade, i.e.~(\ref{eq:inhomogvars})
pretends a linear relationship due to the projective
rep.} to describe Complex lines) fulfil
\begin{equation}
\label{eq:Rsphere}
[X-(s+\rho)]^{2}+[Y-i(s-\rho)]^{2}+[Z-(\sigma-r)]^{2}=(\sigma+r)^{2}\,.
\end{equation}
So the coordinate set\footnote{Note, that $Y'$ is imaginary,
or $iY'$ is real, and remember polar relationships in affine
geometry, too.} $X'=s+\rho$, $Y'=i(s-\rho)$ and $Z'=\sigma-r$ describes
the center of the sphere in $R$-space in terms of line coordinates
(or a shift from an original center $(0,0,0)$) whereas $\sigma+r$
takes the r\^{o}le of an oriented coordinate or even a 'radius'
$H=r+\sigma$ in terms of line coordinates of the line Complex in
$r$-space. This enhances the mapping $r \longleftrightarrow -Z$,
$\rho\longleftrightarrow X+iY$, $s \longleftrightarrow X-iY$ and
$\sigma\longleftrightarrow +Z$ in eq.~(\ref{eq:matrixrep}) into (see
\cite{lie:1872}, \S 9, eq.~(3))
\begin{equation}
\label{eq:inhomogvars}
r=\frac{1}{2}(\pm H'-Z')\,,
\rho=\frac{1}{2}(X'+iY')\,,
s=\frac{1}{2}(X'-iY')\,,
\sigma=\frac{1}{2}(\pm H'+Z')
\end{equation}
which now corresponds to the expression
\begin{equation}
\label{eq:maptopauli}
\frac{1}{2}\left(
\begin{array}{cc} -Z'\pm H' & X'+iY'\\ X'-iY' & +Z'\pm H'\end{array}
\right)
\sim
X'\sigma_{1}-Y'\sigma_{2}-Z'\sigma_{3}\pm H'\sigma_{0}
\,.
\end{equation}
Recalling \PLu's fifth coordinate $\eta=r\sigma-s\rho$,
eq.~(\ref{eq:inhomogvars}) yields $r\sigma=H'^{2}-Z'^{2}$ and
$s\rho=X'^{2}+Y'^{2}$, so $\eta=H'^{2}-Z'^{2}-X'^{2}-Y'^{2}$.
This prepares the basis of the 2-spinor formalism and all its
applications and analytical forms, in addition, we thus map
the quest for 'relativistic' invariance to 2$\times$2-matrix
notation (\ref{eq:maptopauli}) or complexified quaternions,
and invariance of the determinant $\eta$.

Especially, this gives some insight on how (due to the quadratic
nature of the manifold) the unit matrix serves \cite{lie:1872} in
this rep: A line given in $r$-space determines a sphere in $R$.
However, a sphere in $R$ given by $(X,Y,Z,H^{2})$ maps to two
lines in $r$, both being reciprocal polars with respect to the
linear line Complex $\pm H=r+\sigma=0$ in $r$. $H$ in $R$-space
plays the r\^{o}le of a sphere radius, so choosing $H=0$ amounts
to 'point spheres'\footnote{German: Punktkugeln \cite{lie:1872},
p.~171} mapping uniquely to the Complex $r+\sigma=0$ of $r$-space.

Finally, and pointing towards a third important aspect, it is
worth mentioning \cite{lie:1872} article \#28 which relates the
contact of Lie's spheres to intersection of lines. This emphasizes
the relevance of contact interactions in both pictures when
constructing and investigating symmetry and invariance principles.

For us, the essence of the reasoning so far -- remembering all
the various restrictions applied up to this point -- justifies
according to our current use of the Pauli spin (or the quaternion)
algebra in various physical contexts to reverse the viewpoint:
If we are to interpret Pauli matrices with {\it real} coefficients
and including the unit matrix to represent a 'radius', we have
to recall their origin from transformations in $R$-space and
their identification with some (inhomogeneous) line coordinates
which themselves describe, according to their direct relation
with the underlying linear line Complex, automatically an
extended (i.e.~'nonlocal') object -- a set of lines -- in real
3-space $r$.

\subsection{Some Aspects of Study's work}
\label{sec:studyswork}
Driven by some discussions throughout and following this
year's conferences with respect to Cartan's spin and to
unitary symmetries in QFT, especially when based on one
or more su(2) algebras, we've searched through literature.
So before performing some algebra related to sect.~\ref{sec:geom-r-space},
it is necessary and important to recall few historical
but obviously forgotten aspects which allows to rearrange
some aspects back into their original context.

Especially when facing the discussion of spin and unitary
symmetries, typically attributed to Pauli, Cartan and su(2)
(and certain su($n$)) algebras, the origins can be easily
traced back at least to Hesse's transfer principle (1866)
and Meyer's generalization (1883) (for references and an
outline see \cite{klein:1926}, \S 51) of rational curves
of a point $\lambda=\tfrac{\lambda_{1}}{\lambda_{2}}$ on
a line. For $n=2$, we thus obtain (planar) conic sections
parametrized by three homogeneous coordinates
$\rho x_{0}=\lambda_{1}^{2}$, $\rho x_{1}=\lambda_{1}\lambda_{2}$
and $\rho x_{2}=\lambda_{2}^{2}$, or appropriate linear
combinations. Choosing $n=3$ for later use, we obtain
3$^{rd}$ order curves parametrized by the four coordinates
$\rho x_{0}=\lambda_{1}^{3}$, $\rho x_{1}=\lambda_{1}^{2}\lambda_{2}$,
$\rho x_{2}=\lambda_{1}\lambda_{2}^{2}$ and $\rho x_{3}=\lambda_{2}^{3}$.
Now linear transformations of the line, alternatively re-expressed
by matrix transformations of the vector/'spinor' $(\lambda_{1}, \lambda_{2})^{T}$
with non-vanishing determinant, i.e.~by a 3-dim group\footnote{German:
dreigliedrige Gruppe}, lead to collineations in $\mathbbm{R}^{n}$
which exchange points on the (invariant) curve, for $n=2$ the
conic section. For further details see \cite{klein:1926} or
\cite{clebsch:1872}.

In the context of line and Complex geometry -- in a certain
sense continuing the heritage of \PLL and Lie -- one {\it must}
consider and honor Study's work (see \cite{study:1903}, or
\cite{study:1907} and references) which has been definitely
known to Cartan. Ad hoc, without enough time to work through
and synchronize notation, we found references and work in
M{\"u}nchner and Leipziger Berichte (where Cartan published
in german, too), and Mathematische Annalen, besides Study's
remarks on Lie's transfer principle in \cite{study:1917}.
The main task to make the mappings unique will focus on
introducing 'orientation' so that e.g.~(projective) lines
correspond to two (oriented) 'Speere' which -- on the
other hand -- introduces and requires metric (and sometimes
euclidean) concepts and objects, see e.g.~\cite{study:1903}.

Here, mentioning \cite{study:1907}, part II, p.~151, eqns.~(51,l)
and (51,r), Study explains the above 'spinor' notation, and
as such Cartan's 'definition', in 'elliptic' context and
SU(2)$\times$SU(2) (or quaternionic) transformations, whereas
in eq.~(52), he resolves the 'spinor' components linearly in
terms of his 'elliptic' line coordinates.

From our point of view, this emphasizes once more the use of
Complex geometry. However, Study's part II and his reasoning
with respect to 'elliptic' geometry has to be regarded with
time and care in detail, because in eq.~(1) on p.~119 he
assumes the absolute polar system as
$(xy)=x_{0}y_{0}+x_{1}y_{1}+x_{2}y_{2}+x_{3}y_{3}$. This allows
him to introduce real combinations of (homogeneous) line coordinates
in his eq.~(3). However, his eq.~(4), re-expressing the \PLL
condition of the line coordinates $X_{\alpha\beta}$ and using
six line coordinate combinations $X_{i}$, can be cast into
the Complex expression
\begin{equation}
X_{1}^{2}-X_{2}^{2}+X_{3}^{2}-X_{4}^{2}+X_{5}^{2}-X_{6}^{2}=0
\end{equation}
while exhibiting SO(3,3) symmetry for a point interpretation
of $X_{i}$, which directly relates to the fundamental form
of \PLu's line geometry (see also \cite{klein:1926}, \S 23,
especially p.~98).

However, if we switch Study's absolute polar system to
$(xy)=-x_{0}y_{0}+x_{1}y_{1}+x_{2}y_{2}+x_{3}y_{3}$ by introducing
an $i$ in the first (point) coordinate $\{\cdot\}_{0}$ so that the
\PLL coordinates $X_{0k}$ change to $iX_{0k}$, the coordinates
(up to overall $i$'s) in Study's eq.~(3) are Klein's coordinates
$z$ (\cite{klein:1926}, \S 23).

Anyhow, citing Klein's work on six Complexe in involution and their
threefold $\pm$-handedness (\cite{klein:1926}, \S 23, p.~99), or
facing Study's discussion of two spheres (or left/right quaternions)
above, it is evident that these properties represent PG in terms of
line and Complex geometry which reflects in certain known symmetry
groups\footnote{U(1) is almost always evident by planar projections.}
like SU(2), SU(2)$\times$SU(2) or even SU(4) of the (spinorial)
formulation of quantum theories.

\subsection{Basic Spin Commutators}
\label{sect:basiccommutators}
Now, having established the above matrix form of Lie transfer,
we want to insert a brief section related to practical application
and identification.

This time, we start from the matrix reps above in that we define
points in $R$-space right from the beginning and ask for the
r\^{o}le of the commutator as natural (antisymmetric) 'product'
of two such objects\footnote{There is some parallel background
from within classical polar theory of second order surfaces,
however, the calculations here are self-contained so we'll
discuss those issues in projective geometry at a later time.}.
As such, we define two 'points' ${\cal X}\sim\{X,Y,Z\}$ and
${\cal X}'\sim\{X',Y',Z'\}$, keeping the notation of the
inhomogeneous coordinates from above, but switching to positive
signs in eqns.~(\ref{eq:spin}) and (\ref{eq:maptopauli}),
respectively, by
\[
{\cal X}:=X\sigma_{1}+Y\sigma_{2}+Z\sigma_{3}=
\left(
\begin{array}{cc} Z & X-iY\\ X+iY & -Z\end{array}
\right)
\,,\quad
{\cal X}':=
\left(
\begin{array}{cc} Z' & X'-iY'\\ X'+iY' & -Z'\end{array}
\right)\,.
\]
Defining ${\cal C}$ mainly as commutator by
${\cal C}({\cal X},{\cal X}')$:=$\tfrac{1}{2}\left[{\cal X},{\cal X}'\right]$,
straightforward calculation yields
\begin{equation}
\label{eq:pauliproduct}
{\cal C}=
\left(
\begin{array}{cc}
i(XY'-YX') & ZX'-XZ'+i(YZ'-ZY')\\
XZ'-ZX'+i(YZ'-ZY') & -i(XY'-YX')
\end{array}
\right)\,.
\end{equation}
In order to get more insight, by using the two points
${\cal X}$ and ${\cal X}'$, we construct line coordinates
in $R$-space, i.e.~we define and use $P_{12}=XY'-YX'$,
$P_{23}=YZ'-ZY'$ and $P_{31}=ZX'-XZ'$. So eq.~(\ref{eq:pauliproduct})
reads as
\begin{equation}
\label{eq:lineproductR}
{\cal C}=
\left(
\begin{array}{cc}
iP_{12} & P_{31}+iP_{23}\\
-P_{31}+iP_{23} & -iP_{12}
\end{array}
\right)\,=\,
i\left(
\begin{array}{cc}
P_{12} & P_{23}-iP_{31}\\
P_{23}+iP_{31} & -P_{12}
\end{array}
\right)\,,
\end{equation}
where the rhs can be re-expressed in terms of Pauli spin
matrices as ${\cal C}=i(P_{23}\sigma_{1}+P_{31}\sigma_{2}+P_{12}\sigma_{3})$.
Although we are used to having the $i$ accompanying the
commutator of (Pauli) spin matrices, it is easy to transform
eq.~(\ref{eq:lineproductR}) into a real equation by introducing
quaternions, $q_{k}=-i\sigma_{k}$. Eq.~(\ref{eq:lineproductR})
changes into the equation
\begin{equation}
\label{eq:hlplineproduct}
{\cal C}=\frac{1}{2}({\cal X}{\cal X}'-{\cal X}'{\cal X})
=i(P_{23}\sigma_{1}+P_{31}\sigma_{2}+P_{12}\sigma_{3})\,.
\end{equation}
By multiplying both sides with $-1$, i.e.~$(-i)^2$ on the lhs,
we obtain $-{\cal C}=:\underline{{\cal C}}
=\frac{1}{2}(\underline{X}\,\underline{X}'-\underline{X}'\underline{X})
=\underline{P}$ where each underlining now denotes a real
quaternion, respectively, e.g.~$\underline{X}=Xq_{1}+Yq_{2}+Zq_{3}$,
$\underline{P}=P_{23}q_{1}+P_{31}q_{2}+P_{12}q_{3})$, etc.
If we transfer the spin notation above of
$\underline{{\cal C}}=-{\cal C}(\cal{X},\cal{X}')$
to real quaternion calculus, eq.~(\ref{eq:hlplineproduct}) reads as
$\underline{{\cal C}}(\underline{X},\underline{X}')=\underline{P}$,
i.e.~\emph{the product (or commutator) $\underline{{\cal C}}$ of
two real 'point' quaternions $\underline{X}$ and $\underline{X}'$
yields a real quaternion holding the three spatial \PLL coordinates}.
We may, in addition, recognize the striking index ordering in
eqns.~(\ref{eq:lineproductR}) and (\ref{eq:hlplineproduct}) as
well as ask for further commutators of those objects.

\subsection{Advanced Spin Commutators}
\label{sect:advancedcommutators}
If we denote the components $P_{i}$ of the '\PLu' quaternion
$\underline{P}$ above through $\underline{P}=P_{i}q_{i}$, by
performing some algebra we obtain
$\underline{{\cal C}}(\underline{X},\underline{P})=(P_{kj}x_{j})q_{k}
=:\underline{U}$. Whereas in QFT, we would now have to consider
higher and increasing order of 'vector' products, reducable by
quadratic (mass/momentum) constraints and angular momentum algebra,
here we can stress the origin of $\underline{P}$.

By switching to the general context in terms of homogeneous
coordinates, we can use the relation of linear Complexe and
null systems. As such, in terms of homogeneous coordinates
it is $P_{\alpha\beta}$ which relates $x_{\beta}$ to the dual
plane coordinatized by $u_{\alpha}$. Whereas in the polar
case, incidence $u_{\alpha}x_{\alpha}=0$ of point and plane
is special, treating null systems, the incidence relation is
always satisfied, i.e.~point and plane intersect because of
antisymmetry of $P_{\alpha\beta}$ in
$u_{\alpha}x_{\alpha}=P_{\alpha\beta}x_{\beta}x_{\alpha}=0$.

Recalling this background from PG, by considering the real
quaternion $\underline{U}$ above, its three components realize
(almost) the spatial part of a null system in terms of the
associated planar coordinates $u_{i}$.

It is obvious that we have to enhance the mechanism because
at this stage we've lost contact to the $0$-components of the
complete null system, and to the $0$-coordinates of points
and planes in homogeneous rep. What remains open here, is
the question whether this quaternionic calculus is sufficient
to represent inhomogeneous calculations in mechanics and
electrodynamics, i.e.~comparison to experimental (classical)
data.

Possible enhancements are obvious because the su(2) rep above
is related to one line only. By recalling the two skew (and
thus independent) lines above which we can identify either
as opposite edges of a (fundamental) tetrahedron or as the
two lines of a Congruency \cite{dahm:MRST4}, we can almost
automatically enhance the scheme by another independent su(2)
(or quaternion) of the second (skew) line, so that the general
construction scheme comprises SU(2)$\times$SU(2) (or
SL(1,$\mathbbm{H}$)$\times$SL(1,$\mathbbm{H}$)) or SU(4) (or
SL(2,$\mathbbm{H}$)$\cong$SU$*$(4)), so we've closed the loop
to our original starting point SU(4) or Dirac algebra in terms
of SU$*$(4) (see \cite{dahm:MRST4}, \cite{dahm:MRST5} and refs
there). SO(6) and the various real forms SO($n$,$m$), $m+n=6$,
can be related either to their unitary covering groups, or by
starting from SO(3,3) or SO(6) in line geometry by coordinate
complexification, either of lines or points (thus, however,
changing the respective absolute element or polar system, and
in consequence the related underlying geometry). We postpone
further discussions here.

Last not least, while realizing PG aspects by quaternions and
their commutators, it is important to note that (in general)
$\underline{{\cal C}}(\underline{X}'',\underline{P})
\sim[\underline{X}'',\underline{P}]
\sim[\underline{X}'',[\underline{X},\underline{X}']]$. This
discussion can be extended to Jacobi identities, triple systems,
curvature, and further geometric relations.

\subsection{Lagrangean Construction}
\label{sec:lagrangean}
So far, after having related 'spinors' and SU(2) spin reps
by means of Lie transfer to line and Complex geometry, we
have to focus on appropriate Lagrangean constructions in
order to reflect Complex invariants and dynamics, and
provide the Lagrangean (or Hamiltonian) apparatus.

Here, we'll firstly focus on the photon rep of the QED
Lagrangean, i.e.~we'll postpone the construction of matter
fields and the discussion of Dirac or Clifford algebra for
a moment and focus on the construction principle using Complexe.
This reflects the fact\footnote{For details, see \cite{dahm:MRST5}
sec.~III with respect to relativistic symmetry and to symplectic
geometry, thus stabilizing a certain linear Complex.} that
the photon rep almost automatically corresponds to a special
linear Complex \cite{dahm:MRST4}, \cite{dahm:MRST5} while
obeying (and respecting) special relativity. Relativistic
aspects will be treated in more detail in part VIII.

Above, we've shown that the 'spinor' discussion is a subset
of Complex geometry right from Lie's paper. So to discuss
invariance and construct invariant elements in Complex geometry,
we have lots of geometrical possibilities, some of which
we've already mentioned elsewhere. On the ground of Klein's
Erlanger program, being in the regime of projective transformations,
we may stress directly (quadratic) tetrahedral Complexe leaving
anharmonic ratios of line intersections with a (fundamental)
tetrahedron invariant. With respect to second order surfaces
to be discussed in part VIII as absolute elements of non-euclidean
geometry, we may as well consider polar or tangential Complexe.
And possible degeneracy or Clebsch's paper on Complex symbolism
\cite{clebsch:1869} suggests to consider assemblies or powers
of individual (special) linear Complexe as well in the basic
construction process.

Now the first major step is to identify electromagnetism by means
of a special linear Complex. The \PLL condition
$P:=p_{01}p_{23}+p_{02}p_{31}+p_{03}p_{12}=0$ suggests to identify
the field strengths $\vec{E}$ and $\vec{B}$, i.e.~we have
$\vec{E}\cdot\vec{B}=0$, so initially we can identify $\vec{E}_{i}$
and $\vec{B}_{i}$ as six \PLL coordinates. Having argued in
\cite{dahm:MRST5} with Klein's papers of 1869 and 1871 (see also
\cite{klein:1926}), here we introduce some linear combinations
$y$ of \PLu's line coordinates $p\sim x$ according to the notation
\cite{klein:1926}, p.~98, and we obtain (up to a factor 4)
\begin{equation}
\vec{E}^{2}-\vec{B}^{2}\,=\,\vec{E}^{2}+\vec{iB}^{2}
\,=:\,\Omega\,,
\end{equation}
which Klein defines as an invariant $\Omega$ of the linear Complex
and states $\Omega=0$ as condition for a special linear Complex.
Recall that this decomposition historically gave rise to various
discussions of SU(2)$\times$SU(2) reps, as well as various
complexifications thereof, mostly celebrating vector/'spinor'
calculus.

Re-expressed in contemporary notation, we can compare e.g.~with
\[
-F_{\mu\nu}F^{\mu\nu}\sim\vec{E}^{2}-\vec{B}^{2}\,=\,\Omega\,,\quad
G_{\mu\nu}F^{\mu\nu}\sim\vec{E}\cdot\vec{B}=\,P\,,\,
G_{\mu\nu}=\frac{1}{2}\epsilon_{\alpha\beta\mu\nu}F^{\alpha\beta}
\]
being the hodge dual which we've related earlier to conjugation
and polar theory of Complexe.

So working with simple invariants of linear special Complexe,
only, comprises known QED Lagrangean formulations. From the
decomposition of quadratic Complexe or investigating pencils
of linear Complexe, we know that we have to treat regular
Complexe as well, so besides using the above quadratic expressions
to enforce projective invariance or absolute elements, we expect
the individual as well as the simultaneous invariance theory
of general linear Complexe (special as well as regular) to
comprise an appropriate basis of Lagrangean construction.
Standard unitary symmetries are included as we've shown already
above.

\section{Summary and Outlook}
\label{sec:outlook}
Essentially, we have shown that su(2) and the Pauli rep according
to Lie's setup is an artifact emerging from line geometry, and a
degenerated case of Complex geometry. Lie transfer puts classical
PG and sphere geometry side by side, and we've found especially
real quaternion calculus formally realizing known geometry based
on null systems, as soon as one understands the commutator as a
generalized product. However, this needs deeper and more complete
research. The general framework superseding this type of algebra
is Complex geometry, and we have connected previous work by closing
the circle to twofold quaternions and certain unitary symmetries
we've started with. The outline and development, however, suggests
to consider typical spin applications or SU(2) symmetry in physics
from the viewpoint of line or Complex geometry as well.

\section*{References}

redpajama_set_name: RedPajamaArXiv


text:
Tag Archives: Building on the National Dementia Strategy
Dementia Today and Tomorrow (Deloitte / Alzheimer's Society)
Posted on March 6, 2015	by Dementia and Elderly Care News
Summary This report, from the Deloitte UK Centre for Health Solutions in collaboration with the Alzheimer's Society, summarises the emerging consensus and outcomes developed from a series of events and initiatives which aimed to collect the views of people interested … Continue reading →
Posted in Alzheimer's Society, Charitable Bodies, Commissioning, Community Care, Diagnosis, End of Life Care, For Carers (mostly), For Doctors (mostly), For Nurses and Therapists (mostly), For Researchers (mostly), For Social Workers (mostly), Integrated Care, Management of Condition, Models of Dementia Care, National, Non-Pharmacological Treatments, Patient Care Pathway, Person-Centred Care, Personalisation, Quick Insights, Standards, UK, Universal Interest	| Tagged 15-Minute Home Care Visits, Access and Equity For Care Home Residents to Local NHS Services, Access to Care, Acute Hospital Care, Admissions to Nursing Care, Admissions to Residential Care, Adult Social Care Funding, Ageing and Dementia, Ageing and Society, Ageing Policy in the UK, Ageing Population Carer Support, Alternatives to Hospital Admission, Alternatives to Hospital Care, Alzheimer's Society Carers Café's, Amanda Scott: Managing Director of Sunrise Senior Living, Anne-Marie Hamilton: Strategic Programmes at Public Health England, Assistive Technology, Avoidable Hospital Admissions, Awareness Campaigns, Baroness Sally Greengross (APPG on Dementia), Baroness Sally Greengross: Chief Executive of the International Longevity Centre UK, Benefits of Telehealth, Better Care Fund (BCF), Bradford Dementia Group, Building on the National Dementia Strategy, Capitation Bsed Funding Models, Care Act 2014, Care Funding, Care Home Residents, Care Homes, Care in the Community, Care Packages, Care Quality Commission (CQC), Career Pathways for HCAs, Carer Support Services, Carers' Career Pathways, Carers' Career Progression, Challenge on Dementia (David Cameron), Challenges of Reconfiguration, Clinical Commissioning Groups (CCGs), Commissioning Home Care, Commissioning of Homecare Services, Community Support Services, Continuing Care, Cross-Boundary Care Pathway Redesign, Cross-Sector Partnerships, David Cameron, Deborah Sturdy: Red and Yellow Care, Deloitte LLP ("Deloitte"), Deloitte UK Centre for Health Solutions, Dementia Action Alliance (DAA), Dementia Advisers, Dementia Advisor, Dementia Advisor Service, Dementia Advisor Services, Dementia Advisors, Dementia Awareness, Dementia Awareness Training, Dementia Care in Care Homes, Dementia Care in Hospitals, Dementia Challenge, Dementia Friendly Communities Dementia Friends, Dementia Friends, Dementia Friends Campaign, Dementia Friends Champions, Dementia Friends Programme, Dementia Health and Care Champion Group, Dementia Information Prescription, Dementia Pathway Re-Configuration, Dementia Research, Dementia Risk Factors, Dementia Today and Tomorrow (Deloitte), Dementia-Friendly Care Homes, Dementia-Friendly Cities, Dementia-Friendly Communities, Department of Health Dementia Challenge, Department of Health Dementia Challenge (2020), Digital Technology, Dignity in Care, Dignity in Dementia, Disease Modifying Treatment by 2025 (Aim), Dr Martin McShane: NHS England's Director for People With Long Term Conditions, Early Diagnosis, Eligibility Criteria for Social Care, Emerging Technology, Enabling Technology, End-of-Life Support, English National Dementia Strategy, Extra Care Housing, Extra Care Housing and Dementia, Fair Access to Care Services (FACS) Eligibility Criteria, Family Carers, Five Year Forward View (NHS England), Free Care Home Places, Gavin Terry: Policy Manager at Alzheimer's Society, George McNamara: Head of Policy and Public Affairs at Alzheimer's Society, GP Access, Guidepost Trust's Dementia Information Prescription, Health and Social Care Act (2012), Health and Social Care in the Community, Health and Social Care Integration, Health and Wellbeing Boards (HWBs), Health Care for Older Care Home Residents, Healthy Behaviours, Healthy Communities, Healthy Lifestyles Improving Care for People with Dementia, Helen O'Kelly: Strategic Clinical Network Assistant Lead (London Region) at NHS England, Hilary Evans: Charity Director of Alzheimer's Research UK, Home Care, Home Care Funding and Costs, Homecare and Care Home Workers, Hospital Care, Hospitals and Care Homes "Speaking Dementia", House of Care Model, Inappropriate Hospital Admissions, Inappropriate Prescribing, Inappropriate Use of Antipsychotics in Dementia, Independence, Independence at Home, Independent Living At Home, Independent Living With Care, Informal Carers, Information and Support for Patients and Carers, Innovation for an Ageing Population, Integration of Health and Social Care, Involvement and Participation, Jeremy Hughes (Alzheimer's Society Chief Executive), Jewish Care, Jill Rasmussen: Royal College of General Practitioners Dementia Champions, Join Dementia Research, Join Dementia Research: Recruitment Onto Dementia Studies Lifestyle Risk Factors, Jonathan Walden: Public Health England, Josie Dixon: Personal Social Services Research Unit at London School of Economics, Karen Taylor: Director of Centre for Health Solutions (Deloitte), Kristina Glenn: Director of Cripplegate Foundation, Lifestyle Risk Factors, Living Well with Dementia, Living Well with Dementia Research, Local Dementia Action Alliances, Local Dementia Action Alliances in England, Local Government, Local Health and Care Economies, Local Health and Care Services, Local Health and Wellbeing Boards, Local Health Economies, Local Variations, Loneliness and Dementia, Loneliness and Social Isolation, Maelenn Guerchet: King's College London, Maintaining Independence, Making Hospital Admission the Option of Last Resort, Memory Loss, Mobile Technology, National Dementia Strategy, National Funding Streams for Training Social Care Staff, NDSE: National Dementia Strategy (for England), Needs of Older People Living in Care Homes, NHS Continuing Care, NHS England Five Year Forward View, NHS Five Year Forward View (5YFV), NHS Service Reconfiguration, Peer Support, Personal Budgets, Personalised Customised Care Packages, Peter Watson (Carer), Phil Hope: Former Minister of Care Services, PM Challenge on Dementia: Health and Care Champion Group Subgroup on Dementia and Homecare, Pooled Budgets (Pooled Funds), Pooled Funding, Post-Diagnosis Support, Prevalence of Dementia, Prevention, Prime Minister's Challenge on Dementia, Prime Minister's Office, Prime Minister's Challenge On Dementia 2020, Prime Minister's Dementia Challenge, Professor Dawn Brooker, Professor Murna Downs, Professor Sube Banerjee, Professor Sube Banerjee: Brighton & Sussex Medical School, Public Health, Public Health England (PHE), Public Participation in Research, Public Sector, Public Sector Outcomes, Quality of Care, Quality of Care Across the Course of Dementia, Quality of Care and Support, Quality of Care for People With Dementia, Recording Equipment, Recruitment of HCAs, Recruitment Training and Management of HCAs, Redesigning Services, Reducing Admissions to Nursing Care, Reducing Admissions to Residential Care, Reducing Inappropriate Use of Antipsychotics in Dementia, Reducing Stigma, Research and Innovation, Resource and Incentives, Risk Factors, Risk Factors for Alzheimer's Diseease, Risk Management, Roundtable Discussions on Dementia Issues (2014), Royal College of Psychiatrists, Sandra Evans: Fellow, Sarah Bickerstaffe: Institute for Public Policy Research, Sarah Bickerstaffe: Strategy Lead at Care Quality Commission, Sarah Pickup: Deputy Chief Executive at Hertfordshire County Council, Service Redesign, Sheena Wyllie: Director of Dementia Services at Barchester Healthcare, Skills for Care, Staying Independent, Support for Carers, Support to Care Home Residents, Surveillance to Monitor Care, Sustainable Care, Sustainable Health and Care Services, System Re-Design, Tackling Barriers to Innovation, Tamsin Berry: Head of Policy and Programmes at Public Health England, This is Me, Tim Curry: Royal College of Nursing, Timely Diagnosis, Training and Education, Unhealthy Behaviours, Unhealthy Lifestyles, Unhealthy Living, Unmet Needs, Unpaid Caregivers (Carers), Unpaid Carers, Value for Money, Variations in Quality of Care, wilderness, Workforce Development, Workforce Training, Worried About Your Memory, Years	| Leave a comment
National Dementia Policy: Formation of Dementia Advisory Group (Department of Health / Dementia Challenge)
Summary The Department of Health intends to publish a renewed "vision" for strategic direction, with plans up to 2020, on the future of dementia policy in England. It should be ready by early 2015. This will continue and extend existing … Continue reading →
Posted in Acute Hospitals, Age UK, Alzheimer's Society, Carers UK, Charitable Bodies, Commissioning, Community Care, Dementia Action Alliance, Department of Health, Diagnosis, End of Life Care, For Carers (mostly), For Doctors (mostly), For Nurses and Therapists (mostly), For Researchers (mostly), For Social Workers (mostly), Integrated Care, Management of Condition, Models of Dementia Care, National, Non-Pharmacological Treatments, Patient Care Pathway, Person-Centred Care, Quick Insights, Standards, UK, Universal Interest	| Tagged Alzheimer's Research UK, Assistive Technology, Association for Dementia Studies: University of Worcester, Association of Directors of Adult Social Services (ADASS), Awareness and Understanding, Bridget Warr: UK Home Care Association, Bruce Bovill (Carer), Building on the National Dementia Strategy, Care England, Care Models, Carer Support, Carer Support Services, Clara Swinson: Chair of Dementia Advisory Group, Clara Swinson: Director for Social Care Policy at the Department of Health, Cost Neutral Plans on Policy Development, Cross-Boundary Care Pathways, Cross-National Research, Cross-Organisation Learning, Cross-Sector Partnerships, Cross-System Modelling, David Pearson: Association of Directors of Adult Social Services, Dementia Action Alliance (DAA), Dementia Advisory Group, Dementia Care: Unpaid Care Contribution, Dementia Challenge, Dementia Friendly Communities Champion Group, Dementia Health and Care Champion Group, Dementia Policy, Dementia Research, Dementia Research Champions Group, Dementia Research Priorities, Dementia UK, Department of Health Dementia Challenge, Department of Health's National Dementia Strategy (Continuing Development), Department of Health: Dementia Policy Team, Digital Technology, Domestic Dementia Policy (England), Emerging Technology, Enabling Technology, English National Dementia Strategy, Future Commissioning Models, Future of Dementia Advisory Group (aka the Dementia Advisory Group), Graeme Whippy: Lloyds Banking Group, Graeme Whippy: PM Challenge Dementia Friendly Communities Champion Group, Graham Stokes: Chair of Dementia Action Alliance, Health and Care Champion Group, Health Technology, Helen Kay: Local Government Association, Helena Herklots: Carers UK, Hilda Hayo: Chief Executive of Dementia UK, Information Technology, Innovative Models, International Activity, International Collaborations, International Comparisons, Involvement and Participation, Jeremy Hughes (Alzheimer's Society Chief Executive), Jill Rasmussen: Royal College of General Practitioners Dementia Champions, Joy Watson (Person Living With Dementia), Local Government Association: LGA, London School of Economics, Lorraine Jackson: Deputy Chair of Dementia Advisory Group, Lorraine Jackson: Deputy Director for Dementia Domestic Policy, Martin Green: Care England, Martin Knapp: London School of Economics, Mobile Technology, National Council for Palliative Care, National Dementia Plans, National Dementia Policy, National Dementia Strategy, NDSE: National Dementia Strategy (for England), NDSE: National Dementia Strategy (Renewed Plans for England), New Models of Care, New Technology, Outcomes for People with Dementia: Building on the National Dementia Strategy, Patient and Public Involvement, Patient Engagement, Patient Involvement, Paul Lincoln: UK Health Forum, Post-Diagnostic Support, Prevention, Prime Minister's Challenge on Dementia, Prime Minister's Dementia Challenge, Professor Dawn Brooker, Professor Martin Knapp: Director of the Personal Social Services Research Unit at the London School of Economics and Political Science (LSE), Professor Martin Rossor: Former Director of the NIHR Dementia and Neurodegenerative Disease Research Network (DeNDRoN), Professor Martin Rossor: NIHR National Director for Dementia Research, Professor Martin Rossor: UCL Institute of Neurology, Public Engagement, Public Involvement in Research, Quality Outcomes for People with Dementia: Building on the National Dementia Strategy, Research Champion Group, Risk Reduction, Sarah Pickup (ADASS), Sarah Pickup: Hertfordshire County Council, Sarah Pickup: PM Challenge Health and Care Champion Group, Service Models, Simon Chapman: National Council for Palliative Care, Tim Parry: Alzheimer's Research UK, Tom Wright: Age UK, Tony Watson (Carer), UK Dementia Policy Framework, UK Dementia Policy Framework Development, UK Health Forum, UK Home Care Association, University of Worcester, Unpaid Caregivers (Carers), Unpaid Carers, User Involvement	| Leave a comment
Building on the National Dementia Strategy and the PM's Dementia Challenge (APPG)
Summary The All-Party Parliamentary Group on Dementia (APPG) earlier this month released their proposals for a long-term national plan for dementia. This "Building on the National Dementia Strategy: change, progress and priorities" report has been published five years after the … Continue reading →
Posted in Acute Hospitals, Alzheimer's Society, Charitable Bodies, Commissioning, Community Care, Diagnosis, For Carers (mostly), For Doctors (mostly), For Nurses and Therapists (mostly), For Researchers (mostly), In the News, Integrated Care, Management of Condition, Mental Health, Models of Dementia Care, National, Non-Pharmacological Treatments, Patient Care Pathway, Person-Centred Care, Quick Insights, Standards, UK, Universal Interest	| Tagged 15-Minute Home Care Visits, Adult Social Care Outcomes Framework (ASCOF), Advice and Support, All-Party Parliamentary Group (APPG), Alzheimer's Society, ASCOF: Adult Social Care Outcomes Framework, Baroness Sally Greengross (APPG on Dementia), Better Care Fund, Building on the National Dementia Strategy, Care Act, Care and Support, Care Coordinators, Care Funding, Carer Support, Carer Support Services, CCGs, CCGs: Clinical Commissioning Groups, Challenge on Dementia (David Cameron), Clinical Commissioning Groups, Clinical Commissioning Groups (CCGs), Collaborative Working, Commissioning, Commissioning Local Services, Community Support Services, Community-Based Support, Coordination of Care, Crisis Prevention, Crisis Support, Dementia Advisers, Dementia Advisor Service, Dementia Advisors, Dementia Challenge, Dementia Coordinator, Dementia Leadership, Dementia Leads, Dementia Pathway Coordinator, Dementia Practice Coordinator, Dementia Strategy, Dementia Support Services, Dementia-Friendly Communities, Dementia-Supportive Communities, Department of Health Dementia Challenge, Diagnosis and Support, Discharge Coordination, Greater Manchester West Mental Health NHS, Hampshire County Council, Independence, Independence at Home, Independent Living, Independent Living At Home, Institute of Public Policy Research, Integrated Care and Support, Integrated Care Coordinators, Lambeth CCG, Lewisham CCG and London Borough of Lewisham, Living with Dementia, Living With Dementia Group (LWDG), Local Authorities, Local Government Association, Local HealthWatch, London Borough of Hackney, London Borough of Islington, London Borough of Redbridge, Maintaining Independence, Memory Services National Accreditation Programme, Memory Services National Accreditation Programme (MSNAP), MSNAP: Memory Services National Accreditation Programme, Named Care Coordinators, Named Clinician, Named GPs for Over-75s, National Collaboration for Integrated Care and Support, National Dementia Strategy, National Housing Federation, National Housing Federation: Dementia and Housing Working Group, NDSE, NDSE: National Dementia Strategy (for England), New Approaches to Coordinating Care, NHF: National Housing Federation, North Norfolk CCG, Nursing Workforce, Orchard Care, Personal Social Services Research Unit, Personal Social Services Research Unit (PSSRU), Peterborough City Council, Post-Diagnosis Support, Post-Diagnostic Dementia Support, Prime Minister's Challenge on Dementia, Prime Minister's Dementia Challenge, Quality of Life for People With Dementia, Royal College of Nursing (RCN), Skills for Care, Skills for Care (SfC), Social Care Workforce, Sussex Partnership NHS Foundation Trust, UK Home Care Association, UK Homecare Association, Unison, University College London Hospitals, University College London Partners, Voluntary Sector, Voluntary Sector Organisations, Voluntary Sector Strategic Partnerships, West Norfolk CCG, Workforce, Workforce and Skill Mix, Workforce Development, Workforce Issues	| 1 Comment


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"NEVER TELL ME THE ODDS!" – HAN SOLO
[RETROSPECTIVE] THE ABSOLUTELY CORRECT AND FINAL RANKING OF THE MCU FILMS PART 1
Posted On April 29, 2019 April 29, 2019 By Michael Walls-Kelly
Avengers: Endgame is out, and it's the finale that the Marvel Cinematic Universe has been leading towards over 11 years and 21 films. It's the climax of these characters and these storylines. Everything has been building towards this.
If you ignore the story changes and narrative dead-ends leading up to it, and if you ignore the fact that they're still making plenty of films after this.
Clearly, I'm a bit of an MCU skeptic.
Since they'll be making these things until the heat death of the universe — or until Disney stops turning a neat profit from them, whichever comes first — once Endgame comes out seems like a perfectly good time to rank these movies. Now, this isn't going to be your arbitrary, run-of-the-mill list. This is the 100-percent correct way to order them, and I'll hear no arguments to the contrary.
Keep in mind that there may be spoilers from here on out! For Part 1, I'll go over the bottom two tiers of the MCU: Tier F and Tier C. These are the absolute dregs of the cinematic universe. I'll explain why I find each entry terrible or forgettable or a waste of time.
Speaking wastes of time, let's get started!
TIER F
22. Marvel's The Avengers (2012)
I feel like this will be the biggest difference between my list (AKA the Correct List) and someone else's. People usually consider Marvel's The Avengers either a great movie or an important one. I consider it an embarrassing movie. The big team-up movie that concluded the first Phase of the MCU certainly has spectacle, and the actors are mostly game, but it really is a mess. Captain America feels like a completely different character from his first solo outing, Tony Stark is written like a parody of himself, the dialogue is too clever by half, and a big chunk of the film is spent in hallways and boardrooms. Also, it's an incredibly bad-looking film.
I don't blame the cinematographer, because I know Seamus McGarvey can shoot a blockbuster — just look at 2014's Godzilla — so I don't know what happened. The washed-out color palette set a depressing house style for most of the MCU, but the odd, unimaginative framing and blocking choices are wholly original.
Also, the three main Avengers try to murder each other when they all meet. Really cool, guys.
21. Thor: The Dark World (2013)
A forgettable follow-up to a forgettable first film. Thor: The Dark World is competently directed and utterly unremarkable. Its cardinal sin is plastering Christopher Eccleston in prosthetics and making him monologue in a made up language. It wasn't the first time Marvel wasted a great actor on a pointless villain, and it wouldn't be the last. Tom Hiddleston continues to do solid work, and his chemistry with Chris Hemsworth in this outing was a sign of good things to come, but other than a few fun and original action beats, the eighth entry in the MCU never takes hold.
20. Avengers: Infinity War (2018)
Sure, I agree that Thanos is the main character in Avengers: Infinity War. That's fine. But a lot of the two-and-a-half-hour runtime is spent on the actual Avengers, and very little of that time is interesting, revealing, or emotionally satisfying. There are a couple of good things about the movie: Thor meeting the Guardians was well done, Tom Holland was acting his ass off, the fight on Titan was neat and … I mean, that's pretty much it. The majority of the action scenes are insultingly bland, focusing a major plotline we're supposed to get emotionally invested in on two barely-developed characters was a huge mistake, and some of the CGI in the final battle is shockingly bad. The whole movie felt anodyne, and it was just going through the motions.
Infinity War is the definition of sound and fury signifying nothing.
19. Avengers: Age of Ultron (2015)
The best of the Avengers films, which is damning with faint praise. Age of Ultron is a mess of ideas, clearly chopped up in the editing room, with a wasted villain and a brazen retread of a finale. There are two things that put it higher in the ranks than the other films. It looks a little better, and it plays around with some interesting ideas. Joss Whedon continues to write Captain America poorly, but this time, he also rolls back any development Tony Stark had in his solo films. Stark at least gets an interesting-ish "mad scientist" storyline.
The entire film plays around with horror movie imagery like that, i.e., Eastern European castles, Ultron looking like the Mummy, Hulk transforming like the Wolf Man, Vision being a Frankenstein Monster. None of it comes together well though, and they're just tossed off ideas. And, worst of all, Tony Stark is proven right at the end. The guy can do no wrong!
18. Thor (2011)
Thor AKA Kenneth Branagh's take on a Power Rangers movie. This is a real hodgepodge of a film. It meshes the cosmic Shakespearean Asgard parts with a much cheaper fish-out-of-water, small town on Earth storyline. There really isn't much to say about Thor. It's just sort of there. Some of the stuff is really bad (Thor's eyebrows, the plastic-y costumes, the gratuitous Hawkeye cameo) but Stellan Skarsgård, Anthony Hopkins, and Tom Hiddleston make some of the rougher moments watchable. I know there are some people who think Thor is the best film in the MCU. Know what I call those people? Sickos and perverts.
17. Iron Man 2 (2010)
Iron Man 2 has the weird distinction of being considered bad among even the die-hard MCU fans. It has its defenders, like any movie, but even early on, it was pointed to as an example of how the MCU could go wrong (see also: The Dark World and Age of Ultron). Generally, I agree. Iron Man 2 ratchets Tony Stark up to an obnoxious degree, then adds a second Tony Stark with Sam Rockwell's Justin Hammer. The entire S.H.I.E.L.D. plotline is boring, and it's an embarrassing introduction to Scarlett Johansson's Black Widow.
On the plus side, it's a good-looking film since it released pre-washed out MCU house style. The film also has an interesting villain, someone who could make Tony Stark confront his privilege and his family history … but no! The movie gives his character a cheap out, one of the many times the Stark character will be cushioned by the hands of the content creators.
TIER C
16. Avengers: Endgame (2019)
I wouldn't go so far as to call Avengers: Endgame the culmination of the 21 previous films, but it's absolutely the culmination of the Russo Brothers films within the Marvel Cinematic Universe, which involves some heavy referencing to everything else. Endgame is undoubtedly a people-pleaser, and it pays off in fits both obvious and entertaining. At three hours long the thing is a damned beast, and I guess it deserves some credit for at least feeling like a whole product. However, it's a sin that this much money went into a film that ends with two armies running at each other on a brown battlefield. There are some good things about the film: Paul Rudd is a treasure and actually sells the weight of the time jump, Chris Evans is wasted completely in Infinity War but they more than make up for it here. It's also a nice surprise that Nebula happens to be one of the most important characters in this film.
Overall, it's too much of a mess with too little to love. People who enjoyed Infinity War will dig it though.
15. Captain Marvel (2019)
Overall Captain Marvel feels … perfunctory? They wanted Captain Marvel in the MCU, so they did minimum necessary to make that happen. To be fair, the film does try to do some interesting stuff. De-aged Nick Fury is equal parts eerie and fun, and Ben Mendelsohn seems to be enjoying himself, but the '90s setting is never taken advantage of in any meaningful way. The biggest problem is kind of a fault of the story they're telling: Captain Marvel herself is a bit of a black hole at the center of the movie. I know it's about her lost memories and discovering who she truly is, but Brie Larson has been an engaging presence in other films. It's a shame she didn't get a chance to shine here.
14. Captain America: Civil War (2016)
This isn't really a Captain America movie. It's an Avengers movie. As such, it's the best of the bunch! As a solo Captain America film, it's the pits. Civil War tries to do a lot, which I guess is commendable, but it's pretty incompetent at a lot of it. The sides that Tony Stark and Captain America take don't make a lot of sense character-wise, it feels incredibly over-stuffed with two competing leads, the death toll retcons from the previous films are laughable, and that final airport battle is really bad. One of the only sparks of life in the whole thing is Paul Rudd popping up, which seems to be a theme with these team-up movies. The rest of it is a grey slog.
13. Doctor Strange (2016)
Doctor Strange AKA What If Iron Man But Also Batman Begins? Some of the effects are cool, and the ending is novel, but it's mostly a waste of a stacked supporting cast. In fact, you know your movie is in trouble when every supporting cast member would make a much more interesting Doctor Strange. It's also pretty telling that Strange has been a more interesting character every movie he's been in other than his solo film.
12. Ant-Man and the Wasp (2018)
This prequel to Infinity War feels like a lot of wheel-spinning. I don't mind a self-contained film that has little to do with the MCU as a whole — hell, I probably prefer it — but the key to that is to make the self-contained story actually interesting. Paul Rudd continues to be an affable lead for this type of action, and Evangeline Lilly's expanded role is appreciated. You can tell that a lot of the inventive action scenes from the first Ant-Man were likely thought up in pre-production by Edgar Wright before he left the project. Nothing in Ant-Man and the Wasp feels as inventive as anything in the first film.
Plus it should be a capital offense to waste Michelle Pfeiffer like this.
11. The Incredible Hulk (2008)
The redheaded stepchild of the MCU. I kind of want to like The Incredible Hulk just because it's an underdog … but it's pretty bland. A fair bit of it actually works. Edward Norton is an interesting Bruce Banner (and it's really funny to think of Norton running around with Thor and fighting Thanos), and Tim Roth is a great villain. The fight at the university is a standout action scene. By all accounts, a dry-run for what Captain America's powers were going to look like. Unfortunately, the movie drags a lot, and the final act is like a video game cut scene. The effects for the Hulk are boring in this movie, and nowhere near as good as they were a few years earlier in Ang Lee's Hulk.
So that's the first two tiers! We've got the real crap out of the way, and in Part 2 we'll finally get to the good stuff.
#Featured #Movies #Reviews
Tagged: Age of Ultron Ant Man Ant-Man & The Wasp avengers Captain America Captain Marvel Chris Evans Cinematic Universe doctor strange Endgame infinity war Iron Man Marvel MCU Robert Downey Jr The Dark World the incredible hulk thor tony stark
Michael Walls-Kelly
michaelwallskelly@gmail.com
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[TV] YOUR QUICK GUIDE TO STAR TREK: PICARD
[INTERVIEW] THE TALENTED STEPHANIE SHEH
[REVIEW] THE BBC AND NETFLIX'S 'DRACULA' IS A SHAMBLING, WILDLY EXPENSIVE MESS
[REVIEW] HOW DOES A GRAPHIC NOVELIST MAKE MARCEL PROUST RELEVANT AGAIN?
[CRAFTS] DISNEY IS CRACKING DOWN ON ETSY STORES SELLING HANDMADE BABY YODAS
FALL TV '19
UNBELIEVABLE, NETFLIX (SEPT 13)
UNDONE, AMAZON (SEPT 13)
THE LAST KIDS ON EARTH, NETFLIX (SEPT 17)
AMERICAN HORROR STORY, FX (SEPT 18)
PRODIGAL SON, FOX (SEPT 23)
EMERGENCE, ABC (SEPT 24)
MIXED•ISH, ABC (SEPT 24)
STUMPTOWN, ABC (SEPT 25)
CREEPSHOW, SHUDDER (SEPT 26)
SUNNYSIDE, NBC (SEPT 26)
THE POLITICIAN, NETFLIX (SEPT 27)
GODFATHER OF HARLEM, EPIX (SEPT 29(
ALMOST FAMILY (OCT 2)
RAISING DION, NETFLIX (OCT 4)
PRIMAL, THE CW (OCT 7)
NANCY DREW, THE CW (OCT 9)
BATWOMAN, THE CW (OCT 10)
EL CAMINO: A BREAKING BAD MOVIE, NETFLIX (OCT 11)
LIMETOWN, FACEBOOK WATCH (OCT 16)
LOOKING FOR ALASKA, HULU (OCT 18)
LIVING WITH YOURSELF, NETFLIX (OCT 18)
WATCHMEN, HBO (OCT 20)
CATHERINE THE GREAT, HBO (OCT 21)
MRS. FLETCHER, HBO (OCT 27)
DICKENSON, APPLE TV+ (NOV 1)
SEE, APPLE TV+ (NOV 1)
FOR ALL MANKIND, APPLE TV+ (NOV 1)
THE MORNING SHOW, APPLE TV+ (NOV 1)
HIS DARK MATERIALS, HBO (NOV 4)
THE MANDALORIAN, DISNEY+ (NOV 12)
THE L WORD: GEN Q, SHOWTIME (DEC 8)
DOLLFACE. HULU (NOV 15)
THE GILDED AGE, HBO
THE WITCHER, NETFLIX
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text:
namespace llvm {
namespace mca {

class Instruction;

typedef std::pair<unsigned, const Instruction &> SourceRef;

class SourceMgr {
  using UniqueInst = std::unique_ptr<Instruction>;
  ArrayRef<UniqueInst> Sequence;
  unsigned Current;
  const unsigned Iterations;
  static const unsigned DefaultIterations = 100;

public:
  SourceMgr(ArrayRef<UniqueInst> S, unsigned Iter)
      : Sequence(S), Current(0), Iterations(Iter ? Iter : DefaultIterations) {}

  unsigned getNumIterations() const { return Iterations; }
  unsigned size() const { return Sequence.size(); }
  bool hasNext() const { return Current < (Iterations * Sequence.size()); }
  void updateNext() { ++Current; }

  SourceRef peekNext() const {
    assert(hasNext() && "Already at end of sequence!");
    return SourceRef(Current, *Sequence[Current % Sequence.size()]);
  }

  using const_iterator = ArrayRef<UniqueInst>::const_iterator;
  const_iterator begin() const { return Sequence.begin(); }
  const_iterator end() const { return Sequence.end(); }
};

} // namespace mca
} // namespace llvm

#endif // LLVM_MCA_SOURCEMGR_H

redpajama_set_name: RedPajamaGithub