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Barry Schwartz  committed 8aeb9fb

Remove nonlocal_scribbles.xml. It’s now in the wiki instead.

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  • Parent commits 8a78855

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File examples/c3ga_generator_common.pure

   ['cga::NormalVector,  s | s = '[cga::E1,cga::E2,cga::E3]] +
   ['cga::NormalVector2, s | s = '[cga::E1,cga::E2]] +
 
+  ['cga::Scalar, s | s = '[cga::Translator,cga::Translator2]] +
+
   commute ['cga::Multivector,  s | s = '[cga::Multivector,    cga::Multivector2,
                                          cga::EvenVersor,    cga::EvenVersor2,
                                          cga::Translator,    cga::Translator2,

File examples/c3ga_generator_stage1.pure

 binary_op "(::+)"             (+);
 binary_op "(::-)"             (-);
 binary_op "(::*)"             (geometric_product cga::eigensystem);
+binary_op "lc"                (left_contraction cga::eigensystem);
 
 ary_op ('(cga::Scalar,cga::Multivector))    "norm2"   (norm2 cga::eigensystem);
 ary_op ('(cga::Translator,cga::Translator)) "inverse" (inverse cga::eigensystem);

File examples/c3ga_generator_stage2.pure

 
 let reverse_types =
   '[(Multivector,  Multivector),
-    (Multivector2, Multivector2)];            // FIXME: Fill this out.
+    (Multivector2, Multivector2),
+    (EvenVersor, EvenVersor),
+    (EvenVersor2, EvenVersor2),
+    (Translator, Translator),
+    (Translator2, Translator2)];            // FIXME: Fill this out.
 
 let grade_involution_types =
   '[(Multivector,  Multivector),
            '(EvenVersor, EvenVersor, EvenVersor2),
            '(EvenVersor, EvenVersor, Translator),
            '(EvenVersor, EvenVersor, Translator2),
+           '(EvenVersor, EvenVersor, Point),
+           '(EvenVersor, EvenVersor, Point2),
 
            '(EvenVersor2, EvenVersor2, EvenVersor2),
            '(EvenVersor2, EvenVersor2, Translator2),
 
 let norm_types = zip (repeat ('Scalar)) smv_types;
 
+let versor_inverse_types =
+  commute ['(Multivector, Multivector),
+           '(Multivector2, Multivector2),
+           '(EvenVersor, EvenVersor),
+           '(EvenVersor2, EvenVersor2),
+           '(Translator, Translator),
+           '(Translator2, Translator2)];
+
 let plus_scalar_types = scalar_arg_types 1 plus_types;
 let minus_scalar_types = scalar_arg_types 1 minus_types;
 let gp_scalar_types = scalar_arg_types 1 gp_types;
           "operation" => (::*),
           "types"     => gp_types};
 
+write_op {"pure"      => "lc",
+          "fortran"   => "lc",
+          "operation" => lc,
+          "types"     => ['(Multivector, Multivector, Multivector)]};
+
 write_op {"pure"      => "norm2",
           "fortran"   => "norm2",
           "operation" => (\u -> u*(::reverse u)),
           "types"     => norm_types,
           "scalar_result" => true};
 
+write_op {"pure"      => "apply_unit_versor",
+          "fortran"   => "apply_unit_versor",
+          "operation" => (\u v -> u * v * ::reverse u),
+          "types"     => ['(Multivector, Translator, Multivector),
+                          '(Point, Translator, Point)]};
+
+// Some of the type combinations get too complicated to expand
+// apply_unit_versor with write_op.
+pp "apply_unit_versor u v = u*v*(reverse u);\n";
+
+pp "apply_versor u v = apply_unit_versor u v % norm2 u;\n";
+
 //-------------------------------------------------------------------------
 
 write_scalar_arg {"pure"         => "(::+)",

File extras/nonloco_scribbles.xml

-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
-"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
-
-<html xmlns="http://www.w3.org/1999/xhtml">
-  <head>
-    <meta http-equiv="content-type" content="application/xhtml+xml; charset=UTF-8" />
-    <title>Quantum non-loco-ality</title>
-  </head>
-
-  <body>
-    <p>This page is a space I am using to sketch my presentation of
-    disproof of Bell’s argument for non-existent quantum
-    ‘non-locality’.</p>
-
-    <p><em>Not original.</em> This disproof is not novel, though the
-    way it is written is different from how others have written
-    it. This work is a direct descendant of <a href=
-    "http://arxiv.org/abs/1109.6750v2">arXiv:1109.6750v2&nbsp;[physics.gen-ph]</a></p>
-
-    <p><em>Abstraction.</em> There is a tendency in scholarly articles
-    disproving Bell’s conclusion to write in terms of an actual
-    experimental apparatus. Perhaps one has to do this to get a paper
-    past the reviewers. On the other hand, maybe it is just a habit of
-    physicists; in that case, luckily, I am not a physicist.  Bell’s
-    arguments are about a general principle – that detectors of
-    initially ‘like’-oriented ‘particles’ keep in touch with each
-    other via magical walkie-talkies, or perhaps that ‘particles’
-    exist in a Holy Duality with and are accompanied by
-    instantaneously telepathic Probability Angels. Bell says yes,
-    something like that must be going on, and he gives math to ‘prove’
-    it; I say he’s screwed up the math. Let us not get distracted into
-    arguments over experiments whose results are pointless to our
-    subject and uncontroversial, though interesting as technical
-    achievements.</p>
-
-    <p><em>Conformal geometric algebra.</em> A convenient notation for
-    moving geometric objects. See Leo Dorst et al., ‘Geometric Algebra
-    for Computer Science’, Morgan Kaufmann, 2007, ISBN:
-    978-0-12-374942-0 and Daniel Fontijne, ‘Efficient implementation
-    of geometric algebra’, thesis, 2007, ISBN-13:
-    978-90-889-10-142.</p>
-
-    <ul>
-      <li>Translation operator that translates object q by
-      displacement vector d:
-      T<sub>d</sub>&nbsp;q&nbsp;=&nbsp;e<sup>-d∞/2</sup>&nbsp;q&nbsp;e<sup>d∞/2</sup>
-      (here ∞ means the point at infinity)</li>
-
-      <li>Rotation of object q by φ radians about the origin, in the
-      oriented plane through the origin given by bivector I:
-      R<sub>0,I</sub>&nbsp;q&nbsp;=&nbsp;e<sup>-φI/2</sup>&nbsp;q&nbsp;e<sup>φI/2</sup></li>
-
-      <li>Rotation about a point displaced from the origin by vector
-      e:
-      R<sub>e,I</sub>&nbsp;=&nbsp;T<sub>e</sub>&nbsp;R<sub>0,I</sub>&nbsp;T<sub>-e</sub></li>
-
-      <li>
-        <p>Particle path operator: translate by d to get to the
-        orientation-changer, then rotate by φ, then translate by e to
-        get to the detector robot:
-        P<sub>d,φ,e</sub>&nbsp;=&nbsp;T<sub>e</sub>&nbsp;R<sub>d,I</sub>&nbsp;T<sub>d</sub>
-        =&nbsp;T<sub>e</sub>&nbsp;T<sub>d</sub>&nbsp;R<sub>0,I</sub>&nbsp;T<sub>-d</sub>&nbsp;T<sub>d</sub>
-        =&nbsp;T<sub>e</sub>&nbsp;T<sub>d</sub>&nbsp;R<sub>0,I</sub>
-        =&nbsp;T<sub>e&nbsp;+&nbsp;d</sub>&nbsp;R<sub>0,I</sub></p>
-
-        <p>Therefore
-        P<sub>d,φ,e</sub>&nbsp;q&nbsp;=&nbsp;T<sub>e&nbsp;+&nbsp;d</sub>&nbsp;R<sub>0,I</sub>&nbsp;q
-        =&nbsp;e<sup>-(d +
-        e)∞/2</sup>&nbsp;e<sup>-φI/2</sup>&nbsp;q&nbsp;e<sup>φI/2</sup>&nbsp;e<sup>(d
-        + e)∞/2</sup> =&nbsp;e<sup>-(d + e)∞/2 -
-        φI/2</sup>&nbsp;e<sup>-φI/2</sup>&nbsp;q&nbsp;e<sup>(d +
-        e)∞/2 + φI/2</sup></p>
-      </li>
-    </ul>
-
-    <p><em>The particle.</em> We will just call these
-    ‘particles’. Whether they are electrons or photons or gas giant
-    planets does not matter; Bell’s argument is one of mathematical
-    principles, not physical particulars. (Whether a person accepts
-    that observation or not is a test of one’s trust in mathematics
-    over rough hunches.)</p>
-
-    <p><em>The detectors.</em> Here it is important to assume that the
-    detector throws out <em>no</em> relevant information; Bell assumed
-    otherwise and there went awry. Therefore, my detectors will not be
-    some experimental physicist’s device that gives the reader a
-    mental picture full of prejudices, but instead non-ideological
-    robots that measure, record, and consider all the information
-    available to them. In particular, when the particle arrives at the
-    detector, the robot will measure and record not merely the
-    particle’s ‘amplitude’ but also its orientation. [Side note:
-    Bell’s ideological robot discards the orientation. Bell may not
-    have mentioned ideological robots, but here we are being
-    mathematicians, not technicians; Bell’s detectors are
-    <em>equivalent to</em> ideological robots.] The robots <em>do
-    not</em> record information <em>not</em> available to them – in
-    particular, the path taken by the particle from the source to the
-    detector. The sole determinant of whether a robot considers or
-    does not consider some information is whether or not the
-    information is available; the robots have no preconceptions.</p>
-
-    <p>[Side note: I imagine the failure to regard what information
-    is available to a detector has hampered research into just what
-    is going on within an actual detector.]</p>
-  </body>
-</html>