Wedge and common notation for “a line between two points”












0












$begingroup$


I'm using a somewhat old presentation from 2011 that covers twistor geometry.



It uses the notation "$L = Z_1 wedge Z_2$" to suggest that the line $L$ is the "join of the twistors $Z_1$ and $Z_2$, which are simply points in this twistor space.



However, I have always learned that the line between two points, which is essentially what this is, is just given by writing $L=Z_1Z_2$. Is there any difference between the two? Does this wedge notation have any other meaning that I'm not aware of? Is there any other standard notation that I have omitted?



EDIT:
For reference, the full presentation is available at https://indico.cern.ch/event/137430/contributions/146026/attachments/113502/161251/Atrani_1_Duhr.pdf.



See the screenshot of the relevant section here.



EDIT2: Found the answer, will accept in 2 days when I'm allowed to! See below.










share|cite|improve this question











$endgroup$

















    0












    $begingroup$


    I'm using a somewhat old presentation from 2011 that covers twistor geometry.



    It uses the notation "$L = Z_1 wedge Z_2$" to suggest that the line $L$ is the "join of the twistors $Z_1$ and $Z_2$, which are simply points in this twistor space.



    However, I have always learned that the line between two points, which is essentially what this is, is just given by writing $L=Z_1Z_2$. Is there any difference between the two? Does this wedge notation have any other meaning that I'm not aware of? Is there any other standard notation that I have omitted?



    EDIT:
    For reference, the full presentation is available at https://indico.cern.ch/event/137430/contributions/146026/attachments/113502/161251/Atrani_1_Duhr.pdf.



    See the screenshot of the relevant section here.



    EDIT2: Found the answer, will accept in 2 days when I'm allowed to! See below.










    share|cite|improve this question











    $endgroup$















      0












      0








      0





      $begingroup$


      I'm using a somewhat old presentation from 2011 that covers twistor geometry.



      It uses the notation "$L = Z_1 wedge Z_2$" to suggest that the line $L$ is the "join of the twistors $Z_1$ and $Z_2$, which are simply points in this twistor space.



      However, I have always learned that the line between two points, which is essentially what this is, is just given by writing $L=Z_1Z_2$. Is there any difference between the two? Does this wedge notation have any other meaning that I'm not aware of? Is there any other standard notation that I have omitted?



      EDIT:
      For reference, the full presentation is available at https://indico.cern.ch/event/137430/contributions/146026/attachments/113502/161251/Atrani_1_Duhr.pdf.



      See the screenshot of the relevant section here.



      EDIT2: Found the answer, will accept in 2 days when I'm allowed to! See below.










      share|cite|improve this question











      $endgroup$




      I'm using a somewhat old presentation from 2011 that covers twistor geometry.



      It uses the notation "$L = Z_1 wedge Z_2$" to suggest that the line $L$ is the "join of the twistors $Z_1$ and $Z_2$, which are simply points in this twistor space.



      However, I have always learned that the line between two points, which is essentially what this is, is just given by writing $L=Z_1Z_2$. Is there any difference between the two? Does this wedge notation have any other meaning that I'm not aware of? Is there any other standard notation that I have omitted?



      EDIT:
      For reference, the full presentation is available at https://indico.cern.ch/event/137430/contributions/146026/attachments/113502/161251/Atrani_1_Duhr.pdf.



      See the screenshot of the relevant section here.



      EDIT2: Found the answer, will accept in 2 days when I'm allowed to! See below.







      geometry notation twistor-theory






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Jan 14 at 19:18







      Brad

















      asked Jan 14 at 16:38









      BradBrad

      104




      104






















          1 Answer
          1






          active

          oldest

          votes


















          0












          $begingroup$

          Answer lies in Boolean algebra. Why is $wedge$ a minimum and $vee$ a maximum? and http://homepages.math.uic.edu/~kauffman/BooleanAlg.pdf are the resources used. Turns out that in Boolean notation $A wedge B = AB$, who'd've thunk'd it!






          share|cite|improve this answer









          $endgroup$














            Your Answer








            StackExchange.ready(function() {
            var channelOptions = {
            tags: "".split(" "),
            id: "69"
            };
            initTagRenderer("".split(" "), "".split(" "), channelOptions);

            StackExchange.using("externalEditor", function() {
            // Have to fire editor after snippets, if snippets enabled
            if (StackExchange.settings.snippets.snippetsEnabled) {
            StackExchange.using("snippets", function() {
            createEditor();
            });
            }
            else {
            createEditor();
            }
            });

            function createEditor() {
            StackExchange.prepareEditor({
            heartbeatType: 'answer',
            autoActivateHeartbeat: false,
            convertImagesToLinks: true,
            noModals: true,
            showLowRepImageUploadWarning: true,
            reputationToPostImages: 10,
            bindNavPrevention: true,
            postfix: "",
            imageUploader: {
            brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
            contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
            allowUrls: true
            },
            noCode: true, onDemand: true,
            discardSelector: ".discard-answer"
            ,immediatelyShowMarkdownHelp:true
            });


            }
            });














            draft saved

            draft discarded


















            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3073423%2fwedge-and-common-notation-for-a-line-between-two-points%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown

























            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            0












            $begingroup$

            Answer lies in Boolean algebra. Why is $wedge$ a minimum and $vee$ a maximum? and http://homepages.math.uic.edu/~kauffman/BooleanAlg.pdf are the resources used. Turns out that in Boolean notation $A wedge B = AB$, who'd've thunk'd it!






            share|cite|improve this answer









            $endgroup$


















              0












              $begingroup$

              Answer lies in Boolean algebra. Why is $wedge$ a minimum and $vee$ a maximum? and http://homepages.math.uic.edu/~kauffman/BooleanAlg.pdf are the resources used. Turns out that in Boolean notation $A wedge B = AB$, who'd've thunk'd it!






              share|cite|improve this answer









              $endgroup$
















                0












                0








                0





                $begingroup$

                Answer lies in Boolean algebra. Why is $wedge$ a minimum and $vee$ a maximum? and http://homepages.math.uic.edu/~kauffman/BooleanAlg.pdf are the resources used. Turns out that in Boolean notation $A wedge B = AB$, who'd've thunk'd it!






                share|cite|improve this answer









                $endgroup$



                Answer lies in Boolean algebra. Why is $wedge$ a minimum and $vee$ a maximum? and http://homepages.math.uic.edu/~kauffman/BooleanAlg.pdf are the resources used. Turns out that in Boolean notation $A wedge B = AB$, who'd've thunk'd it!







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Jan 14 at 19:18









                BradBrad

                104




                104






























                    draft saved

                    draft discarded




















































                    Thanks for contributing an answer to Mathematics Stack Exchange!


                    • Please be sure to answer the question. Provide details and share your research!

                    But avoid



                    • Asking for help, clarification, or responding to other answers.

                    • Making statements based on opinion; back them up with references or personal experience.


                    Use MathJax to format equations. MathJax reference.


                    To learn more, see our tips on writing great answers.




                    draft saved


                    draft discarded














                    StackExchange.ready(
                    function () {
                    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3073423%2fwedge-and-common-notation-for-a-line-between-two-points%23new-answer', 'question_page');
                    }
                    );

                    Post as a guest















                    Required, but never shown





















































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown

































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown







                    Popular posts from this blog

                    Bressuire

                    Cabo Verde

                    Gyllenstierna