Wedge and common notation for “a line between two points”
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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
asked Jan 14 at 16:38
BradBrad
104
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add a comment |
$begingroup$
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.
geometry notation twistor-theory
asked Jan 14 at 16:38
BradBrad
104
$endgroup$
add a comment |
$begingroup$
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.
geometry notation twistor-theory
asked Jan 14 at 16:38
BradBrad
104
$endgroup$
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
geometry notation twistor-theory
asked Jan 14 at 16:38
BradBrad
104
asked Jan 14 at 16:38
BradBrad
104
edited Jan 14 at 19:18
Brad
asked Jan 14 at 16:38
BradBrad
104
asked Jan 14 at 16:38
BradBrad
104
asked Jan 14 at 16:38
BradBrad
104
104
add a comment |
add a comment |
1 Answer
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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!
answered Jan 14 at 19:18
BradBrad
104
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1 Answer
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$begingroup$
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!
answered Jan 14 at 19:18
BradBrad
104
$endgroup$
add a comment |
$begingroup$
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!
answered Jan 14 at 19:18
BradBrad
104
$endgroup$
add a comment |
$begingroup$
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!
answered Jan 14 at 19:18
BradBrad
104
$endgroup$
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!
answered Jan 14 at 19:18
BradBrad
104
answered Jan 14 at 19:18
BradBrad
104
answered Jan 14 at 19:18
BradBrad
104
answered Jan 14 at 19:18
BradBrad
104
104
add a comment |
add a comment |
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