View Full Version : Gauge theories in economics and physics
Sami Aario
Aug24-04, 04:58 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Hi all,\n\nThis might be slightly (or grossly) off-topic, but economists seem to like\ngauge\ntheories too! A Google search with the terms "gauge theory" and "economics"\ngives the following as the third link:\n\nhttp://www.amazon.com/exec/obidos/tg/detail/-/0471877387/102-7944154-3450560?v=glance\n"Physics of Finance: Gauge Modelling in Non-Equilibrium Pricing"\n\nDISCLAIMER: I can\'t recommend this book since I haven\'t read it! But the\ntable of contents is very interesting, plus the editorial review on the page\nsays it\'s "Written by a respected physicist and endorsed by highly regarded\nfinancial academics". I found some other favorable reviews too with Google.\nI wish\nI had the time to learn more about this stuff (and gauge theories in\ngeneral)!\nI also wish I\'d had the presence of mind to learn this stuff back when I did\nhave\ntime, but what can you do...\n\nI\'d like to know things like:\n\nIs there always some relativistic principle associated with a gauge theory\n("the\nprices of goods can only be expressed relative to each other", "only\nrelative\nvoltages matter physically")?\n\nIs there any point in a gauge theory that doesn\'t specify an *interaction*\nto go\nwith the relativistic principle (there\'s no point in comparing prices unless\nwe\ncan trade, there\'s no point in expressing voltages unless a current can flow\nbetween them)?\n\nIs there always some invariance principle associated with the gauge theory\n(the\nlaws of electrostatics are independent of your position on the circuit, the\nlaws\nof economics are independent of geographic location)?\n\nI am utterly fascinated with this stuff!\n\n--\nSami\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Hi all,
This might be slightly (or grossly) off-topic, but economists seem to like
gauge
theories too! A Google search with the terms "gauge theory" and "economics"
gives the following as the third link:
http://www.amazon.com/exec/obidos/tg/detail/-/0471877387/102-7944154-3450560?v=glance
"Physics of Finance: Gauge Modelling in Non-Equilibrium Pricing"
DISCLAIMER: I can't recommend this book since I haven't read it! But the
table of contents is very interesting, plus the editorial review on the page
says it's "Written by a respected physicist and endorsed by highly regarded
financial academics". I found some other favorable reviews too with Google.
I wish
I had the time to learn more about this stuff (and gauge theories in
general)!
I also wish I'd had the presence of mind to learn this stuff back when I did
have
time, but what can you do...
I'd like to know things like:
Is there always some relativistic principle associated with a gauge theory
("the
prices of goods can only be expressed relative to each other", "only
relative
voltages matter physically")?
Is there any point in a gauge theory that doesn't specify an *interaction*
to go
with the relativistic principle (there's no point in comparing prices unless
we
can trade, there's no point in expressing voltages unless a current can flow
between them)?
Is there always some invariance principle associated with the gauge theory
(the
laws of electrostatics are independent of your position on the circuit, the
laws
of economics are independent of geographic location)?
I am utterly fascinated with this stuff!
--
Sami
Thomas Larsson
Aug26-04, 04:29 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>"Sami Aario" <sami.aario_nospam_@surfeu.fi> wrote in message news:<cgelfj\\$mp1\\$1@phys-news1.kolumbus.fi>...\n> Hi all,\n>\n> This might be slightly (or grossly) off-topic, but economists seem to like\n> gauge\n> theories too! A Google search with the terms "gauge theory" and "economics"\n> gives the following as the third link:\n>\n> http://www.amazon.com/exec/obidos/tg/detail/-/0471877387/102-7944154-3450560?v=glance\n> "Physics of Finance: Gauge Modelling in Non-Equilibrium Pricing"\n>\n\nYou can presumably get a good idea what the book is about by\nchecking out the author\'s papers at the arxiv:\n\nhttp://www.arxiv.org/find/cond-mat/1/au:+Ilinski_K/0/1/0/all/0/1\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Sami Aario" <sami.aario_nospam_@surfeu.fi> wrote in message news:<cgelfj$mp1$1@phys-news1.kolumbus.fi>...
> Hi all,
>
> This might be slightly (or grossly) off-topic, but economists seem to like
> gauge
> theories too! A Google search with the terms "gauge theory" and "economics"
> gives the following as the third link:
>
> http://www.amazon.com/exec/obidos/tg/detail/-/0471877387/102-7944154-3450560?v=glance
> "Physics of Finance: Gauge Modelling in Non-Equilibrium Pricing"
>
You can presumably get a good idea what the book is about by
checking out the author's papers at the arxiv:
http://www.arxiv.org/find/http://www.arxiv.org/abs/cond-mat/1/au:+Ilinski_K/0/1/0/all/0/1
Paul Danaher
Aug26-04, 10:05 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nSami Aario wrote:\n> Hi all,\n>\n> This might be slightly (or grossly) off-topic, but economists seem to\n> like gauge\n> theories too! A Google search with the terms "gauge theory" and\n> "economics" gives the following as the third link:\n>\n>\nhttp://www.amazon.com/exec/obidos/tg/detail/-/0471877387/102-7944154-3450560?v=glance\n> "Physics of Finance: Gauge Modelling in Non-Equilibrium Pricing"\n\n....\n\n> I\'d like to know things like:\n\n....\n\n> I am utterly fascinated with this stuff!\n\nA very good basis for answering your questions is one of the papers in the\nURL cited by Thomas Larsson - "Gauge physics of finance: simple\nintroduction" http://www.arxiv.org/PS_cache/cond-mat/pdf/9811/9811197.pdf\nYou may find the same thing that I do - the mathematics is familiar, but I\ndon\'t know nearly enough physics to benefit from the comparisons. I had a\nvery brief flash of euphoria four years ago when I thought I knew enough\nmath (from econometrics) to understand GR, and then discovered that I don\'t\nknow enough physics to understand Maxwell, and I don\'t have time to do the\nhard thinking required.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Sami Aario wrote:
> Hi all,
>
> This might be slightly (or grossly) off-topic, but economists seem to
> like gauge
> theories too! A Google search with the terms "gauge theory" and
> "economics" gives the following as the third link:
>
>
http://www.amazon.com/exec/obidos/tg/detail/-/0471877387/102-7944154-3450560?v=glance
> "Physics of Finance: Gauge Modelling in Non-Equilibrium Pricing"
....
> I'd like to know things like:
....
> I am utterly fascinated with this stuff!
A very good basis for answering your questions is one of the papers in the
URL cited by Thomas Larsson - "Gauge physics of finance: simple
introduction" http://www.arxiv.org/PS_cache/cond-mat/pdf/9811/9811197.pdf
You may find the same thing that I do - the mathematics is familiar, but I
don't know nearly enough physics to benefit from the comparisons. I had a
very brief flash of euphoria four years ago when I thought I knew enough
math (from econometrics) to understand GR, and then discovered that I don't
know enough physics to understand Maxwell, and I don't have time to do the
hard thinking required.
Eric A. Forgy
Aug26-04, 12:00 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n"Sami Aario" <sami.aario_nospam_@surfeu.fi> wrote:\n\n> I am utterly fascinated with this stuff!\n\nMe too :)\n\nIf you like that kind of thing, you might like\n\nhttp://www.wilmott.com\n\nA while ago, I discussed this topic in a thread called "Arbitrage and\nHolonomies".\n\nArbitrage is basically when you can simultaneously buy and sell stuff\nand make an immediate profit. This would happen if, for example, there\nwere two currency exchange shops next door to each other with\ndifferent exchange rates. In principle, you could take some US\ndollars, exchange them to Euros or something, take the Euros next door\nand exchange them back to US dollars for more than you started with.\nOf course, if such an opportunity existed, it would not last for long\nbecause everyone would jump on the opportunity and the basic rules of\nsupply and demand will settle things down to a kind of equilibrium\npretty quickly.\n\nA holonomy is basically the transformation obtained when you\n(parallel) transport a tangent vector around some loop in a manifold.\nIf the vector receives a nontrivial transformation upon returning to\nthe starting point, this indicates the pressence of curvature on the\nmanifold.\n\nA neat example of this is the Aharonov-Bohm effect. Here though, the\nstate of the electron is a "vector" and a single electron does not\ntraverse a loop. Rather, two electrons begin at the same point and end\nat the same point, but may traverse different paths. If you think\nabout it, though, two paths beginning and ending at the same point is\nlike a "loop", so the math is the same. Please, no one complain about\nmy cavalier use of the word "path" and please avoid any discussion\nabout the true meaning of QM because it really is irrelevent for the\npoint I am tryig to make! :)\n\nThe curvature here is the magnetic field B. If the two paths (forming\na loop) enclose any magnetic flux, then the "vector" representing the\nelectrons undergo a nontrivial transformation, i.e. a phase shift.\n\nAnother common example is transporting a tangent vector around a loop\non a sphere.\n\nNow, a "portfolio" of stuff can be thought of as an abstract vector\nwhose magnitude is the "value" of the portfolio. Each item in the\nportfolio has it\'s own value and you can think of them as components\nof a vector.\n\nAs you carry your portfolio through the market, its value will change\n(as well as the values of the individual components) and this change\nwill depend on the path you traverse through the market. It is kind of\nfun to make analogies to particle creation and annihilation :) You can\nactually "create" a portfolio out of nothing by borrowing it :) If you\ndo this, then you actually end up with two portfolios: a portfolio and\nan anti-portfolio, i.e. a debt :) Given the portfolio and\nanti-portfolio, you can carry them individually through the market\nthrough different paths. If there existed an arbitrage opportunity in\nthe market, then you could find two paths that start and end at the\nsame place where your portfolio and anti-portfolio had equal and\nopposite values at the beginning, but the portfolio has greater\nmagnitude then the anti-portfolio at the end. Then you could sell off\nyour portfolio and pay off your anti-portfolio, i.e. debt, and end up\nmaking a profit. You made money from nothing! :)\n\nIf you think about it, this is nothing but a holonomy :)\n\nIf you can carry a portfolio around a closed loop in the market and\nhave it be transformed in value, then that indicates the existence of\nan arbitrage opportunity.\n\nArbitrage <==> Curvature\n\nThe market tends to snuff out arbitrage opportunities and nature tends\nto snuff out curvature :)\n\nIt\'s the Aharonov-Bohm effect of finance :)\n\nEric\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Sami Aario" <sami.aario_nospam_@surfeu.fi> wrote:
> I am utterly fascinated with this stuff!
Me too :)
If you like that kind of thing, you might like
http://www.wilmott.com
A while ago, I discussed this topic in a thread called "Arbitrage and
Holonomies".
Arbitrage is basically when you can simultaneously buy and sell stuff
and make an immediate profit. This would happen if, for example, there
were two currency exchange shops next door to each other with
different exchange rates. In principle, you could take some US
dollars, exchange them to Euros or something, take the Euros next door
and exchange them back to US dollars for more than you started with.
Of course, if such an opportunity existed, it would not last for long
because everyone would jump on the opportunity and the basic rules of
supply and demand will settle things down to a kind of equilibrium
pretty quickly.
A holonomy is basically the transformation obtained when you
(parallel) transport a tangent vector around some loop in a manifold.
If the vector receives a nontrivial transformation upon returning to
the starting point, this indicates the pressence of curvature on the
manifold.
A neat example of this is the Aharonov-Bohm effect. Here though, the
state of the electron is a "vector" and a single electron does not
traverse a loop. Rather, two electrons begin at the same point and end
at the same point, but may traverse different paths. If you think
about it, though, two paths beginning and ending at the same point is
like a "loop", so the math is the same. Please, no one complain about
my cavalier use of the word "path" and please avoid any discussion
about the true meaning of QM because it really is irrelevent for the
point I am tryig to make! :)
The curvature here is the magnetic field B. If the two paths (forming
a loop) enclose any magnetic flux, then the "vector" representing the
electrons undergo a nontrivial transformation, i.e. a phase shift.
Another common example is transporting a tangent vector around a loop
on a sphere.
Now, a "portfolio" of stuff can be thought of as an abstract vector
whose magnitude is the "value" of the portfolio. Each item in the
portfolio has it's own value and you can think of them as components
of a vector.
As you carry your portfolio through the market, its value will change
(as well as the values of the individual components) and this change
will depend on the path you traverse through the market. It is kind of
fun to make analogies to particle creation and annihilation :) You can
actually "create" a portfolio out of nothing by borrowing it :) If you
do this, then you actually end up with two portfolios: a portfolio and
an anti-portfolio, i.e. a debt :) Given the portfolio and
anti-portfolio, you can carry them individually through the market
through different paths. If there existed an arbitrage opportunity in
the market, then you could find two paths that start and end at the
same place where your portfolio and anti-portfolio had equal and
opposite values at the beginning, but the portfolio has greater
magnitude then the anti-portfolio at the end. Then you could sell off
your portfolio and pay off your anti-portfolio, i.e. debt, and end up
making a profit. You made money from nothing! :)
If you think about it, this is nothing but a holonomy :)
If you can carry a portfolio around a closed loop in the market and
have it be transformed in value, then that indicates the existence of
an arbitrage opportunity.
Arbitrage <==> Curvature
The market tends to snuff out arbitrage opportunities and nature tends
to snuff out curvature :)
It's the Aharonov-Bohm effect of finance :)
Eric
Franz Heymann
Aug27-04, 02:41 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>"Eric A. Forgy" <forgy@uiuc.edu> wrote in message\nnews:3fa8470f.0408260841.52ce3477@posting .google.com...\n\n[snip]\n\n> Now, a "portfolio" of stuff can be thought of as an abstract vector\n> whose magnitude is the "value" of the portfolio. Each item in the\n> portfolio has it\'s own value and you can think of them as components\n> of a vector.\n\nThis sounds remarkably like nonsense. The components of a vector are\nall orthogonal to one another. What does the concept of\n"orthogonality" mean in the present context?\nThe magnitude of a vector can be determined from a knowledge of its\ncomponents. How is this concept handles quantitatively in the\npresentcontext?\n\nHave you ever read the nonsense written in sci.physics by George\nHammond?\nDid the similarity between what you described here and the nonsense he\ndescribed there ever strike you?\n\n[snip]\n\nFranz\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Eric A. Forgy" <forgy@uiuc.edu> wrote in message
news:3fa8470f.0408260841.52ce3477@posting.google.c om...
[snip]
> Now, a "portfolio" of stuff can be thought of as an abstract vector
> whose magnitude is the "value" of the portfolio. Each item in the
> portfolio has it's own value and you can think of them as components
> of a vector.
This sounds remarkably like nonsense. The components of a vector are
all orthogonal to one another. What does the concept of
"orthogonality" mean in the present context?
The magnitude of a vector can be determined from a knowledge of its
components. How is this concept handles quantitatively in the
presentcontext?
Have you ever read the nonsense written in sci.physics by George
Hammond?
Did the similarity between what you described here and the nonsense he
described there ever strike you?
[snip]
Franz
Paul Danaher
Aug27-04, 06:10 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nFranz Heymann wrote:\n> "Eric A. Forgy" <forgy@uiuc.edu> wrote in message\n> news:3fa8470f.0408260841.52ce3477@posting.google.c om...\n>\n> [snip]\n>\n>> Now, a "portfolio" of stuff can be thought of as an abstract vector\n>> whose magnitude is the "value" of the portfolio. Each item in the\n>> portfolio has it\'s own value and you can think of them as components\n>> of a vector.\n>\n> This sounds remarkably like nonsense. The components of a vector are\n> all orthogonal to one another. What does the concept of\n> "orthogonality" mean in the present context?\n> The magnitude of a vector can be determined from a knowledge of its\n> components. How is this concept handles quantitatively in the\n> presentcontext?\n\nWell, orthogonality here would mean that the prices of the individual assets\nare unrelated, i.e. a change in the price of one asset wouldn\'t affect the\nprice of another. However, there\'s no reason to assume this, and it would\ntypically be wrong anyway. The magnitude of the vector would be the value of\nthe portfolio, expressed in a given currency at a given date (showing the\npresent value of assets maturing in the future). Something I haven\'t seen in\nthe papers I\'ve read so far in this collection is discussion of present\nvalue where there are (a) multiple interest rates and (b) negative interest\nrates - if anybody\'s seen that, I\'d be grateful for a pointer.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Franz Heymann wrote:
> "Eric A. Forgy" <forgy@uiuc.edu> wrote in message
> news:3fa8470f.0408260841.52ce3477@posting.google.c om...
>
> [snip]
>
>> Now, a "portfolio" of stuff can be thought of as an abstract vector
>> whose magnitude is the "value" of the portfolio. Each item in the
>> portfolio has it's own value and you can think of them as components
>> of a vector.
>
> This sounds remarkably like nonsense. The components of a vector are
> all orthogonal to one another. What does the concept of
> "orthogonality" mean in the present context?
> The magnitude of a vector can be determined from a knowledge of its
> components. How is this concept handles quantitatively in the
> presentcontext?
Well, orthogonality here would mean that the prices of the individual assets
are unrelated, i.e. a change in the price of one asset wouldn't affect the
price of another. However, there's no reason to assume this, and it would
typically be wrong anyway. The magnitude of the vector would be the value of
the portfolio, expressed in a given currency at a given date (showing the
present value of assets maturing in the future). Something I haven't seen in
the papers I've read so far in this collection is discussion of present
value where there are (a) multiple interest rates and (b) negative interest
rates - if anybody's seen that, I'd be grateful for a pointer.
Jerzy Karczmarczuk
Aug27-04, 06:10 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nFranz Heymann wrote:\n> "Eric A. Forgy" <forgy@uiuc.edu> wrote in message\n> news:3fa8470f.0408260841.52ce3477@posting.google.c om...\n>\n> [snip]\n>\n>\n>>Now, a "portfolio" of stuff can be thought of as an abstract vector\n>>whose magnitude is the "value" of the portfolio. Each item in the\n>>portfolio has it\'s own value and you can think of them as components\n>>of a vector.\n>\n> This sounds remarkably like nonsense. The components of a vector are\n> all orthogonal to one another. What does the concept of\n> "orthogonality" mean in the present context?\n\nI remind you politely that *vectors* can (or not) be orthogonal, *not*\ntheir components. You may make vectors out of many things, e.g. shares,\nmoney of different currencies, etc.\nA vector in the Fock space contains sectors with zero, one, two, etc.\nparticles. Did you think about the meaning of orthogonality there? It\nmeans simply incompatibility. The substrate of a computer program in its\nsymbolic form are vectors as well: compounds gathering all different\nvariables. "x" is one component, "y" is another. Adding "x"-es is adding\nthe same components, x+x=2x, but x+y is that and only that.\nPlease, turn your anger elsewhere. Many vector spaces have no metric...\n\n> The magnitude of a vector can be determined from a knowledge of its\n> components. How is this concept handles quantitatively in the\n> presentcontext?\n\nNow, this demands the knowledge of a concrete model of the space. In\na most primitive case this may be a 1-norm, the sum of component values,\nat least when I have several different coins in my pocket, that\'s it.\nAgain, why getting so nervous?\n\n\n> Have you ever read the nonsense written in sci.physics by George\n> Hammond?\n> Did the similarity between what you described here and the nonsense he\n> described there ever strike you?\n\nNow, this is unfair, and I wonder why the moderator didn\'t react. Mr.\nGH bothers people with "scientific proofs of God", etc. here we see\na nice, even if lightweight analogy between two geometric models.\nEconomy, and even quantitative sociology are theories of dynamical\nsystems. There are problems of measuring, of stability, of probabilis-\ntic reasoning with all, quite strong theorems which go with.\n\nYou have the Theory of Games, all the non-equilibrium stuff, etc.\nEconophysics exists. Search Google. You will find at least 10000\npages.\nhttp://www.unifr.ch/econophysics/\nhttp://www1.elsevier.com/homepage/sak/econophys/index.html\n\nI don\'t know whether the arbitrage can be formally defined as a\ngeometric concept in a formalized manner, but such an impolite\ndismissal is hardly acceptable.\n\nPerhaps you should also say a few harsh words addressed at John Baez\nwho dares to "marry" the categorical structures of quanta and general\nrelativity - apparently completely incompatible and worlds apart?\nhttp://math.ucr.edu/home/baez/quantum/quantum.html\n\nThe best.\n\nJerzy Karczmarczuk\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Franz Heymann wrote:
> "Eric A. Forgy" <forgy@uiuc.edu> wrote in message
> news:3fa8470f.0408260841.52ce3477@posting.google.c om...
>
> [snip]
>
>
>>Now, a "portfolio" of stuff can be thought of as an abstract vector
>>whose magnitude is the "value" of the portfolio. Each item in the
>>portfolio has it's own value and you can think of them as components
>>of a vector.
>
> This sounds remarkably like nonsense. The components of a vector are
> all orthogonal to one another. What does the concept of
> "orthogonality" mean in the present context?
I remind you politely that *vectors* can (or not) be orthogonal, *not*
their components. You may make vectors out of many things, e.g. shares,
money of different currencies, etc.
A vector in the Fock space contains sectors with zero, one, two, etc.
particles. Did you think about the meaning of orthogonality there? It
means simply incompatibility. The substrate of a computer program in its
symbolic form are vectors as well: compounds gathering all different
variables. "x" is one component, "y" is another. Adding "x"-es is adding
the same components, x+x=2x, but x+y is that and only that.
Please, turn your anger elsewhere. Many vector spaces have no metric...
> The magnitude of a vector can be determined from a knowledge of its
> components. How is this concept handles quantitatively in the
> presentcontext?
Now, this demands the knowledge of a concrete model of the space. In
a most primitive case this may be a 1-norm, the sum of component values,
at least when I have several different coins in my pocket, that's it.
Again, why getting so nervous?
> Have you ever read the nonsense written in sci.physics by George
> Hammond?
> Did the similarity between what you described here and the nonsense he
> described there ever strike you?
Now, this is unfair, and I wonder why the moderator didn't react. Mr.
GH bothers people with "scientific proofs of God", etc. here we see
a nice, even if lightweight analogy between two geometric models.
Economy, and even quantitative sociology are theories of dynamical
systems. There are problems of measuring, of stability, of probabilis-
tic reasoning with all, quite strong theorems which go with.
You have the Theory of Games, all the non-equilibrium stuff, etc.
Econophysics exists. Search Google. You will find at least 10000
pages.
http://www.unifr.ch/econophysics/
http://www1.elsevier.com/homepage/sak/econophys/index.html
I don't know whether the arbitrage can be formally defined as a
geometric concept in a formalized manner, but such an impolite
dismissal is hardly acceptable.
Perhaps you should also say a few harsh words addressed at John Baez
who dares to "marry" the categorical structures of quanta and general
relativity - apparently completely incompatible and worlds apart?
http://math.ucr.edu/home/baez/quantum/quantum.html
The best.
Jerzy Karczmarczuk
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