mm-151
The existence of unde'nable reals is pretty
weird, as was discussed> by Bill Taylor and I a while ago. On
the one hand, you can argue that> such things have to exist,
by cardinality considerations. But you> can't begin to
describe one.Well, what about unde'nable ordinals?
It's easy to describe one,e.g., the smallest one. Does that make them
less weird, or weirder?
=>Or you could tell us what causes
v to rotate in the 'rst place.>>There's nothing
that causes v
to rotate. v is a vector - a mathematical>entity that has
direction and magnitude. That's all. It's not a
material>thing, so the notion of causation is utterly
irrelevant.This is such an appalling expression of pre
scienti'c ignorance andmysticism, it leaves me completely
speechless. Quite an achievement.You've managed something no
one else has. Congratulations.
=>Or you could tell us
what causes v to rotate in the 'rst
place.>>There's nothing
that causes v to rotate. v is a vector - a mathematical>entity
that has direction and magnitude. That's all.
It's not a
material>thing, so the notion of causation is utterly
irrelevant.> This is such an appalling expression of pre
scienti'c ignorance and> mysticism, it leaves me completely
speechless. Quite an achievement.> You've managed something
no
one else has. Congratulations.> What were you supposing? A
world with little arrows with feathery tailsattached to
everything?Chuck-- ... The times have been, That, when the
brains were out, the man would die. ... Macbeth Chuck Simmons
chrlsim@earthlink.net>Therefor, it seems to me that there
exists a function (indeed, a>function which algebraists subtly
draw upon without even realizing>it) that associates with each
group it's identity element.What do you mean by function?
What
the algebraist draws upon is nota function as the word is used
in Mathematics.>But I am told that you cannot have a set that
contains every group...> so this function's domain is
nonsense! Not in a set theory that distinguishes between sets
and properclasses. The domain is a proper class, not a
set.>Now before you reply Why are you rebutting a claim that
nobody made?-- Shmuel (Seymour J.) Metz, SysProg and JOATnot
tb@becket.becket.net
=> Besides, as we have seen, there is
no such thing as a function whose> domain is all groups,
because the domain of a function is necessarily a> set, and
there is no set large enough to contain all groups. We can
use> category theory and talk about functors, but the
existence of a group> identity does not in any way depend on
category theory. Groups had> identities as soon as the concept
of a group was formalized, long before> anyone thought up
category theory.I would point out that you don't need
category
theory to make sense ofthis.It's much simpler to use
Godel-Bernays set theory, and you can havefunctions--real
honest-to-God functions--with domains or ranges thatare proper
classes, provided that the actual arguments and values
arealways only sets.In GB set theory, you can take the
cartesian product of any 'nitelist of classes (proper or
not),
and a function is just a certainsubclass of that cartesian
product. Everything Just Works.And then you can have groups,
and a function which maps each group toits identity. The class
of groups is a proper class, and the class o'dentities is a
proper class, and the function exists just 'ne.Thomas
=>>
Besides, as we have seen, there is no such thing as a function
whose>> domain is all groups, because the domain of a function
is necessarily a>> set, and there is no set large enough to
contain all groups. We can use>> category theory and talk
about functors, but the existence of a group>> identity does
not in any way depend on category theory. Groups had>>
identities as soon as the concept of a group was formalized,
long before>> anyone thought up category theory.> I would
point out that you don't need category theory to make sense
of> this.That was precisely my point.> It's much simpler to
use Godel-Bernays set theory, and you can have>
functions--real honest-to-God functions--with domains or
ranges that> are proper classes, provided that the actual
arguments and values are> always only sets.> In GB set theory,
you can take the cartesian product of any 'nite> list of
classes (proper or not), and a function is just a certain>
subclass of that cartesian product. Everything Just Works.>
And then you can have groups, and a function which maps each
group to> its identity. The class of groups is a proper class,
and the class of> identities is a proper class, and the
function exists just 'ne.That's like pointing
out that you
don't need a bazooka to kill amosquito, because a simple
sledgehammer will do.As I said before, the existence of an
identity is part of the de'nitionof a group. You
don't need
anything else at all.-- Judge Yohn's mistakes revealed in
Mumia Abu-Jamal
ruling.<http://www.commoncouragepress.com/index.cfm?action=
=> As I said
before, the existence of an identity is part of the
de'nition>
of a group. You don't need anything else at all.Not to get
an
identity, but the original question had to do with aset of
identities, with functions mapping groups to identities, and
Idon't see any reason that those can't be
mildly interesting
subjectsin their own right.Thomas
=>> As I said before, the
existence of an identity is part of the de'nition>> of a
group. You don't need anything else at all.> Not to get an
identity, but the original question had to do with a> set of
identities, with functions mapping groups to identities, and
I> don't see any reason that those can't be
mildly interesting
subjects> in their own right.No, the original question had to
do with the claim that in order to getan identity, one must
implicitly have used such a function.-- Judge Yohn's
mistakes
revealed in Mumia Abu-Jamal
ruling.<http://www.commoncouragepress.com/index.cfm?action=
=|No, the original
question had to do with the claim that in order to get|an
identity, one must implicitly have used such a function.It's
perhaps worth noting that in certain contexts in
mathematicallogic, use is made of the relationship between for
every x, there exists a y such that P(x,y)and there exists a
function f such that every x satis'es P(x, f(x)).Look for
example at Goedel's Dialectica interpretation, givenin his
paper in volume 12 of Dialectica. There are what areknown as
functional interpretations of languages, where thetruth of
sentences is shown to be witnessed by the existenceof a
suitable function, whose domain often is a set of
functions....When x and y range over the members of given
sets, the aboveequivalence is another way to express the axiom
of choice.Constructively, there is a problem with the above
equivalencedue to the fact that functions are de'ned as
extensional, i.e.if x1=x2 then f(x1)=f(x2). So in many cases
the 'rst statementis constructively equivalent to
what's known
as an operationfrom the domain of x to the domain of y.Here we
seem to be observing a certain temptation to expectthe same
kind of principle to apply even when x and y varyover all
sets. The only thing I want to add to the previousdiscussion
of this is that as I see it, the 'rst statement for every x,
there exists a y such that P(x,y)amounts to the existence of
something with a close familyresemblance to functions. We can
for example composethem; if for every y, there exists a z such
that Q(y,z)then for every x there exists a z satisfying the
compositerelation R(x,z) := there exists a y such that P(x,y)
=> As I
said before, the existence of an identity is part of the
de'nition>> of a group. You don't need anything
else at all.
Not to get an identity, but the original question had to do
with a> set of identities, with functions mapping groups to
identities, and I> don't see any reason that those
can't be
mildly interesting subjects> in their own right. No, the
original question had to do with the claim that in order to
get> an identity, one must implicitly have used such a
function.No. The original question was: Can I de'ne a set of
all theidentities of each group?
=>As I said before, the
existence of an identity is part of the de'nition>of a group.
You don't need anything else at all.>> Not to get an
identity,
but the original question had to do with a>> set of identities,
with functions mapping groups to identities, and I>> don't
see
any reason that those can't be mildly interesting subjects>>
in their own right.>> No, the original question had to do with
the claim that in order to get>> an identity, one must
implicitly have used such a function.> No. The original
question was: Can I de'ne a set of all the> identities of
each
group?I quote the 'rst 16 lines from the posting that began
this thread(including the header:>>questions.>>OK, every group
has an identity element, right? True by de'nition>>It seems
to
me that, given a group, that group therefor determines
a>unique identity element. (The uniqueness of a given
group's
identity>element is easily proved)>>Therefor, it seems to me
that there exists a function (indeed, a>function which
algebraists subtly draw upon without even realizing it)>that
associates with each group it's identity element.There is
more
in the original posting, but the parenthetical comment
justabove is what I have been discussing all along. No, it is
not true thatalgebraists are subtly drawing upon the existence
of such a function inasserting that groups have inverses.
Algebraists are drawing on nothingmore than the de'nition of
a
group in making that assertion.-- Judge Yohn's mistakes
revealed in Mumia Abu-Jamal
ruling.<http://www.commoncouragepress.com/index.cfm?action=
=> There is
more in the original posting, but the parenthetical comment
just> above is what I have been discussing all along. No, it
is not true that> algebraists are subtly drawing upon the
existence of such a function in> asserting that groups have
inverses. Algebraists are drawing on nothing> more than the
de'nition of a group in making that assertion.What started
the
discussion was Sniz Pilbor's question Is it possiblefor a
set
to exist which contains all the units of variousisomorphically
distinct groups that exist?, in Message ID
clari'cation let on that Sniz meant identity when he
saidunit,
and he wanted the set to have a distinct element for
eachisomorphically distinct group.When he was told no, such a
set is too big to be a set, he said butisn't there implicit
reliance on a function from groups toidentities? You are quite
right that in algebra there is no need for such afunction.My
point, from the standpoint of set theory, is that there is
noproblem in having such a function, even if the range and
domain aretoo big to be sets.Thomas
=>> There is more in the
original posting, but the parenthetical comment just>> above is
what I have been discussing all along. No, it is not true
that>> algebraists are subtly drawing upon the existence of
such a function in>> asserting that groups have inverses.
Algebraists are drawing on nothing>> more than the de'nition
of a group in making that assertion.> What started the
discussion was Sniz Pilbor's question Is it possible> for a
set to exist which contains all the units of various>
isomorphically distinct groups that exist?, in Message ID
clari'cation let on that Sniz meant identity when he said>
unit, and he wanted the set to have a distinct element for
each> isomorphically distinct group.said identity, not unit.
You may be referring to some differentthread, but I am talking
about the current one.> When he was told no, such a set is too
big to be a set, he said but> isn't there implicit reliance
on
a function from groups to> identities? > You are quite right
that in algebra there is no need for such a> function.> My
point, from the standpoint of set theory, is that there is no>
problem in having such a function, even if the range and domain
are> too big to be sets.But how do you propose to de'ne such
a
function? Never mind whether thedomain and range are sets or
not. How, exactly, do you know that everygroup has an
identity?My point has been that you are placing the cart
before the horse.-- Judge Yohn's mistakes revealed in Mumia
Abu-Jamal
ruling.<http://www.commoncouragepress.com/index.cfm?action=
=> But how do
you propose to de'ne such a function? Never mind whether the>
domain and range are sets or not. How, exactly, do you know
that every> group has an identity? My point has been that you
are placing the cart before the horse.Actually, the set
forming the group and the operation are suf'cientto
de'ne the
identity. That is, a group can perfectly well bede'ned as a
structure <g, *> such that g and * have the
followingproperties. This works because the identity is
uniquely determinedby the set and the operation.This is less
convenient, so we don't do it.You still seem to be mistaking
me for someone else. I agreecompletely that we don't need
such
a function. I don't thinkalgebraists have any use for it, and
I
don't agree that it isimplicitly necessary.But I still
insist
that it might be a question of mild independentinterest for
set theory.Thomas
=>> But how do you propose to de'ne such a
function? Never mind whether the>> domain and range are sets or
not. How, exactly, do you know that every>> group has an
identity?>> My point has been that you are placing the cart
before the horse.> Actually, the set forming the group and the
operation are suf'cient> to de'ne the identity.
That is, a
group can perfectly well be> de'ned as a structure <g, *>
such
that g and * have the following> properties. This works because
the identity is uniquely determined> by the set and the
operation.> This is less convenient, so we don't do it.And
even if we did, we would still be using the de'nition of a
group inorder to de'ne the identity-valued function.> You
still seem to be mistaking me for someone else. I agree>
completely that we don't need such a function. I
don't think>
algebraists have any use for it, and I don't agree that it
is>
implicitly necessary.Yes, we both agree that the function is
not necessary, but you keepavoiding the question of whether it
is suf'cient. I say it is not.In other words, you seem to
think
there are two ways to establish theexistence of an identity in
an arbitrary group: one way using thede'nition of a group,
and
one way using an identity-valued functionbut without appealing
to the de'nition.I disagree. Both of your methods depend on
the de'nition, whether yourealize it or not. Proof: apply
your
method to semigroups and see howfar you get with constructing
your identity-valued function.> But I still insist that it
might be a question of mild independent> interest for set
theory.L'Hospital's rule is of some interest
to analysts, but
attempting to useit to evaluate lim_{x->0} (sin x)/x is
circular reasoning.-- Judge Yohn's mistakes revealed in
Mumia
Abu-Jamal
ruling.<http://www.commoncouragepress.com/index.cfm?action=
=> You still
seem to be mistaking me for someone else. I agree> completely
that we don't need such a function. I don't
think> algebraists
have any use for it, and I don't agree that it is>
implicitly
necessary. Yes, we both agree that the function is not
necessary, but you keep> avoiding the question of whether it
is suf'cient. I say it is not.I don't care
about that
question. I think your answer to it isright. I haven't said
anything to the contrary.> In other words, you seem to think
there are two ways to establish the> existence of an identity
in an arbitrary group: one way using the> de'nition of a
group, and one way using an identity-valued function> but
without appealing to the de'nition.No, I
haven't said anything
of the kind.> I disagree. Both of your methods depend on the
de'nition, whether you> realize it or not. Proof: apply your
method to semigroups and see how> far you get with
constructing your identity-valued function.My method? What on
earth is that? I think that you are very likelyconfusing me
with someone else.> But I still insist that it might be a
question of mild independent> interest for set theory.
L'Hospital's rule is of some interest to
analysts, but
attempting to use> it to evaluate lim_{x->0} (sin x)/x is
circular reasoning.My point, and my only entry to this whole
subject, has been on theset-theoritic aspects.
=> With all
respect, sir, I can guess your politics right across the>
board. Just for openers, you're a Sierra Club,
save-the-whales
type.> Gotcha, huh?You're about as far off the mark as it is
possible to get. Not that I seethe relevance, but I'm a very
conservative, Religious Right type -- notfar removed from what
most people would call a fundamentalist (thoughI don't use
that
label myself). I'm irrevocably opposed to both abortionand
gun
control, voted for Bush (both of them) and supported the Iraq
war(both of them), and certainly do not support the Sierra
Club, Greenpeace,PETA, or any other environmentalist or
animal-rights group. And no,I don't care to discuss or
defend
any of those positions in sci.math.(Sorry if that sounds a bit
abrupt, but this discussion has already gonepretty far
off-topic and I don't want to get drawn in any further.)I
also
was the kind of kid who grew up reading science 'ction
andplaying with chemistry sets, microscopes, slide rules,
soldering ironsand telescopes while the other kids were
outside playing baseballand football. (To this day I have no
interest whatsoever in sports.)So that probably explains why I
enjoy technology more for its own sakethan for its
applications.-- Wayne Brown (HPCC #1104) | When your tail's
in
a crack, you improvisefwbrown@bellsouth.net | if you're good
enough. Otherwise you give | your pelt to the trapper.e^(i*pi)
= -1 -- Euler | -- John Myers Myers, Silverlock-- Wayne Brown
(HPCC #1104) | When your tail's in a crack, you
improvisefwbrown@bellsouth.net | if you're good enough.
Otherwise you give | your pelt to the trapper.e^(i*pi) = -1 --
Euler | -- John Myers Myers, Silverlock
= With all respect,
sir, I can guess your politics right across the> board. Just
for openers, you're a Sierra Club, save-the-whales type.>
Gotcha, huh? You're about as far off the mark as it is
possible to get. Not that I see> the relevance, but I'm a
very
conservative, Religious Right type -- not> far removed from
what most people would call a fundamentalist (though> I
don't
use that label myself). I'm irrevocably opposed to both
abortion> and gun control, voted for Bush (both of them) and
supported the Iraq war> (both of them), and certainly do not
support the Sierra Club, Greenpeace,> PETA, or any other
environmentalist or animal-rights group. And no,> I don't
care
to discuss or defend any of those positions in
sci.math.You're
right as right can be. Taking what you say at face value,
whichI do, I was indeed off the mark in that assessment. My
apologies. Youalso sound like my kind of guy, for that
describes me absent thereligious overtones. I despise
political liberals, and I'll let it goat that as well in
that
most writers are political liberals,enviro-whackos and PETA
types. Ursula
=> I don't use that label myself). I'm
irrevocably opposed to both abortion> and gun control, voted
for Bush (both of them) and supported the Iraq war> (both of
them), and certainly do not support the Sierra Club,
Greenpeace,What do you think of
this:http://www.deanforamerica.com/site/PageServer?pagename=
policy_statement_civilrights_sensiblegunlaws
=>> I don't use
that label myself). I'm irrevocably opposed to both
abortion>>
and gun control, voted for Bush (both of them) and supported
the Iraq war>> (both of them), and certainly do not support
the Sierra Club, Greenpeace,> What do you think of this:>
http://www.deanforamerica.com/site/PageServer?pagename=policy_
statement_civilrights_sensiblegunlawsAs I said, I don't want
to get drawn any further into this discussionso I'll just
say
this: I disagree with nearly everything on that page,as I
don't consider those laws sensible. And that's
all I'm going
tosay on the subject here.-- Wayne Brown (HPCC #1104) | When
your tail's in a crack, you improvisefwbrown@bellsouth.net |
if you're good enough. Otherwise you give | your pelt to the
trapper.e^(i*pi) = -1 -- Euler | -- John Myers Myers,
Silverlock
=>But that's always been the case. We made a lot
of money doing>work that our customers didn't want or have
to
do. What we>didn't do (when we weren't ing
idiots) was
hide all the>warts under pretty pictures.I'm sorry, WHAT did
you say you were doing to the idiots?!
=>>But that's always
been the case. We made a lot of money doing>>work that our
customers didn't want or have to do. What
we>>didn't do (when
we weren't ing idiots) was hide all the>>warts under
pretty pictures.>>I'm sorry, WHAT did you say you were doing
it as anadjective and not an action
item./BAH
=rusin@vesuvius.math.niu.edu (Dave Rusin)
said:>>But that's always been the case. We made a lot of
money
doing>>work that our customers didn't want or have to do.
What
we>>didn't do (when we weren't ing idiots)
was hide all
the>>warts under pretty pictures.>>I'm sorry, WHAT did you
say
you were doing to the idiots?!I *think* he said that he was
Oing you'. Still, don't take
my wordfor it. I mean, I'm
just passing through and all.adios--We lived the dream -
P.RidsdaleOh really, Peter? How about We lived the dream and
won  all?
=>rusin@vesuvius.math.niu.edu (Dave Rusin)
said:>>But that's always been the case. We made a lot of
money doing>work that our customers didn't want or have to
do. What we>didn't do (when we weren't ing
idiots) was
hide all the>warts under pretty pictures.>>I'm sorry, WHAT
did you say you were doing to the idiots?!>>I *think* he said
that he was Oing you'. Still,
don't take my word>for it. I
mean, I'm just passing through and all.Nope.
De'nition of
ing idiot is a person who knows betterbut does it
anyway./BAH
= With all respect, dear man, you strike me as
that type more enamored> with process rather than function.
Most of us out here have far better> things to do than screw
around for weeks con'guring newsreaders and> the like, even
if
we were so inclined, which most of us clearly are> not. I
suppose we could memorize the phone book, too, but would that>
help us communicate our ideas any better?> Some of us prefer to
view the forest rather than count the trees down> there. Better
view, too. Well, I 'nd the technical aspects of how USENET
functions much more> interesting than most of the discussions
that take place on it. By the> same token, I am much more
interested in the hardware and operating system> software of
the systems I administer than in any of the applications> for
which they are used. Once I hoped that the growing popularity
of personal computers meant> that nearly everyone would learn
to think like programmers. It never> occurred to me that,
sadly, the opposite would happen: That computers> would be
man, that is all 'ne and good, but you'd do
well to examine
your> thinking here a little more closely. You're seeing the
world from a> very narrow vantage point. Technology and
inventive genius exist to> serve those who use and take
advantage of them, not merely those who> design and invent,
otherwise you might just as easily make the> argument that the
world was a far better place when mostly car> builders and
those who tinkered all day with Model T Fords were out> there
driving on the roads. Certainly the roads were safer then,
and> that those driving them generally knew their cars inside
and out, but> that ignores the fundamental purpose behind that
of automobiles, which> is to facilitate transportation. The
same exact argument can be made for telephones, television,>
airplanes and a whole host of other modern conveniences we now
take> for granted and which represent fundamental shifts in the
way we> communicate and get around. They were all once the
domain of a select> few tinkerers and inventors who had
absolutely no idea of what they> were about to unleash on the
world. With all respect, sir, I can guess your politics right
across the> board. Just for openers, you're a Sierra Club,
save-the-whales type.> Gotcha, huh?I think you're
entrenching
him. He said it was cooler when programmersused Oem. You said
it's cooler when people who knew vehicles insideout were the
ones driving them.You guys are agreeing.
=> Shmuel (Seymour
Starblade13@Yahoo.com (Starblade Darksquall) said:>>Really
though, the bad ones are the lousy English/British.>> The
British have a lot to answer for, but so do many other
countries.>> French colonial behavior was worse than the
British, and you really>> don't want to know what Belgium
did.
As for slavery, England outlawed>> it well before we did.>> We
had as much to do with causing the Great Depression as the
English>> did. As to WW I, it was the triumph of diplomacy
over sanity; the>> basic cause of the war was a bunch of
mutual defense treaties with>> hair triggers.>>Then they gave
lands they promised to the Muslims to the Jews>> Actually,
they promised the land to both, and were restricting Jewish>>
immigration even during the Holocaust.>>They totally messed us
up in Vietnam because they didn't help us>>out.>> Indochina
was
a French colony. Why should the British get involved. We>> were
the ones that messed up, 'rst by helping the French get back
in>> and second by going in when the French pulled out. We
should have gone>> in as Ho Chi Mihn's ally when he invited
us...>>*>It is only very rarely that we see this point of view
expressed. The >US mistake in Viet Nam was not that we got
involved in the war; our >problem was we were on the wrong
side.>>Not one in a hundred Americans know that Ho Chi Minh
was a great fan >wanted his country free of outsiders. He made
many trips to the US, >asking congressmen for help to evict the
French.>One cannot reasonably evaluate the decisions the US
made there, at the time, without taking into account what was
going on in Europe, at the same time. Global politics is not
compartmentalized.Mati Meron | When you argue with a
fool,meron@cars.uchicago.edu | chances are he is doing just
the same
=> Shmuel (Seymour J.) Metz
Starblade13@Yahoo.com (Starblade Darksquall) said:>>Really
though, the bad ones are the lousy English/British.>> The
British have a lot to answer for, but so do many other
countries.>> French colonial behavior was worse than the
British, and you really>> don't want to know what Belgium
did.
As for slavery, England outlawed>> it well before we did.>> We
had as much to do with causing the Great Depression as the
English>> did. As to WW I, it was the triumph of diplomacy
over sanity; the>> basic cause of the war was a bunch of
mutual defense treaties with>> hair triggers.>>Then they gave
lands they promised to the Muslims to the Jews>> Actually,
they promised the land to both, and were restricting Jewish>>
immigration even during the Holocaust.>>They totally messed us
up in Vietnam because they didn't help us>>out.>> Indochina
was
a French colony. Why should the British get involved. We>> were
the ones that messed up, 'rst by helping the French get back
in>> and second by going in when the French pulled out. We
should have gone>> in as Ho Chi Mihn's ally when he invited
us...>>*>It is only very rarely that we see this point of view
expressed. The >US mistake in Viet Nam was not that we got
involved in the war; our >problem was we were on the wrong
side.>>Not one in a hundred Americans know that Ho Chi Minh
was a great fan >wanted his country free of outsiders. He made
many trips to the US, >asking congressmen for help to evict the
French.>> One cannot reasonably evaluate the decisions the US
made there, at the > time, without taking into account what
was going on in Europe, at the > same time. Global politics is
not compartmentalized. Mati Meron | When you argue with a
fool,> meron@cars.uchicago.edu | chances are he is doing just
the sameWhat was going on in Europe? And what is meant by Ho
Chi Minh wantingto evict the French? What were they doing in
there?(...Starblade Riven Darksquall...)
=>>Really though,
the bad ones are the lousy English/British.>> The British have
a lot to answer for, but so do many other countries.>> French
colonial behavior was worse than the British, and you really>>
don't want to know what Belgium did. As for slavery, England
outlawed>> it well before we did.>> We had as much to do with
causing the Great Depression as the English>> did. As to WW I,
it was the triumph of diplomacy over sanity; the>> basic cause
of the war was a bunch of mutual defense treaties with>> hair
triggers.>>Then they gave lands they promised to the Muslims
to the Jews>> Actually, they promised the land to both, and
were restricting Jewish>> immigration even during the
Holocaust.>>They totally messed us up in Vietnam because they
didn't help us>>out.>> Indochina was a French colony. Why
should the British get involved. We>> were the ones that
messed up, 'rst by helping the French get back in>> and
second
by going in when the French pulled out. We should have gone>>
in as Ho Chi Mihn's ally when he invited us...>>*>It is only
very rarely that we see this point of view expressed. The >US
mistake in Viet Nam was not that we got involved in the war;
our >problem was we were on the wrong side.>>Not one in a
hundred Americans know that Ho Chi Minh was a great fan
>wanted his country free of outsiders. He made many trips to
the US, >asking congressmen for help to evict the French.>>
One cannot reasonably evaluate the decisions the US made
there, at the > time, without taking into account what was
going on in Europe, at the > same time. Global politics is not
compartmentalized. Mati Meron | When you argue with a fool,>
meron@cars.uchicago.edu | chances are he is doing just the
same What was going on in Europe? And what is meant by Ho Chi
Minh wanting> to evict the French? What were they doing in
there? Evicting the French simply means telling the French
every few years or so that Napoleon was obviously a moron. So
they're obviously better advised to do Frenchish things that
are within their limited cerebral powers to accomplish, such
as buying up some Saudia Arabian or Hong Kong musuem property,
and let Viet Nam take care of Viet Nam trees. Since the only
quicker death that following a Frenchman to the North Pole is
following a Frenchman to a Vietnamese jungle. (...Starblade
Riven Darksquall...)
= Shmuel (Seymour J.) Metz
Starblade13@Yahoo.com (Starblade Darksquall) said:Really
though, the bad ones are the lousy English/British. The
British have a lot to answer for, but so do many other
countries.> French colonial behavior was worse than the
British, and you really> don't want to know what Belgium
did.
As for slavery, England outlawed> it well before we did. We
had as much to do with causing the Great Depression as the
English> did. As to WW I, it was the triumph of diplomacy over
sanity; the> basic cause of the war was a bunch of mutual
defense treaties with> hair triggers.Then they gave lands they
promised to the Muslims to the Jews Actually, they promised the
land to both, and were restricting Jewish> immigration even
during the Holocaust.They totally messed us up in Vietnam
because they didn't help us>out. Indochina was a French
colony. Why should the British get involved. We> were the ones
that messed up, 'rst by helping the French get back in> and
second by going in when the French pulled out. We should have
gone> in as Ho Chi Mihn's ally when he invited us...*It is
only very rarely that we see this point of view expressed. The
US mistake in Viet Nam was not that we got involved in the war;
our problem was we were on the wrong side.Not one in a hundred
Americans know that Ho Chi Minh was a great fan wanted his
country free of outsiders. He made many trips to the US,
asking congressmen for help to evict the French.Our refusal
drove him to China and the communist position that he
eventually took.The Viet Nam constitution, which was authored
by Ho Chi Minh, is patterned after the US constitution.For
much more detail, read Schlessinger's book, Ten Thousand
madrian@pool-141-158-37-173.phil.east.verizon.net
=I know
what these functions are, but how are they
related?Mike
=Take a 3-by-3 grid.Starting in any square, you
can place 1 through 9 in the grid so thatconsecutive integers
are in adjacent (below/above/left/right)grid-squares, and such
that...by some mathematical rule applied to each row and
column, the integersin the row/columns, together with the rule
applied to the integers(intheir order and independently of
integers not in the particularrow/column), produce these
integers as output: --------| | | | 248 --------| | | | 236
--------| | | | 10 -------- 68,92,82And, using the same rule,
but applied to a 4-by-4 grid, and placing 1through 16 (as
above) so as to form a chain of integers, but (here)the 1 and
16 must be adjacent (below/above/left/right), we get
thefollowing integers as
output:rows:2357122925213315columns:525741892421753What is the
mathematical rule, and how are the integers placed intothese
grids?Leroy Quet
=>Take a 3-by-3 grid.>Starting in any
square, you can place 1 through 9 in the grid so
that>consecutive integers are in adjacent
(below/above/left/right)>grid-squares, and such that...>>by
some mathematical rule applied to each row and column, the
integers>in the row/columns, together with the rule applied to
the integers(in>their order and independently of integers not
in the particular>row/column), produce these integers as
output:>> -------->| | | | 248 > -------->| | | | 236>
-------->| | | | 10> -------- > 68,92,82Leroy, shouldn't the
number in the 'rst row be 284 instead of 248?If so, then I
have a solution for the 3x3 puzzle, but not for the 4x4one (I
suspect my formulation of the mathematical rule
generalisesdifferently to 4x4 than yours). -- Erick
=>Take a
3-by-3 grid.>Starting in any square, you can place 1 through 9
in the grid so that>consecutive integers are in adjacent
(below/above/left/right)>grid-squares, and such that...>>by
some mathematical rule applied to each row and column, the
integers>in the row/columns, together with the rule applied to
the integers(in>their order and independently of integers not
in the particular>row/column), produce these integers as
output:>> -------->| | | | 248 > -------->| | | | 236>
-------->| | | | 10> -------- > 68,92,82 Leroy, shouldn't
the
number in the 'rst row be 284 instead of 248?> If so, then I
have a solution for the 3x3 puzzle, but not for the 4x4> one
(I suspect my formulation of the mathematical rule
generalises> differently to 4x4 than yours). -- ErickYou are
right and right...I double double-checked the numbers, but
*still* did not realize I hadexchanged the two digits.And
there is a relatively simple rule for the 3-by-3 case, which
by acertain generalization can extend to all sequences of n
positiveintegers.Leroy Quet
the numbers, but *still* did not realize I had>exchanged the
two digits.>>And there is a relatively simple rule for the
3-by-3 case, which by a>certain generalization can extend to
all sequences of n positive>integers.I'm still at a loss for
what the rule is, but I believe I have determinedthe placement
of the 4x4 grid. Will you con'rm whether this is correct? 10
11
14 15 9 12 13 16 8 5 4 1 7 6 3 2 -- Erick
=Fast ForwardZ:
M-theory may be the 'nal proof of the bankruptcy and
heuristic
exhaustion of the formal-empirical methods of modern physics.
On the other hand, under the right interpretation, it might
open up new vistas. We'll see.No argument from me on that
one!
What a double standard eh? -- about hype in science I mean.
People are always telling me to connect my theories with
experiments and observations. Well that's what I have done
more so that anything on NOVA's Elegant Universe although I
doconnect my math with their stringy alpha' and indeed I
think
what I have done inhttp://qedcorp.com/APS/EmergentGravity.pdf
is good for Witten & Co I have connected their vaporware more
closely to observations of important stuff like the
cosmological constant.Z: But the extravagant resort to these
multi-dimensional hyperspaces looks very suspicious to me --
regardless of how neatly the Standard Model 'ts into the
formalism. Pythagorism run amuck? In any case, Puthoff is not
claiming that his PV theory is any kind of fundamentaltheory
of gravitation -- just a highly computable working model that
might be at least pragmatically justi'ed by some future
deeper
theory.Not so, I think he claims he has a viable alternative to
Einstein.Z: I honestly don't understand why you think you
are
in direct competition with Hal.Because he got all the money
people in the fringe BPP people to think he is on the right
path - not that there is a lot of money there. But because of
his past top security clearances he has in§uence and access
inside USG Black Ops and in fact there is a factional 'ght
inside USG right now about all this - more than that I cannot
say. So theissue is one of whistle blowing on wasting tax
payer money on things that have no chance of working whilst
ignoring things that do.....Z: I'm not sure
we're on the same
page here. But I *am* talking about refutation of Einstein
equivalence -- within the framework of canonical
GR.space-time. It's complicated but standard in MTW et-al.If
ALSO there is TORSION then additional coupling of spinning
test Akimov in Moscow says that is a big effect with weapons
applications. One guy here who came to ISSO 2000 also said
that and he was working on report. Most researcher pooh pooh
that. I do not know'rst-hand.String theory is like 2D
'eld
theory because the string sweeps out aworld sheet in ordinary
space-time rather than the 1D world line. Thisis a great thing
because it essentially does away with the
in'nitiesCosmological
Constant problem, which worries Witten and rightly so.such
problems.NO! String theory give bad prediction /zpg = 10^66
cm^-2 when experiment says /zpf = 10^-56 cm^-2 because
Witten's strings are only 10^-33 cm as Brian Greene repeats
many times in the NOVA vaporware.String theory is no better
than local 'eld theory on this issue! Well only a little
better, but still 122 Powers of Ten off-target!Witten
understands that! They lack my giant vacuum coherent
'eld!http://qedcorp.com/APS/EmergentGravity.docZ: After all -
you get an in'nite mass density and in'nite
electrical
Newtonian gravitational force is in'nite at zero separation
of
two mass points. The classical electron was a hopeless
conundrum even in Lorentz's theory.THIS IS NOT THE
PROBLEM....imprecise and ambiguous - goodfor poetry not for
physics.Z: Your simple dichotomy between ordinary words and
math is a false one IMO. There is ordinary language, there is
*technical* and *scienti'c* language, and there is the highly
re'ned and abstract language of natural philosophy. Then
there
is mathematics.If the formal mathematics is to have a
well-de'ned physical meaning -- a physical interpretation --
then it must be arrived at and expressed in extra-mathematical
technical and philosophical language.Even Einstein had an
equivalence principle -- expressed in what you call equations
and before he even had a metric tensor representation of the
g-'eld. Yet we still don't know what these
'eld equations mean
exactly, except in purely formal-empirical terms, since
Einstein's equivalence principle is problematic.I do not
mean
that ordinary language is not useful or important. I meant
that it is not enough. Einstein had math to back up his
essential points in ordinary language. So far, I am not aware
of even ONE math formula to back up any of your key points
that you have expressed so far only in ordinary informal
language. Am I mistaken here? Please correct me if I missed
something. We have been going back and forth on this for
almost 2 years now without any relevant math from your corner.
Einstein's equivalence principle is classical and the
boundary
of its domain of validity is fuzzy and problematical, which is
part of its greatness like great Art and Poetry. For example
the classical Einstein equivalence principle and the quantum
Heisenberg uncertainty principle work hand in hand to produce
the random micro-quantum Diff(4) covariant additional term
/zpf(x)guv(x) in Einstein's local 'eld
equation. See John
Peacock's Cosmological Physics pp 25-6 for that derivation.
Einstein's equivalence principle has a nice mathematical
expression in the tetradtransformationFLAT SPACE-TIME = TETRAD
(CURVED SPACE-TIME)and inverselye.g.nab =
ea^u(P)eb^v(P)guv(P)As far as I can see the math of the point
you are making is thatTORSION-FREE CONNECTION = HOMOGENEOUS
3rd RANK TENSOR + INHOMOGENEOUS PIECESo your inertial 'eld is
the second piece on RHS.What more is there to be said here?
It's in the standard Einstein theory. One can quibble about
the informal language attached to this formula, but I think it
is a quibble. EEP here also means that locally at event P one
can 'nd timelike geodesic frames in which theTORSION-FREE
CONNECTION = 0 at P but not in neighborhood of P when tensor
curvature =/= 0 at P.torsion 'eld was not considered in
Einstein's original theory. But that is a straight forward
extension.Einstein's theory guv(P) is from locally gauging
the
LINEAR TRANSLATIONS inCONFORMAL = DILATION x NONLINEAR SPECIAL
TRANSLATIONS x LINEAR TRANSLATIONS x SPACE-TIME
ROTATIONSTORSION is local compensating gauge 'eld from
SPACE-TIME ROTATIONS.We should LOCALLY GAUGE EVERYTHING! Why
stop at a subgroup?The torsion-free connection can probably be
split into the homogeneoustensor part + the inhomogeneous part.
Indeed I remember that and can quickly look it up. So if that
is all you mean, then that is standard Einstein.What then is
the point here?Z: That's not it. The decomposition I am
talking about is orthogonal to this.I have no idea of what you
mean here if you cannot produce a math formula to give the
informal sentence meaning.Z: I have explained the point many
times. We are separating the inertial and gravitational
contributions to the connection 'eld.You have explained
nothing to my mind unless there is math to give the words
meaning and/or a precise operational gedankenexperiment in
sense of the Bohr-Einstein debates. Also, showing how your new
insight predicts some new physics and/or explains an important
mystery in the old physics is also desired. I gather
deformational means Ruvwl curvature tensor =/= 0 at P ?Z: It
means the contribution to the connection 'eld (i.e.
metricgradients) that results from the deformation of the
spacetime manifold, where Ruvwl =/= 0.Transformational is when
Ruvwl = 0?Z: It's what you have left when you set Ruvwl = 0.
It
is obviously still present even when Ruvwl =/= 0 in almost all
frames.Fine.Z: OK.I think that is what I said above. It's
already there in Einstein's original theory. Nothing new
here
IMHO.Z: This is really a matter of pure differential geometry,
since it holds generally in the abstract, without any speci'c
reference to spacetime manifolds.I do not understand what you
mean by inertial compensation above.Z: Just think of how
inertial and electrical forces interact and howthis is
described mathematically in *standard GR*. The EM 'eld is not
geometrodynamic, while the pure inertial 'eld (no
gravitational sources) is.Ruv = 0 has curved vacuum solutions
without ordinary matter Tuv sources.EM 'eld is
geometrodynamical in Kaluza-Klein with one extra
spacedimension.Z:That's not *standard GR*, JackZ: Are you
telling me that Kaluza-Klein is now canonical? Or are you
talking about superstring theory?Yes, in sense there is
well-de'ned math meaning to their concepts, which is lacking
in most of your thesis here unless I have missed something
speci'c? I think the 'ctitious or inertial
g-force i.e. the
metric torsion-free connection for parallel transport in the
original 1915 theory is LOCALLY equivalent to a gravity
force.Z: Einstein's principle was that a uniform
gravitational
'eld is*fundamentally indistinguishable* from an inertial
'eld.
That is all in the historical record.Depends what one means by
fundamentally.Z: It is quite clear what Einstein meant. He was
quite forthcoming onthis. I think it's important to
recognize
that this is the cornerstone of Einstein's concept of
general
relativity. The meaning of Einstein's principle is quite
unambiguous when placed in context.Fine, but nothing wrong
with what Einstein said above except thatphysically we never
have a global uniform gravity 'eld.Z: There is nothing wrong
with it except that it is almost certainly false as a matter
of empirical fact.Yes, but one could imagine a universe like
that in terms of the parameters of the theory.Z: Einstein had
to pretend that while Riemann curvature distinguishes almost
all permanent gravitational 'elds (Eddington, Tolman,
Bergmann) from all inertial 'elds, it has no direct physical
meaning, at least in the immediate neighborhood of a spacetime
point.No, again I think you are mis-interpreting here. If the
local curvature is not zero it is not zero in any frame at P.
However, its tidal effect at P is ignorable in a small enough
neighborhood of P provided:1. Not near a space-time
singularity2. Not inside the effective Planck area Lp*^2End of
story. It's and approximate statement or a correspondance
principle. Einstein was not thinking about Lp^2 = hG/c^3 in
1915, Heisenberg did not do his thing until 1925!Z: As far as
I can see Einstein was simply (although understandably)
confused about the distinctions between empirical
correspondence, formal correspondence, formal analogy, and the
literal identity of inertial and gravitational phenomena.Quite
possibly, but so what? It's no big deal today unless you can
use your new insight to explain why cosmological constant is
small, and the true nature of both dark energy and dark matter
and also the string structure of lepto-quarks and gauge force
bosons etc. As a minor historical point maybe you are correct.
I don't know without studying the classic writings more
deeply.Z: As far as I can see this approach is a hangover from
the fundamentally wrong- headed logical empiricism of the
1920s. How is the MTW argument regarding localized vacuum
stress-energy based on theEEP any different from arguing that
since the speed of an object cannot be measured at an instant,
the speed of the object has no physical meaning at an instant?
Hence, as Zeno might argue, motion is impossible, since at
each instant the object cannot be said to be moving? We
enlightened moderns have the differential calculus. We are
supposed to know better. Eddington pointed out in 1922 that
there is no rational foundation for insistence on such a
sweeping universal assumption (Einstein equivalence) -- that
it is merely a conjecturethat is subject to empirical test and
that it is a mistake to assume that the hypothesis *must* be
true. And whether it is or is not is as far as
*formal-empirical* GR is concerned a purely empirical
matter.In other words, it was merely Einstein's guess. A
sweeping extrapolation. A bold hypothesis. Based on what we
know now, as a general law of nature, quite possibly a huge
RED HERRING. This was later reiterated by Feynman in his
Lectures on Gravitation, where he actuallymade some gentle fun
of Einstein (or at least Einstein's more fanatical
followers).
Clearly, we know there is a formal-empirical *analogy* between
gravitational and inertial 'elds, but only a partial one
(Eddington 1922). But a partial analogy -- short of
identi'cation-- is a perfectly adequate basis for a weaker
physical interpretation of the so-called EEP as technically
formulated by Wheeler et al. that does not imply the identity
of gravitational and inertial phenomena.That's only an
idealization.Z: The EEP is an idealization. But the EEP does
not capture Einstein equivalence without an additional layer
of interpretation.IMO EEP amounts to an *ad hoc* stratagem
whereby, in order to appear to save the Einstein equivalence
hobbyhorse, the fundamental distinction between equivalence as
identity, and equivalence as mere local correspondence with
§at-spacetime SR, is systematicallyobfuscated, and a minimal
agnostic epsilon-delta type technical formulation is
misleadingly represented as somehow capturing the content of
Einstein's principle (hence the misnomer EEP). It
doesn't. It
is *consistent* with it, but it does not capture the full
content of Einstein equivalence. That is why I call the MTW
development of canonical GR a shell game. You have to keep
your eyes on that pea.What they do in Gravitation in certain
important contexts is to tacitly attach the additional layer
of Einsteinian interpretation in their supposed proof of the
non-locality of vacuum stress-energy.The physical 'eld is
supposed to be eliminated (i.e. annihilated) at a point in a
free-fall frame. But that is Einstein equivalence, and not
merely EEP. If Einstein equivalence is empirically false, then
it can hardly be invoked as the theoretic basis for the
of'cial
interpretation of the GR formalism, of the EEP, or as the basis
for an argument against localized vacuum stress-energy, as MTW
would have it.However, under a suitable reinterpretation, the
entire general-covariant formal machinery of canonical GR
still works 'ne. But at the same time, the reinterpreted
theory may point in very different directions as
correspondence relation between the two theories. That this
very bold Einstein concept of gravitational-inertial
equivalence historically led Einstein to the GR tensor 'eld
equations in the manner of a *heuristic guide*, or that
Einstein himself may never have explicitly abandoned his bold
hypothesis, are neither here nor there as far as the
contemporary objective critical discussion of the subject is
concerned. IMHO. However, this was all pointed out by
Eddington and von Laue in the early 1920s. Too bad M, T, and W
apparently ignored them.Tidal differences in the g-force
between P and P + dP means curvaturei.e. real gravity as
opposed to simulated gravity.Z: Yes, exactly. That is what is
meant by a permanent or intrinsicgravitational 'eld.Fine, so
what's the problem?Z: The problem is the GR
de'nition of
vacuum stress-energy, the question of its covariant formal
representation, and the question of its localizability -- as I
think you know.Again your point here is only interesting if you
say there should be more terms inGuv + /zpfguv =
-alpha'Tuvalpha' = Ed Witten's
inverse string tension (h = c =
1 convention).i.e. if you say there is some kind of power
series in alpha'^n with n factors of Guv?Then you have
something interesting. Otherwise your point is trivial
becauseLOCAL CLASSICAL GEOMETRIC VACUUM STRESS-ENERGY DENSITY
TENSOR = alpha'^-1Guv = Tuv(Geometry)LOCAL MICRO-QUANTUM
RANDOM ZERO POINT VACUUM STRESS-ENERGY DENSITY TENSOR =
alpha'^-1/zpfguvTherefore Einstein's local
geometrodynamic
'eld equation is:Sum off all local stress-energy density
tensors from classical geometry + random virtual zero point
quantum §uctuations + matter + coherent virtual near 'eld
+
radiation = 0When no torsion and no hyperspace violations of
metricity then we have a simple situation from the Bianchi
identities that the 4-covariant divergence of the classical
geometry stress-energy density currents locally vanish if the
vacuum is NOT exotic, but NOT OTHERWISE!Z: Again, you are
reverting to your straw man here according to which I am
supposed to be 'nding a technical problem with
Wheeler's
minimal agnostic technical statement of the so- called EEP.
I'm not -- except that it is only valid at a spacetime
point.As every School Boy knows I suppose -- at least at Cal
Tech. :-)Z: But if you want to glimpse part of what I'm
getting at, just exchange the epsilon and the delta in
Wheeler's formulation of EEP. For any given
'nite neighborhood
of a spacetime point, we can in (GR) principle always construct
a gravitometer that is suf'cientlysmall and sensitive to
detect
the effects of non-vanishing Riemann curvature around that
point, regardless of the state of motion of the object. All
inside Einstein's famous elevator. This turns
EEP' on its
head. It turns out (and I didn't know this when I
'rst got
onto it) that the position I am advancing here is essentially
Eddington's as set out in 1924. At that time he viewed
Einstein equivalence as heuristic and tentative in character,
and not as a fundamental principle. I say he was right on the
money. This is the view that was later echoed by Bergmann,
Synge, and others. EEP as technically formulated by Wheeler is
'ne -- but it is consistent with either interpretation
(Einstein's or Eddington's).So it seems your
point is one of
the history of relativity on howEinstein's ideas evolved.Z:
You don't seem to see that this entails a profound shift in
the physical meaning of the GR 'eld equations, and that this
means that *we do not have actual general relativity*,
regardless of the impressive empirical accuracy of standard
GR.You lost me again.Z: If we do not have actual general
relativity, then we have not in fact *explained* the equality
of gravitational and inertial mass, as Einstein thought he
had. We have simply *assumed* it.Again you are too subtle for
me here. The crux here is simply thatlight rays move on null
geodesics, and nothing moves on spacelike geodesics in
torsion-free space-time. You cannot have light, you cannot
have anything move on a timelike non-geodesic unless there are
charged physically if there were no electric charges. This
already shows that gravity must emege from electromagnetism.
No charges no weight!Z: The term general relativity, like EEP,
is thus in that case a misnomer. In the MTW development of GR
it amounts to an elaborate bait-and-switch routine. It also
opens up a prospect for the resurrection of a suitably re'ned
neo-Lorentzian concept of a non-material aether (physical yet
non-material medium of propagationacross the vacuum) to be
sharply distinguished from spacetime as a void. Under this
model, it is the *physical disturbance* of this aether by the
presence of matter that causes deviations from straight-line
motion.Less words more math would help clarity here.Z: If we
don't actually have *general* relativity, then we
don't have
relativity, period -- since that implies and demands the
physical relativity of *all* motion (A. Einstein). No Einstein
equivalence, no general relativity. This *according to
Einstein's own classic arguments*.This is more a legal
argument then a physics argument. :-)Z: This is IMO profoundly
iconoclastic and could have deep implications for the further
development of gravitational theory. But the logic is
inescapable IMO.Depends what you mean by logic. :-) Is
renormalization theory for before and why should it now? Look
at Niels Bohr as a good example. :-)I do not see however how
this will lead to new physics today unless youmean that
addition torsion local gauge 'eld and possibly local gauge
'elds from ALL of the conformal group will modify EEP which
is
only based upon the 4-parameter translation group of the 15
parameter Conformal Group for Minkowski space-time.Z: I am not
trying to modify EEP. I am simply proposing an alternative
interpretation to those based on Einstein equivalence. The
alternative interpretation points to a very different
correspondence model betweenstandard GR and a deeper theory of
gravitation. It may hold some important clues to how the
analogical relationship between physical gravitation and
mechanical inertia, and the basis for weak equivalence (strict
proportionality of gravitational and inertial mass) will
beexplained in the deeper theory -- which will presumably be
some kind of quantum 'eld theory of the gravitational
vacuum.I
don't see how without speci'c toy models of
gedankenexperiments
and/or mathematics. I refer to the paper by Utiyama I think in
mid-60's also Kibble's later paper in which
the general
relativity principle is rederived as a kind of local Yang
Mills gauge principle in the curved space-time base space of
the 'ber bundle where the 'ber is the
U(1)SU(2)SU(3) or its
GUT internal symmetry generalization. Roughly, the gauge
forces are in the principle bundle with unstable globally §at
space-time as a coset space mod the internal symmetry subgroup
of the total group and the lepto-quarks are the associated
vector bundle. One then does the same trick again inside the
coset space whose symmetry group is the Conformal Group.Z:
Fine. This was also Feynman's approach. He also alluded to
gauge symmetries as the basis for EEP *by way of formal
correspondence* with standard GR.Yes, that is how everyone in
theoretical physics today thinks about it.Z: Does this gauge
symmetry of the underlying Yang-Mills 'eld imply that
gravitational and inertial 'elds are, physically speaking,
literally one and the same phenomenon?I do not understand your
question unless you give the math.Connection = Tensor +
non-TensorReal gravity is from tidal gradients of Tensor part
of ConnectionConnection = 0 in any LIF.g-FORCE = ConnectionIn
LIFTensor g-force + non-Tensor g-force = 0So that's
compensation at g-force level.Tidal force is the derivative of
g-Force!i.e. f(P) = 0 but df(P)/dx^u =/= 0 in LIFZ: If not,
then such theories are inconsistent with Einstein equivalence
-- although perhaps not with the so-called EEP in its most
agnostic formulation.You lost me.was Einstein's. It is
inconsistent with Eddington's as stated in Mathematical
Theory
of Relativity. MTW seem to use both, which strikes me as an
example of Bohrian complementarity -- AKA speaking with forked
tongue -- in the context of spacetime physics. That is a very
bold hypothesis, as Feynman pointed out on many occasions. But
it is at the core of Einstein's concept of general
relativity,
as Einstein himself consistently emphasized (speci'cally to
von Laue). Of course, this was later formulated as a local
frame, together with our ability to rendertidal effects
negligible by going to a suf'ciently small neighborhood. This
makes it look on the surface like the Einstein principle is
still valid -- hence the misleading acronym EEP.Forget what
Einstein allegedly thought in his early days.Z: Jack, this was
integral and indispensable to Einstein's idea ofgeneral
relativity. So, if you forget about this -- and also Pauli's
entire 1921 exposition of GR -- you then have general
relativity *without actual general relativity*, as I said
early on.I mean, this is a historical point about the initial
immatureconception of relativity that got further re'ned into
the modern ideas launched in MTW.Z: No, it means that there is
in fact no such thing as general relativity. That is a very
profound shift of interpretation IMO.All we really have now is
*general covariance* and a tensor representation of the
gravitational 'eld, and EEP for empirical correspondence with
SR.That's good enough.Z: Even Einstein eventually admitted
that general covariance in and of itself is empty of physical
content (see Autobiographical Notes).Common knowledge.Z: Looks
like I was right.But if you are willing to drop this and hew to
a consistentnon-Einsteinian interpretation of EEP, then 'ne.
But then, the MTW argument against localized vacuum
gravitational stress-energyfalls apart (though of course that
does not in itself mean there areno other valid
objections).The only way you can attack MTW there is to say
that their initialassumption that the localized vacuum tensor
is quadratic in the connection is a Straw Man, i.e. not
complete.Z: Here you are ignoring, or not understanding, my
proposal for a canonical local decomposition of the connection
'eld, which I contend avoids all these
dif'culties even within
the existing GR formalism with its uni'ed abstract
metric.like
I did above. That there is another form based only on the
nonlinear products of the curvature tensor but that would
change the 'eld equation from (neglecting zero point
/zpfguv)Guv = -(8piG/c^4)TuvtoGuv + Nonlinear products of 4th
rank curvature tensor = -(8piG/c^4)TuvThe extra terms are a
power series in Lp^2 = hG/c^3they may be there, but are too
small on the macro-scale.Is that what you mean?Z: I don't
think so. I am talking about a local decomposition of the
standard Christoffel connection.Like I showed above - standard
stuff. So what? I cannot understand really what you mean until
I see formal statements in math that pin down the ambiguities
of ordinary language.Z: OK. Of course this has to be done.I
think I did it above. This should not take years to do.Z: I
gave you a formal expression some time ago but you apparently
ignored it.Z: This is principally a matter of proper
interpretation of the metric gradients -- even in the abstract
context of pure differential geometry... which breaks down when
scale ~ Lp* and which emerges from local giant vacuum coherent
wave.Z: On the physical level, it is tied to a close analysis
of exactly what it means to mathematically meld physical time
into a Riemannian spacetime manifold, and precisely how to
properly interpret the local transformational properties of
the connection 'eld on a curved (i.e.deformed) Riemannian
manifold.You lost me without the math.Z: Einstein may simply
have gone wrong there -- a victim of his own wishful thinking
-- regardless of his impressive heuristic success in arriving
at the GR 'eld equations.I crave heuristic success! :-)This
is
why I feel uneasy about Bohr's reliance on ordinary language
inthe quantum reality problem.Z: This is a complex issue that
I don't really have the time to get into here. But I do
agree
that Bohr's insistence on the irreducible use of ordinary
language and common sense concepts in describing the results
of experiments is very dubious. At the same time I don't
think
this means that the only satisfactory language for discussion
and analysis of the problems of QM is formal mathematics. I
would say that this approach simply avoids the entire problem
of the proper interpretation of the QM formalism. I believe
this was Bohm's view.Which is what I originally argued: the
bare EEP does not establishthat the gravitational energy
density must vanish at a point, or that its components depend
upon the frame of reference in a non-covariant manner. It only
requires that the net measurable combined gravitational and
inertial forces vanish at a point in some coordinate system.
To get the true gravitational stress-energy, we simply ignore
theinertial contribution -- that's all. Eddington himself
explicitly states that in GR the inertial 'eld has a
stress-energy that is frame-dependent and represented by a
non-tensor. But this is a *'ctitious* stress-energy, unless
you believe in Einstein equivalence *as originally stated* --
which it now appears that you don't.He was perhaps a bit
confused whilst the theory was immature.The point is that
it's
coherent conceptually today in the form MTWhave.Z: I cannot
agree. See above. This is a *real interpretive dichotomy* at
the most fundamental level. Now you could say somethinglike
this about Schroedinger, who really thought he had a wave
theory in the classical sense -- but later had to give this up
for a number of reasons. Einstein never explicitly abandoned
equivalence and true general relativity. Not even in his
Autobiographical Notes, which is just about his last word on
the subject.You cannot render tidal effects negligible in the
approach to asingularity until effective Planck scale is
reached. That scale may not be 10^19 Gev after all. It may be
1 Gev?Z: That may well be the case, but this is not part of
canonical GR. No doubt a deeper theory, if it ever 'nally
comes, will answer such questions.Ed Witten thinks that's
M-theory. It's now on NOVA! I am beginning toread Witten. I
am
getting a little uneasy about all this duality stuff in string
theory because it is beginning to remind me of my debate with
Hal Puthoff on his use of isotropic r vs. curvature rin the
SSS model. This debate is described in my Dec 2002 book
Space-Time and Beyond II.Z: M-theory may be the 'nal proof of
the bankruptcy and heuristic exhaustion of the
formal-empirical methods of modern physics. On the other hand,
under the right interpretation, it might open up new vistas.
We'll see.No argument from me on that one! What a double
standard eh? -- about hype in science I mean. People are
always telling me to connect my theories with experiments and
observations. Well that's what I have done more so that
anything on NOVA's Elegant Universe although I doconnect my
math with their stringy alpha' and indeed I think what I
have
done inhttp://qedcorp.com/APS/EmergentGravity.pd's good for
Witten & Co I have connected their vaporware more closely to
observations of important stuff like the cosmological
constant.Z: But the extravagant resort to these
multi-dimensional hyperspaces looks very suspicious to me --
regardless of how neatly the Standard Model 'ts into the
formalism. Pythagorism run amuck?My debate with Puthoff was
that he was misinterpreting the physics notrealizing that the
expansion of space inside a critical radius was an illusion of
not realizing what the coordinate patch was in the curved
differential manifold.Z: OK.Matt Visser makes this clear in
Lorentzian Wormholes in the context of Kruskal coordinates.
There is a kind of duality there withr' = r*^2/rbut
r' and r
are both OUTSIDE the horizon. Puthoff and Ibison makethe
conceptual error that r' is INSIDE the horizon! Actually
they
have no horizon because of their exponential, but they have a
critical min turning point radius that plays a similar role.Z:
Couldn't this simply be the result of a mathematical
ambiguity?No, good books like Matt Visser's Lorentzian
Wormholes are good on this. I don't think Puthoff and Ibison
ever really read that book or pondered its meaning if they
did.Z: In any case, Puthoff is not claiming that his PV theory
is any kind of fundamental theory of gravitation -- just a
highly computable working model that might be at least
pragmatically justi'ed by some future deeper theory.Not so, I
think he claims he has a viable alternative to Einstein.Z: I
honestly don't understand why you think you are in direct
competition with Hal.Because he got all the money people in
the fringe BPP people to think he is on the right path - not
that there is a lot of money there. But because of his past
top security clearances he has in§uence and access inside USG
Black Ops and in fact there is a factional 'ght inside USG
right now about all this - more than that I cannot say. So
theissue is one of whistle blowing on wasting tax payer money
on things that have no chance of working whilst ignoring
things that do.I am wondering if Witten, Greene & Co are
making a similar conceptualerror in that really they ignore
the physics INSIDELp*^2 which G.E. Volovik in Universe in a
Helium Drop says isessential for solving the smallness of the
CosmologicalConstant problem. It's like in condensed matter
physics not goinginside the unit cell of the crystal lattice.
If you do that youwill get a zero point energy for phonons
that is much too large! Thisis Volovik's insight.String
theory
is like 2D 'eld theory because the string sweeps out aworld
sheet in ordinary space-time rather than the 1D world line.
Thisis a great thing because it essentially does away with the
in'nitiesCosmological Constant problem, which worries Witten
and rightly so.such problems.NO! String theory give bad
prediction /zpg = 10^66 cm^-2 when experiment says /zpf =
10^-56 cm^-2 because Witten's strings are only 10^-33 cm as
Brian Greene repeats many times in the NOVA vaporware.String
theory is no better than local 'eld theory on this issue!
Witten understands that! They lack my giant vacuum coherent
'eld!http://qedcorp.com/APS/EmergentGravity.docZ After all -
you get an in'nite mass density and in'nite
electrical
Newtonian gravitational force is in'nite at zero separation
of
two mass points. The classical electron was a hopeless
conundrum even in Lorentz's theory.THIS IS NOT THE
PROBLEM.There are analogies of string theory with lattice spin
Ising modelswhich have a duality relating a T theory to a 1/T
theory in a duallattice.Witten introduces the famous alpha'
as
basically a new stringfundamental constant. He does not seem to
connect it to the Salamgravity I worked on in 1973.Z: Yet more
knobs and dials. Is any of this really physics? Can this kind
of theory really be said to predict anything? Other than in
the *ad hoc* formal manner of abstract mathematical
description? I'll see if I can comment on the stuff below
after I have looked at Witten.Using his h = c = 1 units.
Witten's alpha' is essentially an
effective'eld Planck area.
If we believe Susskind's world hologram we
havealpha' = Lp*^2
= Lp^4/3L^1/3at scale LIf we choose L = c/Ho in a kind of Mach
Principle of large scalein§uence on small scaleHo = HubbleLp* ~
1 fermiThe problem with this is the time dependence in H(t)
where Ho is thepresent epoch value.Note, in Witten's
conventions, energy is 1/LengthThereforealpha' is the
universal Regge slope, which for hadronic resonance
hasalpha'
~ (1 fermi)^2Quantized spin of resonance = alpha'(Energy of
resonant peak)^2 +interceptalpha' is reciprocal string
tension
since Energy/Length ~ 1/Area in theh = c = 1 convention used by
Witten & Co.In my theory/zpf =
(alpha')^-1[(alpha')3/2|Vacuum
Coherence|^2 - 1}Einstein's gravity emerges fromguv =
(Minkowski)uv + (alpha'){Goldstone Phase of
VacuumCoherence)(,u,v)}Z: So this seems to map directly over
to some bi-metric version of GR.No I do not see that at all.
The SUM on RHS is not bimetric anymore than 2 = 1 + 1 is in
reality a pair of two 1's with independent parallel
existences.Z: You have a §at Minkowski background with a
Lorentz metric, with inertial 'elds conceived as artifacts of
non-linear spacetime coordinate transformations, PLUS a
*physical metric* describing gravitational phenomena that is
directly related to your BEC Goldstone phase. Am I right?Yes,
but it is only the sum that is physical. I do not see two
coexisting independent metrics apart from locally §at tangent
bundle idea of standard GR with tetrad map between LIF
geodesic 'ber and non-geodesic LNIF base local framesZ: If
so,
then this is NOT Einstein's gravity. It is
*Eddington's*
gravity. This was also Feynman's general approach in his
Lectures on Gravitation.It is BOTH! I haveGuv + /zpfguv =
alpha'TuvZ: As I said, I think your task is going to be a
lot
easier, as far as correspondence with GR is concerned, under
my proposed alternative interpretation of the EEP. You cannot
simply sweep all these problems under the carpet emergence
IMO.anholonomic torsion 'eld potential =
(alpha'){Goldstone
Phase ofVacuum Coherence)[,u,v]The O(2) internal symmetry of
this complex numbered scalar VacuumCoherence local 'eld
implies 1D string topological defects in 4Dspacetime as a
rigorous theorem in the text books.Z: OK.More generalized
models of O(N) hypercomplex numbered MACRO-QUANTUMVACUUM More
is different (P.W. Anderson) coherence order parameterswill
give the brane world topological defect generalizations of
thesestrings that should also have torsion on the
microscale.Z: OK. The most from the least. BTW, how does your
theory explain mechanical inertia?Exactly as in Wheeler's
book
Geometrodynamics with Mass withoutmass except now I have G* =
10^40 G(Newton) at the fermi scale.Z: OK. I'll have a look.I
started working on Wheeler's book Geometrodynamics in 1966.
Wheeler spoke at UCSD frequently then. The characteristic rest
mass of the spatially extended lepto quark of Charge without
charge rotating with Spin without spin ism = e^2/zpf^1/2 =
e^2/Lp* = e^2(alpha')^-1/2because Vacuum Coherence -> inside
the Type II superconductorquantized §ux vortex vibrating
string exotic vacuum dark mattercore with ends pinned to the
3Dim brane world we are stuck on like EdAbbott's Flatlanders
if the basic Witten & Co ideas are on righttrack.Z: So in your
theory, inertial effects result from the physical interaction
of matter, conceived as branes, with the quantum vacuum,
conceived as a virtual BEC?BRANES emerge FROM virtual BEC.
Strings emerge from virtual O(2) BEC which is only low energy
long-range limiting case of shorter-scale O(N) BEC in some
kind of O(N') or G(Mystery) group hypercomplex number
generalization of Einstein's real space-time continuum.Z:
Say
bye bye to Mach's principle.Not ifLp*^2 =
Lp^4/3(c/Ho)^2/3which has a problem however.These 1 Dim
strings vibrate in the extra boson space dimensions and
theextra fermion supersymmetry matrix space-dimensions forming
theCalabi-Yau space generalization of the Kaluza-Klein
hyperspace of the1920's.Z: OK. But it only takes one
physical
effect that is not locallynegligible in this sense to blow out
Einstein equivalence.Einstein equivalence is only a classical
weak 'eld approximation oryour correspondence principle in
the
informal sense for the zerotorsion limit.Z: I'm not sure
exactly what you mean here. Einstein thought it heldwithout
restriction. Looks like you don't agree.I am not sure
without
doing a careful look. In any case, of coursethere have been
subtle modi'cations or re'nements of
Einstein's early
thinking. These are small corrections so to speak. Only minor
clari'cations of his great insights.Z: This is simply not the
case, Jack. What I am talking about is a profound counter-
revolutionary paradigmatic shift back to some kind of an
aether, conceived as a non-material yet physical medium of
propagation across the physical vacuum.Z: So it is precisely
Einstein's original insight -- that both gravitation and
inertia could be jointly reduced to a distortion of an
abstract metric in an absolute void, without reference to any
physical medium of propagation -- that is in question here.
Look, Einstein was a wonderful man and a creative genius, but
business is business.Not according to Evan Harris Walker and
Einstein's 'rst wife. Music from
OThe God Father plays in
background. :-)Z: We need to move forward. Let's not be too
sentimental about this.There is nothing revolutionary in the
distinctions you propose here that I am able to understand at
least.Z: Then perhaps -- and I don't say this lightly -- you
don't really understand Einstein. You don't
seem to realize
that you have in fact abandoned his theory of general
relativity. Quite rightly, IMO, since THERE IS NO GENERAL
RELATIVITY.There you go again sounding like Brian Greene on
NOVA! ;-)Z: That is a lot more than a mere detail of history.
That can hardly be described as a slight adjustment or
re'nement to Einstein's original insight.You
lost me. I am
only a humble post-Quantum non-mechanic.Z: It is in fact a
wholesale *abandonment* of Einstein's original insight,
which
is now demoted to the status of a mere heuristic tool -- mere
scaffolding to be discarded once the cathedral is built, in
favor of more solid and durable buttressing that is more in
keeping with the 'nal architecture.I am not sure what happens
when there is torsion-spincoupling. It can break down for a
variety of reasons.Z: Exactly -- you're not sure. The fact
is
it's anybody's guess and isultimately an
empirical
question.Not quite - there is a lot of work in the published
literature - it'sonly my personal lack of knowledge here I
allude to.Z: I'm not sure we're on the same
page here. But I
*am* talking about refutation of Einstein equivalence --
within the framework of canonical GR.space-time. It's
complicated but standard in MTW et-al. If ALSO there is
torsion 'elds.Akimov in Moscow says that is a big effect with
weapons applications. One guy here who came to ISSO 2000 also
said that and he was working on report. Most researcher pooh
pooh that. I do not know 'rst-hand.Z: Yet Einstein thought he
was completely sure, and said so. That's whyFeynman made fun
of him in Lectures on Gravitation.Again this is very minor
compared to what is happening now and what I am talking about
above in relation to Witten & Co.Z: See above. It changes the
entire meta-theoretic relationship between GR and the deeper
'eld theories of gravitation. It profoundly changes our
understanding of the vacuum and its relationship to
gravitational and inertial phenomena.Show me how in detail. I
do not have time to absorb all your points below. Later.Z:
OK.
= I am a newbie in Galois Field. I wondoned that the
relationship betweenthe codewords and generator polymial? I
want to know that how to get ageneratorpolynomial in
matlab?Yang Jun
=Let b(1) = 1;and for k >= 2,b(k) = x
*sum{j|k, j<k} b(j).(Sum is over positive PROPER divisors of
k.) Let B(r) = sum{k=1 to oo} b(k)/k^r,for those r's where
the
sum converges.Then B(r) =1/(1 +x -x *zeta(r)),where zeta(r) is
Riemann zeta function.So, a few questions:Each b(k) is a
polynomial in terms of x. What is closed form for
thecoef'cients?B(r) (or analytical continuation) has a pole
at
r = R,where zeta(R) = 1 + 1/x.So, is the sequence {b(j)} =
O(j^(R-1)) (just guessing) or somethingelse based upon R?Also,
'nally, an obvious but curious fact:If x = 1/zeta(q), for a
FIXED q,thenB(q) = zeta(q) itself.LeroyQuet
=I don't get it
exactly, must be because I'm not a mathematician and
canhardly
grasp what you're doing :) Please see my remarks between
thelines. Let b(1) = 1; and for k >= 2, b(k) = x *sum{j|k,
j<k} b(j).So if x=0 then b(k)=0. (Sum is over positive PROPER
divisors of k.) Let B(r) = sum{k=1 to oo} b(k)/k^r,So if x=0
then B(r)=0, because b(k)=0 for those r's where the sum
converges. Then B(r) = 1/(1 +x -x *zeta(r)),So if x=0, then
B(r)=1. This does not agree with B(r)=0 from a few
linesearlier? where zeta(r) is Riemann zeta function. So, a
few questions: Each b(k) is a polynomial in terms of x. What
is closed form for the> coef'cients? B(r) (or analytical
continuation) has a pole at r = R,> where zeta(R) = 1 + 1/x.>
So, is the sequence {b(j)} = O(j^(R-1)) (just guessing) or
something> else based upon R? Also, 'nally, an obvious but
curious fact: If x = 1/zeta(q), for a FIXED q,> then B(q) =
zeta(q) itself. Leroy> Quet Jeroen
=[First, I am glad that
Jeroen's reply contains all of my originalmessage, since the
original message did not appear on Math Forum atleast.] As for
my apparent error: You are forgetting *one* little thing,
...that b(1) always = 1, whatever x is.;)Leroy Quet I don't
get it exactly, must be because I'm not a mathematician and
can> hardly grasp what you're doing :) Please see my remarks
between the> lines. Let b(1) = 1; and for k >= 2, b(k) = x
*sum{j|k, j<k} b(j). So if x=0 then b(k)=0. > (Sum is over
positive PROPER divisors of k.) Let B(r) = sum{k=1 to oo}
b(k)/k^r, So if x=0 then B(r)=0, because b(k)=0 > for those
r's where the sum converges. Then B(r) = 1/(1 +x -x
*zeta(r)),
So if x=0, then B(r)=1. This does not agree with B(r)=0 from a
few lines> earlier? > where zeta(r) is Riemann zeta function.
So, a few questions: Each b(k) is a polynomial in terms of x.
What is closed form for the> coef'cients? B(r) (or analytical
continuation) has a pole at r = R,> where zeta(R) = 1 + 1/x.>
So, is the sequence {b(j)} = O(j^(R-1)) (just guessing) or
something> else based upon R? Also, 'nally, an obvious but
curious fact: If x = 1/zeta(q), for a FIXED q,> then B(q) =
zeta(q) itself. Leroy> Quet
= [First, I am glad that
Jeroen's reply contains all of my original> message, since
the
original message did not appear on Math Forum at> least.] > As
for my apparent error:> You are forgetting *one* little thing,
...That's hardly a Olittle thing'
I overlooked , but more a
capitalblunder... :( that b(1) always = 1, whatever x is.> ;)
Leroy Quet> I don't get it exactly, must be because
I'm not a
mathematician and can> hardly grasp what you're doing :)
Please see my remarks between the> lines.>> Let b(1) = 1;>>
and for k >= 2,>> b(k) = x *sum{j|k, j<k} b(j).>> So if x=0
then b(k)=0.> (Sum is over positive PROPER divisors of k.)>>
Let B(r) = sum{k=1 to oo} b(k)/k^r,>> So if x=0 then B(r)=0,
because b(k)=0> for those r's where the sum converges.>>
Then B(r) =>> 1/(1 +x -x *zeta(r)),>> So if x=0, then B(r)=1.
This does not agree with B(r)=0 from a few lines> earlier?>
where zeta(r) is Riemann zeta function.>> So, a few
questions:>> Each b(k) is a polynomial in terms of x. What is
closed form for the> coef'cients?>> B(r) (or analytical
continuation) has a pole at r = R,> where zeta(R) = 1 + 1/x.>
So, is the sequence {b(j)} = O(j^(R-1)) (just guessing) or
something> else based upon R?>> Also, 'nally, an obvious but
curious fact:>> If x = 1/zeta(q), for a FIXED q,> then>> B(q)
= zeta(q) itself.>> Leroy> Quet>> Jeroen
=Error indicated
where it occurs: I don't get it exactly, must be because
I'm
not a mathematician and can> hardly grasp what you're doing
:)
Please see my remarks between the> lines. >Let b(1) = 1;>>and
for k >= 2,>>b(k) = x *sum{j|k, j<k} b(j). > So if x=0 then
b(k)=0.Except that b(1) = 1 for all x. >>(Sum is over positive
PROPER divisors of k.)>>Let B(r) = sum{k=1 to oo} b(k)/k^r, >
So if x=0 then B(r)=0, because b(k)=0No - if x=0, then B(r) =
1, since b(0)=1. >>for those r's where the sum
converges.>>Then B(r) =>>1/(1 +x -x *zeta(r)), > So if
x=0, then B(r)=1. This does not agree with B(r)=0 from a few
lines> earlier? >>where zeta(r) is Riemann zeta
function.>>So, a few questions:>>Each b(k) is a polynomial
in terms of x. What is closed form for
the>>coef'cients?>>B(r) (or analytical continuation) has a
pole at r = R,>>where zeta(R) = 1 + 1/x.>>So, is the sequence
{b(j)} = O(j^(R-1)) (just guessing) or something>>else based
upon R?>>Also, 'nally, an obvious but curious fact:>>If x
= 1/zeta(q), for a FIXED q,>>then>>B(q) = zeta(q)
itself.>>Leroy>>Quet > Jeroen
=what's wrong with the TI-89
calculator?For integration( e^(ax) ) with respect to
xS(e^(ax),x)the TI-89 answers: e^(ax)*xBut my book and
www.quickmath.com say: e^(ax)/aIs the TI-89 wrong? Or can
somehow both be right?Confused,Andi
=>For integration(
e^(ax) ) with respect to x>S(e^(ax),x)>the TI-89 answers:
e^(ax)*xIf the TI-89 reads ax as a single variable, then
integrating withrespect to x would make ax, and therefore
e^ax, constant. The TI's answerfollows immediately.Try
entering e^(a*x) instead. The only reason I guess this to be
theissue is because Mathematica handles things the same
way.Doug
=Doug Norris <norrisdt@rintintin.colorado.edu>
scribbled the following:>>For integration( e^(ax) ) with
respect to x>>S(e^(ax),x)>>the TI-89 answers: e^(ax)*x> If the
TI-89 reads ax as a single variable, then integrating with>
respect to x would make ax, and therefore e^ax, constant. The
TI's answer> follows immediately.> Try entering e^(a*x)
instead. The only reason I guess this to be the> issue is
because Mathematica handles things the same way.The TI-89
supports multi-letter variables. Therefore it understands axas
just that, ax (to rhyme with a tool for chopping 'rewood).
Tomake it realise it's supposed to be a multiplied by x, you
have to typea*x.The CASIO CFX-9970G, which does not support
multi-letter variables,would regard AX and A*X as identical.--
/-- Joona Palaste (palaste@cc.helsinki.') -------------
Finland
---------- http://www.helsinki.'/~palaste
---------------------
rules! --------/The obvious mathematical breakthrough would be
development of an easy way tofactor large prime numbers. -
Bill Gates
=> what's wrong with the TI-89 calculator?>> For
integration( e^(ax) ) with respect to x>> S(e^(ax),x)>> the
TI-89 answers: e^(ax)*x>> But my book and www.quickmath.com
say: e^(ax)/aThat's a correct antiderivative.> Is the TI-89
wrong? Or can somehow both be right?My guess (since I'm not
familiar with the TI-89) is that it's thinking ofax as a
single entity, constant with respect to x. If that's the
case,then its answer is correct, although it is not answering
the question youwant it to answer. (Perhaps you need to type a
space between the a andthe x.)David
=geschrieben:>> what's
wrong with the TI-89 calculator?>> For integration( e^(ax) )
with respect to x>> S(e^(ax),x)>> the TI-89 answers:
e^(ax)*x>> But my book and www.quickmath.com say: e^(ax)/a>>
That's a correct antiderivative.> Is the TI-89 wrong? Or can
somehow both be right?>> My guess (since I'm not familiar
with
the TI-89) is that it's thinking of> ax as a single entity,
constant with respect to x. If that's the case,> then its
answer is correct, although it is not answering the question
you> want it to answer. (Perhaps you need to type a space
between the a and> the x.)the x. And it gets the right result
now. Great!!!Markus
=Andreas Schmidt <schmidt.2002@gmx.de>
grava .88 la saucisse et au marteau:> the TI-89 answers:
e^(ax)*x> But my book and www.quickmath.com say: e^(ax)/a>
Is the TI-89 wrong? Or can somehow both be right?Yes, if x =
1/a-- Nicolas, what ?
=I've forgotten the proof for inverses
in a ring of integers mod n. Cansomeone remind me why inverses
=> I've forgotten
the proof for inverses in a ring of integers mod n. Can>
someone remind me why inverses only exist for m<n s.t.
> 1 then every integer multiple of m will also be a multiple of
d, and when you reduce that integer multiple of m mod n by
subtracting a multiple of n you will be subtracting a multiple
of d from a multiple of d, so you will get a multiple of d, so
you won't get 1.--
= I've forgotten the proof for
inverses in a ring of integers mod n.>> Can someone remind me
why inverses only exist for m<n s.t. gcd(m,n)=1. Because if m
and n have a common divisor d > 1 then every integer> multiple
of m will also be a multiple of d, and when you reduce> that
integer multiple of m mod n by subtracting a multiple of n>
you will be subtracting a multiple of d from a multiple of d,
so> you will get a multiple of d, so you won't get 1.I.e.
suppose jm = 1 + kn, that is jm = 1 (mod n)Then d divides jm -
kn = 1when d divides m & n-Bill Dubuque
=I'm looking for
information about an operator that I'venever seen before but
that I'm sure must exist, alongwith a list of its
properties,
somewhere in the literature.If I have a sequence of numbers,
de'ned by a function,I can use the summation operator to
denote the sum ofthe 'rst n terms of the sequence. I can also
use theproduct operator to denote the product of the 'rst
nterms. What I would like to do is denote the exponentationof
the 'rst n terms. For example, if I had a sequenceof
numbers:f(x1), f(x2), f(x3), f(x4)...and (using
O^' to
indicate exponentiation) I wanted
todenote:[[f(x1)^f(x2)]^f(x3)]^f(x4)...what operator,
analogous to the classical summation andproduct operators,
would I use?Kevin
= Kevin Grant
[CapitalEth][EDoubleDot][Micro] .b3 .b9[EDoubleDot].b9>> I'm
looking for information about an operator that I've> never
seen before but that I'm sure must exist, along> with a list
of its properties, somewhere in the literature.>> If I have a
sequence of numbers, de'ned by a function,> I can use the
summation operator to denote the sum of> the 'rst n terms of
the sequence. I can also use the> product operator to denote
the product of the 'rst n> terms. What I would like to do is
denote the exponentation> of the 'rst n terms. For example,
if
I had a sequence> of numbers:>> f(x1), f(x2), f(x3), f(x4)...>>
and (using O^' to indicate exponentiation) I
wanted to>
denote:>> [[f(x1)^f(x2)]^f(x3)]^f(x4)...>> what operator,
analogous to the classical summation and> product operators,
would I
use?http://www.4reference.net/encyclopedias/wikipedia/Hyper4.
html> Kevin--Ioannis
Galidakishttp://users.forthnet.gr/ath/jgal/-------------------
-----------------------Eventually, _everything_ is
understandable
=> I'm looking for information about an
operator that I've> never seen before but that
I'm sure must
exist, along> with a list of its properties, somewhere in the
literature. If I have a sequence of numbers, de'ned by a
function,> I can use the summation operator to denote the sum
of> the 'rst n terms of the sequence. I can also use the>
product operator to denote the product of the 'rst n> terms.
What I would like to do is denote the exponentation> of the
'rst n terms. For example, if I had a sequence> of numbers:
f(x1), f(x2), f(x3), f(x4)... and (using O^' to
indicate
exponentiation) I wanted to> denote:
[[f(x1)^f(x2)]^f(x3)]^f(x4)... what operator, analogous to the
classical summation and> product operators, would I use?> This
grouping is uninteresting, since it equals f(x1)^[product]More
interesting is:f(x1)^[f(x2)^[f(x3)^...]]But even this is so
seldom used that no sumbol has been proposed for it.
=>
sure how this cashes out where the logic of identity is>
concerned. One might construe the classical Ax[x=x <->
Ey(x=y)]> as characterizing by exclusion the relation between
self-identity and> identity-with-something: no self-identical
is an identical-with-nothing,> and no identical-with-something
is a non-self-identical.Id really like to learn from you what
it is like for something to benon-self-identical!Let me try to
give an answer myself:- Two things that are identical with each
other are not different fromeach other--and vice versa.- One
thing that is identical with itself is not different
fromitself, and vice versa- One thing that is not identical
with itself is different fromitself.So what is it like for
something to be different from itself?What does a is different
from itself.mean in the 'rst place?In what respect could
something be different from itself?Well, it could a) be
numerically different from itselforb) be qualitatively
different from itself.ad (a):I am convinced that the notion of
Onumerical self-difference' does notmake any
real sense!Is it
logically possible for one thing to be not one thing, i.e. to
betwo or many things (of the same kind), or no thing at all?!
- I dontthink so!I venture to assert that anybody employing
the notion of numericalself-difference doesnt really know what
s/hes talking about!And if Onumerical
self-difference' is
unintelligible, then
Onumericalnon-self-identity' is
unintelligible as well!One thing must be one thing (of the
same kind)!!!In other words, everything is necessarily
numerically self-identical!ad (b):If something is
qualitatively self-different, it possesses someproperties not
possessed by it and, hence, must be a
self-inconsistentobject:a /= a -> EP(Pa & ~Pa)Is it possible
for there to be any real objects that
areself-inconsistent?Well, dialetheists such as Graham Priest
believe it is--but I dont!Summary:We have seen that the only
intelligible meaning ofnon-self-identical is
qualitativelynon-self-identical/qualitatively self-different,
i.e. possessingsome properties not possessed by it!Both the
notion of numerical non-self-identity and the related one
ofqualitative non-self-identity are *inherently*
contradictory!!!In my opinion that is the decisive reason why
it is absolutelyimpossible for there to be anything
non-self-identical!!!PHP.S.:To avoid a misunderstanding, in
*pure* logic there may be consistentformalistic theories of
non-self-identity, but there cannot be anyontological 'eld of
application for those!
=>> If something is qualitatively
self-different, it possesses some> properties not possessed by
it and, hence, must be a self-inconsistent> object:>Inyou will
'nd a description of a universe that is a proper part of
itself.He calls it counterintuitive. I view it with about the
same sense that yousuggest above.I believe it to be a failure
to understand the relationships between mereology(part), set
theory (element), and de'nite description (equals).It is not
a
matter of seeing whose is right and who is wrong. It is not
amatter of this alternative foundation is better than that
alternativefoundation. It is a matter of seeing how the
identity puzzles are resolvingthemselves.Of course, everyone
is so busy comparing deductive calculi and formal systems,they
seem to have forgotten that these things arose from
philosophicalconsiderations that were being debated prior to
the introduction of suchcalculi.To the best of my knowledge,
the only person out here quoting large passagesfrom
philosophical texts is me.Perhaps Mr. Greene is right. Perhaps
not.:-)mitch
=> If something is qualitatively self-different,
it possesses some> properties not possessed by it and, hence,
must be a self-inconsistent> object:> In > you will 'nd a
description of a universe that is a proper part of itself. He
calls it counterintuitive. I view it with about the same sense
that you> suggest above. I believe it to be a failure to
understand the relationships between mereology> (part), set
theory (element), and de'nite description (equals). It is not
a matter of seeing whose is right and who is wrong. It is not
a> matter of this alternative foundation is better than that
alternative> foundation. It is a matter of seeing how the
identity puzzles are resolving> themselves. Of course,
everyone is so busy comparing deductive calculi and formal
systems,> they seem to have forgotten that these things arose
from philosophical> considerations that were being debated
prior to the introduction of such> calculi. Well, not
everybody's doing that. Given that the philisophers who
invented deductive calculi were Lawyers, science has
bequeathed the whole issue to chemists and their
mathema-lawyers. Everybody with regular computers is working
on robots. To the best of my knowledge, the only person out
here quoting large passages> from philosophical texts is me.
Perhaps Mr. Greene is right. Perhaps not. :-) mitch
=>
busy comparing deductive calculi > and formal systems,> they
seem to have forgotten that these things arose from
philosophical> considerations that were being debated prior to
the introduction of such> calculi.Yes indeed. - And the
philosophical debates continue even *after* thesuccessful
construction of diverse calculi, each of which is
provablyconsistent.No calculus can decide a philosophical
problem.[Wittgenstein, L.. /The Big Typescript/ (Wiener
Ausgabe, Bd. 11/Viennese Edition, vol. 11). Vienna: Springer.
(p. 362)]Philosophers have been infatuated with the
quanti'er.
Understandablyso, since logicians showed the power and elegance
of the predicatecalculus. And it is always tempting to want to
put shiny new tools touse. If we translate some idiom of
natural language into quanti'erform we feel we know how it
works; we feel we have tamed it.[McGinn, C. (2000). /Logical
Properties/. Oxford: Clarendon Press. (p.69)]PH
=>Yes
indeed. - And the philosophical debates continue even *after*
the>successful construction of diverse calculi, each of which
is provably>consistent.>>No calculus can decide a
philosophical problem.>>[Wittgenstein, L.. /The Big
Typescript/ (Wiener Ausgabe, Bd. 11/>Viennese Edition, vol.
11). Vienna: Springer. (p. 362)]No philosophy can decide a
calculus problem.
=>
although Benjamin Franklin is> necessarily self-identical, the
inventor of bifocals is not> necessarily self-identical. ? -
The inventor of bifocals existed, and whoever was the inventor
ofbifocals was, of course, necessarily self-identical as long
as heexisted!PH
=> In another post I suggested that John
Correy's ideas aboutnon-re§exive> identity might have a
rational formulation with respect tosomething> called
counterpart theory.>> (I think categoreal would be the right
term here--in my humble> opinion, the apparent
self-contradictions associated with John's> intuitions arise
from vagueness and ambiguity associated withstandard>
presuppositions rather than irrational error on his part. For
the> record, Langholm's investigation of determinability
and>
indeterminability in 'rst-order contexts includes
incoherentformulas.> Exclusion negation is not informationally
well-behaved.)>> The link,>>
http://www.sussex.ac.uk//Users/muralir/kct_'nal.pdf>
<>((x=x) & ~(x=x))>> is discussed as well as what is actually
done in counterpart theoryto> exclude such an incoherent
result.>> :-)>> mitch>
http://www.sussex.ac.uk//Users/muralir/kct_'nal.pdf>
<>((x=x) & ~(x=x))>> is discussed as well as what is actually
done in counterpart theoryto> exclude such an incoherent
result.>> :-)>> mitch>> The tie-in with contingent identity is
as asserted by (1).>> (1) AxAy(x=y -> (N(x=x & y=y) <->
N(x=y)))>> That is, identical(x,y) are necessarily identical
if, ond only if,> N(x=x) and N(y=y). Thus, granted that the
Morning Star and the> Evening Star are each necessarily
self-identical, if the Morning Star> and the Evening Star are
identical, they are necessarily identical.> Hence the Morning
Star and the Evening Star are necessarily> identical. The same
is not true, however, for Benjamin Franklin> and the inventor
of bifocals. For although Benjamin Franklin is> necessarily
self-identical, the inventor of bifocals is not> necessarily
self-identical. This is why Benjamin Franklin> and the
inventor of bifocals, although identical are not> necessarily
identical.>> --John>> I am not sure that my remarks are
welcome here, I have had enough ofthe> remarks from (G.
Frege)(II)> : stupid asshole, ing bitch, and all of that
childish rhetoric, Icannot> reply to him at all.>> I assume
that you guys are more mature than He.>> As to John's claim
that: (John Correy = John Correy) is necessarilytrue, I>
disagree.> It is not suf'cient to say, x=y <-> AF(Fx <->
Fy).>
Rather, it is suf'cient to say, x=y <->. E!x & E!y &AF( Fx
<->
Fy).>> After all, (ix: x=John Correy) is (John Correy).>>
E!(John Correy) is just as doubtful as E!(The poster who
claims that> ~Ax(x=x)).>> We cannot assume that E!(John
Correy) any more than we can assume> E!(Vulcan)!>> (x=y) ->
[](x=y) and E!x -> [](E!x), are consequences of Leibnitz's
Law.>> There are no contingent existences nor contingent
identities.> Exisence and Identity (and Membership) are
analytic properties.>> Can we assume that: []Exists(George W.
Bush)?>> I don't think so, do you?>> Surely, the existence
of,
George W. Bush, is contingent.>> There cannot be an assumption
that all names of purported physicalentities> refer!>> Santa
dosen't work, Vulcan doesn't work, Pegasus
dosen't work,
etc.>> For although Benjamin Franklin is necessarily
self-identical, theinventor> of bifocals is not> necessarily
self-identical.>> Benjamin Franklin = Benjamin Franklin, is
not necessarily true.> (the inventor of bifocals)=(the
inventor of bifocals), is also not> necessarily true, imo.>>
Necessary identity and existence, applies to
logical/mathematicalobjects,> not to emprical objects,
imho.> Witt>> (1) states necessary and suf'cient conditions
for the necessity of> (material) identity:>> (1) AxAy(x=y ->
(N(x=x & y=y) <-> N(x=y)))Necessary self-identity is necessary
existence.(1a) AxAy(x=y -> ((N(E!x) & N(E!y)) <-> N(x=y))If x
and y are physical objectsI don't see necessity having sense
wrt empirical things.If p is necessarily true then, it is
logically true, ie. true in all timesfor which mind
exists(within a speci'ed method of decision).Facts are not
necessary, even though they are true. They happen to be truein
our Opossible' world.[]E!(John Corry), means,
John Correy
exists is logically true.But, surely there are times at which
John Correy, or any other proper nameof a physical object,does
not refer to anything.Is E!(John Correy) true at (2,000,000 BC)
or at (2,000,000 AD) ? Surelynot!Can we deduce that E!(John
Correy)?For Ological objects' it is true, eg.
E!1 is true at
all times (for whichminds exist).But, I don't think that any
physical object or physical relation, haslogical necessity, do
you?>> If identicals x and y are necessarily self-identical,
then--and> only then--is their identity a necessary one.
Beyond this,> (1) states nothing more: from (1) it neither
follows that> John Correy is necessarily self-identical nor
that John> Correy is contingently self-identical--or indeed
that John> Correy is self-identical at all. (1) does not say
which of> the foregoing is the case.>> We can sit around and
argue about whether you or I are necessarily> self-identical.
However, although logicians do argue about such> matters--Who
else would bother?--it is not as logicians that they> argue
but as metaphysicians, or as pataphysicians, or as what have>
you?>> So, when I claim that (e.g.) Benjamin Franklin is
necessarily> self-identical while the inventor of bifocals is
not, my main> warrant for this claim is that if Benjamin
Franklin is necessarily> self-identical but the inventor of
bifocals is not, then Benjamin> Franklin and the inventor of
bifocals are not necessarily identical> (although they are
identical). In other words, I take the necessary>
self-identity of the former and the contingent self-identity
of the> latter to constitute, together with (1), an
*explanation* for the> contingent identity of Benjamin
Franklin and the inventor of bifocals.>> To this you might
object that these would be also be contingently> identical if
both Benjamin Franklin and the inventor of bifocals were>
contingently self-identical. To which I would respond that
identities> involving what linguistically oriented analytical
philosophers refer> to as rigid designators, are identities
whose terms are necessarily> self-identical; whereas
identities involving what such philosophers> refer to as
non-rigid designators, are identities whose terms are>
contingently self-identical. Therefore, granted that I take
rigid and> non-rigid designation as the linguistic marks of
necessary and> contingent self-identity--putting the cart back
behind the horse,> rather than approaching the matter bass
ackwards as it is> fashionable to do these days--and granted
that I take> Benjamin Franklin and John Correy to be
Origid'
designators> and Othe inventor of bifocals' to
be Onon-rigid',
I conclude> that the contingent identity of Benjamin Franklin
and the inventor> of bifocals has as its basis the contingent
self-identity of the> inventor of bifocals, while Benjamin
Franklin is necessarily> self-identical.Your distinction
between named objects and described objects
needsjusti'cation.Do you axiomatically grant necessary
existence to named objects and possibleexistence to described
objects?Why is Ben Franlklin more Onecessary'
than the
inventor of bi-focals?Note: Vulcan is the proper name given to
a described planet which does notexist.Is there a Onecessary
attribution' in the granting of proper names?>> As to
whether
physical or mathematical objects are contingently>
self-identical or necessarily so, some sort of metaphysical
argument> (rather than a logical one) warranting one or the
other of these> conclusions would have to be made. I suspect
that mathematical> properties are both essential in, and
necessary to, mathematical> objects--but this is an intuition
and nothing more.Our intuituitive Ometaphysics'
entails that
physical objects are indeedcontingent,contingent on presence,
within a speci'ed time. There are no timelessphysical objects
at all, are there?Given the existence of mind, all empirical
things are time dependent, and,abstractthings are not.Witt>>
John>> PS It won't surprise me if Paul Holbach or G. Frege
bring in talk> about Oscope', which I think is
only
peripherally relevant to> discussions of necessary and
contingent identity.
=>> (1) states necessary and suf'cient
conditions for the necessity of> (material) identity:>> (1)
AxAy(x=y -> (N(x=x & y=y) <-> N(x=y))) Necessary self-identity
is necessary existence. (1a) AxAy(x=y -> ((N(E!x) & N(E!y)) <->
N(x=y)) If x and y are physical objects I don't see
necessity
having sense wrt empirical things.> If p is necessarily true
then, it is logically true, ie. true in all times> for which
mind exists> (within a speci'ed method of decision).> Facts
are not necessary, even though they are true. They happen to
be true> in our Opossible' world. []E!(John
Corry), means,
John Correy exists is logically true.> But, surely there are
times at which John Correy, or any other proper name> of a
physical object,> does not refer to anything.> Is E!(John
Correy) true at (2,000,000 BC) or at (2,000,000 AD) ? Surely>
not!> Can we deduce that E!(John Correy)?There's a
difference
between N[Ex(John Correy = x)], which is false,and Ex(N[John
Correy = x])--which is true. Not cashing assertionsout in
primitive notation leads to a failure to discriminate
suchreadings, in the 'rst of which N has operated on the
sentence,Ex(John Correy = x), to make a sentence; and in the
second ofwhich N has operated on an open formula, John Correy
= x,to yield the open formula N(John Correy - x), which then
gets'existentially' quanti'ed.
For Ological objects' it is
true, eg. E!1 is true at all times (for which> minds exist).>
But, I don't think that any physical object or physical
relation, has> logical necessity, do you?> If identicals x and
y are necessarily self-identical, then--and> only then--is
their identity a necessary one. Beyond this,> (1) states
nothing more: from (1) it neither follows that> John Correy is
necessarily self-identical nor that John> Correy is
contingently self-identical--or indeed that John> Correy is
self-identical at all. (1) does not say which of> the
foregoing is the case.>> We can sit around and argue about
whether you or I are necessarily> self-identical. However,
although logicians do argue about such> matters--Who else
would bother?--it is not as logicians that they> argue but as
metaphysicians, or as pataphysicians, or as what have> you?>>
So, when I claim that (e.g.) Benjamin Franklin is necessarily>
self-identical while the inventor of bifocals is not, my main>
warrant for this claim is that if Benjamin Franklin is
necessarily> self-identical but the inventor of bifocals is
not, then Benjamin> Franklin and the inventor of bifocals are
not necessarily identical> (although they are identical). In
other words, I take the necessary> self-identity of the former
and the contingent self-identity of the> latter to constitute,
together with (1), an *explanation* for the> contingent
identity of Benjamin Franklin and the inventor of bifocals.>>
To this you might object that these would be also be
contingently> identical if both Benjamin Franklin and the
inventor of bifocals were> contingently self-identical. To
which I would respond that identities> involving what
linguistically oriented analytical philosophers refer> to as
rigid designators, are identities whose terms are necessarily>
self-identical; whereas identities involving what such
philosophers> refer to as non-rigid designators, are
identities whose terms are> contingently self-identical.
Therefore, granted that I take rigid and> non-rigid
designation as the linguistic marks of necessary and>
contingent self-identity--putting the cart back behind the
horse,> rather than approaching the matter bass ackwards as it
is> fashionable to do these days--and granted that I take>
Benjamin Franklin and John Correy to be Origid'
designators>
and Othe inventor of bifocals' to be
Onon-rigid', I conclude>
that the contingent identity of Benjamin Franklin and the
inventor> of bifocals has as its basis the contingent
self-identity of the> inventor of bifocals, while Benjamin
Franklin is necessarily> self-identical. Your distinction
between named objects and described objects needs>
justi'cation.> Do you axiomatically grant necessary existence
to named objects and possible> existence to described objects?
Why is Ben Franlklin more Onecessary' than the
inventor of
bi-focals?--One reason: replacing the dotted lines in ... need
not have been ...by the inventor of bi-focals yields the true
sentence, the inventorof bi-focals need not have been the
inventor of bi-focals, whilereplacement with Benjamin Franklin
yields the false sentence,Benjamin Franklin need not have been
Benjamin Franklin. --Another reason: (1) is false but (2) is
true.1) Benjamin Franklin didn't have to be Benjamin
Franklin.
2) The inventor of bifocals didn't have to be the inventor
of
bifocals. Note: Vulcan is the proper name given to a described
planet which does not> exist. Is there a Onecessary
attribution' in the granting of proper names?> As to whether
physical or mathematical objects are contingently>
self-identical or necessarily so, some sort of metaphysical
argument> (rather than a logical one) warranting one or the
other of these> conclusions would have to be made. I suspect
that mathematical> properties are both essential in, and
necessary to, mathematical> objects--but this is an intuition
and nothing more. Our intuituitive Ometaphysics'
entails that
physical objects are indeed> contingent,> contingent on
presence, within a speci'ed time. There are no timeless>
physical objects at all, are there?> Given the existence of
mind, all empirical things are time dependent, and,> abstract>
things are not. Witt--John
=>
V1qrb.188420$7B1.55593@news04.bloor.is.net.cable.rogers.com>..
.> Why is Ben Franlklin more Onecessary' than
the inventor of
bi-focals?> --One reason: replacing the dotted lines in > ...
need not have been ...> by the inventor of bi-focals yields
the true sentence, the inventor> of bi-focals need not have
been the inventor of bi-focals, while> replacement with
Benjamin Franklin yields the false sentence,> Benjamin
Franklin need not have been Benjamin Franklin. --Another
reason: (1) is false but (2) is true. 1) Benjamin Franklin
didn't have to be Benjamin Franklin. 2) The inventor of
bifocals didn't have to be the inventor of bifocals. Youre
mistaken!It is true that Benjamin Franklin didnt have to be
the inventor ofbifocals, and it is equally true that the
inventor of bifocals didnthave to be Benjamin Franklin.It is
also true that the person actually referred to by the
inventorof bifocals might have not invented the bifocals; and
if that werethe case, we certainly wouldnt nowadays refer to
*that* particularperson by the inventor of bifocals. But all
this does in no wayimply that whoever is the one we refer to
by the inventor ofbifocals is not necessarily self-identical!
Even if new historicalresearch showed surprisingly that the
particular person we actuallyrefer to by the inventor of
bifocals didnt actually invent thebifocals, that person we
would then erroneously refer to by theinventor of bifocals
would nevertheless remain necessarilyself-identical!The
inventor of bifocals would be necessarily self-identical, even
ifthat particular person had not invented the bifocals. If that
were thecase, then the inventor of bifocals would be a
pseudo-descriptionfunctioning just like any arbitrary proper
noun!We can successfully identify particular objects even by
means ofpseudo-descriptions.ixFx = ixFxis necessarily true,
whileFixFx is contingently true.Your basic mistake is to
suppose that the contingency of OFixFx'implies
the contingency
of OixFx = ixFx'--but this is simply not
thecase!The way we
linguistically refer to things doesnt affect their
beingnecessary self-identical at all!For example, we could
decide to henceforth refer to Bill Clinton bythe inventor of
bifocals, knowing that not Clinton but Franklinactually
invented the bifocals (the latter might then be re-baptizedthe
real inventor of bifocals ;-)). But that wouldnt turn[](the
inventor of bifocals = the inventor of bifocals)into a false
statement!Your notion of Ocontingent identity'
is based on a
misconstruction!PH
=>
V1qrb.188420$7B1.55593@news04.bloor.is.net.cable.rogers.com>..
.> Why is Ben Franlklin more Onecessary' than
the inventor
of bi-focals?> --One reason: replacing the dotted lines in>
... need not have been ...> by the inventor of bi-focals
yields the true sentence, the inventor> of bi-focals need not
have been the inventor of bi-focals, while> replacement with
Benjamin Franklin yields the false sentence,> Benjamin
Franklin need not have been Benjamin Franklin.>> --Another
reason: (1) is false but (2) is true.>> 1) Benjamin Franklin
didn't have to be Benjamin Franklin.>> 2) The inventor of
bifocals didn't have to be the inventor of bifocals.> Youre
mistaken!>> It is true that Benjamin Franklin didnt have to be
the inventor of> bifocals, and it is equally true that the
inventor of bifocals didnt> have to be Benjamin Franklin.> It
is also true that the person actually referred to by the
inventor> of bifocals might have not invented the bifocals;
and if that were> the case, we certainly wouldnt nowadays
refer to *that* particular> person by the inventor of
bifocals. But all this does in no way> imply that whoever is
the one we refer to by the inventor of> bifocals is not
necessarily self-identical! Even if new historical> research
showed surprisingly that the particular person we actually>
refer to by the inventor of bifocals didnt actually invent
the> bifocals, that person we would then erroneously refer to
by the> inventor of bifocals would nevertheless remain
necessarily> self-identical!>> The inventor of bifocals would
be necessarily self-identical, even if> that particular person
had not invented the bifocals. If that were the> case, then the
inventor of bifocals would be a pseudo-description> functioning
just like any arbitrary proper noun!> We can successfully
identify particular objects even by means of>
pseudo-descriptions.>> ixFx = ixFx>> is necessarily true,
while>> FixFx is contingently true.Not so, for Russell's
description theory.1. G(ix:Fx) <-> Ey(Ax(x=y <-> Fx) & Gy),
see PM *14.12. E!(ix:Fx) <-> Ey(Ax(x=y <-> Fx), see *14.23.
E!(ix:Fx) <-> F(ix:Fx)4. E!(ix:Fx) <-> (ix:Fx)=(ix:Fx)5.
E!(ix:Fx) <-> EG(G(ix:Fx))6. F(ix:Fx) <-> (ix:Fx)=(ix:Fx)7.
[](F(ix:Fx)) <-> []((ix:Fx)=(ix:Fx))By: 6, |-p -> |-[]p, and,
[](p <-> q) -> ([]p <-> []q).8. []E!(ix:Fx) <->
[]((ix:Fx)=(ix:Fx)).Witt> Your basic mistake is to suppose
that the contingency of OFixFx'> implies the
contingency of
OixFx = ixFx'--but this is simply not the>
case!>> The way we
linguistically refer to things doesnt affect their being>
necessary self-identical at all!>> For example, we could
decide to henceforth refer to Bill Clinton by> the inventor of
bifocals, knowing that not Clinton but Franklin> actually
invented the bifocals (the latter might then be re-baptized>
the real inventor of bifocals ;-)). But that wouldnt turn>>
[](the inventor of bifocals = the inventor of bifocals)>> into
a false statement!>> Your notion of Ocontingent
identity' is
based on a misconstruction!>> PH
=>
IIVrb.16233$Rah1.1560@twister01.bloor.is.net.cable.rogers.com>
...> ixFx = ixFx>> is necessarily true, while>> FixFx is
contingently true. > Not so, for Russell's description
theory.
1. G(ix:Fx) <-> Ey(Ax(x=y <-> Fx) & Gy), see PM *14.1 2.
E!(ix:Fx) <-> Ey(Ax(x=y <-> Fx), see *14.2 3. E!(ix:Fx) <->
F(ix:Fx)> 4. E!(ix:Fx) <-> (ix:Fx)=(ix:Fx)> 5. E!(ix:Fx) <->
EG(G(ix:Fx))> 6. F(ix:Fx) <-> (ix:Fx)=(ix:Fx) 7. [](F(ix:Fx))
<-> []((ix:Fx)=(ix:Fx))> By: 6, |-p -> |-[]p, and, [](p <-> q)
-> ([]p <-> []q). 8. []E!(ix:Fx) <-> []((ix:Fx)=(ix:Fx)).Youre
not wrong insofar as there really seems to be a problem for
theNFL-logician, for whom(1) ixFx = ixFx -> E!ixFxis
impeccable.If the normal rules of modal logic (particularly
the rule ofnecessitation and the rule of box distribution),
are applied to (1),we indeed get the following result:[](ixFx
= ixFx) -> []E!ixFxBut once again, were being confronted with
the notorious ambiguity ofmodal formulas.Read de dicto we
have:If OixFx = ixFx' is necessarily true, then
OE!ixFx' is
necessarilytrue.The point is that in negative free logic ixFx
= ixFx is not anecessary truth, since it is possibly false (in
case ~E!ixFx). Thereis a possible world in which ixFx = ixFx is
false because ixFx doesnot exist in that world; and if there is
a possible world in whichixFx doesnt exist, E!ixFx cannot be a
necessary truth either, sincenecessary truth is de'ned as
truth in all worlds!Even though (ixFx = ixFx) -> E!ixFx is a
necessary NFL-truth, bothixFx = ixFx and E!ixFx are no
necessary NFL-truths!But, luckily, that circumstance does not
render the followingimplication untrue:[](ixFx = ixFx ->
E!ixFx) -> ([](ixFx = ixFx) -> []E!ixFx)The antecedent is true
but neither the antecedent nor the consequentof the consequent
are true in NFL!So we have1 -> (0 -> 0) 1 -> 11 !By the way,
the rule of necessitation can also be unproblematicallyapplied
to the following NFL-theorem:Ax(x = x -> E!x)[]Ax(x = x ->
E!x)[](Ax(x = x) -> AxE!x)[]Ax(x = x) -> []AxE!xSince in NFL
both Ax(x = x) and AxE!x are axioms, everythings 'nehere!What
if we interpreted (1) *de re*?In NFLE!x <-> Ey(y = x)holds (by
de'nition), and so we can write(1*) ixFx = ixFx -> Ey(y =
ixFx)and [](ixFx = ixFx) -> Ey[](y = ixFx)If ixFx is
necessarily self-identical, then there is something suchthat
it is necessarily identical with ixFx.(It doesnt mean ...
there necessarily is something such that...!!!)This de re
interpretation is impeccable, for now both the antecedentand
the consequent are true!PH
=>
V1qrb.188420$7B1.55593@news04.bloor.is.net.cable.rogers.com>..
.> Necessary self-identity is necessary existence.I dont think
so!While Ax[]([](x = x) -> E!x)is true,Ax([](x = x) ->[]E!x)is
not.Modality *de re* is modality thought of as applying to a
thing(Ores'), more precisely, as a way a thing
possesses a
property. [...]Modality *de dicto* is the modality applied to
a statement (Odictum').It refers to the manner
or mode of a
statements being true.[Konyndyk, K. (1986). /Introductory
Modal Logic/. Notre Dame, IN:University of Notre Dame Press.
(p. 78f)]Now we are ready to try to give a properly de re
reading ofstatements like OSocrates is essentially
rational'.
An individual issaid to have a given property essentially if
and only if it is notpossible that the individual exist and
lack the property.Alternatively, an individual must have the
property in every world inwhich it exists. This account [...]
has some implications of its ownthat should be observed. The
'rst implication is that anything thatexists has existence
essentially.[Konyndyk, K. (1986). /Introductory Modal Logic/.
Notre Dame, IN:University of Notre Dame Press. (p. 89)]I can
sum up what I just argued by saying that in a modal
sentencethe copula is not modally neutral. And isnt this
exactly the way weread such sentences? Dont they precisely say
that a property is hadin the mode of necessity or in the mode
of contingency? We start byremarking that Socrates is a man
and then, when our thoughts turnmodal, we want to know whether
this property inheres in Socrates inthe necessary way or the
contingent way: *how* is he a man? What weare interested in is
*mode of instantiation*. Modals are modes. To saythat modal
words modify the copula is the linguistic counterpart ofthe
ontological doctrine that modality is a matter of the strength
ofthe instantiation relation: does the object in question
instantiatethe predicated property only accidentally or is
this a matter o§ogical or metaphysical necessity ($). Thus,
according to the copulamodi'er theory, we do not work with an
ontology of modal properties;rather, we take the stock of
non-modal properties and think of them aspossessed in
different modes. If you like, the instantiation relationis the
only thing that gives rise to modal properties--the
propertiesof being instantiated necessarily or
contingently.($: What of Oa is possibly F',
where this can be
true even though theobject doesnt actually have the property?
In this case, obviously, wecannot be saying in what mode the
object *has* the property, since itdoesnt have it. Instead, we
are saying that the object possiblyinstantiates the property,
where again the modal expression modi'esthe copula, as in
OSocrates possibly-is a man'.)[McGinn, C.
(2000). /Logical
Properties/. Oxford: Clarendon Press. (p.77)]In that sense the
statementsEverything is necessarily
self-identical.andEverything is necessarily existent.mean
thatEverything instantiates the property of self-identity in
thenecessary way.andEverything (i.e. every existing thing!)
instantiates the property ofexistence in the necessary way.The
latter statement is, of course, not equivalent toEverything
(i.e. every existing thing!) instantiates the property
ofnecessary existence in the necessary way. !PH
=>
V1qrb.188420$7B1.55593@news04.bloor.is.net.cable.rogers.com>..
.> (Necessary self-identity is necessary existence.)Put that
way, one can state the following without there being
anyinconsistency whatsoever:Ax(E!x -> []E!x)Correction:It now
seems to me thatAx[](E!x -> E!x)is the adequate formulation
ofEverything is essentially such that if it exists, it
exists.Nothing can exist without existing.PH
=>
V1qrb.188420$7B1.55593@news04.bloor.is.net.cable.rogers.com>..
.> Necessary self-identity is necessary existence.Depends on
what a theory of modal logic is intended to validate!(Frankly,
Im not a fan of the Barcan formulas ...)In other words, the
matter of scope is decisive.I think the only acceptable EG of
O[](a = a)' is as follows:[](a = a) -> Ex[](x =
a)If a is
necessarily identical with itself, then there is somethingsuch
that a is necessarily identical with it.Here, the box is
interpreted *de re*, for the necessity lies in therelation of
identity and not in the possession of existence!> []E!(John
Corry), means, John Correy exists is logically true.This is
the de dicto reading, but one could as well read it de re,i.e.
asJohn Correy necessarily exists .In classical logic
existential statements of the type OEx(x = a)'
aretheorems
which are considered necessary truths *by mere
stipulation*,for--by de'nition--non-referring singular terms
are not allowed init.But since there are in actual fact many
non-referring singular termsin ordinary language, free logic
is preferable to classical logic. Inthe former, no existential
statement of the type OE!a' [<-> Ex(x = a)]is a
theorem.> But,
I don't think that any physical object or physical relation,
has> logical necessity, do you?Ex[](x = John Correy)There is
something such that it is necessarily identical with
JohnCorrey.It does not follow thatThere necessarily exists
something such that it is identical withJohn Correy.Once
again, one must systematically differentiate between de
dictonecessities (necessary truths) and de re necessities
(essentialproperties)!We are going to take *de re* modality to
express the essentialpossession of a property by an individual.
We use the O[]' torepresent *de re* as well as
*de dicto*
modality. In our symbolism, wewill continue to regard an
occurrence of a modality sign asrepresenting modality *de
dicto* if and only if that formula and onlythat formula within
the scope of modality contains no free occurrencesof any
individual variables. The easiest way to apply this test is
asfollows:Delete all parts of the whole formula except for
what appears withinthe scope of the modal sign under
consideration. If what remainscontains no free occurrences of
any individual variable, the modalityis *de dicto*.
Correspondingly, a modality is considered *de re* ifand only
if the formula within the scope of the modality does containat
least one free occurrence of an individual variable. Hence, in
thefollowing example, the 'rst (outermost) occurrence of
O[]'
ismodality *de dicto* and the second occurrence of
O[]' is
modality *dere*: [](x)[](Cx -> Hx)In giving rules for
quanti'ed modal logic, we frequently will beforced to take
stands on complex and hotly disputed metaphysicalissues
involved in understanding essence and existence, and *de
re*and *de dicto* modality.[...]7. An individual has a
property essentially just in case thatindividual has that
property in every world in which that individualexists.8. The
*de re* understanding of Onecessarily' or
O[]' is
as'essentially'.[Konyndyk, K. (1986).
/Introductory Modal
Logic/. Notre Dame, IN:University of Notre Dame Press. (pp. 83
+ 91)]Put that way, one can state the following without there
being anyinconsistency whatsoever:Ax(E!x -> []E!x)For every x,
if x exists, then x is essentially existent.That is, as long as
x exists it is impossible for it to benon-existent.It may
appear illogical at 'rst sight, but theres nothing wrong
insaying that existence is not an accidental but an essential
propertyof every contingent thing--of every existing
contingent thing!That existence is an essential property means
that it is possible fornothing to lose the property of
existence without ceasing to exist!There is a crucial
difference between Every existent necessarily_is
existent.andEvery existent is
necessarily_existent.,forEverything necessarily_has the
property of existence.certainly doesnt mean the same
asEverything (necessarily) has the property of
necessary_existence.Its a real blemish of modal logic that its
formulas are veryambiguous.For example, in the case of
self-identity it might be useful if wedwriteAx(x []= x)instead
ofAx[](x = x) (both de re formulations).But in my opinion
Konyndyks interpretation (see above) is
agreeablealready.PH
=According to a researcher at Sandia
National Labs, the 3-D Ising Model iscomputationally
intractible. Supposedly, the critical temperature,magnetic
susceptibility, etc. cannot be evaluated analytically like in
the2-D Ising
Model.http://www.sandia.gov/media/NewsRel/NR2000/ising.htmIs
this considered to be a de'nitive proof that the long-studied
3-DIsing Model can't be solved analytically, or are there
differentinterpretations of these results?
=> According to a
researcher at Sandia National Labs, the 3-D Ising Model is>
computationally intractible. Supposedly, the critical
temperature,> magnetic susceptibility, etc. cannot be
evaluated analytically like in the> 2-D Ising Model.
http://www.sandia.gov/media/NewsRel/NR2000/ising.htm Is this
considered to be a de'nitive proof that the long-studied 3-D>
Ising Model can't be solved analytically, or are there
different> interpretations of these results?Recently, I heard
a talk of an experimental physicist who thinks thatsimulation
of such models will be the 'rst useful application of
quantumcomputing in 5 to 10 years.--
=>According to a
researcher at Sandia National Labs, the 3-D Ising Model
is>computationally intractible. Supposedly, the critical
temperature,>magnetic susceptibility, etc. cannot be evaluated
analytically like in the>2-D Ising
Model.>http://www.sandia.gov/media/NewsRel/NR2000/ising.htm>Is
this considered to be a de'nitive proof that the long-studied
3-D>Ising Model can't be solved analytically, or are there
different>interpretations of these results?I took a brief look
at Istrail's 'rst paper, Statistical
Mechanics,
Three-Dimensionality and NP-completeness I. Universality of
Intractabilityfor the Partition Function of the Ising Model
Across Non-Planar Latticeswhen it came out about 3 years ago,
and it seems to me that there's a bit less here than what
the
press release claimed.Onsager's solution of the 2D Ising
model
consists basically of a closed-form expression for the free
energy (in the in'nite-volumelimit, as a function of the
interaction strength J). Now one way of obtaining Onsager's
result, using Pfaf'ans, is related to a counting problem. As
far as I can tell, the connection to NP-completeness is that
on a planar lattice the Pfaf'an provides a polynomial-time
method for solving a certain class of counting problem.
Therefore (unless P=NP) this class of problems can't be
NP-hard. It seems that Istrail shows that on anon-planar
lattice the analogous class of problems is NP-hard. But that
is a far cry from saying that there is no
closed-formexpression for the free energy. At most it shows
that one particularmethod of obtaining such an expression
won't work. Robert Israel israel@math.ubc.caDepartment of
Mathematics http://www.math.ubc.ca/~israel University of
British Columbia Vancouver, BC, Canada V6T 1Z2
=>According
to a researcher at Sandia National Labs, the 3-D Ising Model
is>computationally intractible. Supposedly, the critical
temperature,>magnetic susceptibility, etc. cannot be evaluated
analytically like inthe>2-D Ising
Model.>>http://www.sandia.gov/media/NewsRel/NR2000/ising.htm>>
Is this considered to be a de'nitive proof that the
long-studied 3-D>Ising Model can't be solved analytically,
or
are there different>interpretations of these results?>> I took
a brief look at Istrail's 'rst paper,
Statistical Mechanics,>
Three-Dimensionality and NP-completeness I. Universality of
Intractability> for the Partition Function of the Ising Model
Across Non-Planar Lattices> when it came out about 3 years
ago, and it seems to me that there's a> bit less here than
what the press release claimed.>> Onsager's solution of the
2D
Ising model consists basically of> a closed-form expression for
the free energy (in the in'nite-volume> limit, as a function
of
the interaction strength J). Now one way of> obtaining
Onsager's result, using Pfaf'ans, is related to
a counting>
problem. As far as I can tell, the connection to
NP-completeness is that> on a planar lattice the Pfaf'an
provides a polynomial-time method for> solving a certain class
of counting problem. Therefore (unless P=NP) this> class of
problems can't be NP-hard. It seems that Istrail shows that
on
a> non-planar lattice the analogous class of problems is
NP-hard.> But that is a far cry from saying that there is no
closed-form> expression for the free energy. At most it shows
that one particular> method of obtaining such an expression
won't work.>>
=> Some languages have several sets of words
for numbers, with different> sets used for counting different
things. Analogous too close to the> 're pragmatic redundancy
is seen a typical C program (even more> in C++), where the
very same thing is coded 5 different ways, each> named in
accordance with its application (as good naming convention>
dictates), thus totally obscuring the fact that it was the
same thing.Well, I agree that redundancy is not just a
phenomenon in mathematics.However, I see it as a result of
arbitrary decisions instead of more reasonable natural
ones.Well, mathematics is not a Naturwissenschaft. It rather
depends on application on nature whether or not mathematics is
actually natural.If causal functions of time do not need a
second limit of integration, then the second limit might be
redundant in this particular case.What might correspond to the
'x limit of integration?Derivative also tacitly relates to
zero.Having removed the perhaps redundant second limit, I
wonder that integration and derivative are more of the same
kind.So far, derivative of a function of time is considered to
loose information.
=>>I repeatedly found the word causal in
titles of books on mathematical>>subjects. > I didn't.For
instance:Academic Press 1977 includes many referencesA. Aulin:
Foundation of mathematical system dynamics: The fundamental
theory of causal recursion and its application to social
science and economics, Pergamon Press 1989
= >>I repeatedly
found the word causal in titles of books on
mathematical>subjects.>> I didn't. > For instance: Academic
Press 1977 includes many references A. Aulin: Foundation of
mathematical system dynamics: The fundamental> theory of
causal recursion and its application to social science and>
economics, Pergamon Press 1989Aha! repeatedly equals
twice!Incidentally I found neither of these books on
MathSciNethttp://e-math.ams.org/mathscinet-- Robin Chapman,
www.maths.ex.ac.uk/~rjc/rjc.htmlNeedless to say, I had the
last laugh. Alan Partridge, _Bouncing Back_ (14
times)
=>Aha! repeatedly equals twice!Isn't it standard
mathematical notation to imply countably in'nitesequences as
1,2,...? That means once you have two you can extrapolateto
in'nity.
=>Aha! repeatedly equals twice! Isn't it standard
mathematical notation to imply countably in'nite> sequences
as
1,2,...?Is it?One hears tales of remote tribes whose counting
is limitedto one and many ...> That means once you have two
you can extrapolate> to in'nity.Ah yes! As there are two twin
primes, there must be in'nitelymany :-)-- Robin Chapman,
www.maths.ex.ac.uk/~rjc/rjc.htmlNeedless to say, I had the
last laugh. Alan Partridge, _Bouncing Back_ (14 times)
=I
apologize for being somewhat busy and lazy. If you are really
interested in the topic, you will already 'nd further titles
with the word causal within a comprehensive list of references
provided by the 'rst reference I pointed you to. As I
alluded,
this hardbound book is a little bit too mathematical to me. I
mainly looked into the introduction and was rather
disappointed albeit I got the impression that the author has
been knowing a lot of previous and related work.Eckard
Blumschein >Aha! repeatedly equals twice!>>Isn't it
standard mathematical notation to imply countably
in'nite>>sequences as 1,2,...? > Is it? One hears tales of
remote tribes whose counting is limited> to one and many ...
>>That means once you have two you can extrapolate>>to
in'nity. > Ah yes! As there are two twin primes, there must
be
in'nitely> many :-)>
=I do not know much about prepositional
resolution and have aquestion, which sounds trivial, yet I am
still not sure what theanswer is.We have that:1)The empty
clause {} is unsatis'able.2)The empty set of clauses is
satis'able.A set of clauses that contain just the empty
clause
- is itsatis'able or unsatis'able?
= I do not know much about
prepositional resolution and have a> question, which sounds
trivial, yet I am still not sure what the> answer is. We have
that:> 1)The empty clause {} is unsatis'able.> 2)The empty
set
of clauses is satis'able. A set of clauses that contain just
the empty clause - is it> satis'able or
unsatis'able?Assuming
the obvious de'nition for satis'ability of sets
of clauses -
i.e. that a set of clauses is satis'able if and only if all
its members are - the answer is no, since the set containing
just the empty clause does not have all its members
satis'able.-- Aatu Koskensilta
(aatu.koskensilta@xortec.')Wovon man nicht sprechen kann,
daruber muss man schweigen - Ludwig Wittgenstein, Tractatus
Logico-Philosophicus
=integral from 0 to in'nity of sin(x) /
x is pi/2.What sould I do to calculate out this result? it
out?
=> integral from 0 to in'nity of sin(x) / x is pi/2.>
What sould I do to calculate out this result?There is a
complex variable approach to this problem. Considerthe
function f(z) = (exp(i z) - 1)/z for z different from 0
andf(0) = i; consider also, for each R > 0, the following
path:it goes from -R to R in a straight linea and then from R
to -Ragain through the half-circle with center in 0 that
passesthrough iR. Then, since f is analytic, the integral of f
alongthis path is 0. You can use this to prove that the limit
ofthe integral of f between -oo and +oo is equal to i.pi.
Sincesin(x)/x = Im(f(x)), it follows that the integral of
sin(x)/xbetween -oo and +oo is equal to pi.Jose Carlos Santos
out?
= integral from 0 to in'nity of sin(x) / x is pi/2.>
What sould I do to calculate out this result?Use Fourier
transform, very easy. Quick outline, all sorts of constantsare
not considered here:If f(t) is de'ned as: f(t) = 0, |t| > 1
f(t) = 1, |t| <= 1then its Fourier transform F(w) is of the
form sin(w)/w (see lookuptables...): +infty 1 F(w) = INT f(t)
exp(-jwt) dt = INT exp(-jwt) dt -infty -1Or easy to compute
yourself also...The transform back is de'ned by: +infty f(t)
=
1/(2pi) INT F(w) exp(jwt) dw -inftyIn your case: +infty f(0) =
1/(2pi) INT F(w) dw -infty Because F(w) is even: +infty
pi*f(0) = pi = INT F(w) dw 0 Something like that... You've
to
work it out to get the constants right. Jeroen
=>> integral
from 0 to in'nity of sin(x) / x is pi/2.>> What sould I do to
calculate out this result? > Use Fourier transform, very easy.
Quick outline, all sorts of constants> are not considered here:
If f(t) is de'ned as: f(t) = 0, |t| > 1> f(t) = 1, |t| <= 1
then its Fourier transform F(w) is of the form sin(w)/w (see
lookup> tables...): +infty 1> F(w) = INT f(t) exp(-jwt) dt =
INT exp(-jwt) dt> -infty -1j?> The transform back is de'ned
by: +infty> f(t) = 1/(2pi) INT F(w) exp(jwt) dw> -inftyDe'ned
by, or is? Of course, in our case F is not an L_1 functionand
so one has to be careful about these improper
limits.Incidentally, in this case, is your formula true for t
= 1?I seem to remember from my undergraduate daysthat the
proof we saw of the Fourier inversion theoremwas dependent on
the identity pi/2 = integral_0^in'nity sin(x)/ x dx.Could you
outline a proof of the Fourier inversion theorem,valid
pointwise (under suitable hypotheses) not using this
identity?-- Robin Chapman,
www.maths.ex.ac.uk/~rjc/rjc.htmlNeedless to say, I had the
last laugh. Alan Partridge, _Bouncing Back_ (14
times)
=>integral from 0 to in'nity of sin(x) / x is
pi/2.>What sould I do to calculate out this result?>> Use
Fourier transform, very easy. Quick outline, all sorts of
constants>> are not considered here:>> If f(t) is de'ned as:
f(t) = 0, |t| > 1>> f(t) = 1, |t| <= 1>> then its Fourier
transform F(w) is of the form sin(w)/w (see lookup>>
tables...):>> +infty 1>> F(w) = INT f(t) exp(-jwt) dt = INT
exp(-jwt) dt>> -infty -1>>j?> The transform back is de'ned
by:>> +infty>> f(t) = 1/(2pi) INT F(w) exp(jwt) dw>>
-infty>>De'ned by, or is? Of course, in our case F is not an
L_1 function>and so one has to be careful about these improper
limits.>Incidentally, in this case, is your formula true for t
= 1?>>I seem to remember from my undergraduate days>that the
proof we saw of the Fourier inversion theorem>was dependent on
the identity pi/2 = integral_0^in'nity sin(x)/ x dx.>>Could
you
outline a proof of the Fourier inversion theorem,>valid
pointwise (under suitable hypotheses) not using this
identity?Not going to get the constants straight - using the
Extended Littlewood Convention, to the effect that pi = 2pi =
-1 = etc = 1.(Of course this makes 'nding that integral
easy...) Using * onlyfor convolution; using ^ both for the
Fourier Transform and the(formal) inverse Fourier
Transform:Roughly speaking you only need to calculate _any_
suitableFourier Transform pair (ie 'nd f^ and f^^ for any
suitablef). The approaches I know all involve knowing at least
onenot-quite-elementary integral, but it doesn't have to
besin(x)/x.My favorite uses G(x) = exp(-xx/2), because then
there's onlyone Fourier Transform to calculate: You note
that
G'(x) + x G(x) = 0,you verify that under suitable hypotheses
(xf(x))^ and(f')^ are what they should be, and it follows
that
G^ satis'es the same differential equation. So G^ is
amultiple
of G, and calculating the integral of G showsthat G^ = G.Now
Fubini shows that int f^ g = int f g^ for f, g in L^1.It
follows that (*) (f^ g)^ = f * g^ (f, g in L^1).Let G_d(x) = d
G(dx) and G__d(x) = G(x/d). If you apply(*) with g = G__d and
let d -> in'nity it follows thatf = f^^ (ae) if f and f^ are
both in L^1. You alsoget the Plancherel theorem from (*)
(prove 'rst withf in L^1 intersect L^2, using (*) with g =
G__d andf replaced by the f*h, where h(x) = f(-x), or
maybeit's conjugate(f(-x)), whatever so that h^ =
conjugate(f^).)So now the FT is an isometry on L^2 which
agrees with theoriginal FT on L^2 intersect L^1.Ok. Now let
s(x) = sin(x)/x, chi = the characteristicfunction of [-1,1].
You calculate that chi^ = s, and itfollows that s^ = chi. Of
course we're not done, becausethat s^ is the L^2 FT, not the
limit of the integralfrom -A to A.But an elementary argument
shows that the principal-valueintegral of s is equal to the
limit of int s G__d asd -> in'nity (the same argument that
shows the tailof int s -> 0 shows that the tail of int s G__d
-> 0,_uniformly_ in d...) So we need only evaluate thelimit of
int s G__d.But (*) (with f = chi, an L^1 function) shows
thatint(s G__d) = int(chi G_d), and this tends to chi(0)as d
-> in'nity because chi is continuous at 0.(Yes, if we just
want int s then the thing you postedis much simpler - the
trickiness there is the sameas in the elementary argument two
paragraphs above.But you asked, and it does seem worth noting
thatthe integral of s is not essential in proving thebasic
facts about the Fourier Transform. Me, I wasbrought up wrong,
with an emphasis on convergencein norm instead of pointwise
convergence - I'm notgoing to tell you how old I was the day
I
got thatstrange look from a colleague after revealing
Ididn't
even realize that the integral of s hadanything to do with the
FT...)>-- >Robin Chapman,
www.maths.ex.ac.uk/~rjc/rjc.html>Needless to say, I had the
last laugh.> Alan Partridge, _Bouncing Back_ (14 times)David
C. Ullrich
=>Could you outline a proof of the Fourier
inversion theorem,>>valid pointwise (under suitable
hypotheses) not using this identity? Not going to get the
constants straight - using the Extended> Littlewood
Convention, to the effect that pi = 2pi = -1 = etc = 1.> (Of
course this makes 'nding that integral easy...) Using * only>
for convolution; using ^ both for the Fourier Transform and
the> (formal) inverse Fourier Transform: Roughly speaking you
only need to calculate _any_ suitable> Fourier Transform pair
(ie 'nd f^ and f^^ for any suitable> f). The approaches I
know
all involve knowing at least one> not-quite-elementary
integral, but it doesn't have to be> sin(x)/x. My favorite
uses G(x) = exp(-xx/2), because then there's only> one
Fourier
Transform to calculate: You note that G'(x) + x G(x) = 0,
you
verify that under suitable hypotheses (xf(x))^ and> (f')^
are
what they should be, and it follows that G^> satis'es the
same
differential equation. So G^ is a> multiple of G, and
calculating the integral of G shows> that G^ = G. Now Fubini
shows that int f^ g = int f g^ for f, g in L^1.> It follows
that (*) (f^ g)^ = f * g^ (f, g in L^1). Let G_d(x) = d G(dx)
and G__d(x) = G(x/d). If you apply> (*) with g = G__d and let
d -> in'nity it follows that> f = f^^ (ae) if f and f^ are
both in L^1. You also> get the Plancherel theorem from (*)
(prove 'rst with> f in L^1 intersect L^2, using (*) with g =
G__d and> f replaced by the f*h, where h(x) = f(-x), or maybe>
it's conjugate(f(-x)), whatever so that h^ =
conjugate(f^).)>
So now the FT is an isometry on L^2 which agrees with the>
original FT on L^2 intersect L^1. Ok. Now let s(x) = sin(x)/x,
chi = the characteristic> function of [-1,1]. You calculate
that chi^ = s, and it> follows that s^ = chi. Of course
we're
not done, because> that s^ is the L^2 FT, not the limit of the
integral> from -A to A. But an elementary argument shows that
the principal-value> integral of s is equal to the limit of
int s G__d as> d -> in'nity (the same argument that shows the
tail> of int s -> 0 shows that the tail of int s G__d -> 0,>
_uniformly_ in d...) So we need only evaluate the> limit of
int s G__d. But (*) (with f = chi, an L^1 function) shows
that> int(s G__d) = int(chi G_d), and this tends to chi(0)> as
d -> in'nity because chi is continuous at 0. (Yes, if we just
want int s then the thing you posted> is much simpler - the
trickiness there is the same> as in the elementary argument
two paragraphs above.> But you asked, and it does seem worth
noting that> the integral of s is not essential in proving
the> basic facts about the Fourier Transform. Me, I was>
brought up wrong, with an emphasis on convergence> in norm
instead of pointwise convergence - I'm not> going to tell
you
how old I was the day I got that> strange look from a
colleague after revealing I> didn't even realize that the
integral of s had> anything to do with the FT...)Well done
David! I hope Mr Boschma now realizesall the little details
he's sweeping under the carpet ... :-)-- Robin Chapman,
www.maths.ex.ac.uk/~rjc/rjc.htmlNeedless to say, I had the
last laugh. Alan Partridge, _Bouncing Back_ (14
times)
=>>Could you outline a proof of the Fourier
inversion theorem,>>valid pointwise (under suitable
hypotheses) not using this identity?>> Not going to get the
constants straight - using the Extended> Littlewood
Convention, to the effect that pi = 2pi = -1 = etc = 1.> (Of
course this makes 'nding that integral easy...) Using * only>
for convolution; using ^ both for the Fourier Transform and
the> (formal) inverse Fourier Transform:>> Roughly speaking
you only need to calculate _any_ suitable> Fourier Transform
pair (ie 'nd f^ and f^^ for any suitable> f). The approaches
I
know all involve knowing at least one> not-quite-elementary
integral, but it doesn't have to be> sin(x)/x.>> My favorite
uses G(x) = exp(-xx/2), because then there's only> one
Fourier
Transform to calculate: You note that>> G'(x) + x G(x) =
0,>>
you verify that under suitable hypotheses (xf(x))^ and>
(f')^
are what they should be, and it follows that G^> satis'es the
same differential equation. So G^ is a> multiple of G, and
calculating the integral of G shows> that G^ = G.>> Now Fubini
shows that int f^ g = int f g^ for f, g in L^1.> It follows
that>> (*) (f^ g)^ = f * g^ (f, g in L^1).>> Let G_d(x) = d
G(dx) and G__d(x) = G(x/d). If you apply> (*) with g = G__d
and let d -> in'nity it follows that> f = f^^ (ae) if f and
f^
are both in L^1. You also> get the Plancherel theorem from (*)
(prove 'rst with> f in L^1 intersect L^2, using (*) with g =
G__d and> f replaced by the f*h, where h(x) = f(-x), or maybe>
it's conjugate(f(-x)), whatever so that h^ =
conjugate(f^).)>
So now the FT is an isometry on L^2 which agrees with the>
original FT on L^2 intersect L^1.>> Ok. Now let s(x) =
sin(x)/x, chi = the characteristic> function of [-1,1]. You
calculate that chi^ = s, and it> follows that s^ = chi. Of
course we're not done, because> that s^ is the L^2 FT, not
the
limit of the integral> from -A to A.>> But an elementary
argument shows that the principal-value> integral of s is
equal to the limit of int s G__d as> d -> in'nity (the same
argument that shows the tail> of int s -> 0 shows that the
tail of int s G__d -> 0,> _uniformly_ in d...) So we need only
evaluate the> limit of int s G__d.>> But (*) (with f = chi, an
L^1 function) shows that> int(s G__d) = int(chi G_d), and this
tends to chi(0)> as d -> in'nity because chi is continuous at
0.>> (Yes, if we just want int s then the thing you posted> is
much simpler - the trickiness there is the same> as in the
elementary argument two paragraphs above.> But you asked, and
it does seem worth noting that> the integral of s is not
essential in proving the> basic facts about the Fourier
Transform. Me, I was> brought up wrong, with an emphasis on
convergence> in norm instead of pointwise convergence - I'm
not> going to tell you how old I was the day I got that>
strange look from a colleague after revealing I> didn't even
realize that the integral of s had> anything to do with the
FT...)>> Well done David! I hope Mr Boschma now realizes> all
the little details he's sweeping under the carpet ...
:-)>Still, it's possible he answered the question OP asked,
which might beassuming all the details you mathematicians
worry about, how do I calculatethe answer I need for my
engineering calculations. In other words, (Ihope) I took a
course once where I saw this proved, so I know it's true,
Ijust need to know how to calculate to get the answers I need.
Rather thanthe (I fear) I don't care about the math, I just
need the answer.Jon Miller out?
= >> integral from 0 to
in'nity of sin(x) / x is pi/2.>> What sould I do to calculate
out this result?> Use Fourier transform, very easy. Quick
outline, all sorts of constants> are not considered here:>> If
f(t) is de'ned as: f(t) = 0, |t| > 1> f(t) = 1, |t| <= 1>>
then
its Fourier transform F(w) is of the form sin(w)/w (see lookup>
tables...):>> +infty 1> F(w) = INT f(t) exp(-jwt) dt = INT
exp(-jwt) dt> -infty -1 j? The transform back is de'ned by:>>
+infty> f(t) = 1/(2pi) INT F(w) exp(jwt) dw> -infty De'ned
by,
or is? Of course, in our case F is not an L_1 function> and so
one has to be careful about these improper limits.>
Incidentally, in this case, is your formula true for t = 1? I
seem to remember from my undergraduate days> that the proof we
saw of the Fourier inversion theorem> was dependent on the
identity pi/2 = integral_0^in'nity sin(x)/ x dx. Could you
outline a proof of the Fourier inversion theorem,> valid
pointwise (under suitable hypotheses) not using this
identity?> I'm sorry, like Phil already detected
I'm just an
engineer (with my owndialect) and not being a native speaker
also contributes to sloppy useof Ois de'ned
by' or whatever is
mathematically more consistent. SinceI also forgot a lot of
what I learned at university, I do not have theproof available
(if it exists...) you request. I have to look it up inthe
books, but you can do that also. Jeroen> --> Robin Chapman,
www.maths.ex.ac.uk/~rjc/rjc.html> Needless to say, I had the
last laugh.> Alan Partridge, _Bouncing Back_ (14 times)
= >>
Could you outline a proof of the Fourier inversion theorem,>>
valid pointwise (under suitable hypotheses) not using this
identity?> I'm sorry, like Phil already detected
I'm just an
engineer (with my own> dialect) and not being a native speaker
also contributes to sloppy use> of Ois de'ned
by' or whatever
is mathematically more consistent. Since> I also forgot a lot
of what I learned at university, I do not have the> proof
available (if it exists...) you request. I have to look it up
in> the books, but you can do that also.So, your answer is
no.-- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.htmlNeedless
to say, I had the last laugh. Alan Partridge, _Bouncing Back_
(14 times) out?
= >> Could you outline a proof of the
Fourier inversion theorem,>> valid pointwise (under suitable
hypotheses) not using this identity?>> I'm sorry, like Phil
already detected I'm just an engineer (with my own> dialect)
and not being a native speaker also contributes to sloppy use>
of Ois de'ned by' or whatever is
mathematically more
consistent. Since> I also forgot a lot of what I learned at
university, I do not have the> proof available (if it
exists...) you request. I have to look it up in> the books,
but you can do that also. So, your answer is no.> It is! But
just saying no sounds a bit rude to me...> --> Robin Chapman,
www.maths.ex.ac.uk/~rjc/rjc.html> Needless to say, I had the
last laugh.> Alan Partridge, _Bouncing Back_ (14 times) it
out?
=> integral from 0 to in'nity of sin(x) / x is
pi/2.>> What sould I do to calculate out this result?> Use
Fourier transform, very easy. Quick outline, all sorts of
constants> are not considered here:>> If f(t) is de'ned as:
f(t) = 0, |t| > 1> f(t) = 1, |t| <= 1>> then its Fourier
transform F(w) is of the form sin(w)/w (see lookup>
tables...):>> +infty 1> F(w) = INT f(t) exp(-jwt) dt = INT
exp(-jwt) dt> -infty -1>> j?Engineering dialect for i.--
P.A.C. SmithThe vast majority of Iraqis want to live in a
peaceful, free world.And we will 'nd these people and we will
bring them to justice. it out?
=> +infty 1> F(w) = INT f(t)
exp(-jwt) dt = INT exp(-jwt) dt> -infty -1>>j? Engineering
dialect for i.I always thought it was exclusive to
*Electrical*engineering, to avoid confusing i with
electricalcurrent (Amps).Carlos-- it out?
=>> +infty 1> F(w)
= INT f(t) exp(-jwt) dt = INT exp(-jwt) dt> -infty -1>>j?>>
Engineering dialect for i.>> I always thought it was exclusive
to *Electrical*> engineering, to avoid confusing i with
electrical> current (Amps).Isn't that I?-- P.A.C. SmithThe
vast majority of Iraqis want to live in a peaceful, free
world.And we will 'nd these people and we will bring them to
justice. it out?
=> integral from 0 to in'nity of sin(x) / x
is pi/2.> What sould I do to calculate out this result?First
work out the integral from -oo to +oo by considering the
integral ofexp(iz)/z on the contour formed by:(i) The real
axis from -R to -e and e to R;(ii) The semicircle |z| = e in
the upper half-plane;(iii) The semicircle |z| = R in the upper
half-plane;using the residue calculus for (ii) and the total
contour, Jordan'slemma for (iii), and taking the limit as e
->
0 and R -> oo.-- P.A.C. SmithThe vast majority of Iraqis want
to live in a peaceful, free world.And we will 'nd these
people
and we will bring them to justice.
=>> integral from 0 to
in'nity of sin(x) / x is pi/2.> What sould I do to calculate
out this result?>> First work out the integral from -oo to +oo
by considering the integral of> exp(iz)/z on the contour formed
by:>> (i) The real axis from -R to -e and e to R;> (ii) The
semicircle |z| = e in the upper half-plane;> (iii) The
semicircle |z| = R in the upper half-plane;>> using the
residue calculus for (ii) and the total contour, Jordan's>
lemma for (iii), and taking the limit as e -> 0 and R ->
oo.That is a nice textbook solution. I was just wandering, is
there a simpleway to evaluate the integral without using
residues?-Michael.
= That is a nice textbook solution. I was
just wandering, is there a simple> way to evaluate the integral
without using residues?Yes.Prove thatpi/2 = integral_0{pi/2}
sin ((2n+1)y)/sin y dySet I_n = integral_0^{(2n+1)pi/2} sin
x/x dx= integral_0^{pi/2} sin((2n+1)/y)/y dy.Using these
integral representations, prove that|pi/2 - I_n| -> 0 as n ->
in'nity. (BasicallyRiemann-Lebesgue applied to y |-> 1/y -
1/sin(y)).-- Robin Chapman,
www.maths.ex.ac.uk/~rjc/rjc.htmlNeedless to say, I had the
last laugh. Alan Partridge, _Bouncing Back_ (14 times)
=>
<snip> By the time I saw your response to my other post, I
have already>replied to this post of yours. I would not have
otherwsie.>>Put it in your think head. You cannot demand; you
can only request. HUH?!> New technology: read head, write
head, erase head, think head.As it's Monday morning mine
feels
mostly like the third in the list.
=>> <snip> By the time I
saw your response to my other post, I have already>>replied to
this post of yours. I would not have otherwsie.>>Put it in
your think head. You cannot demand; you can only request.>>
HUH?!>New technology: read head, write head, erase head, think
head.Ahh!! That explains the idiocy. Empty head, then
think.>>As it's Monday morning mine feels mostly like the
third in the list.<GRIN> In our biz, we called it refreshed.
That was what youdid to a disk when it had lots of lost blocks
or bad spots oryou were creating a new system disk. Another
option was destroy./BAH
=>> 3 Africans I met in Computer
science department in the last 4>>years were way above average
in thier programming skills in>>the midst of Chinese and Indian
grad students who are the>>overwhelming majority in that
department.>>You will always 'nd bright smart people in
just about any >> naturally>>occuring group of humans. Race is
nothing. Culture is everything.>>Bob Kolker>>That's my
point.>>What point? Culture Shmulture....that is
simplistic politically >> correct>>heurist bull of the
'rst kind. >>No, it is not.>If it were that simple
>>It is THAT simple where I grew up. >>Children in the
poor neighborhood with their parents making ends meet>and
the children having to do the house work like an adult and
start>working while they themslevs are children (rather than
play or study,>do not get a chance to test their brain since
there is no books (not>referring to school text books and
notes) lying around the house.>>That's a lot of bull.
House work (or farm work) is so boring>one has nothing else to
do but think. It also gives one an incentive>to go to school
and study real hard so that one can get a job that>doesn't
involve either. >> Afriend of mine from Wisconsan said justt
hat.>> He had to get up and helped his father milk the cows in
the farm and>>it was boring for him. He became a programmer.
It was possible for him>>because he is the this US of A.>> A
country which was built by people. Nobody gave them
anything;>> they did the work themselves. Since you want us to
believe that>> you are from an underprivileged country that
contains no books,>> no schools, no business opportunities, I
suggest that you begin>> to work to build an infrastructure.
However, since you're complaining>> about having to do
housework from dawn to dusk, I conclude that>> there exist
people who are able to hire other people to clean.>> That
implies that they make the money they pay those
housecleaners>> in some other industry than housecleaning.
Thus, that country>> has opportunities available for
thousands.>>Can you read well? Some days I read very well,
including in between the lines.>>When did I ever say I had to
work from dawn to dusk? First of all, I>wasn't talking about
myself.Then your comments were not based on experience but on
yourhypothesis of what poor people cannot do.> .. Secondly,
here is how my day started.>Get up, brush my teeth and wash my
face. Have breafast which was>already on the the table. Get
ready for school. Grab my lunch box and>go wait for school bus
which arrives around 8:20Am.>>School starts at 9:15 and
releaseed at 3:15. That was one of your problems. That's
only
4-5 hours of class timeper day.>>School bus brought me home.
Change my clothes. Have some snack and>wait for my Math tutor
(not everyday; in that case, I did my Math>homework, the only
homework I was keen to do). Have dinner around 6.>Then , it
varies how my day ends. That was 6th grade. In 7th garde,>my
Math tutoring moved to 7Am till 8:30 in the morning and so I
had to>catch the school bus when it came around the senodn
time by walking to>a friend's house on the next block. In
8th
grade, it was after school.>So on.>>Now, say that I was
spoiled or privileged. Yup. You didn't have to work and earn
money.> ..But notice that there>wasn't extracurricular
activites sponsored by school like during my>older siblings
time. You poor baby. You were so underprivileged.> ..They went
to Private schools (founded during>British time) which did not
exist anymore in my time. That's because>there was no budget
for it except for short term ones, which I joined>some
times.Heaven forbid that you or your parents pay for
extracirricular activities rather than forcing the rest of the
population pay for your bidding.>>I did learn swimming one
summer at a private place. But before 7th>grade, i.e when we
were not old enough to be rebellious, in summer, my>mother
would teach us.>>With college education during my time, unlike
my oldest sister's time,>I would not qualify to be
considered
privileged. I wasn't complaining>about that.>About your
telling me I suggest that you begin> to work to build an
infrastructure., I tell you this: stay within>the context of
diuscussion and ...>> ..do not act so dumb not to know that
there are countries where>people are not free to do (build)
their infrastructure. But mostly,>just stay within the
context, will you?I've been trying to stay within
context.>Housework is a very good lesson in >eliminating
some choices of employment. >>Not for those who is left with
no time to study when it is not just>>helping around the house
with chores.>> Excuse me? Housework has ample opportunity for
study. Since it>> takes no thinking (or not much) to vacuum or
wash a §oor, one>> can use their brains to learn at the same
time. >I would set a book>> up, read a paragraph, and think
about it while doing other work.>> If I still hadn't got it,
I
would read it again and continue doing>> the physical work.
When I 'gured it out, I would read the next>> part of the
text. In the computer biz, we called this §avor>> of doing
many things at once, timesharing.> Well..I never was so keen
to study like a bookworm. That just means that you were not
motivated to learn. Youclaimed that poor people who did
housework didn't have anyaccess to books; thus, those who
did
have high IQs wouldnever be allowed to learn beyond housework
jobs.<snip more bio>>the point was that I was NOT talking
about me. I was talking about>the kids from the poor
family.Which you also don't have a clue about. I also was
talking aboutkids and adults who don't have lots of money.>
.
Do you know how poor family lives in>3rd world countries?
Obviosuly not.yes, I have some idea. I also know how poor
families live inthe US.<snip>>Public libraries? You seem to
think that all countries have good>>public libraries.>> This
thread was talking about US schools and such.>No it was not.
It was about Asians. IIRC, the thread drifted to the question
about why Asians didwell in US schools. Now, you tend to
commit continental drift.Which Asians (Asia is a very big
place) were referencing?China has a system in place that
detects gifted kids and provideslearning opportunities to
those kids (and the majority of Chineseare poor according to
your standards). Did you want to talk aboutanother place?<snip
ducking>>In fact, Josh halpern's reply was enough. I
shouldn't
even have>bothered to reply to you. You were so way out of the
context of the>topic in discussion.When you name drop, you
should be choosy./BAH
=>> 3 Africans I met in Computer
science department in the last > 4>>years were way above
average in thier programming skills in>>the midst of Chinese
and Indian grad students who are the>>overwhelming majority in
that department.>>You will always 'nd bright smart people
in just about any > naturally>>occuring group of humans. Race
is nothing. Culture is > everything.>>Bob Kolker>>That's
my point.>>What point? Culture Shmulture....that is
simplistic politically > correct>>heurist bull of the
'rst
kind. >>No, it is not.>If it were that simple >>It is
THAT simple where I grew up. >>Children in the poor
neighborhood with their parents making ends > meet>and the
children having to do the house work like an adult and
start>working while they themslevs are children (rather than
play or > study,>do not get a chance to test their brain
since there is no books (not>referring to school text books
and notes) lying around the house.>>That's a lot of
bull.
House work (or farm work) is so boring>one has nothing else to
do but think. It also gives one an incentive>to go to school
and study real hard so that one can get a job that>doesn't
involve either. >> Afriend of mine from Wisconsan said justt
hat.>> He had to get up and helped his father milk the cows in
the farm and>>it was boring for him. He became a programmer.
It was possible for him>>because he is the this US of A.>> A
country which was built by people. Nobody gave them
anything;>> they did the work themselves. Since you want us to
believe that>> you are from an underprivileged country that
contains no books,>> no schools, no business opportunities, I
suggest that you begin>> to work to build an infrastructure.
However, since you're complaining>> about having to do
housework from dawn to dusk, I conclude that>> there exist
people who are able to hire other people to clean.>> That
implies that they make the money they pay those
housecleaners>> in some other industry than housecleaning.
Thus, that country>> has opportunities available for
thousands.>>Can you read well? Some days I read very well,
including in between the lines.>When did I ever say I had to
work from dawn to dusk? First of all, I>wasn't talking about
myself. Then your comments were not based on experience but on
your> hypothesis of what poor people cannot do. It was basee on
seeing children selling things (eg. cigarettes) onthe
roadside.> .. Secondly, here is how my day started.>Get up,
brush my teeth and wash my face. Have breafast which
was>already on the the table. Get ready for school. Grab my
lunch box and>go wait for school bus which arrives around
8:20Am.>>School starts at 9:15 and releaseed at 3:15. That was
one of your problems. That's only 4-5 hours of class time>
per
day. Class time may be 4-5 hours (school was released at
3:45pm, I forgot)but it was not bull  teaching like in
your publich schools.Besides, my mother taught us so much that
we thought we were inprison, never getting enough time to play.
(One of my brothers got toskip Kindergarten just from her
teaching; that option was not availabein my time). We would
literally hide from her sight but she wouldalways call out our
names, and one better be obedient. Then wereached the age where
she got private tutors teaching us. Among thesubjects was
Arabic, staring at age 5. Don't ask me to elaborate.>School
bus brought me home. Change my clothes. Have some snack
and>wait for my Math tutor (not everyday; in that case, I did
my Math>homework, the only homework I was keen to do). Have
dinner around 6.>Then , it varies how my day ends. That was
6th grade. In 7th garde,>my Math tutoring moved to 7Am till
8:30 in the morning and so I had to>catch the school bus when
it came around the senodn time by walking to>a friend's
house
on the next block. In 8th grade, it was after school.>So
on.>>Now, say that I was spoiled or privileged. Yup. You
didn't have to work and earn money. There was nothing wrong
with that since when the time came for me todo it (after
getting to US), I could do it. ..But notice that
there>wasn't
extracurricular activites sponsored by school like during
my>older siblings time. You poor baby. You were so
underprivileged. Is that all you can say? ..They went to
Private schools (founded during>British time) which did not
exist anymore in my time. That's because>there was no budget
for it except for short term ones, which I joined>some times.
Heaven forbid that you or your parents pay for extracirricular
> activities rather than forcing the rest of the population pay
> for your bidding. The sentence was meant to refer public
school in our time (undermilitary rle) not having budget. I
addedd a sentence in the middle andhence looking like I was
talking about extracurricular activites. Butthen again,
whatever few activites available, one better can affordthe
supplies.On the other hand, my grandfather donated so much to
the school thathis children were in (sometimes paying for the
whole X'Mas party), itwas practically as if he was paying
for
those activites. But then hewas a rich and powerful man in his
time and it was expaected that hedid that.>>I did learn
swimming one summer at a private place. But before 7th>grade,
i.e when we were not old enough to be rebellious, in summer,
my>mother would teach us.>>With college education during my
time, unlike my oldest sister's time,>I would not qualify to
be considered privileged. I wasn't complaining>about
that.>About your telling me I suggest that you begin> to
work to build an infrastructure., I tell you this: stay
within>the context of diuscussion and ...>> ..do not act so
dumb not to know that there are countries where>people are not
free to do (build) their infrastructure. But mostly,>just stay
within the context, will you? I've been trying to stay
within
context.>>Housework is a very good lesson in >eliminating
some choices of employment. >>Not for those who is left with
no time to study when it is not just>>helping around the house
with chores.>> Excuse me? Housework has ample opportunity for
study. Since it>> takes no thinking (or not much) to vacuum or
wash a §oor, one>> can use their brains to learn at the same
time. >>I would set a book>> up, read a paragraph, and think
about it while doing other work.>> If I still hadn't got it,
I
would read it again and continue doing>> the physical work.
When I 'gured it out, I would read the next>> part of the
text. In the computer biz, we called this §avor>> of doing
many things at once, timesharing.> Well..I never was so keen
to study like a bookworm. That just means that you were not
motivated to learn. Why would I need to keep reading school
stuff like a bookworm when Ihad other books I could be reading
(whether it was realated to schoolwork or not) when I already
know the school material I needed to know?Is it possible for
you to understand that for some people, especiallythe
materials up till the end of high school are a piece of
cake.Just because you have to repeatedly study the same
material over andover again, it deosn't mean that everyone
would need to do the samewayto achive learning. You are
hopeless to keep insisitng that poor people could have
accessto books if they want. Get out of your little world and
see the worlda bit before you die, will you? > You> claimed
that poor people who did housework didn't have any> access
to
books; thus, those who did have high IQs would> never be
allowed to learn beyond housework jobs.Yes that's what
happened. In this guy's case, it was farm works. Hecame from
very remote rural area.He worked for my brother. He was in his
30s when we got to know him.He found my family and presented
hismelf to be reliable andtrustworhty. The guy was very
bright, in fact higly intelligent buthe could barely read or
write.Because he was reliable and trustworthy AND bright, he
got the job inmy brother's jewelry business. Despite no
education, he 'tted rightin tot he extent that in time, all
of
us treated him like a familymember.. <snip more bio>the point
was that I was NOT talking about me. I was talking about>the
kids from the poor family. Which you also don't have a clue
about. That's your opinion. I said children from poor
families... > I also was talking about> kids and adults who
don't have lots of money.You are hopeless with no clue.
Typical American who knows nothingabout the world beyond your
borders. . Do you know how poor family lives in>3rd world
countries? Obviosuly not. yes, I have some idea. I also know
how poor families live in> the US. I was not talking about US.
I was talking about MY country (I saidwhere I grew up) where
there is no government programs for the poor.Even mandatory
education requirement eatsbalished by law is notenforced.
Somehow, the kids in the cities manage to be literate whilethe
people in remote rural area joined short term programs (if
theprograms come to their region; usually, goverment send
those programsonly to areas where the Burman is a majority) to
learn how to read andwrite as adults. <snipPublic
libraries? You seem to think that all countries have
good>>public libraries.>> This thread was talking about US
schools and such.>No it was not. It was about Asians. IIRC,
the thread drifted to the question about why Asians did> well
in US schools. Now, you tend to commit continental drift.>
Which Asians (Asia is a very big place) were referencing?Learn
to read in context. China has a system in place that detects
gifted kids and provides> learning opportunities to those kids
(and the majority of Chinese> are poor according to your
standards). Did you want to talk about> another place? I was
not talking about China. Again, learn to stay within
context.No amount of briging in more crap won't undo your
status as a typicalaverage American. <snip ducking>In fact,
Josh halpern's reply was enough. I shouldn't
even
have>bothered to reply to you. You were so way out of the
context of the>topic in discussion. When you name drop, you
should be choosy.You are a Hopeless, Clueless, Typical Average
American. If you want tochsnge that, may I suggest that you
start with reading and listeningto news from sources other
than your media. /BAH>
=>> <snip> By the time I saw your
response to my other post, I have already>>replied to this
post of yours. I would not have otherwsie.>>Put it in your
think head. You cannot demand; you can only request.>>
HUH?!>>Did you have to use the word Of***ing'?
>>You could
have asked What countries were they from?And you still
haven't
answered the damned^W question./BAH
=>> <snip> By the time
I saw your response to my other post, I have already>>replied
to this post of yours. I would not have otherwsie.>>Put it
in your think head. You cannot demand; you can only request.>>
HUH?!>>Did you have to use the word Of***ing'?
>>You could have
asked What countries were they from? And you still haven't
answered the damned^W question.I am not obligated to answer,
am I? /BAH>
=><snip>By the time I saw your response to my
other post, I have already>replied to this post of yours. I
would not have otherwsie.>>Put it in your think head. You
cannot demand; you can only request.>>HUH?!>>Did you have to
use the word Of***ing'? >>You could have asked
What countries
were they from?>> And you still haven't answered the
damned^W
question.>>I am not obligated to answer, am I?Gawd, I hate
cute. Nope, you aren't obliged to answer,especially when you
used the datum as the basisof your argument. When asked for a
clari'cation of thatdatum, you deliberately ignore the
question, add all kindsof red lines to divert the lack of an
answer. Ergo, youdon't feel very strongly about the subject
but do wantto get a free ride based on perceived
discrimination./BAH
=>>And you still haven't answered the
damned^W question.> I am not obligated to answer, am I?That
depends on whether you're the asker or answeree.
=>When you run a race, you don't automatically award
'rst>>place to every runner.There were six
hundred places. What is the difference between the
599th>person in that class and the 601st in terms of
ability? The wonderprof>simply abdicated any responsiblity
for educating the students. Quite>common.>Exactly.
That is why a rational society only cares about win,
place,>>and show rather than compassionately about a huge pool
of>>incompetents.>>Uncle Al>>I wouldn't insist too strongly
on your idea, Al. The treatment of the>incompetents has to be
cared about by society, otherwise they,>or many of them, will
come to your house and tell you to beat it>and kick your ass
out without thought nor regrets.>>I sympathize with you that
things should be as simple as you say.>But it just isn't in
the cards. If it were that straight forward then>the solution
would have been found long ago and would have >been practiced
all over the place. Utopia would be at hand.>hanson>Actually
they are very good at kicking ass, and Al knows allabout them,
which explains much of his pain.josh halpern
=Sure, the I don't fail you you fail you bull. He
didn't>>educate anyone either. He didn't go
out and get
more>>resources for more students.>>When you run a
race, you don't automatically award 'rst>place
to every
runner.>There were six hundred places. What is the
difference between the 599th>>person in that class and the
601st in terms of ability? The wonderprof>>simply abdicated
any responsiblity for educating the students. Quite>>common.>>
about win, place,>and show rather than compassionately about a
huge pool of>incompetents. >Right, by your own terms you lost
the minute you didn'tgo to MIT or Cal Tech. Now go away and
stop whining.josh halpern
=>> populated by Asians and Jews
with astounding credentials>> 'gure out how Asians and Jews
can universally do so well.>> that was exactly how the Chinese
students functioned.>What a mutual minority admiration
society.......ahahahaha.....I've never seen before such a
self
exposee by some of/in the minorities about expressing their
self-in§icted inferiority complex to such an extent,
especially in the view that they could have hardly excelled to
the extent they did and do were they in their own society of
ethnic origin, or so they claim. Therefore, to alleviate the
curse from this albatross that is hanging around their minds,
I suggest:Sweet Amanda, ask macho Al to **donate** to your
uterus a sample from his paid, applause garnishing 6 cc sperm
donations.You two could spawn the superspecies' that the
Nazis
and the Jewish comic book authors of Superman had only orgasms
in their dreams about.... You guys could bring this epic
yearning to fruition and reality........for a better
world.Christen...eh,..ah... no,no... just label your offspring
as the long nosed slit eyed one, which in all probability will
be his/her most pronounced features.> Indian students
functioned similarly too.>Ooohh my gahhhhd, there's the
nigger
in the wood pile.Here are them Indians, Al, the ones you are so
envious ofbecause they have, according to you, only some 10
§ush toilet on the entire sub-continent.This unfortunately
means that you'll be able to produce anoffspring with only
2/3
rd of the max of the full potential thatthe human genome would
allow.You jokers are nuts! But then, this is the Usenet, a
24/7 cyberparty, where prodigies that failed have to come to
die.........Therefore, let'em sing.....all of
them....it's a
beautiful
choir!ahahahah....ahahahahah...ahahahaha.....ahahahanson
=>
You jokers are nuts! But then, this is the Usenet, a 24/7
cyber> party, where prodigies that failed have to come to
die.........> Therefore, let'em sing.....all of
them....it's a
beautiful choir! Sig 'le!!!Usenet - where failed prodigies
come
to die.Mr. Shambat, how do you say that in Russian?
=> You
jokers are nuts! But then, this is the Usenet, a 24/7 cyber>
party, where prodigies that failed have to come to
die.........> Therefore, let'em sing.....all of
them....it's a
beautiful choir!>> Sig 'le!!!bob, are you a wanna-be or
closet
Nazi? ........anyway, Bob, it would be Sieg Heil.>> Usenet -
where failed prodigies come to die.> Mr. Shambat, how do you
say that in Russian?>I don't know about any Mr. Shambat,but
to
play with or to shave her Schambart, THAT is a lovely
thing.ahahaha.....ahahahanson
=>> populated by Asians and
Jews with astounding credentials>> 'gure out how Asians and
Jews can universally do so well.>> that was exactly how the
Chinese students functioned.> What a mutual minority
admiration society.......ahahahaha..... I've never seen
before
such a self exposeeI don't function with your standard
Hanson.
Your standard == I won'texpose the dirty things my group
does.Beside, I was never a part of any group. I was always
minortity amongminortities but that is not the reason I tell
it like it is.Even within my family, I always get into trouble
because I speak thetruth but no one will change my nature. I am
me and am happy aboutit.> by some of/in the > minorities about
expressing their self-in§icted inferiority complex > to such
an extent, especially in the view that they could have >
hardly excelled to the extent they did and do were they in
their > own society of ethnic origin, or so they claim. I
don't know about self-inferiority complex blah..blah..blah
but
youspelled out what I wanted to say, i.e if it were not for
their stronggroup, neither Chinese nor Indians will dominate
in science programsin grad school. They know that too but
still some had the nerve to actsnobbish. Aside form all that,
I did not convey that none of themwould have excelled to the
extent they did in those programs if theyhave to do it alone.
As far as doing it in their own society of ethnicorigin, I
said nothing about it. I think that you are just grabbing my
post as an excuse to spew outthe garbage you have wanted to
spew for a long time.> Therefore, to alleviate the curse from
this albatross that is > hanging around their minds, I
suggest: Sweet Amanda, ask macho Al to **donate** to your
uterus a > sample from his paid, applause garnishing 6 cc
sperm donations.> You two could spawn the superspecies' that
the Nazis and the > Jewish comic book authors of Superman had
only orgasms in > their dreams about.... You guys could bring
this epic yearning to > fruition and reality........for a
better world.> Christen...eh,..ah... no,no... just label your
offspring as the > long nosed slit eyed one, which in all
probability will be his/her > most pronounced features. I know
your kind Hanson. You will collaborate with whoever is
winningat the moment, be it Chinese or Indians, just to make a
buck. Indian students functioned similarly too.> Ooohh my
gahhhhd, there's the nigger in the wood pile.> Here are them
Indians, Al, the ones you are so envious of> because they
have, according to you, only some 10 §ush toilet > on the
entire sub-continent.> This unfortunately means that you'll
be
able to produce an> offspring with only 2/3 rd of the max of
the full potential that> the human genome would allow. You
jokers are nuts! But then, this is the Usenet, a 24/7 cyber>
party, where prodigies that failed have to come to
die.........> Therefore, let'em sing.....all of
them....it's a
beautiful choir!
ahahahah....ahahahahah...ahahahaha.....ahahahanson
=> I know
your kind Hanson. You will collaborate with whoever> is winning
at the moment, be it Chinese or Indians,> just to make a
buck.>Amen!>
ahahahah....ahahahahah...ahahahaha.....ahahahanson
=> I know
your kind Hanson. You will collaborate with whoever> is winning
at the moment, be it Chinese or Indians,> just to make a buck.>
Amen! ahahahah....ahahahahah...ahahahaha.....ahahahanson ..
just to make a buck at the expense of truth and facts. If all
the energy you used in writing your granage on regular
basiscould be used in .. Never mind. You are not capable to do
that.
=> I know your kind Hanson. You will collaborate with
whoever> is winning at the moment, be it Chinese or Indians,>
just to make a buck.>> Amen!>> .. just to make a buck at the
expense of truth and facts.>Amen!.... just because your truth
ain't fact and your facts ain't
true.ahahahah....ahahahahah...ahahahaha.....ahahahanson
=> I
know your kind Hanson. You will collaborate with whoever> is
winning at the moment, be it Chinese or Indians,> just to make
a buck.>> Amen!>> .. just to make a buck at the expense of
truth and facts.>> Amen!> .... just because your truth ain't
fact and your facts ain't true.
ahahahah....ahahahahah...ahahahaha.....ahahahansonGo take your
med, really!
=> I know your kind Hanson. You will collaborate
with whoever> is winning at the moment, be it Chinese or
Indians,> just to make a buck.>> Amen!>> .. just to make a
buck at the expense of truth and facts.>> Amen!> .... just
because your truth ain't fact and your facts
ain't true.>> Go
take your med, really!>So,...... you wanna play doctor with me
now, after you have failed miserably in politics, sociology,
psychology, philosophy &
economics?..........AHAHAH.....ahahahaha...... Babe, listen,
you are not very successful, except when it comes to nagging
and whining....about YOUR own
problems.......ahahahahaha....ahahahah....ahahahahah...
ahahahaha.....ahahahanson
=> So,...... you wanna play doctor
with me now, after you have failed > miserably in politics,
sociology, psychology, philosophy & economics?>
..........AHAHAH.....ahahahaha...... Babe, listen, you are not
very > successful, except when it comes to nagging and whining>
....about YOUR own problems.......ahahahahaha....>
ahahahah....ahahahahah...ahahahaha.....ahahahansonHaving a
woman volunteer to play doctor is bad? Howzzat????
= >
So,...... you wanna play doctor with me now, after you have
failed > miserably in politics, sociology, psychology,
philosophy & economics?> ..........AHAHAH.....ahahahaha......
Babe, listen, you are not very > successful, except when it
comes to nagging and whining> ....about YOUR own
problems.......ahahahahaha....>
ahahahah....ahahahahah...ahahahaha.....ahahahanson Having a
woman volunteer to play doctor is bad? Howzzat????Ilsa: SS
Doctor
=>So,...... you wanna play doctor with me now,
after you have failed >miserably in politics, sociology,
psychology, philosophy &
economics?>..........AHAHAH.....ahahahaha...... Babe,
listen, you are not very >successful, except when it comes
to nagging and whining>....about YOUR own
problems.......ahahahahaha....>ahahahah....ahahahahah...
ahahahaha.....ahahahanson>>Having a woman volunteer to play
doctor is bad? Howzzat????> Ilsa: SS DoctorNews§ash: Ilsa does
not qualify as a woman. Female,perhaps.
=> hanson [ retorted
to a woman, not you, Bill, > [ sheesh, you're too old and
ugly.....ahahaha..]: So,...... you wanna play doctor with me
now, after you have failed > miserably in politics, sociology,
psychology, philosophy & economics?>
..........AHAHAH.....ahahahaha...... Babe, listen, you are not
very > successful, except when it comes to nagging and whining>
....about YOUR own problems.......ahahahahaha....
ahahahah....ahahahahah...ahahahaha.....ahahahanson> [Bill]>
Having a woman volunteer to play doctor is bad? Howzzat????>
.....with all her nagging and bitching?
.....ahahahahhaa..........I doubt that even a superb
dictation, nor much less a profound recti'cation will keep
her
quiet and make her happy. And in case of her having keen oral
interests, even such a notorious machinationwill not keep her
occupied in silence and solace for long neither. Do you have
any advanced ideas, Bill, to bring inner peace to thatpoor and
agitated woman? We must be good Samaritans, don't
we?ahahahaha........ahahahahanson......
=>>hanson [ retorted
to a woman, not you, Bill, >>[ sheesh, you're too old and
ugly.....ahahaha..]:>So,...... you wanna play doctor with me
now, after you have failed >miserably in politics, sociology,
psychology, philosophy &
economics?>..........AHAHAH.....ahahahaha...... Babe,
listen, you are not very >successful, except when it comes
to nagging and whining>....about YOUR own
problems.......ahahahahaha....>ahahahah....ahahahahah...
ahahahaha.....ahahahanson> [Bill]>>Having a woman volunteer to
play doctor is bad? Howzzat????> .....with all her nagging and
bitching? .....ahahahahhaa..........> I doubt that even a
superb dictation, nor much less a profound > recti'cation
will
keep her quiet and make her happy. And in case > of her having
keen oral interests, even such a notorious machination> will
not keep her occupied in silence and solace for long neither.
> Do you have any advanced ideas, Bill, to bring inner peace
to that> poor and agitated woman? We must be good Samaritans,
don't we?>
ahahahaha........ahahahahanson......Paci'cation is
just around the corner in Amanda's case. In factI think it
an
easily achievable goal. In general, I think passiona good
thing. If I'm wrong in everything else in this exchange, Ido
know she's given some very good replies.Keeping true to your
persona, don't fret over it. There's room
forall of this in
sci.physics.
=>populated by Asians and Jews
with astounding credentials>'gure out how Asians and Jews
can universally do so well.> that was exactly how
the Chinese students functioned.hanson, take yours
meds. you were improving.josh halpern>What a mutual minority
admiration society.......ahahahaha.....>>I've never seen
before such a self exposee by some of/in the >minorities about
expressing their self-in§icted inferiority complex >to such an
extent, especially in the view that they could have >hardly
excelled to the extent they did and do were they in their >own
society of ethnic origin, or so they claim. >Therefore, to
alleviate the curse from this albatross that is >hanging
around their minds, I suggest:>>Sweet Amanda, ask macho Al to
**donate** to your uterus a >sample from his paid, applause
garnishing 6 cc sperm donations.>You two could spawn the
superspecies' that the Nazis and the >Jewish comic book
authors of Superman had only orgasms in >their dreams
about.... You guys could bring this epic yearning to >fruition
and reality........for a better world.>Christen...eh,..ah...
no,no... just label your offspring as the >long nosed slit
eyed one, which in all probability will be his/her >most
pronounced features.>>Indian students functioned similarly
too.Ooohh my gahhhhd, there's the nigger in the wood
pile.>Here are them Indians, Al, the ones you are so envious
of>because they have, according to you, only some 10 §ush
toilet >on the entire sub-continent.>This unfortunately means
that you'll be able to produce an>offspring with only 2/3 rd
of the max of the full potential that>the human genome would
allow.>>You jokers are nuts! But then, this is the Usenet, a
24/7 cyber>party, where prodigies that failed have to come to
die.........>Therefore, let'em sing.....all of
them....it's a
beautiful
choir!>>ahahahah....ahahahahah...ahahahaha.....ahahahanson
=> hanson, take yours meds. you were improving.Recently
he's been better than ever, whatever thereason. Keep it up,
I
say.
=> hanson, take yours meds. you were improving.
Recently he's been better than ever, whatever the> reason.
Keep it up, I say.>since everything is up and running.
Nevertheless, your kind words are balsam for my soul. You are
a good man, Bill......on the other hand..... for Josh I have a
warm spot in my heart too , despite hisonly major §aw, which is
his seeing the world thru toomuch green tint, which make him
extrude and expeloccasionally green turds, precipitating his
bigger thanlife brooding seriousness. But, the fact that Josh
was notcapable to post his 7 words above in the best
grammartradition, that I will not hold against him. The faux
pas of Josh's gauche literary ejaculation may have been
precipitated because it happened on a Saturdayevening, while
he was gargling copiously with cheap CA wine, which made him
miss the joke or perhaps his EtOH decripition didn't let him
get the joke........ahahahaha....Things like that can and do
happen and this appears tobe really one of Josh's endearing
qualities, in that he takes everything so serious. One of the
'rst time I conversed with him over NG's he
asked me why I
did/said something, to whichI responded that one of the
priorities in my life was to pissoff everybody......to which
Josh retorted with a serious andearnest, admonishmental
sermon......which made me ROTL.It was then that I began to
watch Josh because I am hoping to 'nd a ghost, a dear ghost,
a
buddy of yore, of a long time ago, a friend I have lost track
of. I am hoping to 'nd a JoshHalpern who called himself
JoHal.
--- Is that you Josh? Your posting manners have a lot in common
with JoHal's. --- If so, then 'll in and post,
for ID purposes,
the questions described in the following events .Nam. We got
between the 101(?) and ARVN (when, whereJoHal ?). -- The
gooks' mortars were pounding, pinning us down but you had to
take a . Pants down, you stood up and shook your 'sts
against the old A16's that camein laying down napalm, you
shouting on top of your voice: For that , the ing govt
has money... but to give me toilet paper, for my , I have
to write a requisition.I'll always remember that, JoHal,
----
Still ROTFL and feelingthe taste of the earth in my mouth ---
still thinking about that ing game of so long ago, a time
of long periods of total, excruciating boredom pierced by a
few moments or minutes of sheer and absolute terror and near
terminal adrenaline shock. Salvage Operations, (was it
Bora-Bora, Tahiti, Rara-Tonga, Pelelu, which?) when we 2 had
that gig, that memorablegang bang with the 2 big boobed French
AC/DC bulldikes, happened there and where ....ahahahahaha....
if you Josh are 2 BB was incessantly humming Edith Pilaf's
those were the daysmy friend... hope they will never end
........and then in typicalJoHal fashion of superb sense of
seriousness and commitmentyou wanted to marry both, the 2 of
them, because they had aprofound love of life............I
still ROTF thinking about that.I hope that you are JoHal and
answer. If you ain't then maybesomebody may know of/about
JoHal about whom I last heard that he went precious opal
mining in Australia's outback butsomewhere the  hit the
fan and they allegedly threw himinto a mine shaft followed by
a bundle of dynamite... How did you get out of this one,
JoHal? Did you fake your own demise?I wouldn't put it past
you. But stop worrying. Everything is now way past all
statutes of limitations. Come on, show up, for we still have
some un'nished, grand biz to accomplish, undun remants from
those years of stark terror and silly ecstasies. That was
life, big time! ..... I am hoping, dude,.....hanson,........
kk57v5....alpha-charly-tango....over......
=hanson, take yours meds. you were improving.Recently he's been better than ever, whatever
the>>reason. Keep it up, I say.since everything is up
and running. Nevertheless, your kind >words are balsam for my
soul. You are a good man, Bill.>>.....on the other hand.....
>to troll the troll or not to troll the troll; that is the
question. whethertis' better to endure the slang and grammar
arrows from anunder medicated troll, or simply to plonk.....ah
bless'd delete keyjosh halpern
=>hanson, take yours meds.
you were improving.>Recently he's been better than ever,
whatever the>>reason. Keep it up, I say.>>since everything
is up and running. Nevertheless, your kind >words are balsam
for my soul. You are a good man, Bill.>>.....on the other
hand..... > to troll the troll or not to troll the troll; that
is the question. > whether tis' better to endure the slang
and
grammar arrows from an> under medicated troll, or simply to
plonk.....ah bless'd delete key> josh halpernWell, Josh, I
am
so sorry to hear that you are not JoHal. But, for the
consolation price you offered in admitting that it cranked
enormously, I must truly thank you...............AND.... on
the other hand..........is it perhaps not me, but the
hellgrammites that are still active within your cranium?
It's
only Sunday morning...and your metabolism slows with age,
buddy,ahahahaha....ahahahahahanson
= Speaker: William Wertz
on Schiller: Poet of Freedom. Schiller, poet of Romantic
Dreck. > Have your read the words to -Ode an die Freude-?> Bob
Kolker>This poem from Schiller and Mileva's know-how were
Einstein'shis Christian wife, Mileva Maric, over and over
again...until he dumped her, right after she had put HER ideas
into writingand gave it to her hubby. This, HER work, which
Albert published, without HER name on it, was his 1905 paper
on special relativity.Speicher and such, will get a hernia and
a pile of hemmies whenthey hear that, but a recent 1 hrs PBS
show really insinuated that.Belief survey says: Jews: 100%
false - Goyim: 100% true
AHAHAHAHAH.........ahahahaha.......ahahahanson
=> The
LaRouche Show is a weekly audio talk show, broadcast live on
the> Internet every Saturday, featuring interviews with Lyndon
LaRouche,> his associates, and special guests. Hosted by
Michele Steinberg,> Counterintelligence co-director of
Executive Intelligence Review, and> by Marcia Merry Baker, EIR
Economics Intelligence director.> Live Broadcast TODAY>
3:00-4:00 p.m. Eastern Standard Time (2000-2100 UTC)> Speaker:
William Wertz on Schiller: Poet of Freedom.> During the live
broadcast, you can ask questions by calling one of the>
following numbers:>> been practiced all over the place. Utopia
You are a good man.Unfortunately (a), I have no time for
Lyndon LaRouche, other when he comes on really big on the
networks, usually every 4 years for 1 hr on the eve of the
presidential elections. If you, his disciple, havemore
in§uence on LaRouche, your role model and idol, then does his
janitor, then please tell him to spread his message with a
weee bit during his delivery his is depressing and bulimic.
Unfortunately (b), in your condition and zeal you probably did
hope for me to be this gent here,
http://www.marvunapp.com/Appendix/cobrajal.htm#Hansonwhich
would account for your wild guess and association,
but.....Unfortunately (c), its is just re§ecting your own
blossoming paranoia.ahahahahaha.......ahahahanson
=> amanda
<amanda94621@yahoo.com> grava .88 la saucisse et au marteau:>
[SNIP] Could you *please* the lines you are not responding to.
Otherwise, this> is very hard and unpleasant to read and,
besides, it takes more time to> download (and it's
signi'cative with a low-speed modem).Well..when I used to do
that (not in this group though), I was accusedof leaving out
the info to mislead the reader, etc. Anyway, I am very sorry.
I will do that from now on.
=amanda <amanda94621@yahoo.com>
grava .88 la saucisse et au marteau:> Well..when I used to do
that (not in this group though), I was accused> of leaving out
the info to mislead the reader, etc.Both can be done. You can
quote some of the lines to make your answerunderstandable for
someone who did not see the previous post, but stilldeleting
the others.> Anyway, I am very sorry. I will do that from now
i;@/WO(?;[KC9sW;wG/4@H[_VFFH4?QHJ#O(?m}7fQMrJ,]0THA'|e-EPG_>
56Mi}_RRhBS'a2}u_7jm)0_+'=$V#E2r4#IQE/d)yMv3_4
@hl<)mA&*tDN/
=In sci.math, Nicolas Le
Roux<nicolas@bisounours.net><slrnbqqc7p.ilp.nicolas@
zen.via.ecp.fr>:> amanda <amanda94621@yahoo.com> grava .88 la
saucisse et au marteau:> [SNIP] Could you *please* the lines
you are not responding to.Erm...are you sure you didn't
inadvertantly snip the word snip?Pleasing the lines sounds
impossible; I've never quite 'guredout whether
chocolates or
§owers will make the sentence This statement is falsehappy.:-)
;-) :-)> Otherwise, this> is very hard and unpleasant to read
and, besides, it takes more time to> download (and it's
signi'cative with a low-speed modem).> I can relate to that
to
some extent; I've a 56k myself. Fortunately,I also use
leafnode
(fetchnews) -- though that doesn't do a thingfor having to
pay
by the connection minute.-- #191, ewill3@earthlink.netIt's
still legal to go
.sigless.
=<ewill@sirius.athghost7038suus.net> grava .88 la
saucisse et au marteau:> Could you *please* the lines you are
not responding to.> Erm...are you sure you didn't
inadvertantly snip the word snip?Actually, as far as I
remember, I think it was the word delete.-- NicolasWow,
THAT'S
i;@/WO(?;[KC9sW;wG/4@H[_VFFH4?QHJ#O(?m}7fQMrJ,]0THA'|e-EPG_>
56Mi}_RRhBS'a2}u_7jm)0_+'=$V#E2r4#IQE/d)yMv3_4
@hl<)mA&*tDN/
=In sci.math, Nicolas Le
Roux<nicolas@bisounours.net><slrnbqr566.nkf.nicolas@
zen.via.ecp.fr>:> <ewill@sirius.athghost7038suus.net> grava
.88 la saucisse et au marteau:> Could you *please* the lines
you are not responding to. Erm...are you sure you didn't
inadvertantly snip the word snip? Actually, as far as I
remember, I think it was the word delete.> Close enough. :-)--
#191, ewill3@earthlink.net -- insert random word hereIt's
still
legal to go .sigless.
=> Do you really mean>> C_i is also
joined to C_{i-3} and C_{i+2} (subscripts read mod 7),no> or>>
C_i is also joined to C_{i-2} and C_{i+2} (subscripts read mod
7),> ?yes-- Robin Chapman,
www.maths.ex.ac.uk/~rjc/rjc.htmlNeedless to say, I had the
last laugh. Alan Partridge, _Bouncing Back_ (14 times)
=In
my previous thread, there seemed to be a general lack of
consensuswith regard to whether algebraists implicitly invoke
a functor whenthey say If G is a group, let G_e be its
identityMore generally, if something is de'ned in such a way
that it mustpossess something else (as, for instance, a group
having to have anidentity, by the very de'nition of a group),
it seems to me that thatdoes not mean we are no longer using a
hidden function/functor when wecall up that something else.It
is largely a matter of notation. Suppose mathematical
notationwere de'ned in such a way that, when it was clear by
context, wecould use the phrase its' square instead of x^2,
as, for instance:Let x be a real greater than 1. Then x <
its'
squareWe are not used to such weird notation. But in more
down-to-earthnotation, we say x < x^2, and I believe you will
agree that we arethus implicitly using the function
f(x)=x^2.How, then, is it any different to say,Let G be a
group. Then G's identity is in GHere the culprit is the
phrase
G's identity. The way I see it, thisis the same as using a
functor implicitly, just like its'
[x's]square.Suppose we
explicitly de'ned the functorI(g) = the identity of G. Then
our above statement could be rewordedLet G be a group. Then
I(G) is in GHere, we are explicitly using a functor (you
won't
deny that much!). But if we are not using one in the original
phrase, then where did itcome from and where does it go? What
I am saying is, the twostatements are the same exact thing.
Therefor, since one uses thefunctor, both do.I am not trying
to stir up trouble, just trying to get a grasp ofthese
abstract things and very much eager for the help that
youradvanced mathematical knowledge will no doubt shed upon
the murkysubject.Sniz Pilbor
=[cu]> It is largely a matter
of notation. Suppose mathematical notation> were de'ned in
such a way that, when it was clear by context, we> could use
the phrase its' square instead of x^2, as, for instance: Let
x
be a real greater than 1. Then x < its' square We are not
used
to such weird notation. But in more down-to-earth> notation,
we say x < x^2, and I believe you will agree that we are> thus
implicitly using the function f(x)=x^2.I don't agree that we
are implicitly using the function f(x) = x^2.The x^2 in x <
x^2 is an element (I assume) in the natural numbers.I am not
sure what of many ways you could be interpreting x^2
asimplictly using the function f(x) = x^2.Consider the
situation where I de'ne the function f to bethe subset of NxN
such that f = { (a,b) in NxN | a in N and b = a*a}.That last
a*a cannot be implicitly using the function fsince I am
de'ning it (ie f). Otherwise, the de'nition of f
wouldbe
circular.Just because you could replace my use of x^2 by
referring tothe explicit use of the funciton f(x) = x^2 does
not mean thatyou must be doing it implicitly. Sometimes there
is an advantageto putting a particular situation into a more
general context,but that does not mean you were implicitly
invoking that moregeneral context.I am all for casting
mathematical concepts into set theory terms,like functions
being viewed as subset of cartesian product ofdomain and
range. But, it appears that you are trying to castevery
mathematical statement into terms of functions. Aspointed out
by other posters, category theory provides a generalcontext
where ideas viewed as distinct become to be viewed
asparticular cases of a more general catogorical
situation.This unifying viewpoint is more important than just
beingable to say that you have a functor from the class of all
groupsto its identity element.-- Bill Hale
= > [...] we say x
< x^2, and I believe you will agree that we are> thus
implicitly using the function f(x)=x^2. I don't agree that
we
are implicitly using the function f(x) = x^2.> Here we are at
a disagreement. I am not trying to bash you or claimyou're
wrong, I'm merely saying I still am not convinced. Here is
myreasoning:1. If two statements are the same, then they both
make use of the samethings2. The statements x < x^2 and x <
f(x) are the same (whenf(x)=x^2)3. Clearly, the second
statement above uses f(x)4. Therefor, by 1), 2), and 3), we
conclude that the statement x <x^2 makes use of f(x).Now I am
not trying to be stubborn, it's just that I am the type
ofperson who urgently needs to understand things. This is
probably whyI'm a math major rather than a comp prog major.
To
convince me thatI've overlooked something, you have only to
point out a §aw in anyone of the above 4 steps. Please
don't
misconstrue my continuedargument as anything less than the
highest of esteem and respect foryourself.With regard to your
example f={(a,b)|a in N, b=a*a}, that does indeedpoint out
that things are even more interesting than I thought. Clearly
a de'nition like h(x)=h(x) is circular. However,
ade'nition of
the form h(x)=i(x) is not, assuming i(x) is alreadyadequately
de'ned. However, since h(x) and i(x) are equal
(byde'nition),
the replacement axiom tells us it is safe to replace i(x)by
h(x), which results in h(x)=h(x). This is very weird,
andsomething's wrong. I'm wondering if perhaps
I ought to go
tosci.logic to 'nd answers.Sniz Pilbor
tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate:
admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Punge:
Micro$oft
= at 06:37 PM, snizpilbor@yahoo.com (Sniz Pilbor)
said:>1. If two statements are the same, then they both make
use of the>same thingsWhat do you mean by the same? If you
really mean that they are thesame, then your next statement is
false.>2. The statements x < x^2 and x < f(x) are the same
(when>f(x)=x^2)Only if you are using a different meaning of
the same from the onein 1. above.>Now I am not trying to be
stubborn, it's just that I am the type of>person who
urgently
needs to understand things. Try reading the responses you
already got.>Clearly a de'nition like h(x)=h(x) is circular.
Don't confuse a de'nition with a theorem.>the
replacement
axiomApplies to theorems.>This is very weird, Yes. The Devil
is in the details, and you need to start payingattention to
the details or you will keep getting wierd results.-- Shmuel
(Seymour J.) Metz, SysProg and JOATnot reply to
=>
1. If two statements are the same, then they both make use of
the same> things.I have no idea what it means for a statement
to make use of a thing.
=>> [...] we say x < x^2, and I
believe you will agree that we are>> thus implicitly using the
function f(x)=x^2.>> I don't agree that we are implicitly
using
the function f(x) = x^2.> Here we are at a disagreement. I am
not trying to bash you or claim> you're wrong,
I'm merely
saying I still am not convinced. Here is my> reasoning:> 1. If
two statements are the same, then they both make use of the
same> things> 2. The statements x < x^2 and x < f(x) are the
same (when> f(x)=x^2)This is wrong. The statements are not the
same, because only one of themmentions a function f.> 3.
Clearly, the second statement above uses f(x)> 4. Therefor, by
1), 2), and 3), we conclude that the statement x <> x^2> makes
use of f(x).No, it's exactly the other way around.
It's the
de'nition of thefunction f that makes implicit use of the
multiplication operation on thereals.-- Judge Yohn's
mistakes
revealed in Mumia Abu-Jamal
ruling.<http://www.commoncouragepress.com/index.cfm?action=
book&bookid=228>
=> 2. The statements x < x^2 and x < f(x)
are the same (when> f(x)=x^2) This is wrong. The statements
are not the same, because only one of them> mentions a
function f.> Let P(x) denote the logic statement x < x^2Let
Q(x) denote the logic statement x < f(x)P and Q are unequal
iff there is some real x such that P(x) != Q(x)Else, they are
equalIt seems to me upon inspection (though I keep an open
mind tocorrection since I am but an amateur) that P and Q are
equal- in thesense that for any x, P(x)=Q(x).And since they
are equal, if one has a given property, the other mustas well.
The property employs the function f(x)=x^2 is possessed byQ,
and therefor by P as well.Where am I erring?This is all quite
confusing, and I fear I am outwearing my welcome atsci.math by
pushing this issue so stubbornly, so I beg that youforgive me
and know that I am just a naive person who humbly desiresto
understand these things.Sniz Pilbor
<bopmjg$q8e$1@mozo.cc.purdue.edu>
tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate:
admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Punge:
Micro$oft
said:>if one has a given property, What do you mean by has a
given property? Your usage seems totranscend the values of the
propositional functions, in which case twopropositional
functions with the same values need not have the
sameproperties.-- Shmuel (Seymour J.) Metz, SysProg and
tb@becket.becket.net
=> Let P(x) denote the logic statement
x < x^2> Let Q(x) denote the logic statement x < f(x) P and Q
are unequal iff there is some real x such that P(x) != Q(x)>
Else, they are equalThey are not equal, because sentences are
not extensional. Differentsentences can be logically
equivalent, and yet they are stilldifferent sentences.For
example:George W. Bush is president.The eldest son of George
H. W. Bush is president.are logically equivalent in any world
in which GWB is the eldest sonof GHWB (such as, for example,
the real world). But they are hardlyequal sentences which
share all properties. For example, the 'rstone has twenty-two
letters and two periods; the second hasthirty-seven letters
and three periods.Also, the 'rst does not mention GHWB, but
the second does.Thomas
=>> 2. The statements x < x^2 and x <
f(x) are the same (when>> f(x)=x^2)>> This is wrong. The
statements are not the same, because only one of them>>
mentions a function f.> Let P(x) denote the logic statement x
< x^2> Let Q(x) denote the logic statement x < f(x)> P and Q
are unequal iff there is some real x such that P(x) != Q(x)>
Else, they are equalThe statements are logically equivalent,
but they are not the same statement.> It seems to me upon
inspection (though I keep an open mind to> correction since I
am but an amateur) that P and Q are equal- in the> sense that
for any x, P(x)=Q(x).> And since they are equal, if one has a
given property, the other must> as well. The property employs
the function f(x)=x^2 is possessed by> Q, and therefor by P as
well.> Where am I erring?The following statements are logically
equivalent when applied to the naturalnumbers, but they are not
equal: 1. P(x) =def x is prime. 2. Q(x) =def x > 1 and x is not
composite.P(x) employs 8 letters. Therefore, Q(x) must employ 8
letters as well.> This is all quite confusing, and I fear I am
outwearing my welcome at> sci.math by pushing this issue so
stubbornly, so I beg that you> forgive me and know that I am
just a naive person who humbly desires> to understand these
things.-- Judge Yohn's mistakes revealed in Mumia Abu-Jamal
ruling.<http://www.commoncouragepress.com/index.cfm?action=
book&bookid=228>
=>In my previous thread, there seemed to be
a general lack of consensus>with regard to whether algebraists
implicitly invoke a functor when>they say If G is a group, let
G_e be its identityNo, there was no lack of consensus. Most of
us simply did not addressthe claim and simply went on to say
how one could de'ne such
a'function'. But the fact is, there
is no need to have a functionwhose domain is all groups before
you can start talking about theidentity of a given group.There
are many ways of describing a group; it can be a set G with
abinary operation * which satis'es certain axioms, in which
case thefact that G satis'es the axioms automatically gives
you anidentity. A more obvious way is to say it is a set G,
with threeoperations; a binary operation *, a unary operation
^{-1}, and anullary operation e, which satis'es certain
identities. The groupitself already comes equipped with a way
of identitfying its identity:the nullary operation e.In fact,
that is all you need: for every group G, a nullary
operationG->G whose image is the identity. Then you are not
invoking a generalfunction whose arguments are any group, and
whose response is theidentity of the group. You are invoking a
very speci'c function,associated to the group G itself, which
gives you the identity of G.The existence of such a function
is guaranteed by the very propertiesthat de'ne a group.Or
there are other ways in which one can de'ne a function that
hasthe properties you described. Though such a function is not
NEEDED todo group theory.>More generally, if something is
de'ned in such a way that it must>possess something else (as,
for instance, a group having to have an>identity, by the very
de'nition of a group), it seems to me that that>does not mean
we are no longer using a hidden function/functor when we>call
up that something else.Nor does it mean we ->ARE<-. And
certainly, it does ->not<- mean weMUST have a function whose
domain is all such somethings and whosecodomain is all things
that they possess. All you need is for eachsomething G, a
function whose domain is G^{0} = {emptyset}, and whosecodomain
is the singleton consisting of the something else itpossesses.
In the example you mentioned, given a group G, let e be
itsidentity. You do not need to invoke a function de'ned for
ALL groups:you may simply invoke a function whose domain is
{emptyset} and whosecodomain is {e}. You don't care about
any
other groups besides the onethat show up in your
argument.
==
==It's not denial. I'm just very
selective
about what I accept as reality. --- Calvin (Calvin and
Hobbes)
tb@becket.becket.net
=> In my previous thread, there seemed
to be a general lack of consensus> with regard to whether
algebraists implicitly invoke a functor when> they say If G is
a group, let G_e be its identityThere was no lack of consensus.
Everyone agreed that algebraists donot need such a function,
nor do they invoke it.The discussion was about the different
question of whether such afunction is possible, which is a
question of which particular settheory you are using, and
whether your set theory allows functionswith domains or ranges
that are proper classes.> How, then, is it any different to
say,> Let G be a group. Then G's identity is in G> Here the
culprit is the phrase G's identity. The way I see it, this>
is
the same as using a functor implicitly, just like its'
[x's]>
square.The phrase Let G be a group is really an abbreviation
for:Let G = <g, *, e> be a group. (Where you've decided that
the orderis set, operation, identity.Thomas
=In the
Pfaf'andU = A_1.dx_1 + A_2.dx_2 + ...+A_n.dx_nif A_1,
A_2,...are twice continuously differentiable _functions_ ofthe
variables x_1, x_2,...etc. then a necessary condition for
theintegrability of dU is the equality of the partial
derviatives@A_i/@dx_k = @A_k/@x_iand there is also a much
longer expression involving any three of theA's that will
give
the suf'cient condition for the existence of anintegrating
factor.My question is, what if the A_i are not simply
functions of x_k butrather functionals? Say, for exmaple, A_1
depends explicitly on (x_1 *x_2), or (h*x_1), where * denotes
the convolution operator and h(t) isa given function, what can
then guarantee the integrability of dU?
=|> If A is a
nonsingular 3 x 3 matrix with nonnegative entries, then why
must A|> have a positive real eigenvalue?|> ...The
characteristic equation (setting the determinant with the
eigenvaluesubtracted from the diagonal to zero) is equivalent
to 'nding the rootsof a cubic polynomial; so
it's clear that
there must be a real eigenvalue.Writing down the de'nition of
the eigenvalue as A*v = lambda *vfor an eigenvector v and
playing around with the signs it is alsoclear that lambda must
stay positive (at least if all threeCartesian components of v
are positive or negative... which is effectivleythe same as
eigenvectors are only de'ned up to a const...)
=> If A is a
nonsingular 3 x 3 matrix with nonnegative entries, then why>>
must A have a positive real eigenvalue?>> Mike This is not
true. For example 1 0 0> 0 0 1> 0 1 0 has eigenvalues 1,So, 1
is no longer positive ?> 1, and -1. To the OP: this is (part
of) the Perron-Frobenius theorem.-- Robin Chapman,
www.maths.ex.ac.uk/~rjc/rjc.htmlNeedless to say, I had the
last laugh. Alan Partridge, _Bouncing Back_ (14 times)
=
Howdy everybody, I'm reading Peskin and
Schroeder's Intro to
QFT and in this> book the author constantly refers to
c-numbers... without> saying what a c-number is. I couldn't
'nd c-number> on mathworld.wolfram.com or
physicsworld.wolfram.com. Can someone please tell me what the
hell a c-number is?Adding yet another interpretation besides
commuting and classical: Ithink they mean a complex number
(which obviously is both commuting andclassical).I think they
de'ned it in this way somewhere in their book, butscanning
the
'rst few pages, I can't 'nd it...
:-(Bye,Bjoern#
= Forbidden
archeology by Cremo, Thompson! Like the name says: Forbidden I
urge you not to read it!You might try
reading<http://www.talkorigins.org/faqs/mom/groves.html>
instead.Bye,Bjoern
=>Let's be serious for
once.>>Consider an object being accelerated by a idealistic
jet of water or a>continuous Ostream of elastic ping pong
balls'. What is its subsequent
velocity>pattern?>>accelerated beyond the operating speed of
the accelerating 'elds, ie at Oc'.
I>hope it might also produce
a relationship that is equivalent to
mass>'appearing' to
increase with velocity by gamma.)>Please de'ne what you
mean by the operating speed of an>>accelerating 'eld.
I've
been in physics research for over 20>>years, and I've never
heard that term.>>Do you mean phase velocity, group velocity,
how fast the>>operators turn the knobs, what?>>I think you
forgot to answer the question, Henry.>Why is that?>> yes, for
some strange reason I Oforget' to answer
anything EjP
asks.Considering that he asked you about the meaningof a
meaningless statement, I don't 'nd the reason
strange at
all.Paul, not puzzledExpires: 28 days
=>accelerated
beyond the operating speed of the accelerating 'elds, ie at
Oc'. I>>hope it might also produce a
relationship that is
equivalent to mass>>'appearing' to increase
with velocity by
gamma.)>>Please de'ne what you mean by the operating
speed of an>accelerating 'eld. I've been in
physics research
for over 20>years, and I've never heard that term.>Do you
mean phase velocity, group velocity, how fast the>operators
turn the knobs, what?>>I think you forgot to answer the
question, Henry.>>Why is that?>> yes, for some strange
reason I Oforget' to answer anything EjP
asks.>>Considering
that he asked you about the meaning>of a meaningless
statement, I don't 'nd the reason strange at
all.>>Paul, not
puzzled>Paul, is your memory failing?I explained this to you
last year. If 'elds acted instantaneously, we would beable to
use them for instantaneous comunication.Do you really want
that?Henri Wilson.See why relativity is
wrong:http://www.users.bigpond.com/HeWn/index.htm
=>>
accelerated beyond the operating speed of the accelerating
'elds, ie at Oc'. I>>hope it might
also produce a relationship
that is equivalent to mass>>'appearing' to
increase with
velocity by gamma.)>Please de'ne what you mean by the
operating speed of an>accelerating 'eld. I've
been in
physics research for over 20>years, and I've never heard
that term.>Do you mean phase velocity, group velocity, how
fast the>operators turn the knobs, what?>>I think you
forgot to answer the question, Henry.>>Why is that?>> yes,
for some strange reason I Oforget' to answer
anything EjP
asks.>>Considering that he asked you about the meaning>of a
meaningless statement, I don't 'nd the reason
strange at
all.>>Paul, not puzzled> Paul, is your memory failing?>> I
explained this to you last year.Henry, is your memory
failing?Because this year, your aswer was: No I cannot
explain.> If 'elds acted instantaneously, we would be> able
to
use them for instantaneous communication.Please explain how you
can use the fact that a force isa static electric 'eld, for
instantaneous communication.Paul, puzzledExpires: 28
days
=>>I think you forgot to answer the question,
Henry.>Why is that?>>yes, for some strange reason I
Oforget' to answer anything EjP
asks.>>Considering that he
asked you about the meaning>>of a meaningless statement, I
don't 'nd the reason strange at all.>>Paul,
not
puzzled>> Paul, is your memory failing?>> I explained
this to you last year.>>Henry, is your memory failing?>Because
this year, your aswer was:> No I cannot explain.> If 'elds
acted instantaneously, we would be>> able to use them for
instantaneous communication.>>Please explain how you can use
the fact that a force is>a static electric 'eld, for
instantaneous communication.>>Paul, puzzled>I'm sure some
bright QMian would 'nd a way.Henri Wilson.See why relativity
is wrong:http://www.users.bigpond.com/HeWn/index.htm
=>I
understand very well why you are desperate to divert>the
attention from the fact that you know very well that>the SR
prediction I showed above is experimentally veri'ed>in
accelerators all over the world all the time, while>the
Newtonian prediction is falsi'ed all the time.>> Your idea of
the ONewtonian prediction' is just a
diversion... from the
fact that the prediction of NM fails by ordersof magnitude
while the prediction of SR is correct?> Read what I said to
Randy. That is the real reason why mass appears to increase>
and the required energy shoots up enormously as c is
approached.And Henry knows the REAL reason is: As the electron
approaches the speed at which the 'eld acts, back radiation
from the electron Oneutralizes' a volume around
itself. The
'eld in its vicinity is more or less reversed by the
electron's own movement. This requires a great deal of
energy;
one single charge creating a Olittle neutral
sphere' in a
strong 'eld. This energy also shows up in bolometer
experiments.Paul, dazzled
=>I understand very well why you
are desperate to divert>the attention from the fact that you
know very well that>the SR prediction I showed above is
experimentally veri'ed>in accelerators all over the world all
the time, while>the Newtonian prediction is falsi'ed all the
time.>> Your idea of the ONewtonian prediction'
is just a
diversion. .. from the fact that the prediction of NM fails by
orders> of magnitude while the prediction of SR is correct?
Read what I said to Randy. That is the real reason why mass
appears to increase> and the required energy shoots up
enormously as c is approached. And Henry knows the REAL reason
is:> As the electron approaches the speed at which the 'eld
acts,> back radiation from the electron
Oneutralizes' a volume
around itself.> The 'eld in its vicinity is more or less
reversed by the electron's own> movement. This requires a
great deal of energy; one single charge creating a> Olittle
neutral sphere' in a strong 'eld. This energy
also shows up
in> bolometer experiments.> I missed this explanation. Having
read it, I can't makeheads or tails of it.Henry: Does
whatever
you are trying to describe have anequivalent in the ping-pong
model? If I am trying todrive a vehicle by throwing 100 m/sec
ping-pong ballsat it, so it has a limiting velocity of 100
m/sec,will the kinetic energy continue to rise
beyond0.5*m*100^2 and the momentum continue to rise
beyondm*100 due to some sort of back 'eld?If not, what do
electrons have that a ping-pong-balldriven vehicle does not? -
RandyExpires: 28 days
=>>I understand very well why you
are desperate to divert>>the attention from the fact that you
know very well that>>the SR prediction I showed above is
experimentally veri'ed>>in accelerators all over the world
all
the time, while>>the Newtonian prediction is falsi'ed all the
time.>> Your idea of the ONewtonian prediction'
is just a
diversion.>> .. from the fact that the prediction of NM fails
by orders>> of magnitude while the prediction of SR is
correct?>> Read what I said to Randy. That is the real reason
why mass appears to increase>> and the required energy shoots
up enormously as c is approached.>> And Henry knows the REAL
reason is:>> As the electron approaches the speed at which the
'eld acts,>> back radiation from the electron
Oneutralizes' a
volume around itself.>> The 'eld in its vicinity is more or
less reversed by the electron's own>> movement. This
requires
a great deal of energy; one single charge creating a>> Olittle
neutral sphere' in a strong 'eld. This energy
also shows up
in>> bolometer experiments.>>I missed this explanation. Having
read it, I can't make>heads or tails of it.>>Henry: Does
whatever you are trying to describe have an>equivalent in the
ping-pong model? If I am trying to>drive a vehicle by throwing
100 m/sec ping-pong balls>at it, so it has a limiting velocity
of 100 m/sec,>will the kinetic energy continue to rise
beyond>0.5*m*100^2 and the momentum continue to rise
beyond>m*100 due to some sort of back 'eld?>>If not, what do
electrons have that a ping-pong-ball>driven vehicle does
not?>> - RandyMass of dimension 2.Henri Wilson.See why
relativity is
wrong:http://www.users.bigpond.com/HeWn/index.htmExpires: 28
days
=>I understand very well why you are desperate to
divert>>the attention from the fact that you know very well
that>>the SR prediction I showed above is experimentally
veri'ed>>in accelerators all over the world all the time,
while>>the Newtonian prediction is falsi'ed all the time.>>
Your idea of the ONewtonian prediction' is just
a
diversion.>>.. from the fact that the prediction of NM fails
by orders>of magnitude while the prediction of SR is
correct?> Read what I said to Randy. That is the real reason
why mass appears to increase>> and the required energy shoots
up enormously as c is approached.>>And Henry knows the REAL
reason is:> As the electron approaches the speed at which the
'eld acts,> back radiation from the electron
Oneutralizes' a
volume around itself.> The 'eld in its vicinity is more or
less reversed by the electron's own> movement. This requires
a
great deal of energy; one single charge creating a> Olittle
neutral sphere' in a strong 'eld. This energy
also shows up
in> bolometer experiments.>That's OK Paul. A physical
explanation is worth a thousand meaningless
mathsequations.>>Paul, dazzled...by the novelty.....>Henri
Wilson.See why relativity is
wrong:http://www.users.bigpond.com/HeWn/index.htm
=>>And
they claim a simple Omass increase'.>>No they
don't. If you
actually read this newsgroup, you'd>>know that the term mass
is used by most physicists to>>to refer to an invariant
quantity.>>The term used is Orelativistic mass
increase'.If
you actually read this newsgroup, you'd know that the
termrelativistic mass is no longer favored, and that most
physiciststhese days prefer to reserve the term mass to refer
to an invariantquantity. Where m used to appear in some
formulas (such as E =mc^2), gamma*m is now used. -
RandyExpires: 28 days
=> Henri Wilson.>> See why
relativity is wrong:>>
http://www.users.bigpond.com/HeWn/index.htm>>It would be nice
if you used more text and fewer programs. I'm not
>explanation
appears to be contained in them, your website says nothing
>that I am willing to look at.All my programs have been
discussed at length on the NG. I gather you are newehere.Henri
Wilson.See why relativity is
wrong:http://www.users.bigpond.com/HeWn/index.htm
=>It would
be nice if you used more text and fewer programs. I'm
not>explanation appears to be contained in them, your website
says nothing>that I am willing to look at.If the speed of
light is a universal constant in all frames of reference,and
in a certain situation light takes a longer path when seen
from oneperspective than it does from another, then it must
take a longer time fromthat perspective than it does from the
other.Or - the longer path takes the longer time.Usually, the
relativist will say something like...The beam moves vertically
in the moving frame, but this is seen as adiagonal line in the
stationary frame.|| | | Therefore time in the moving frame is
less than time in the stationaryframe, taa-daaaa!, I'm so
clever, I understand relativity, mom!Then he does some
elementary algebra which I won't bore you with, and
walksoff,
con'dent he's right.Trouble is, if we bend the
light beam
through the angle arctan(v/c) in themoving frame, this is what
happens.t0.........* at1........t1.........*
bt2......t2........t2.........*
ct3..t3.....t3.......t3.........* dThe moving source has moved
left as time passed, but the ray is vertical inthe stationary
frame. The tip of the ray, *, remains the same distance
fromthe edge of the page, at a,b,c,and d, but the source has
moved to the left.So, applying our rule that the longer path
takes the longer time, the longertime is in the moving frame,
not the stationary frame, contrary to therelativists claim
that he understands anything at all.At this point the
relativist will start to splutter about
unsynchronizedclocks.(Did I mention any clocks until now? No,
of course not.)He will claim that in the stationary frame two
clocks are separated|S| | | A Bby a distance vt, and work this
into his argument.(Oh no he won't, you cry!)Oh yes he will,
I've seen it done.Now, of course it is true that the
distance
S-A-B is greater than thedistance S-A, so he has found a trick
up his sleeve to make time less in themoving frame once more.
What a clever relativist!But......... that isn't the path
the
light takes. It doesn't go from S to A and A to B,bending
through a right-angle. It takes the short-cut, direct from S
to B.The frame with the longer path has the longer time.
Moving clocks speed up,and all because I tilted the §ashlight.
Ergo, Einstein's relativity isstupidity, and relativists are
gullible fools.(To Henri: No special math needed, old chap.
Keep it simple :-)AndroclesExpires: 28 days
=>It would be
nice if you used more text and fewer programs. I'm
not>>explanation appears to be contained in them, your website
says nothing>>that I am willing to look at.>>If the speed of
light is a universal constant in all frames of reference,>and
in a certain situation light takes a longer path when seen
from one>perspective than it does from another, then it must
take a longer time from>that perspective than it does from the
other.>Or - the longer path takes the longer time.>>Usually,
the relativist will say something like...>>The beam moves
vertically in the moving frame, but this is seen as a>diagonal
line in the stationary frame.>|>| >Therefore time in the moving
frame is less than time in the stationary>frame, taa-daaaa!,
I'm so clever, I understand relativity, mom!>Then he does
some
elementary algebra which I won't bore you with, and
walks>off,
con'dent he's right.Yes. All relativists seem
to suffer from
the same Ospatial-ability
de'ciencysyndrome'.As I have pointed
out many times, a vertical beam appears vertical in allframes.
(http://www.users.bigpond.com/hewn/movingframe.exe) Each
in'nitesimalelement of the vertical beam follows its own
unique diagonal path in the movingframe. There is no
conceiveable reason to believe that such an astractconstruct
constitutes light, traveling at c. My demo shows that such an
elementcannot be the same as one belonging to a laser beam
deliberately aimeddiagonally in the moving frame. Raindrops
take the same time to reach the ground even though they appear
to bemoving diagonally through the window of your moving
car.>>Trouble is, if we bend the light beam through the angle
arctan(v/c) in the>moving frame, this is what
happens.>t0.........* a>>t1........>t1.........*
b>>t2......>t2........>t2.........*
c>>t3..>t3.....>t3.......>t3.........* d>The moving source has
moved left as time passed, but the ray is vertical in>the
stationary frame. The tip of the ray, *, remains the same
distance from>the edge of the page, at a,b,c,and d, but the
source has moved to the left.>So, applying our rule that the
longer path takes the longer time, the longer>time is in the
moving frame, not the stationary frame, contrary to
the>relativists claim that he understands anything at all.>At
this point the relativist will start to splutter about
unsynchronized>clocks.>(Did I mention any clocks until now?
No, of course not.)>He will claim that in the stationary frame
two clocks are separated>|S>| >A B>by a distance vt, and work
this into his argument.>(Oh no he won't, you cry!)>Oh yes he
will, I've seen it done.>Now, of course it is true that the
distance S-A-B is greater than the>distance S-A, so he has
found a trick up his sleeve to make time less in the>moving
frame once more. What a clever relativist!>>But....>.>.>.>.>.>
that isn't the path the light takes. It
doesn't go from S to A
and A to B,>bending through a right-angle. It takes the
short-cut, direct from S to B.>The frame with the longer path
has the longer time. Moving clocks speed up,>and all because I
tilted the §ashlight. Ergo, Einstein's relativity
is>stupidity,
and relativists are gullible fools.Very true.>(To Henri: No
special math needed, old chap. Keep it simple :-) Nothing can
show this more simply than my demo.However, clocks can appear
to run either slow or fast depending on whether theyare
receding or approaching.In reality, they don't PHYSICALLY
change at all with movement.The term Ogamma' is
wrong. It
cannot contain Ov^2'. >Androcles>Henri
Wilson.See why
relativity is
wrong:http://www.users.bigpond.com/HeWn/index.htm
=>>It
would be nice if you used more text and fewer programs. I'm
not>>explanation appears to be contained in them, your website
says nothing>>that I am willing to look at.>>If the speed of
light is a universal constant in all frames of reference,>and
in a certain situation light takes a longer path when seen
from one>perspective than it does from another, then it must
take a longer timefrom>that perspective than it does from the
other.>Or - the longer path takes the longer time.>>Usually,
the relativist will say something like...>>The beam moves
vertically in the moving frame, but this is seen as a>diagonal
line in the stationary frame.>|>| >Therefore time in the moving
frame is less than time in the stationary>frame, taa-daaaa!,
I'm so clever, I understand relativity, mom!>Then he does
some
elementary algebra which I won't bore you with,
andwalks>off,
con'dent he's right.>> Yes. All relativists
seem to suffer
from the same Ospatial-abilityde'ciency>
syndrome'.> As I have
pointed out many times, a vertical beam appears vertical in
all> frames.
(http://www.users.bigpond.com/hewn/movingframe.exe)
Eachin'nitesimal> element of the vertical beam follows its
own
unique diagonal path in themoving> frame. There is no
conceiveable reason to believe that such an astract> construct
constitutes light, traveling at c. My demo shows that such
anelement> cannot be the same as one belonging to a laser beam
deliberately aimed> diagonally in the moving frame.>> Raindrops
take the same time to reach the ground even though they
appearto be> moving diagonally through the window of your
moving car.>Trouble is, if we bend the light beam through
the angle arctan(v/c) inthe>moving frame, this is what
happens.>t0.........* a>>t1........>t1.........*
b>>t2......>t2........>t2.........*
c>>t3..>t3.....>t3.......>t3.........* d>The moving source has
moved left as time passed, but the ray is verticalin>the
stationary frame. The tip of the ray, *, remains the same
distancefrom>the edge of the page, at a,b,c,and d, but the
source has moved to theleft.>So, applying our rule that the
longer path takes the longer time, thelonger>time is in the
moving frame, not the stationary frame, contrary to
the>relativists claim that he understands anything at all.>At
this point the relativist will start to splutter about
unsynchronized>clocks.>(Did I mention any clocks until now?
No, of course not.)>He will claim that in the stationary frame
two clocks are separated>|S>| >A B>by a distance vt, and work
this into his argument.>(Oh no he won't, you cry!)>Oh yes he
will, I've seen it done.>Now, of course it is true that the
distance S-A-B is greater than the>distance S-A, so he has
found a trick up his sleeve to make time less inthe>moving
frame once more. What a clever relativist!>>But....>.>.>.>.>.>
that isn't the path the light takes. It
doesn't go from S to A
and A toB,>bending through a right-angle. It takes the
short-cut, direct from S toB.>The frame with the longer path
has the longer time. Moving clocks speedup,>and all because I
tilted the §ashlight. Ergo, Einstein's relativity
is>stupidity, and relativists are gullible fools.>> Very
true.>>(To Henri: No special math needed, old chap. Keep it
simple :-)>> Nothing can show this more simply than my demo.>>
However, clocks can appear to run either slow or fast depending
on whetherthey> are receding or approaching.Of course. Doppler
shift.> In reality, they don't PHYSICALLY change at all with
movement.Quite right.> The term Ogamma' is
wrong. It cannot
contain Ov^2'.Err...The distance the light moves
from S to A
is ct.The distance from A to B is vt.The distance from S to B
is sqrt([ct]^2 +[vt]^2) by Pythagoras.We can choose an
arbitrary unit of time for t, and make t = 1S to B =
hypotenuse = sqrt(c^2 +v^2)AndroclesExpires: 28 days
=>
However, clocks can appear to run either slow or fast
depending on whether>they>> are receding or approaching.>Of
course. Doppler shift.> In reality, they don't PHYSICALLY
change at all with movement.>Quite right.>> The term
Ogamma'
is wrong. It cannot contain Ov^2'.>Err...>The
distance the
light moves from S to A is ct.>The distance from A to B is
vt.>The distance from S to B is sqrt([ct]^2 +[vt]^2) by
Pythagoras.>We can choose an arbitrary unit of time for t, and
make t = 1>S to B = hypotenuse = sqrt(c^2 +v^2)>Androcles>What
moves diagonally is not light.The diagonal is just a line
representing the path of an in'nitesimally smallelement of
the
light beam. The beam itself remains vertical but appears to
movesideways in the moving observer's frame. The vertical
component of eachelement's velocity is not affected by
observer movement. How could it be?So Yes, each in'nitesimal
element moves at sqrt(c^2+v^2) along it owndiagonal. It is the
only element that moves along that diagonal. Thereforethere is
no diagonal light beam moving at c. Therefore SR is the
greatest loadof codswallop ever dumped on the human race.Henri
Wilson.See why relativity is
wrong:http://www.users.bigpond.com/HeWn/index.htm
=> So Yes,
each in'nitesimal element moves at sqrt(c^2+v^2) along it
own>
diagonal. It is the only element that moves along that
diagonal. Therefore> there is no diagonal light beam moving at
c. Therefore SR is the greatestload> of codswallop ever dumped
on the human race.Whoa... ease up, there, H! If I'm §ying
a
microlite at 100mph across atennis court (along the net) just
as a 100mph ace is served straight downthe middle, the ball
takes a diagonal path in *my frame of reference*. Theonly
silly part would be if I insisted the ball's speed was
100mph
insteadof 141mph.The light certainly does move diagonally. Of
course, if my clock sloweddown, it would appear to move even
faster, and that's the codswallop :)AndroclesExpires: 28
days
=> So Yes, each in'nitesimal element moves at
sqrt(c^2+v^2) along it own>> diagonal. It is the only element
that moves along that diagonal. Therefore>> there is no
diagonal light beam moving at c. Therefore SR is the
greatest>load>> of codswallop ever dumped on the human
race.>>Whoa... ease up, there, H! If I'm §ying a
microlite at
100mph across a>tennis court (along the net) just as a 100mph
ace is served straight down>the middle, the ball takes a
diagonal path in *my frame of reference*. The>only silly part
would be if I insisted the ball's speed was 100mph
instead>of
141mph.But if a stream of balls was 'red from a machine gun
along that same line, thestream would always remain aligned
vertically in your frame. Each ball wouldmove along its own
diagonal path at sqrt(c^2+v^2). Take that to the limit by
decreasing ball size and increasing frequency and youhave the
Olight ray equivalent'. And, of course, each
ball takes the
same time to reach its target irrespectiveof your speed. No
nonsense about clocks changing rates.>The light certainly does
move diagonally. Of course, if my clock slowed>down, it would
appear to move even faster, and that's the codswallop
:)>Androcles>Sure is! Clock rates are not physically dependent
on velocity. My demo Omovingrame.exe' well
illustrates this
monumental blunder made byEinstein et al. It takes only a few
seconds to run. See also: Overtical.exe'It is
quite obvious
that a diagonally aimed laser beam in the rest observerframe
is NOT identical to an apparently diagonally moving element of
a verticallight ray that moves sideways acros that frame.How
could SRians be so plainly stoopid?Henri Wilson.See why
relativity is
wrong:http://www.users.bigpond.com/HeWn/index.htm
=>> So
Yes, each in'nitesimal element moves at sqrt(c^2+v^2) along
it
own>> diagonal. It is the only element that moves along that
diagonal.Therefore>> there is no diagonal light beam moving at
c. Therefore SR is thegreatest>load>> of codswallop ever dumped
on the human race.>>Whoa... ease up, there, H! If I'm
§ying a
microlite at 100mph across a>tennis court (along the net) just
as a 100mph ace is served straight down>the middle, the ball
takes a diagonal path in *my frame of reference*.The>only
silly part would be if I insisted the ball's speed was
100mphinstead>of 141mph.>> But if a stream of balls was 'red
from a machine gun along that sameline, the> stream would
always remain aligned vertically in your frame. Each
ballwould> move along its own diagonal path at
sqrt(c^2+v^2).>> Take that to the limit by decreasing ball
size and increasing frequencyand you> have the Olight ray
equivalent'.>> And, of course, each ball takes the same time
to reach its targetirrespective> of your speed. No nonsense
about clocks changing rates.>The light certainly does move
diagonally. Of course, if my clock slowed>down, it would
appear to move even faster, and that's the codswallop
:)>Androcles> Sure is! Clock rates are not physically
dependent on velocity.>> My demo
Omovingrame.exe' well
illustrates this monumental blunder made by> Einstein et al.
It takes only a few seconds to run. See
also:'vertical.exe'>>
It is quite obvious that a diagonally aimed laser beam in the
restobserver> frame is NOT identical to an apparently
diagonally moving element of avertical> light ray that moves
sideways acros that frame.>> How could SRians be so plainly
stoopid?>> Henri Wilson.Beats me. I think they get convinced
and then there's no going back. But Iwill tell you
something.
The debates on this newsgroup used to beaetherialists against
relativists. The aetherialists are losing ground, andemission
theory is gaining. Young people are now more convinced that
everbefore that the speed of light is source dependent as
their intuition tellsthem, and not aether dependent. As time
passes relativity will fall intodisrepute, and the younger
ones will investigate a whole new physics, rebornout of
Newton. They'll build accelerators for EM radiation that
will
vastlyimprove interplanetary communication, and someday FTL
probes to investigatedistant stars and their planets. Other
facets, unimaginable to us now, willcome out of it. This I
predict.Glad to have you aboard. Keep the focus on the
newbies, and treat them withlogic. It does no good 'ghting
the
diehards, although I'll agree it can befun.AndroclesExpires:
28
days
=>>So Yes, each in'nitesimal element moves at
sqrt(c^2+v^2) along it own>diagonal. It is the only element
that moves along that diagonal.>Therefore>there is no diagonal
light beam moving at c. Therefore SR is the>greatest>>load>of
codswallop ever dumped on the human race.>>Whoa... ease up,
there, H! If I'm §ying a microlite at 100mph across
a>>tennis
court (along the net) just as a 100mph ace is served straight
down>>the middle, the ball takes a diagonal path in *my frame
of reference*.>The>>only silly part would be if I insisted the
ball's speed was 100mph>instead>>of 141mph.>> But if a
stream
of balls was 'red from a machine gun along that same>line,
the>> stream would always remain aligned vertically in your
frame. Each ball>would>> move along its own diagonal path at
sqrt(c^2+v^2).>> Take that to the limit by decreasing ball
size and increasing frequency>and you>> have the Olight ray
equivalent'.>> And, of course, each ball takes the same time
to reach its target>irrespective>> of your speed. No nonsense
about clocks changing rates.>>The light certainly does
move diagonally. Of course, if my clock slowed>>down, it would
appear to move even faster, and that's the codswallop
:)>>Androcles>> Sure is! Clock rates are not physically
dependent on velocity.>> My demo
Omovingrame.exe' well
illustrates this monumental blunder made by>> Einstein et al.
It takes only a few seconds to run. See
also:>'vertical.exe'>> It is quite obvious
that a diagonally
aimed laser beam in the rest>observer>> frame is NOT identical
to an apparently diagonally moving element of a>vertical>>
light ray that moves sideways acros that frame.>> How could
SRians be so plainly stoopid?>> Henri Wilson.>Beats me. I
think they get convinced and then there's no going back. But
I>will tell you something. The debates on this newsgroup used
to be>aetherialists against relativists. The aetherialists are
losing ground, and>emission theory is gaining. Young people are
now more convinced that ever>before that the speed of light is
source dependent as their intuition tells>them, and not aether
dependent. As time passes relativity will fall into>disrepute,
and the younger ones will investigate a whole new physics,
reborn>out of Newton. They'll build accelerators for EM
radiation that will vastly>improve interplanetary
communication, and someday FTL probes to investigate>distant
stars and their planets. Other facets, unimaginable to us now,
will>come out of it. This I predict.>Glad to have you aboard.
Keep the focus on the newbies, and treat them with>logic. It
does no good 'ghting the diehards, although
I'll agree it can
be>fun.>Androcles>I think there is more to source dependency
than has hitherto been considered.There must be other factors
involved because De Sitter was basically correct.(I know you
will disagree) There is no doubt that many binary pairs
shouldappear differently if straight c+v is correct.As you
know, my H-aether theory attempts to provide ONE explanation.
Lightalways leaves a source at c but changes speed as it
travels, due to bothgravity gradients and weak interaction
with other EM. This seems the only way to explain how all
photons can travel through space ata (nearly) common velocity.
Relativity certainly provides no solution to this,even though
know-alls like Dick the Fumble would like to believe it does.
In the case of binary pairs, is there a chance that light
speed from each issomehow in§uenced by other factors. For
instance, might the centre of gravityof the pair somehw enter
the picture? Henri Wilson.See why relativity is
wrong:http://www.users.bigpond.com/HeWn/index.htm
Glad to have you aboard. Keep the focus on the newbies, and
treat them with> logic.A 'ne pair
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/
AndersenLogic.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/
LogicBull.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/
Gibberish.html
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/
Cornered.htmlDirk Vdm
=Suppose x1,x2,...,xn is a random
permutation of 1,...,n.Now sweep through x1,x2,...,xn
left-to-right, looking for 1,...,n in increasing order. Let m
be the greatest value found in the sweep. If m < n, sweep
again, looking for m+1,...,n. Repeat until n is
found.Example:Sweep 864513729----- --------- 1 1 2 2 3 3 45 4
6 7 5 8 9What is the distribution of the number of sweeps?
I.e., if S is the number of sweeps, what is
Pr(S=s)(s=1,...,n)?
=> Suppose x1,x2,...,xn is a random
permutation of 1,...,n.> Now sweep through x1,x2,...,xn
left-to-right, looking for > 1,...,n in increasing order. Let
m be the greatest value > found in the sweep. If m < n, sweep
again, looking for > m+1,...,n. Repeat until n is found.
Example:> Sweep 864513729> ----- ---------> 1 1 2> 2 3> 3 45>
4 6 7> 5 8 9 What is the distribution of the number of sweeps?
I.e., > if S is the number of sweeps, what is
Pr(S=s)(s=1,...,n)?I am not sure, but I think this has
something to do with
Euleriannumbers:http://mathworld.wolfram.com/
EulerianNumber.html(Do not confuse with Euler numbers!)I do
not know if the Mathworld info is correct, nor if the info
wouldbe helpful anyway, but this is probably a good start to
=>
Suppose x1,x2,...,xn is a random permutation of 1,...,n.> Now
sweep through x1,x2,...,xn left-to-right, looking for >
1,...,n in increasing order. Let m be the greatest value >
found in the sweep. If m < n, sweep again, looking for >
m+1,...,n. Repeat until n is found. Example:> Sweep 864513729>
----- ---------> 1 1 2> 2 3> 3 45> 4 6 7> 5 8 9 What is the
distribution of the number of sweeps? I.e., > if S is the
number of sweeps, what is Pr(S=s)(s=1,...,n)? > I am not sure,
but I think this has something to do with Eulerian> numbers:
http://mathworld.wolfram.com/EulerianNumber.htmlYes! I
didn't
know the terminology, but it seems that my sweeps are properly
called permutation
runs:http://mathworld.wolfram.com/
PermutationRun.htmlApparently, P(S=k) = A(n,k)/n!
(k=1..n)where the A(n,k) are Eulerian numbers given byA(n,1) =
A(n,n) = 1A(n,k) = (n-k+1) A(n-1,k-1) + k A(n-1,k),
k=2,...,n-1.r.e.s.
=>Suppose x1,x2,...,xn is a random
permutation of 1,...,n.>Now sweep through x1,x2,...,xn
left-to-right, looking for >1,...,n in increasing order. Let m
be the greatest value >found in the sweep. If m < n, sweep
again, looking for >m+1,...,n. Repeat until n is
found.>Example:>Sweep 864513729>----- ---------> 1 1 2> 2 3> 3
45> 4 6 7> 5 8 9>What is the distribution of the number of
sweeps? I.e., >if S is the number of sweeps, what is
Pr(S=s)(s=1,...,n)?I have not been able to get a complete
solution of theproblem. However, there are partial results.The
distribution is symmetric. That is, since a permutationand its
reverse have their number of sweeps adding up ton+1, P(S=s) =
P(S = n+1-s).For the following, observe that we do not need
that thex's be the integers, but any n ordered objects will
do,and a sweep still consists of the number of
consecutiveobjects, starting from the smallest. So let G_n(t)
bethe generating function of the sweeps from n objects,i.e.,
G_n(t) = sum P_n)(S=s)*t^n. If the 'rst elementof the
permutation is k, the contribution to G_n is P_{n-1}(t)/n,
k=1; t*P_{n-1}(t)/n, k=n; P_{k-1}(t)*P_{n-k}(t)/n, 1 < k <
n.So n*P_n(t) = (1+t)*P_{n-1}(t) + sum
P_{k-1}(t)*P_{n-k}(t).If we multiply this by z^{n-1} and sum,
and let Q(t,z) = sum P_n(t)*z^n, we get Q' - t = (1+t)*Q +
Q^2,differentiating being on z. I have not succeeded in
getting the appropriate solution.The 'rst few generating
functions are: 1 t 2 (t + t^2)/2! 3 (t + 4t^2 + t^3)/3! 4 (t +
11t^2 + 11t^3 + t^4)/4! 5 (t + 26t^2 + 66t^3 + 26t^4 +
t^5)/5!-- This address is for information only. I do not claim
that these viewsare those of the Statistics Department or of
Purdue University.Herman Rubin, Department of Statistics,
Purdue University
=>Suppose x1,x2,...,xn is a random
permutation of 1,...,n.>Now sweep through x1,x2,...,xn
left-to-right, looking for >1,...,n in increasing order. Let m
be the greatest value >found in the sweep. If m < n, sweep
again, looking for >m+1,...,n. Repeat until n is
found.Example:>Sweep 864513729>----- ---------> 1 1 2> 2 3> 3
45> 4 6 7> 5 8 9What is the distribution of the number of
sweeps? I.e., >if S is the number of sweeps, what is
Pr(S=s)(s=1,...,n)? I have not been able to get a complete
solution of the> problem. However, there are partial results.
The distribution is symmetric. That is, since a permutation>
and its reverse have their number of sweeps adding up to> n+1,
P(S=s) = P(S = n+1-s). For the following, observe that we do
not need that the> x's be the integers, but any n ordered
objects will do,> and a sweep still consists of the number of
consecutive> objects, starting from the smallest. So let
G_n(t) be> the generating function of the sweeps from n
objects,> i.e., G_n(t) = sum P_n)(S=s)*t^n. If the 'rst
element> of the permutation is k, the contribution to G_n is
P_{n-1}(t)/n, k=1;> t*P_{n-1}(t)/n, k=n;>
P_{k-1}(t)*P_{n-k}(t)/n, 1 < k < n. So n*P_n(t) =
(1+t)*P_{n-1}(t) + sum P_{k-1}(t)*P_{n-k}(t). If we multiply
this by z^{n-1} and sum, and let > Q(t,z) = sum P_n(t)*z^n, we
get Q' - t = (1+t)*Q + Q^2, differentiating being on z. I
have
not succeeded in > getting the appropriate solution. The 'rst
few generating functions are: 1 t> 2 (t + t^2)/2!> 3 (t + 4t^2
+ t^3)/3!> 4 (t + 11t^2 + 11t^3 + t^4)/4!> 5 (t + 26t^2 + 66t^3
+ 26t^4 + t^5)/5!This and Leroy Quet's reply make the
connection to the Eulerian number triangle:11 1 1 4 1 1 11 11
11 26 66 26 1
...http://mathworld.wolfram.com/EulerianNumber.htmlr.e.s.
=
How long has the relation between complex numbers and
particular 2x2matrixes been known?Are there any future plans
to Ophase out' complex numbers and replacethem
with 2x2
matrixes which work exactly the same?(...Starblade Riven
Darksquall...)
=> How long has the relation between complex
numbers and particular 2x2> matrixes been known?As long as
matrices have been studied.> Are there any future plans to
Ophase out' complex numbers and replace> them
with 2x2
matrixes which work exactly the same?No.-- Robin Chapman,
www.maths.ex.ac.uk/~rjc/rjc.htmlNeedless to say, I had the
last laugh. Alan Partridge, _Bouncing Back_ (14 times)
=>
Are there any future plans to Ophase out'
complex numbers and
replace> them with 2x2 matrixes which work exactly the same?
No.How do you know?
=> Are there any future plans to
Ophase out' complex numbers and replace>> them
with 2x2
matrixes which work exactly the same?>> No.>>How do you know?I
don't know how he knows, but your question leads to
thequestion: Suppose that we had in fact replaced complex
numberswith those matrices that work exactly the same. Since
theywork exactly the same, how would we know that this had
happened?David C. Ullrich
=>Are there any future plans to
Ophase out' complex numbers and replace>them
with 2x2 matrixes
which work exactly the same?>No.>>How do you know?> I don't
know how he knows, but your question leads to the> question:
Suppose that we had in fact replaced complex numbers> with
those matrices that work exactly the same. Since they> work
exactly the same, how would we know that this had >
happened?Sounds like something out of a Steven Wright comedy
routine.But the part I'm trying to 'gure out
is, what are
future plans, andhow do they differ from ordinary plans?--
Judge Yohn's mistakes revealed in Mumia Abu-Jamal
ruling.<http://www.commoncouragepress.com/index.cfm?action=
book&bookid=228>
=>But the part I'm trying to 'gure out is,
what are future plans, and>how do they differ from ordinary
plans?--begin excerpt from a post to sci.skeptic in 1993-- In
his essay on Irreversibility in _Surprises in Theoretical
Physics_, We may try to analyze the problem somewhat more
deeply by asking why it is that we can easily perform
experiments in which initial conditions have to be speci'ed,
but never any requiring terminal conditions. This is the real
distinction between past and future. A little thought shows
that this is connected with the fact that we can remember the
past, and that we can make plans for the future, but not vice
versa. It is evident that these statements are correct, but
they do not follow from any known laws of physics. We could
speculate that these facts have something to do with the way
our brain functions, but we have no way of explaining the
origin of this one-sidedness. We must not, of course, try to
attribute it to some thermodynamic irreversibility in our
brain cells, because this would amount to invoking the Second
Law in a study aimed at understanding the origin of the Second
Law, and we would have a circular argument.--end excerpt--HTH.
HAND!Lee Rudolph
=>Are there any future plans to Ophase
out' complex numbers and replace>them with 2x2 matrixes
which
work exactly the same?>No.>>How do you know?> I don't
know how he knows, but your question leads to the> question:
Suppose that we had in fact replaced complex numbers> with
those matrices that work exactly the same. Since they> work
exactly the same, how would we know that this had > happened?
Sounds like something out of a Steven Wright comedy routine.
But the part I'm trying to 'gure out is, what
are future
plans, and> how do they differ from ordinary plans?What I mean
is, say there are futuree plans to phase out the Englishsystem
in America. We'd start by using both the English system
andAmerican system. But we're certainly not going to just
get
rid of theEnglish system just like that. That's what
I'm
saying.At least, what we should recognize is that complex
numbers and theirreal 2x2 matrix counterparts are identical in
function, as long as weremember that when we imbed 2x2 matrixes
in larger matrixes, that thetransposing in the classical system
should not disturb the inner 2x2matrixes, and the conjugatation
in the classical syswtem should notpurturb the position of the
2x2 matrixes but would transpose eachindividual 22 matrix, and
combining a transpose with a conjugation inthe classical system
is equivilent to just using a regulartranspotition of the
entire matrix in the new system.Also, this means that all
matrixes using trans-real numbers can bereduced to larger
matrixes which use real numbers, either meaning thatreal
matrixes are the only things that exist, or all types
ofmatrixes, using real numbers only, using complex numbers,
quaternions,et cetera, are acceptable.(...Starblade Riven
Darksquall...)
=>Are there any future plans to Ophase
out' complex numbers and replace>them with 2x2 matrixes
which
work exactly the same?>No.>>How do you know?> I don't
know how he knows, but your question leads to the> question:
Suppose that we had in fact replaced complex numbers> with
those matrices that work exactly the same. Since they> work
exactly the same, how would we know that this had > happened?
Sounds like something out of a Steven Wright comedy routine.
But the part I'm trying to 'gure out is, what
are future
plans, and> how do they differ from ordinary plans? What I
mean is, say there are futuree plans to phase out the English>
system in America. We'd start by using both the English
system
and> American system. But we're certainly not going to just
get rid of the> English system just like that. That's what
I'm
saying.> Whops! I meant the English system and the METRIC
system. Also, this isjust an analogy, this isn't what I
meant
by future plans.(...Starblade Riven Darksquall...)
matrixes)
=>>Are there any future plans to Ophase out'
complex numbers and replace>them with 2x2 matrixes which work
exactly the same?>>No.>How do you know?>> I don't know how
he knows, but your question leads to the> question: Suppose
that we had in fact replaced complex numbers> with those
matrices that work exactly the same. Since they> work exactly
the same, how would we know that this had> happened?>> Sounds
like something out of a Steven Wright comedy routine.>> But
the part I'm trying to 'gure out is, what are
future plans,
and> how do they differ from ordinary plans? What I mean is,
say there are futuree plans to phase out the English> system
in America. We'd start by using both the English system and>
American system. But we're certainly not going to just get
rid
of the> English system just like that. That's what
I'm
saying.lol. Americans are not smart enough to deal with
complex numbers?Wilbert
= >Are there any future plans to
Ophase out' complex numbers and replace>them
with 2x2 matrixes
which work exactly the same?>No.>>How do you know?> I
don't know how he knows, but your question leads to the>
question: Suppose that we had in fact replaced complex
numbers> with those matrices that work exactly the same. Since
they> work exactly the same, how would we know that this had>
happened?>> Sounds like something out of a Steven Wright
comedy routine.>> But the part I'm trying to
'gure out is,
what are future plans, and> how do they differ from ordinary
plans? What I mean is, say there are futuree plans to phase
out the English> system in America. We'd start by using both
the English system and> American system. But we're certainly
not going to just get rid of the> English system just like
that. That's what I'm saying. lol. Americans
are not smart
enough to deal with complex numbers? WilbertThat's not what
I'm saying.Also, can we have things such as e^(quat) or
ln(quat) where quat is aquaternion? Has anybody ever 'gured
out how to do this? Also, whatabout using lie algebras which
work on quaternions?(...Starblade Riven
Darksquall...)
=>Also, can we have things such as e^(quat)
or ln(quat) where quat is a>quaternion? Has anybody ever
'gured out how to do this? Exponentials, and logarithms of
invertible elements, exist in any Banach algebra. Look up
holomorphic functional calculus.Robert Israel
israel@math.ubc.caDepartment of Mathematics
http://www.math.ubc.ca/~israel University of British Columbia
Vancouver, BC, Canada V6T 1Z2
=