Re: [OT] Re: [9fans] Getting started in Plan9 - help

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[presotto]

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Gosh, I moved into computing because I wasn't smart
enough for anything else.

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From: "Douglas A. Gwyn" <DAGwyn@null.net>
To: 9fans@cse.psu.edu
Subject: Re: [OT] Re: [9fans] Getting started in Plan9 - help
Date: Thu, 31 Jan 2002 01:10:31 -0500
Message-ID: <3C58DFD7.33AFB32B@null.net>

Non-conservation of parity is usually discussed under "CPT",
which should be in the index of many textbooks, predating the Web.
My assessment of the analytical error dates back to around 1967 but
has not been published.  In fact I got out of physics as a profession
mainly because my attempts to publish (other) theoretical work met
with repeated opposition from reviewers who did not want to
recognize that they had been chasing chimeras.  I didn't want to
be frustrated my whole career, so I moved into computing instead.

Re: [9fans] Getting started in Plan9 - help

[Dan Cross]

> In formal languages theory, "product" is usually concatenation,
> "exponentiation" is repeated concatenation.  (For example, one says
> that a DFA can scan A^n but not A^n B^n; one says that a context free
> grammar can parse A^n B^n but not A^n B^n C^n.)

Whoops, I should have realized that's what you were refering to.  My bad.

	- Dan C.

Re: [9fans] Getting started in Plan9 - help

[Boyd Roberts]

> In formal languages theory, "product" is usually concatenation,
> "exponentiation" is repeated concatenation.

Depends on your domain.  In mathematics a product could be a dot
[rc's ^] or a cross product [trickier].

Re: [9fans] Getting started in Plan9 - help

[Douglas A. Gwyn]

Boyd Roberts wrote:
> Depends on your domain.  In mathematics a product could be a dot
> [rc's ^] or a cross product [trickier].

There are all sorts of "products" in mathematics,
but the so-called "cross product" is one of the least qualified
to go by that name.

[OT] Re: [9fans] Getting started in Plan9 - help

[paurea]

Douglas A. Gwyn writes:
 > There are all sorts of "products" in mathematics,
 > but the so-called "cross product" is one of the least qualified
 > to go by that name.

I don't think so. It is the dual of the sesquilineal projection of the
tensorial product. I couln't resist writing it. :-)

The fact that it is anticonmutative doesn't stop it being a product,
it distributes with the sum and has an absorbing element (I don't know if
it is called so in English) and has all sorts of properties which make it a
product.

--
                 Saludos,
                         Gorka

"Curiosity sKilled the cat"

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[Thomas Bushnell, BSG]

paurea@gsyc.escet.urjc.es writes:

> The fact that it is anticonmutative doesn't stop it being a product,
> it distributes with the sum and has an absorbing element (I don't know if
> it is called so in English) and has all sorts of properties which make it a
> product.

I think "absorbing element" in English is just called "zero" (if I'm
guessing right at what you mean).  In whatever ring, the additive
identity is always called "zero".

Thomas

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[Douglas A. Gwyn]

paurea@gsyc.escet.urjc.es wrote:
> I don't think so. [The "cross product"] is the dual of the
> sesquilineal projection of the tensorial product. ...

As usually defined the c.p. is supposed to result in the same
type as its arguments, but e.g. the c.p. of two vectors is
*not* a vector (it's a so-called pseudo- or axial vector,
which can indeed be thought of as a *component* of the tensor
product).  So while it might be a "product" it is not as nice
as the kinds of products that map from space x space into space.
The "non-conservation of parity" work that was awarded a Nobel
prize seems to actually have been confusion on this very score.

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[paurea]

Douglas A. Gwyn writes:
 > As usually defined the c.p. is supposed to result in the same
 > type as its arguments, but e.g. the c.p. of two vectors is
 > *not* a vector (it's a so-called pseudo- or axial vector,

Well, as everything, depends on what you call type. Everything here
are Tensors at least. (and also vectors, because tensor spaces are
vector spaces).

Anyway I think you confusing the c.p. with the wedge product which is
it's dual in an special case. As far as I know the c.p. of two vectors
is a vector. In fact, it is the special case of aplying the dual
operator to the wedge product with N=3 and r=2, that is, the result is
also a vector in the same space, that is why it is called vector
product too.

The tensors which written as a wedge product form a tensor are called its
strict components (I think you are referring to that). Anyway, the
wedge product of a group of tensors is a tensor too. And *all* of this
operations are called products, though that is exterior algebra and maybe
the analogy has been taken a little bit too far.

--
                 Saludos,
                         Gorka

"Curiosity sKilled the cat"

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[Thomas Bushnell, BSG]

paurea@gsyc.escet.urjc.es writes:

> Well, as everything, depends on what you call type. Everything here
> are Tensors at least. (and also vectors, because tensor spaces are
> vector spaces).

Two tensors are of the same type if they have the same formal
character: that is, the same rank (and, if you are allowing covectors,
then the same rank and the same indexes "up" and "down").

> Anyway I think you confusing the c.p. with the wedge product which is
> it's dual in an special case. As far as I know the c.p. of two vectors
> is a vector.

Only in three dimensions.

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[Douglas A. Gwyn]

paurea@gsyc.escet.urjc.es wrote:
> Anyway I think you confusing the c.p. with the wedge product which is
> it's dual in an special case.

No, read on...

> As far as I know the c.p. of two vectors is a vector.

No, it is not, and the fact that people treat it as one is the problem.
The *geometric object* that is the closest thing to the c.p. is a skew
tensor (practically the same as wedge product), which (only) in 3D has
Cartesian components that resemble those of a vector, *except* that
this pseudo-vector *flips* under reflection (unlike a genuine vector).
Unfortunately, physicists have been trained to express Maxwell's laws
as a relationship between a genuine vector (field) and a c.p., which
means that that expression of those laws *changes* under reflection,
something that physicists are *not* taught and which appears to have
been overlooked in the analysis of the (nonconservation of) parity
experiment.

Apologies for being off-topic, but the subject arose in this group..

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[Thomas Bushnell, BSG]

"Douglas A. Gwyn" <DAGwyn@null.net> writes:

> As usually defined the c.p. is supposed to result in the same
> type as its arguments, but e.g. the c.p. of two vectors is
> *not* a vector (it's a so-called pseudo- or axial vector,
> which can indeed be thought of as a *component* of the tensor
> product).  So while it might be a "product" it is not as nice
> as the kinds of products that map from space x space into space.
> The "non-conservation of parity" work that was awarded a Nobel
> prize seems to actually have been confusion on this very score.

Sure enough.  The cross product as tensor-product-with-volume-element
makes this even clearer; the result of the "product" is actually a
higher rank tensor than the arguments.

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[Andrew Simmons]

>The "non-conservation of parity" work that was awarded a Nobel
>prize seems to actually have been confusion on this very score.
>
Apologies to the group for wasting bandwidth, but I'd be interested if you
could provide a pointer to somewhere I could find out more about this
(amateur's interest, having done a PhD in this stuff years ago).

Thanks

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[George Michaelson]

>>The "non-conservation of parity" work that was awarded a Nobel
>>prize seems to actually have been confusion on this very score.
>>
>Apologies to the group for wasting bandwidth, but I'd be interested if you
>could provide a pointer to somewhere I could find out more about this
>(amateur's interest, having done a PhD in this stuff years ago).
>
>Thanks

Martin Gardiner wrote this up years ago in a Pelican. If you search on
his name at amazon for:

	"The Ambidextrous Universe"


You'll find the re-issue brought up to date.

cheers
	-George

You'll find the information.

cheers
	-George

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[Douglas A. Gwyn]

Non-conservation of parity is usually discussed under "CPT",
which should be in the index of many textbooks, predating the Web.
My assessment of the analytical error dates back to around 1967 but
has not been published.  In fact I got out of physics as a profession
mainly because my attempts to publish (other) theoretical work met
with repeated opposition from reviewers who did not want to
recognize that they had been chasing chimeras.  I didn't want to
be frustrated my whole career, so I moved into computing instead.

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[Lucio De Re]

On Thu, Jan 31, 2002 at 12:28:13AM -0500, Douglas A. Gwyn wrote:
>
> [ ... ] I didn't want to
> be frustrated my whole career, so I moved into computing instead.

Huh?!

++L

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[Douglas A. Gwyn]

Lucio De Re wrote:
> Huh?!

Drat, that was the second time I tried to reply to "sender" in
Netscape and had it go to Reply-To rather than to From (Andrew).

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[Lucio De Re]

On Thu, Jan 31, 2002 at 09:43:15AM +0000, Douglas A. Gwyn wrote:
>
> Lucio De Re wrote:
> > Huh?!
>
> Drat, that was the second time I tried to reply to "sender" in
> Netscape and had it go to Reply-To rather than to From (Andrew).

Well, you made it sound like computing was less frustrating than
mainline physics.  Heard any good M$ jokes lately?

++L

PS: I dunno about comp.os.plan9 but 9fans is pleasantly tolerant of
off-topic discussion, I vote to keep it that way.

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[Douglas A. Gwyn]

Lucio De Re wrote:
> Well, you made it sound like computing was less frustrating than
> mainline physics.  Heard any good M$ jokes lately?

Undoubtedly *some* aspects of computing are frustrating
(how about everybody who tries to get Plan 9 working on
unsupported hardware?), but I don't find the whole
*profession* frustrating.  At least not until mandatory
certification, which is something that we're threatened
with every so often.

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[Boyd Roberts]

"Douglas A. Gwyn" wrote:
> ... I didn't want to
> be frustrated my whole career, so I moved into computing instead.

Another physics / comp sci swap.  Interesting.

I think we have 3 or 4 here.

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[Douglas A. Gwyn]

Non-conservation of parity is usually discussed under "CPT",
which should be in the index of many textbooks, predating the Web.
My assessment of the analytical error dates back to around 1967 but
has not been published.  In fact I got out of physics as a profession
mainly because my attempts to publish (other) theoretical work met
with repeated opposition from reviewers who did not want to
recognize that they had been chasing chimeras.  I didn't want to
be frustrated my whole career, so I moved into computing instead.

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[Thomas Bushnell, BSG]

DAGwyn@null.net (Douglas A. Gwyn) writes:

> Non-conservation of parity is usually discussed under "CPT",
> which should be in the index of many textbooks, predating the Web.
> My assessment of the analytical error dates back to around 1967 but
> has not been published.

So the usual rule (as I was taught it) is that parity alone is not
conserved, but the product of parity, time, and charge is conserved.
(Perhaps I've got that slightly wrong.)  Is this not actually correct?
Gardner says roughly what I said.

So are there references that back up what you are saying, that this is
not in fact the case?

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[Douglas A. Gwyn]

"Thomas Bushnell, BSG" wrote:
> So are there references that back up what you are saying, ...

What I am saying is that if parity was *not* conserved, the
theoretical analysis behind the famous experiments (on weak
decay) did not demonstrate it, due to not accounting for the
non-vectorial nature of the c.p. in the form of Maxwell's laws
used in the analysis.

I have my own reasons to think that mirror symmetry *has* to
be a fundamental property of physics and that any asymmetry
is environmentally induced.

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[Thomas Bushnell, BSG]

"Douglas A. Gwyn" <DAGwyn@null.net> writes:

> What I am saying is that if parity was *not* conserved, the
> theoretical analysis behind the famous experiments (on weak
> decay) did not demonstrate it, due to not accounting for the
> non-vectorial nature of the c.p. in the form of Maxwell's laws
> used in the analysis.

Gotcha.  Where can I read about it?

> I have my own reasons to think that mirror symmetry *has* to
> be a fundamental property of physics and that any asymmetry
> is environmentally induced.

Sure, I think that's why the original result was so
counter-intuitive.  There are profound metaphysical reasons to insist
on certain physical symmetries.

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[Thomas Bushnell, BSG]

"Douglas A. Gwyn" <DAGwyn@null.net> writes:

> The "non-conservation of parity" work that was awarded a Nobel
> prize seems to actually have been confusion on this very score.

Um, the non-conservation of parity is part of the assymetry of certain
weak decay modes, right?