Let Q = {1, -1, i, -i, j, -j, k, -k}
It is clear that the only NTP (non-trivial proper) subgroups of Q have order 2 or 4 and are:
H = {1, -1} ~= C_2
I = {1, i, -1, -i} ~= C_4
J = {1, j, -1, -j} ~= C_4
K = {1, k, -1, -k} ~= C_4
Therefore, no two NTP subgroups have trivial intersection, and all of them are normal. Therefore there is no (direct or) semidirect product of groups which is equal to Q.
However I do notice that Q = IJ. Therefore I am led to wonder: is there a general product corresponding to this fact?
Here are my initial thoughts on such a product:
1) Internally, it is a product of two subgroups with nontrivial intersection.
2) As |I| = |J| = 4, the underlying set from the external product could not be IxJ (as with the direct/semidirect products) since this would have order 16. However, the actual underlying set could be IxJ quotiented out by an equivalence relation dependent on the elements in the intersection InJ.
Is there a known product corresponding to this situation?
Bicrossproducts.
-- m
Please try to hit the carriage return after every 65-75 characters;
MathForum does not format its messages properly, resulting in lines
that either run off the right edge of the screen, or wrap around and
are difficult to read.
>Let Q = {1, -1, i, -i, j, -j, k, -k}
>
>It is clear that the only NTP (non-trivial proper) subgroups of Q
>have order 2 or 4 and are:
>
>H = {1, -1} ~= C_2
>I = {1, i, -1, -i} ~= C_4
>J = {1, j, -1, -j} ~= C_4
>K = {1, k, -1, -k} ~= C_4
>
>Therefore, no two NTP subgroups have trivial intersection, and all of
>them are normal. Therefore there is no (direct or) semidirect product
>of groups which is equal to Q.
>
>However I do notice that Q = IJ. Therefore I am led to wonder: is
>there a general product corresponding to this fact?
Given two subgroups H and K, the set HK = {hk : h in H, k in K} is a
subgroup if and only if HK=KH. We say G is the product of two
subgroups if G = HK for some subgroups H and K. There is a fair amount
of work on groups which have such decompositions when you place
restrictions on the subgroups H and K (e.g., groups that are the
product of two abelian subgroups, like Q above).
>Here are my initial thoughts on such a product:
>1) Internally, it is a product of two subgroups with nontrivial
>intersection.
>2) As |I| = |J| = 4, the underlying set from the external product
>could not be IxJ (as with the direct/semidirect products) since this
>would have order 16. However, the actual underlying set could be IxJ
>quotiented out by an equivalence relation dependent on the elements
>in the intersection InJ.
>
>Is there a known product corresponding to this situation?
The product of subgroups. If either H or K is normal and maximal, then
G = HK provided H and K are distinct, but the condition is far from
necessary.
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================
Arturo Magidin
magidin-at-member-ams-org
I am familiar with this product of subgroups, it being the underlying idea behind the internal direct/semidirect product. However, I was really looking more for a product with an external analogue, probably more specialised than the product of subgroups. AFAIK the product of subgroups in general does not have an external analogue.
This is interesting. I have not heard of such a product before, but a Google search returns many results on Hopf Algebras, and not much really about groups. Perhaps you could provide a reference? In any case I am going to be working on this problem myself over the next few days and I will let you know how I get on.
As I said, the construction you are looking for is
the bicrossproduct.
Given groups H and K, a left action
of K on the set H and a right action of H on the set K
satisfying appropriate compatibility conditions, you can
provide the set H x K with a unique group structure
such that the subsets H x {1} and {1} x K are
subgroups isomorphic to H and K, respectively,
in the obvious way, and every element of H x K
is the product of one from H x {1} and one from {1} x K,
in that order.
The compatibility conditions for the two actions,
you can deduce from the situation of a factorization
G = HK of a group into the product of two groups.
The way the multiplication on H x K is defined
in terms of these two actions also can be seen
from that.
This construction, and its Hopf-theoretic analogues,
are quite popular in the context of quantum groups.
See, for example, Kassel's book on Quantum Groups
for a detailed presentation of the construction
in the case of groups.
-- m
But, as I said in my original post, Q = IJ but |IxJ| = 16. Therefore no set based on IxJ can be isomorphic to Q (since |Q| = 8).
So it is not really a question of providing HxK with a group operation, it is finding some equivalence relation ~ on HxK such that (HxK)/~ forms a group under some operation on there.
> The compatibility conditions for the two actions,
> you can deduce from the situation of a factorization
> G = HK of a group into the product of two groups.
> The way the multiplication on H x K is defined
> in terms of these two actions also can be seen
> from that.
>
> This construction, and its Hopf-theoretic analogues,
> are quite popular in the context of quantum groups.
> See, for example, Kassel's book on Quantum Groups
> for a detailed presentation of the construction
> in the case of groups.
Since you do not give the construction explicitly, it is quite hard for me to analyse. I think that Quantum Groups do seem interesting, but I have always found them very hard, and probably a bit too advanced for me at my current level.
>
> -- m
The quotienting step is often called "amalgamation", but
the specific product you have here is not terribly well
behaved. At least I normalizes J, so you can construct
the semidirect product I |x J of order 16, and then
amalgamate the two subgroups of order 2 (since I and J
both normalize both subgroups of order 2 in the semidirect
product).
This takes <a,b:a^4=b^4=1, [a,b]=b^2> and adds a single
relation a^2=b^2, giving a standard presentation for
the quaternion group.
A more common version of this handles groups such as
< a,b,x,y,z : a^2 = b^2 = x^2 = y^2 = [a,b] = [x,y] = z,
z^2 = [a,x] = [a,y] = [b,x] = [b,y] = 1 >
which is a product of commuting normal subgroups <a,b,z>
and <x,y,z>, both quaternion groups. This is called a
central product, and is described in most group theory
texts. It has an external version, but it just says
to take a direct product and amalgamate subgroups of
the centers of the factors.
I mentioned Quantum Groups simply for context;
the book by Kassel has a section on bicrossed products
which he uses as an example of a `classical' construction
and which is completely elementary and absolutely
independent on anything else.
Have you tried arXiv?
The simplest search gives me <http://front.math.ucdavis.edu/
0703.5471>,
for example.
-- m
Again, PLEASE hit the carriage return when you get to about 65-70
characters. DO NOT rely on Mathforum's editor to break up your lines:
it doesn't do it properly. Your reply was one long line that ran off
the right edge of my screen.
>I am familiar with this product of subgroups, it being the underlying
>idea behind the internal direct/semidirect product.
No, it is not. Because nowhere was there a requirement that H and K
intersect trivially.
I think it is a problem with your web browser. For example my most recent post at
http://mathforum.org/kb/message.jspa?messageID=6223261
looks fine to me. Perhaps upgrade to the latest version of IE or Firefox?
> >I am familiar with this product of subgroups, it
> being the underlying
> >idea behind the internal direct/semidirect product.
>
> No, it is not. Because nowhere was there a
> requirement that H and K
> intersect trivially.
>
Yes, I was not saying that the example I gave was a direct/semidirect product, only that the product of subgroups is the underlying idea behind those products (with the extra condition that they have trivial intersection and that one/both subgroups be normal).
> --
> ======================================================
> ================
> "It's not denial. I'm just very selective about
> what I accept as reality."
> --- Calvin ("Calvin and Hobbes" by Bill
> Bill Watterson)
> ======================================================
> ================
>
> Arturo Magidin
> magidin-at-member-ams-org
>
I am surprised, normally groups of small order exhibit quite good behaviour.
> At least I normalizes J, so you can
> construct
> the semidirect product I |x J of order 16, and then
> amalgamate the two subgroups of order 2 (since I and
> J
> both normalize both subgroups of order 2 in the
> semidirect
> product).
>
> This takes <a,b:a^4=b^4=1, [a,b]=b^2> and adds a
> single
> relation a^2=b^2, giving a standard presentation for
> the quaternion group.
>
>
I was expecting this to occur, since the standard presentation for Q is relatively straightforward. In any case I have found several papers referencing this amalgamation concept, and will enjoy reading up about it.
Allow me to explain perhaps a little more formally what gives me this notion. Normally, with a direct or semidirect product of subgroups H and K, we have |HxK| = |HK|. It is certainly not surprising here that |IJ| = |IxJ|/|InJ|, because this is just the formula for the size of the product of subgroups, which is easily derivable from the theory of fibres.
However, in the direct/semidirect product case, we have that the sequence of elements of HK is just a simple re-ordering of the sequence of elements "hk : (h,k) e HxK". Since this is not true for Q, we look at what elements of the latter sequence are equal, and we find:
[a]
(1)(-1) = (-1)(1) = -1
[b]
(1)(1) = (-1)(-1) = 1
[c]
jk = (-j)(-k) = i
ij = (-i)(-j) = k
ki = (-k)(-i) = j
[d]
i(-1) = (-i)(1) = -i
[e]
(-1)j = (1)(-j) = -j
[f]
i(-j) = (-i)j = -k
My intuition is based on the role of (-1) in these equalities. In particular, the following properties of the element give exactly the equalities stated above:
[a] (-1) e InJ
[b] (-1) has order 2
[c] (-1) has order 2
[d] (-1) commutes with every element
[e] (-1) e InJ
[f] (-1) commutes with every element
So now let G be a group, H,K subgroups, x e HnK a non-identity element of order 2 which commutes with every other element. Can we then make such a product once more?
And further, can we generalise this, by:
i) Allowing other orders than just 2?
ii) Alllowing more than one non-identity element in the intersection?
there is a construction known as
the generalised quaternion algebra construction
given a field k (char(k) =/= 2)
and two elements a, b of the multiplicative group k^x
one defines two elements i, j with
i^2 = a
j^2 = b
ij = -ji
this construction plays a prominent role
in the theory of division algebras
and central simple algebras
{1, i, j, ij} is known as the quaternion basis
also note that
central simple algebras containing a galois splitting field
are crossed products
which is the fundamental construction you point out
(also sometimes called crossproducts or smash products)
(they are also bicrossed products
as others have pointed out
but the additional structure is not needed here)
although kassel has been mentioned
perhaps shahn majid's text is better here
though he uses a much looser language
because he does explore more of the relevant properties
for a deeper text
that explores the relationship of quaternion algebras
and this construction
to the deeper questions of division algebras
and brings the topic up to the level of motivic cohomology
the great text
"central simple algebras and galois cohomolgy"
by gille and szamuely
cannot be recommended enough
i just finished this text recently
and have not been able to stop referring back to it
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
I don't read the newsgroup through a browser. That's part of the
problem. Not everyone reads the newsgroup through a browser, or
through (bleach) MathForum.
The problem is MathForum's formatting, not me.
>For example my most recent post at
>http://mathforum.org/kb/message.jspa?messageID=6223261
>looks fine to me.
You are looking at the message through MathForum; Mathforum's
formatting reads okay through MathForum, of course, but the point is
that not everyone uses MathForum (or a web-browser) to read the
newsgroup.
Compare the SOURCE message, for example, with Google:
http://groups.google.com/group/sci.math/msg/2ee7aba4bccc8c5d?dmode=source
Now look at my message, and see how my text does not keep going to the
right.
http://groups.google.com/group/sci.math/msg/50b1d566cd55f437?dmode=source
>Perhaps upgrade to the latest version of IE or Firefox?
I ->am<- using the latest version of Firefox, son. Thank you for your
"tip".
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
>So now let G be a group, H,K subgroups, x e HnK a non-identity
>element of order 2 which commutes with every other element. Can we
>then make such a product once more?
>
>And further, can we generalise this, by:
>i) Allowing other orders than just 2?
>ii) Alllowing more than one non-identity element in the intersection?
There are plenty of ways to do this. One is the "central product", if
you want elements of H to commute with elements of K.
Let H and K be any two groups; let
Z(H) = { h in H : hx = xh for all x in H} (the center of H)
Z(K) = { k in K : ky = yk for all y in K}.
Let A be an abelian group, and suppose there are one-to-one
homomorphisms f:A->Z(H) and g:A->Z(K) (i.e., A is a subgroup of both
Z(H) and Z(K)).
The central product of H and K identifying A is the group
G = (H x K)/ { (f(a),g(a)^{-1}) : a in A}
[sometimes you will see the normal subgroup being given as the set of
all pairs (f(a),g(a)) instead; since A is abelian, x|->x^{-1} is an
automorphism of A, so this is obtained by replacing g with the map
obtains by first applying this automorphism and then the old mapping;
the resulting group is isomorphic to this one).
This product has the following characteristicts:
(i) G contains subgroups that are isomorphic to H and to K.
(ii) G is equal to the product of these two subgroups.
(iii) The intersection of these two subgroups is equal to A.
(iv) [H,K] = {1}.
This is not the case with the quaternion subgroup, because H and K do
not commute in the quaternion case. You can define a similar situation
when you have H and K acting on each other in a compatible way, as has
been mentioned earlier, or you can get it more generally if you drop
the requirement that the underlying set of G be some quotient of
H x K. For example, the free product with amalgamation.
Let H, K, C be three groups, and let f:C->H and g:C->K be any two
one-to-one group homomorphisms. The "free product with amalgamation"
of H and K amalgamating C, H*_C K, is given by taking F=H*K to be the
free product of H and K; let N be the least normal subgroup of F that
contains all elements of the form f(c)g(c)^{-1}, with c in C. Then F/N
= H*_C K is a group that:
(i) There are one-to-one group homomorphisms i:H->H*_C K, j:K->H*_C K.
(ii) For all c in C, i(f(c))=j(g(c)), and i(H)/\j(K)=i(f(C)).
(iii) H*_C K = <i(H),j(K)>.
(iv) If G is any group, m:H->G and n:K->G are group homomorphisms
such that m o f = n o g, then there exists a unique group
homomorphism F: H*_C K --> G such that m=Fi and n=Fj.
This works even if C is not central in H and in K.
In particular, any group that you want to create like this will be a
quotient of this group.
>> I think it is a problem with your web browser.
>
> I don't read the newsgroup through a browser. That's part of the
> problem. Not everyone reads the newsgroup through a browser, or
> through (bleach) MathForum.
[snip]
>> Perhaps upgrade to the latest version of IE or Firefox?
>
> I ->am<- using the latest version of Firefox, son. Thank you for your
> "tip".
USENET: A forever cryptic computer mystery for some, endless fun for others :-)
--
I.N. Galidakis
I don't quite understand this, but I posted the message to a Maths forum on the internet called "Math Forum". It is located at mathforum.org. If my post has somehow been copied to other forums, and copied incorrectly (all as one line) then I apologise for that.
> Compare the SOURCE message, for example, with Google:
>
> http://groups.google.com/group/sci.math/msg/2ee7aba4bc
> cc8c5d?dmode=source
>
Yes, I see that the message all runs as one line there. However, I did not post the message to Google Groups, I posted it to "Math Forum". Obviously someone has copied the message onto this Google site, and copied it incorrectly. As I stated earlier, I can only apologise for this.
> >Perhaps upgrade to the latest version of IE or
> Firefox?
>
> I ->am<- using the latest version of Firefox, son.
> Thank you for your
> "tip".
Okay, I was only trying to help, there is no need to get angry with me.
Perhaps in future just ignore my messages if they appear on another forum, as someone is obviously copying them across to there, and this is not what I intended.
However if you like maths then I would really recommend that you try going on Math Forum, it is quite good and they have a lot of maths topics on there. I have never really tried Google or the "newsgroup", so I can't comment on those.
Anyway I am sorry if I offended you.
As Arturo indicated, you *are* currently posting to the sci.math
USENET newsgroup. You are using Drexel's Math Forum web interface
to do this. If you do not understand any of the above terms then
investigate what they mean using your prefered internet search
engine.
Math Forum is broken. Google groups is just as broken. Ask
your ISP or system administrator about USENET and about how
you can access it the way it was designed to be accessed.
(I.e. not via some web forum interface.)
Phil
--
Dear aunt, let's set so double the killer delete select all.
-- Microsoft voice recognition live demonstration
(it ceases not to amaze me how conservative
otherwise somewhat reasonable people can be!)
-- m
I know. You notice I even named it?
The Math Forum is a web interface that allows you to read and post to
a Usenet Newsgroup called "sci.math". Newsgroups predate web browsers.
See http://en.wikipedia.org/wiki/Usenet
>It is located at
>mathforum.org. If my post has somehow been copied to other forums, and
>copied incorrectly (all as one line) then I apologise for that.
Math Forum's interface does not provide appropriate end-of-line
characters to the text it sends (as opposed to other web interfaces;
even google knows how to send a proper end-of-line character.
When you type in the Math Forum's editor, it automatically provides
you a new line when you reach the edge of the screen; but this is in
fact an illusion: it only works when you are dealing with Math Forum's
interface or with other similar interfaces (like google). When you
read the message through some of the standard interfaces (like I do,
using text-based trn), there is no end-of-character line.
And you are continuing to do it.
There is a very simple way to solve the problem: don't rely on Math
Forum's editor to start a new line for you when you type. When you are
approaching the edge of the screen as you type, hit ENTER instead of
continuing to type. Back in the days of typewriters, this was called
the "carriage return", because it sent the "carriage" back to the
beginning (again, you can see
http://en.wikipedia.org/wiki/Carriage_return )
>> Compare the SOURCE message, for example, with Google:
>>
>> http://groups.google.com/group/sci.math/msg/2ee7aba4bc
>> cc8c5d?dmode=source
>>
>
>Yes, I see that the message all runs as one line there. However, I
> did not post the message to Google Groups, I posted it to "Math
> Forum".
No, you did not. You posted the message to sci.math, THROUGH "Math
Forum". Math Forum is not a location, in this guise it is a PORTAL to
Usenet. Your message was posted to sci.math. Again, if you have no
clue what I'm talking about, check out wikipedia.
> Obviously someone has copied the message onto this Google
> site, and copied it incorrectly.
No, they didn't. YOU posted it to Usenet, distributed worldwide,
through the Math Forum. Google happens to receive Usenet messages and
have them available. I'm reading it through the Newsserver at UC
Berkeley. Others read it from all kinds of other places.
>Perhaps in future just ignore my messages if they appear on another
>forum, as someone is obviously copying them across to there, and this
>is not what I intended.
All your messages are appearing WORLDWIDE. If this was not your
intention, perhaps you should stop posting and learn a bit about what
it is you got into instead of wondering how come everyone is saying
those big words you don't understand.
>However if you like maths then I would really recommend that you try
>going on Math Forum, it is quite good and they have a lot of maths
>topics on there. I have never really tried Google or the "newsgroup",
>so I can't comment on those.
You ARE in a newsgroup. son. And I've been posting to sci.math for
over 15 years.
What exactly does `conservative' mean here?
Two simple facts:
Google's web interface to USENET is broken.
Drexel Math Forum's web interface to USENET is broken.
Many readers of sci.math
must compensate for these broken interfaces
--
Michael Press
Michael Press wrote:
> In article
> <31a7855b-fcbb-421c...@x35g2000hsb.googlegroups.com>,
> Mariano Su�rez-Alvarez <mariano.su...@gmail.com> wrote:
>
> > On May 19, 6:53�pm, Phil Carmody <thefatphil_demun...@yahoo.co.uk>
> > wrote:
> > > Adam Burley <ajbur...@googlemail.com> writes:
> > > > However if you like maths then I would really recommend that you try going on Math Forum, it is quite good and they have a lot of maths topics on there. I have never really tried Google or the "newsgroup", so I can't comment on those.
> > >
> > > As Arturo indicated, you *are* currently posting to the sci.math
> > > USENET newsgroup. You are using Drexel's Math Forum web interface
> > > to do this. If you do not understand any of the above terms then
> > > investigate what they mean using your prefered internet search
> > > engine.
> > >
> > > Math Forum is broken. Google groups is just as broken. Ask
> > > your ISP or system administrator about USENET and about how
> > > you can access it the way it was designed to be accessed.
> > > (I.e. not via some web forum interface.)
> >
> > (it ceases not to amaze me how conservative
> > otherwise somewhat reasonable people can be!)
>
> What exactly does `conservative' mean here?
A line such as "[...] how you can access it the way it was designed
to be accessed [...]" would be utmostly surprising to the people
that designed the beast ;-)
The notion that since USENET comes from an era where
things were like they were, it ought to be used/accessed
just as at that time in perpetuity is, IMHO, absurd, and not
at all different from other flavors of conservatism.
> Two simple facts:
> Google's web interface to USENET is broken.
> Drexel Math Forum's web interface to USENET is broken.
>
> Many readers of sci.math
> must compensate for these broken interfaces
The same people that came up with USENET and
so on came up also with an incredibly useful principle
which has amazing consequences with respect to
interaction: be lenient with what you accept, be
strict with what you produce.
In the end, one must decide whether, say, strict
adherence to a given maximum line length etiquette
outweighs reaching more people (in any case, I
consider broken any application designed to deal
with human-generated text which does not make
it absolutely trivial to reformat text which goes
beyond my favourite max line length, to
continue with the example!) If not, then every
individual is absolutely free to ignore anything
which dares use the 81st column, and it is
probably trivial to use that as a filtering criterion on most
news readers. From that to turning half of the threads into
byzantine arguments on how many characters
fit on the head of a pin, there is quite a difference:
the difference between being the signal and being the
noise. And the endless discussion of the form, IME,
tends to be part of the noise...
-- m
> Michael Press wrote:
> > In article
> > <31a7855b-fcbb-421c...@x35g2000hsb.googlegroups.com>,
> > Mariano Su?rez-Alvarez <mariano.su...@gmail.com> wrote:
> >
> > > On May 19, 6:53?pm, Phil Carmody <thefatphil_demun...@yahoo.co.uk>
Yes, all that. It remains that Google Groups and Drexel
Math Forum web portals to USENET are broken. They are not
ignorant individuals eager to learn, but legal corporate
entities with power beyond that of any individual using
their power selfishly and without regard for anyone. They
lie to their clients about the nature of their `message board'.
--
Michael Press
> I know. You notice I even named it?
> The Math Forum is a web interface that allows you to read and post to
> a Usenet Newsgroup called "sci.math". Newsgroups predate web browsers.
> See http://en.wikipedia.org/wiki/Usenet
I am looking at:
http://en.wikipedia.org/wiki/Internet_forum
and it mentions
"...forums perform a function similar to that of Usenet newsgroups ...that were common from the late 1970s to the 1990s."
"Precursor systems like Usenet have been archived as far back as 1981 by Google Groups"
> >It is located at
> >mathforum.org. If my post has somehow been copied to
> other forums, and
> >copied incorrectly (all as one line) then I
> apologise for that.
>
> Math Forum's interface does not provide appropriate
> end-of-line
> characters to the text it sends (as opposed to other
> web interfaces;
> even google knows how to send a proper end-of-line
> character.
>
It provides appropriate end-of-line characters to me, as shown by the link I sent you.
[...]
> > Obviously someone has copied the message onto this
> Google
> > site, and copied it incorrectly.
>
> No, they didn't. YOU posted it to Usenet,
> distributed worldwide,
> through the Math Forum. Google happens to receive
> Usenet messages and
> have them available. I'm reading it through the
> Newsserver at UC
> Berkeley. Others read it from all kinds of other
> places.
>
If "Math Forum" has posted my messages to "Usenet", then again, I am sorry for this, but it is out of my hands.
> >Perhaps in future just ignore my messages if they
> appear on another
> >forum, as someone is obviously copying them across
> to there, and this
> >is not what I intended.
>
> All your messages are appearing WORLDWIDE. If this
> was not your
> intention, perhaps you should stop posting and learn
> a bit about what
> it is you got into instead of wondering how come
> everyone is saying
> those big words you don't understand.
>
Please do not patronise me. I have a 2:1 Masters degree in Maths from a major university (graduated last July) and I really do not appreciate it when you use phrases like "saying those big words you don't understand" and calling me "son" like I am still in high school.
> >However if you like maths then I would really
> recommend that you try
> >going on Math Forum, it is quite good and they have
> a lot of maths
> >topics on there. I have never really tried Google or
> the "newsgroup",
> >so I can't comment on those.
>
> You ARE in a newsgroup. son. And I've been posting to
> sci.math for
> over 15 years.
>
>
I am trying to be reasonable with you here and give you some tips to solve our problem. And I did apologise several times in my last post, both for offending you and for the initial problem. I do not understand why you are taking such an aggressive tone with me, I am not meaning to offend you or make life difficult for you. I must admit that I have not been posting to the math forum for 15 years, but I have been on here for more than 5 years (my first post: http://mathforum.org/kb/thread.jspa?forumID=226&threadID=540531&messageID=1639372).
I do not intend to stop posting, as I enjoy this forum, and I do not think that many people are experiencing the same problems as you. I re-iterate, however, that you can feel free to just ignore my posts, and I will not be offended.
> --
> ======================================================
> ================
> "It's not denial. I'm just very selective about
> what I accept as reality."
> --- Calvin ("Calvin and Hobbes" by Bill
mathforum.org does not maintain their own forums: the site's
discussion area is entirely an interface for certain usenet groups and
mailing lists. As a user of the mathforum discussion site, you are
automatically also user of those groups and mailing lists and you are
therefore responsible for following established community conventions
within those groups.
It's unfortunate that the site does not make it clearer that this is
the case; this unpleasantness could've been avoided.
(This also means that mathforum.org's administration is not
responsible for anything you read here, or for setting or enforcing
guidelines.)
Sigh.
A cat has four legs and a tail. But if you call the tail a leg, then
how many legs does a cat have?
Four. Calling the tail a leg does not make it one.
Drexel's Math Forum is not an "Internet forum" within the meaning of
the wikipedia page you are reading, despite its name> Drexel's Math
Forum is a portal that administers a number of mailing lists, AND a
portal to the usenet groups sci.math, sci.math.num-analysis,
sci.math.research, sci.math.symbolic, sci.stat.math, and
sci.stat.edu.independent.
http://mathforum.org/kb/forumindex.jspa
has a list of everything they have. Click on "sci.math*", you will get
sent to
http://mathforum.org/kb/forumcategory.jspa?categoryID=16
and you will see right at the top that it reads:
sci.math.*
Usenet newsgroups about mathematics.
^^^^^^
And you have been posting (59 times since December 2005) through the
sci.math usenet group.
Clearly, you were not aware that you were posting to sci.math and to a
usenet group. But when you were informed of this, your reply was to
blame me, then blame mysterious "others" who had been "copying" your
message in places you did not intend, etc. Rather silly, and
demonstrating profund ignorance about the nature of the medium in
which you are participating.
>>> It is located at mathforum.org. If my post has somehow been copied
>>> to other forums, and copied incorrectly (all as one line) then I
>>> apologise for that.
>> Math Forum's interface does not provide appropriate end-of-line
>> characters to the text it sends (as opposed to other web
>> interfaces; even google knows how to send a proper end-of-line
>> character.
>
>It provides appropriate end-of-line characters to me, as shown by the link I sent you.
Sigh.
The MESSAGE contains no end-of-line characters. What you are seeing is
the INTERFACE that is introducing those characters.
Most usenet portals provide formatting for their messages (trn, emacs,
even google). This formatting includes either soft or hard
carriage-return/end-of-line characters for formatting. MathForum is
one of the few that does NOT provide such characters in the message,
and instead relies on its own interface to provide them when
displaying. That is why it messes up the quotations so much, as you
can see in your own message, giving long/short/long/short lines and
often messing up multiple quotations.
If you were to hit Enter at the end of lines, your messages would
still be readable exactly the same on Math Forum, but they would also
be easily readable by everyone else, as they would then conform to the
standards of the medium in which you are posting. Apparently, however,
this is a bit too much to ask.
>[...]
>
>> > Obviously someone has copied the message onto this
>> Google
>> > site, and copied it incorrectly.
>>
>> No, they didn't. YOU posted it to Usenet,
>> distributed worldwide,
>> through the Math Forum. Google happens to receive
>> Usenet messages and
>> have them available. I'm reading it through the
>> Newsserver at UC
>> Berkeley. Others read it from all kinds of other
>> places.
>>
>
>If "Math Forum" has posted my messages to "Usenet", then again, I am
>sorry for this, but it is out of my hands.
Math Forum posted your messages to Usenet because that is what ->it is
supposed to do<-. The section of the Math Forum you are posting to is
MEANT to post your messages to usenet. In fact, that is its ->sole<-
purpose: to post to usenet and to provide access to messages in
usenet. Apparently, you were unaware of this.
>> >Perhaps in future just ignore my messages if they
>> appear on another
>> >forum, as someone is obviously copying them across
>> to there, and this
>> >is not what I intended.
>>
>> All your messages are appearing WORLDWIDE. If this
>> was not your
>> intention, perhaps you should stop posting and learn
>> a bit about what
>> it is you got into instead of wondering how come
>> everyone is saying
>> those big words you don't understand.
>>
>
>Please do not patronise me.
I could say the same, Mr "If you are interested in maths you should
check out the forum", nee "Perhaps you should update your browser".
> I have a 2:1 Masters degree in Maths from a major university
>(graduated last July)
Congratulations! I have a Ph.D. from, let's say a reasonably good
university, and have had it for a bit longer than 11 months.
>and I really do not appreciate it when you use phrases like "saying
>those big words you don't understand" and calling me "son" like I am
>still in high school.
You are demonstrating that you enjoy giving advise from a position of
ignorance, and blaming mysterious "others" for doing what you yourself
did (in ignorance). That suggests how you ought ot be treated.
>I am trying to be reasonable with you here and give you some tips to
>solve our problem.
You were patronizing, from a position of ignorance, to someone who
actually knew far better than you what was going on and tried to
explain it. You were not reasonable, you are not reasonable. You are
being unreasonable, in denial, and contrary.
>I do not intend to stop posting, as I enjoy this forum,
You claimed that you did not wish to post to Usenet. Since the forum
you are using IS usenet, and is exclusively usenet, and is meant to be
usenet, and is nothing BUT usenet, you must either change your desire
"not to post to usenet", or else you must stop posting in this forum.
> and I do not think that many people are experiencing the same
> problems as you.
How would you know? It is pretty clear you don't really have much of a
clue as to what you are doing or what is going on.
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
No, I think mathforum.org is responsible for this, not me. I have posted to mathforum.org. I intend my message to be read by other users of mathforum.org. If mathforum.org decides to transmit my message via Usenet, then it is responsible for the consequences, not me.
Analogy: if I tell my friend something in private, and they decide to spread it around the whole world, then I am not really responsible if others find my words inappropriate.
I am, however, prepared to follow the community guidelines of mathforum.org. This will be a subset of those of Usenet, but will not include everything, and in particular not limiting the length of my lines.
Your intentions are immaterial. You are simply unaware of the nature
of mathforum. The section you are in is INTENDED to be a portal to Usenet.
> If mathforum.org decides to transmit my message via
> Usenet, then it is responsible for the consequences, not me.
Mathforum did not "decide" to transmit your messages to Usenet. YOU
instruct mathforum to post your messages to usenet by your choice of
the section of the Matforum that you are using. The section on
"Discussions", "sci.math*" that you are in is expressly meant to be a
portal to usenet.
>Analogy: if I tell my friend something in private, and they decide to
>spread it around the whole world, then I am not really responsible if
>others find my words inappropriate.
The analogy is flawed because you are not in fact telling "your
friend" something in private. You are sending a letter to the editor
in the mistaken impression that you are telling something to your
friend in private. The mistake is yours, in misunderstanding the
nature of the forum in which you are participating.
>I am, however, prepared to follow the community guidelines of
> mathforum.org.
So long as you can do so while pretending that nothing is your fault,
at any rate.
> >I am looking at:
> >http://en.wikipedia.org/wiki/Internet_forum
> >
> >and it mentions
> >"...forums perform a function similar to that of
> Usenet newsgroups ...that were common from the late
> 1970s to the 1990s."
> >"Precursor systems like Usenet have been archived as
> far back as 1981 by Google Groups"
>
> Sigh.
>
> If you call the tail of a cat a leg, then how many
> legs does the cat
> have?
>
> Answer: Four. Calling the tail a leg does not make it
> one.
>
I would say "five", but I think you would then say I was being "contrary".
> Your intentions do not control the nature of the
> medium you are using.
>
No, unfortunately I have no control over said medium.
> It's not just a river in Egypt, dear, and it's about
> time you realize
> that you are quite simply wrong and mistaken about
> the nature of the
> messages you have been sending.
>
Again, very patronising.
> Drexel's Math Forum is not an "Internet forum" within
> the meaning of
> the wikipedia page you are reading, despite its name>
> Drexel's Math
> Forum is a portal that administers a number of
> mailing lists, AND a
> portal to the usenet groups
[...]
> and you will see right at the top that it reads:
>
> sci.math.*
>
> Usenet newsgroups about mathematics.
> ^^^^^^
Yes, indeed my posts have been sent to usenet newsgroups by mathforum.org.
I am quite prepared to accept that mathforum.org is, technically, an interface to Usenet. But I choose to ignore it.
This is not a new concept. When I _finally_ beat that last race in the video game, I choose to ignore that really all that is happening is a lot of zeros and ones buzzing about inside my games console. When I watch that emotional scene on my DVD player for the umpteenth time, I choose to ignore that really it is a tiny laser shining onto a load of bumps and troughs on the back of a disc. The interface is an abstraction of the boring technical stuff underneath. It is _meant_ to make you ignore what is really going on.
> Clearly, you were not aware that you were posting to
> sci.math and to a
> usenet group. But when you were informed of this,
> your reply was to
> blame me
I did not blame you. If by asking you to check if you were running the latest version of Firefox, you thought I was blaming you, then you misunderstand me. I was merely offering a suggestion to attempt to solve the problem. I was trying to help.
> then blame mysterious "others" who had been
> "copying" your
> message in places you did not intend, etc.
The reason why these "others" are mysterious is because they do not exist. What is happening is that the message is being transmitted automatically over Usenet. But it is mathforum.org who have chosen to set up their system this way.
> >It provides appropriate end-of-line characters to
> me, as shown by the link I sent you.
>
> Sigh. Are you really this dense, or just contrary?
>
I do not believe I am either.
> Math Forum does not in fact provide end-of-line
> characters. What you
> are seeing is a rendering of the message you are
> sending, local to
> Math Forum's display.
>
> Most portals to Usenet (of which, whether you like it
> or not, Drexel's
> Math Forum is one) format their messages in some way.
> Most include
> either soft or hard carriage-return characters for
> formatting purposes
> ->in<- the text. Drexel's Math Forum does not. The
> interface of the Math
> Forum handles this (as does the Google interface).
> But this is not
> part of the MESSAGE, it is part of the interface.
>
>
I agree. Math Forum provides appropriate end-of-line characters to me, through its interface.
> >Please do not patronise me.
>
> Then perhaps you should not try patronizing me,
> telling me about
> checking my browser or learning all about the Maths
> Forum if I am
> "interested in Math".
>
> I could say the same, Mr "If you are interested in
> maths you should
> check out the forum", nee "Perhaps you should update
> your browser".
>
You have interpreted my comments as patronising, that was not how I intended them. I think that mathforum.org is a great site, obviously you don't, but I was just suggesting maybe you could give it a second chance. This is not patronising, I am not assuming that you are stupid. I just thought that perhaps you had not realised the full scope of what was offered by mathforum.org, and perhaps I was mistaken.
> >I have a 2:1 Masters degree in Maths from a major
> university
> >(graduated last July) and I really do not appreciate
> it when you use
> >phrases like "saying those big words you don't
> understand" and
> >calling me "son" like I am still in high school.
>
> Congratulations. Then perhaps you can stop calling me
> "Doctor" or
> "Professor" and stop patronizing me about visiting
> the Math Forum if I
> am "interested in maths".
>
> Point is, you just don't know what you are talking
> about but you
> pretend you do. That's why you are being patronized.
> Son.
>
> Congratulations! I have a Ph.D. from, let's say a
> reasonably good
> university, and have had it for a bit longer than 11
> months.
>
Well congratulations back then. I think you have misunderstood me as perhaps boasting or claiming superiority. I was merely asserting that I am not still in high school and I found the tone of your messages to be a little patronising. I was _not_ demanding respect, or anything of the sort. Certainly the rank of professor does demand some respect. However, you continue to patronise me.
> You are demonstrating that you enjoy giving advise
> from a position of
> ignorance, and blaming mysterious "others" for doing
> what you yourself
> did (in ignorance). That suggests how you ought ot be
> treated.
Yes. However, we are all "ignorant". There is no one who knows everything there is to know. All of us are still learning and that is the prerogative of any academic or further, any individual. However, we still give advice, that is human nature, we are attempting to help our fellow man, especially when he is in trouble.
> > and I do not think that many people are
> experiencing the same
> > problems as you.
>
> How would you know? It is pretty clear you don't
> really have much of a
> clue as to what you are doing or what is going on.
>
I didn't attest to know, I simply stated that I _think_ this to be the case. This assumption comes from the fact that in the last 5 years I have not encountered anyone else with this problem.
Suppose I am a prolific author (I'm not by the way) and I write books in English which are distributed worldwide. And everyone who understands them, reads them, but those who don't just ignore them. It is just a normal, status quo. However then one day, someone comes along from Japan and says to me that they don't understand my books because they don't speak English. And could I, from now on, translate all my published books into Japanese, so that they can understand them. I might consider it, but eventually refuse, because my target audience is those who speak English, and I do not feel that I am obligated to appease those who speak a different language.
It is the same here: I am writing posts intended for people who use mathforum.org, but they are being read worldwide by people who use other Usenet interfaces. And some of those are not compatible with the messages that I am sending. However, I am fine with that, because I expect such people to just ignore my posts. I know that anyone who uses mathforum.org, or any other interface which wraps my lines, can understand and reply to my messages, and this is a large enough target audience.
I know previously I "suggested" that you just ignore my posts from now on. Well perhaps I should go a little further and "request" that you ignore them. We are at a complete \textit{impasse} here, and I do not think there is anything to be gained from continuing this discussion, as we have conflicting viewpoints. I will just get more offended, you will get more angry, and anyone else reading this thread will get more bored! I will try, from now on, not to reply directly to any of your posts, and I will not expect you to reply to any of mine. There is nothing stopping you from doing so, though, and so you have the "last word" in this discussion.
Once again, despite the fact that you believe it to be an "empty phrase", I am truly sorry for the problems I have caused you.
One of the messages was canceled because it was sent prematurely by
accident. Yet another of the drawbacks of Drexel's Math Forum, that
despite it being a portal to Usenet it does not acknowledge a number
of standard control messages, such as cancel commands.
>> If you call the tail of a cat a leg, then how many
>> legs does the cat
>> have?
>>
>> Answer: Four. Calling the tail a leg does not make it
>> one.
>>
>
>I would say "five", but I think you would then say I was being
> "contrary".
No. I would simply say that you missed the point. And that I was not
surprised at that.
[...]
>The reason why these "others" are mysterious is because they do not
>exist. What is happening is that the message is being transmitted
>automatically over Usenet. But it is mathforum.org who have chosen to
>set up their system this way.
What is actually happening is that YOU are sending your messages TO
Usenet. They are not being "automatically transmitted". They are MEANT
for Usenet, because that is what mathforum is meant to do.
Your comments are like complaining that your telephone "automatically
transmits" what you say in your house to the other end of the line,
and that this is beyond your intentions even though you are the one
who picked it up and dialed.
That's what you are doing each time you are posting: you are picking
up the phone, and dialing sci.math. It's just that your local
telephone central happens to be Drexel's Math Forum.
>I agree. Math Forum provides appropriate end-of-line characters to
>me, through its interface.
Math Forum DISPLAYS end-of-line characters in its graphic
interface. Click on the "plain text" button next time to see how Math
Forum does not in fact provide end-of-line characters. There is a
difference between "providing" and "displaying".
[...]
>You have interpreted my comments as patronising, that was not how I
>intended them. I think that mathforum.org is a great site, obviously
>you don't,
Mathforum.org is a pretty lousy interface, as such interfaces go. I
speak with some experience both in using and in programming user
interfaces in general. The CONTENT of the site, on the other hand, is
not mathforum's. I am familiar not only with most of the content of
mathforum, but with a lot more that Mathforum does not provide because
of its limited scope.
I was commenting on the INTERFACE, but again, since you were
apparently utterly confused about the nature of the beast, you
misinterpreted it and then proceded to make what was, in fact, a
rather patronizing remark whether you intended it be such or not.
> However, you continue to patronise me.
You continue to behave as if your intentions and your
misinterpretation (and ignorance) about mathforum and usenet should
somehow control everything. That's why you are being treated with a
certain modicum of contempt.
>I didn't attest to know, I simply stated that I _think_ this to be
>the case. This assumption comes from the fact that in the last 5
>years I have not encountered anyone else with this problem.
Many people don't bother making the suggestion.
>Suppose I am a prolific author (I'm not by the way) and I write books
>in English which are distributed worldwide. And everyone who
>understands them, reads them, but those who don't just ignore
>them. It is just a normal, status quo. However then one day, someone
>comes along from Japan and says to me that they don't understand my
>books because they don't speak English. And could I, from now on,
>translate all my published books into Japanese, so that they can
>understand them. I might consider it, but eventually refuse, because
>my target audience is those who speak English, and I do not feel that
>I am obligated to appease those who speak a different language.
You really do love to make utterly ridiculous and misguided
analogies.
I did not ask you to "start translating" your messages in Japanese or
anything close to that. Simply suggesting pressing the carriage
return key at the end of the line is hardly a good parallel to
that. Apparently, however, it is indeed too much work.
>It is the same here:
No, it is not.
Here is a better analogy: speaking clearly and loudly is a good way
to communicate. One can still communicate while mumbling, or while
saying "er" and "like" every other word; however, this makes it more
difficult for your words to reach the audience. I was not asking you
to learn a new language, I was asking you take a breath, speak clearly
and not mumble, when you speak.
> I am writing posts intended for people who use mathforum.org,
Which is prima facie nonsense, and betrays deep misunderstandings
about the nature of the beast. Misunderstandings that have been
explained, but which you prefer to adhere to because it is too much
work to try to figure out what is really happening or the real nature
of what you are doing.
Just for what it may be worth...
>
>It is the same here: I am writing posts intended for people who use
>mathforum.org, but they are being read worldwide by people who use
>other Usenet interfaces.
From what I can tell, you've made 145 posts since 2002. These posts
have generated 184 replies; of these, no more than 62 have come from
the Math Forum, and 40 of these were in 2002; of more recent posts,
the ratio is much worse. For example, the recent thread "Principles of
induction in non-well-founded set theories" generated 36 replies, none
of which came from the MathForum.
You might want to rethink the notion that you only intend to reach
those who use mathforum.
> I do not intend to stop posting, as I enjoy this forum, and I do not think that many people are experiencing the same problems as you. I re-iterate, however, that you can feel free to just ignore my posts, and I will not be offended.
As it happens others people are experiencing the same problems.
I am, for instance. Had you read carefully all the replies you
received you would know this is the case, and would not have
made this false assertion.
If it were possible to ignore you, I would; but you insist
upon putting yourself forward in a manner that cannot be ignored.
--
Michael Press
Michael Press wrote:
> In article
> <9303181.12115184356...@nitrogen.mathforum.org>,
> Adam Burley <ajbu...@googlemail.com> wrote:
>
> > I do not intend to stop posting, as I enjoy this forum, and I do not think that many people are experiencing the same problems as you. I re-iterate, however, that you can feel free to just ignore my posts, and I will not be offended.
>
> [...]
>
> If it were possible to ignore you, I would; [...]
Cf. <http://en.wikipedia.org/wiki/Kill_file>.
HTH,
-- m
I know all about kill files. It is not possible to ignore a barking dog.
I cannot ignore Adam Burley broadcasting assertions contrary to fact.
You should take the word `can' in the strict dictionary sense.
I can ignore most net loons because only people hearing the
ravings for the first time entertain them seriously.
--
Michael Press