So I'll make this post to note the problem, which hopefully will clear
up in a few days, and to point out some things:
First, my infinite series was not previously known as you would have
seen something like the following in a mathematical text on the
subject and as so much has been written about Pell's Equation, I doubt
you'd have missed it:
1. x^2 + Dy^2 = F
2. (x-Dy)^2 + D(x+y)^2 = F*(D+1)
3. ((1-D)x-2Dy)^2 + D(2x + (1-D)y)^2 = F*(D+1)^2
4. ((1-3D)x + (2D^2 - 4D)y)^2 + D((3-D)x + (1-3D)y)^2 = F*(D+1)^3
and that goes out to infinity. To get successive terms in the series
you use the algebraic result that given:
u^2 + Dv^2 = C
it must be true that
(u-Dv)^2 + D(u+v)^2 = C*(D+1).
And where whenever the exponent of (D+1) is even, you can have a case
where you just have a multiple of x and y, so you can solve for D,
which defines possible values for F in terms of x or y.
Like with the third in the series:
((1-D)x-2Dy)^2 + D(2x + (1-D)y)^2 = F*(D+1)^2
you can consider
(1-D)x-2Dy = +/-(D+1)x or +/-(D+1)y
and
2x + (1-D)y = +/-(D+1)x or +/-(D+1)y
because trivially
(+/-(D+1)x)^2 + ((D+1)y)^2 = F*(D+1)^2
and solving for those possibilities gives a value for D. I got D=1,
for the case of
(1-D)x-2Dy = (D+1)x and 2x + (1-D)y = (D+1)y.
So you can map the series as a super structure, where D is set at
various levels.
One poster lobs a criticism that
u^2 + Dv^2 = C
requiring that
(u-Dv)^2 + D(u+v)^2 = C*(D+1)
is derivable from an equation known to Brahmagupta. Fine, so show
that Brahmagupta derived that particular result and USED it to
generate an infinite series.
Hey, you people missed the result right in front of you too, which may
be why I'm seeing so many angry replies with insults.
Your chance of a lifetime was a post away and you missed it so anger
can be a reaction.
And missing it against me when the opportunity to upstage me was there
for days may really anger people who have argued with me or listened
to and believed in other posters who argued with me as well.
That social stuff is powerful with a lot of people. Having people
trust and believe in you, like when you're criticizing a "crackpot"
can be powerful magic making a person feel all warm and fuzzy inside
like they're actually SOMEBODY.
Getting upstaged pops the bubble. Reality is so annoying at times for
some people, you know?
But you are now up against the worldwide community of people
interested in mathematics who might want to explore that number
theoretic super structure, and hatred is not an excuse for denigrating
valuable mathematical ideas...not if you wish to be taken seriously
later. Ever.
Students again I remind you of your futures. Angry sci.math posters
are there because they're not good enough to go anywhere else, and I'm
there because I'm an amateur who has been blocked out of usual
circles, so I post to several math newsgroups including the one full
of angry idiots.
But it is YOUR future. Angry losers on sci.math will probably keep
ripping on this result just because...well, because they're losers,
who you'll notice could not see that infinite series right in front of
them for days.
They were too busy still ripping on me.
Don't make it personal. It's math. You make it personal and you
lose.
So you all lost round one. Easy mathematical fame escaped you with
the find of the series, so now it's up to you what you do next.
Continue to listen to angry idiots, or do the math.
James Harris
No insults from me! I've already advocated that you publish this. I
think your paper should include the name of your new series. "The JSH
series" has a nice ring to it, but you might prefer "The Harris series".
It's your call.
[snip irrelevancies]
>> Hey, you people missed the result right in front of you too, which may
>> be why I'm seeing so many angry replies with insults.
>
> No insults from me! I've already advocated that you publish this. I
> think your paper should include the name of your new series. "The JSH
> series" has a nice ring to it, but you might prefer "The Harris series".
> It's your call.
It does not matter *what* you say. To people suffering from this
condition, *everything* sounds like an insult.
If you feel sorry for them, you ignore them and don't reply.
If you want to tease them, you reply, and what you say does not
even matter.
In a sense these people only allow some effective but very limited
form of one-way communication: they have nothing of interest to
tell you, and every noise you make, triggers the same alarm bell
with them.
Dirk Vdm
I wouldn't even say your result is derivable from his result--I'd only
say B is derivable from A if there is at least some minimal effort
involved in getting B from A. Getting your result from Brahmagupta's
result involves no noticeable effort. It simply involves substituting 1
for two free variables in his result. Since it is obvious at a glance
that substituting 0 for one or both of those variables is useless,
substituting 1 for both is the first case that might be interesting--and
it gives your result. At best, your result is an example of his result.
--
--Tim Smith
"JSH" <jst...@gmail.com> wrote in message
news:15562c5e-c226-47d5...@a3g2000prm.googlegroups.com...
>
> Google Groups! I'm a google-poster! Look at me! I gots a gmail address!
>
No, I can't name an infinite series I discovered after myself.
I do find it interesting replying in a rational manner to a post where
you talked about me as if I were some thing you find distasteful.
But I can do what you cannot because I see you as a human being,
regardless of what you said, while you clearly do not see me as one.
James Harris
Not distateful. Just modestly interesting.
Dirk Vdm
>On Oct 5, 3:40 am, "Dirk Van de moortel"
><dirkvandemoor...@nospAm.hotmail.com> wrote:
>
>> It does not matter *what* you say. To people suffering from this
>> condition, *everything* sounds like an insult.
>> If you feel sorry for them, you ignore them and don't reply.
>> If you want to tease them, you reply, and what you say does not
>> even matter.
>>
>> In a sense these people only allow some effective but very limited
>> form of one-way communication: they have nothing of interest to
>> tell you, and every noise you make, triggers the same alarm bell
>> with them.
>
>No, I can't name an infinite series I discovered after myself.
>
>I do find it interesting replying in a rational manner to a post where
>you talked about me as if I were some thing you find distasteful.
>
>But I can do what you cannot because I see you as a human being,
>regardless of what you said, while you clearly do not see me as one.
Exactly. Spot on. There you have one of the central problems of
psychiatry (in its widest sense) in a ... nutshell. How (if at
all) should you conceptualise delusional (or presumably delusional)
states, such as yours (or other mental states, such as mine, which
are believed by the person in question and/or by some other person
to be `wrong' - in some sense of that overloaded word) in /human/
terms, without either reducing a person to a thing, or else taking
that person's communications at face value? One way is to presume
the person in question to be a liar. (I think you can take it from
there ...) :-)
(N.B. I'm not presuming that Dirk was actually regarding James as a
thing rather than a person - I'm just responding to James's reply.)
Obligatory declaration: my postings to JSH-related threads since
Thu 25 Sep 2008 have raised Ł6.00 for "Charity". (That's one post
per day on average. Am I perhaps on the road to recovery at last?)
--
Angus Rodgers
(twirlip@ eats spam; reply to angusrod@)
Contains mild peril
But what have I done that would suggest insanity?
Turns out I post my own amateur mathematical ideas, where I admit to
being, an amateur.
When I think I'm right I defend those ideas despite others disagreeing
with me.
I make over the top posts often enough, but have noted that's
necessary to keep readers, so a lot of it is about entertainment.
Like talking about the end of the world, noting the power of myth, and
incessantly harping on the lying by mathematicians (which is
entertainment but they DO lie).
Now then, on what basis can a reasonable person call me insane?
From what I've noticed simply POSTING and not just accepting it if
other posters (other people who post) claim I'm wrong is presented as
proof of my insanity.
If pushed they'll probably say that posting for years, as I've posted
for over 10, is further proof, but clearly I enjoy posting, and enjoy
posting about my amateur research, so what is the basis for the
insanity call?
I've noticed that mathematicians routinely call other people insane.
James Harris
Shall we ask David Ullrich?
>
> Turns out I post my own amateur mathematical ideas, where I admit to
> being, an amateur.
>
> When I think I'm right I defend those ideas despite others disagreeing
> with me.
>
> I make over the top posts often enough, but have noted that's
> necessary to keep readers, so a lot of it is about entertainment.
> Like talking about the end of the world, noting the power of myth, and
> incessantly harping on the lying by mathematicians (which is
> entertainment but they DO lie).
See, you are insane.
>
> Now then, on what basis can a reasonable person call me insane?
Shall we ask the Oklahoma District Attorney?
So Paris Hilton is insane? She has an incessant need for attention.
> > I've noticed that mathematicians routinely call other people insane.
>
> Or, on second thought, maybe your paranoia.
Plenty of people are paranoid. Are mathematicians calling them all
insane too?
What has happened is you all made up your own rules.
Short answer is: anyone who doesn't follow along with what you want
them to do, you call them insane.
James Harris
> > > I've noticed that mathematicians routinely call other people insane.
>
> > Or, on second thought, maybe your paranoia.
>
Plus, on top of it all, your grammar sucks!
>
> Plenty of people are paranoid. Are mathematicians calling them all
> insane too?
>
> What has happened is you all made up your own rules.
>
> Short answer is: anyone who doesn't follow along with what you want
> them to do, you call them insane.
>
No, that's actually your expertise.
When you're responding to comments you are defending your arguments.
When mathematicians do it they're lying.
I believe the term for this is "projection"
> James Harris
M
While to me, you are not.
Initial survey is complete.
To the limits of the math newsgroup the infinite series is a unique
discovery, with profound implications sparking irrational behavior
(mostly typical ape status response along past lines) consistent with
the size of the discovery.
1. x^2 + Dy^2 = F
2. (x-Dy)^2 + D(x+y)^2 = F*(D+1)
3. ((1-D)x-2Dy)^2 + D(2x + (1-D)y)^2 = F*(D+1)^2
4. ((1-3D)x + (2D^2 - 4D)y)^2 + D((3-D)x + (1-3D)y)^2 = F*(D+1)^3
which shows the functional behavior.
Additional terms in the series are found by using the relation:
Given
u^2 + Dv^2 = C
it must be true that
(u-Dv)^2 + D(u+v)^2 = C*(D+1).
This result unlike others has a rapid pounce ability in that I can
push a result in hours, with little effort.
And I can simply skip the journal system completely, so that journals
are now out of the loop.
Because now I don't need them. Any of them.
James Harris
Ah, so you think Paris Hilton is mentally ill.
I'm not surprised. From what I've seen, mathematicians love to
diagnose mental illness in others.
Thank you for at least being honest here.
James Harris
or crank or crackpot or some other belittlement
ignore the word "insanity"
james
you're not insane
it's folk-psychology at it's worst
a vague term used to pin monster-masks on the world
what is important is the dynamics
in particular
the linguistic dynamics
what logical connectives does a person use?
is this adaptive?
(i.e. do they lead to healthy actions?)
it is an important part
of any science of human dynamics
that these dynamics be classified
and mechanisms understood
-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-
at the bottom of it all is honesty
james
your act makes you say you solved fermat's last theorem
even though you know that is not true
and even though you have publicly admitted it
in your act
and your attacks on abstract algebra
and a few other minor slips
that kind of dishonesty
implies that others should not trust your function
and it does not matter
that your prime counting algorithm works
or that you understand a good portion
of the theory of pells
because the flaws mask that part of your art that is interesting
and could make for very clever stories
your act is hurting you
james
it causes others to see the flaws
and in their imperfect ways try to fix them
what you see
the lies and anger and frustrations posted your way
have been the monkeyscream faces
of a hundred or more engineers over the years
you see
artists love attention
and you are an artist
james
and most just think you're a con artist
a spinner
unreliable
a problem to be fixed in their interaction with environment
you see
artists still have to be good
the whole point of the arrogance
is that you have something important to contribute
locked up inside
something new
and the practice of their art
is a devotion
your act is self-destructive
james
people try to fix you
and along the way
they take you apart
as an artist
as an actor
as a contributor to the word
you draw attention to yourself
what you see is the result
a quick sampling of humankind
and it's imperfect response
to your imperfect art
and
well
a lot of people still say you're pretty smart
the stories you weave of intellectual efforts and world events
are all quite clever
and they show you enjoy playing with symbols
and you have a wide scope
writing about many different fields of study
demonstrating the existential struggle for meaning
that has become the shrieking background noise of our era
but there is a dynamic in your art working against you
james
violations of trust
that you have learned to ignore
o--o
artists can never ignore
they must constantly fight
to develop the detail of their representations
become unblind
^..^
but
a great artist cannot be told to be great
it is something they do to themselves
some deep drive to practice
that pushes their message
their art
to fulfill it's hubris
you are not yet a great artist
james
some people say you will never be
i say you are just lazy
you see
i have hope
a lazy artist takes some arbitrary iteration sequence
and displays it as their art
a better artist gives some motivation of interest
proves some interesting properties
maybe sketches some conjectures for the future
an untrustworthy artist
will make claims of experiential conflict
a clever artist
will find a way forward anyway
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
> I'm not surprised. From what I've seen, mathematicians love to
> diagnose mental illness in others.
>
Which "others"? I believe it is only you they refer to. (Or have you
now developed multiple personalities?)
> Thank you for at least being honest here.
>
*I've* never been anything but.
>
> James Harris
Keep on responding if you want: I've made my point.
Besides, your juvenile logic is too easy to shoot down and bores me at
this point.
M
It's a powerful tactic that costs me money.
I can't ignore it.
> you're not insane
>
> it's folk-psychology at it's worst
> a vague term used to pin monster-masks on the world
>
> what is important is the dynamics
>
> in particular
> the linguistic dynamics
>
> what logical connectives does a person use?
> is this adaptive?
> (i.e. do they lead to healthy actions?)
>
> it is an important part
> of any science of human dynamics
> that these dynamics be classified
> and mechanisms understood
>
> -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-
>
> at the bottom of it all is honesty
>
> james
> your act makes you say you solved fermat's last theorem
>
> even though you know that is not true
It is true.
You have a good rhythmn to your words.
Google "a poet's cry" and read my poem, and consider if you wish to
talk to me about poetry and not math.
And if so, email me.
> and even though you have publicly admitted it
> in your act
That's not true.
Tautological spaces which lead me to this latest result, the infinite
series and the general solution for binary quadratics, were discovered
by me in order to solve FLT. And they accomplished that feat.
That's where I gained the confidence to move on, and found my prime
counting function and everything else since.
So the real start was with the proof of FLT.
> and your attacks on abstract algebra
> and a few other minor slips
>
> that kind of dishonesty
> implies that others should not trust your function
I am not dishonest. And what people trust is irrelevant. Trust is
about what some people try.
But there are others who will try without trust.
And evolution is about getting it right, however you did it.
It's not that the strong survive.
It's that the most intelligent--truly intelligent--survive.
So time is the answer beyond the debates, when people so loud now are
long silent in death. Their thoughts their fears so vibrant before--
nothing left, nothing more.
A dream to some, a nightmare to others, that end so soon, so soon and
not one to escape.
Our wishes our hopes our dreams and our lives trapped forever like
amber in our fates.
Yes, your Fate.
Your destiny, which you will not. Cannot, escape.
> and it does not matter
> that your prime counting algorithm works
Of course it works. It counts primes.
Hard for math people to lie about that, eh?
And it DOES matter as it gave me confidence. Confidence to continue
when people like you told me I was wrong, and I learned you were
wrong, but wouldn't accept it.
Why wouldn't you?
Because you wanted to feel safe, and safe to you was being
mathematically wrong.
We all have our place in this world, great or small, short or tall,
something we didn't ask for, or maybe we did, long ago, in some
certain world.
But that place is not necessarily admitted or accepted, or even
thought out, try as we may, to work it all out.
Life is a mystery, maybe because, for many of us, a lot of us, the
answer is, the last thing we'd ever want to see.
Because regardless we have no choice but to be. Until, of course, we
die. And then maybe...
James Harris
I actually only used the adjective "delusional".
From The Chambers Dictionary (1998 edition):
*delude*, /vt/ to deceive or cause to accept what is false as
true; to play with (someone) so as to frustrate them or their
hopes (/obs./); to elude (/obs./) ... /adj/ *deluded* holding
or acting under false beliefs
*delusion*, /n/ the act of deluding; the state of being deluded;
a hallucination; a false belief (/esp psychol/); error. - /adj/
*delusional* relating to or afflicted with delusions.
>Turns out I post my own amateur mathematical ideas, where I admit to
>being, an amateur.
>
>When I think I'm right I defend those ideas despite others disagreeing
>with me.
>I make over the top posts often enough, but have noted that's
>necessary to keep readers, so a lot of it is about entertainment.
>Like talking about the end of the world, noting the power of myth, and
>incessantly harping on the lying by mathematicians (which is
>entertainment but they DO lie).
>
>Now then, on what basis can a reasonable person call me insane?
It wouldn't be unreasonable to do so, but it would generate more
heat than light, because the word carries a lot of baggage. (The
dictionary definition sheds no light on it at all.) I would only
call you "insane" if I were in a particularly bad mood with you.
But when I call you "delusional", I am only expressing in simple
terms my experience of you as a person, and not (or at least not
intentionally) buying into a vast (and vastly muddled) ideology.
>From what I've noticed simply POSTING and not just accepting it if
>other posters (other people who post) claim I'm wrong is presented as
>proof of my insanity.
>
>If pushed they'll probably say that posting for years, as I've posted
>for over 10, is further proof, but clearly I enjoy posting, and enjoy
>posting about my amateur research, so what is the basis for the
>insanity call?
>
>I've noticed that mathematicians routinely call other people insane.
I'm rather wrapped up in my own psychological problems at the moment,
and I'm reluctant to get drawn too deeply into this or any other JSH
thread (as I'm liable to do, simply because such threads provide foci
for obscure identifications, and off-topic psychological ramblings of
a tempting kind), so I'll just say that a person can, in principle at
least, wonder about their own "divided self", without getting caught
up in any of the competing ideologies about "mental health". (I can't
even be bothered to look that term up in the dictionary, because I'm
so disgusted with all the idiotic nonsense there is around the term.)
But you'll find it hard to reflect honestly on the workings of your
own mind while you're so caught up in this quixotic public conflict
with the mathematical world. I don't know how you'll find peace and
quiet to do so - at the moment, you're not giving yourself any peace.
Obligatory declaration: my postings to JSH-related threads since
Thu 25 Sep 2008 have raised £6.50 for "Charity".
========================================
>
> 1. x^2 + Dy^2 = F
>
> 2. (x-Dy)^2 + D(x+y)^2 = F*(D+1)
>
> 3. ((1-D)x-2Dy)^2 + D(2x + (1-D)y)^2 = F*(D+1)^2
>
> 4. ((1-3D)x + (2D^2 - 4D)y)^2 + D((3-D)x + (1-3D)y)^2 = F*(D+1)^3
>
Here's some more:
U(n)^2 + DV(n)^2 = F(D+1)^n
U(4) = x - 6Dx - 4Dy + D^2x + 4D^2y
V(4) = 4x + y - 4Dx - 6Dy + D^2y
U(5) = x - 10Dx - 5Dy + 5D^2x + 10D^2y - D^3y
V(5) = 5x + y - 10Dx - 10Dy + D^2x + 5D^2y
U(6) = x - 15Dx - 6Dy + 15D^2x + 20D^2y - D^3x - 6D^3y
V(6) = 6x + y - 20Dx - 15Dy + 6D^2x + 15D^2y - D^3y
U(7) = x - 21Dx - 7Dy + 35D^2x + 35D^2y - 7D^3x - 21D^3y + D^4y
V(7) = 7x + y - 35Dx - 21Dy + 21D^2x + 35D^2y - D^3x - 7D^3y
U(8) = x - 28Dx - 8Dy + 70D^2x + 56D^2y - 28D^3x - 56D^3y + D^4x +
8D^4y
V(8) = 8x + 1y - 56Dx - 28Dy + 56D^2x + 70D^2y - 8D^3x - 28D^3y +
1D^4y
Enrico
more insults :-)
Dirk Vdm
By recognizing how one person treats another. No need to classify.
--
Michael Press
+++++++++++++++++++++++++++++++++++++++++++++
> > 1. x^2 + Dy^2 = F
>
> > 2. (x-Dy)^2 + D(x+y)^2 = F*(D+1)
>
> > 3. ((1-D)x-2Dy)^2 + D(2x + (1-D)y)^2 = F*(D+1)^2
>
> > 4. ((1-3D)x + (2D^2 - 4D)y)^2 + D((3-D)x + (1-3D)y)^2 = F*(D+1)^3
Equation 4. is wrong. Here's the whole lot:
U(0) = x
V(0) = y
U(1) = x - Dy
V(1) = x + y
U(2) = x - Dx - 2Dy
V(2) = 2x + y -Dy
U(3) = x - 3Dx - 3Dy +D^2y
V(3) = 3x + y -Dx -3Dy
Thanks Enrico!!!!
James
> You have a good rhythmn to your words.
>
> Google "a poet's cry" and read my poem, and consider if you wish to
> talk to me about poetry and not math.
i like to associate situations to song lyrics
so i've wondered what might be appropriate here
"atmosphere" by joy division seemed to ring a little
but nothing popular seemed to catch the essential points
so i had to pick one of my own
it's an old one
but i think it has a clever fit
(you're not the only one people mention npd to)
it's called thirty dollar poem
*..**..**..**..**..**..**..**..**..*
scorpion embers
trace past the empty stone wall
wispy on the tail of tiger steel
recant
and let the ancients fall
tribal songs ejaculate this quiet
pastel
night
and fifteen songs ago
i was still alone
let it fall
and taste the razor clitoris
turns
and flees
at dawn:
autonomic dreams
distract the threads of self-delusion
sheets ripple serpentine
to dawn's end game
and hold
we can't hold back the chains that stroke the backs
of dead men crawling for a place to hide
to die
laughter in the breeze
children's games
no longer
mammalian fantasies
/
something crashes through the down and down
fast stops
..
there once was a time
when i thought
in stunted
malformed thoughts
that all would be well
well
these landscapes have eroded
down to nothing
and dust
and dirty dreams
i was the one who was crazy all those days
golden breath convince myself
of new and wondrous things
that break apart
i've begun to see better
what it was to cause this sweet collapse
a mariner's song
a cowboy's weathered eyes
these are the points of pain
which acupuncture this slow-rotting numbness
it goes like this:
a kid too stupid to realise
that dreams are the wrong way to go
tortures herself
'til she learns to love the pain
the slashing guilt of fallen stars
the bread-pan pounding of regret
the bright insanity of madmen's whispers
breaking through the night
again
and again
and
shit
i should have known better
--
we used to tell such beautiful lies
reclined on wicker chairs
beneath a brilliant azure sky
but i believed
we used to dream of dreams
that no one could have ever dreamed before
but i believed
and we planned and schemed
and tore on through
like bullets in a headlong race
through childhood's disease-like grace
and i believe
now
fear replaces everything
i believe that hope is for the hopeless
i believe that innocence is better left disturbed
and i believe that nothing can atone this
so
now
trapped in towers vaguely skeletal
i have watched while all my dreams fell
silently
and out into this ashen hell
i whisper
or i scream:
yes!
goddamnit yes!
i've learned my lesson well!
and i am trembling
Indeed, modesty might compel you to name the series after
some other mathematician - so what about "Lie series"?