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John Jones · Guest

There>s no left or right in a string of beads. And the middle of a
string of beads is only dependent on our being able to ascertain left
and right. But the string itself doesn>t have a left or right: thus, a
middle doesn>t belong to a string.

David C. Ullrich · Guest

On Sat, 04 Oct 2008 00:45:53 +0100, John Jones <jonescardiff@aol.com>
wrote:

[quote]There>s no left or right in a string of beads. And the middle of a
string of beads is only dependent on our being able to ascertain left
and right. But the string itself doesn>t have a left or right: thus, a
middle doesn>t belong to a string.
[/quote]
You know, it>s sad. You seem to have been born several
centuries after your time.
David C. Ullrich

"Understanding Godel isn>t about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)

Guest · Posted: Sun Oct 05, 2008 9:11 pm Post subject: Re: The middle of the string

On 4 Okt, 12:00, David C. Ullrich <dullr...@sprynet.com> wrote:
[quote]On Sat, 04 Oct 2008 00:45:53 +0100, John Jones <jonescard...@aol.com
wrote:

There>s no left or right in a string of beads. And the middle of a
string of beads is only dependent on our being able to ascertain left
and right. But the string itself doesn>t have a left or right: thus, a
middle doesn>t belong to a string.

You know, it>s sad. You seem to have been born several
centuries after your time.
David C. Ullrich

"Understanding Godel isn>t about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
[/quote]
I am sorry David, but you are wrong to insult our forefathers!

William Elliot · Guest

On Sat, 4 Oct 2008, John Jones wrote:

[quote]There>s no left or right in a string of beads. And the middle of a
string of beads is only dependent on our being able to ascertain left
and right. But the string itself doesn>t have a left or right: thus, a
middle doesn>t belong to a string.

In the middle of a string of beads is a neck.[/quote]

georgie · Guest

On Oct 6, 1:53 am, William Elliot <ma...@hevanet.remove.com> wrote:
[quote]On Sat, 4 Oct 2008, John Jones wrote:
There>s no left or right in a string of beads. And the middle of a
string of beads is only dependent on our being able to ascertain left
and right. But the string itself doesn>t have a left or right: thus, a
middle doesn>t belong to a string.

In the middle of a string of beads is a neck.
[/quote]
One could also say that the string runs down the middle.

george · Guest

On Oct 3, 7:45 pm, John Jones <jonescard...@aol.com> wrote:
[quote]There>s no left or right in a string of beads.
[/quote]
Of course there is, once you pick it up, once you put one end in your
left hand and the other in your right, and stretch it out and look at
it,
so you can actually obvserve the beads. Strings on the page HAVE
ALWAYS
ALREADY HAD this done to them. You ARE LOOKING at the evidence of
this
right now, while reading this message, so if you continue to deny it,
that
just makes you stupid.

[quote]And the middle of a string of beads is only dependent
on our being able to ascertain left
and right.
[/quote]
Oh, BULLSHIT.
You do NOT need to know left from right in order to tell where the
middle is.
The middle is wherEVER there is the SAME number of beads on EACH side!
You DO have to be able to split the string in two, but you do NOT need
to be able
to tell WHICH half is left and which is right! Grasp BOTH ends of
the string of beads
in the SAME hand and let the string hang VERTICALLY! The middle will
be the
BOTTOMmost bead(or midpoint between beads if there are an even number
of beads)
and NO concept of left or right will be needed prior, or even imputed
afterward!

[quote]But the string itself doesn>t have a left or right: thus, a
middle doesn>t belong to a string.
[/quote]
If it has a middle, then it has some beads on one side and some OTHER
beads
on the OTHER side. What you CALL the sides does NOT matter.
The point is that you have a middle IF AND ONLY IF you DO have things
on
TWO OPPOSITE SIDES OF that middle (and those things match up).

Mitch · Guest

On Oct 3, 7:45 pm, John Jones <jonescard...@aol.com> wrote:
[quote]There>s no left or right in a string of beads.
[/quote]
OK. But there is one end and the other distinct end.

[quote]And the middle of a
string of beads is only dependent on our being able to ascertain left
and right.
[/quote]
Let>s say the middle depends on having two ends then...

[quote]But the string itself doesn>t have a left or right: thus, a
middle doesn>t belong to a string.
[/quote]
But it does have one end and another, so it -does- have a middle.

Mitch

John Jones · Guest

george wrote:
[quote]On Oct 3, 7:45 pm, John Jones <jonescard...@aol.com> wrote:
There>s no left or right in a string of beads.

Of course there is, once you pick it up, once you put one end in your
left hand and the other in your right, and stretch it out and look at
it,
[/quote]
Then it>s not a string any more. It>s now an asymmetric ring.

[quote]so you can actually obvserve the beads.
[/quote]
No. You observe a hands/beads composite.

[quote]Strings on the page HAVE
ALWAYS
ALREADY HAD this done to them.
[/quote]
That is why they are not strings. There are only different page styles.

[quote]You ARE LOOKING at the evidence of
this
right now, while reading this message, so if you continue to deny it,
that
just makes you stupid.
[/quote]
No. The context of a string has been jettisoned. It is no longer a
string but is a complex object whose identity is a function of
everything in my field of view, and out of view.

[quote]And the middle of a string of beads is only dependent
on our being able to ascertain left
and right.

Oh, BULLSHIT.
You do NOT need to know left from right in order to tell where the
middle is.
The middle is wherEVER there is the SAME number of beads on EACH side!
[/quote]
How do I know I haven>t counted the same side twice if I can>t tell left
from right?

[quote]You DO have to be able to split the string in two, but you do NOT need
to be able
to tell WHICH half is left and which is right!
[/quote]
How do I know I have split the string in the middle if I can>t tell left
from right?

[quote]Grasp BOTH ends of
the string of beads
in the SAME hand and let the string hang VERTICALLY! The middle will
be the
BOTTOMmost bead(or midpoint between beads if there are an even number
of beads)
and NO concept of left or right will be needed prior, or even imputed
afterward!
[/quote]
Thank god we have gravity, hands, etc., that allow us to construct
complex objects which have a middle. Because the string won>t tell us
its middle. That>s because A STRING HAS NO MIDDLE! Idiot!

[quote]But the string itself doesn>t have a left or right: thus, a
middle doesn>t belong to a string.

If it has a middle, then it has some beads on one side and some OTHER
beads
on the OTHER side.
[/quote]
Unfortunately, a string doesn>t have different sides or segments.

[quote]What you CALL the sides does NOT matter.
[/quote]
A string doesn>t have any anyway.

[quote]The point is that you have a middle IF AND ONLY IF you DO have things
on
TWO OPPOSITE SIDES OF that middle (and those things match up).

[/quote]
Yes, do things like create an entirely different object which, lo and
behold, has a middle.

Mitch · Guest

On Oct 8, 6:59 pm, John Jones <jonescard...@aol.com> wrote:
[quote]Mitch wrote:
On Oct 3, 7:45 pm, John Jones <jonescard...@aol.com> wrote:
There>s no left or right in a string of beads.

OK. But there is one end and the other distinct end.

And the middle of a
string of beads is only dependent on our being able to ascertain left
and right.

Let>s say the middle depends on having two ends then...

Yes, ok. We have defined our string as having two ends. That>s our
definition of a string, we must define it in that way.
[/quote]
What? 'must'? Not necessarily.

[quote]And two ends MUST have a middle.
[/quote]
same response as above.

A lot of the progress on your problem would be made much easier if you
were a bit more precise, and by that I mean mathematical. Lack of
precision allows you to conjecture wildly in multiple directions
simultaneously, your choice of direction influenced by metaphorical
whim.

[quote]All I can offer against that objection is that I do not need to specify
a middle to have two ends. There is another object that has two ends - a
pair of points. But if we define 'ends' as being a property of length,
then that would get rid of that counter-example.
[/quote]
but... but then you>re talking about something different?

[quote]So it comes down to this: Does a finite line have a middle? Yes it does.
[/quote]
OK I guess.

[quote]So does a string have a middle? Only if it is a line.
[/quote]
What? Why would that possibly be relevant?

[quote]But I say that a string is not a line.
[/quote]
Sure you can say that by fiat...define string, define point, then the
rest of us can decide.

[quote]We cannot tell left from right in a string because
a string is not a line. And if a string is not a line then it has no middle.

So your example refuted my own, but only in the sense that I needed to
give a related reason why a string has no middle, viz. a string has no
middle because it is not a line, and not because it we cannot determine
left from right. In that case, my string of beads example is up the
spout. I should have kept to a mathematical string.

Wait a minute though. If all the beads are the same on a string of beads
then a string of beads has no length. I was right after all. Phew.
[/quote]
if all the beads are the same... then a string of beads has no length?
really? How does that follow?

Mitch

John Jones · Guest

Mitch wrote:
[quote]On Oct 3, 7:45 pm, John Jones <jonescard...@aol.com> wrote:
There>s no left or right in a string of beads.

OK. But there is one end and the other distinct end.

And the middle of a
string of beads is only dependent on our being able to ascertain left
and right.

Let>s say the middle depends on having two ends then...
[/quote]
Yes, ok. We have defined our string as having two ends. That>s our
definition of a string, we must define it in that way. And two ends MUST
have a middle.
All I can offer against that objection is that I do not need to specify
a middle to have two ends. There is another object that has two ends - a
pair of points. But if we define 'ends' as being a property of length,
then that would get rid of that counter-example.

So it comes down to this: Does a finite line have a middle? Yes it does.
So does a string have a middle? Only if it is a line. But I say that a
string is not a line. We cannot tell left from right in a string because
a string is not a line. And if a string is not a line then it has no middle.

So your example refuted my own, but only in the sense that I needed to
give a related reason why a string has no middle, viz. a string has no
middle because it is not a line, and not because it we cannot determine
left from right. In that case, my string of beads example is up the
spout. I should have kept to a mathematical string.

Wait a minute though. If all the beads are the same on a string of beads
then a string of beads has no length. I was right after all. Phew.

[quote]But the string itself doesn>t have a left or right: thus, a
middle doesn>t belong to a string.

But it does have one end and another, so it -does- have a middle.

Mitch
[/quote]

Mitch · Guest

On Oct 9, 2:11 pm, John Jones <jonescard...@aol.com> wrote:
[quote]Mitch wrote:
On Oct 8, 6:59 pm, John Jones <jonescard...@aol.com> wrote:
Mitch wrote:
On Oct 3, 7:45 pm, John Jones <jonescard...@aol.com> wrote:
There>s no left or right in a string of beads.
OK. But there is one end and the other distinct end.
And the middle of a
string of beads is only dependent on our being able to ascertain left
and right.
Let>s say the middle depends on having two ends then...
Yes, ok. We have defined our string as having two ends. That>s our
definition of a string, we must define it in that way.

What? 'must'? Not necessarily.

And two ends MUST have a middle.

same response as above.

I>m referring to the plain observation that a finite string has length
with two ends. It would seem obvious.
[/quote]
Define 'string', 'end', and 'middle'.

I wasn>t thinking about this before but I can immediately apply my own
logical pedantry with the single example of the empty string.

By my account, I>d guess that to call anything a middle one must have
ends respect to which it is a middle, but the empty string or null
string (the string of zero length) may have two ends the left and the
right (of course they don>t go anywhere) but no middle. or maybe the
middle of of length zero. I>ll leave that up to you.

[quote]A lot of the progress on your problem would be made much easier if you
were a bit more precise, and by that I mean mathematical. Lack of
precision allows you to conjecture wildly in multiple directions
simultaneously, your choice of direction influenced by metaphorical
whim.

It isn>t accuracy we are striving for. I don>t want to know the exact
length of the string. We are looking to the everyday principles that
inform mathematical reasoning.
[/quote]
We may not be looking for accuracy in length, but we sure are trying
to find accuracy in definition. Otherwise, how will we know when we>ve
made progress?

[quote]So it comes down to this: Does a finite line have a middle? Yes it does.

OK I guess.

So does a string have a middle? Only if it is a line.

What? Why would that possibly be relevant?

A string can have a middle if it is a finite line.
[/quote]
'can' is not 'must' (you were saying 'must' before'; I agree with
"...can...if...finite line" though)

Are you talking about strings that are like shoe-laces? or like
sequences of characters in text? or some curve in space? or what?

[quote]But I say that a string is not a line.

Sure you can say that by fiat...define string, define point, then the
rest of us can decide.

We cannot tell left from right in a string because
a string is not a line. And if a string is not a line then it has no middle.

So your example refuted my own, but only in the sense that I needed to
give a related reason why a string has no middle, viz. a string has no
middle because it is not a line, and not because it we cannot determine
left from right. In that case, my string of beads example is up the
spout. I should have kept to a mathematical string.

Wait a minute though. If all the beads are the same on a string of beads
then a string of beads has no length. I was right after all. Phew.

if all the beads are the same... then a string of beads has no length?
really? How does that follow?

If all the beads are the same I will be unable to differentiate them and
make a reliable count. If I can>t make a reliable count then I don>t
have a sequenced line. Woof.
[/quote]
What do you mean by same? indistinguishable? Then logically, you>d
have to say that if you have a set of indistinguishable items, then
you really only have 1 (or 0) items.

You>re letting your words come back to you as truth. If you know you
have a sequence of beads (0 or more), and you also know that they are
indistinguishable (pick bead x, pick bead y, every time you do this x
= y), then you have either 1 (or 0) beads. The context that you are
missing that most people presume in the culture of mathematics that
relegate this misunderstanding to a degenerate boundary case, is that
the beads are indistinguishable -up to position-, that is everything
is the same about the beads except their position in the string of
beads. Likewise with a set of beads, if you have a set of n
distinguishable items, one assumes that in a formalization, there is a
unique label on each of the n items so that no property of the item
(except for the label) is different.

As to making a reliable count, I>d say that is built in to the
definition of a string, the position of items along the string. Even
if they are otherwise identical, the position along the string is
enough to allow counting.

Mitch

John Jones · Guest

Mitch wrote:
[quote]On Oct 8, 6:59 pm, John Jones <jonescard...@aol.com> wrote:
Mitch wrote:
On Oct 3, 7:45 pm, John Jones <jonescard...@aol.com> wrote:
There>s no left or right in a string of beads.
OK. But there is one end and the other distinct end.
And the middle of a
string of beads is only dependent on our being able to ascertain left
and right.
Let>s say the middle depends on having two ends then...
Yes, ok. We have defined our string as having two ends. That>s our
definition of a string, we must define it in that way.

What? 'must'? Not necessarily.

And two ends MUST have a middle.

same response as above.
[/quote]
I>m referring to the plain observation that a finite string has length
with two ends. It would seem obvious.

[quote]A lot of the progress on your problem would be made much easier if you
were a bit more precise, and by that I mean mathematical. Lack of
precision allows you to conjecture wildly in multiple directions
simultaneously, your choice of direction influenced by metaphorical
whim.
[/quote]
It isn>t accuracy we are striving for. I don>t want to know the exact
length of the string. We are looking to the everyday principles that
inform mathematical reasoning.

[quote]All I can offer against that objection is that I do not need to specify
a middle to have two ends. There is another object that has two ends - a
pair of points. But if we define 'ends' as being a property of length,
then that would get rid of that counter-example.

but... but then you>re talking about something different?
[/quote]
Yes. But I need to say why it is different. It is different because a
pair of points has no length even though its range (like a finite line)
is covered completely by two points.

[quote]So it comes down to this: Does a finite line have a middle? Yes it does.

OK I guess.

So does a string have a middle? Only if it is a line.

What? Why would that possibly be relevant?
[/quote]
A string can have a middle if it is a finite line.

[quote]But I say that a string is not a line.

Sure you can say that by fiat...define string, define point, then the
rest of us can decide.

We cannot tell left from right in a string because
a string is not a line. And if a string is not a line then it has no middle.

So your example refuted my own, but only in the sense that I needed to
give a related reason why a string has no middle, viz. a string has no
middle because it is not a line, and not because it we cannot determine
left from right. In that case, my string of beads example is up the
spout. I should have kept to a mathematical string.

Wait a minute though. If all the beads are the same on a string of beads
then a string of beads has no length. I was right after all. Phew.

if all the beads are the same... then a string of beads has no length?
really? How does that follow?
[/quote]
If all the beads are the same I will be unable to differentiate them and
make a reliable count. If I can>t make a reliable count then I don>t
have a sequenced line. Woof.

Virgil · Guest

In article <gclhha$r28$1@aioe.org>, John Jones <jonescardiff@aol.com>
wrote:

[quote]Mitch wrote:
On Oct 8, 6:59 pm, John Jones <jonescard...@aol.com> wrote:
Mitch wrote:
On Oct 3, 7:45 pm, John Jones <jonescard...@aol.com> wrote:
There>s no left or right in a string of beads.
OK. But there is one end and the other distinct end.
And the middle of a
string of beads is only dependent on our being able to ascertain left
and right.
Let>s say the middle depends on having two ends then...
Yes, ok. We have defined our string as having two ends. That>s our
definition of a string, we must define it in that way.

What? 'must'? Not necessarily.

And two ends MUST have a middle.

same response as above.

I>m referring to the plain observation that a finite string has length
with two ends. It would seem obvious.
[/quote]
Furthermore, any string, finite or infinite, with two ends, one end or
no ends, has the property that between any two of its members there are
at most only finitely many others.

This is quite different from a line, ray or line segment.
[quote]
A lot of the progress on your problem would be made much easier if you
were a bit more precise, and by that I mean mathematical. Lack of
precision allows you to conjecture wildly in multiple directions
simultaneously, your choice of direction influenced by metaphorical
whim.

It isn>t accuracy we are striving for. I don>t want to know the exact
length of the string. We are looking to the everyday principles that
inform mathematical reasoning.

All I can offer against that objection is that I do not need to specify
a middle to have two ends. There is another object that has two ends - a
pair of points. But if we define 'ends' as being a property of length,
then that would get rid of that counter-example.

but... but then you>re talking about something different?

Yes. But I need to say why it is different. It is different because a
pair of points has no length even though its range (like a finite line)
is covered completely by two points.

So it comes down to this: Does a finite line have a middle? Yes it does.

OK I guess.

So does a string have a middle? Only if it is a line.
[/quote]
My strings have middles whenever they consist of an odd number of items.
[quote]
What? Why would that possibly be relevant?

A string can have a middle if it is a finite line.
[/quote]
Strings, unlike lines, have no more than finitely many members between
any two of their members.
[quote]
But I say that a string is not a line.
[/quote]
Right!

[quote]
Sure you can say that by fiat...define string, define point, then the
rest of us can decide.

We cannot tell left from right in a string because
a string is not a line. And if a string is not a line then it has no
middle.
[/quote]
The string "abc" has a middle.

george · Guest

On Oct 9, 2:11 pm, John Jones <jonescard...@aol.com> wrote:
[quote]I>m referring to the plain observation that a finite string has length
with two ends. It would seem obvious.
[/quote]
It IS obvious.
It is THEREFORE EQUALLY obvious that it has a middle.
If it has an odd number of beads/characters/whatEVER then the middle
is just the middle one OF THOSE. And it doesn>t even MATTER which way
you choose to orient the string, which END you NAME left OR right!
The middle IS UNchanged!
If it has an even number then the middle is not a bead but it is still
a breakpoint BETWEEN two characters/beads/whatEVER, and AGAIN,
its location does NOT change EVEN if you reverse left and right!
Strings with 2 ends have 2 orientations; every string has a reverse.
Strings of length 0 and length 1 are EQUAL to their reverses, though
they
of course are not the only strings with this property.

John Jones · Guest

Virgil wrote:
[quote]In article <gclhha$r28$1@aioe.org>, John Jones <jonescardiff@aol.com
wrote:

Mitch wrote:
On Oct 8, 6:59 pm, John Jones <jonescard...@aol.com> wrote:
Mitch wrote:
On Oct 3, 7:45 pm, John Jones <jonescard...@aol.com> wrote:
There>s no left or right in a string of beads.
OK. But there is one end and the other distinct end.
And the middle of a
string of beads is only dependent on our being able to ascertain left
and right.
Let>s say the middle depends on having two ends then...
Yes, ok. We have defined our string as having two ends. That>s our
definition of a string, we must define it in that way.
What? 'must'? Not necessarily.

And two ends MUST have a middle.
same response as above.
I>m referring to the plain observation that a finite string has length
with two ends. It would seem obvious.

Furthermore, any string, finite or infinite, with two ends, one end or
no ends, has the property that between any two of its members there are
at most only finitely many others.

This is quite different from a line, ray or line segment.
A lot of the progress on your problem would be made much easier if you
were a bit more precise, and by that I mean mathematical. Lack of
precision allows you to conjecture wildly in multiple directions
simultaneously, your choice of direction influenced by metaphorical
whim.
It isn>t accuracy we are striving for. I don>t want to know the exact
length of the string. We are looking to the everyday principles that
inform mathematical reasoning.

All I can offer against that objection is that I do not need to specify
a middle to have two ends. There is another object that has two ends - a
pair of points. But if we define 'ends' as being a property of length,
then that would get rid of that counter-example.
but... but then you>re talking about something different?
Yes. But I need to say why it is different. It is different because a
pair of points has no length even though its range (like a finite line)
is covered completely by two points.

So it comes down to this: Does a finite line have a middle? Yes it does.
OK I guess.

So does a string have a middle? Only if it is a line.

My strings have middles whenever they consist of an odd number of items.
What? Why would that possibly be relevant?
A string can have a middle if it is a finite line.

Strings, unlike lines, have no more than finitely many members between
any two of their members.
But I say that a string is not a line.

Right!

Sure you can say that by fiat...define string, define point, then the
rest of us can decide.

We cannot tell left from right in a string because
a string is not a line. And if a string is not a line then it has no
middle.

The string "abc" has a middle.
[/quote]
Any 'structure' which has unnamed (unpositioned) elements between any
two of its named (positioned) points is fragmented, whether or not there
are a finite or infinite number of elements.

So while you use the argument that a finite number of elements
distinguishes a string line from another (mendellsonian) line, neither
of your formulations are, in fact, lines.


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