| Topic: |
Science > Physics |
| User: |
"Lester Zick" |
| Date: |
19 Sep 2005 09:57:55 AM |
| Object: |
Real Number Space |
Real Number Space
---------
It is to hoped the idea of any single real number line has been or
shortly will be extirpated from the lexicon of mathematics. This is
the unequivocal conclusion of numerous posts in the spring semester
Epistemology 201: The Science of Science thread subsequently endorsed
by Robert Kolker in Epistemology 202: Advanced Topics thread.
It turns out that rational and irrationals lie together on one
straight line and transcendentals associated with curves do not. But
where transcendentals actually lie has never been made clear. Robert
Kolker vouchsafed that they lie in a plane with a rational/irrational
line but this becomes unsatisfactory when we consider the nature of
curves in general and their commensuration with straight lines.
~v~~
For example we know that transcendentals such as pi do not reside on
any straight line together with rationals and irrationals because pi
lies on a circular arc defined by a straight line segment diameter.
Consequently we can say definitely that pi lies in a plane with its
straight line segment diameter. But what of other transcendentals?
Clearly this depends on the nature and complexity of curves. For if we
define transcendentals in terms of their ratio and approximation with
straight line segments it becomes apparent that we cannot approximate
all curves in any given plane. Pi lies in a plane with straight line
rationals and irrationals.But this is only because the curve described
by pi is a plane figure, the circle.
~v~~
If we regard curves in general it is clear there are plane curves
lying in two dimensions and what I refer to as coils lying in three
dimensions and that characteristic ratios for these have to be located
in three dimensional space relative to any rational/irrational number
line. However coils can lie along a straight line axis or they can lie
along a curved axis and the curved axis itself can be a plane or three
dimension curve resulting in a kind of supercoil. And further layers
of axial coiling can presumably result in unlimited hypercoils. So how
are we to describe where a progression of transcendental coiling lies?
~v~~
Clearly transcendentals describing ratios between straight lines
segments and various curves lie somewhere in three dimensional space
because that's the only place they and their curves can lie. Yet we
must also accommodate the fact that transcendental ratios for 3D coils
cannot lie on a 2D plane together with transcendental ratios for 2D
figures like circles. So what are we to make of transcendental ratios
for super and hypercoils?
~v~~
They have to reside in space but how to describe where in space they
lie.
~v~~
It turns out that we can make as many successive right angle turns as
we want and each successive right angle turn defines a new direction
in space for the purpose of defining transcendental ratios between
straight line segments and curves and coils. But each of these further
right angle turns only defines a new direction and not a new dimension
in space because they are only successive and not mutually coincident
like the three basic mutually orthogonal spatial dimensions.
~v~~
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| User: "David R Tribble" |
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| Title: Re: Real Number Space |
20 Sep 2005 02:31:10 PM |
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Lester Zick wrote:
For example we know that transcendentals such as pi do not reside on
any straight line together with rationals and irrationals because pi
lies on a circular arc defined by a straight line segment diameter.
Consequently we can say definitely that pi lies in a plane with its
straight line segment diameter.
I always thought that pi was the irrational (transcendental) number
3.14159265358978..., so it is a point falling somewhere between
3.14 and 3.15 on the real number line.
Are you saying pi is not a point value, but a circular locus?
.
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| User: "Lester Zick" |
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| Title: Re: Real Number Space |
20 Sep 2005 03:25:22 PM |
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On 20 Sep 2005 12:31:10 -0700, "David R Tribble" <david@tribble.com>
in comp.ai.philosophy wrote:
Lester Zick wrote:
For example we know that transcendentals such as pi do not reside on
any straight line together with rationals and irrationals because pi
lies on a circular arc defined by a straight line segment diameter.
Consequently we can say definitely that pi lies in a plane with its
straight line segment diameter.
I always thought that pi was the irrational (transcendental) number
3.14159265358978...,
Pi is first and foremost the ratio between a circle and its diameter.
The fact that it has a non repeating fractional expression in cardinal
arithmetic is misleading. The only exact representation of pi occurs
on circular arcs and is not present on straight lines.
so it is a point falling somewhere between
3.14 and 3.15 on the real number line.
Yeah this is where the cardinal approximation of pi is misleading. The
approximation only indicates how close the ratio comes to a straight
line segment, in other words how close we can pin down a circular arc
to a straight line. The actual limit for any transcendental does not
fall on any straight line even though the approximations for them do.
Are you saying pi is not a point value, but a circular locus?
The phrasing here bothers me a little, but this is the general idea.
Pi is a point value but only on circular arcs. It does not fall on any
straight line segment. Point correspondence for transcendentals only
exists on curves of various descriptions.
~v~~
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| User: "HMS Beagle" |
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| Title: Re: Real Number Space |
21 Sep 2005 01:54:37 AM |
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On Tue, 20 Sep 2005 20:25:22 GMT,
(Lester Zick) wrote:
Are you saying pi is not a point value, but a circular locus?
The phrasing here bothers me a little, but this is the general idea.
Pi is a point value but only on circular arcs. It does not fall on any
straight line segment. Point correspondence for transcendentals only
exists on curves of various descriptions.
i.e. There is no finite list of linear functions that derive pi.
This only means you have realized pi is irrational (i mean to say, pi
has the *property* of irrationality).
This is only the first step. sqrt(2) only has a point correspondence
on a curved function. But sqrt(2) is not as strange as pi. Pi is a
transcendental number, which is a much stranger beast. sqrt(2) is
called "algebraic".
sqrt(2) is a "solution" to the polynomial x^2 = 2
Writing this in normal form we get x^2 + 0x - 2 = 0
Listing the coefficients, we get a vector <1,0,-2> in polynomial
space. This vector corresponds to the set of solutions {2,-2}
There exists no finite vector in polynomial space whose corresponding
solution set contains pi. Even if we "extend" the polynomial space
to contain algebraic numbers, still, none of them will have solution
sets containing pi. This is the defn of transcendental.
Zick's argument is that since it takes a COUNTABLE infinity of
operations to obtain pi exactly, that pi cannot be somehwere on the
same number line as the coefficients we "harvested" to get the
infinite sequence.
He is wrong. Because the infinite sequence is COUNTABLE, meaning the
set we need in order to iterate the infinite sequence is easily
defined by regular old positive integers. Since those are already in
the number line, there is no reason we can't use them to go onto
define other numbers in the set using them as counters and
coefficients.
.
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| User: "Lester Zick" |
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| Title: Re: Real Number Space |
21 Sep 2005 12:15:42 PM |
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On Wed, 21 Sep 2005 02:54:37 -0400, HMS Beagle <bgates@microsoft.org>
in comp.ai.philosophy wrote:
On Tue, 20 Sep 2005 20:25:22 GMT,
(Lester Zick) wrote:
Are you saying pi is not a point value, but a circular locus?
The phrasing here bothers me a little, but this is the general idea.
Pi is a point value but only on circular arcs. It does not fall on any
straight line segment. Point correspondence for transcendentals only
exists on curves of various descriptions.
i.e. There is no finite list of linear functions that derive pi.
This only means you have realized pi is irrational (i mean to say, pi
has the *property* of irrationality).
Yeah. See, the basic problem I have with your rhetorical technique,
Beagle, is that I advance certain succinct claims with supporting
rationale and answer questions addressed in those terms whereas you
reinterpret what I say and demand I analyze the correctness of what
you claim I mean. What are you trying to do, give me terminal liplash?
This is only the first step. sqrt(2) only has a point correspondence
on a curved function. But sqrt(2) is not as strange as pi. Pi is a
transcendental number, which is a much stranger beast. sqrt(2) is
called "algebraic".
You're an idiot. Sqrt(2) has an exact point correspondence on a
straight line segment defined with a right angle and unit side
lengths. You and Bob deserve each other.
sqrt(2) is a "solution" to the polynomial x^2 = 2
Writing this in normal form we get x^2 + 0x - 2 = 0
Listing the coefficients, we get a vector <1,0,-2> in polynomial
space. This vector corresponds to the set of solutions {2,-2}
There exists no finite vector in polynomial space whose corresponding
solution set contains pi. Even if we "extend" the polynomial space
to contain algebraic numbers, still, none of them will have solution
sets containing pi. This is the defn of transcendental.
Zick's argument is that since it takes a COUNTABLE infinity of
operations to obtain pi exactly, that pi cannot be somehwere on the
same number line as the coefficients we "harvested" to get the
infinite sequence.
Zick's argument was clearly stated by Zick and not your spin of Zick's
argument.
He is wrong. Because the infinite sequence is COUNTABLE, meaning the
set we need in order to iterate the infinite sequence is easily
defined by regular old positive integers. Since those are already in
the number line, there is no reason we can't use them to go onto
define other numbers in the set using them as counters and
coefficients.
You might be better off trying to locate the sqrt(2) using curves.
~v~~
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| User: "HMS Beagle" |
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| Title: Re: Real Number Space |
21 Sep 2005 08:14:41 PM |
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On Wed, 21 Sep 2005 17:15:42 GMT,
(Lester Zick) wrote:
On Wed, 21 Sep 2005 02:54:37 -0400, HMS Beagle <bgates@microsoft.org>
in comp.ai.philosophy wrote:
On Tue, 20 Sep 2005 20:25:22 GMT,
(Lester Zick) wrote:
Are you saying pi is not a point value, but a circular locus?
The phrasing here bothers me a little, but this is the general idea.
Pi is a point value but only on circular arcs. It does not fall on any
straight line segment. Point correspondence for transcendentals only
exists on curves of various descriptions.
i.e. There is no finite list of linear functions that derive pi.
This only means you have realized pi is irrational (i mean to say, pi
has the *property* of irrationality).
Yeah. See, the basic problem I have with your rhetorical technique,
Beagle, is that I advance certain succinct claims with supporting
rationale and answer questions addressed in those terms whereas you
reinterpret what I say and demand I analyze the correctness of what
you claim I mean. What are you trying to do, give me terminal liplash?
This is only the first step. sqrt(2) only has a point correspondence
on a curved function. But sqrt(2) is not as strange as pi. Pi is a
transcendental number, which is a much stranger beast. sqrt(2) is
called "algebraic".
You're an idiot. Sqrt(2) has an exact point correspondence on a
straight line segment defined with a right angle and unit side
lengths. You and Bob deserve each other.
sqrt(2) lies on the curve in the cartesian plane defined by
[1] y = sqrt x
Its corresponding point on the x-axis is (2,0)
sqrt(2) is also a coordinate of the intersection of [1] and the
vertical line, x=2
You might be better off trying to locate the sqrt(2) using curves.
sqrt(2) lies on the curve in the cartesian plane defined by
y = sqrt x
Its corresponding point on the x-axis is (2,0)
sqrt(2) is also a coordinate of the intersection of [1] and the
vertical line, x=2
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| User: "Lester Zick" |
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| Title: Re: Real Number Space |
22 Sep 2005 09:36:50 AM |
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Christ, more philosophy. Are there any first year plane geometry
students around who'd care to explain the pythagorean theorem to
Beagle here?
On Wed, 21 Sep 2005 21:14:41 -0400, HMS Beagle <bgates@microsoft.org>
in comp.ai.philosophy wrote:
On Wed, 21 Sep 2005 17:15:42 GMT,
(Lester Zick) wrote:
On Wed, 21 Sep 2005 02:54:37 -0400, HMS Beagle <bgates@microsoft.org>
in comp.ai.philosophy wrote:
On Tue, 20 Sep 2005 20:25:22 GMT,
(Lester Zick) wrote:
Are you saying pi is not a point value, but a circular locus?
The phrasing here bothers me a little, but this is the general idea.
Pi is a point value but only on circular arcs. It does not fall on any
straight line segment. Point correspondence for transcendentals only
exists on curves of various descriptions.
i.e. There is no finite list of linear functions that derive pi.
This only means you have realized pi is irrational (i mean to say, pi
has the *property* of irrationality).
Yeah. See, the basic problem I have with your rhetorical technique,
Beagle, is that I advance certain succinct claims with supporting
rationale and answer questions addressed in those terms whereas you
reinterpret what I say and demand I analyze the correctness of what
you claim I mean. What are you trying to do, give me terminal liplash?
This is only the first step. sqrt(2) only has a point correspondence
on a curved function. But sqrt(2) is not as strange as pi. Pi is a
transcendental number, which is a much stranger beast. sqrt(2) is
called "algebraic".
You're an idiot. Sqrt(2) has an exact point correspondence on a
straight line segment defined with a right angle and unit side
lengths. You and Bob deserve each other.
sqrt(2) lies on the curve in the cartesian plane defined by
[1] y = sqrt x
Its corresponding point on the x-axis is (2,0)
sqrt(2) is also a coordinate of the intersection of [1] and the
vertical line, x=2
You might be better off trying to locate the sqrt(2) using curves.
sqrt(2) lies on the curve in the cartesian plane defined by
y = sqrt x
Its corresponding point on the x-axis is (2,0)
sqrt(2) is also a coordinate of the intersection of [1] and the
vertical line, x=2
~v~~
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| User: "Sam Wormley" |
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| Title: Re: Real Number Space |
19 Sep 2005 10:08:10 AM |
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Lester Zick wrote:
For example we know that transcendentals such as pi do not reside on
any straight line together with rationals and irrationals because pi
lies on a circular arc defined by a straight line segment diameter.
Consequently we can say definitely that pi lies in a plane with its
straight line segment diameter. But what of other transcendentals?
Remind me not to let you teach any of my offsprings!
.
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| User: "Lester Zick" |
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| Title: Re: Real Number Space |
19 Sep 2005 12:21:12 PM |
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On Mon, 19 Sep 2005 15:08:10 GMT, Sam Wormley <swormley1@mchsi.com> in
comp.ai.philosophy wrote:
Lester Zick wrote:
For example we know that transcendentals such as pi do not reside on
any straight line together with rationals and irrationals because pi
lies on a circular arc defined by a straight line segment diameter.
Consequently we can say definitely that pi lies in a plane with its
straight line segment diameter. But what of other transcendentals?
Remind me not to let you teach any of my offsprings!
You know who they are?
~v~~
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| User: "" |
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| Title: Re: Real Number Space |
20 Sep 2005 09:47:09 PM |
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Lester Zick wrote:
Real Number Space
---------
It is to hoped the idea of any single real number line has been or
shortly will be extirpated from the lexicon of mathematics. This is
the unequivocal conclusion of numerous posts in the spring semester
Epistemology 201: The Science of Science thread subsequently endorsed
by Robert Kolker in Epistemology 202: Advanced Topics thread.
Quite a claim, Professor Zick, and _endorsed_ by Robert Kolker, no
less. We'd better believe it.
Small snag: "real number line" appears to have a Doppelganger. You have
made it clear that when mathematicians talk about the real number line
(RNL), they are talking about the wrong thing. Their definition is
wrong, you say, since actually "the real number line" means what I'll
refer to as ZRNL (that is, the Zick miscomprehension of RNL).
I'm still not entirely clear what the implications of this are: the
mathematician who says something true about RNL is unwittingly saying
something false about ZRNL? Like the Italian worker told to paint 'TUO'
on a glass door of a corner shop in the North of England, who thinks he
is writing a genitive second person pronoun, but is unwittingly doing
something entirely different? Well, what is it, exactly, that you
aspire to the extirpation of? The term ("RNL"), or one or other of its
referents (RNL or ZRNL)? Surely not the term - after all, we use terms
with nonexistent referents all the time - "the nonexistent largest
finite number" for example. So which referent? The one you can't
understand, or the one that doesn't make any sense? I dunno - I
wouldn't get your hopes up, if I were you (which mercifully I am not).
<snipple snopple>
Clearly this depends on the nature and complexity of curves. For if we
define transcendentals in terms of their ratio ...
We do? What ratio would this be, exactly? Give an example please.
If we regard curves in general it is clear ...
Good. Glad something is.
... there are plane curves
lying in two dimensions and what I refer to as coils lying in three
dimensions and that characteristic ratios for these have to be located
in three dimensional space relative to any rational/irrational number
line. However coils can lie along a straight line axis or they can lie
along a curved axis and the curved axis itself can be a plane or three
dimension curve resulting in a kind of supercoil. And further layers
of axial coiling can presumably result in unlimited hypercoils. So how
are we to describe where a progression of transcendental coiling lies?
Obviously, convolutedly, the way you do it best.
Clearly transcendentals describing ratios between straight lines
segments and various curves lie somewhere in three dimensional space
because that's the only place they and their curves can lie.
What does it mean, incidentally, this "lie"? Don't numbers all tell the
truth?
It turns out ...
I think in this case I'd prefer to start "It turns in ..." but have it
your own way. I hope this thread isn't destined to bog down sci.math
for thousands of posts, by the way.
Brian Chandler
http://imaginatorium.org
.
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| User: "Lester Zick" |
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| Title: Re: Real Number Space |
21 Sep 2005 10:48:10 AM |
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On 20 Sep 2005 19:47:09 -0700, in
comp.ai.philosophy wrote:
Lester Zick wrote:
Real Number Space
---------
It is to hoped the idea of any single real number line has been or
shortly will be extirpated from the lexicon of mathematics. This is
the unequivocal conclusion of numerous posts in the spring semester
Epistemology 201: The Science of Science thread subsequently endorsed
by Robert Kolker in Epistemology 202: Advanced Topics thread.
Quite a claim, Professor Zick, and _endorsed_ by Robert Kolker, no
less. We'd better believe it.
Small snag: "real number line" appears to have a Doppelganger. You have
made it clear that when mathematicians talk about the real number line
(RNL), they are talking about the wrong thing. Their definition is
wrong, you say, since actually "the real number line" means what I'll
refer to as ZRNL (that is, the Zick miscomprehension of RNL).
I'm still not entirely clear what the implications of this are: the
mathematician who says something true about RNL is unwittingly saying
something false about ZRNL? Like the Italian worker told to paint 'TUO'
on a glass door of a corner shop in the North of England, who thinks he
is writing a genitive second person pronoun, but is unwittingly doing
something entirely different? Well, what is it, exactly, that you
aspire to the extirpation of? The term ("RNL"), or one or other of its
referents (RNL or ZRNL)? Surely not the term - after all, we use terms
with nonexistent referents all the time - "the nonexistent largest
finite number" for example. So which referent? The one you can't
understand, or the one that doesn't make any sense? I dunno - I
wouldn't get your hopes up, if I were you (which mercifully I am not).
Let me know when you manage to reduce this to a mathspeak formalism
so we can consider whether it's true or false, assuming modern math
has actually stopped just assuming the truth of its definitions.
<snipple snopple>
Clearly this depends on the nature and complexity of curves. For if we
define transcendentals in terms of their ratio ...
We do? What ratio would this be, exactly? Give an example please.
Pi, the ratio of a circle's circumference to its diameter.
If we regard curves in general it is clear ...
Good. Glad something is.
... there are plane curves
lying in two dimensions and what I refer to as coils lying in three
dimensions and that characteristic ratios for these have to be located
in three dimensional space relative to any rational/irrational number
line. However coils can lie along a straight line axis or they can lie
along a curved axis and the curved axis itself can be a plane or three
dimension curve resulting in a kind of supercoil. And further layers
of axial coiling can presumably result in unlimited hypercoils. So how
are we to describe where a progression of transcendental coiling lies?
Obviously, convolutedly, the way you do it best.
Clearly transcendentals describing ratios between straight lines
segments and various curves lie somewhere in three dimensional space
because that's the only place they and their curves can lie.
What does it mean, incidentally, this "lie"? Don't numbers all tell the
truth?
Mine do.
It turns out ...
I think in this case I'd prefer to start "It turns in ..." but have it
your own way. I hope this thread isn't destined to bog down sci.math
for thousands of posts, by the way.
Sure, Brian, counting your contributions which I admit didn't amount
to much but did help to fan the fires to some eight thousand posts by
last count.
~v~~
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| User: "" |
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| Title: Re: Real Number Space |
21 Sep 2005 12:16:26 PM |
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Lester Zick wrote:
On 20 Sep 2005 19:47:09 -0700, in
comp.ai.philosophy wrote:
Lester Zick wrote:
Real Number Space
---------
It is to hoped the idea of any single real number line has been or
shortly will be extirpated from the lexicon of mathematics. This is
the unequivocal conclusion of numerous posts in the spring semester
Epistemology 201: The Science of Science thread subsequently endorsed
by Robert Kolker in Epistemology 202: Advanced Topics thread.
Quite a claim, Professor Zick, and _endorsed_ by Robert Kolker, no
less. We'd better believe it.
Small snag: "real number line" appears to have a Doppelganger. You have
made it clear that when mathematicians talk about the real number line
(RNL), they are talking about the wrong thing. Their definition is
wrong, you say, since actually "the real number line" means what I'll
refer to as ZRNL (that is, the Zick miscomprehension of RNL).
I'm still not entirely clear what the implications of this are: the
mathematician who says something true about RNL is unwittingly saying
something false about ZRNL? Like the Italian worker told to paint 'TUO'
on a glass door of a corner shop in the North of England, who thinks he
is writing a genitive second person pronoun, but is unwittingly doing
something entirely different? Well, what is it, exactly, that you
aspire to the extirpation of? The term ("RNL"), or one or other of its
referents (RNL or ZRNL)? Surely not the term - after all, we use terms
with nonexistent referents all the time - "the nonexistent largest
finite number" for example. So which referent? The one you can't
understand, or the one that doesn't make any sense? I dunno - I
wouldn't get your hopes up, if I were you (which mercifully I am not).
Let me know when you manage to reduce this to a mathspeak formalism
so we can consider whether it's true or false, assuming modern math
has actually stopped just assuming the truth of its definitions.
What does it mean to "assume the truth of a definition"? If I define
the term "frangible" of an integer to mean that it has at least three
distinct prime factors, can this definition be "wrong"? How?
<snipple snopple>
Clearly this depends on the nature and complexity of curves. For if we
define transcendentals in terms of their ratio ...
We do? What ratio would this be, exactly? Give an example please.
Pi, the ratio of a circle's circumference to its diameter.
OK. Does every Ztranscendental have its own "ratio"? I've forgotten the
details: you think the standard definition of "transcendental" is
"wrong", no? So how about, say, Liouville's number
(0.1100010000000000000000010000... or sigma(10^-n!)); does this have a
"ratio", or is it not a Ztranscendental after all? (I believe it was
the first number shown to be transcendental, in the normal sense.)
Clearly transcendentals describing ratios between straight lines
segments and various curves lie somewhere in three dimensional space
because that's the only place they and their curves can lie.
What does it mean, incidentally, this "lie"? Don't numbers all tell the
truth?
Mine do.
Ah, yes, but I remember now - we never found out what "lie on a curve"
means, so we have no way of knowing whether or not they are lying.
~v~~
Oh, right! It's "not or not not"? Or not?
Brian Chandler
http://imaginatorium.org
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| User: "Lester Zick" |
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| Title: Re: Real Number Space |
21 Sep 2005 05:05:22 PM |
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On 21 Sep 2005 10:16:26 -0700, in
comp.ai.philosophy wrote:
Lester Zick wrote:
On 20 Sep 2005 19:47:09 -0700, in
comp.ai.philosophy wrote:
Lester Zick wrote:
Real Number Space
---------
It is to hoped the idea of any single real number line has been or
shortly will be extirpated from the lexicon of mathematics. This is
the unequivocal conclusion of numerous posts in the spring semester
Epistemology 201: The Science of Science thread subsequently endorsed
by Robert Kolker in Epistemology 202: Advanced Topics thread.
Quite a claim, Professor Zick, and _endorsed_ by Robert Kolker, no
less. We'd better believe it.
Small snag: "real number line" appears to have a Doppelganger. You have
made it clear that when mathematicians talk about the real number line
(RNL), they are talking about the wrong thing. Their definition is
wrong, you say, since actually "the real number line" means what I'll
refer to as ZRNL (that is, the Zick miscomprehension of RNL).
I'm still not entirely clear what the implications of this are: the
mathematician who says something true about RNL is unwittingly saying
something false about ZRNL? Like the Italian worker told to paint 'TUO'
on a glass door of a corner shop in the North of England, who thinks he
is writing a genitive second person pronoun, but is unwittingly doing
something entirely different? Well, what is it, exactly, that you
aspire to the extirpation of? The term ("RNL"), or one or other of its
referents (RNL or ZRNL)? Surely not the term - after all, we use terms
with nonexistent referents all the time - "the nonexistent largest
finite number" for example. So which referent? The one you can't
understand, or the one that doesn't make any sense? I dunno - I
wouldn't get your hopes up, if I were you (which mercifully I am not).
Let me know when you manage to reduce this to a mathspeak formalism
so we can consider whether it's true or false, assuming modern math
has actually stopped just assuming the truth of its definitions.
What does it mean to "assume the truth of a definition"? If I define
the term "frangible" of an integer to mean that it has at least three
distinct prime factors, can this definition be "wrong"? How?
It might actually have four distinct prime factors.
<snipple snopple>
Clearly this depends on the nature and complexity of curves. For if we
define transcendentals in terms of their ratio ...
We do? What ratio would this be, exactly? Give an example please.
Pi, the ratio of a circle's circumference to its diameter.
OK. Does every Ztranscendental have its own "ratio"?
Hard to tell what you mean. Transcendentals have ratios.
I've forgotten the
details: you think the standard definition of "transcendental" is
"wrong", no?
The standard definition has nothing to do with the true definition.
So how about, say, Liouville's number
(0.1100010000000000000000010000... or sigma(10^-n!)); does this have a
"ratio", or is it not a Ztranscendental after all?
You indicate it has some ratio by specifying a cardinal approximation.
I can't tell what else you might think you're doing or not doing.
(I believe it was
the first number shown to be transcendental, in the normal sense.)
And I think you're wrong. At least Archimedes seems to have shown pi
is transcendental in the true sense.
Clearly transcendentals describing ratios between straight lines
segments and various curves lie somewhere in three dimensional space
because that's the only place they and their curves can lie.
What does it mean, incidentally, this "lie"? Don't numbers all tell the
truth?
Mine do.
Ah, yes, but I remember now - we never found out what "lie on a curve"
means, so we have no way of knowing whether or not they are lying.
Just as empiricists have no way of knowing whether or not their
guesses are lying and you have no idea whether or not your definitions
are lying.
~v~~
Oh, right! It's "not or not not"? Or not?
Got it on your first guess.
~v~~
.
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| User: "" |
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| Title: Re: Real Number Space |
22 Sep 2005 01:09:15 AM |
|
|
Lester Zick wrote:
On 21 Sep 2005 10:16:26 -0700, in
comp.ai.philosophy wrote:
Lester Zick wrote:
On 20 Sep 2005 19:47:09 -0700, in
comp.ai.philosophy wrote:
Lester Zick wrote:
Real Number Space
---------
It is to hoped the idea of any single real number line has been or
shortly will be extirpated from the lexicon of mathematics. This is
the unequivocal conclusion of numerous posts in the spring semester
Epistemology 201: The Science of Science thread subsequently endorsed
by Robert Kolker in Epistemology 202: Advanced Topics thread.
Quite a claim, Professor Zick, and _endorsed_ by Robert Kolker, no
less. We'd better believe it.
Small snag: "real number line" appears to have a Doppelganger. You have
made it clear that when mathematicians talk about the real number line
(RNL), they are talking about the wrong thing. Their definition is
wrong, you say, since actually "the real number line" means what I'll
refer to as ZRNL (that is, the Zick miscomprehension of RNL).
I'm still not entirely clear what the implications of this are: the
mathematician who says something true about RNL is unwittingly saying
something false about ZRNL? Like the Italian worker told to paint 'TUO'
on a glass door of a corner shop in the North of England, who thinks he
is writing a genitive second person pronoun, but is unwittingly doing
something entirely different? Well, what is it, exactly, that you
aspire to the extirpation of? The term ("RNL"), or one or other of its
referents (RNL or ZRNL)? Surely not the term - after all, we use terms
with nonexistent referents all the time - "the nonexistent largest
finite number" for example. So which referent? The one you can't
understand, or the one that doesn't make any sense? I dunno - I
wouldn't get your hopes up, if I were you (which mercifully I am not).
Let me know when you manage to reduce this to a mathspeak formalism
so we can consider whether it's true or false, assuming modern math
has actually stopped just assuming the truth of its definitions.
What does it mean to "assume the truth of a definition"? If I define
the term "frangible" of an integer to mean that it has at least three
distinct prime factors, can this definition be "wrong"? How?
It might actually have four distinct prime factors.
It? The _definition_ might have prime factors? Or what is the referent
of 'it', and how would this suggest the definition is "wrong"?
<snipple snopple>
Clearly this depends on the nature and complexity of curves. For if we
define transcendentals in terms of their ratio ...
We do? What ratio would this be, exactly? Give an example please.
Pi, the ratio of a circle's circumference to its diameter.
OK. Does every Ztranscendental have its own "ratio"?
Hard to tell what you mean. Transcendentals have ratios.
Have to take your word for that, I suppose.
So how about, say, Liouville's number
(0.1100010000000000000000010000... or sigma(10^-n!)); does this have a
"ratio", or is it not a Ztranscendental after all?
You indicate it has some ratio by specifying a cardinal approximation.
Could you explain what a "cardinal approximation" is? I assume you
don't use 'cardinal' to mean what it normally means in mathematics.
Brian Chandler
http://imaginatorium.org
.
|
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| User: "Lester Zick" |
|
| Title: Re: Real Number Space |
22 Sep 2005 09:44:08 AM |
|
|
On 21 Sep 2005 23:09:15 -0700, in
comp.ai.philosophy wrote:
Lester Zick wrote:
On 21 Sep 2005 10:16:26 -0700, in
comp.ai.philosophy wrote:
Lester Zick wrote:
On 20 Sep 2005 19:47:09 -0700, in
comp.ai.philosophy wrote:
Lester Zick wrote:
Real Number Space
---------
It is to hoped the idea of any single real number line has been or
shortly will be extirpated from the lexicon of mathematics. This is
the unequivocal conclusion of numerous posts in the spring semester
Epistemology 201: The Science of Science thread subsequently endorsed
by Robert Kolker in Epistemology 202: Advanced Topics thread.
Quite a claim, Professor Zick, and _endorsed_ by Robert Kolker, no
less. We'd better believe it.
Small snag: "real number line" appears to have a Doppelganger. You have
made it clear that when mathematicians talk about the real number line
(RNL), they are talking about the wrong thing. Their definition is
wrong, you say, since actually "the real number line" means what I'll
refer to as ZRNL (that is, the Zick miscomprehension of RNL).
I'm still not entirely clear what the implications of this are: the
mathematician who says something true about RNL is unwittingly saying
something false about ZRNL? Like the Italian worker told to paint 'TUO'
on a glass door of a corner shop in the North of England, who thinks he
is writing a genitive second person pronoun, but is unwittingly doing
something entirely different? Well, what is it, exactly, that you
aspire to the extirpation of? The term ("RNL"), or one or other of its
referents (RNL or ZRNL)? Surely not the term - after all, we use terms
with nonexistent referents all the time - "the nonexistent largest
finite number" for example. So which referent? The one you can't
understand, or the one that doesn't make any sense? I dunno - I
wouldn't get your hopes up, if I were you (which mercifully I am not).
Let me know when you manage to reduce this to a mathspeak formalism
so we can consider whether it's true or false, assuming modern math
has actually stopped just assuming the truth of its definitions.
What does it mean to "assume the truth of a definition"? If I define
the term "frangible" of an integer to mean that it has at least three
distinct prime factors, can this definition be "wrong"? How?
It might actually have four distinct prime factors.
It? The _definition_ might have prime factors? Or what is the referent
of 'it', and how would this suggest the definition is "wrong"?
Come, come, Brian, stop being childish. I imagine the "it" I refer to
is the same as "it" you refer to.If you have as much trouble cyphering
as parsing it's little wonder you prefer modern math to mathematics.
<snipple snopple>
Clearly this depends on the nature and complexity of curves. For if we
define transcendentals in terms of their ratio ...
We do? What ratio would this be, exactly? Give an example please.
Pi, the ratio of a circle's circumference to its diameter.
OK. Does every Ztranscendental have its own "ratio"?
Hard to tell what you mean. Transcendentals have ratios.
Have to take your word for that, I suppose.
You'd rather take someone elses word?
So how about, say, Liouville's number
(0.1100010000000000000000010000... or sigma(10^-n!)); does this have a
"ratio", or is it not a Ztranscendental after all?
You indicate it has some ratio by specifying a cardinal approximation.
Could you explain what a "cardinal approximation" is? I assume you
don't use 'cardinal' to mean what it normally means in mathematics.
Cardinal normally means equal differences in mathematics. I don't know
what it normally means in modern mathspeak. Cardinal approximation
means you indicate an approximation in terms of cardinal integers.
~v~~
.
|
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| User: "" |
|
| Title: Re: Real Number Space |
22 Sep 2005 12:46:04 PM |
|
|
Lester Zick wrote:
On 21 Sep 2005 23:09:15 -0700, in
comp.ai.philosophy wrote:
Lester Zick wrote:
On 21 Sep 2005 10:16:26 -0700, in
comp.ai.philosophy wrote:
Lester Zick wrote:
On 20 Sep 2005 19:47:09 -0700, in
comp.ai.philosophy wrote:
Lester Zick wrote:
Real Number Space
---------
It is to hoped the idea of any single real number line has been or
shortly will be extirpated from the lexicon of mathematics. This is
the unequivocal conclusion of numerous posts in the spring semester
Epistemology 201: The Science of Science thread subsequently endorsed
by Robert Kolker in Epistemology 202: Advanced Topics thread.
Quite a claim, Professor Zick, and _endorsed_ by Robert Kolker, no
less. We'd better believe it.
Small snag: "real number line" appears to have a Doppelganger. You have
made it clear that when mathematicians talk about the real number line
(RNL), they are talking about the wrong thing. Their definition is
wrong, you say, since actually "the real number line" means what I'll
refer to as ZRNL (that is, the Zick miscomprehension of RNL).
I'm still not entirely clear what the implications of this are: the
mathematician who says something true about RNL is unwittingly saying
something false about ZRNL? Like the Italian worker told to paint 'TUO'
on a glass door of a corner shop in the North of England, who thinks he
is writing a genitive second person pronoun, but is unwittingly doing
something entirely different? Well, what is it, exactly, that you
aspire to the extirpation of? The term ("RNL"), or one or other of its
referents (RNL or ZRNL)? Surely not the term - after all, we use terms
with nonexistent referents all the time - "the nonexistent largest
finite number" for example. So which referent? The one you can't
understand, or the one that doesn't make any sense? I dunno - I
wouldn't get your hopes up, if I were you (which mercifully I am not).
Let me know when you manage to reduce this to a mathspeak formalism
so we can consider whether it's true or false, assuming modern math
has actually stopped just assuming the truth of its definitions.
What does it mean to "assume the truth of a definition"? If I define
the term "frangible" of an integer to mean that it has at least three
distinct prime factors, can this definition be "wrong"? How?
It might actually have four distinct prime factors.
It? The _definition_ might have prime factors? Or what is the referent
of 'it', and how would this suggest the definition is "wrong"?
Come, come, Brian, stop being childish. I imagine the "it" I refer to
is the same as "it" you refer to.If you have as much trouble cyphering
as parsing it's little wonder you prefer modern math to mathematics.
OK, there's only one 'it' in my sentence, so:
If I define "frangible" to mean (of an integer) that it, the integer,
has at least three disctinct prime factors, then it, the same integer
may well have four distinct prime factors. Well, for any particular
frangible integer, that is indeed true, since four is more than three.
And is this supposed to suggest something is "wrong" about the
definition?
<snip snap>
Cardinal normally means equal differences in mathematics. I don't know
what it normally means in modern mathspeak.
Would you care to give us a reference that describes "cardinal" as
meaning "equal differences" (whatever _that_ is supposed to mean in
this context), or possibly a century being the most recent such a usage
obtained?
Brian Chandler
http://imaginatorium.org
.
|
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|
| User: "Lester Zick" |
|
| Title: Re: Real Number Space |
22 Sep 2005 03:29:54 PM |
|
|
On 22 Sep 2005 10:46:04 -0700, in
comp.ai.philosophy wrote:
Lester Zick wrote:
On 21 Sep 2005 23:09:15 -0700, in
comp.ai.philosophy wrote:
Lester Zick wrote:
On 21 Sep 2005 10:16:26 -0700, in
comp.ai.philosophy wrote:
Lester Zick wrote:
On 20 Sep 2005 19:47:09 -0700, in
comp.ai.philosophy wrote:
Lester Zick wrote:
Real Number Space
---------
It is to hoped the idea of any single real number line has been or
shortly will be extirpated from the lexicon of mathematics. This is
the unequivocal conclusion of numerous posts in the spring semester
Epistemology 201: The Science of Science thread subsequently endorsed
by Robert Kolker in Epistemology 202: Advanced Topics thread.
Quite a claim, Professor Zick, and _endorsed_ by Robert Kolker, no
less. We'd better believe it.
Small snag: "real number line" appears to have a Doppelganger. You have
made it clear that when mathematicians talk about the real number line
(RNL), they are talking about the wrong thing. Their definition is
wrong, you say, since actually "the real number line" means what I'll
refer to as ZRNL (that is, the Zick miscomprehension of RNL).
I'm still not entirely clear what the implications of this are: the
mathematician who says something true about RNL is unwittingly saying
something false about ZRNL? Like the Italian worker told to paint 'TUO'
on a glass door of a corner shop in the North of England, who thinks he
is writing a genitive second person pronoun, but is unwittingly doing
something entirely different? Well, what is it, exactly, that you
aspire to the extirpation of? The term ("RNL"), or one or other of its
referents (RNL or ZRNL)? Surely not the term - after all, we use terms
with nonexistent referents all the time - "the nonexistent largest
finite number" for example. So which referent? The one you can't
understand, or the one that doesn't make any sense? I dunno - I
wouldn't get your hopes up, if I were you (which mercifully I am not).
Let me know when you manage to reduce this to a mathspeak formalism
so we can consider whether it's true or false, assuming modern math
has actually stopped just assuming the truth of its definitions.
What does it mean to "assume the truth of a definition"? If I define
the term "frangible" of an integer to mean that it has at least three
distinct prime factors, can this definition be "wrong"? How?
It might actually have four distinct prime factors.
It? The _definition_ might have prime factors? Or what is the referent
of 'it', and how would this suggest the definition is "wrong"?
Come, come, Brian, stop being childish. I imagine the "it" I refer to
is the same as "it" you refer to.If you have as much trouble cyphering
as parsing it's little wonder you prefer modern math to mathematics.
OK, there's only one 'it' in my sentence, so:
If I define "frangible" to mean (of an integer) that it, the integer,
has at least three disctinct prime factors, then it, the same integer
may well have four distinct prime factors. Well, for any particular
frangible integer, that is indeed true, since four is more than three.
And is this supposed to suggest something is "wrong" about the
definition?
Anything is possible when you work with assumptions of truth.
<snip snap>
Cardinal normally means equal differences in mathematics. I don't know
what it normally means in modern mathspeak.
Would you care to give us a reference that describes "cardinal" as
meaning "equal differences" (whatever _that_ is supposed to mean in
this context), or possibly a century being the most recent such a usage
obtained?
You asked for the definition of cardinal in the part you snipped,
which I gave. Now you're complaining about the definition? Did I give
you some reason to complain? Did I claim it was the modern math
assumption for definition of the term? Did I claim it was the most
frequently assumed definition of the term? If you wanted some other
definition you should have qualified the question. You asked. I
answered the question you asked.
~v~~
.
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|
|
| User: "HMS Beagle" |
|
| Title: Re: Real Number Space |
21 Sep 2005 10:38:20 PM |
|
|
On Wed, 21 Sep 2005 22:05:22 GMT,
(Lester Zick) wrote:
I've forgotten the
details: you think the standard definition of "transcendental" is
"wrong", no?
The standard definition has nothing to do with the true definition.
Ok. What is the "true definition"?
(I believe it was
the first number shown to be transcendental, in the normal sense.)
And I think you're wrong. At least Archimedes seems to have shown pi
is transcendental in the true sense.
What exactly are you claiming that Archimedes showed?
.
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| User: "Lester Zick" |
|
| Title: Re: Real Number Space |
22 Sep 2005 09:38:23 AM |
|
|
On Wed, 21 Sep 2005 23:38:20 -0400, HMS Beagle <bgates@microsoft.org>
in comp.ai.philosophy wrote:
On Wed, 21 Sep 2005 22:05:22 GMT,
(Lester Zick) wrote:
I've forgotten the
details: you think the standard definition of "transcendental" is
"wrong", no?
The standard definition has nothing to do with the true definition.
Ok. What is the "true definition"?
For transcendentals? The ratio between straight line segments and
curves.
(I believe it was
the first number shown to be transcendental, in the normal sense.)
And I think you're wrong. At least Archimedes seems to have shown pi
is transcendental in the true sense.
What exactly are you claiming that Archimedes showed?
That pi is transcendental.
~v~~
.
|
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| User: "Robert J. Kolker" |
|
| Title: Re: Real Number Space |
22 Sep 2005 10:00:08 AM |
|
|
Lester Zick wrote:
What exactly are you claiming that Archimedes showed?
That pi is transcendental.
Archimedes never proved that. It was not shown until the late 19-th
century c.e. He did not even prove that pi was irrational.
John Heinrich Lambert proved pi is irrational in 1761.
The Lindeman-Weirstrass theorem showing pi is transcendental was proved
in 1861 and a slicker proof by Hilbert in 1896.
You do not know the history of mathematics very well, do you?
Archimedes produced an -approximation- to pi using inscribed and
circumscibed polygons to a circle. He got to about the equivalent of 6
decimal places which is pretty good for someone with no computers or
decent arithmetic or algebra.
Bob Kolker
.
|
|
|
| User: "Lester Zick" |
|
| Title: Re: Real Number Space |
22 Sep 2005 03:23:04 PM |
|
|
On Thu, 22 Sep 2005 11:00:08 -0400, "Robert J. Kolker"
<nowhere@nowhere.com> in comp.ai.philosophy wrote:
Lester Zick wrote:
What exactly are you claiming that Archimedes showed?
That pi is transcendental.
Archimedes never proved that. It was not shown until the late 19-th
century c.e. He did not even prove that pi was irrational.
Can you prove that, Bob? My recollection is contrary.
John Heinrich Lambert proved pi is irrational in 1761.
The Lindeman-Weirstrass theorem showing pi is transcendental was proved
in 1861 and a slicker proof by Hilbert in 1896.
You do not know the history of mathematics very well, do you?
Well enough to know Archimedes proved pi could not be constructed of
straight line segments.
Archimedes produced an -approximation- to pi using inscribed and
circumscibed polygons to a circle. He got to about the equivalent of 6
decimal places which is pretty good for someone with no computers or
decent arithmetic or algebra.
If memory serves he also proved a lack of commensuration between
straight line segments and circular curves for the calculation of pi.
~v~~
.
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| User: "Robert Israel" |
|
| Title: Re: Real Number Space |
22 Sep 2005 05:39:34 PM |
|
|
In article <433312b4.52513671@netnews.att.net>,
Lester Zick <lesterDELzick@worldnet.att.net> wrote:
On Thu, 22 Sep 2005 11:00:08 -0400, "Robert J. Kolker"
<nowhere@nowhere.com> in comp.ai.philosophy wrote:
Lester Zick wrote:
What exactly are you claiming that Archimedes showed?
That pi is transcendental.
Archimedes never proved that. It was not shown until the late 19-th
century c.e. He did not even prove that pi was irrational.
Can you prove that, Bob? My recollection is contrary.
You want him to prove that Archimedes didn't prove something?
How could he possibly do that? But certainly nothing we have of
Archimedes' writings contains anything close to the mathematical
tools necessary to prove transcendentality of pi. He didn't even
have the concept of a polynomial, so he couldn't even define
"transcendental". And no, I haven't read all of Archimedes' known
works - but if it was there I'm pretty confident I would have
heard about it.
John Heinrich Lambert proved pi is irrational in 1761.
The Lindeman-Weirstrass theorem showing pi is transcendental was proved
in 1861 and a slicker proof by Hilbert in 1896.
You do not know the history of mathematics very well, do you?
Well enough to know Archimedes proved pi could not be constructed of
straight line segments.
Nonsense.
Archimedes produced an -approximation- to pi using inscribed and
circumscibed polygons to a circle. He got to about the equivalent of 6
decimal places which is pretty good for someone with no computers or
decent arithmetic or algebra.
If memory serves he also proved a lack of commensuration between
straight line segments and circular curves for the calculation of pi.
Your memory doesn't serve you very well.
Robert Israel
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.
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| User: "Lester Zick" |
|
| Title: Re: Real Number Space |
22 Sep 2005 08:31:19 PM |
|
|
On 22 Sep 2005 22:39:34 GMT, (Robert Israel) in
comp.ai.philosophy wrote:
In article <433312b4.52513671@netnews.att.net>,
Lester Zick <lesterDELzick@worldnet.att.net> wrote:
On Thu, 22 Sep 2005 11:00:08 -0400, "Robert J. Kolker"
<nowhere@nowhere.com> in comp.ai.philosophy wrote:
Lester Zick wrote:
What exactly are you claiming that Archimedes showed?
That pi is transcendental.
Archimedes never proved that. It was not shown until the late 19-th
century c.e. He did not even prove that pi was irrational.
Can you prove that, Bob? My recollection is contrary.
You want him to prove that Archimedes didn't prove something?
How could he possibly do that?
Probably the same way he expects me to deduce Planck's constant from
analytical considerations. The only difference is that I succeed where
he fails.
But certainly nothing we have of
Archimedes' writings contains anything close to the mathematical
tools necessary to prove transcendentality of pi.
Let me simplify it for your pedestrian mentality. Did Archimedes
demonstrate a lack of commensuration between straight line segments
and circular curves for the approximation of pi?
He didn't even
have the concept of a polynomial, so he couldn't even define
"transcendental".
It's not clear what you imagine the relevance of polynomials is to the
determination of transcendentals.
And no, I haven't read all of Archimedes' known
works -
Well perhaps you can comment intelligently on the issue when you have.
but if it was there I'm pretty confident I would have
heard about it.
I'm sure you'd make a good confidence man.
John Heinrich Lambert proved pi is irrational in 1761.
The Lindeman-Weirstrass theorem showing pi is transcendental was proved
in 1861 and a slicker proof by Hilbert in 1896.
You do not know the history of mathematics very well, do you?
Well enough to know Archimedes proved pi could not be constructed of
straight line segments.
Nonsense.
So pi can be constructed of straight line segments?
Archimedes produced an -approximation- to pi using inscribed and
circumscibed polygons to a circle. He got to about the equivalent of 6
decimal places which is pretty good for someone with no computers or
decent arithmetic or algebra.
If memory serves he also proved a lack of commensuration between
straight line segments and circular curves for the calculation of pi.
Your memory doesn't serve you very well.
Probably better than yours serves you unless you claim to calculate pi
using straight line segments instead of curves.
~v~~
.
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| User: "Virgil" |
|
| Title: Re: Real Number Space |
22 Sep 2005 08:51:35 PM |
|
|
In article <4333592a.53554524@netnews.att.net>,
(Lester Zick) wrote:
On 22 Sep 2005 22:39:34 GMT, (Robert Israel) in
comp.ai.philosophy wrote:
Let me simplify it for your pedestrian mentality. Did Archimedes
demonstrate a lack of commensuration between straight line segments
and circular curves for the approximation of pi?
He didn't even
have the concept of a polynomial, so he couldn't even define
"transcendental".
It's not clear what you imagine the relevance of polynomials is to
the determination of transcendentals.
I do not know what definition of transcendental Lester Zick is using,
but the one I am familiar with, and suspect that Robert Israel is using,
is that a number is transcendental if and only if it is not a zero
(root) of any polynomial with rational coefficients.
By this definition polynomials are relevant.
I would be interested in seeing a definition of transcendental in which
polynomials were entirely irrelevant, though I doubt any such definition
exists.
.
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| User: "Lester Zick" |
|
| Title: Re: Real Number Space |
23 Sep 2005 02:14:02 PM |
|
|
On Thu, 22 Sep 2005 19:51:35 -0600, Virgil
<ITSnetNOTcom#virgil@COMCAST.com> in comp.ai.philosophy wrote:
In article <4333592a.53554524@netnews.att.net>,
lesterDELzick@worldnet.att.net (Lester Zick) wrote:
On 22 Sep 2005 22:39:34 GMT, (Robert Israel) in
comp.ai.philosophy wrote:
Let me simplify it for your pedestrian mentality. Did Archimedes
demonstrate a lack of commensuration between straight line segments
and circular curves for the approximation of pi?
He didn't even
have the concept of a polynomial, so he couldn't even define
"transcendental".
It's not clear what you imagine the relevance of polynomials is to
the determination of transcendentals.
I do not know what definition of transcendental Lester Zick is using,
but the one I am familiar with, and suspect that Robert Israel is using,
is that a number is transcendental if and only if it is not a zero
(root) of any polynomial with rational coefficients.
By this definition polynomials are relevant.
Oh, I see the problem now. You're talking about the modern math
defintion of transcendental whereas I'm using my own definition of
transcendental as the ratio between curve and straight line segment.
Now what makes you think your definition is true and mine false?
I would be interested in seeing a definition of transcendental in which
polynomials were entirely irrelevant, though I doubt any such definition
exists.
A transcendental is the ratio between a curve and straight line
segment.
~v~~
.
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| User: "Robert J. Kolker" |
|
| Title: Re: Real Number Space |
23 Sep 2005 03:15:50 PM |
|
|
Lester Zick wrote:
Oh, I see the problem now. You're talking about the modern math
defintion of transcendental whereas I'm using my own definition of
transcendental as the ratio between curve and straight line segment.
Now what makes you think your definition is true and mine false?
In a mathematical conversation in a mathematical context, you use
conventional mathematical definitions, not you coo coo ideosyncratic
nonsense. When in Rome, speak Italian or Latin.
Definitions are neither true nor false. They are conventions that are
used or not used depending on the context.
Bob Kolker
.
|
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| User: "Lester Zick" |
|
| Title: Re: Real Number Space |
24 Sep 2005 11:00:09 AM |
|
|
On Fri, 23 Sep 2005 16:15:50 -0400, "Robert J. Kolker"
<nowhere@nowhere.com> in comp.ai.philosophy wrote:
Lester Zick wrote:
Oh, I see the problem now. You're talking about the modern math
defintion of transcendental whereas I'm using my own definition of
transcendental as the ratio between curve and straight line segment.
Now what makes you think your definition is true and mine false?
In a mathematical conversation in a mathematical context, you use
conventional mathematical definitions, not you coo coo ideosyncratic
nonsense. When in Rome, speak Italian or Latin.
So in conversations with liars I should lie?
Definitions are neither true nor false. They are conventions that are
used or not used depending on the context.
Well I don't say you're never wrong, Bob, so much as hardly ever
right. It might help in your contention above if you knew what true
and false actually meant instead of just assuming you know what they
mean and assuming that definitions and conventions cannot be false.
~v~~
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| User: "Robert J. Kolker" |
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| Title: Re: Real Number Space |
24 Sep 2005 01:05:18 PM |
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Lester Zick wrote:>
Well I don't say you're never wrong, Bob, so much as hardly ever
right. It might help in your contention above if you knew what true
and false actually meant instead of just assuming you know what they
mean and assuming that definitions and conventions cannot be false.
True = conformant with fact.
False = contrary to fact.
Next question?
Bob Kolker
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| User: "Lester Zick" |
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| Title: Re: Real Number Space |
24 Sep 2005 03:47:11 PM |
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On Sat, 24 Sep 2005 14:05:18 -0400, "Robert J. Kolker"
<nowhere@nowhere.com> in comp.ai.philosophy wrote:
Lester Zick wrote:>
Well I don't say you're never wrong, Bob, so much as hardly ever
right. It might help in your contention above if you knew what true
and false actually meant instead of just assuming you know what they
mean and assuming that definitions and conventions cannot be false.
True = conformant with fact.
False = contrary to fact.
Next question?
Next question, Bob, is exactly where you learned these evasions?
These are just terminological regressions. Empiricism has no
reductions for true or false except "not inconsistent/inconsistent"
which reduce nothing to "fact".
~v~~
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| User: "Autymn D. C." |
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| Title: Re: Real Number Space |
25 Sep 2005 07:23:17 AM |
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Robert J. Kolker wrote:
True = conformant with fact.
False = contrary to fact.
Facts are deeds; they are sunthetic axioms only. Hey, let's stick with
English:
true = fitting within given framework
fake = fitting without given framework
-Aut
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| User: "Robert J. Kolker" |
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| Title: Re: Real Number Space |
25 Sep 2005 11:29:39 AM |
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Autymn D. C. wrote:
Robert J. Kolker wrote:
True = conformant with fact.
False = contrary to fact.
Facts are deeds; they are sunthetic axioms only. Hey, let's stick with
English:
true = fitting within given framework
fake = fitting without given framework
Facts are what the world is. World states.
Bob Kolker
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