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Re: Units of measurement in the USA
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Richard Heathfield
Jun 11, 2016, 4:15:42 PM6/11/16
to
Sorry to dump this on sci.math - just a matter of definition to clear
up. To save you ploughing through a lot of nonsense (below), I'll
summarise here. The question at issue is specifically regarding
Euclidean geometry. Euclid drew a distinction between "line" and
"straight line". Do modern Euclidean geometers do the same, or would
they nowadays consider that a line is straight by definition?
On 11/06/16 20:54, Peter T. Daniels wrote:
> On Saturday, June 11, 2016 at 3:11:36 PM UTC-4, Richard Heathfield wrote:
>> On 11/06/16 19:35, Peter T. Daniels wrote:
>>> On Saturday, June 11, 2016 at 11:09:14 AM UTC-4, Richard Heathfield wrote:
>>>> On 11/06/16 14:55, Peter T. Daniels wrote:
>
>>>>> I do not deny that after Book I I am lost in *Elements*, but I'm quite certain
>>>>> that in later books spheres are dealt with.
>>>> He did, yes. His definition is in Book XI: "When a semicircle with fixed
>>>> diameter is carried round and restored again to the same position from
>>>> which it began to be moved, the figure so comprehended is a sphere."
>>>> And he defines the semicircle in terms of the circle, and he calls the
>>>> bounding curve of the circle a "line", yes.
>>> Q.E.D.
>>
>> All you've demonstrated is that Euclid defined his terms in one way, and
>> nowadays we define them in another. This was not in dispute.
>
> No, I demonstrated that what you labeled as "In Euclidean geometry" was in
> fact in post-Euclidean geometry.
It may well be, whatever post-Euclidean geometry is. But my claim (that
a straight line cannot lie flat on the surface of a sphere) is also true
in Euclidean geometry (but the claim is /not/ true in elliptic geometry).
>
>>>> And nowadays we would
>>>> consider that to be outdated.
>>> If you had introduced your comment with "In post-Euclidean" or "non-Euclidean
>>> geometry," there would have been nothing to complain about.
>>
>> There is still nothing to complain about. Euclidean geometry continues
>> to be known as Euclidean geometry, even though we have moved on somewhat
>> since Euclid's day. For example, we don't insist that Euclidean
>> geometers discuss Euclidean geometry in Ancient Greek. Nor do we insist
>> on their being nailed to Euclid's precise wording. We insist only that
>> Euclid's five postulates hold. To label such a geometry as
>> 'non-Euclidean' would have been pointlessly confusing to most people.
>
> The definition of "line" as 'straight line' is simply NOT Euclidean.
Enough already. Cross-posted to sci.math - let the mathematicians have
their say.
>
>>>> We can forgive Euclid for being outdated
>>>> occasionally, given that he lived well over two thousand years ago, but
>>>> that doesn't mean we should continue to be outdated nowadays. If I come
>>>> across a 19th century treatise on number theory that considers 1 to be
>>>> prime, I don't say it's wrong - because at the time it was considered
>>>> correct. But the same usage in the 21st century would be a mistake,
>>>> because we have redefined primality to exclude 1.
>>>
>>> But you don't say, "In the 19th century 1 was not considered a prime number."
>>
>> That's right. I don't. But we're chasing a wild goose. All we're talking
>> about here is the definition of "line" (vs "straight line"), and Robert
>> Bannister specifically talked about a "straight line".
>
> No, all we're talking about is what you mistakenly claimed Euclid said.
You are misremembering. I have not misquoted Euclid anywhere.
<snip>
>>>> I'm not sure what point you're trying to prove here. Let's look at the
>>>> claim under dispute: it was claimed (and I'm rephrasing here but, I
>>>> hope, retaining the intended meaning) that, when an angle of 180 degrees
>>>> is subtended, the two 'ends' of the angle lie in a straight line.
>>>
>>> Actually no, the original claim was that from North Pole to South Pole is 180 deg.
>>
>> I am not referring to the original claim. I am referring to the claim
>> under dispute. That is why I said "the claim under dispute". The claim
>> under dispute is the claim that we have been disputing, which is a
>> rather pointless one about Euclid's prototype definitions.
>
> It is about your mischaracterization of them.
Well, it's a dispute, so you're bound to stick your oar in, and I can
hardly fault you for that, but obviously I disagree.
<snip>
>> And, in so doing, he provided an
>> opportunity for an interesting discussion about geometry.
>
> There was nothing interesting about your mistake.
Well, I don't agree that I made a mistake, and neither do I agree that
the discussion hasn't been interesting.
>>>> In elliptic geometry, the term "straight line" is used to describe what
>>>> we would ordinarily call a great circle. Let us imagine that such a
>>>> straight line has been drawn. If you mark a point on that line, put the
>>>> cross of a protractor on the point, and measure the angle subtended by
>>>> the two drawn line segments, you will find that it is 180 degrees.
>>>
>>> On the surface of the earth, a "straight line" journey necessarily follows a
>>> portion of a "Great Circle." Since the original observation was couched in terms
>>> of North Pole and South Pole, that's the relevant frame of reference.
>>
>> I would agree. So the question becomes: if we define two points A and B
>> as lying on the same great circle route drawn on the Earth, and we draw
>> a line segment from A to a new point C (also on the surface of the
>> Earth) such that the angle between AC and AB is 180 degrees, do AB and
>> AC lie on the same great circle route? And the answer is that they do.
>>
>> And quod, Mr Daniels, is what really erat demonstrandum.
>
> There was no dispute about that (since you'd omitted it from consideration).
You think I omitted from consideration the very point that I discussed
in my first reply on the subject? Okaaaaaay....
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within
up. To save you ploughing through a lot of nonsense (below), I'll
summarise here. The question at issue is specifically regarding
Euclidean geometry. Euclid drew a distinction between "line" and
"straight line". Do modern Euclidean geometers do the same, or would
they nowadays consider that a line is straight by definition?
On 11/06/16 20:54, Peter T. Daniels wrote:
> On Saturday, June 11, 2016 at 3:11:36 PM UTC-4, Richard Heathfield wrote:
>> On 11/06/16 19:35, Peter T. Daniels wrote:
>>> On Saturday, June 11, 2016 at 11:09:14 AM UTC-4, Richard Heathfield wrote:
>>>> On 11/06/16 14:55, Peter T. Daniels wrote:
>
>>>>> I do not deny that after Book I I am lost in *Elements*, but I'm quite certain
>>>>> that in later books spheres are dealt with.
>>>> He did, yes. His definition is in Book XI: "When a semicircle with fixed
>>>> diameter is carried round and restored again to the same position from
>>>> which it began to be moved, the figure so comprehended is a sphere."
>>>> And he defines the semicircle in terms of the circle, and he calls the
>>>> bounding curve of the circle a "line", yes.
>>> Q.E.D.
>>
>> All you've demonstrated is that Euclid defined his terms in one way, and
>> nowadays we define them in another. This was not in dispute.
>
> No, I demonstrated that what you labeled as "In Euclidean geometry" was in
> fact in post-Euclidean geometry.
It may well be, whatever post-Euclidean geometry is. But my claim (that
a straight line cannot lie flat on the surface of a sphere) is also true
in Euclidean geometry (but the claim is /not/ true in elliptic geometry).
>
>>>> And nowadays we would
>>>> consider that to be outdated.
>>> If you had introduced your comment with "In post-Euclidean" or "non-Euclidean
>>> geometry," there would have been nothing to complain about.
>>
>> There is still nothing to complain about. Euclidean geometry continues
>> to be known as Euclidean geometry, even though we have moved on somewhat
>> since Euclid's day. For example, we don't insist that Euclidean
>> geometers discuss Euclidean geometry in Ancient Greek. Nor do we insist
>> on their being nailed to Euclid's precise wording. We insist only that
>> Euclid's five postulates hold. To label such a geometry as
>> 'non-Euclidean' would have been pointlessly confusing to most people.
>
> The definition of "line" as 'straight line' is simply NOT Euclidean.
Enough already. Cross-posted to sci.math - let the mathematicians have
their say.
>
>>>> We can forgive Euclid for being outdated
>>>> occasionally, given that he lived well over two thousand years ago, but
>>>> that doesn't mean we should continue to be outdated nowadays. If I come
>>>> across a 19th century treatise on number theory that considers 1 to be
>>>> prime, I don't say it's wrong - because at the time it was considered
>>>> correct. But the same usage in the 21st century would be a mistake,
>>>> because we have redefined primality to exclude 1.
>>>
>>> But you don't say, "In the 19th century 1 was not considered a prime number."
>>
>> That's right. I don't. But we're chasing a wild goose. All we're talking
>> about here is the definition of "line" (vs "straight line"), and Robert
>> Bannister specifically talked about a "straight line".
>
> No, all we're talking about is what you mistakenly claimed Euclid said.
You are misremembering. I have not misquoted Euclid anywhere.
<snip>
>>>> I'm not sure what point you're trying to prove here. Let's look at the
>>>> claim under dispute: it was claimed (and I'm rephrasing here but, I
>>>> hope, retaining the intended meaning) that, when an angle of 180 degrees
>>>> is subtended, the two 'ends' of the angle lie in a straight line.
>>>
>>> Actually no, the original claim was that from North Pole to South Pole is 180 deg.
>>
>> I am not referring to the original claim. I am referring to the claim
>> under dispute. That is why I said "the claim under dispute". The claim
>> under dispute is the claim that we have been disputing, which is a
>> rather pointless one about Euclid's prototype definitions.
>
> It is about your mischaracterization of them.
Well, it's a dispute, so you're bound to stick your oar in, and I can
hardly fault you for that, but obviously I disagree.
<snip>
>> And, in so doing, he provided an
>> opportunity for an interesting discussion about geometry.
>
> There was nothing interesting about your mistake.
Well, I don't agree that I made a mistake, and neither do I agree that
the discussion hasn't been interesting.
>>>> In elliptic geometry, the term "straight line" is used to describe what
>>>> we would ordinarily call a great circle. Let us imagine that such a
>>>> straight line has been drawn. If you mark a point on that line, put the
>>>> cross of a protractor on the point, and measure the angle subtended by
>>>> the two drawn line segments, you will find that it is 180 degrees.
>>>
>>> On the surface of the earth, a "straight line" journey necessarily follows a
>>> portion of a "Great Circle." Since the original observation was couched in terms
>>> of North Pole and South Pole, that's the relevant frame of reference.
>>
>> I would agree. So the question becomes: if we define two points A and B
>> as lying on the same great circle route drawn on the Earth, and we draw
>> a line segment from A to a new point C (also on the surface of the
>> Earth) such that the angle between AC and AB is 180 degrees, do AB and
>> AC lie on the same great circle route? And the answer is that they do.
>>
>> And quod, Mr Daniels, is what really erat demonstrandum.
>
> There was no dispute about that (since you'd omitted it from consideration).
You think I omitted from consideration the very point that I discussed
in my first reply on the subject? Okaaaaaay....
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within
quasi
Jun 12, 2016, 3:04:49 AM6/12/16
to
Richard Heathfield wrote:
>
>Sorry to dump this on sci.math - just a matter of definition
>to clear up. To save you ploughing through a lot of nonsense
>(below), I'll summarise here. The question at issue is
>specifically regarding Euclidean geometry. Euclid drew a
>distinction between "line" and "straight line". Do modern
>Euclidean geometers do the same, or would they nowadays
>consider that a line is straight by definition?
So long as the implied or stated context is _Euclidean_ geometry,
>
>Sorry to dump this on sci.math - just a matter of definition
>to clear up. To save you ploughing through a lot of nonsense
>(below), I'll summarise here. The question at issue is
>specifically regarding Euclidean geometry. Euclid drew a
>distinction between "line" and "straight line". Do modern
>Euclidean geometers do the same, or would they nowadays
>consider that a line is straight by definition?
all lines are straight.
quasi
Richard Heathfield
Jun 12, 2016, 3:15:12 AM6/12/16
to
we can do in return - a quick parse, maybe, or a synonym for 'thesaurus'
- just say the word. :-)
John Gabriel
Jun 12, 2016, 4:01:56 AM6/12/16
to
Why this is marked as abuse? It has been marked as abuse.
Report not abuse
On Saturday, 11 June 2016 22:15:42 UTC+2, Richard Heathfield wrote:
> Sorry to dump this on sci.math - just a matter of definition to clear
> up. To save you ploughing through a lot of nonsense (below), I'll
> summarise here. The question at issue is specifically regarding
> Euclidean geometry. Euclid drew a distinction between "line" and
> "straight line". Do modern Euclidean geometers do the same, or would
> they nowadays consider that a line is straight by definition?
Modern geometers are morons so I can't speak for them. A line is by definition, the distance between two points. That's why there is no such thing as "infinite length" lines.
> Sorry to dump this on sci.math - just a matter of definition to clear
> up. To save you ploughing through a lot of nonsense (below), I'll
> summarise here. The question at issue is specifically regarding
> Euclidean geometry. Euclid drew a distinction between "line" and
> "straight line". Do modern Euclidean geometers do the same, or would
> they nowadays consider that a line is straight by definition?
Since there are innumerable paths between any two points, it follows the most notable path is that which is shortest, that is, a straight line.
When Euclid referred to a line being extended indefinitely in either direction, he did not mean "infinitely" as academic morons imagine. To put it simply, all he was saying is that it can be made as long as you wish.
Peter Percival
Jun 12, 2016, 6:28:02 AM6/12/16
to
--
A high and rising proportion of children are being born to mothers
least fitted to bring children into the world.... Some are of low
intelligence, most of low educational attainment. They are unlikely
to be able to give children the stable emotional background, the
consistent combination of love and firmness.... They are producing
problem children.... The balance of our human stock, is threatened...
Sir Keith Joseph
quasi
Jun 12, 2016, 3:05:27 PM6/12/16
to
Peter Percival wrote:
>quasi wrote:
>>Richard Heathfield wrote:
>>>
>>>Sorry to dump this on sci.math - just a matter of definition
>>>to clear up. To save you ploughing through a lot of nonsense
>>>(below), I'll summarise here. The question at issue is
>>>specifically regarding Euclidean geometry. Euclid drew a
>>>distinction between "line" and "straight line". Do modern
>>>Euclidean geometers do the same, or would they nowadays
>>>consider that a line is straight by definition?
>>
>>So long as the implied or stated context is _Euclidean_
>>geometry, all lines are straight.
>
>The lines of line integrals don't conform.
Conform to what?
>quasi wrote:
>>Richard Heathfield wrote:
>>>
>>>Sorry to dump this on sci.math - just a matter of definition
>>>to clear up. To save you ploughing through a lot of nonsense
>>>(below), I'll summarise here. The question at issue is
>>>specifically regarding Euclidean geometry. Euclid drew a
>>>distinction between "line" and "straight line". Do modern
>>>Euclidean geometers do the same, or would they nowadays
>>>consider that a line is straight by definition?
>>
>>So long as the implied or stated context is _Euclidean_
>>geometry, all lines are straight.
>
>The lines of line integrals don't conform.
Quoting from Wikipedia:
<https://en.wikipedia.org/wiki/Line_integral>
"In mathematics, a line integral is an integral where the
function to be integrated is evaluated along a curve."
The terminology "line integral" is traditional (and undoubtedly
old), but the use of the word "line" in "line integral" doesn't
require that the integration is to be done along a line. Of
course, a line is a special case of a curve, but line integrals
allow for greater generality.
>Any other exceptions?
Exception to what?
I don't see an exception.
quasi
Peter Percival
Jun 12, 2016, 3:36:16 PM6/12/16
to
quasi wrote:
> Peter Percival wrote:
>> quasi wrote:
>>> Richard Heathfield wrote:
>>>>
>>>> Sorry to dump this on sci.math - just a matter of definition
>>>> to clear up. To save you ploughing through a lot of nonsense
>>>> (below), I'll summarise here. The question at issue is
>>>> specifically regarding Euclidean geometry. Euclid drew a
>>>> distinction between "line" and "straight line". Do modern
>>>> Euclidean geometers do the same, or would they nowadays
>>>> consider that a line is straight by definition?
>>>
>>> So long as the implied or stated context is _Euclidean_
>>> geometry, all lines are straight.
>>
>> The lines of line integrals don't conform.
>
> Conform to what?
Lines being straight. I apologize for being unclear.
> Peter Percival wrote:
>> quasi wrote:
>>> Richard Heathfield wrote:
>>>>
>>>> Sorry to dump this on sci.math - just a matter of definition
>>>> to clear up. To save you ploughing through a lot of nonsense
>>>> (below), I'll summarise here. The question at issue is
>>>> specifically regarding Euclidean geometry. Euclid drew a
>>>> distinction between "line" and "straight line". Do modern
>>>> Euclidean geometers do the same, or would they nowadays
>>>> consider that a line is straight by definition?
>>>
>>> So long as the implied or stated context is _Euclidean_
>>> geometry, all lines are straight.
>>
>> The lines of line integrals don't conform.
>
> Conform to what?
>
> Quoting from Wikipedia:
>
> <https://en.wikipedia.org/wiki/Line_integral>
>
> "In mathematics, a line integral is an integral where the
> function to be integrated is evaluated along a curve."
>
> The terminology "line integral" is traditional (and undoubtedly
> old), but the use of the word "line" in "line integral" doesn't
> require that the integration is to be done along a line. Of
> course, a line is a special case of a curve, but line integrals
> allow for greater generality.
>
>> Any other exceptions?
>
> Exception to what?
>
> I don't see an exception.
>
> quasi
>
> Quoting from Wikipedia:
>
> <https://en.wikipedia.org/wiki/Line_integral>
>
> "In mathematics, a line integral is an integral where the
> function to be integrated is evaluated along a curve."
>
> The terminology "line integral" is traditional (and undoubtedly
> old), but the use of the word "line" in "line integral" doesn't
> require that the integration is to be done along a line. Of
> course, a line is a special case of a curve, but line integrals
> allow for greater generality.
>
>> Any other exceptions?
>
> Exception to what?
>
> I don't see an exception.
>
> quasi
>
quasi
Jun 12, 2016, 3:47:56 PM6/12/16
to
Peter Percival wrote:
>quasi wrote:
>>Peter Percival wrote:
>>>quasi wrote:
>>>>Richard Heathfield wrote:
>>>>>
>>>>>Sorry to dump this on sci.math - just a matter of definition
>>>>>to clear up. To save you ploughing through a lot of nonsense
>>>>>(below), I'll summarise here. The question at issue is
>>>>>specifically regarding Euclidean geometry. Euclid drew a
>>>>>distinction between "line" and "straight line". Do modern
>>>>>Euclidean geometers do the same, or would they nowadays
>>>>>consider that a line is straight by definition?
>>>>
>>>>So long as the implied or stated context is _Euclidean_
>>>>geometry, all lines are straight.
>>>
>>>The lines of line integrals don't conform.
>>
>>Conform to what?
>
>Lines being straight. I apologize for being unclear.
As explained in my prior reply, it's not really an exception.
>quasi wrote:
>>Peter Percival wrote:
>>>quasi wrote:
>>>>Richard Heathfield wrote:
>>>>>
>>>>>Sorry to dump this on sci.math - just a matter of definition
>>>>>to clear up. To save you ploughing through a lot of nonsense
>>>>>(below), I'll summarise here. The question at issue is
>>>>>specifically regarding Euclidean geometry. Euclid drew a
>>>>>distinction between "line" and "straight line". Do modern
>>>>>Euclidean geometers do the same, or would they nowadays
>>>>>consider that a line is straight by definition?
>>>>
>>>>So long as the implied or stated context is _Euclidean_
>>>>geometry, all lines are straight.
>>>
>>>The lines of line integrals don't conform.
>>
>>Conform to what?
>
>Lines being straight. I apologize for being unclear.
Line integrals apply to general curves, not just lines. And in
modern terminolgy, those curves are _called_ "curves". They are
not called lines (unless they actually are lines).
Of course the word "line" is context dependent, but if the
context is Euclidean geometry, the unqualified term "line"
means straight line.
Adam Funk
Jun 13, 2016, 5:45:12 AM6/13/16
to
On 2016-06-12, Richard Heathfield wrote:
> On 12/06/16 08:01, quasi wrote:
>> Richard Heathfield wrote:
>>>
>>> Sorry to dump this on sci.math - just a matter of definition
>>> to clear up. To save you ploughing through a lot of nonsense
>>> (below), I'll summarise here. The question at issue is
>>> specifically regarding Euclidean geometry. Euclid drew a
>>> distinction between "line" and "straight line". Do modern
>>> Euclidean geometers do the same, or would they nowadays
>>> consider that a line is straight by definition?
>>
>> So long as the implied or stated context is _Euclidean_ geometry,
>> all lines are straight.
>
> Thank you very much for confirming that small point. If there's anything
> we can do in return - a quick parse, maybe, or a synonym for 'thesaurus'
> - just say the word. :-)
Customer in bookshop: "I'm looking for that book that looks like a
> On 12/06/16 08:01, quasi wrote:
>> Richard Heathfield wrote:
>>>
>>> Sorry to dump this on sci.math - just a matter of definition
>>> to clear up. To save you ploughing through a lot of nonsense
>>> (below), I'll summarise here. The question at issue is
>>> specifically regarding Euclidean geometry. Euclid drew a
>>> distinction between "line" and "straight line". Do modern
>>> Euclidean geometers do the same, or would they nowadays
>>> consider that a line is straight by definition?
>>
>> So long as the implied or stated context is _Euclidean_ geometry,
>> all lines are straight.
>
> Thank you very much for confirming that small point. If there's anything
> we can do in return - a quick parse, maybe, or a synonym for 'thesaurus'
> - just say the word. :-)
dictionary but sounds like a dinosaur."
--
It is probable that television drama of high caliber and produced by
first-rate artists will materially raise the level of dramatic taste
of the nation. --- David Sarnoff, CEO of RCA, 1939; in Stoll 1995
abu.ku...@gmail.com
Jun 21, 2016, 4:48:13 PM6/21/16
to
only as long as Euclid meant, and no further
> When Euclid referred to a line being extended indefinitely in either direction, he did not mean "infinitely" as academic morons imagine. To put it simply, all he was saying is that it can be made as long as you wish.
> When Euclid referred to a line being extended indefinitely in either direction, he did not mean "infinitely" as academic morons imagine. To put it simply, all he was saying is that it can be made as long as you wish.
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