Freethought & Rationalism Archive

Jarlaxle · 05-08-2002, 06:56 AM

If a point by definition has zero volume, and a line by definition is made up of an infinite number of points, how can a line have a length greater than zero?

Jarlaxle

Kenny · 05-08-2002, 07:29 AM

Quote:

Originally posted by Jarlaxle:
<strong>If a point by definition has zero volume, and a line by definition is made up of an infinite number of points, how can a line have a length greater than zero?

Jarlaxle</strong>

Actually, in geometry, the concept of a line is regarded as more fundamental than a point. A point is defined in terms of the limit of a line segment as its length approaches zero.

God Bless,
Kenny

Jarlaxle · 05-08-2002, 08:24 AM

A point has a dimension of zero, and a line has a dimension of one; correct? Yet the greater dimension is more fundamental? If so, is a plane more fundamental than a line?

Jarlaxle

Kenny · 05-08-2002, 10:19 AM

Quote:

A point has a dimension of zero, and a line has a dimension of one; correct?

Correct

Quote:

Yet the greater dimension is more fundamental?

In this particular case, in terms of definition, yes.

Quote:

If so, is a plane more fundamental than a line?

No, because a plane can be defined in terms of intersecting lines, and you don’t need to invoke the concept of a plane to define a line.

God Bless,
Kenny

Jarlaxle · 05-08-2002, 01:49 PM

So then line is the most fundamental geometric "shape"? Is this one reason why String Theory has high potential?

Jarlaxle

Kenny · 05-08-2002, 05:05 PM

Quote:

Originally posted by Jarlaxle:
<strong>So then line is the most fundamental geometric "shape"? Is this one reason why String Theory has high potential?

Jarlaxle</strong>

Well, I doubt that there is any direct connection between how geometers choose to define things and the structure of the universe.

owleye · 05-08-2002, 05:36 PM

Jarlaxle...

With respect to this question you ask:

"If a point by definition has zero volume, and a line by definition is made up of an infinite number of points, how can a line have a length greater than zero?"

Traditional subject-predicate logic was never able to solve this problem, though Newton had his finger on it with his fluxion theory of the calculus. That is, prior to modern mathematics (roughly since the advent of mathematics based on the new logic of quantification, developed by Frege, in 1879), time was used as that variable used to solve the problem you raise. That is, integration and differentiation were based on the flux theory developed by Newton.

With respect to how modern mathematics solves this problem, you might want to take a look at any book on real analysis in which a line is constructed from a continuum of points, i.e., is put in one-to-one relationship with the so-called real number continuum. It makes use of a modern theory of linear order.

owleye

Ender · 05-10-2002, 08:32 AM

Quote:

Originally posted by Kenny:Well, I doubt that there is any direct connection between how geometers choose to define things and the structure of the universe.

Watch it. Someone's bound to call you a neo-kantist with that attitude.

~WiGGiN~

Adrian Selby · 05-10-2002, 10:41 AM

Kenny, you're such a neo-Kantist...doh!

What is a neo-Kantist in this respect? I never studied much Kant, so I wonder how this term would apply.

Adrian

ChrisJ · 05-10-2002, 11:53 AM

Adrian! I guess I should have known I would run into familiar faces if I peeked my head out of Misc.

Sorry for the off topic insert...

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05-08-2002, 06:56 AM	#11
Jarlaxle Junior Member Join Date: Feb 2001 Location: Starkville, MS Posts: 60	If a point by definition has zero volume, and a line by definition is made up of an infinite number of points, how can a line have a length greater than zero? Jarlaxle

05-08-2002, 08:24 AM	#13
Jarlaxle Junior Member Join Date: Feb 2001 Location: Starkville, MS Posts: 60	A point has a dimension of zero, and a line has a dimension of one; correct? Yet the greater dimension is more fundamental? If so, is a plane more fundamental than a line? Jarlaxle

05-08-2002, 01:49 PM	#15
Jarlaxle Junior Member Join Date: Feb 2001 Location: Starkville, MS Posts: 60	So then line is the most fundamental geometric "shape"? Is this one reason why String Theory has high potential? Jarlaxle

05-08-2002, 05:36 PM	#17
owleye Regular Member Join Date: Feb 2002 Location: Home Posts: 229	Jarlaxle... With respect to this question you ask: "If a point by definition has zero volume, and a line by definition is made up of an infinite number of points, how can a line have a length greater than zero?" Traditional subject-predicate logic was never able to solve this problem, though Newton had his finger on it with his fluxion theory of the calculus. That is, prior to modern mathematics (roughly since the advent of mathematics based on the new logic of quantification, developed by Frege, in 1879), time was used as that variable used to solve the problem you raise. That is, integration and differentiation were based on the flux theory developed by Newton. With respect to how modern mathematics solves this problem, you might want to take a look at any book on real analysis in which a line is constructed from a continuum of points, i.e., is put in one-to-one relationship with the so-called real number continuum. It makes use of a modern theory of linear order. owleye

05-10-2002, 10:41 AM	#19
Adrian Selby Senior Member Join Date: Jan 2002 Location: Farnham, UK Posts: 859	Kenny, you're such a neo-Kantist...doh! What is a neo-Kantist in this respect? I never studied much Kant, so I wonder how this term would apply. Adrian

05-10-2002, 11:53 AM	#20
ChrisJ Junior Member Join Date: Apr 2002 Location: Fleuriduh Posts: 43	Adrian! I guess I should have known I would run into familiar faces if I peeked my head out of Misc. Sorry for the off topic insert...

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