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Topic: A question about straight lines
Replies: 103   Last Post: Feb 8, 2014 8:28 AM

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Joe Niederberger

Posts: 3,045
Registered: 10/12/08
Re: A question about straight lines
Posted: Jan 28, 2014 12:17 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

>What is that which divides a line into two lines? Is not that a point?

That's kind of cute. Its very similar to the brilliant idea of Dedekind's from which came one of the first modern developments of real numbers.

The standard technical answer to the rest of your line here is that the "ends" of a line segment are of two types: open or closed. Did you really never hear that before? An open interval has no (least,greatest) point by the usual ordering. Its hard to imagine such, and it may not even exist in physical reality, but their are ways of grappling with it successfully for the purposes of mathematics.

More fundamentally, there are some long standing philosophical questions at the heart of the issues you raise.

#1. What is the relationship between mathematics and physical reality?

#2. How do mathematicians proceed in their work these days so as to not have to bump up against #1 too often?

I have my own partial answer to #1 that the margins are too small to contain.

The answer to #2 is that they have adopted the notion of building their theories up from axioms and definitions, which more or less remove them from worrying too much about #1 and instead forces the issue to be one of the rigid "mechanistic" relationships of a formal theory. When some questions cannot be answered within such a theory there are various ways of enlarging or bifurcating the theory.

Cheers,
Joe N


Date Subject Author
1/26/14
Read A question about straight lines
Neighbor
1/26/14
Read Re: A question about straight lines
kirby urner
1/27/14
Read Re: A question about straight lines
Neighbor
1/27/14
Read Re: A question about straight lines
Robert Hansen
1/27/14
Read Re: A question about straight lines
Bishop, Wayne
1/27/14
Read Re: A question about straight lines
kirby urner
1/27/14
Read Re: A question about straight lines
Neighbor
1/27/14
Read Re: A question about straight lines
Robert Hansen
1/27/14
Read Re: A question about straight lines
Neighbor
1/27/14
Read Re: A question about straight lines
Neighbor
1/28/14
Read Re: A question about straight lines
Neighbor
1/28/14
Read Re: A question about straight lines
Robert Hansen
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
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Robert Hansen
1/28/14
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Neighbor
1/28/14
Read Re: A question about straight lines
Robert Hansen
1/28/14
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Joe Niederberger
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Neighbor
1/28/14
Read Re: A question about straight lines
Robert Hansen
1/28/14
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Joe Niederberger
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
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Robert Hansen
1/28/14
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Neighbor
1/28/14
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Gary Tupper
1/28/14
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Robert Hansen
1/28/14
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Joe Niederberger
1/28/14
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Joe Niederberger
1/28/14
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Louis Talman
1/28/14
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Joe Niederberger
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
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Joe Niederberger
1/29/14
Read Re: A question about straight lines
Robert Hansen
1/29/14
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Bishop, Wayne
1/29/14
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GS Chandy
1/29/14
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Domenico Rosa
1/29/14
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Neighbor
1/29/14
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Joe Niederberger
1/29/14
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1/29/14
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Domenico Rosa
1/30/14
Read Re: A question about straight lines
Bishop, Wayne
1/29/14
Read Re: A question about straight lines
Joe Niederberger
1/29/14
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Neighbor
1/29/14
Read Re: A question about straight lines
Robert Hansen
1/29/14
Read Re: A question about straight lines
Joe Niederberger
1/29/14
Read Re: A question about straight lines
Joe Niederberger
1/29/14
Read Re: A question about straight lines
Robert Hansen
1/30/14
Read Re: A question about straight lines
Neighbor
1/29/14
Read Re: A question about straight lines
Robert Hansen
1/29/14
Read Re: A question about straight lines
Joe Niederberger
1/30/14
Read Re: A question about straight lines
Louis Talman
1/29/14
Read Re: A question about straight lines
Joe Niederberger
1/30/14
Read Re: A question about straight lines
Neighbor
1/30/14
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Jonathan Crabtree
1/30/14
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Joe Niederberger
1/30/14
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Joe Niederberger
1/31/14
Read Re: A question about straight lines
kirby urner
1/30/14
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Joe Niederberger
1/31/14
Read Re: A question about straight lines
Neighbor
1/30/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Neighbor
1/31/14
Read Re: A question about straight lines
Robert Hansen
1/31/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Robert Hansen
1/31/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Neighbor
1/31/14
Read Re: A question about straight lines
Robert Hansen
1/31/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Robert Hansen
1/31/14
Read Re: A question about straight lines
Neighbor
1/31/14
Read Re: A question about straight lines
Robert Hansen
1/31/14
Read Re: A question about straight lines
GS Chandy
1/31/14
Read Re: A question about straight lines
GS Chandy
1/31/14
Read Re: A question about straight lines
GS Chandy
1/31/14
Read Re: A question about straight lines
Joe Niederberger
2/1/14
Read Re: A question about straight lines
GS Chandy
2/1/14
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Robert Hansen
2/1/14
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kirby urner
2/1/14
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Robert Hansen
2/1/14
Read Re: A question about straight lines
Joe Niederberger
2/1/14
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Robert Hansen
2/1/14
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Joe Niederberger
2/2/14
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Robert Hansen
2/2/14
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kirby urner
2/1/14
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Joe Niederberger
2/2/14
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Robert Hansen
2/2/14
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James Elander
2/2/14
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GS Chandy
2/2/14
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Robert Hansen
2/2/14
Read Re: A question about straight lines
GS Chandy
2/2/14
Read Re: A question about straight lines
Robert Hansen
2/2/14
Read Re: A question about straight lines
Joe Niederberger
2/2/14
Read Re: A question about straight lines
GS Chandy
2/2/14
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Robert Hansen
2/2/14
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GS Chandy
2/4/14
Read Re: A question about straight lines
GS Chandy
2/4/14
Read Re: A question about straight lines
GS Chandy
2/4/14
Read Re: A question about straight lines
GS Chandy
2/8/14
Read Re: A question about straight lines
GS Chandy

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