Deeper than primes

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Let us research the follows:

There are two line segments, one is blue and the other is red:

________

It is quite clear that there is a zero dimension break point between the blue and the red line segments, which is not blue and not red, and it is not blue and not red only if it is observed from the point w.r.t any one of the segments, because a point does not have a direction, as line segments have.

The perception is changed if the same location is observed from one of the line segments. Now this location has a direction (left or right w.r.t the line segment) or in other words, it has a color (blue or red).

If the location has a color, than it is observed as the line segment, and the line segment (blue or red) is non-local exactly as the point (which is not blue and not red) is local.

So as we can see, there is an essential difference between a line's edge (that has a color AND direction) and a point (that does not have a color AND no direction).

By understanding this beauty, one clearly distinguishes between non-local and local elements, and one also understands that any non-finite collection of points (the elements that do not have a color AND no direction) can be a line segment (that has a color AND direction).
 
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doronshadmi said:
Let me ask you a question (it is an analogy, so please be careful):

The dimension of . (= its magnitude of existence) is exactly 0.

The dimension of _____ (= its magnitude of existence) is exactly 1.

Can a sum of non-finite . be _____ ?
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To nitpick, this is a not an analogy, it's two statements and a question.

Please define "its magnitude of existence".
Please confirm that when you say "The dimension of ." you are using '.' (without the quotes) to mean a single point and that the '_______' (without the quotes) in the phrase "The dimension of ________" means a line.
 
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doronshadmi said:
Let us research the follows:

There are two line segments, one is blue and the other is red:

________

It is quite clear that there is a zero dimension break point between the blue and the red line segments, which is not blue and not red, and it is not blue and not red only if it is observed from the point w.r.t any one of the segments, because a point does not have a direction, as line segments have.
Click to expand...

No, it is not "quite clear". There is no break. The rest of your post appears to be based on that flaw. If I draw a line segment on the X axis of a graph using the Cartesian coordinate system, between negative five (-5) and positive 5 (+5) and to include the fives, and make the red line equal to all numbers greater than zero (0) and equal to 5, the blue line would stop on zero and red would be visable at 0.000000...0001 and terminate at five. Now assuming that your red and blue line segments are a continuous part of one greater single line segment, my arguement holds true.

The rest of your post falls apart if your segments are not continuous, so your arguement is flawed.
 
Little 10 Toes said:
No, it is not "quite clear". There is no break. The rest of your post appears to be based on that flaw. If I draw a line segment on the X axis of a graph using the Cartesian coordinate system, between negative five (-5) and positive 5 (+5) and to include the fives, and make the red line equal to all numbers greater than zero (0) and equal to 5, the blue line would stop on zero and red would be visable at 0.000000...0001 and terminate at five. Now assuming that your red and blue line segments are a continuous part of one greater single line segment, my arguement holds true.

The rest of your post falls apart if your segments are not continuous, so your arguement is flawed.
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Wrong.

You have missed the difference between a point and an edge.

A point does not have a direction.

An edge has a direction.

This is a qualitative difference and not a quantitative difference.

You cannot capture this difference by using points with different values that are based on a quantitative viewpoint, because from a quantitative viewpoint you have the pairs [-5,0] and [0,5], and you miss the qualitative viewpoint (by the way, it holds for any [x,y],[y,z] pairs, such that x<y<z).

The value 0 is not blue and not red if it is a point (it does not have a direction).

The value 0 is blue or red if it is an edge (it does have a direction).

For more details, please see http://www.internationalskeptics.com/forums/showpost.php?p=4709153&postcount=2815 (including the links).


Some correction at the end of http://www.internationalskeptics.com/forums/showpost.php?p=4710310&postcount=2822 :

It has to be:
By understanding this beauty, one clearly distinguishes between non-local and local elements, and one also understands that any non-finite collection of points (the elements that do not have a color AND no direction) can't be a line segment (that has a color AND direction).
Click to expand...
 
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Little 10 Toes said:
To nitpick, this is a not an analogy, it's two statements and a question.

Please define "its magnitude of existence".
Please confirm that when you say "The dimension of ." you are using '.' (without the quotes) to mean a single point and that the '_______' (without the quotes) in the phrase "The dimension of ________" means a line.
Click to expand...
You have missed the analogy.
 
zooterkin said:
Why don't you answer the questions I asked first? Are you really interested in explaining your ideas?
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I do not know how to communicate with you, so in order to start please tell
me what is 'crisp' for you, and we shell continue from there.
 
From Dictionary.com:

1. Firm but easily broken or crumbled; brittle: crisp potato chips.
2. Pleasingly firm and fresh: crisp carrot and celery sticks.
3.
1. Bracing; invigorating: crisp mountain air.
2. Lively; sprightly: music with a crisp rhythm.
4. Conspicuously clean or new: a crisp dollar bill.
5. Marked by clarity, conciseness, and briskness: a crisp reply. See Synonyms at incisive.
6. Having small curls, waves, or ripples.

I would assume you were aiming for number 5, but actually it is more widely associated with 1-4.

This actually is a good example for why we use the mathematical language; it allows people to communicate clearly no matter what their mother tongue is. You insist on making up your own terms, and your mother tongue is not English. Posts you write are thus often misunderstood. In most cases I must admit they do not make any sense, to put it mildly.
 
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Little 10 Toes said:
Then it your fault for using a wrong analogy or for not defining what you mean. How can you fault me when you can't explain words that you use?
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Please read all of http://www.internationalskeptics.com/forums/showpost.php?p=4711347&postcount=2826 .

The two posts ( http://www.internationalskeptics.com/forums/showpost.php?p=4708998&postcount=2805 and http://www.internationalskeptics.com/forums/showpost.php?p=4710310&postcount=2822 ) are talking on the same thing, and you have missed both of them.
 
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sympathic said:
From Dictionary.com:

1. Firm but easily broken or crumbled; brittle: crisp potato chips.
2. Pleasingly firm and fresh: crisp carrot and celery sticks.
3.
1. Bracing; invigorating: crisp mountain air.
2. Lively; sprightly: music with a crisp rhythm.
4. Conspicuously clean or new: a crisp dollar bill.
5. Marked by clarity, conciseness, and briskness: a crisp reply. See Synonyms at incisive.
6. Having small curls, waves, or ripples.

I would assume you were aiming for number 5, but actually it is more widely associated with 1-4.

This actually is a good example for why we use the mathematical language; it allows people to communicate clearly no matter what their mother tongue is. You insist on making up your own terms, and your mother tongue is not English. Posts you write are thus often misunderstood. In most cases I must admit they do not make any sense, to put it mildly.
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No, it is indeed 5, and this is the way Mathematicians use this concept (see by youself over the internet, for example: http://www.socwkp.sinica.edu.tw/CharlesRagin/Ragin_NTU-day3.pdf ).
 
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Who says it was written by Mathematicians? This site is a Sociological Methodology Workshop. This does not look like a math paper - we insiders can tell...
 
Be that as it may, you are doing the same thing again. You took the word "crisp" from the term "crisp set" and used it in another context. Don't you see that it confuses whom ever you are discussing this with?
 
doronshadmi said:
Wrong.

You have missed the difference between a point and an edge.

A point does not have a direction.

An edge has a direction.

This is a qualitative difference and not a quantitative difference.

You cannot capture this difference by using points with different values that are based on a quantitative viewpoint, because from a quantitative viewpoint you have the pairs [-5,0] and [0,5], and you miss the qualitative viewpoint (by the way, it holds for any [x,y],[y,z] pairs, such that x<y<z).

The value 0 is not blue and not red if it is a point (it does not have a direction).

The value 0 is blue or red if it is an edge (it does have a direction).

For more details, please see http://www.internationalskeptics.com/forums/showpost.php?p=4709153&postcount=2815 (including the links).


Some correction at the end of http://www.internationalskeptics.com/forums/showpost.php?p=4710310&postcount=2822 :

It has to be:
Click to expand...

Your blue and red line segments can be defined in several different ways.

If we use the intervals you have given above say as [-5,0] is blue and [0,5] is red, then the ‘0’ point is included in both of those intervals. Thus would meet the requirement of being both red and blue, which by your own ‘definitions’ would make that point ‘non-local’ with respect to color.

We could use the intervals [-5,0) is blue and (0,5] is red. As the ‘0’ point is not included in either of these intervals it would be neither blue nor red by those defined intervals. Of course as L10T noted that would make your blue-red line segment not continuous and your claim about a zero dimensional boundary without color would then be correct.

We could also use the intervals [-5,0] blue and (0,5] red making ‘0’ blue or [-5,0) blue and [0,5] red making ‘0’ red.

It is quite ironic that you use the closed intervals [-5,0] and [0,5] that would actually make ‘0’ both red and blue and thus ‘non-local’ with respect to ‘color’, by your own definitions (what limited and variable definitions you have given).

A boundary is one of those ‘"well defined" agreed definitions, terms, concepts, etc …” . That can be included in a internal (closed) or excluded (open) they can even be included in multiple intervals making that boundary mutually inclusive in those intervals. Your concept of ‘edge’ is as yet undefined as is your ascription of ‘direction’, but then the lacking of definition seems to be a prerequisite for your notions.
 
The Man said:
Your blue and red line segments can be defined in several different ways.

If we use the intervals you have given above say as [-5,0] is blue and [0,5] is red, then the ‘0’ point is included in both of those intervals. Thus would meet the requirement of being both red and blue, which by your own ‘definitions’ would make that point ‘non-local’ with respect to color.

We could use the intervals [-5,0) is blue and (0,5] is red. As the ‘0’ point is not included in either of these intervals it would be neither blue nor red by those defined intervals. Of course as L10T noted that would make your blue-red line segment not continuous and your claim about a zero dimensional boundary without color would then be correct.

We could also use the intervals [-5,0] blue and (0,5] red making ‘0’ blue or [-5,0) blue and [0,5] red making ‘0’ red.

It is quite ironic that you use the closed intervals [-5,0] and [0,5] that would actually make ‘0’ both red and blue and thus ‘non-local’ with respect to ‘color’, by your own definitions (what limited and variable definitions you have given).

A boundary is one of those ‘"well defined" agreed definitions, terms, concepts, etc …” . That can be included in a internal (closed) or excluded (open) they can even be included in multiple intervals making that boundary mutually inclusive in those intervals. Your concept of ‘edge’ is as yet undefined as is your ascription of ‘direction’, but then the lacking of definition seems to be a prerequisite for your notions.
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This post is a perfect example of how Standard Mathematics cannot distinguish between the qualitative difference between a point (that has no direction) and an edge, which is inseparable of the line and therefore has a direction.

It does not matter at all that we are talking on the same location, because a point is local w.r.t this location (it is not red and not blue) and a line is non-local w.r.t this location (it is blue or red).

[x,y] = ____ where y the right blue edge of ____

[y,z] = ____ where y is the left red edge of ____

[x,y][y,z] = ________

If y is a point, ( notated as [x,y) (y,z] ) then it is not blue and not red, because a point does not have a direction (it is not left and not right).

Standard Math is based on the illusion that a point can be in more than a one location (blue AND red) by giving a one name to both blue and red line edges ( notated as [x,y] [y,z] ).

Let us make it clearer.

The minimal representation of a boundary is actually a point.

Let us use the minimal representation.

A point must be local w.r.t to the boundary (it is exactly OR not exactly the boundary).

A line segment must be non-local w.r.t the boundary (it is exactly AND not exactly the boundary).

The Man said:
A boundary is one of those ‘"well defined" agreed definitions, terms, concepts, etc …”
Click to expand...
A boundary is one of those non well defined agreed definitions, exactly as a 'dragged' point is a non well defined agreed definition ( http://www.internationalskeptics.com/forums/showpost.php?p=4709081&postcount=2811 ).
 
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doronshadmi said:
This post is a perfect example of how Standard Mathematics cannot distinguish between the qualitative difference between a point (that has no direction) and an edge, which is inseparable of the line and therefore has a direction.

It does not matter at all that we are talking on the same location, because a point is local w.r.t this location (it is not red and not blue) and a line (blue or red) is non-local w.r.t this location.

[x,y] = ____ where y the right blue edge of ____

[y,z] = ____ where y is the left red edge of ____

Standard Math is based on the illusion that a point can be in more than a one location (blue AND red) by giving a one name to both blue and red line edges.
Click to expand...

This post is a perfect example of Doron’s inability to distinguish his misinterpretations from ‘Standard Mathematics’. It does not matter that we are talking about ‘Standard Mathematics’ (or in this case intervals) Doron will simply assert his misunderstanding as some failing in ‘Standard Mathematics’. Again Doron uses a notation that indicates his point ‘y’ is included in both of his red and blue intervals and presents his misinterpretation that this indicates point ‘y’ is “in more than a one location (blue AND red)” . Doron’s misunderstanding is simply a result of him not reading (or understanding) the post he is responding to, indicating that his ascriptions of red and blue, as shown above, both include the same location ‘y’ while the intervals [x,y) (y,z] would not include that location. The illusion Doron is that you understand ‘Standard Mathematics’ or common notation and you are the only one (at least on this thread) succumbing to that illusion. Again a boundary is one of those ‘"well defined" agreed definitions, terms, concepts, etc …” while your application of the words ‘edge’ and ‘direction’ are still undefined.
 
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