Continuum

What is the basis for reason? And mathematics?

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Skepdick
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Re: Continuum

Post by Skepdick »

Eodnhoj7 wrote: Thu Aug 20, 2020 3:52 am A point is that which is absent of any form or volume
Yes. That is how physicists think about it.
Eodnhoj7 wrote: Thu Aug 20, 2020 3:52 am it can only be observed as the change of one phenomenon to another. Phenomenon composed of points are composed of change.
Photons don't change from one phenomenon to another. They just move.
Eodnhoj7 wrote: Thu Aug 20, 2020 3:52 am An example of this would be the line. The point observes the change of one line into another line.
Photons don't form lines.
Eodnhoj7 wrote: Thu Aug 20, 2020 3:52 am Another example would be all phenomenon resulting in points. An object at a distance is reduced to a point. An object up close is reduced to points. The change in one position of a phenomenon to another results in the phenomenon expanding an contracting from a point. The expansion or contraction of a phenomenon is reduced to (a) point(s) where the point is the median of change from one phenomenon to another.
Sounds like you are describing fixed points.
Belinda
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Re: Continuum

Post by Belinda »

Skepdick wrote: Fri Aug 21, 2020 8:27 am
Eodnhoj7 wrote: Thu Aug 20, 2020 3:52 am A point is that which is absent of any form or volume
Yes. That is how physicists think about it.
Eodnhoj7 wrote: Thu Aug 20, 2020 3:52 am it can only be observed as the change of one phenomenon to another. Phenomenon composed of points are composed of change.
Photons don't change from one phenomenon to another. They just move.
Eodnhoj7 wrote: Thu Aug 20, 2020 3:52 am An example of this would be the line. The point observes the change of one line into another line.
Photons don't form lines.
Eodnhoj7 wrote: Thu Aug 20, 2020 3:52 am Another example would be all phenomenon resulting in points. An object at a distance is reduced to a point. An object up close is reduced to points. The change in one position of a phenomenon to another results in the phenomenon expanding an contracting from a point. The expansion or contraction of a phenomenon is reduced to (a) point(s) where the point is the median of change from one phenomenon to another.
Sounds like you are describing fixed points.
Skepdick wrote:
Photons don't change from one phenomenon to another. They just move.
Can photons be differentiated one from another? If so they must be subject to relativity? Location is relative to the entity that moved to it? If photons accelerate or slow down these changes relate to the observer not to the thing in itself?
Eodnhoj7
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Re: Continuum

Post by Eodnhoj7 »

Skepdick wrote: Fri Aug 21, 2020 8:27 am
Eodnhoj7 wrote: Thu Aug 20, 2020 3:52 am A point is that which is absent of any form or volume
Yes. That is how physicists think about it.
Eodnhoj7 wrote: Thu Aug 20, 2020 3:52 am it can only be observed as the change of one phenomenon to another. Phenomenon composed of points are composed of change.
Photons don't change from one phenomenon to another. They just move.

photons as composing from one phenomenon to another necessitate each photon as being defined through the relations which form it. Each photon differs through the relations which form it.
Eodnhoj7 wrote: Thu Aug 20, 2020 3:52 am An example of this would be the line. The point observes the change of one line into another line.
Photons don't form lines.

In traveling from point A to point B a line is formed. This line is the underlining summation of movements.
Eodnhoj7 wrote: Thu Aug 20, 2020 3:52 am Another example would be all phenomenon resulting in points. An object at a distance is reduced to a point. An object up close is reduced to points. The change in one position of a phenomenon to another results in the phenomenon expanding an contracting from a point. The expansion or contraction of a phenomenon is reduced to (a) point(s) where the point is the median of change from one phenomenon to another.
Sounds like you are describing fixed points.
The point is an ever present median, that of change, across a variety of phenomenon as it progresses through itself as itself thus is ever changing. The point is not fixed in any given phenomenon considering all points are composed and change through further points.
Last edited by Eodnhoj7 on Sat Aug 22, 2020 4:39 am, edited 2 times in total.
Skepdick
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Re: Continuum

Post by Skepdick »

Eodnhoj7 wrote: Fri Aug 21, 2020 4:54 pm In traveling from point A to point B a line is formed. This line is the underlining summation of movements.
https://en.wikipedia.org/wiki/World_line

Where is your world-line? I don't see it.
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bahman
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Re: Continuum

Post by bahman »

wtf wrote: Wed Aug 19, 2020 4:01 pm
bahman wrote: Wed Aug 19, 2020 9:00 am All I am saying in simple word is that if a line exists, continuum, then it is divisible no matter how many times you try to divide it otherwise you get a point after some divisions, lets call it Ω times, which leads to absurd result.
You're correct that you can always divide a line segment in half. But you persist in incorrectly using Cantor's absolute infinity Ω. It's not something you can calculate with. It's not a number. It's not a set.
I see. Therefore what you are saying is that there is no mathematician who believe that the largest natural number doesn't exist. My OP is however valid since line is made of points and there is no largest number of points on a line. That is how you could have continuum, otherwise the line was discrete, made of atoms with dimension.
wtf
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Re: Continuum

Post by wtf »

bahman wrote: Fri Aug 21, 2020 5:48 pm I see. Therefore what you are saying is that there is no mathematician who believe that the largest natural number doesn't exist.
The opposite. There is no mathematicians who does believe a largest natural number exists. Of course there are a lot of mathematicians and some of them might believe crazy things. But in mainstream math, there is no largest natural number.


bahman wrote: Fri Aug 21, 2020 5:48 pm My OP is however valid
You've already gone back on it.
bahman wrote: Fri Aug 21, 2020 5:48 pm since line is made of points and there is no largest number of points on a line.
What does that mean? The number of points is an uncountable infinity, specifically 2^(Aleph-null). This is well known. That's the "largest number of points on a line" if you want to look at it that way.
bahman wrote: Fri Aug 21, 2020 5:48 pm That is how you could have continuum, otherwise the line was discrete, made of atoms with dimension.
Mathematical lines are not made of atoms, they're made of mathematical points. You are confusing physics with math; something I asked you about days ago.
Eodnhoj7
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Re: Continuum

Post by Eodnhoj7 »

Skepdick wrote: Fri Aug 21, 2020 5:10 pm
Eodnhoj7 wrote: Fri Aug 21, 2020 4:54 pm In traveling from point A to point B a line is formed. This line is the underlining summation of movements.
https://en.wikipedia.org/wiki/World_line

Where is your world-line? I don't see it.

The world line, as evidenced by the graph shown, depends on strictly linear portions of time and space the particle is measured against thus necessitating the shortest path between two points still being the line. The concepts of space and time, as evidenced by the graph, are still expressed as strictly linear as one set of points, that of the particles trajectory, are measured against another set of points, that of time and space.
As to the particles:

Each curve is composed of a distance between two points within the distance between two other points. In simpler terms the curve is composed of quantum angles which are composed of minute straight lines. The shortest distance between two points is always a line. A curve is just a series of angles.

The only time it is not a line straight is when measuring an already curved object however this does not negate the fact a linear distance between points does not already exist. Take for example a sphere. Keeping the surface distance into account the shortest distance is a curve. However this does not negate that the shortest distance between two points on the sphere is in fact a straight line if one is to ignore the curvature. Dually quantum angles exist simultaneously.
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bahman
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Re: Continuum

Post by bahman »

wtf wrote: Fri Aug 21, 2020 7:01 pm
bahman wrote: Fri Aug 21, 2020 5:48 pm I see. Therefore what you are saying is that there is no mathematician who believe that the largest natural number doesn't exist.
The opposite. There is no mathematicians who does believe a largest natural number exists. Of course there are a lot of mathematicians and some of them might believe crazy things. But in mainstream math, there is no largest natural number.
bahman wrote: Fri Aug 21, 2020 5:48 pm My OP is however valid
You've already gone back on it.
bahman wrote: Fri Aug 21, 2020 5:48 pm since line is made of points and there is no largest number of points on a line.
What does that mean? The number of points is an uncountable infinity, specifically 2^(Aleph-null). This is well known. That's the "largest number of points on a line" if you want to look at it that way.
What are Aleph and null? Are you saying that a line is made of these number of points? If yes where is the length dependence?
wtf wrote: Fri Aug 21, 2020 7:01 pm
bahman wrote: Fri Aug 21, 2020 5:48 pm That is how you could have continuum, otherwise the line was discrete, made of atoms with dimension.
Mathematical lines are not made of atoms, they're made of mathematical points. You are confusing physics with math; something I asked you about days ago.
I am not confusing things.
wtf
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Re: Continuum

Post by wtf »

bahman wrote: Sat Aug 22, 2020 12:10 pm
and null? Are you saying that a line is made of these number of points? If yes where is the length dependence?
Aleph-0 (or Aleph-null) is the smallest infinite cardinal. It's the cardinality of the integers.

2^(Aleph-0) is the cardinality of the real numbers; that is, the number of points on a line. The ^ symbol stands for cardinal exponentiation.

The number of points on a line does not determine its length. All line segments, finite or infinite, have exactly the same number of points; namely, 2^(Aleph-null). The ^ symbol indicates cardinal exponentiation.

https://en.wikipedia.org/wiki/Aleph_number
bahman wrote: Sat Aug 22, 2020 12:10 pm I am not confusing things.
Your thoughts about points and lines are unclear.
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bahman
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Re: Continuum

Post by bahman »

wtf wrote: Sat Aug 22, 2020 4:07 pm
bahman wrote: Sat Aug 22, 2020 12:10 pm
and null? Are you saying that a line is made of these number of points? If yes where is the length dependence?
Aleph-0 (or Aleph-null) is the smallest infinite cardinal. It's the cardinality of the integers.

2^(Aleph-0) is the cardinality of the real numbers; that is, the number of points on a line. The ^ symbol stands for cardinal exponentiation.

The number of points on a line does not determine its length. All line segments, finite or infinite, have exactly the same number of points; namely, 2^(Aleph-null). The ^ symbol indicates cardinal exponentiation.

https://en.wikipedia.org/wiki/Aleph_number
bahman wrote: Sat Aug 22, 2020 12:10 pm I am not confusing things.
Your thoughts about points and lines are unclear.
The number of points for any line is similar! That sounds absurd to me.
Skepdick
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Re: Continuum

Post by Skepdick »

bahman wrote: Sun Aug 23, 2020 9:01 am The number of points for any line is similar! That sounds absurd to me.
The ideas off "infinitely smaller" or "infinitely larger" would've sounded absurd to Archimedes too...

https://en.wikipedia.org/wiki/Archimedean_property
wtf
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Re: Continuum

Post by wtf »

bahman wrote: Sun Aug 23, 2020 9:01 am The number of points for any line is similar! That sounds absurd to me.
Here is a classic visual proof for two finite line segments. You can pair up the points on each line segment by drawing a line from p through a point on the upper segment that then hits some point on the lower segment, and vice versa.

Image

Picture is from https://www.chegg.com/homework-help/ill ... 763904-exc

It's also true that the set of points in a finite line segment and an infinite line can be paired up in a one-to-one correspondence via the use of the tangent/arctangent functions from trigonometry.

Also see https://math.stackexchange.com/question ... ne-segment
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bahman
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Re: Continuum

Post by bahman »

wtf wrote: Sun Aug 23, 2020 7:43 pm
bahman wrote: Sun Aug 23, 2020 9:01 am The number of points for any line is similar! That sounds absurd to me.
Here is a classic visual proof for two finite line segments. You can pair up the points on each line segment by drawing a line from p through a point on the upper segment that then hits some point on the lower segment, and vice versa.

Image

Picture is from https://www.chegg.com/homework-help/ill ... 763904-exc

It's also true that the set of points in a finite line segment and an infinite line can be paired up in a one-to-one correspondence via the use of the tangent/arctangent functions from trigonometry.

Also see https://math.stackexchange.com/question ... ne-segment
What if we shrink AB to zero?
PeteJ
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Re: Continuum

Post by PeteJ »

I feel wtf is correct to say that there is some confusion here between what Hermann Weyl calls the 'arithmetical' and 'intuitive' continuum. The former works for mathematics and everyday physics, The latter is the continuum as it is experienced. The former is extended, the latter not.

Weyl deals with this problem comprehensively. Nothing but problems arise when we treat the fictional continuum of mathematics as if it is a real thing.
wtf
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Re: Continuum

Post by wtf »

bahman wrote: Mon Aug 24, 2020 1:45 pm What if we shrink AB to zero?
Then AB is a point and the theorem no longer applies.

Do you understand that we can match up the points of any two finite line segments in a one-to-one correspondence?

PeteJ wrote: Mon Aug 24, 2020 7:18 pm I feel wtf is correct to say that there is some confusion here between what Hermann Weyl calls the 'arithmetical' and 'intuitive' continuum. The former works for mathematics and everyday physics, The latter is the continuum as it is experienced. The former is extended, the latter not.

Weyl deals with this problem comprehensively. Nothing but problems arise when we treat the fictional continuum of mathematics as if it is a real thing.
Agreed. I never make any claims about the reality of the real numbers. On the contrary, they're a highly abstract technical construction. They're useful as heck for the physical sciences, but I doubt they are instantiated in the physical world. I don't claim they're any kind of true continuum, only that they are taken as the mathematical continuum.
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