Measurement: a math mystery

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Measurement: a math mystery
What is it that determines the distance between two points (say along a straight line). Suppose arbitrarily the two points are three inches apart. Counting the number of points in between is no good because no matter what the distance, there are always the same number of infinite points in between. Using a measuring stick also doesn't solve the problem because then you must agree on the distance the stick represents (plus other factors such as temperature). So if the points in between don't matter, then what does the three inches depend on?
PhilX
PhilX
Re: Measurement: a math mystery
Zeno's paradox really? You must be really bored right now?
The speed of light in a vacuum that travels x distance, considering gravity and ruling out all other factors that might change this value defines the second and the distance hence.
The speed of light is a constant, it is called c it never changes, it might have in the past but as of right now it is exact by all measurement we know.
The speed of light in a vacuum that travels x distance, considering gravity and ruling out all other factors that might change this value defines the second and the distance hence.
The speed of light is a constant, it is called c it never changes, it might have in the past but as of right now it is exact by all measurement we know.
Re: Measurement: a math mystery
Distance is not a function of the number of points in a line, as you say.Philosophy Explorer wrote:What is it that determines the distance between two points (say along a straight line). Suppose arbitrarily the two points are three inches apart. Counting the number of points in between is no good because no matter what the distance, there are always the same number of infinite points in between. Using a measuring stick also doesn't solve the problem because then you must agree on the distance the stick represents (plus other factors such as temperature). So if the points in between don't matter, then what does the three inches depend on?
PhilX
But distance is exactly a function of the stick length laid next to the line you are comparing it with, which you deny.
Why do you deny the connection between the length of the stick and the length of the line?

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Re: Measurement: a math mystery
Due to additional factors such as temperature so the length of the stick is an estimate.Breath wrote:Distance is not a function of the number of points in a line, as you say.Philosophy Explorer wrote:What is it that determines the distance between two points (say along a straight line). Suppose arbitrarily the two points are three inches apart. Counting the number of points in between is no good because no matter what the distance, there are always the same number of infinite points in between. Using a measuring stick also doesn't solve the problem because then you must agree on the distance the stick represents (plus other factors such as temperature). So if the points in between don't matter, then what does the three inches depend on?
PhilX
But distance is exactly a function of the stick length laid next to the line you are comparing it with, which you deny.
Why do you deny the connection between the length of the stick and the length of the line?
PhilX
Re: Measurement: a math mystery
Philosophy Explorer wrote:What is it that determines the distance between two points (say along a straight line). Suppose arbitrarily the two points are three inches apart. Counting the number of points in between is no good because no matter what the distance, there are always the same number of infinite points in between.
There may not be an infinite number of distinct points between your two points, in fact most likely there are not.
Using a measuring stick also doesn't solve the problem because then you must agree on the distance the stick represents (plus other factors such as temperature).
For many years a bar was kept in Paris that defined the length of a metre. It is no longer used as the definition of a metre but the principle is the same.

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Re: Measurement: a math mystery
A_Seagull said:
"There may not be an infinite number of distinct points between your two points, in fact most likely there are not."
What leads you to say this? (keep in mind I'm talking about ideal dimensionless points)
PhilX
"There may not be an infinite number of distinct points between your two points, in fact most likely there are not."
What leads you to say this? (keep in mind I'm talking about ideal dimensionless points)
PhilX
 GreatandWiseTrixie
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Re: Measurement: a math mystery
Just a bird, dude. Of course there an infinite amount of points between two points, it's common sense. Heshe's probably talking about atoms or something.Philosophy Explorer wrote:A_Seagull said:
"There may not be an infinite number of distinct points between your two points, in fact most likely there are not."
What leads you to say this? (keep in mind I'm talking about ideal dimensionless points)
PhilX
Re: Measurement: a math mystery
It there were an infinite number of points between two places, then it would require an infinite amount of information to describe the position of a point. Infinity is an idealised mathematical concept that has not been found to have any correspondence with nay physical quantity in the real world. In other words, infinity does not exist in the real world. It is much more likely that space is quantised.Philosophy Explorer wrote:A_Seagull said:
"There may not be an infinite number of distinct points between your two points, in fact most likely there are not."
What leads you to say this? (keep in mind I'm talking about ideal dimensionless points)
PhilX
There is a length, called the Planck Length, which is approximately 10**35 metres. This may be the limit the of length in the real world. Any points separated by a distance of less than this would actually be indistinguishable and hence be the same point.
PS It is quite an elegant and surprisingly simple process to calculate the Planck Length. All yo need to do is take the physical constants of the speed of light c. the gravitational constant G and Planck's constant h, together with their associated units. Then arrange the constants so that their units combine to a single length l, et voila!
 GreatandWiseTrixie
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Re: Measurement: a math mystery
Like I said, atoms or something. Planks' length applies to physical space. In math space the only limit is how much time you got and how many decimal points you wanna write.A_Seagull wrote:It there were an infinite number of points between two places, then it would require an infinite amount of information to describe the position of a point. Infinity is an idealised mathematical concept that has not been found to have any correspondence with nay physical quantity in the real world. In other words, infinity does not exist in the real world. It is much more likely that space is quantised.Philosophy Explorer wrote:A_Seagull said:
"There may not be an infinite number of distinct points between your two points, in fact most likely there are not."
What leads you to say this? (keep in mind I'm talking about ideal dimensionless points)
PhilX
There is a length, called the Planck Length, which is approximately 10**35 metres. This may be the limit the of length in the real world. Any points separated by a distance of less than this would actually be indistinguishable and hence be the same point.
PS It is quite an elegant and surprisingly simple process to calculate the Planck Length. All yo need to do is take the physical constants of the speed of light c. the gravitational constant G and Planck's constant h, together with their associated units. Then arrange the constants so that their units combine to a single length l, et voila!
Re: Measurement: a math mystery
It would have to be further points observed inherently within the line, external of the line, inherent with the points and/or external of the points. In these respect the points must have a quantative value, in order for the measurement to "exist". As a quality the point may be a symmetrical dual to 1 as quantity.Philosophy Explorer wrote: ↑Sun Mar 08, 2015 1:19 am What is it that determines the distance between two points (say along a straight line). Suppose arbitrarily the two points are three inches apart. Counting the number of points in between is no good because no matter what the distance, there are always the same number of infinite points in between. Using a measuring stick also doesn't solve the problem because then you must agree on the distance the stick represents (plus other factors such as temperature). So if the points in between don't matter, then what does the three inches depend on?
PhilX
From a qualitative perspective this thread applies here loosely:
Synthesis of Axiomatic Measurement as Modal Realism
viewtopic.php?f=16&t=23056
 GreatandWiseTrixie
 Posts: 1547
 Joined: Tue Feb 03, 2015 9:51 pm
Re: Measurement: a math mystery
Distance is about ratios.Philosophy Explorer wrote: ↑Sun Mar 08, 2015 1:19 am What is it that determines the distance between two points (say along a straight line). Suppose arbitrarily the two points are three inches apart. Counting the number of points in between is no good because no matter what the distance, there are always the same number of infinite points in between. Using a measuring stick also doesn't solve the problem because then you must agree on the distance the stick represents (plus other factors such as temperature). So if the points in between don't matter, then what does the three inches depend on?
PhilX
Re: Measurement: a math mystery
The absolute value of the difference of their coordinates on the real line. That is actually the definition of the distance between two real numbers. The distance is defined, not determined. That's a philosophical point worth noting, if that's what you are thinking about.Philosophy Explorer wrote: ↑Sun Mar 08, 2015 1:19 am What is it that determines the distance between two points (say along a straight line).
Now this is essentially an arbitrary number. Suppose we have a copy of the real line, but without any coordinates (real numbers) marked on it.
We pick two points. One, we call zero. The other, we call 1. All other real numbers are now defined. The integers are all the multiples of 1 in the right and left direction. The rationals are all the halves, thirds, quarters, etc. And the reals are the limits of Cauchy sequence of rationals.
If we picked a different point for our 1, all the distances would be scaled proportionally.
Re: Measurement: a math mystery
Measurement can be observed as the application of "dimensions" as "directions" which these directions (quantitatively) have a dual qualitative number as "spatial".
The process of measurement, in many degrees, depends on a degree of "individuation" and "unity" where the percieve phenomena is measured through a process of "multiple related parts" or "as a unified whole" and in these respects measurement is the application of symmetry through the application of dimension.
Considering all dimensions as number have corresponding spatial features, number in itself as a measurement is the manifestation of spatial properties.
Considering all measurement is the application of 1, in many respects measurement is a process of selfreflection that manifests further structures as extensions of that same measurement system. In these respects, measurement is a process of consciousness through the application of symmetry and in these respects all forms of measurements are forms of selfawareness.
The process of measurement, in many degrees, depends on a degree of "individuation" and "unity" where the percieve phenomena is measured through a process of "multiple related parts" or "as a unified whole" and in these respects measurement is the application of symmetry through the application of dimension.
Considering all dimensions as number have corresponding spatial features, number in itself as a measurement is the manifestation of spatial properties.
Considering all measurement is the application of 1, in many respects measurement is a process of selfreflection that manifests further structures as extensions of that same measurement system. In these respects, measurement is a process of consciousness through the application of symmetry and in these respects all forms of measurements are forms of selfawareness.