Pi is a number that says ... how big circumference of a circle to its diameter
Reality shows that this number depends on the actual size of the circuit
Actual size is the number of mm
Math decided actual size does not matter.
Who would say math is wrong?
Because Pi is not a normal number, it is a theoretical formula which extends to Planck scale, and
which is beyond our ability to express (notate) in reality, except as a theoretical function.
Your comments are very good
2 mm can be 2.0003 mm
100 mm can be 100.001 mm
Do you think it might make sense to build a precise instrument to examine the theory of variable Pie
We cannot build a physical instrument to study universal properties and variants, except by approximation. The instruments of observation and measurement themselves introduce variants.
In theoretical mathematics 2mm can never be 2.0003 mm and 100 mm cannot ever be 100.001 mm. The numbers are NOT equal.
And moreover .0003 deviation in 2 mm does not translate in a .001 deviation in 100 mm. YOU are introducing the variants and render any calculation inexact. You are still saying that 2 can be NOT 2 and that 100 can be NOT 100, which totally disregards the exact mathematical function of theoretical science.
I can see why you say that "practical application" of science can be inexact, such as used by a machinist turning a steel cylinder or a ball bearing to within a deviation of .001 degrees, but applied science (approximation) is not the same as exact theoretical science.
Did you know that it is impossible to construct a perfect sphere on earth? Gravity alone introduces deviations.
But YOU ARE WRONG when you say that abstract mathematics are variant. You want to do away with objective science altogether!
The truth is that ONLY abstract mathematics can be exact, because it is not hindered by consideration of variant physical conditions.
And, of course, is the reason why you insist that a circle is a physical object, rather than a theoretical abstraction.
Theoretical science says (A1:A2) = (O1:O2)
Practical science says (A1:A2) > (O1:O2)
Who is right? Practical science
For practical purposes, yes, because practical science uses "finitary logic" (finite limits) and is unable to use "infinitary logic, except by approximation.
and,
An infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs. Some infinitary logics may have different properties from those of standard first-order logic. In particular, infinitary logics may fail to be compact or complete. Notions of compactness and completeness that are equivalent in finitary logic sometimes are not so in infinitary logics. Therefore for infinitary logics, notions of strong compactness and strong completeness are defined. This article addresses Hilbert-type infinitary logics, as these have been extensively studied and constitute the most straightforward extensions of finitary logic
http://en.wikipedia.org/wiki/Infinitary_logic
and
1) The concept of infinitely-small and infinitely-large variable magnitudes is a fundamental concept in mathematical analysis. The idea which was held prior to the modern approach to the concept of the infinitely small was, to wit, that finite magnitudes were composed of an infinitely-large number of infinitely-small "indivisibles" (cf. Indivisibles, method of), which were not regarded as variables, but rather as constants smaller than any finite magnitude. This idea is an example of an illegitimate separation of the infinite from the finite: The only meaningful procedure is to subdivide finite magnitudes into a without limit increasing number of components which decrease without limit
http://www.encyclopediaofmath.org/index.php/Infinity
Your comments are very good
2 mm can be 2.0003 mm
100 mm can be 100.001 mm
Do you think it might make sense to build a precise instrument to examine the theory of variable Pie
We cannot build a physical instrument to study universal properties and variants, except by approximation. The instruments of observation and measurement themselves introduce variants.
In theoretical mathematics 2mm can never be 2.0003 mm and 100 mm cannot ever be 100.001 mm. The numbers are NOT equal.
And moreover .0003 deviation in 2 mm does not translate in a .001 deviation in 100 mm. YOU are introducing the variants and render any calculation inexact. You are still saying that 2 can be NOT 2 and that 100 can be NOT 100, which totally disregards the exact mathematical function of theoretical science.
I can see why you say that "practical application" of science can be inexact, such as used by a machinist turning a steel cylinder or a ball bearing to within a deviation of .001 degrees, but applied science (approximation) is not the same as exact theoretical science.
Fixed pie is the first mistake of mathematics.
Second mistake of mathematics - infinite points can replace a curved line.
Line is the basic concept of geometry, and its data are the length and shape.
The second mistake is due - mathematics losing the shape of the line
Therefore, a mathematical calculation that takes into account the form of a line - does not exist
Physical measurement also takes into account the shape of the line, so the physics discovered the idea of changing pie.
Did you know that it is impossible to construct a perfect sphere on earth? Gravity alone introduces deviations.
But YOU ARE WRONG when you say that abstract mathematics are variant. You want to do away with objective science altogether!
The truth is that ONLY abstract mathematics can be exact, because it is not hindered by consideration of variant physical conditions.
And, of course, is the reason why you insist that a circle is a physical object, rather than a theoretical abstraction.
Theoretical science says (A1:A2) = (O1:O2)
Practical science says (A1:A2) > (O1:O2)
Who is right? Practical science
For practical purposes, yes, because practical science uses "finitary logic" (finite limits) and is unable to use "infinitary logic, except by approximation.
and,
An infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs. Some infinitary logics may have different properties from those of standard first-order logic. In particular, infinitary logics may fail to be compact or complete. Notions of compactness and completeness that are equivalent in finitary logic sometimes are not so in infinitary logics. Therefore for infinitary logics, notions of strong compactness and strong completeness are defined. This article addresses Hilbert-type infinitary logics, as these have been extensively studied and constitute the most straightforward extensions of finitary logic
http://en.wikipedia.org/wiki/Infinitary_logic
and
1) The concept of infinitely-small and infinitely-large variable magnitudes is a fundamental concept in mathematical analysis. The idea which was held prior to the modern approach to the concept of the infinitely small was, to wit, that finite magnitudes were composed of an infinitely-large number of infinitely-small "indivisibles" (cf. Indivisibles, method of), which were not regarded as variables, but rather as constants smaller than any finite magnitude. This idea is an example of an illegitimate separation of the infinite from the finite: The only meaningful procedure is to subdivide finite magnitudes into a without limit increasing number of components which decrease without limit
http://www.encyclopediaofmath.org/index.php/Infinity