The Holographic Universe and Pi = 4 in Kinematics!

[MarkE]

...but what is a perfect circle?  Is it formed non-physically / abstractly on paper, or physically by inertia of a moving mass and some quasi-centripetal force?
These two circles are not equivalent. ...but both have circumferences and diameters that are measured differently and analyzed differently by math since the former does not contain a time variable and the latter does.

A circle is a well defined geometric shape.  You appear to be diving deeper and deeper into Sophistry.

Agreed.  But when you measure the circumference of a perfect circle with constant tangential velocity of a moving mass and its diameter with the constant velocity of equal magnitude then you are dealing with a physical circle and the two lengths of these two different physical paths obtained by this method, refer to that physical circle  ...and the ratio of these two lengths is 4.

The very fact that the ratio value that you obtain does not correspond to the defined ratio of the length of a circle's circumference to its diameter tells you that by definition what you are measuring is not the ratio of the length of some circle's circumference to its diameter.

When you measure a non-physical circle (e.g. abstract circle on paper) then the ratio of its circumference to diameter is 3.1415...
If you limit your definition of Π as the ratio of circumference to diameter in abstract circles only, then you are only correct.

You will find Pi defined as the ratio of a circle's circumference to its diameter everywhere from Wolfram-Alpha to Mirriam-Webster.

[verpies]

A circle is a well defined geometric shape.

It is - in abstract geometry devoid of time.

You appear to be diving deeper and deeper into Sophistry.

Instead of writing that borderline Ad Hominem remark your time would be better spent proving that abstract timeless circles are equivalent to physical circles.

The very fact that the ratio value that you obtain does not correspond to the defined ratio of the length of a circle's circumference to its diameter tells you that by definition what you are measuring is not the ratio of the length of some circle's circumference to its diameter.

Not necessarily. This discrepancy can also be an indication that physical circles are not the same as non-physical circles.

You will find Pi defined as the ratio of a circle's circumference to its diameter everywhere from Wolfram-Alpha to Mirriam-Webster.

Abstract geometric circles - yes.  Not physical ones.

[MarkE]

It is - in abstract geometry devoid of time.
Instead of writing that borderline Ad Hominem remark your time would be better spent proving that abstract timeless circles are equivalent to physical circles.
Not necessarily. This discrepancy can also be an indication that physical circles and non-physical circles are not the same.
Abstract geometric circles - yes.  Not physical ones.

Begin with the definition:  Pi is the ratio of a given circle's circumference to its diameter.
Take the ratio that you propose represents the ratio of a given circle's circumference to that circle's diameter of your proposed "circle".
Compare that ratio to a numerical evaluation of Pi to a precision commensurate to the accuracy you have obtained your test ratio.

You state that your comparison fails on a gross level:  by over 20%.  Ergo your interpretation of your "circle's" dimensions fails to demonstrate a basic property of circles.  You are free to set about trying to prove all that: your "circle" that according to your evaluation grossly fails to demonstrate a basic property of circles is really a circle, and your measurement of the circumference is correct, and your measurement of the diameter is correct.  Good luck with all that.

[verpies]

Begin with the definition:  Pi is the ratio of a given circle's circumference to its diameter.

I agree with that definition, but not all distance has to be measured by a flexible string.

Take the ratio that you propose represents the ratio of a given circle's circumference to that circle's diameter of your proposed "circle".

Yes and my proposed circle is formed as described here.

You state that your comparison fails on a gross level:  by over 20%.  Ergo your interpretation of your "circle's" dimensions fails to demonstrate a basic property of circles.

That conclusion is non-sequitur. 
This disparity just proves that physical circles have different properties from abstract geometric circles.
Instead of vaguely attacking my "interpretation" maybe you could point out concrete errors in my measurements of the circumference of my circle.

You are free to set about trying to prove all that: your "circle" that according to your evaluation grossly fails to demonstrate a basic property of circles is really a circle, and your measurement of the circumference is correct, and your measurement of the diameter is correct.  Good luck with all that.

That's why I wrote it would be fun.
Instead of brushing it off, try to prove that my circle is not a real circle or that your abstract geometric circle and my physical circle are the same, because if they are not then you cannot expect them to have the same properties and use that disparity to prove/disprove anything.

Failure to distinguish between abstract geometric circles and physical circles led to the Explorer 1 anomaly.
"The launch of Explorer 1 in 1958, presided over by none other than Werner von Braun, provided an orbit that was more than 1/3 higher than expected. The orbit was so much larger that the rocket was at first thought to be lost. The expected signal was late, not by a few seconds, but by 12 minutes. Later that decade, Explorers 3 and 4 confirmed the anomaly, as did the three navy rockets of the Vanguard program."
Since then that 27% error was buried in a constant. 

You can read more about it here or just brush it off as an inconvenient piece of data that does not fit your preconceptions.

[MarkE]

 

Quote from: MarkE on May 17, 2014, 07:48:11 PM

    Begin with the definition:  Pi is the ratio of a given circle's circumference to its diameter.

I agree with that definition, but not all distance has to be measured by a flexible string.

Straw man:  No one has stated that that "all distance has to be measured by a flexible string.

Quote from: MarkE on May 17, 2014, 07:48:11 PM

    Take the ratio that you propose represents the ratio of a given circle's circumference to that circle's diameter of your proposed "circle".

Yes and my proposed circle is formed as described here.[/quote]
The proposal literally goes off the track with the statement associated with Diag. 3.  In order to establish a circular path, a continuous acceleration must be centripetal:  orthogonal to the instant velocity which directs it to the center of a circle.

Quote from: MarkE on May 17, 2014, 07:48:11 PM

    You state that your comparison fails on a gross level:  by over 20%.  Ergo your interpretation of your "circle's" dimensions fails to demonstrate a basic property of circles.

That conclusion is non-sequitur.

Hardly:  Pi is defined as the ratio of the length of a circle's circumference to its diameter.  By your own account your proposed geometry fails to adhere to that ratio.

This disparity just proves that physical circles have different properties from abstract geometric circles.

You make the claim that there are "physical circles" that are somehow different than "abstract geometric circles" without first establishing that these so called "physical circles" meet the criteria for any circle.  You then by your own account show that these "physical circles" fail to satisfy a basic property of circles:  that the circumference and the diameter satisfy an established ratio.

Instead of vaguely attacking my "interpretation" maybe you could point out concrete errors in my measurements of the circumference of my circle.

Does your "circle" satisfy the relation that all points on the circumference are equidistant from the center?  Does it satisfy the relation that the circumference is a closed path?  That is for you to show.  The fact that you state that the ratio of the length of the circumference and the diameter doesn't satisfy the established ratio for such an object strongly suggests that the points on your circumference are not all equidistant from the center.

Quote from: MarkE on May 17, 2014, 07:48:11 PM

    You are free to set about trying to prove all that: your "circle" that according to your evaluation grossly fails to demonstrate a basic property of circles is really a circle, and your measurement of the circumference is correct, and your measurement of the diameter is correct.  Good luck with all that.

That's why I wrote it would be fun.

Then have at it.  It is up to you.

Instead of brushing it off, try to prove that my circle is not a real circle or that your abstract geometric circle and my physical circle are the same, because if they are not then you cannot expect them to have the same properties and use that disparity to prove/disprove anything.

You make the extraordinary claim of the existence of some "physical circle" that is a circle yet fails to satisfy a basic property of circles.  You can prove your outlandish claim or not.

Failure to distinguish between abstract geometric circles and physical circles led to the Explorer 1 anomaly.
"The launch of Explorer 1 in 1958, presided over by none other than Werner von Braun, provided an orbit that was more than 1/3 higher than expected. The orbit was so much larger that the rocket was at first thought to be lost. The expected signal was late, not by a few seconds, but by 12 minutes. Later that decade, Explorers 3 and 4 confirmed the anomaly, as did the three navy rockets of the Vanguard program."

Your quote says nothing about circles.

Since then that 27% error was buried in a constant.

That is an assertion of yours that whether or not it is correct, you have done nothing to connect it to your claim of these "physical circles".

You can read more about it here or just brush it off as an inconvenient piece of data that does not fit your preconceptions.

An unexpected orbit means that the path taken did not match the path expected based on the presumed forces.  The author of your citation admits in that citation that he merely assumes that NASA took up his odd idea.