The Holographic Universe and Pi = 4 in Kinematics!

[MarkE]

Again, we can visually see in each successive squaring method the number of inner square vertices are also exponentially increasing around the circumference, and at the planck length, the inner square vertices will be at all points on the rectilinear circumference of the circle itself.

Gravock

That is both true and irrelevant.  Since we can connect the inner vertices with chords, as the number of chords tends towards a large number, such as 1/lP, all the vertices being on the circumference, the chords will closely approximate the path of the circumference.  If they did not, then the area approximation established by those vertices would not match the area of the circle.  Ergo the path formed by taking a straight line between those vertices closely approximates the true circumferential path length.  Since that path length converges towards ~3.1415953 and not 4.0, the claim that the sum of 1/lP diversions from the circumference and back matches the path length of the circumference fails.

[gravityblock]

That is both true and irrelevant.  Since we can connect the inner vertices with chords, as the number of chords tends towards a large number, such as 1/lP, all the vertices being on the circumference, the chords will closely approximate the path of the circumference.  If they did not, then the area approximation established by those vertices would not match the area of the circle.  Ergo the path formed by taking a straight line between those vertices closely approximates the true circumferential path length.  Since that path length converges towards ~3.1415953 and not 4.0, the claim that the sum of 1/lP diversions from the circumference and back matches the path length of the circumference fails.

No, the inner vertices at the planck length can not be connected with chords in a real circle with a time variable.  By connecting the inner vertices at the planck length with chords, then you are saying matter moves in a continuous motion and not in discrete jumps.

Gravock   

[MarkE]

I already answered that directly.

I have yet to see any such description.  If you think you have provided one kindly point at the post that provides it.

Just answer directly "yes" or "no" instead of writing about bushes.
That's not what I am disagreeing with.
You have also stated that if Pi so defined is not 3.14 then the circle fails to have the property of the circle that you are familiar with and because of that is not a real circle.
You also disqualified a physical circle as a circle because physical circle is not a two-dimensional figure.  These two are not Straw Men.

Once again you misstate what I have said.  Pi is a defined relationship.  The value of that relationship has been reliably approximated to eight decimal digits as: ~3.1415953.  I have said that a geometric object that purports to have a circumference to diameter ratio that does not conform within the measured and/or calculated error bands to a correspondingly precise expression of Pi, then the the object fails to demonstrate a basic property of circles.  This tortured idea that an object that fails to demonstrate a circumference to diameter ratio in close accord with a reliably approximated value of Pi is completely silly.  How long do you two intend to keep this nonsense up?

Circles are plane geometry objects.  They exist in two dimensions.  That is not my doing.  That is the accepted definition.
I have yet to see a definition of a "physical circle" from you that allows for the special pleadings that you make that such an object has a time component or any other property distinct from the plane geometry object known as a circle.

I asked you whether that circle in the article you quoted qualified as a circle and if not then what is it in your opinion.   I still have not received a direct answer.

Even the form of the question is silly.

Prove it for kinematic circles.

What is a kinematic circle?

"Not the same" as in "not identical".  Not the same time coordinate for each point.

Time is irrelevant to plane geometry.

In abstract geometry - yes. All of the points belonging to an abstract geometric figure exist at the same instance in time, so the time can be disregarded.

Time never entered.  It is not a matter of disregarding something that is not significant. Time plays no part.

In physics time cannot be disregarded and a physical circle is not a strictly 2D object.

Kindly provide an academic link that identifies and describes one of these time dependent "physical circles".

Did you pay attention which limit is reached first?
[/quote]Apparently among other things, Mr. Mathis did not.  If you wish to attempt to show by deriving the limit of the chord slope that the limit is other than zero, feel free to show your math.

[MarkE]

No, the inner vertices at the planck length can not be connected with chords in a real circle with a time variable.  By connecting the inner vertices at the planck length with chords, then you are saying matter moves in a continuous motion and not in discrete jumps.

Gravock   

A plane geometry object has nothing to do with time.  Plane geometry is a field of mathematics.  If you want to play:  "You can't do XYZ in the physical world" then you are already stuck with much bigger problems than whether chords can be mapped between presumed squares with presumed vertices at static positions in space.

[MarkE]

Matter doesn't move in a continuous motion, it moves in discrete jumps at the planck length.  When the squaring method reaches the planck length, the inner square vertices will be at all points on the rectilinear circumference of the circle itself, which is not continuous and is made of discrete jumps.  The Manhattan path does correctly simulate the time variable in real circles at the planck length!

Edited for better clarification.

Gravock

That's rubbish.  The Manhattan path has no time element to it.  It is plane geometry.  How long are you going to insist on this silly game?