The Holographic Universe and Pi = 4 in Kinematics!

[MarkE]

Where can I read a rigorous critique of his paper ?

One particularly humorous one can be found by Googling:  "Miles Pantload Mathis".

[verpies]

There is only one kind of circle.

An abstract timeless circle - yes.
...but a circular path of motion is something different.

Straw man:  no such statement was made.  If you object to the idea that a flexible string can be used to measure either the circumference of a circle or the perimeter of a square...

I quoted your own words.
I don't object to measuring the circumference of an timeless geometric circle by a string (nor a perimeter of a geometric square).
I object to applying it to a circular path of motion (...or a square path).  Motion should be measured with motion - not a string.

[TinselKoala]

Earth's orbital radius = about 149.6 million km. Duration of one full orbit is of course one sidereal year, 365.256 days or about 31,558,118 seconds.
(wikipedia).

The tangential velocity of the Earth in its orbit is 29814 meters per second, derived from v²=GMs/r.

Now let us calculate.
The circumference of the orbit (assuming pi = 3.1416 and a circular orbit) is 2 x pi x 149.6 million km, or about 939.97 million km.

The tangential speed computed from the radius and the conventional value of pi is therefore 939.97 million km / 31,558,118 seconds or about 29785 meters/second.

The diameter of the orbit is about 299.2 million km. Traversing this distance at the tangential velocity of 29814 m/sec will therefore take about 10035553 seconds. Four times that is 40,142,212 seconds... but a year is only 31,558,118 seconds.  Curiously.... 10035553 x  3.1416 = about 31,527,693 seconds.... nearly exactly the number of seconds in a sidereal year.

Conclusion.....  The value of pi, for the real figure of the Earth's orbit, taking TIME and velocity into account, must be very close to 3.1416, and not close at all to 4.

Please feel free to show a working that demonstrates otherwise.

[MarkE]

An abstract timeless circle - yes.
...but a circular path of motion is something different.

If a path does not map out a circle, then it is not a circular path.

I quoted your own words.
I don't object to measuring the circumference of an timeless geometric circle by a string (nor a perimeter of a geometric square).

Then as any fourth grader can be successfully taught you can learn that the circumference of a circle is much less than the perimeter of the square it inscribes.

I object to applying it to a circular path of motion (...or a square path).  Motion should be measured with motion - not a string.

Object all you want.  Howl at the moon if you want. 

[gravityblock]

Take any object with one or more points that are at a fixed distance from the center, and rotate that object about its center.  The points remaining a fixed distance from the center by definition follow the same circular path.   The path between those points around the original shape has nothing to do with the rotation of that object.

Pop quiz:  Take any solid object that is a close approximation to a circle:  soda can, pill bottle, whatever you like.  Place it on a piece of paper and carefully draw a square that the circular end of the object inscribes.  Next wrap a string around circle, and cut that string where it meets the start.  Now lay the string out and see how much of the perimeter of your square you can cover.  Are we done with this mindless game yet?

According to your definition in the bold portion above, the square does inscribe a circular path within.  Also, a circular path is a real physical circle with a time variable according to your definition.  So, according to your logic and definitions, this circular path inscribed by the rotation of the square by 1/4 has a time element?

Gravock