It actually proves what I said. There is no surface.river said:What would a " dent " mean ?
It actually proves what I said. There is no surface.river said:What would a " dent " mean ?
It actually proves what I said. There is no surface.
I have no idea where you picked this up but it is entirely untrue.Fractals are only present in life forms .
Show that my post # 102 is wrong .
Incorrect: Various objects in nature approximate fractals. Coast lines are one example.Fractals are only found in life forms
Fractals are only found in life forms
Incorrect: Various objects in nature approximate fractals. Coast lines are one example.
True fractals are mathematical entities which do not appear in nature. Examples are the Mandelbrot Set & graphics generated via use of successive approximations to the solution of cubic equations.
BTW: The graphic generated via successive approximations to the three cube roots of a number (2 are complex) has an interesting property when its various regions are colored using three colors.
The borders between regions are all triple border points like the center of a circle divided into three slices. None are like the linear borders from the center to the circumference.
Approximate fractals is not an argument to my point of life fractals .
Just as with any real world fractals, this is not true for life. Of course it has a lower limit!!The form repeats no matter how small we go . We take the smaller and it will be exactly the same as the larger form .
Just like in life.The further we get into a focus on a coastline the less we can build a dupicate of the FULL coastline.
Not true.But in life the focus small or large does does not affect the completeness of the whole .
My Post #6 (slightly edited)If we have a 2 dimensional plane and roll it into a cylinder, is it now a 3 dimensional object or is it a 2 dimensional object.
Care to discuss?
A solid cylinder would be a 3D object, although plane geometry would be applicable to the surface.
Plane geometry is applicable to this surface, although plane topology might not be.
Note that the Pythagorean formula can be used for right triangles.
If you apply differential geometry to this surface, the metric is the same as that for a plane.?
Similar remarks apply to any surface which can be cut & flattened without crinkling.
There is a more formal way to express the above remark. I do not think that crinkling is a scientific term in the above context.
Quantum Quack Post # 1
My Post #6 (slightly edited)
My above Post pretty much tells the entire tale.
I find it incredible that there are 127 Posts to this thread, most of which I have not read.
Mea culpa for not pointing out that the discussion of fractals is a digression with little or no relevance the question asked in Post 1.
False. In the world of our senses (or life as you express it), There is a lower limit to fractals at or before the level of a single atom or single molecule.Fractals , real fractals are from life , the further one looks into life fractals , the repetition continues . The form repeats no matter how small we go . We take the smaller and it will be exactly the same as the larger form .
https://en.wikipedia.org/wiki/Causal_dynamical_triangulationCausal dynamical triangulation (abbreviated as CDT) theorized by Renate Loll, Jan Ambjørn and Jerzy Jurkiewicz, and popularized by Fotini Markopoulou and Lee Smolin, is an approach to quantum gravity that like loop quantum gravity is background independent.
This means that it does not assume any pre-existing arena (dimensional space), but rather attempts to show how the spacetime fabric itself evolves.