But not pure fractals , as organic has .
Fractals , organically , represent the whole of .
2 dimensions into 3 dimensions
- Thread starter Quantum Quack
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But not pure fractals , as organic has .
Fractals , organically , represent the whole of .
As written in very plain understandable English just before that list of both inorganic and organic examples it reads (with minor excision):
No comprende amigo? That Wikipedia text matches what I wrote back in #96. You don't like it, well take it up with them. As I suggested earlier.
You couldn't define such a surface. If you froze a moment in time the surface would consist of a finite number of atoms at within a certain depth range. A surface IS a surface because of the electromagnetic fields of the atoms within a certain thickness create the illusion of a "hard" surface that other things with surfaces bounce off.
It is NOT a two-dimensional phenomenon. It's very three-dimensional.
It's vital not to confuse idealized mathematical abstractions with what physics tells us about the actual world.
There is no 2-d surface except in your mind. If you zoomed in you'd see a cloud of atoms and you couldn't draw a strict demarcation between table and not-table.
As stated earlier 1D and 2 D objects have no physical existence, but these concepts are required for various modeling
It is pure nonsense to claim that the glass knows that it is lying on a 2 D surface of zero thickness.
danshawen
Valued Senior Member
Okay. What would be its volume?
If it had a mass / energy of 1 eV, what would be its density?
Now make its velocity relativistic, say 0.99c relative to you. What is its density now? In what direction did you measure the increase in mass? Is the corresponding volume still the same? How did inertia change in different directions?
What is the relative time dilation? Is that effect in any particular direction, or in every direction at once? Why is time dilation free of the 1 dimensional geometric consideration when other dimensions are not affected in this manner?
A preferred direction in space makes no more sense than a fixed position does, or a fixed area, or a fixed volume. But it (direction) makes sense for fundamental (bound) particles of matter with spin or angular momentum. Why is that?
Which kind of motion (particle spin or linear relative velocity) is the best candidate for a more fundamental understanding of time? Hint: both are needed, depending on the form the energy may take, but which would be able to change FASTER? And a time interval may not be equivocated with an instant of time) Show your work. Do not use any geometry relative to fixed positions in space that is outside of a fundamental particle.
Which type of motion is, like time dilation, omnidirectional?
My geometrical point is, it's all too easy to get confusing or paradoxical answers by choosing the wrong geometry, or one predicated on the wrong underlying assumptions. It might not work at all, only half work, or as in the case of spacetime, only give the right answer 0.99% of the time.
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DaveC426913
Valued Senior Member
Heh. What you mean is "nuh uh!"
The only irrelevant thing is your insistence on not understanding.
DaveC426913
Valued Senior Member
What??? Don't be silly!
Fractal life is certainly popular.But some of us read beyond popular.
danshawen
Valued Senior Member
Someone here mentioned "infinitesimal" element of volume. This has relativistic consequences. The universe is not static like geometry.
QQ's previous rhread eventually got around to discussing time. Not derailing it. Taking a short cut.
Don't really care about rolled up cylinders or other crazy geometries. A volume has consequences. Even a relativistic rolled up cylinder will have different vplumes depending on orientation. How is this not relevantl?
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I am not talking about QQ, I liked his OP and despite Q-reeus correct resolution very early, I pushed the thread to cover what we know as common sense/Euclid. Derailment process initiation is by DaveC12345.
Infinitesimal!!!
This word has evoked significant interest here on SF.
Please note infinitesimal has no physical meaning or relevance other than usage in mathematical models. They help us in doing calculus easily.
For example if volume charge density is given (uniform or otherwise), then calculating the total charge contained in a volume may be easily done by considering the infinitesimal element of volume "dV". Do not attach any further significance to this.
danshawen
Valued Senior Member
https://nerdyjokes.wordpress.com/tag/banach-tarski-paradox/
"The Banach-Tarski Paradox...
...Imagine a 3D solid ball...Now imagine breaking <it> into a finite number of <3D> pieces. Next, rearrange the pieces to form two solid daughter balls from the broken pieces of the original. You can't stretch or add pieces, only move and rotate existing pieces.
Now...imagine each daughter ball has the exact same volume as the parent.
...mathematically <geometrically> you can...furthermore, you can do so endlessly, meaning that a single ball can be replicated endlessly until the universe is <filled> with balls." If one can make two, two can make four, etc, etc.
Say you have a single perfectly round solid gold sphere. Perform this operation as many times as it takes to fill your pockets with gold coins. Who says this doesn't really work? Gold atoms are just protons, neutrons, and electrons, right? We are surrounded by the raw stuff of wealth, infinitesimally speaking. There is no Law of the Conservation of Wealth, either. Unlike mass / energy, wealth CAN be created, rather like volume. You simply need to be infinitely twisted or crooked.
This paradox occurs because "a <mathematically> infinitely rough surface has an undefined volume". Rather like the "crinkles" in the rolled-up cylinder QQ was talking about. Iron out all of the crinkles and how much volume of the cylinder do you get? Evidently, the same operation can be performed with the 1D lines that make up letters also, if they are wrinkled and subdivided infinitesimally enough.
In the end, this geometrical paradox is just like any other silly proportional division by zero <yawn>. QQ has, however, found a better and easier volume and shape to work the paradox with.
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and if you kept on zooming in you would eventually observe nothing at all...(zero dim.)
A physicist would say the table has no surface. The atoms are just places that electrons can interact with protons. When you touch the "surface" of a table, there are electrons interacting across space. There is no surface.