Mindblowing Mengersponge Animation

[Timeroot]

First of all, let's agree on one thing:

Stacking cubes together in that pattern (with successive scaling) produces the same shape as digging it out. Try this: dig out one iteration, then multiply in size by three. It's the same as stacking. Or, if you prefer, stack one iteration of cubes on each other, and divide in size by three. They're all equivalent. In fact, it can even be described by an L-System of a line. So it's equally valid to argue it has no surface area. It's 3D cantor dust, really.

Mass=Density*Volume. Volume=0, so Mass=0. Of course, there's the issue where the gaps become smaller than a planck scale, at which point this all becomes meaningless. On the other, at much higher scales, the gaps become small enough to exclude any air molecules - or at least the soot and dust, which is heavier. So the sponge, filled with these small vacuums, might end up floating up until it reaches clean air. Or it could sink, due to the particles (which [maybe, see next sentence] are still there!). It all depends on whether on not it has mass at a quantum level or not.

Define your terms before you start arguing about them. It's like the monk asking, "How does one attain happiness?", and his teacher responds, "What one earth is that?"

[Sockratease]

Define your terms before you start arguing about them.

But...  I choose to define the terms differently!

This is a "3D" Representation of an abstract concept  (the image itself is still 2D).

While abstract concepts have no mass, should this object manifest itself in our reality, in such a way that the need to discuss survival should it fall on you ever arose...  it would no longer have the properties mentioned.

Would Cantor Dust have mass?  I say yes!  Folks used to believe Light was massless, but later decided that it does indeed have it.

Also, Cantor dust would not be able to maintain such a rigid structure in the real world if it were massless - so I still think it would be a Massive Object and crush the Frac (tal) out of any humans in it's path 

[jehovajah]

You guys! Can't a body dream? Does everything have to be correct in somebodies eyes? It is enough to ask the question and come up with a godzillion of answers! That is the fun! That is my reality

[Sockratease]

I thought the use of the Devil Smiley indicated that I was only having Fun with the concept.

Besides, such banter and sardonic questioning was the Hallmark of He Who Inspired my user-name, so I feel justified in the statements 

I trust all involved in this realize that it's an un-answerable question and the replies here nothing more than Intellectual Gymnastics.  Great fun so long as nobody sprains their brain in the process!

[KRAFTWERK]

Jeah, I like this too, and was going to put out the fire with gasoline... 

If I get hit by an infinite amount of infinitely sharp edges that are infinitely packed together (are they?) how will that affect me?
 

[Nahee_Enterprises]

OK I give up!!!  Under the pressure of nothing...

But still posting questions and statements to this topic after the fact anyway!!!      

So, if it was a REAL "subtracted" Mengersponge (unlike the animation), you think i would be cut into infinitely small cubes?

...was going to put out the fire with gasoline... 
If I get hit by an infinite amount of infinitely sharp edges that are infinitely packed together (are they?) how will that affect me? 

Ever seen what ground meat looks like when it comes out of those small holes at the end of the grinder ??   
 

[kram1032]

That's close, Nahee.
The only two differences: The "cords" of meat all have different sizes and are square

Btw, the whole cube would cut equally easy throught the earth, splitting some atoms on its way to the core, lol. (Well, at least assuming, it had any mass.)
If it had no mass, it would basically stay in place where it is and wouldn't ever move from there, but everything that touches it, would be cut into pieces. (Well, additionally assuming, it can't either be affected by any of the other forces^^)