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[Blargityblarg]

Why, beard hair, of course.

[silverskull39]

By the maths of geometric sequences, assuming each part was half the mass of the one before, and the first part weighed 1 kilo, it would weigh 2 kilos in total.

You'd also end up with an infinit surface and as a result an infinit amount of surface energy. Since mass and energy are interchangable, according to Einstein, you still end up with infinit mass.

I'm not sure what kind of energy you think a surface has, but I don't think it works that way.

[buckets]

By the maths of geometric sequences, assuming each part was half the mass of the one before, and the first part weighed 1 kilo, it would weigh 2 kilos in total.

You'd also end up with an infinit surface and as a result an infinit amount of surface energy. Since mass and energy are interchangable, according to Einstein, you still end up with infinit mass.

I'm not sure what kind of energy you think a surface has, but I don't think it works that way.

What, you've never heard of elastic non-potential energy?

[silverskull39]

elastic potential energy? yes. Elastic kinetic energy? Yes. elastic "non-potential" energy? nope, but even if I had I'm pretty sure it doesn't work the way you were saying. besides which, the surface area wouldn't be infinite, as Fictionpuss said it would asymptote around a certain value, probably just less than the surface area of the largest rendition of the fractal. Say the largest rendition had an area of 1 m^2 it most likely wouldn't ever hit 2m^2 total. This is because, while there are infinite renditions, each rendition is smaller than the last to the point where the additions become insignificant, each a fraction of the last. Say we take a common recursive pattern, the Sierpiński carpet. This carpet is begun with a square split into nine parts with the middle part removed. The smaller squares are then divided into nine parts with the middle part removed, and so on, giving us something like this;

Spoiler (click to show/hide)

#########
#  ##  ##  #
#########
###      ###
#  #      #  #
###      ###
#########
#  ##  ##  #
#########

In this case, surface is removed rather than added, but the principle is the same. Suppose the surface area was initially 81m^2. That makes each # worth a m^2
after the first removal it would remove 9m^2 giving us 72m^2.
after the second it would remove 8m^2 giving us 64m^2
and it would continue to get smaller and smaller, but each time it would remove a smaller portion. Eventually, it would approach 0, but it would never reach 0. It is the same with adding surface area except you would never double the surface area rather than reduce it to zero.

Edit: fixed some basic math failure.

[Fictionpuss]

By the maths of geometric sequences, assuming each part was half the mass of the one before, and the first part weighed 1 kilo, it would weigh 2 kilos in total.

You'd also end up with an infinit surface and as a result an infinit amount of surface energy. Since mass and energy are interchangable, according to Einstein, you still end up with infinit mass.

Infinity is a property, not a number.  Compare:

• You can add 1+1, and the rules of mathematics will allow you to infinitely keep adding additional ones to the previous result to continually achieve larger numbers - there is no theoretical limit, only practical ones.
  
• You will never reach infinity by this method.
  
  Also, there is nothing in the universe which is demonstrably infinite.  Mathematics (including concepts such as infinity) are a map, the universe is the territory, and it doesn't do to confuse the two.
  

[silverskull39]

yay math!   
my brain feels squishy now.

[buckets]

What, you've never heard of elastic non-potential energy?

elastic potential energy? yes. Elastic kinetic energy? Yes. elastic "non-potential" energy? nope, but even if I had I'm pretty sure it doesn't work the way you were saying. besides which, the surface area wouldn't be infinite, as Fictionpuss said it would asymptote around a certain value, probably just less than the surface area of the largest rendition of the fractal. Say the largest rendition had an area of 1 m^2 it most likely wouldn't ever hit 2m^2 total. This is because, while there are infinite renditions, each rendition is smaller than the last to the point where the additions become insignificant, each a fraction of the last. Say we take a common recursive pattern, the Sierpiński carpet. This carpet is begun with a square split into nine parts with the middle part removed. The smaller squares are then divided into nine parts with the middle part removed, and so on, giving us something like this;

Spoiler (click to show/hide)

#########
#  ##  ##  #
#########
###      ###
#  #      #  #
###      ###
#########
#  ##  ##  #
#########

In this case, surface is removed rather than added, but the principle is the same. Suppose the surface area was initially 81m^2. That makes each # worth a m^2
after the first removal it would remove 9m^2 giving us 72m^2.
after the second it would remove 8m^2 giving us 64m^2
and it would continue to get smaller and smaller, but each time it would remove a smaller portion. Eventually, it would approach 0, but it would never reach 0. It is the same with adding surface area except you would never double the surface area rather than reduce it to zero.

Edit: fixed some basic math failure.

One of the people here was not being serious...

[atomfullerene]

Well, even if you made a fractal like this, assuming it was made of normal "stuff" you wouldn't have any fine detail below the atomic level.  So you'd wind up with large surface areas, but certainly not infinite ones.  Even if you could use some finer-scale substance you would still bump into the plank length...the basic pixel size of the universe, if you will.  Can't get smaller than that (unless someone's changed it since I last read about it)!

Of course, in DF the basic granularity of the universe is a bit arbitrary

[Urist McOverlord]

Actually, considering that the jasper in question is engraved with itself, the infinite regression formed would result in the item's mass asymptoting to zero. I think.

Of course, I also think Urist McGemCarvingEscher has actually created dilithium, and that Urist McScotty needs to reverse the polarity in a preemptive measure to fix the Enterprise magma turbines before the klingons Clowns can TECHNOBABBLETECHNOBABBLETECH!

[Dabi]

Actually, considering that the jasper in question is engraved with itself, the infinite regression formed would result in the item's mass asymptoting to zero. I think.

Of course, I also think Urist McGemCarvingEscher has actually created dilithium, and that Urist McScotty needs to reverse the polarity in a preemptive measure to fix the Enterprise magma turbines before the klingons Clowns can TECHNOBABBLETECHNOBABBLETECH!

So your saying if I threw this massless object into the sky it would move at the speed of light?
Cool.

[Urist McOverlord]

And it fits perfectly within the boundaries given by dwarven physics!

But yeah. I don't know where that was coming from... its officially time for me to sleep...

[Dabi]

And it fits perfectly within the boundaries given by dwarven physics!

But yeah. I don't know where that was coming from... its officially time for me to sleep...

We all do it .
Except me, I'm a dwarf "prodigy".

[Virex]

By the maths of geometric sequences, assuming each part was half the mass of the one before, and the first part weighed 1 kilo, it would weigh 2 kilos in total.

You'd also end up with an infinit surface and as a result an infinit amount of surface energy. Since mass and energy are interchangable, according to Einstein, you still end up with infinit mass.

I'm not sure what kind of energy you think a surface has, but I don't think it works that way.

Surface energy, supplied to you by courtesty of wikipedia.org

[silverskull39]

By the maths of geometric sequences, assuming each part was half the mass of the one before, and the first part weighed 1 kilo, it would weigh 2 kilos in total.

You'd also end up with an infinit surface and as a result an infinit amount of surface energy. Since mass and energy are interchangable, according to Einstein, you still end up with infinit mass.

I'm not sure what kind of energy you think a surface has, but I don't think it works that way.

Surface energy, supplied to you by courtesty of wikipedia.org

That kind of surface energy is more the ability of a liquid to "wet" a surface, where adhesion forces are stronger than cohesion ones. Strictly, its definition is the work required to increase the
surface area of a substance by unit area. So if something has high surface energy that means that it requires more work to increase the surface area of that substance. this generally refers to how much work is required to make a liquid spread out rather than clump to gether. With liquids, this is usually very small and thus the force of gravity easily does the job. However, it can be applied to solids as well. It is an input energy, not an output one. And like I said earlier, it doesn't work the way you were thinking.

[Virex]

If something has a high surface energy density, it does require a lot of energy to generate more surface of that substance. This means that if you would shape an object of that substance with a surface of, say a square meter, then the energy needed to do that is indeed 1 times the energy density per square meter. However, that energy then becomes some other kind of energy (as per conservation of energy). It is known that a deformed drop will revert to a round drop when left to it's own devices, implying it is gaining the energy needed for motion from somewhere. It is generaly asumed this energhy is drawn from the decrease in surface and the ascociated energy being freed (with the left-over energy going into heating the drop a few millikelvin). This means that the surface of an object has a certain amount of potential energy and potential energy is a well-known form of energy which does indeed equate to mass (Which can be seen in the loss of mass resulting from the release of binding energy during nuclear decay).