The You Game!

Ah, but going through zero could create all sorts of problems with that argument! < acknowledges that volume and area would also go negative, which is harder to explain than a simple direction change, but surely not that weird.
< wonders if ^ has heard of negative temperature. It's kind of similar to that, mathematically.
 
Ambidextroid said:
< has been thinking about what an object with negative size would theoretically look like.
< imagines the volume would "wrap around" to infinity, similar to a tangent wave, and you'd be left with an empty space of negative size. So a -1 metre cube would be a cube-shaped empty space with sides of 1 metre within a solid that stretches out in all directions infinitely.
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This is assuming that normal of each face has a positive and a negative direction, and that one of them points to which side the volume is on. If the cube is negative (with inverted normals), then < doesn't think that the cube would have any volume at all, as it's no longer a closed surface. It would be like saying that a plane has an infinite volume extending forever backwards because there's nothing stopping it from doing so on the other side, which of course isn't the case.
 
PluMGMK said:
Ah, but going through zero could create all sorts of problems with that argument! < acknowledges that volume and area would also go negative, which is harder to explain than a simple direction change, but surely not that weird.
< wonders if ^ has heard of negative temperature. It's kind of similar to that, mathematically.
Click to expand...
< is just thinking in a virtual space, if the dimensions of the cube become negative but the volume stayed "inside" the cube (i.e. the right face is always right of the volume), then when you negate the cube it's almost like turning it inside out. The right side would be on the left, thus the volume would extend to the outside of the left... < is rambling now...

< thinks < has heard of negative temperature before, but not looked into it. Sounds interesting!

Edit: (@ad)
The closed surface of the cube is the hollow cube space. Just as an object approaching infinite size approaches bit never reaches infinite volume, an object approaching negative infinite size approaches but never reaches zero volume. Bla bla bla < doesn't know < is just typing what comes to <'s head at this point.
 
< is watching Om Shanti Om at school. :fou:

Adsolution said:
Hunchman801 said:
< sees inco just keeps digging.
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Maybe ^ should hire incognito to help out with the yard.
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5bf.jpg
 
Ambidextroid said:
an object approaching negative infinite size approaches but never reaches zero volume.
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It does? < can't quite work that one out.

Sensibly speaking, volume is a measurement made relative to the coordinates of the surface. If a cube has a size of -1,-1,-1 and is centred at the origin, then the coordinate values will range between -1 and 0; (0) - (-1) = 1, and so the volume is 1^3.
 
Adsolution said:
Ambidextroid said:
an object approaching negative infinite size approaches but never reaches zero volume.
Click to expand...
It does? < can't quite work that one out.
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If you imagine a -1 metre cube to be an infinitely spanning volume with a hollow space of size 1 metre cubed, and you decrease the size further to say -2 m cubed, you would have an infinite volume minus 2 cubic metres.
As the size of the actual cube decreases, the hollow space increases exponentially in size and the apparently infinite volume decreases exponentially, approaching 0 but of course never reaching it as there will always be some solid volume (just like a positive cube can approach infinite volume but never reach it as there is always infinite space to fill).
This kind of goes against the way we think about infinity (that "decreasing" it is not possible) but it makes sense if you parallel infinity with zero, for example in <'s theoretical world a cube with zero metre dimensions has both zero and infinite volume, as you cannot have either negative or positive zero, if that makes sense (the asymptote of the point where volume approaches zero is also the point where volume approaches infinity)
 
PluMGMK said:
Ah, but going through zero could create all sorts of problems with that argument! < acknowledges that volume and area would also go negative, which is harder to explain than a simple direction change, but surely not that weird.
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< agrees with PluM.

Adsolution said:
Sensibly speaking, volume is a measurement made relative to the coordinates of the surface. If a cube has a size of -1,-1,-1 and is centred at the origin, then the coordinate values will range between -1 and 0; (0) - (-1) = 1, and so the volume is 1^3.
Click to expand...
Exactly. Ambi's just created his own new definition of volume which is interesting but unfortunately his reasonings contain quite a few mistakes:

Ambidextroid said:
The closed surface of the cube is the hollow cube space. Just as an object approaching infinite size approaches bit never reaches infinite volume, an object approaching negative infinite size approaches but never reaches zero volume. Bla bla bla < doesn't know < is just typing what comes to <'s head at this point.
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If you meant that the volume of an object tends towards infinity as its dimensions (or some of them) tend towards infinity, this is wrong. Take the area under the curve y = 1/x² from x = 1 to infinity, make it a volume by adding another finite dimension z = 1, and you have an infinitely long object with a volume of 1 × ∫1; +∞dx/x² = 1 × 1 = 1.

Ambidextroid said:
If you imagine a -1 metre cube to be an infinitely spanning volume with a hollow space of size 1 metre cubed, and you decrease the size further to say -2 m cubed, you would have an infinite volume minus 2 cubic metres.
As the size of the actual cube decreases, the hollow space increases exponentially in size and the apparently infinite volume decreases exponentially, approaching 0 but of course never reaching it as there will always be some solid volume (just like a positive cube can approach infinite volume but never reach it as there is always infinite space to fill).
Click to expand...
The growth of the hollow space is polynomial with regard to the dimensions of the cube, not exponential.
 
Hunchman801 said:
Take the area under the curve y = 1/x² from x = 1 to infinity, make it a volume by adding another finite dimension z = 1, and you have an infinitely long object with a volume of 1 × ∫1; +∞dx/x² = 1 × 1 = 1.
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< should have thought of that. < also finds the BBCode integral kinda sexy...
 
Hunchman801 said:
If you meant that the volume of an object tends towards infinity as its dimensions (or some of them) tend towards infinity, this is wrong. Take the area under the curve y = 1/x² from x = 1 to infinity, make it a volume by adding another finite dimension z = 1, and you have an infinitely long object with a volume of 1 × ∫1; +∞dx/x² = 1 × 1 = 1.
Click to expand...
< only really meant a cube, as each side changes equally, so you only have to deal with one dimension for size and one for volume.

But now that < thinks about it, if it were a y = x^3 graph it wouldn't have any asymptotes... < was only daydreaming though, < didn't suspect <'s theory would actually hold any ground. < was basing it on the constrictions that it had to have a conventional "volume" and "dimensions" rather than a spooky anti-volume, but now that < thinks about it <'s theory doesn't make too much sense
 
Ah screw it, < knew < probably didn't need LaTeX that time, but < was just trying to get some practice! :fou:
 
Bradandez said:
Where else is < gonna findshare the hottest fetish art?
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< fixed that for you. We all know damn well that you're the one making this stuff.

< picked a copy of Pokémon Moon, but < also find MGSV at 15 euros. < didn't resist.
 
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