Yes I suppose so, but that's only if the hexes are enormously tall (like in there is ONE hex and it reaches up into the sky and into the ground ... if Erfworld did happen to be a Sphere then at the center of the Sphere move would be ... rather expensive ...).
If there are hexagonal prisms or hexagonal dipyramids stacked in 3D space that are roughly
1 kilometer in diameter, then if Erfworld is the same size as Earth ...
Radius of Erfworld average ground level (at the equator since Erfworld is actually a bit egg-shaped so geographic pole-to-pole circumference is actually bigger): 6,378 km
Radius of Erfworld +1 3D hex(whatever) from ground level: 6,379 km
Circumference of a Circle: 2*pi*r
2*pi*6,378 km = 40,074.1559 km
2*pi*6,379 km = 40,080.4391 km
40,074.1559 km - 40,080.4391 km = 6.2832 km difference in circumference
There are 40,074 hexes (each imperceptibly wider in he horizontal direction to make up for 0.1559 of a hex left over ... 0.1559 km left over / 40,074 hexes (each a kilometer wide) = 3.89030294 × 10^-6 km that each hex is lengthened in horizontal direction)
3.89030294 × 10^-6 km = 3.89030294 × 10^-3 m = 3.89030294 mm
So out of an entire kilometer-wide 3D hex, the bottom is 3.89030294 millimeters longer than a kilometer to account for extra decimals in the circumference of Erfworld not breaking down into a neat rational number
As for the top of the 3D hex, that would be:
0.4391 km left over / 40,080 hexes (each a kilometer wide) = 1.09555888 × 10-5 km = 1.09555888 x 10^-2 m = 1.09555888 cm
So the top of each hex is 1.1 cm wider at the top to account for the rounding
6.2832 km difference in circumference / 40,080 hexes = 1.56766467 x 10^-4 km to account for different circumfrences = 1.56766467 x 10^-1 m = 0.15677 m difference at top of ground hex vs bottom to account for different circumferences
So bottom of ground 3D hex = 1 km + 3.89 mm rounding fix = 1.00000139 km
Top of ground 3D hex = 1 km + 1.096 cm rounding fix + 0.15677 m circumference difference fix = 1.00016773 km
1.00016773 km - 1.00000139 km = 16.63 centimeters
A kilometer's a little big for a hex but a decimeter sounds just about right (100 meters is a little big for a Gate to a City to be 1 Hex big for example), but regardless of the hex size you choose the Circumference difference remains
proportionally the same magnitude. So if the hex size was 10 meters (a decimeter) then we'd just change a few 10^Xs and end up with 1.66 millimeters as the difference between the bottom and top of the ground hex that is a decimeter wide as our answer. That's hard to spot, 1.66 millimeters difference in 10 meters (about 30 feet)!
Alternatively, you could have hexes be say pi*whatever in diameter and that would get rid of a lot of the decimals. Let's assume that's the case (and that it's pi decimeters, which is about 90 feet ... a little big but about 9 feet (pi meters) is too small for a hex, period)):
(6378 km radius of Erfworld / pi * 10^-2 km/hex diameter) * 2 * pi = 1,275,600 hexes at the surface of Erfworld
(6379 km radius of Erfworld / pi * 10^-2 km/hex diameter) * 2 * pi = 1,275,800 hexes at +1 hex above the surface of Erfworld
1,275,800 hexes - 1,275,600 hexes = 200 hex difference between circumferences
200 hex difference / 1,275,800 hexes = about 1.56764383 x 10^-4 hex stretch per hex to account for difference
= 1.56764383 x 10^-4 * pi decimeters
= 1.56764383 x 10^-3 * pi meters
= 1.56764383 * pi millimeters
= about 4.92489834 millimeters
= about 4.925 millimeters
Note: this does not take into account Earth's non-perfect-sphere egg shape as that makes its pole-to-pole circumference a slight ellipsoid instead of a circle (though the equatorial one might still be a perfect circle more or less), but ... Jesus gimme a break. This does account for 3D hexes being polygonal solids, though, so long as the 3D hexes aren't flat on the bottom and instead wrap around the surface of Erfworld's spherical shape so that the bottom of a hex is a little convex and the top of a hex is a little concave. If Erfworld was just a sphere floating in space and not the center of its universe, perhaps we shouldn't wrap the hexes and then the stretching the top to make it bigger would GO AWAY because the hexes stack without regard to fitting around a central point ... unfortunately then how would hexes be oriented in such a way on Erfworld, with the hexes always being hexagons ... ex: hexagonal bipyramids stacked oriented with pyramidal base being perpendicular to Erfworld's geographical equator ... the equatorial hexes would be a vertical cross-section of the hexagonal bipyramid and be very strangely shaped with two points and a middle while the polar hexes would be very close to the familiar hexagaon except when the horizontal-ish cross-section happened to be not quite a perfect hexagon perfectly in the middle of the figure (which is almost all of the time).
In conclusion, assuming Erfworld's hexes' diameters are irrational numbers (that can multiply up to pi) so that the irrational number pi doesn't cause Erfworld to have partial hexes left over when it is a perfect sphere (unlike Earth which is egg-shaped) then ... for a pi decimeter diameter 3D hex that is curved around Erfworld's surface like the hexagons are curved around Bubble Shields in the game Halo, we are looking in general for differences in millimeters between the top and bottom of the hex. Whether that is stretching or displacement we don't know.
If the hex isn't curved then the only difference is that the bottom faces of hexes in Erfworld aren't actually on the spherical surface of Erfworld, the bottom face is slightly below it except on its edges ... they touch the surface of Erfworld. This is like how you can draw lots and lots of straight lines inside of a perfect circle to approximate it.
The big question is whether or not 3D hexes (for this example think about hexagonal prisms) should be ADDITIVELY stretched (the stretch that made the top of the hex below bigger being the starting point for the bottom of the hex above ... which is streched more to make the top of the hex above ... ad infinitum) because if they aren't then the 3D hexes as you go up in altitude are displaced (slightly) horizontally from the others below them were to account for the fact that to keep no gaps between the hexes and there are more hexes than there were before. So the choice is:
- keep the hex where they were horizontally and start getting larger and larger gaps as you go up in altitude, until those gaps can fit extra hexes in them ... this looks ugly trust me ... basically right before you can add in more hexes the units are almost teleporting an entire hex distance between every hex because that's almost how big the gaps are!)
- Best choice in my opinion: compact the 3D hexes in the new layer to remove the gaps so that the bunch of tiny gaps are converted into just a few larger gaps outside of your compacted hex formation ... voila! That's where the spare hexes go ... the ones that make up the increase in circumference of the sphere they exist in compared to the hexes below. Note: if hexagonal dipyramids were used then the displacement from this would be a problem since the pyramids would be invading the below hexes' personal space, and there would be empty spaces where the pyramids would have gone were they not displaced. Attempting to curve the pyramids to compensate doesn't help because the displacement could cause the pyramid to end up anywhere ... near the edge of the lower hex ... in the middle of the lower hex ... depending on which displaced hex you choose.
In the end ... if Erfworld is spherical then Hexagonal dipyramids would have serious problems with gaps, displacement, or stretching to ridiculously-sized hexes at higher altitudes ... but Hexagonal prisms would do just fine (except that there would be gaps, displacement - but at least the pyramids would not invade the other hexes space - (vertical movement would still be buggy though), or stretching).
These choices are completely unacceptable (if Erfworld is a sphere). I have to conclude that actually, gravity in Erfworld is what fixes this problem. Imagine these cubes were hexagonal prisms. The top and bottom faces of which were oriented to point away from the center of Erfworld. The stretching here is exactly the stretching I was discussing earlier to prevent gaps between hexes of different spherical layers. BOOM ... relativity isn't scienticically proven to be in Erfworld, but with electricity and magnetism probably working the same (Parson's solar calculator watch works) ... well ... Lorentz contraction (a part of Relativity) came directly from the failure of the Michelson–Morley experiment and ... all of that was because electromagnetism works the way it does. If it works the same in Erfworld then someone could be standing still observing an electric field and someone zooming by would see a magnetic field and ... the only way for the two reference frames to be consistent was if time slowed down for the observer in motion, relative to the electric field (Look at the appropriate chapter in The Cartoon Guide to Physics it does a good job of coming up with Relativity without invoking gravity or acceleration in the proof).But I thought Erfworldians said that time is relative but not in the Earthworld relativity way?
Yes ... yes they did. There can only be two explanations:
- Erfworld is really actually a flat world with gravity that ONLY points downwards ... downwards like from above the tabletop to below the tabletop, regardless of if that part of Erfworld had a mountain on it. Since gravity doesn't point to the center of an object, the curving space to fix the hexes and also pop out with relativity thing never comes up, since the hexes are truly stacked vertically in a cube-shaped volume above and below Erfworld's surface, without trying to point to the center of a sphere they simply have their top and bottom faces exactly perpendicular to Erfworld's surface.
- Erfworld may actually have relativity and the Sun's position is lying about Time. The sun's position simply keeps track of turn order/stuff for each individual unit but has nothing at all to do with "real time." This unfortunately makes perfect sense ... (I added the italic stuff in parentheses)
Quote:
Parson remembered time zones and the weirdness of the international dateline. Watching the Olympics at 2 am, people running in the hot sun on the other side of the planet, where it was tomorrow. Erfworlders carried their own personal time zones around. Was that odder than anything else about this place?
Yes, yes it was. It meant the whole universe worked differently here, and he wasn't prepared to let it go at that. He leaned forward even farther and put his elbows on his knees. "Aha! What if I come back?"
Sizemore looked at him blankly. Maggie watched them both, a dreamy grin on her face.
"It's four hours later to me, but maybe four minutes to you." (in real time)
"Yes?" said Sizemore.
Could he really not see the problem? "Where is the sun?" asked Parson in exasperation.
Sizemore squinted at him. "In that hex? Four minutes further along in the sky." (the sun simply shows the turn order of the dominant Observer in that hex, NOT anything to do with "real time")
"It jumps backwards when I enter the hex?!"
"Of course! To you," said Sizemore. "Because you traveled and were observed from that hex. If you weren't observed, you would find the sun in the same position as the previous hex."
"Ridonkulous!"
Maggie slumped backward on the blanket and giggled helplessly up at the sunlit sky.
- Erfworld Summer Update - 029