Is Tamriel Flat in Topological Space?

Ectheliontnacil

albesca wrote: »

Ectheliontnacil wrote: »

Again don't really get what you're trying to do here, /riamverysmart or something?

I find the fact that Echtelion questions the motives of Iluvatar disturbing

Iluvatar is omniscient. He'd know the answers to all his questions... Iluvatar asking questions (on the eso forums of all places), made me suspicious.

Neoealth

Well if you look at the art work for the TES Aurbis (Universe) You will see nirn is a planet, as are the so called "planes" of oblivion. Indeed even the Aedra themselves became the planets that are near Nirn when they gave their very being to become part of Mundus.

The stars are holes in the fabric of mundus, caused by the followers of magnus (Magna Ge) when they fled creation at the very last moment. The holes are rips in mundus which leak magicka from Aetherius.

Kram8ion

No silly, it’s spherical but the flat earth revolves around it hexagonaly

Neoealth

Earth is actually flat though, obviously.

Illuvatarr

In three dimensional space, actually four dimensional space, as explained to me by someone (my new friend and an actual compelling reason to return to Abilene at some point to visit) of genius level intelligence, the earth is indeed round. So is the moon. So is anything that accumulateds enough mass due to gravity. This explains my wonderful neighbor who is adorable yet she is clearly round. She bakes me cookies so I love her all the same.

In topological space, the rules of gravity stay the same but the number of dimensions increases and cannot be observed with the naked eye unless we model it as such (which according to my new professor friend can reach as high as 11 dimensions which supports my previous understanding of concepts like string theory but on a layman’s level mind you).

The earth/Nirn in the case might take the shape of a twisted plane or a tube that appears round to the naked eye but yet is non Euclidean on a micro level.

Illuvatarr

Ectheliontnacil wrote: »

albesca wrote: »

Ectheliontnacil wrote: »

Again don't really get what you're trying to do here, /riamverysmart or something?

I find the fact that Echtelion questions the motives of Iluvatar disturbing

Iluvatar is omniscient. He'd know the answers to all his questions... Iluvatar asking questions (on the eso forums of all places), made me suspicious.

Ilúvatar is always up to something:)

Neoealth

Illuvatarr wrote: »

In three dimensional space, actually four dimensional space, as explained to me by someone (my new friend and an actual compelling reason to return to Abilene at some point to visit) of genius level intelligence, the earth is indeed round. So is the moon. So is anything that accumulateds enough mass due to gravity. This explains my wonderful neighbor who is adorable yet she is clearly round. She bakes me cookies so I love her all the same.

In topological space, the rules of gravity stay the same but the number of dimensions increases and cannot be observed with the naked eye unless we model it as such (which according to my new professor friend can reach as high as 11 dimensions which supports my previous understanding of concepts like string theory but on a layman’s level mind you).

The earth/Nirn in the case might take the shape of a twisted plane or a tube that appears round to the naked eye but yet is non Euclidean on a micro level.

Can I have some of the drugs you've taken?

Illuvatarr

Neoealth wrote: »

Illuvatarr wrote: »

In three dimensional space, actually four dimensional space, as explained to me by someone (my new friend and an actual compelling reason to return to Abilene at some point to visit) of genius level intelligence, the earth is indeed round. So is the moon. So is anything that accumulateds enough mass due to gravity. This explains my wonderful neighbor who is adorable yet she is clearly round. She bakes me cookies so I love her all the same.

In topological space, the rules of gravity stay the same but the number of dimensions increases and cannot be observed with the naked eye unless we model it as such (which according to my new professor friend can reach as high as 11 dimensions which supports my previous understanding of concepts like string theory but on a layman’s level mind you).

The earth/Nirn in the case might take the shape of a twisted plane or a tube that appears round to the naked eye but yet is non Euclidean on a micro level.

Can I have some of the drugs you've taken?

Convinced the special ingredient for the ribs at Logan’s Roadhouse is cocaine. You will eat them until you can’t eat anymore:)

Ectheliontnacil

Illuvatarr wrote: »

In three dimensional space, actually four dimensional space, as explained to me by someone (my new friend and an actual compelling reason to return to Abilene at some point to visit) of genius level intelligence, the earth is indeed round. So is the moon. So is anything that accumulateds enough mass due to gravity. This explains my wonderful neighbor who is adorable yet she is clearly round. She bakes me cookies so I love her all the same.

In topological space, the rules of gravity stay the same but the number of dimensions increases and cannot be observed with the naked eye unless we model it as such (which according to my new professor friend can reach as high as 11 dimensions which supports my previous understanding of concepts like string theory but on a layman’s level mind you).

The earth/Nirn in the case might take the shape of a twisted plane or a tube that appears round to the naked eye but yet is non Euclidean on a micro level.

Hmm I'm a bit confused. The way I understand it is a set X with a family/collection T (can't do Greek letters so T must suffice xD) of open subsets of X.

The conditions it must meet are as follows:
- X and the empty set are in T
- The intersection of (a finite number of) elements of T is in T
- The union of elements of T is in T

The standard topology on the real numbers for example is the one defined by our definition 'open' in R, i.e. if U open and x in U, then there must be an 'epsilon'>0 so that (x-E,x+E) is still in U.

Maybe not completely correct as I didn't learn this stuff in English and I have no clue about topology.

My question is, why are there at most 11 dimensions for topological spaces? Won't a norm on say 12 dimensions induce a topological space? I thought a topology can exist on an arbitrary number of dimensions.

Maybe you can elaborate on this a bit?

Solariken

Digiman wrote: »

More of a plane then a planet... the original lore said it was pieces of many shattered worlds put into one... everyone basically migrated to tamerial. It could be thus endlessly sustained by the Aedra divines.

Then there is space, many lore books point out that what our characters see is what only what there minds can comprehend from up above because there is more to the night sky then stars and the moons. Stars are meant be spirits that ascended to aetherias and the moon the shattered body of the dead god lorkan.

To take it further, what if what their minds can perceive is all there is. The shape of the plane is irrelevant because it's a kind of virtual existence held in place by persistent conscious thought of the Aedra and all other conscious beings. A co-created "dream world" of a sort.

There is no "space", only the currently-perceivable outer limit of the illusory planet construct. To venture into that limit is simultaneously to extend or render new space.

Illuvatarr

Ectheliontnacil wrote: »

Illuvatarr wrote: »

In three dimensional space, actually four dimensional space, as explained to me by someone (my new friend and an actual compelling reason to return to Abilene at some point to visit) of genius level intelligence, the earth is indeed round. So is the moon. So is anything that accumulateds enough mass due to gravity. This explains my wonderful neighbor who is adorable yet she is clearly round. She bakes me cookies so I love her all the same.

In topological space, the rules of gravity stay the same but the number of dimensions increases and cannot be observed with the naked eye unless we model it as such (which according to my new professor friend can reach as high as 11 dimensions which supports my previous understanding of concepts like string theory but on a layman’s level mind you).

The earth/Nirn in the case might take the shape of a twisted plane or a tube that appears round to the naked eye but yet is non Euclidean on a micro level.

Hmm I'm a bit confused. The way I understand it is a set X with a family/collection T (can't do Greek letters so T must suffice xD) of open subsets of X.

The conditions it must meet are as follows:
- X and the empty set are in T
- The intersection of (a finite number of) elements of T is in T
- The union of elements of T is in T

The standard topology on the real numbers for example is the one defined by our definition 'open' in R, i.e. if U open and x in U, then there must be an 'epsilon'>0 so that (x-E,x+E) is still in U.

Maybe not completely correct as I didn't learn this stuff in English and I have no clue about topology.

My question is, why are there at most 11 dimensions for topological spaces? Won't a norm on say 12 dimensions induce a topological space? I thought a topology can exist on an arbitrary number of dimensions.

Maybe you can elaborate on this a bit?

You can have an infinite number or dimensions in topological space. They have found 11 that describe our reality and that is limited by probabilities.

josiahva

therift wrote: »

Androconium wrote: »

Yes, but the Tamriel planet mass is not solid.
Its a hollow spherical crust only.

So, inebriated amateur geophysicists, we need to understand

A) how thick the crust is
when it will implode

Thanks so much.

Assuming the interior of Nirn is hollow, we can estimate the minimum thickness of the crust necessary to support the weight of the oceans and mountains on the crust's surface.

Mountains in Tamriel are of prodigious height and quite steep when compared to all but the youngest mountain ranges on Earth (Andes). Two deductions may be made from this observation:

1) There must be active plate tectonics on Nirn, or the catastrophic effects of Dragonbreaks must produce a side effect closely resembling the action of plate tectonics but in a greatly compressed time frame.

2) Whether the process of mountain building is due to plate tectonics or due to Dragonbreaks, there must be a substantial amount of water distributed through the crust in order to make rock pliable and elastic enough to form mountainous structures rather than shattering into rubble.

We can assume, then, that the density of the crust of Nirn is similar to the density of the crust of Earth. However, in order to support the overlying mountains and oceans over a hollow interior, the crust of Nirn must be much thicker than the crust of Earth, which overlies a much denser mantle. Furthermore, the crust of Nirn is subject to compression, tensile, and shearing forces due to the gravitation effects of closely-orbiting Masser and Secunda, and also by whatever body serves as a source of heat and light like our Sun (I believe Nirn's sun is not a star but rather a magical effect).

The crust of Earth varies between 7 and 10 kilometers in the ocean floors (continents are much thicker). I'm not a geologist nor a materials scientist, but my wag ( wild-ass guess) suggests a thickness of 150% to 200% of the Earth's crustal thickness would be required for the crust of Nirn to support itself over a hollow interior, keeping in mind the crust is subject to aforementioned competing stresses, not to mention being riven with delves, dungeons, dwemer excavations, daedric intrusions, and other, unknown burrowings.

So, at minimum, I'd say the crust on Nirn runs between 15km thick under the oceans to at minimum, 60km thick under the continents.

This still leaves a vast interior volume, as the radius of Nirn appears to be between the radius of Mars and Venus, which is about 2,100km and 6,000km respectively.


Regarding your concern about the implosion of Nirn, it is at least a millenium in the future since TES 4 and 5 are set in that future, so there is no immediate cause for concern.

You are forgetting gravity...if there is gravity on Nirn, its impossible for it to be hollow, entropy would demand that the crust crumble inward. In fact...if Nirn formed under the normal rules for planetary formation, it couldn't have formed as a hollow sphere to begin with...no planet could. So if you are applying real world physics to an imaginary world then its all or nothing...either Nirn is a normal planet...or it is not...if it is not a normal planet it could very well be flat, even if the moons that orbit it were spheres. The question is really whether gravity exists to begin with in TES universe or whether magic accounts for the things we see in game that approximate the real world

Bald_templar

This question does not make much sense since flat is the property associated with the metric rather than topology. However, topology, on the other hand, tells you what kind of metric is allowed.

A more interesting question would be what is the structure of Artaeum. Is the visible magical barrier the "boundary"? Since there is ocean going through the "boundary", I don't think it's like a leaking balloon in the oblivion. A reasonable guess would be Artaeum is a 3-dimensional real projective space or like 2-d projective space times an interval (with 2 poles). In this case, first of all, the oblivion must be a higher dimensional space to allow such embedding. And since the island is removed from the Tamriel, the structure of the latter one must be more complicated.

Ruckly

If Tamriel or Nirn were round it would have to be at the center of the universe with everything rotating around it in order for Newtonian laws to work in non-inertial reference frames. Or rather there can't be non-inertial reference frames since in those cases Newtonian laws are not followed on Nirn. If it is flat Newtonian laws wouldn't work anyways since it is really based on gravity being reduced to a point of a spherical integral. In the flat scenario there might be a huge dynamo or an infinite series of dynamos under Nirn and Nirn might have a high a relatively homogeneous iron content.

Note: I'm not going to explain why the dynamo case doesn't work. Nightmarish and all that.

therift

josiahva wrote: »

therift wrote: »

Androconium wrote: »

Yes, but the Tamriel planet mass is not solid.
Its a hollow spherical crust only.

So, inebriated amateur geophysicists, we need to understand

A) how thick the crust is
when it will implode

Thanks so much.

Assuming the interior of Nirn is hollow, we can estimate the minimum thickness of the crust necessary to support the weight of the oceans and mountains on the crust's surface.

Mountains in Tamriel are of prodigious height and quite steep when compared to all but the youngest mountain ranges on Earth (Andes). Two deductions may be made from this observation:

1) There must be active plate tectonics on Nirn, or the catastrophic effects of Dragonbreaks must produce a side effect closely resembling the action of plate tectonics but in a greatly compressed time frame.

2) Whether the process of mountain building is due to plate tectonics or due to Dragonbreaks, there must be a substantial amount of water distributed through the crust in order to make rock pliable and elastic enough to form mountainous structures rather than shattering into rubble.

We can assume, then, that the density of the crust of Nirn is similar to the density of the crust of Earth. However, in order to support the overlying mountains and oceans over a hollow interior, the crust of Nirn must be much thicker than the crust of Earth, which overlies a much denser mantle. Furthermore, the crust of Nirn is subject to compression, tensile, and shearing forces due to the gravitation effects of closely-orbiting Masser and Secunda, and also by whatever body serves as a source of heat and light like our Sun (I believe Nirn's sun is not a star but rather a magical effect).

The crust of Earth varies between 7 and 10 kilometers in the ocean floors (continents are much thicker). I'm not a geologist nor a materials scientist, but my wag ( wild-ass guess) suggests a thickness of 150% to 200% of the Earth's crustal thickness would be required for the crust of Nirn to support itself over a hollow interior, keeping in mind the crust is subject to aforementioned competing stresses, not to mention being riven with delves, dungeons, dwemer excavations, daedric intrusions, and other, unknown burrowings.

So, at minimum, I'd say the crust on Nirn runs between 15km thick under the oceans to at minimum, 60km thick under the continents.

This still leaves a vast interior volume, as the radius of Nirn appears to be between the radius of Mars and Venus, which is about 2,100km and 6,000km respectively.


Regarding your concern about the implosion of Nirn, it is at least a millenium in the future since TES 4 and 5 are set in that future, so there is no immediate cause for concern.

You are forgetting gravity...if there is gravity on Nirn, its impossible for it to be hollow, entropy would demand that the crust crumble inward. In fact...if Nirn formed under the normal rules for planetary formation, it couldn't have formed as a hollow sphere to begin with...no planet could. So if you are applying real world physics to an imaginary world then its all or nothing...either Nirn is a normal planet...or it is not...if it is not a normal planet it could very well be flat, even if the moons that orbit it were spheres. The question is really whether gravity exists to begin with in TES universe or whether magic accounts for the things we see in game that approximate the real world

Not necessarily. Nirn could have been formed by magical agency with a gaseous interior, or it could have been assembled rather than formed by accretion.

The question was how thick would the crust need to be to prevent collapse. A hollow sphere is essentially a suspension bridge without end points. The structure (crust) needs to be elastic enough to absorb stresses and rigid enough to resist deformation under compression.

Of course the issue remains of how Nirn retains one g of gravity while the mass of the interior is missing, but however that question is answered, the analysis of crust thickness remains.

Nestor

Oddly enough, the Tamriel Worldspace we play in is a Flat(ish)map that represents a spherical planet. Now I say that not having noticed any curvature in oceans when looking at them, but the fog probably prevents seeing that.

Also, there is no time difference between the East side of the map and the West side. If its 10PM in one place, its 10PM everywhere.

SirAndy

Nestor wrote: »

Oddly enough, the Tamriel Worldspace we play in is a Flat(ish)map that represents a spherical planet. Now I say that not having noticed any curvature in oceans when looking at them, but the fog probably prevents seeing that.
Also, there is no time difference between the East side of the map and the West side. If its 10PM in one place, its 10PM everywhere.

Not just flat(ish), the maps are indeed build on a completely flat "surface", no curvature. Any height differences are a simple +/- offset from the (flat) ground plane.

This is by design and speeds up rendering (and physics) because one can use axis aligned bounding boxes for collision detection (and visual culling), which is considerably faster than using bounding boxes that are aligned on a curved surface.

Darios_Heliodromos

Soon they were walking across the eastern sea to the land of snakes and snow demons. Vivec wanted to show the Hortator the fighting styles of foreign tongues. They learned the idiom stroke from the pillow book of the Tsaesci king. It is shaped like the insight of this page. The Tsaesci serpents vowed to have their vengeance on the west at least three times.

They walked farther and saw the spiked waters at the edge of the map. Here the spirit of limitation gifted them with a spoke and bade them find the rest of the wheel.

- 36 Lessons of Vivec, Sermon 17

Maybe this story is more allegory than anything, but it also does strike me as somewhat similar to the idea of a flat Arda (pre-downfall of Numenor) with the Walls of the Sun being located at the eastern edge of the world.

Didgerion

It is just bytes to me. Fun bytes thought. But now you i seriously wondering what is the topology of my first game (for those who does not know my first game - it was moving the cursor around back in eighties)

zaria

SirAndy wrote: »

Nestor wrote: »

Oddly enough, the Tamriel Worldspace we play in is a Flat(ish)map that represents a spherical planet. Now I say that not having noticed any curvature in oceans when looking at them, but the fog probably prevents seeing that.
Also, there is no time difference between the East side of the map and the West side. If its 10PM in one place, its 10PM everywhere.

Not just flat(ish), the maps are indeed build on a completely flat "surface", no curvature. Any height differences are a simple +/- offset from the (flat) ground plane.

This is by design and speeds up rendering (and physics) because one can use axis aligned bounding boxes for collision detection (and visual culling), which is considerably faster than using bounding boxes that are aligned on a curved surface.

Yes, having an round surface complicate stuff a lot, spore and kerbal space program does it but its pointless in ESO and other TES ganes.
Yes in Morrowind you could perhaps get high enough levitation to reach orbital speeds but let not design an game around the most OP exploit in the history of video games.

Illuvatarr

Bald_templar wrote: »

This question does not make much sense since flat is the property associated with the metric rather than topology. However, topology, on the other hand, tells you what kind of metric is allowed.

A more interesting question would be what is the structure of Artaeum. Is the visible magical barrier the "boundary"? Since there is ocean going through the "boundary", I don't think it's like a leaking balloon in the oblivion. A reasonable guess would be Artaeum is a 3-dimensional real projective space or like 2-d projective space times an interval (with 2 poles). In this case, first of all, the oblivion must be a higher dimensional space to allow such embedding. And since the island is removed from the Tamriel, the structure of the latter one must be more complicated.

Illuvatarr

So ya a speak easy

http://i.imgur.com/imLPcvd.jpg

Vietfox

Pay attention to the sky and you'll know

Ruckly

Illuvatarr wrote: »

I already have an answer to this question:) I/we were curious what the community at large would say:)

And yes as Eru Ilúvatar, all of this is by design. I do like the fact you pointed out a fellow Greek to support your statements:)

What's the answer you arrived at? My answer: metaphysically it can be round or flat and physically it can be neither. Physically in the round case there is a double contradiction and in the flat case gravity gets wonky. Metaphysically the game makers are the "Creators" and thus hold some kind of deity status and round or flat depend on their rule set. From their rule set I would say it is a flat world that tries to simulate a round one. And if you are immersed in the game it does simulate a round one. There are limits it being an mmo. It's not just supposed to be a simulation rather more a theme park. And in real theme parks you don't pay attention to the strings holding the puppets. You don't look at the seal making a joke and say "ah an expression of operant conditioning".

I think the game engine is built in this space:

https://en.wikipedia.org/wiki/Quaternion

This I believe is the space the forms are transformed within and thus is the topological space for ESO.

Varana

As for geology, which implications have regions like Stonefalls and Vvardenfell for the structure of Nirn?
They have ridiculously hyperactive volcanism; I'd suspect that this would at least make something like a planetary mantle under the crust necessary, making the hollow-Nirn theory even less probable.

Billdor

Androconium wrote: »

Yes, but the Tamriel planet mass is not solid.
Its a hollow spherical crust only.

So, inebriated amateur geophysicists, we need to understand

A) how thick the crust is
when it will implode

Thanks so much.

Isn't it just Clockwork Machinary within Nirn? Wheels of Lull or something.

Illuvatarr

albesca wrote: »

Ectheliontnacil wrote: »

Again don't really get what you're trying to do here, /riamverysmart or something?

I find the fact that Echtelion questions the motives of Iluvatar disturbing

Didn’t Gothmog and Ecthelion kill each other in the fountain at the Siege of Gondolin?:)

Caligamy_ESO

Gotta get some Darwin awards ready for when they inevitably freeze to death at the south pole...

wait, what were we talking about?

kamimark

The lore books claim the world is a sphere, or at least "round".

However, my research has shown that the world only exists in 50m square "chunks" which load in as you run forward, and during times of bad psychic weather called "lag" they may fail to load, giving you the flat-shaded void where you keep running but go nowhere. This is often hidden by the strange projections called "load screens" which prevent you from seeing the unloaded world.

Also, in several places it is possible to slip outside the invisible daedric magic which limits each nation's borders with only a few doors to neighboring nations, and see the edge of a chunk or the weird projections of distant lands which cannot normally be reached.

Ruckly

Ah I think I see it now. Topology is a bit complicated approach. If you have a sphere with a pole defined to be infinity(because a sphere has no beginning or end?) you can transform it into a flat unbounded plane. This because the flat unbounded plane can be wrapped around into itself at infinity to form a sphere.

e.g.

https://en.wikipedia.org/wiki/Riemann_sphere

And the plane of Nirn might extend to infinity because there is nothing in the map of Tamriel that says otherwise and thus it could be topologically the same as a sphere?