My search-fu is poor.
Years ago I think there was a discussion about the Schism War and moving mountains..
Specifically rolling waves of dirt over an aegis, in order to bury a Covenant site.
How high would you need to roll dirt up so that gravity would carry it across the aegis and bury all within?
An Aegis is hemispherical, so its height is its radius. So probably at least twice that?
Why?
It's either that or a cylindrer. But then what height does it extend to? The lunar sphere?
Certainly a T: Boundary does not need to be circular.
Couldn't the form of the Aegis be anything in between? This looks like smuggling in house rules by sheer assertiveness.
I can't remember the answer, but I thought about this when I was writing about covenants on columns of magically created rock in the sea. I'd look there...
I'm not trying to force anything, but I find that a conical shape would be weirder than either of the two options.
Obviously, if the area protected by the aegis is square, then the aegis would be some form of square based 3-D shape. Do you play it more "cubic", as in as high as it is long?
My party is likely to invest in an aegis in a few sessions, so we have not set it in stone yet.
I going to have to agree with you here @OneShot
My best guess is that the assumption of a hemispherical or cylindrical aegis comes from the insert on pae 113 of the core rulebook which states that a base boundary is 100 paces in diameter.
The natural generalisation of this is to assume that going up the spell is either infinitely tall or it bounds inwards resulting in cylinder and (hemi)spheres respectively. I do think that a hemispherical aegis is less reasonable than a spherical one, as it would otherwise leave e.g. cave systems outside the aegis if the ritual is cast at ground level, and it seems kind of dumb to force covenants with underground holdings to dig "circumference-tunnels" purely to include their underground holdings in the protection of the aegis.
However 100 paces diameter is not the actual shape of a typical boundary because a spell with the target Boundary must actually follow a real boundary. Most boundaries in the Ars magica world are unlikely to be perfect circles, so it stands to reason that most aegises will have some geometrically complex shape that is intuitively simple to understand or describe, such as "the circumference of the walls of the castle" or the traditional boundary of the village as determined by the route the villagers walk on their annual boundary-determining-walk or whatever fits the specific situation.
This of course leaves undetermined what the "airspace" border of a boundary target spell is. It is not clear to me that the core book takes a stand on this and I do not care to go through the various splatbooks for a ruling.
You either determine that something that would be inside the boundary if it were on the ground is in the warded airspace, which would result in a 3d cylinder for a perfectly circular boundary or you can determine that it goes up into the air (and into the ground?). This is to me the most Ars Magica-ey solution that I can think up easily.
That is indeed a problem I had in mind as well, when reading the first answers.
So assume, that we have a magical cliff, with its height double its width in the sea. So the sea around the cliff forms an obvious T: Boundary for an Aegis, and magi can be rowed around the cliff when casting that Aegis.
But how much of the cliff is now protected? And why?
Do you still recall the book you wrote about this?
I was largely thinking that all the other wards explicitly were. Though they're ring rather than boundary. While nothing is explicitly stated, I'd go for the average boundary distance as a good enough estimate (because I do not want to think about how you would calculate it exactly).
I agree that cylindrical is the other natural option, in which case dropping a wave of earth wouldn't bypass an aegis.
TME - the Isle of magicians maybe?
Also, why not an egg or ellipsoid shape?
I didn't find it there - though I looked up all the mentions of 'Aegis' in the text, and reread p.71f Ritual Wards and Other Boundary Spells.
Hmmm, what about a Vilano solution?
I'm trying to figure out a version of Invisible Sling of Vilano capable of hurling mountains, but I'm stuck trying to figure out level, damage and range increments (I'm confident about it having T: Part, because the mountain is going to be part of a mountain range and so on, but then what? Increasing base size to cover the full mountain should also have an impact on damage and range? Or could the first mountain hurler come with a first spell able to throw mountains 20 paces away doing +5 damage?).
Another natural (at least in my mind) option would be to say that a ward protects what is inside it.
This would mean that the height of an aegis - or a circular ward - is determined by what it protects/contains. This solves a few problems:
Some problems remain - like determining if underground structures/objects are contained or how to ward a doorway with a circle in the floor.
In my opinion a reasonable way forward would be:
Yup. Even for circular wards I prefer to use a prolate spheroid, which fits neither of those two.
And then there is your even more important point about Boundary not being circular.
You make an important observation. A boundary target is never going to be 3D (except in cases where it could qualify as room or structure) because there is no natural boundary above, except the lunar sphere, which would break the size limit for any reasonably levelled spell.
Hence, by RAW, boundary targets can only be understood in terms of 2D projections (if at all).
I am not sure I like to treat Aegis as boundary target though. There is too much in the text which points to a special legacy target defined by the ritual procession marching along the perimeter, but we are still only describing a planar border.
There is nothing there to suggest a circular shape. Every set in a metric space has a diameter, no matter the shape or number of dimensions.
In most of my games individual aegis have different shapes- cylindrical, spheroid, pyramidal, and nobody knows why they manifest as they do in different situations, whether it is a feature of the magi involved, the land itself, the magical aura...
since we agree that a boundary is defined only in 2d terms in RAW that leaves a lot of room for interpretation regarding what is considered to be inside a boundary and what is not.
The first obvious interpretation, that the boundary has no height and as such does not affect anything above or below it, is obviously false.
Normally I would favor not interpreting at all, however that is also obviously not an option for anyone actually playing the game.
So what is inside a boundary and what is not? Personally I favor a metaphysical answer rather than a geometric one. IMO ars magica is much more concerned with whether or not something is considered to be inside the boundary in the way we would understand that to be the case in everyday speech than it is with precise estimations of the 3D geometry of various complex shapes. It just feels wrong to me to say that a tall tower erected just on the boundary that is the target of a spell juts out of the boundary at some point midway in its height. I think it is much more reasonable to consider the example tower to be a single entity that is either included in its entirety or not included at all.
I agree with you that the Aegis seems to break with many rules for how "normal" magic behaves, including the boundary target. But it is clearly specified as having "Target:Boundary" so we have to take that into account when discussing how the spell plays out.
I absolutely agree. But Peter already solved that a few posts above!
I’m going to frame these words and make them my new default.
That’s interesting because all definitions of “diameter” I’d seen have the world “circle” or “circumference” on their very first sentence. What’s the diameter of a triangle? And of a torus? And of a parabola? And of the white squares of a chess board under the metric of the knight moves?
How do you find the diameter of a triangle? - Quora
apparently the diameter of a triangle would be the length of the longest side.
for squares on a chessboard it would be the length of the diagonal- it is apparently defined as the greatest distance between any 2 points in the figure.