What is a Wall of Force?

What actually is a Wall of Force?

Well, the thing to note is that it is an evocation, not a conjuration. Very different.

A conjurer creates matter having certain properties by knotting the aether into a particular “shape”. A spray of something an acidic, a ball of burning stuff. It will exist for a period of time, usually, and then unravel.

Evocation is quite different, and goes back to Plato’s ideal forms.

What is the nature of fire? Well, the nature of fire is to burn. An evoker “evokes” – “manifests”, if you prefer – this inner nature of fire, without recourse to any gross matter on which the burniness subsists, and so creates a spherical region of sheer burniness – burniness in and of itself. (The concussion and sound are consequences of this, rather than being things in themselves.) Thus, a Fireball. Likewise, a Cone of Cold is a cone of sheer freeziness; and a Sound Burst a burst of loudness.

Now, what is the nature of solid matter, qua being solid matter? As the mage Pauli explains, the nature of solid matter is that it excludes other solid matter from the volume it occupies, and exerts force on other solid matter that tries to do so. Why can you not press your hand through a brick wall? Because the brick wall pushes back on your hand, in order to keep it out.

That is what a Wall of Force is – a volume in which is evoked sheer solidity, solidity in and of itself. Such walls need to be thin because they need to displace the air previously occupying the space. Even a Bigby’s Hand (showing my years – we no longer call the spell that, for legal reasons) is only a thin membrane in the approximate shape of a hand. Of course, these ideal forms can only be manifested briefly on Prime – often instantaneously – as Prime is not the place where these forms reside (they normally reside in the same place that fictional objects do). Maintaining an evocation for longer than an instant is always more advanced magic.

Assignment: 200 words. Summarise pp 453-460, “on the nature of fictional objects”.
Additional Credit: explain why a Disintegrate unfailingly dispels a Wall of Force.

He’s our buoy!

So, everything has gone to shit, Coin is probably dead, Limen was probably in the holy-of-holies – the tesseract – and has kinda stolen our plan. The dimensional anchor is imbedded in Coin’s portrait, and the rope extends off to … somewhere.

We had a bit of a chat to these kinda godlike dudes, who are Coin’s “children”. Maybe. We were going to want to catch up with Limen at the other end of this rope thing. We could follow that rope (which no doubt let through the Plane of Infinite Rats), or maybe take a shortcut.

We opted for the shortcut. We were waned that it might get a little damp.

Now, there’s a bit of history there. One of the doorways opened out onto a ship, which we sank a while ago and which “now” probably lies on the bottom of an ocean.

Checkov’s Gun was mentioned.

Oh, and we needed to find a wizard who was not very good (at being a wizard), but who was going to help in some unspecified way.

And they gave us a little thingy which would stop time while we all had a full nights rest and levelled up. Nice. And a second one. For later. Because we are going to need it.

In the “morning”, John gives everyone a Water Breathing spell, which will last for a while, ditto a Wind Walk.

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First door. Opened out into a sewer. There were all these skeletons that had had the flesh sucked off them, but it was ok because they were fully dead. Nice.

Our key/compass pointed “thataway” to the next door, so we went thataway. Tied up in the middle of the fetor was some dude calling for help. “Please help!”, he yelled, “He’s coming back!”. A brief interrogation during which Brus for the first time ever used his “Detect Lies” class ability determined that he was lying his ass off. We ignored him and went for the door. Oh, and I think Picklick shot him a bit just to see what would happen, because even though Morgs was not at the table that’s just how he rolls.

Anyway. As soon as we got close the dude, of course, attacked and a couple more emerged out of the scenery (it was a sewer – lot’s of scenery). We managed to get them down without too much trouble, because it turns out they were flesh-suckers. Every sucked cooked flesh off a chicken bone? Well, they did that. Faugh has taken 3 points of Charisma drain, which – well – doesn’t really do much to him. I think Will took some as well, which does affect him. But, he’s rocking about 20 normally, so he’s ok for the moment.

There was a ping from a pile of scenery, and we uncovered a Ring of Water Walking. We gave it to Faugh, on account of he is a gnome and occasionally gets in over his head.

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Next door. Wood panelled rooms which smelled awesome with beeswax. Brus drops a Bloodhound spell every day, so was relived to be out of the sewer. Following our compass, we found a wooden shield that had been pierced through with a very odd foot-and-a-half long shortspear, made of a weird material, kinda chitinous and aww shit: is that a bee stinger?

You bet your booty it was.

Anyway. We found this nice room with a boiling kettle, some tea making gear, and no wizard. We opened a door and looked down a corridor to see a dude in a wizard’s hat bolting towards us, pursued by a swarm of unhappy bees. We admit the wizard, slam the door shut, and Picklick proceeds to wedge the door.

Thud!

Them is some big-ass bees. The wizard mentions that he seems to have upset them. Then there’s a knock on the other door. We reason that bees usually don’t knock, so we let the guy in. Wizard looks like he’s seen a ghost.

Guy says “I’m sorry!” and splits open, and a swarm of bees emerge. Then the other swarm breaks through the wedged door.

Fight fight. Will (or Bottom) gets stung, takes Dex damage. We hightail it to the next door, dragging the wizard along.

But there are two doors! One goes to the bottom of the ocean, and one goes – well, somewhere else. We opt for waterworld. But first, a plan is needed. We rope ourselves together – a good start. We will close the other doors, open the portal door and wait for the inrushing water to equalise pressure. Cool. But we have two problems – we have dudes in armour, and we have a wizard who did not get this morning’s Water Breathing.

For the Wizard, we decide to stuff him into a Bag of Holding. He won’t be in there too long, so will probably not suffocate. Rather than try to convince him to to this, Picklick saps him and we stuff his uncoscious body into the bag. We actually have two, but one of them has a few corpses in it (it’s a long story) so we put him in the other one.

Now, our first thought was to use Wind Walk. But after a moment we recall that that spell doesn’t really work well underwater.

But remember that ring of Water Walking? That we gave Faugh?

If the spell is cast underwater (or while the subjects are partially or wholly submerged in whatever liquid they are in), the subjects are borne toward the surface at 60 feet per round until they can stand on it.

We decide that Faugh is our buoy. Problem solved!

So we secure our loos items (ioun stones, in particular) and open the door.

Well Brus, who opened the door, takes damage, people are washed back, there’s pummelling and cold damage and John drops a Resist Energy (cold), Mass. Much damage. The other doors in the room strain to control the pressure, and John’s invisible Fairy Dragon puts up a Wall of Force It won’t last long.

We get through the door and underwater, and far enough away from the portal to not be sucked back in once the WoF goes down. It’s cold, but we are warmed by the thought of what is going to happen to those fucking bees.

Faugh pops us to the top, cork-like. There is a fortuitous boat just nearby, the crew a little startled by people bobbing to the surface of the sea out of absolutely nowhere, and possibly also by the sight of a deep gnome calmly walking on the water like it ain’t no thing.

Aboard the boat, we let our wizard out of the bag. He’s a little bluish, but not too bad. He is also wet, having made the mistake of opening the bag for a moment.

And here we are. Alive, but still racing the clock.

I do math

Well, maybe not really complicated math. Or maths, depending on where you come from.

It’s like this. I recently discovered 3d printing. Yay! My thinginverse page is here. Saw a thing by a dude doing a loxodromic lampshade and I am like “man, I am all over that shit like stink on vomit!”

So I decided to do a better one. Mainly because what I really want to do is a quasifuchsian curlicue lampshade.

So. I need to write a 3-d bilinear transform that moves the xy plane onto the unit sphere.

Any bilinear transform can be done using two sphere inversions, which are easy-peasy.

So, what pair of sphere inversions do the thingy that I want?

Well, we need more invariants. I want the unit circle to be constant. I want all points on the xy plane to be moved to the unit sphere. I want the z<0 half-plane to be moved to the exterior of the sphere.

Now, for some math(s).

I think it’s pretty obvious that the two inversion spheres will be centered on the xy=0 axis. This means that I only have four numbers to figure out. In fact, I can just work with one slice of the space and just do it as a 2-d operation, which makes visualising it muuuch easier.

Three points is enough to fully specify a mobius transform, and I have three points here:
[1,0,0]->[1,0,0]; [0,0,0]->[0,0,1]; ∞->[0,0,-1].

But I don’t want to do this as a mobius transform … although it would be a hell of a lot easier if I did. No! I will stick to the original plan. A pair of sphere inversions. Because you can do arbitrary stuff with it, that’s why.

So, what two inversions accomplish my little plan?

lets call our spheres (circles) Γ1=[0,0,c1]*r1 and Γ2=[0,0,c2]*r2. I invert the point *first* in Γ2 and *then* in Γ1. IOW, p’ = Γ1(Γ2(p)) .

To do a cirlce inversion, you move the center of the circle to the origin, scale the radius to 1, invert, and then move things back again. Inversion is a matter of dividing the coordinates by the square of the distance, which is easy to get

the halfway point is [ x/r, (z-c)/r].
the distance squared of that halfway point is (x/r)^2 + ((z-c)/r)^2 , which is (x^2+(z-c)^2)/r^2

so invertiing we get
[ x/r / ((x^2+(z-c)^2)/r^2), ((z-c)/r)/((x^2+(z-c)^2)/r^2)]

simplify
[ x / ((x^2+(z-c)^2)/r), ((z-c))/((x^2+(z-c)^2)/r)]

[ rx / (x^2+(z-c)^2), (r(z-c))/(x^2+(z-c)^2)]
and then move everything back

[ r^2 x / (x^2+(z-c)^2), (r^2 (z-c))/(x^2+(z-c)^2) + c]

so the effect of Γ2 is

[ r2^2 x / (x^2+(z-c2)^2), (r2^2 (z-c2))/(x^2+(z-c2)^2) + c2]

and the effect of Γ1 Γ2 is
…

ooh-kay. Let’s just do that common term first

K = ({r2^2 x / (x^2+(z-c2)^2)}^2+({(r2^2 (z-c2))/(x^2+(z-c2)^2) + c2}-c1)^2)

giving us

[ r1^2 x / K, (r1^2 (z-c1))/K + c1]

Now, the only way (sorta) this can map the point at infinity to [0,-1] is if K is infinite for [∞,0] and c1 = -1.

So that’s one of our constants sorted. Yay! Let’s substitute it in:

K = ({r2^2 x / (x^2+(z-c2)^2)}^2+({(r2^2 (z-c2))/(x^2+(z-c2)^2) + c2}+1)^2)

Γ1 Γ2 [x, z] = [ r1^2 x / K, (r1^2 (z+1))/K – 1]

Now, what’s going to make K infinite for [∞,0] ? Well, (x^2+(z-c2)^2) needs to be zero. That ain’t going to happen. But that x^2 term in the bottom means that … have we got an infinite radius for one of the circles?? That’s … possible. In fact, inverting the

got it.

If you invert the xy plane through a with radius 2 that is tangent to the origin, this moves the xy plane onto a unit circle centered at .5. Problem is, it’s inverted because it has only been throug one reflection. So invert it through [0,0,-2],r=2, and then reflect the z coordinate at -.25 (or just reflect z and subtract 1). The problem with *that* is that you can’t express it as a pair of sphere inversions if you paramterise it the way I have been doing.

But you know what? Screw it. I only want one specific job done, so I’ll do that.

Thanks guys!