Mythic Tower

Hi everyone,
For those reading the Lough Caillte saga you would have noticed that we were debating the sizes and dimensions of the spell "Summon the Mythic Tower". The spell has base 3 (stone), +1 Touch, +4mags size, +3 complexity)
Base for stone is 1 cubic pace.
4 magnitudes is 10,000 cubic paces.
1 pace is 2.5 ft

Therefore 10,000 cubic paces becomes 156,250 cubic feet.

The spell creates a stone tower that it 100ft tall and 30 across. It doesn't mention if it is circular or square, but either is fine.

Taking as a base walls/ceiling as 5ft thick, and each floor will have 8ft of headroom. 8+5 =13. 80/13 ~ 6 floors

Circular tower (solid stone):
Total volume is (pi * r^2 * h) : pi * 15 * 15 *100 = 70685 cu ft.
Foundations are 20ft deep - therefore 1/5th of total volume (14137 cu ft).
Each Floor is 13 * 15 * 15 * pi = 9189 cu ft

Square tower (solid stone):
Total volume is (l^2 * h) : 30 * 30 *100 = 90000 cu ft.
Foundations are 20ft deep - therefore 1/5th of total volume (18000 cu ft).
Each Floor is 13 * 30 * 30 = 11700 cu ft

Now these are the figures for SOLID STONE, which is no-use to anyone. If we use hollow spaces in each tower, the overall stone used goes down.

Taking as a base walls/ceiling as 5ft thick, and each floor will have 8ft of headroom. 8+5 =13. 80/13 ~ 6 floors

Circular tower (living spaces):
Total volume is (pi * r^2 * h) : pi * 15 * 15 *100 = 70685 cu ft.
Foundations are 20ft deep - therefore 1/5th of total volume (14137 cu ft).
Each Floor is (vol of floor - vol of space)
(13 * 15 * 15 * pi) - (8 * 10 * 10 * pi) = 9189 - 2513 = 6676 cu ft
Total Stone used is (6 * 6676) + 14137 = 54193 cu ft

Square tower (living spaces):
Total volume is (l^2 * h) : 30 * 30 *100 = 90000 cu ft.
Foundations are 20ft deep - therefore 1/5th of total volume (18000 cu ft).
Each Floor is (vol of floor - vol of space)
(13 * 30 * 30) - (8 * 20 * 20) = 11700 - 3200 = 8500 cu ft
Total Stone used is (6 * 8500) + 18000 = 69000 cu ft

As you can see, neither 69K cu ft or 54K cu ft come close to the 156 cu ft of stone that the spell can create. So it seems that the spell was designed NOT to create the maximum amount of stone and use it. Therefore it should be possible to create a larger structure using the same level effect.

Putting 1/5th into a foundation to keep the tower solid, we could have a square tower of 14 floors, or a circular one of 18 floors.

Or the same basic 6 floor tower could be made larger
Foundations are 1/5th of total volume (31250 cu ft).
156,250 - 31,250 = 125,000K cu ft.
125000/6 = 39788 cu ft per floor.
Each Floor is (vol of floor - vol of space)

Large Circular tower (living spaces):
(13 * r * r * pi) - (8 * (r-5) * (r-5) * pi) = 39788

Large Square tower (living spaces):
(13 * w * l) - (8 * (w-10) * (w-10) )= 39788 cu ft

My maths knowledge gives out here, been too many years since I did algebra. :confused:
But I'm guessing that those 6 floors would be a lot larger :smiley:

What does everyone else think?

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The original spell is probably designed with the basis that the tower be massive since it allows for it. After all, the description says you design the interior layout, and there is no reason why there really needs to be any interior if you'd like for it not to be... (I.e. a magus may deside he needs a tower chamber, but to avoid being bothered by mundanes, he designs the tower to only have a single chamber in the top floor, and the rest be only massive stone...)

My magus is currently working on a greater mystic tower - a magnitude higher, that comes complete with its own hill (in the same massive block of stone).

I think you are using too much maths there :slight_smile:

The tower is supposed to have 6 flors being 10 metres wide and 30 metres high. I always assumed it would be round, but that is me. IN fact the sanctum floor map that appears in covenants seems to have the dimensions that a mystic tower lab would have.

Number crunching the surface area of the tower feels extremely un-mythic to me. YMMV. :confused:



Xavi- the tower is supposed to have whatever interior design the caster wants. (See below re purpose of math.)

And I tend to agree with Ulf- the outside dimensions are what matter, as anything else would become far too fuzzy, with discussions of the thickness of interior walls/floors/etc, and that WOULD be too much math, by far!

What this discussion sprang from, was the desire to CrTe some lab space for an influx of (7!) new magi into an Autumn Covenant. The "30 foot" tower does not allow for the minimum 500 sq feet of lab space required on any one floor, not without very thin walls (don't forget a stairway, folks!). But let's avoid that discussion- we wanted to roughly reverse-engineer the spell, so we could know what another, similar spell could create, or what one a magnitude larger/smaller would get us.

And that's where things started to fall apart.

In short, the volume of the 30'x100' tower (with foundation) doesn't match the Hermetic volumes, not that we can make out.

Above, Brutus states with confidence that 1 pace = ~2.5 feet - I'm not sure about that. I was originally thinking that a "pace" was equal to about a yard or meter, but not precisely defined so that both Metric meter and Anglo yard would work equally well. At one point in Aquam, the book states that 5 paces = 15 feet (p 121, col i, last par in general Aquam section.)

But now that I think about it, isn't that just far too big? I'm tall (6'4"/193), and I don't take even a 2.5'/75cm stride unless I try (and then it's obvious that I'm "pacing something off". That, or doing a Monte Python "funny walk".)

(Note- The tower is defined as "30 ft x 100 ft" (with foundation)- but it's not specified if that's round or square. Both calculations are shown below, and are not significantly different in final value.)

Reverse-engineering the spell as written, the math works like this:

The 30'x30'x100' tower (including foundation) is 90,000 cubic feet.
That tower is derived from a Hermetic volume of 10,000 cubic "paces" of stone.
So, if 90,000 cubic feet = 10,000 cu paces,
then 1 cubic pace = 9 cubic feet,
or 1 pace = ~2.08 feet (25 inches, or .63m.)
That's starting to make more sense for a typical human's "pace".

The round 30' x 100' tower yields a "pace" of 1.92' (23"), or .58m.

A "pace" is not tightly defined, so the above would imply a loosely defined value lying anywhere around 2' or 2/3 (.667) meter seems like a good, universally friendly number.

Note that the 30x30x100 tower is a factor of exactly x3 too small for 10,000 cubic paces if 1 pace = 1 yard (10,000 cu yards should be 270,000 cu feet, but 30x30x100 = 90,000). Is this a math glitch, where some dead-line battered writer got square/cubic yards confused and multiplied/divided by x9 and not x27?? (I can see it all too easily!)

Just to toss another wrench into the works, note that a pure Terram tower doesn't have any Herbem Requisite for any wooden doors/shutters/etc. That would require another Magnitude. More errata? :confused:

So, what gives?

Is this spell significantly undersized for a pace = 1 yard/1meter?
Is a pace = 2 feet/.667 meters?
Is a pace really loosely defined, anywhere from 2-3 feet? (.6- 1.0 m)?
Something else?

Make the tower create enough space for a lab in any given floor. It is what it was defined for according to official cannon, so I see no problems with that. Can't remember if it is stated in GotF or the rulebook, but it is there, somewhere: it reads something like "each floor of the (mystic) tower is the perfect size for an hermetic laboratory". IIRC it is GotF, yeah, in the description of the Great Library.

Stretcvhing the hard numbers of the core book so thyat the size of each floor is the 500 needed square feet would be perfectly fine for me. :slight_smile: It does not detract from a mystic tower at all. Hell, it is mystic for a reason! :smiley:



(That does make sense, but that's off topic- that's not what we're talking about here. Thanks for that clarification and reference, tho'! That had worrying me. I guess if it's a mystic tower, 2-3' walls aren't a problem.) :wink:

For those losing track, the question is...

Why is The Mystic Tower closer in volume to 1/3 of the 10,000 cubic paces of stone that it should be?

1 cubic pace base.
+4 Mags = x10x10x10x10 = 1 x 10,000 = 10,000 cubic paces
30'x30'x100' = 90,000 cubic feet.

If a pace ~ 1 yard, 90,000/27 = 3,333 cubic paces, << 10,000. (by a factor of exactly x3!)
Otoh, if 90,000 cubic feet = 10,000 cubic paces, 1 pace = 2 ft/.6 m.

THAT is the topic. :wink:

Because once we clear that up, we can confidently build a similar spell of +/- 1 magnitude.

Because the original inventor didn't need a bigger tower.

The reason seems rather easy to me: The mystic tower has been around since 3rd (the first edition of ArM that I have) so it was invented before such clear guidelines about the exact ammount of stone created were in place. It is a building of 30x10 metres, quite a massive thing, and level 35 sounded "right" for the designers of the game.

Right now it is quite low magnitude given the power levels implied for magi (I would up 2 magnitudes all the spells above level 20 just for the sakes of it, since now I find mega-spells of 7th magnutude too easy to reach) but hey. Basically, nobody bothered to make any of your calculations when the spell was designed. it sounded OK to have the tower be as it is. :slight_smile:

Now, if you want to construct a tower that is 3 times as big with the same spell, you should be able to do it. or drop the level of the tower by 1 magnitude. No biggie here.



Each adjustment in magnitude results in an adjustment of a factor 10 of size...

My bad. I guess my saga's handwaving of this stuff is playing bawdy jokes again :stuck_out_tongue:



Yes, Ulf, and above both Brutus and I discussed (and showed mathematically) how the spell is off by a magnitude of x3 too small, according to the Hermetic guidelines. So Xavi made that comment because he had read the above posts, and was responding to the topic.

Xavi- of all the possible explanations, yours actually makes the most sense. A simple application of "The Central Rule"- that a tower 3x that size seemed just too big. And quite possibly a grandfather clause somewhere. Meh.

But the problem remains- if this Level 35 spell is "not quite right", btr, then what is right for a Level 30 or Level 40 spell? :confused:

Without hearing from the authors (to acknowledge that this spell is somehow arbitrarily small and not strictly by the guidelines), I'd say that the lower magnitude spell should be closer to the rules, and a higher one suffer the same reduction, but... any other thoughts?

Maybe you do generate that ammount of stone but 2/3 go to waste? Might be that the tower appears in a large puff of stone, or it is "sculpted" out of the large stone block by invisible hands in the blink of an eye (does not appear already formed)..... so 2/3 of the stone ends up around you in the form of stone dust. I like the image.

You can also adjust the size slightly to accomodate 1-2 mages more due to this "glitch" in the tower, I guess. Or you can assign the ornamentation (+1 to +3 aesthetics to working in the tower) a "half a magnitude" worth of effect.

Papa Bonisagus said this is how a tower is made" also makes sense from the point of view of traditionalist magi.

In fact, I am starting to see the heated tractatus/paper debate surrounding this spell, with one school defining it as 7th magnitude because it follows reasons A & B and a group defending that the spell is an awful waste of vis. In fact there are rules for spell optimization somewhere (TMRE?) that could fit in this schiolarly debate quite well. Being a ritual, it explains why people do not experiment more with the tower to set one of the theories as the "definitive" answer. In fact you can have a magus come to see how you cast it (or wanting to cast it himself, offering to pay some of the vis) and record the results just because it fits with this debate. There you go. Story hook in your doorstep. :wink:.



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Personally I think you guys are overthinking things... You're starting with the basis that you could make a bigger tower with the same magnitude spell, but what if you wanted a tower of those exact dimentions?

The orginal designer didn't need 3 times the stone. He simply needed a useful tower, and considered those dimensions to be right. In many ways this is something that feels more "right" for most magi - figure out what you want first, and then using lab-time to understand how difficult it is to produce... Later magi may feel they could do better, but most figure it a waste of time... (easier to learn the spell from a labtext - or even casting it from a casting tablet).

That is... possible.

But could you tell us where else in the rules they give such an example?
Where an example spell is, unannounced, significantly smaller than the guidelines, not because of game balance, but simply because "the inventor didn't feel like it"? :confused:

The spell wizard's mount creates a normal horse(size +2 or +3) - based on the maximum of the guidelines, it could have created a giant horse (size +4).

Spells that can be adjusted considerably during casting tend to be of higher magnitude (complexity) and so this one has preset dimensions.

Except the spell -does- have significant amounts of complexity added :slight_smile:

Offcourse it does - othervise you'd get a single massive block of stone, rather than a tower with an interior.
To have adjustable size, you'd need at least a magnitude more of complexity.

You might still get "charged" as much for a hollow block of stone as for a solid one.

Yes... and what would you do with it? A 18-floor tower? This is Ars Magica, not Final Fantasy. You might want to go after something like Conjure the Divine Cathedral instead. Or use a Group target and create a cluster of buildings. Of course, keep in mind that covenant buildings often cause both fear and envy among mundanes, so something on that scale... The keep of Pembroke Castle is only 19'x75'. The Mystic Tower is twice as big and you're there talking about something 3 times as big again?

Keeping aside the fact that the spell was in fact carried over from the previous editions, I think Bonisagus just went with a size that was useful to him. If you look at Durenmar, they have 3 towers, each originally erected by and for a single magus (plus apprentices, specialists, grogs, library, storage...) Furthermore, a larger tower made of a single block of stone, may not be structurally sound (stone splits and shatters).

I'm confused a little with this topic.
If I want a tower 42-46 (the more is the best) feet wide and at least 50 feet tall with appropriate basement and 3 feet outer walls (architect estimated) what would be the level of the ritual?
Maybe the outer walls could be 2feet wide because it is from a single block.

Assuming 20 foot foundations, and a rough diameter of 50 feet or so, you're talking 137,444 cubic feet.

Which would be Base Stone, +4 size, which covers you up to 270,000 cubic feet.

You could happily make it 100 feet tall if you really wanted, and still be covered by the +4 size. 50 foot wide, 100 foot high tower and 35 feet of foundations would be 265k cubic feet.

At any rate, you can make both of those with a level 35 ritual.. conjuring the mystic tower is indeed just making a semi plausible medieval tower.. whereas if you really -wanted-.. you could indeed make your own version of the ritual that makes a much bigger tower.