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Ravingdork
2010-03-29, 11:14 PM
There is a huge debate going on, on other forums, in which people are trying to figure out what cubic feet even means.

For example, a 10th-level caster can cast shrink item on one touched object of up to 20 cu. ft.

One group is arguing that, that is twenty 1-ft. cubes in any configuration (so if you lined them up side by side, you would end up with a 20x1x1 shape).

The other group is arguing that it means 20x20x20.

Which is right?

It looks as though proper math supports the former, but game sense supports the latter. After all, what is the point of shrinking an object that is already REALLY small? (A 20th-level caster gets 40 cubic feet with shrink item, which according to the first group would mean he could only shrink an item that is 3.42 x 3.42 x 3.42 feet)

This effects other spells as well, such as the Stone Shape spell. A 10th-level caster with the former interpretation can barely make a passage through a wall. A wizard operating under the latter interpretation could probably shape himself a small house.

A math major friend of a friend (not joking) tells me that the former interpretation is for #^3, or feet cubed, and that the latter interpretation describes cubic feet (which is what the rules refer to). However, I have found web sites that say cubic feet is as per the former interpretation.

Hope I haven't confused you all.

WeeFreeMen
2010-03-29, 11:18 PM
The first one is right mathematically.
Our group has always followed that as its ruling.

Ravingdork
2010-03-29, 11:19 PM
The first one is right mathematically.
Our group has always followed that as its ruling.

You mean the 20x1x1 group?

Okay, but do you believe that to be the INTENT of the rules?

UglyPanda
2010-03-29, 11:20 PM
Are you sure you're not just getting 20 cubic feet mixed with 20-foot-cube in your head?

The right answer is the first one, of course. It's an area equivalent to 20 1-ft cubes.

Zeful
2010-03-29, 11:25 PM
For Reference: Shrink Item (http://www.d20srd.org/srd/spells/shrinkitem.htm)

Note:
Target: One touched object of up to 2 cu. ft./level
So in the debate a tenth level wizard is casting this spell to get the required 20 cu. ft. Correct?

The measurement of Cubic feet is one of volume in can be annotated as ft3 or as cu. ft. both refer to the space inside a 3 dimensional figure. Since the distance is not measured in feet, for example Fireball (http://www.d20srd.org/srd/spells/fireball.htm), it already is a measurement of volume.

In short: The first interpretation (i.e. 20 1-ft cubes in any configuration) is the correct one.

Ravingdork
2010-03-29, 11:26 PM
Are you sure you're not just getting 20 cubic feet mixed with 20-foot-cube in your head?

The right answer is the first one, of course. It's an area equivalent to 20 1-ft cubes.

This is hardly a simple question.

For Reference: Shrink Item (http://www.d20srd.org/srd/spells/shrinkitem.htm)

Note:
So in the debate a tenth level wizard is casting this spell to get the required 20 cu. ft. Correct?

The measurement of Cubic feet is one of volume in can be annotated as ft3 or as cu. ft. both refer to the space inside a 3 dimensional figure. Since the distance is not measured in feet, for example Fireball (http://www.d20srd.org/srd/spells/fireball.htm), it already is a measurement of volume.

In short: The first interpretation (i.e. 20 1-ft cubes in any configuration) is the correct one.

But wouldn't that mean that a 20th-level caster could only shrink a cubed object with a little less than 3.5 feet on a side? That's ridiculous!

A 20th-level wizard should be shrinking large boats, not small chairs.

AslanCross
2010-03-29, 11:26 PM
(S) Shapeable:
If an Area or Effect entry ends with (S), you can shape the spell. A shaped effect or area can have no dimension smaller than 10 feet. Many effects or areas are given as cubes to make it easy to model irregular shapes.

Not exactly a definitive RAW answer, but the intent of stone shape seems similar. Besides, each caster level gives +1 Cubic foot area, so it's rather easy to get irregular numbers.

Occasional Sage
2010-03-29, 11:28 PM
As everybody else has said.

The other one would be "twenty feet, cubed" which sounds similar but is very totally different.

Ravingdork
2010-03-29, 11:29 PM
As everybody else has said.

The other one would be "twenty feet, cubed" which sounds similar but is very totally different.

So my friend's math major friend has the two terms reversed then?

Kylarra
2010-03-29, 11:30 PM
So my friend's math major friend has the two terms reversed then?Yes he or she does. Either that or they're failing a math course.

TheOOB
2010-03-29, 11:30 PM
There really is only one answer. A 20' by 20' by 20' cube is 8000 cubic feet. The spells pretty clearly mark in said situation to be 20 cubic feet, which could be a 20'-1'-1', a 5'-2'-2', a 4'-5'-1', or whatever other dimensions you desire. cubic feet is a measure of volume, and is fairly consistent.

AslanCross
2010-03-29, 11:31 PM
On the other hand, if you look at say, fire storm, its area is listed as "two 10 ft. cubes per level (S)," so instead of a 13th level caster getting 260 1 ft. cubes to shape as he or she wills, she instead gets 26 cubes that are 10 feet on each side to shape. There's a clear difference in wording.

Zeful
2010-03-29, 11:33 PM
But wouldn't that mean that a 20th-level caster could only shrink a cubed object with a little less than 3.5 feet on a side? That's ridiculous!

A 20th-level wizard should be shrinking large boats, not small chairs.

I don't know where your math is coming from as I just got 13-1/3 feet to a side for the final figure (2*20/3 PEDMAS rules state that 2*20 (40), then 40/3 (13.3 repeating or 13-1/3).

Also as wizards, by 5th level, completely dominate every other class in the game, I fail to see the lack of boat shrinkage to be a problem.

UglyPanda
2010-03-29, 11:34 PM
It seems your friend [can't/couldn't] tell the difference between (20 ft) ^ 3 and 20 ft ^ 3.

It really is a simple question, your friends are probably only really arguing because of momentum. Once one person sets an argument in motion, it stays in motion; mostly because nobody wants to look stupid.

And here's the thing: Shrink Item is only a third level spell! Do you really expect the third level spells to still be impressive at level 20?

Yes he or she does. Either that or they're failing a math course.More likely to be a physics course. You stop doing actual math when you're a math major and start screwing up your head with absurdly specific calculus.

Private-Prinny
2010-03-29, 11:40 PM
I don't know where your math is coming from as I just got 13-1/3 feet to a side for the final figure (2*20/3 PEDMAS rules state that 2*20 (40), then 40/3 (13.3 repeating or 13-1/3).

Also as wizards, by 5th level, completely dominate every other class in the game, I fail to see the lack of boat shrinkage to be a problem.

His math is correct. You take the cube root, not divide by 3. I always saw the use of Shrink Item as keeping all those pesky items stored. It's much easier to carry loot when you can take 4,000 times more.

Ravingdork
2010-03-29, 11:40 PM
I don't know where your math is coming from as I just got 13-1/3 feet to a side for the final figure (2*20/3 PEDMAS rules state that 2*20 (40), then 40/3 (13.3 repeating or 13-1/3).

Also as wizards, by 5th level, completely dominate every other class in the game, I fail to see the lack of boat shrinkage to be a problem.

A 20th-level wizard casting shrink item can shrink a touched object of up to 40 cubic feet, yes?

So by everyone's definition here, that means...

Oh.

I see what you mean.

The math I WAS using was:

40 ^ (1/3)

Or the cubed root of 40.

Ravingdork
2010-03-29, 11:41 PM
His math is correct. You take the cube root, not divide by 3. I always saw the use of Shrink Item as keeping all those pesky items stored. It's much easier to carry loot when you can take 4,000 times more.

Argh! I've been tricked!

Further evidence that it is NOT SIMPLE AT ALL!

A wizard likely doesn't have 4,000 castings of the spell prepared, however.

Human Paragon 3
2010-03-29, 11:42 PM
My fridge is 20 cubic feet.

Kylarra
2010-03-29, 11:42 PM
More likely to be a physics course. You stop doing actual math when you're a math major and start screwing up your head with absurdly specific calculus....

fair enough.

Ravingdork
2010-03-29, 11:43 PM
My fridge is 20 cubic feet.

So how many fridges are in 40 cubic feet?

Private-Prinny
2010-03-29, 11:45 PM
Argh! I've been tricked!

Further evidence that it is NOT SIMPLE AT ALL!

A wizard likely doesn't have 4,000 castings of the spell prepared, however.

I think you misunderstood. Your math, saying that about 3.5 ft/side was 40 ft^3, was correct.

Lycanthromancer
2010-03-29, 11:46 PM
So how many fridges are in 40 cubic feet?Generally refrigerators are measured by internal space, so...less than 2, but more than 1.

Ravingdork
2010-03-29, 11:53 PM
I think you misunderstood. Your math, saying that about 3.5 ft/side was 20 ft^3, was correct.

a cube 3.5 ft to a side = 42.875 cubic feet. A 20th-level wizard can only shrink an object that is 40 cubic feet.

That doesn't strike anyone else as seriously FUBAR?

Such an object is Small-sized. If that was the maximum volume of the spell pre-epic, why would it even bother saying the object is four sizes smaller? You can't even go four sizes smaller than small!

HunterOfJello
2010-03-30, 12:00 AM
This would be a good question to ask on the offical forums.

Also, cubic foot =/= foot cubed.

Evard
2010-03-30, 12:01 AM
And this is one reason 4e is better -_-;;;

To much time spent on something like this

Private-Prinny
2010-03-30, 12:02 AM
a cube 3.5 ft to a side = 42.875 cubic feet. A 20th-level wizard can only shrink an object that is 40 cubic feet.

That doesn't strike anyone else as seriously FUBAR?

Such an object is Small-sized. If that was the maximum volume of the spell pre-epic, why would it even bother saying the object is four sizes smaller? You can't even go four sizes smaller than small!

You have the power to shoot lightning from your fingertips and rewrite reality, and you're complaining about not being able to fit a house in your Bag of Holding? Because that strikes me as FUBAR.

Beorn080
2010-03-30, 12:15 AM
By one reading, the sane way, yes, it's a bit underpowered at 20. However, the other way is to shape it so that you are only shrinking the mass that you want shrunk, and not the air inside of it. Admittedly, you won't be shrinking large sailboats, but you just might be able to shrink a barge.

Other possible methods would be multiple castings on 40 cubic feet of wood each, followed by permanency and several months of craft checks. Set all the castings to one key word, and you can craft a fairly large boat for yourself that's the size of the parties fighter and much more useful.

HunterOfJello
2010-03-30, 12:19 AM
Because that strikes me as FUBAR.

You mean that I can't keep shrunken mountains in my pocket? This game sucks! Spells are underpowered!

Haven
2010-03-30, 12:20 AM
A 20th-level wizard should be shrinking large boats, not small chairs.

I think that just means there should be a higher level spell for it.

Ravingdork
2010-03-30, 01:09 AM
On another side note, using shrink item you can fit 4000 pints, or 500 gallons of acid (or holy water) into a single flask, which will expand to its full volume on impact.

At what caster level is that though? If it's 20th, then it does little good when you first pick up the spell.

I read all the time about people shrinking and dropping boulders. I'm beginning to realize that these boulders must have been really, REALLY small even before being shrunk.

Other spells that use the cu. ft. terminology:
- fabricate (@ CL 20th can build a 5.85 x 5.85 x 5.85 foot object)
- major creation (@ CL 20th can create a 2.7 x 2.7 x 2.7 foot object)
- make whole (@ CL 20th can repair a 5.85 x 5.85 x 5.85 foot object)
- minor creation (@ CL 20th can create a 2.7 x 2.7 x 2.7 foot object)
- shrink item (@ CL 20th can shrink a 3.42 x 3.42 x 3.42 foot object)
- stone shape (@ CL 20th can shape a 3.10 x 3.10 x 3.10 foot object)

Some of these spells are next to useless as written. Surely the game designers meant feet cubed, rather than cubic feet (in fact one told me so a long time ago, sadly I can no longer find the reference as the v3.5 boards are no more).

Items use the same terminology in places as well:
- bags of holding (the biggest can only hold a 6 x 6 x 6 foot item)
- hand haversack (largest pocket can only hold a 2 x 2 x 2 foot item)

Most of the above parenthetical sizes are rounded up. Also, I am well aware that you can make irregular shapes, I just that cubes make for easy representations.

Ravingdork
2010-03-30, 01:24 AM
You could do it at CL 5. You'd shrink 10 cubic feet, or 80 gallons, or 320 pints per casting, and it'd only keep for 5 days, but its doable. I suppose you could just half/half or some such, and it'd still make for a pretty nice splash.

You could your 4000 pints in 2 shots at CL 15.625...really it's not so much optimal, as just a funny trick to try out some time, one that doesn't necessarily cost anything to do, since there's no GP cost, and you can prepare it days, if not weeks, ahead of time.

I used to think that my 9th-level wizard could steal a volume of 18 x 18 x 18 feet of water with which to drown someone with later (he even tried with lava once or twice). That would make for 43,623.36 gallons of water.

Ravingdork
2010-03-30, 02:05 AM
I've always been a bit fuzzy on 'control water,' but I believe it actually creates new liquid (besides, the Decanter is based off it). So when your wizard gets it at level 11, he can create about (110' x 110' x 22' x 8gal/ ' ) 2130 standard 5' cubes of water, I believe he could create 2 million gallons in a single casting. I really wish I could find more info on how that spell is meant to work.

If nothing else, a widened 'flash flood' (Sandstorm 114, level 8) creates a 240' cone of water 20' high (originally 120' by 10'), which works out to 6,272 standard 5' cubes of water, or about 6.3 million gallons. You might be able to drown someone with that those :P

We play the Pathfinder RPG for the most part, so those supplements do me little good (though I do own those books).

hamishspence
2010-03-30, 02:44 AM
a 3 ft by 3 ft by 3 ft object might be Small- but a person's volume is a lot less than this.

So, a 20 cubic ft object might be medium, or even large, depending on its shape- what's the volume of a 9 ft tall humanoid statue?

Yora
2010-03-30, 05:24 AM
Other spells that use the cu. ft. terminology:
- fabricate (@ CL 20th can build a 5.85 x 5.85 x 5.85 foot object)
- major creation (@ CL 20th can create a 2.7 x 2.7 x 2.7 foot object)
- make whole (@ CL 20th can repair a 5.85 x 5.85 x 5.85 foot object)
- minor creation (@ CL 20th can create a 2.7 x 2.7 x 2.7 foot object)
- shrink item (@ CL 20th can shrink a 3.42 x 3.42 x 3.42 foot object)
- stone shape (@ CL 20th can shape a 3.10 x 3.10 x 3.10 foot object)

Some of these spells are next to useless as written. Surely the game designers meant feet cubed, rather than cubic feet (in fact one told me so a long time ago, sadly I can no longer find the reference as the v3.5 boards are no more).
I'd say these numbers are for the ammount of raw material without the air within cavities. A boat is essentially an empty container, so with 1 cubic meter of wood planks, I'd say you could create a large or even huge boat.
Or lets say a masonry wall, which is half a foot thick, would be 40 square feet in size. An average human person is probably less then 3 cubic feet of volume, so with 20 cubic feet, you could make quite an impressive statue. 12 feet tall by a quick estimation.

Drend
2010-03-30, 05:49 AM
The big problem with foregoing the air is that your miniature boat will create a phenomenon of implosive recompression, which could very easily tear the boat to shreds. I've played with models in vacuum chambers. Everyone of them implodes when you let air in suddenly, as would happen when you magically enlarge the boat. The sudden increase in volume of the container creates a vacuum which sucks air in so forcefully, it dies. (Granted, most of the models were made of balsa, not the strongest or least porous wood)

On the other hand, how do you make the magical ships in a bottle without shrink item?

2010-03-30, 06:01 AM
The big problem with foregoing the air is that your miniature boat will create a phenomenon of implosive recompression, which could very easily tear the boat to shreds. I've played with models in vacuum chambers. Everyone of them implodes when you let air in suddenly, as would happen when you magically enlarge the boat. The sudden increase in volume of the container creates a vacuum which sucks air in so forcefully, it dies. (Granted, most of the models were made of balsa, not the strongest or least porous wood)

It's magic. Technically shrink item takes place in instantaneous time, so either you're pushing the air out of the way faster than the speed of light, or the net effect is that you marginally increase the air pressure in the general vicinity, and the boat's already full of air.

Lycanthromancer
2010-03-30, 09:32 AM
Shrink item affects the object you touch, and the air around or within the object isn't the target of the spell. Thus, you could definitely shrink a Large (or even Huge) sized boat, as you can create one from the volume of material you can shrink. (Air is more or less a non-entity anyway, as the effects of air pressure are universally ignored in D&D aside from wind-effects.)

Another thing to keep in mind is a trick using shrink item and fabricate. Break what you want up into pieces (or get the materials you want in smaller chunks), shrink all of the pieces down to Itty Bitty Size (yes, this is a technical term), then fabricate them into a single item. You can make whole castles this way, and very very very quickly, at that.

ericgrau
2010-03-30, 10:15 AM
A 20 foot cube is 20x20x20. 20 cubic feet is 20x1x1. It's a simple matter of definitions.

jiriku
2010-03-30, 10:39 AM
I read all the time about people shrinking and dropping boulders. I'm beginning to realize that these boulders must have been really, REALLY small even before being shrunk.

Other spells that use the cu. ft. terminology:
fabricate - major creation - make whole - minor creation - shrink item - stone shape

Some of these spells are next to useless as written. Surely the game designers meant feet cubed, rather than cubic feet (in fact one told me so a long time ago, sadly I can no longer find the reference as the v3.5 boards are no more).

Items use the same terminology in places as well:
- bags of holding (the biggest can only hold a 6 x 6 x 6 foot item)
- hand haversack (largest pocket can only hold a 2 x 2 x 2 foot item)

In short, these spells are just not as good as you thought they were. However, they're still quite useful. One simply has to use finesse instead of brute-forcing it. Fabricate can't build a four-masted schooner in one casting...but it could be used to build the tools you need to steal a ship, or repair the one you've got. You could also make a raft or a coracle with it, if you're willing to accept more modest transportation. Further, it can also be used to make masterwork weapons on short notice, even out of exotic materials, or most any other piece of personal gear. Make whole won't repair the gatehouse -- but it will repair the gate. Shrink item won't shrink a ship, but it can be used to shrink a weapon or a stolen treasure you need to get past the guards, or a dead body, or an object that's too large to fit into your bag of holding (since you're now realizing that those bags are smaller than you'd expected).

Stone shape is a particularly useful spell in a dungeon setting. It can't be used to rip open a wall or delve a tunnel, but it can be used to unseat the hinges on a locked door you can't pass, or seal a door or archway with a thin layer of stone.

But to echo your thoughts...yes, a 20th level wizard ought to be able to tear apart stone walls and pull a ship out of his back pocket. However, he uses disintigrate or passwall (or greater passwall) to bypass the wall, and uses wish to acquire his boat, or else he crafts himself a folding boat. (More importantly, a 20th level wizard has little use for doorways and boats in the first place, as he can place himself most anywhere in the multiverse as a standard action with greater plane shift and greater teleport). There are ways to do what you're wanting to do...just not using the spells you're thinking of currently.

ericgrau
2010-03-30, 10:49 AM
Shrink item is amazingly useful as written (with the given cubic feet limits). Now you can stock up on even the big mundane items. If you're using it to deal damage you're doing it the boring way.

Yukitsu
2010-03-30, 11:07 AM
a cube 3.5 ft to a side = 42.875 cubic feet. A 20th-level wizard can only shrink an object that is 40 cubic feet.

That doesn't strike anyone else as seriously FUBAR?

Such an object is Small-sized. If that was the maximum volume of the spell pre-epic, why would it even bother saying the object is four sizes smaller? You can't even go four sizes smaller than small!

Because if you're on the elemental plane of earth, and come across a 3*3*4 diamond, the net value is absurd, but it weighs more than you can carry.

The most typical use from my perspective, is to shrink my spell book and put it in my false boot heel, making it hard to find. Obviously a full sized book won't fit in there.

DragoonWraith
2010-03-30, 11:25 AM
cubic foot =/= foot cubed.
Uhhh... no? A "foot cubed" is "ft3" (why does everyone keep using the caret when we have a perfectly good sup tag?), which is the same as a cubic foot ("cu. ft.", maybe, but "ft3" would be more appropriate).

On the other hand, "foot cube" (not "cubed") would not be a unit, but rather a description of a shape - in this case, the unit is foot, and it's preceded by a number which gives the number of feet along a side of said cube. So a "20 ft. cube" is a cube 20 ft. on one side. Which is 8000 ft3.

Ravingdork
2010-03-30, 02:46 PM
Uhhh... no? A "foot cubed" is "ft3" (why does everyone keep using the caret when we have a perfectly good sup tag?), which is the same as a cubic foot ("cu. ft.", maybe, but "ft3" would be more appropriate).

On the other hand, "foot cube" (not "cubed") would not be a unit, but rather a description of a shape - in this case, the unit is foot, and it's preceded by a number which gives the number of feet along a side of said cube. So a "20 ft. cube" is a cube 20 ft. on one side. Which is 8000 ft3.

I have had no less than two math majors (I went to my college's math lab today) tell me that "cubic feet" and "feet cubed" are two completely different things--as have dozens of other people from forums, math sites, and in my neighborhood.

Why do you think they are all wrong?

Ravingdork
2010-03-30, 02:48 PM
Shrink item is amazingly useful as written (with the given cubic feet limits). Now you can stock up on even the big mundane items. If you're using it to deal damage you're doing it the boring way.

Not all that big really. You could shrink something akin to a real life mini-fridge...AT 20TH LEVEL.

Ooh! Aah!

Yukitsu
2010-03-30, 02:51 PM
Meh. If you can't think of anything useful you could do with that manner of thing, then don't use it. Doesn't mean other people haven't used it for a dozen esoteric or useful things, nor that they won't continue to do so.

Kylarra
2010-03-30, 02:55 PM
I'm not sure why you're expecting an unmodified third level spell to be worldshaking. I mean at 20th level you can hold someone in place for 2 minutes (http://www.d20srd.org/srd/spells/holdPerson.htm) ooh aah.:smalltongue:

You don't like the possibilities with the listed shrink item, homebrew up a higher level one with greater volume manipulation.

Ravingdork
2010-03-30, 03:01 PM
It's not just that I think it's underwhelming, it's also that I KNOW it to be against designer intent (a designer told me so).

I just can't prove it because the v3.5 forums no longer exist. Does anybody else remember the post in which a designer said it was supposed to mean # x # x #?

Yukitsu
2010-03-30, 03:09 PM
It's not just that I think it's underwhelming, it's also that I KNOW it to be against designer intent (a designer told me so).

I just can't prove it because the v3.5 forums no longer exist. Does anybody else remember the post in which a designer said it was supposed to mean # x # x #?

Unless it's adressed in the rules compendium or the spell compendium, that particular designer probably wasn't the one that wrote the spell, or was overruled in hindsight by the other designers. I can't imagine how the series of spells that use the cubic feet parlance could be considered balanced using an X by X cube as the formula instead though considering the level they fall at. Most are considered broken even using the cubic formulas.

jiriku
2010-03-30, 03:27 PM
You can manipulate more than you think with that volume. You're imagining a compact shape. Many shapes are not compact.

Some common shapes:
a large bucket holding about 28 liters of liquid = 1 cubic foot
a large barrel containing a tun of wine = 35 cubic feet
a typical dungeon door = 1 to 3 cubic feet
a kayak = 9 to 12 cubic feet
an average rowboat = 27 to 36 cubic feet
55 suits of Medium full plate armor = 1 cubic foot
a suit of full plate armor sized for a Huge creature = 6.5 cubic feet
18 board-feet of unfinished lumber (2x4, any wood) = 1 cubic foot
500 pounds of lumber (cypress) = 12 cubic feet
500 pounds of lumbver (oak) = 6 cubic feet
a Medium human-shaped statue:
Male = 1.8 to 5.4 cubic feet
Female = 1.6 to 3.2 cubic feet
a1 Large ogre-shaped statue:
Male = 14 to 43 cubic feet
Female = 12.8 to 25.6 cubic feet

Ravingdork
2010-03-30, 03:35 PM
I can't imagine how the series of spells that use the cubic feet parlance could be considered balanced using an X by X cube as the formula instead though considering the level they fall at. Most are considered broken even using the cubic formulas.

The 20x20x20 interpretation gives maximum dimensions. Whatever you are creating/mending/shrinking has to fit in the entirety of the area. It's not a versatile as the current wording, merely larger.

huttj509
2010-03-30, 03:38 PM
On another side note, using shrink item you can fit 4000 pints, or 500 gallons of acid (or holy water) into a single flask, which will expand to its full volume on impact.

MWAHAHAHAHAHAHAHAHAHA!

Excellent.

DragoonWraith
2010-03-30, 03:40 PM
I have had no less than two math majors (I went to my college's math lab today) tell me that "cubic feet" and "feet cubed" are two completely different things--as have dozens of other people from forums, math sites, and in my neighborhood.

Why do you think they are all wrong?
English.

I'm serious. There's an ambiguity here. If you say "a foot cubed", I think "ft3", which is a cubic foot.

On the other hand, if you meant "cubed" as a verb (as in, "having cubed this 1 ft. length"), then you're right. I had not considered that.

I can't claim to know how the terms are usually used, but I imagine they avoid saying that at all to begin with. And I would also suggest that a math major would not be particularly qualified to say one way or the other, at least by virtue of being a math major, since math majors don't deal with units the majority of the time. As for forums and websites, you could link to some but I don't really care. I agree that depending on how the sentence is parsed, it could mean what you have said.

a_humble_lich
2010-03-30, 03:52 PM
As someone else noted, you need to stop talking to math majors--they barely use numbers let alone units. Physicists on the other hand would tell you that cu ft and ft3 are the same thing (in fact one is right now). And that ever reliable source of wikipedia agrees with me http://en.wikipedia.org/wiki/Cubic_feet.

As DragoonWraith said, saying (for example) a 20 foot cube is something completely different. Feet cubed, is not a unit. But if you do say 20 feet cubed that would most likely mean (20 feet)3; however, in speech many people would not hear the parenthesis and take you to mean 20 cubic feet. But the point is this is completely different from 20 ft3 which is by universal standard the way to write 20 cu ft.

Ravingdork
2010-03-30, 04:14 PM
As someone else noted, you need to stop talking to math majors--they barely use numbers let alone units. Physicists on the other hand would tell you that cu ft and ft3 are the same thing (in fact one is right now). And that ever reliable source of wikipedia agrees with me http://en.wikipedia.org/wiki/Cubic_feet.

As DragoonWraith said, saying (for example) a 20 foot cube is something completely different. Feet cubed, is not a unit. But if you do say 20 feet cubed that would most likely mean (20 feet)3; however, in speech many people would not hear the parenthesis and take you to mean 20 cubic feet. But the point is this is completely different from 20 ft3 which is by universal standard the way to write 20 cu ft.
So when referring to a cube, 20 feet on a side, how is it properly stated? We know it's not 20 cubic feet (which only gives us a cube, ~2.71 feet to a side).

Ashtagon
2010-03-30, 04:14 PM
I always took it to mean 20x1x1 cu ft, or the mass of the equivalent volume of water (about 62 lb per cu ft), whichever the caster prefers. That allows for quick an easy conversion of objects that aren't easily measured in cubic feet.

a_humble_lich
2010-03-30, 04:36 PM
So when referring to a cube, 20 feet on a side, how is it properly stated? We know it's not 20 cubic feet (which only gives us a cube, ~2.71 feet to a side).

I would say "a 20 foot cube." Or if you really want to be sure to avoid ambiguity you could say a cube, 20 feet on a side.:smallsmile:

Jayabalard
2010-03-30, 04:37 PM
One group is arguing that, that is twenty 1-ft. cubes in any configuration (so if you lined them up side by side, you would end up with a 20x1x1 shape).

The other group is arguing that it means 20x20x20.The former.
a 20x20x20 cube is 8000 cubic feet.

ericgrau
2010-03-30, 04:42 PM
Not all that big really. You could shrink something akin to a real life mini-fridge...AT 20TH LEVEL.

Ooh! Aah!

No, you can shrink a huge 40 CF fridge and 19 other items for 1 spell slot per day, since it has a duration of 20 days. Now you have a portable battering ram, barrel of [holy] water, a hunk of bread to feed 2500 people a meal, the corpses of your slain enemies to prevent resurrection and facilitate faster looting, etc., etc. You gotta get creative instead of merely finding ways to chuck rocks at things.

tyckspoon
2010-03-30, 04:57 PM
If you do just want to chuck rocks at things, remember that you don't actually need large rocks. A 1x1x1 block of limestone weighs in at about 163 pounds, and you only need it up to 200 for most efficient drop damage. (And, incidentally, if you actually ran into one of those while tilling your field or something you'd be wondering where the hell such a huge rock came from. 'Boulder' doesn't actually mean "gigantic man-sized rock.")

Ormur
2010-03-30, 05:15 PM
Agh, those aren't the proper units for doing science.

But anyway if we take shrink item then it says what, 2 cu. ft. /level. Google tells us that a single cu. ft. is 28,3 litres while 2 cu. ft. are 56,6 litres. So on fifth level you'd be shrinking 12 cu. ft. or 340 litres not a cube with dimensions of 12*12*12 feet or 48.932 litres. Otherwise the volume affected would increase exponentially for each level.

Private-Prinny
2010-03-30, 05:25 PM
Silent Image (http://www.d20srd.org/srd/spells/silentImage.htm) has a volume in 10 foot cubes. That means 10x10x10 cubes, which have to have those dimensions.

Minor Creation (http://www.d20srd.org/srd/spells/minorCreation.htm) has a volume in cubic feet, which can have any dimensions you want as long as x*y*z<your caster level.

If you can't think of a way to exploit a spell in cubic feet, that's your problem. I'll just go ahead and use standard action, 100% real Shadow Illusions to use Major Creation to get free shopping.

Ravingdork
2010-03-30, 05:56 PM
Using cubic feet in the context of a roleplaying game is so difficult to adjudicate accurately that it essentially becomes meaningless for anything other than solid cubed boulders and liquids. Most objects that you would want to create/mend/shrink are too complex for most any roleplayer or GM to be able to determine it's volume on the fly.

It basically comes down to asking your GM if any particular casting is legal and hoping it thinks the object is within your limits.

I think that's why the game designer told me that it's supposed to mean whatever fits in a nice neat cube--it is infinitely easier to adjudicate.

I mean, seriously, can you tell me accurately, what the volume is for the following object is on the fly, in under 20 seconds?

- A 3' high chair
- A 2x2' chest.
- A rowboat
- A suit of medium full plate
- A life sized bronze statue of a hydra
- A carriage
- A bowl of popcorn

Even if you do end up giving me fairly accurate estimates, I'm willing to bet you didn't determine them quickly enough for it to be practical during play.

Once something is so complex as to be arbitrary within the game, it needs to be either removed or changed. The vast majority of the spells that use the "cu. ft." terminology could just as easily have used weight limitations or cube limitations (where whatever you are working with HAS to fit entirely inside the cube).

Private-Prinny
2010-03-30, 06:06 PM
Using cubic feet in the context of a roleplaying game is so difficult to adjudicate accurately that it essentially becomes meaningless for anything other than solid cubed boulders and liquids. Most objects that you would want to create/mend/shrink are too complex for most any roleplayer or GM to be able to determine it's volume on the fly.

It basically comes down to asking your GM if any particular casting is legal and hoping it thinks the object is within your limits.

I think that's why the game designer told me that it's supposed to mean whatever fits in a nice neat cube--it is infinitely easier to adjudicate.

I mean, seriously, can you tell me accurately, what the volume is for the following object is on the fly, in under 20 seconds?

- A 3' high chair
- A 2x2' chest.
- A rowboat
- A suit of medium full plate
- A life sized bronze statue of a hydra
- A carriage
- A bowl of popcorn

Even if you do end up giving me fairly accurate estimates, I'm willing to bet you didn't determine them quickly enough for it to be practical during play.

Once something is so complex as to be arbitrary within the game, it needs to be either removed or changed. The vast majority of the spells that use the "cu. ft." terminology could just as easily have used weight limitations or cube limitations (where whatever you are working with HAS to fit entirely inside the cube).

If 20 cubic feet was supposed to say "a 20 foot cube," which they have no issue whatsoever saying in other spell descriptions, why would they bother writing it differently? By RAW, it is not one giant, exponentially growing cube. It's still plenty powerful if you decide to put a little thought into it.

jiriku
2010-03-30, 06:14 PM
Using cubic feet in the context of a roleplaying game is so difficult to adjudicate accurately that it essentially becomes meaningless for anything other than solid cubed boulders and liquids. Most objects that you would want to create/mend/shrink are too complex for most any roleplayer or GM to be able to determine it's volume on the fly.

It basically comes down to asking your GM if any particular casting is legal and hoping it thinks the object is within your limits.

I think that's why the game designer told me that it's supposed to mean whatever fits in a nice neat cube--it is infinitely easier to adjudicate.

I mean, seriously, can you tell me accurately, what the volume is for the following object is on the fly, in under 20 seconds?

- A 3' high chair
- A 2x2' chest.
- A rowboat
- A suit of medium full plate
- A life sized bronze statue of a hydra
- A carriage
- A bowl of popcorn

Even if you do end up giving me fairly accurate estimates, I'm willing to bet you didn't determine them quickly enough for it to be practical during play.

Once something is so complex as to be arbitrary within the game, it needs to be either removed or changed. The vast majority of the spells that use the "cu. ft." terminology could just as easily have used weight limitations or cube limitations (where whatever you are working with HAS to fit entirely inside the cube).

Ahem. I realize that your question is rhetorical. However, I already gave you the volume of the rowboat, and the Medium full plate. the Huge statue could be extrapolated from the volume I gave you for a large statue simply by multiplying by 8. I also gave you several examples of volumes of lumber, from which you could quickly infer the chair and the chest. Using the magic of the internet, I figured all of these things in less than a minute each. Of your other items, the bowl of popcorn is manifestly less than one cubic foot, and only the carriage is difficult.

Frankly, RavingDork, if you like the spells, you can sit down and be friends with Mr. Google for 5 minutes, make a list of the volumes of 10 or 20 common objects just like I did, and you're good to go. If you don't like doing a little math...well, you can confine yourself to small objects that are obviously within your size limit, or you can ask your DM to set some guidelines for you. Or you can play a class that doesn't ask you to use geometry. Hey, I know you're bitter about a perceived nerf to your favorite spells, but you're reacting pretty emotionally to something that can be solved quickly with medium amounts of logic and small amounts of elbow grease. I can nerd rage with the best of them too, but it really doesn't seem justified.

DaedalusMkV
2010-03-30, 06:24 PM
So when referring to a cube, 20 feet on a side, how is it properly stated? We know it's not 20 cubic feet (which only gives us a cube, ~2.71 feet to a side).
That would be a 20-foot cube, or a 20x20x20 cube, or possibly a cube with sides measuring 20 feet in length. 20 feet cubed, 20 cu ft or 20 ft^3 would refer to 20 cubic feet. Again, if you want units talk to a physicist or chemist; math majors stop worrying about units after their first class, and never use them again.

Can I go back to working in meters like a sane man now?

sofawall
2010-03-30, 07:24 PM
A 20th-level wizard should be shrinking large boats, not small chairs.

a) 20th level wizards should have CL boosters.
b) Polymorph any object.
c) A small chair is much much less that 20 cu. ft. A large chair might not fit in a 3.5 ft. cube, but it does fit in 20 cu. ft. For boats, just don't shrink the air inside! You can get a decently sized boat shrunk that way. For reference, this (http://i7.tinypic.com/4lpz3b6.jpg) is 20 cu. ft. of dirt. Now imagine a chair made of that much dirt. It's a fairly large chair.

DragoonWraith
2010-03-30, 09:08 PM
Using cubic feet in the context of a roleplaying game is so difficult to adjudicate accurately that it essentially becomes meaningless
Uhm. Well, honestly, it seems like you're the only one who's having problems, and... it seems like you're having problems because you're refusing to accept that it doesn't work the way you want it to. I don't think the unit of measure is unusable, at all...

tbarrie
2010-03-30, 10:19 PM
That would be a 20-foot cube, or a 20x20x20 cube, or possibly a cube with sides measuring 20 feet in length. 20 feet cubed, 20 cu ft or 20 ft^3 would refer to 20 cubic feet. Again, if you want units talk to a physicist or chemist; math majors stop worrying about units after their first class, and never use them again.

Can I go back to working in meters like a sane man now?

It's D&D. The medievalesque units add to the fantasy ambience.

huttj509
2010-03-30, 10:31 PM
a) 20th level wizards should have CL boosters.
b) Polymorph any object.
c) A small chair is much much less that 20 cu. ft. A large chair might not fit in a 3.5 ft. cube, but it does fit in 20 cu. ft. For boats, just don't shrink the air inside! You can get a decently sized boat shrunk that way. For reference, this (http://i7.tinypic.com/4lpz3b6.jpg) is 20 cu. ft. of dirt. Now imagine a chair made of that much dirt. It's a fairly large chair.

Tell me you did not dump 20 ft^3 of dirt on your driveway just to take a picture to use in an internet argument, please.

rubycona
2010-03-30, 10:44 PM
Tell me you did not dump 20 ft^3 of dirt on your driveway just to take a picture to use in an internet argument, please.

Hehe! That'd be hilarious.

I have to agree with most of the posters here. The 20*1*1 approach makes the most sense, and a bunch of the stuff in D&D is randomly determined by the DM, anyway. As a DM, I have to randomly BS my way through a lot of garbage. "How many knives are in this kitchen drawer?" Me: Why the hell... "Um, 5 knives."

If a player asked me if X item were shrinkable via the Shrink Item spell, I'd have to do the exact same thing... pull a number out of my rear, and go with it. When the player disagrees, we go to Google. That simple.

Ormur
2010-03-30, 10:45 PM
Using cubic feet in the context of a roleplaying game is so difficult to adjudicate accurately that it essentially becomes meaningless for anything other than solid cubed boulders and liquids.

Yes they should have used litres or cubic metres. :smallamused:

Seriously though while measuring the volume of the object is the most sensible way of determining the effect of those spells you may be right in it being inconvenient. However I don't quite like the idea of using things that fit in cubes since it would make it harder to affect unusually shaped volumes. Using weight might be better but it would still mean the DM would have to determine how heavy the objects are and it would create a discrepancy between dense and less dense materials (what's the antonym for dense?). Would you be much quicker to determine how heavy the objects you mentioned are.

I haven't used those spells much and I don't think my friends would be to annoyed with a little pause in the game for determining the volume of some object. It might be different in other groups.
Although I also think that because of the measurements used in D&D I'd have to stop the game anyway to convert the volume to the SI system. It's the same for any measurements that don't relate to the battle map really.

jiriku
2010-03-30, 11:14 PM
Tell me you did not dump 20 ft^3 of dirt on your driveway just to take a picture to use in an internet argument, please.

No sir! Sofawall is a smart cookie. He dumped 20 cubic feet of dirt in his neighbor's yard.

Thrawn183
2010-03-30, 11:57 PM
If you grew up doing yard work where your parents loved to order yards of dirt, mulch and gravel like I did... you'd never underestimate just how much is in a single cubic yard. NEVER.

On a side note, when my parents moved to Albuquerque, my father ordered 15 dump truck loads of gravel for our yard. Yes. 15. :smallmad:

DaedalusMkV
2010-03-31, 12:51 AM
Indeed, 20 cubic feet is quite a bit, as long as you only count actual volume and ignore wasted space. For reference, you can fit the following items into 10 cubic feet:
Two people sitting on chairs, in full plate armour, carrying a sword each.
A small catapult or ballista
A small catamaran or a slightly smaller other sailboat.
2-3 Dinghies
20+ inflatable rafts
A large shack or cottage
Over 9000 sheets of paper

Of course, if we assume that the spell can shrink 1 cubic foot of matter per caster level, ignoring empty space, we can thus ignore the 99.99...% of everything in existance that is empty space. Using this approach, a 20th level wizard can shrink all of the matter in the universe, at once. An even more effective method of killing all life on the planet than a wall of force; at 5th level a Wizard can cut the size of the planet to 1/8th of its current size, causing everything to fly off into space as it will now be outside of the planet's vastly reduced gravity well, as well as destabilizing its orbit thanks to the instanataneous change in mass!

Ravingdork
2010-03-31, 01:04 AM
Wow. :smalleek:

Manga Shoggoth
2010-03-31, 03:52 AM
20 feet cubed is a volume of 20 * 20 * 20

20 cubic feet is a volume of 20 * 1 * 1, or ~2.71 feet cubed

For calculation purposes:

The spell creates [whatever volume] of material. Given the [average] density of the material you can find out how much this amount of material weighs.

If you know the weight of the item you need the material for you can tell if you have enough for the purpose you want.

Taelas
2010-03-31, 04:05 AM
"20 feet cubed" is just another way of saying "20 cubic feet". It means "20 feet^3", not "(20 feet)^3". I don't see how it can be understood in any other way -- that's just how English works.

What you mean is a 20-ft. cube, or a cube that is 20 ft. per side.

potatocubed
2010-03-31, 04:29 AM
In short, these spells are just not as good as you thought they were. However, they're still quite useful. One simply has to use finesse instead of brute-forcing it.

Or you can take advantage of the fact that 20 cubic feet is a more flexible volume than just 'a cube'.

A CL 20th stone shape can affect approximately 3 x 3 x 3 feet of stone. Or it can affect a plane of stone 18 feet by 18 feet by 1 inch, which is enough to slice the side off a two-storey building or carve loose a 10 foot by 10 foot block of stone from a 2 foot thick wall.

Better yet, a CL 5th casting of stone shape can do a plane 13 feet by 13 feet by 1 inch, or a 9 foot by 9 foot block from a 2 foot wall. Once you start getting clever, caster level becomes less important.

Sure, you're going to need somebody to give the resulting block a push before you can get past, but so long as the height/base ratio is large enough it'll tip without much effort at all.

You can cheerfully abuse this with a wand, which will make a mockery of any stone-based fortifications, or you can try to convince your GM to let you make micron-thin volumes and slice the sides off mountains. (Technically RAW, I think, but good luck persuading anyone to let it fly.) I put the limit at 1 inch; I find this allows cleverness but stops things from getting too absurd.

huttj509
2010-03-31, 04:40 AM
20 feet cubed, as written, is a confusing method of stating things.

20 feet, cubed, would be 8000 cu. ft. The comma between feet and cubed is important.

20 (feet cubed), which would be how someone might say 20 ft^3 (dunno how to do superscript), is different. This would be 20 cubic feet, 20 ft^3, or 20 cu. ft. Those are all ways of stating or abbreviating the same unit.

It is simply an improper way of stating a unit because it can have different meanings based on assumed punctuation.

Remove the punctuation and you just have a confusing string of "had"s, while with punctuation it can make some sort of sense (say they're in a grammar class or something).

The actual text (from 3.5 PHB) says "1 touched object of up to 2 cu. ft./level". This is unambiguous, and thus any discussion about "20 feet cubed" is irrelevant. A cubic foot is a unit of measure of volume defined as the volume that would be contained in a cube that is 1 foot on an edge.

Now, I do agree that english units are *muckle muckle* for purposes of calculations, but for most usage of these various spells an assumption of 3 feet ~ 1 meter works fine for approximations, so 9 cubic feet is 1 cubic meter, or 1 cubic foot is about 36,000 cubic centimeters, if you're more comfortable working in metric. Hmmm, thought the cm conversion would help because I for one have more trouble visualising 1/3 meter than 1 foot offhand (used to english units for general usage, silly Americans making things hard) but it kinda goes from too small parts of the unit to too many units when using volume.

Edit: and being a DnD based thread my brain wanted to write "feat" instead of "feet" each time.

rubycona
2010-03-31, 12:37 PM

A cu. foot is a measure of volume. Straight up. If you double the volume, you have twice as much. Everyone agrees with that statement? Good, because that's how volume works.

If you call "doubling" a 20'-on-each-side cube to be 40'-on-each-side, you are WAY more than doubling. You're going from 8,000 cu. feet (the measurement of volume), to 64,000 cu. feet (again, the measure of volume). That is 8X the amount. If volume confuses you... say the 20'-on-each-side substance weights 20 lbs. A 40'-on-each-side will NOT weigh 40 lbs, it will weigh 160 lbs.

That alone pretty much decides this flat out. 40*1*1 is double 20*1*1, and 40*40*40 is 8 times 20*20*20. Since doubling volume = twice as much is a true statement, then only the 20*1*1 example can be true.

Which makes it Blatantly obvious to me that since it's obviously trying to talk about volume, it's talking about measurements of volume. Having taken a number of university chemistry classes, volume is pretty straightforward. It's some distance measurement (feet, meters, centimeters, whatever) cubed. For instance, cubic centimeters (usually seen as cc, as in, "3 cc's of this medication, please!").

And that's what this is. A distance measurement (feet) cubed. It is therefore a volume measurement, and it should therefore be regarded mathematically as volume.

Math doesn't deal with volumes much. I can assure you, chemists deal with volumes regularly. Very regularly.

Edit: In case anyone fusses about the fact that liters are also used in chemistry, let me remind you that the liters measurement is a derivative of cubed distance. The measure is 1 cubic centimeter = 1 milliliter. Volume can be measured most easily by measuring the lengths of the walls of a container, and from there, getting the (distance)^3 measurement. From that point, it can be converted into liters. (And of course, because it's chemistry, you can convert these things into just about whatever you like, via density measurements, etc. I can go on. I'm not going to.)

In case anyone cares why we convert it into liters, it's because of this very problem, actually. People get confused about multiples of cubic measurements, for instance, people think 100 cubic centimeters = 1 cubic meter, because a meter is 100 centimeters. This is FALSE. 1 cubic meter is actually way, way, way more than that. As I recall, the math is a cubic meter is 100^3 cubic centimeters, or 1,000,000 cubic centimeters. Liters, being the converted form, don't have this problem, hence their usage

Edit2: Still sciency here. The math for increasing volume in more than 1 dimension (3, for our 3D world) is percentage increase (1=100%)^(# of dimensions). So, increasing a 20*1*1 to 40*1*1 is 2^1, or just 2. 20*1*1 going to 40*2*1 is doubling on 2 dimensions, so it's 2^2, or 4 times. And finally, 20*1*1 going to 40*2*2 is doubling in 3 dimensions, which is 2^3, or 8 times. And that is why "doubling" the size of something (by all 3 dimensions) increases the weight (and volume) by 8 times.

Now that the math is listed out, there really should be no further disagreement. Hopefully. Sorry for getting so numbers intensive there XD

Edit3: Corrected my centimeters/meters math. Gah, I cannot believe I missed that -.-

Doug Lampert
2010-03-31, 01:26 PM
Using cubic feet in the context of a roleplaying game is so difficult to adjudicate accurately that it essentially becomes meaningless for anything other than solid cubed boulders and liquids.
{Scrubbed}

Ravingdork
2010-03-31, 01:37 PM
{Scrubbed}

It's not hard, it's hard to do on the fly. Most games will end up having the GM giving the player an arbitrary "yes it works" or "no it doesn't." That tells me that a simpler method should have been used to begin with.

Also, not everyone has internet access during their games (I'm forbidden from using my laptop at the table, for example, because the GM thinks I might be tempted to look up monster stats in the SRD).

Ravingdork
2010-03-31, 01:41 PM
But hey, if you DO have internet at the table, or are planning your neat trick way in advance of the game's start, then you can find stuff rather easily:

Material Specific Gravity lb. per cf-
Acetic acid, 90% 1.06 66.3
Alcohol, ethyl 0.789 49.0
Alcohol, methyl 0.791 49.0
Alfalfa, ground 0.26 16.0
Alum, lumpy 0.88 55.0
Alum, pulverized 0.75 47.0
Alumina 0.96 60.0
Aluminum, solid 2.64 165.0
Aluminum, oxide 1.52 95
Ammonia gas 0.00 0.048
Ammonium sulfate 0.83 52
Andesite, solid 2.77 173
Antimony, cast 6.70 418
Apple wood, dry 0.71 44
Apples 0.64 40
Arsenic 5.67 354
Asbestos, shredded 0.35 22
Asbestos, solid 2.45 153
Ash wood, black, dry 0.54 34
Ash wood, white, dry 0.67 42
Ashes 0.66 41
Aspen wood 0.42 26
Asphalt, crushed 0.72 45
Babbitt 7.28 454
Bagasse 0.12 7.5
Bakelite, solid 1.36 85
Baking powder 0.72 45
Barium 3.78 236
Bark, wood refuse 0.24 15
Barley 0.61 38
Barite, crushed 2.88 180
Basalt, broken 1.96 122
Basalt, solid 3.01 188
Bauxite, crushed 1.28 80
Beans, castor 0.58 36
Beans, cocoa 0.59 37
Beans, navy 0.80 50
Beans, soy 0.72 45
Beeswax 0.96 60
Beets 0.72 45
Bentonite 0.59 37
Bicarbonate of soda 0.69 43
Birch wood, yellow 0.71 44
Bismuth 9.79 611
Bones, pulverized 0.88 55
Borax, fine 0.85 53
Bran 0.26 16
Brass, cast 8.56 534
Brass, rolled 8.56 534
Brewers grain 0.43 27
Brick, common red 1.92 120
Brick, fire clay 2.40 150
Brick, silica 2.05 128
Brick, chrome 2.80 175
Brick, magnesia 2.56 160
Bronze 8.16 509
Buckwheat 0.66 41
Butter 0.87 54
Calcium carbide 1.20 75
Caliche 1.44 90
Carbon, solid 2.15 134
Carbon, powdered 0.08 5
Carbon dioxide 0.00 0.1234
Carbon monoxide 0.00 0.0781
Cardboard 0.69 43
Cedar, red 0.38 24
Cement, Portland 3.15 94
Cement, mortar 2.16 135
Cement, slurry 1.44 90
Chalk, solid 2.50 156
Chalk, lumpy 1.44 90
Chalk, fine 1.12 70
Charcoal 0.21 13
Cherry wood, dry 0.56 35
Chestnut wood, dry 0.48 30
Chloroform 1.52 95
Chocolate, powder 0.64 40
Chromic acid, flake 1.20 75
Chromium 6.86 428
Chromium ore 2.16 135
Cinders, furnace 0.91 57
Cinders, Coal, ash 0.64 40
Clay, dry excavated 1.09 68
Clay, wet excavated 1.83 114
Clay, dry lump 1.07 67
Clay, fire 1.36 85
Clay, wet lump 1.60 100
Clay, compacted 1.75 109
Clover seed 0.77 48
Coal, Anthracite, solid 1.51 94
Coal, Anthracite, broken 1.11 69
Coal, Bituminous, solid 1.35 84
Coal, Bituminous, broken 0.83 52
Cobalt 8.75 546
Coconut, meal 0.51 32
Coconut, shredded 0.35 22
Coffee, fresh beans 0.56 35
Coffee, roast beans 0.43 27
Coke 0.42 26
Concrete, Asphalt 2.24 140
Concrete, Gravel 2.40 150
Concrete, Limestone w/Portland 2.37 148
Copper, cast 8.69 542
Copper, rolled 8.91 556
Copper sulfate, ground 3.60 225
Copra, medium size 0.53 33
Copra, meal, ground 0.64 40
Copra, expeller cake ground 0.51 32
Copra, expeller cake chopped 0.46 29
Cork, solid 0.24 15
Cork, ground 0.16 10
Corn, on the cob 0.72 45
Corn, shelled 0.72 45
Corn, grits 0.67 42
Cottonseed, dry, de-linted 0.56 35
Cottonseed, dry, not de-linted 0.32 20
Cottonseed, cake, lumpy 0.67 42
Cottonseed, hulls 0.19 12
Cottonseed, meal 0.59 37
Cottonseed, meats 0.64 40
Cottonwood 0.42 26
Cryolite 1.60 100
Cullet 1.60 100
Culm 0.75 47
Cypress wood 0.51 32
Dolomite, solid 2.90 181
Dolomite, pulverized 0.74 46
Dolomite, lumpy 1.52 95
Earth, loam, dry, excavated 1.25 78
Earth, moist, excavated 1.44 90
Earth, wet, excavated 1.60 100
Earth, dense 2.00 125
Earth, soft loose mud 1.73 108
Earth, packed 1.52 95
Earth, Fullers, raw 0.67 42
Ebony wood 0.96 60
Elm, dry 0.56 35
Emery 4.01 250
Ether 0.74 46
Feldspar, solid 2.56 160
Feldspar, pulverized 1.23 77
Fertilizer, acid phosphate 0.96 60
Fir, Douglas 0.53 33
Fish, scrap 0.72 45
Fish, meal 0.59 37
Flaxseed, whole 0.72 45
Flour, wheat 0.59 37
Fluorspar, solid 3.21 200
Fluorspar, lumps 1.60 100
Fluorspar, pulverized 1.44 90
Garbage 0.48 30
Glass, window 2.58 161
Glue, animal, flaked 0.56 35
Glue, vegetable, powdered 0.64 40
Gluten, meal 0.63 39
Gneiss, bed in place 2.87 179
Gneiss, broken 1.86 116
Gold, pure 24Kt 19.29 1204
Granite, solid 2.69 168
Granite, broken 1.65 103
Graphite, flake 0.64 40
Gravel, loose, dry 1.52 95
Gravel, w/sand, natural 1.92 120
Gravel, dry 1/4 to 2 inch 1.68 105
Gravel, wet 1/4 to 2 inch 2.00 125
Gypsum, solid 2.79 174
Gypsum, broken 1.81 113
Gypsum, crushed 1.60 100
Gypsum, pulverized 1.12 70
Halite (salt), solid 2.32 145
Halite (salt), broken 1.51 94
Hydrochloric acid 40% 1.20 75
Ice, solid 0.92 57.4
Ice, crushed 0.59 37
Ilmenite 2.31 144
Iridium 22.16 1383
Iron, cast 7.21 450
Iron, wrought 7.77 485
Iron oxide pigment 0.40 25
Ivory 1.84 115
Kaolin, green crushed 1.03 64
Kaolin, pulverized 0.35 22
Leather 0.95 59
Lignite, dry 0.80 50
Lignum Vitae, dry 1.28 80
Lime, quick, lump 0.85 53
Lime, quick, fine 1.20 75
Lime, stone, large 2.69 168
Lime, stone, lump 1.54 96
Lime, hydrated 0.48 30
Limonite, solid 3.80 237
Limonite, broken 2.47 154
Limestone, solid 2.61 163
Limestone, broken 1.55 97
Limestone, pulverized 1.39 87
Linseed, whole 0.75 47
Linseed, meal 0.51 32
Locust, dry 0.71 44
Magnesite, solid 3.01 188
Magnesium, solid 1.75 109
Magnesium sulfate, crystal 1.12 70
Magnetite, solid 5.05 315
Magnetite, broken 3.29 205
Mahogany, Spanish, dry 0.85 53
Mahogany, Honduras, dry 0.54 34
Malt 0.34 21
Manganese, solid 7.61 475
Manganese oxide 1.92 120
Manure 0.40 25
Maple, dry 0.71 44
Marble, solid 2.56 160
Marble, broken 1.57 98
Marl, wet, excavated 2.24 140
Mercury @ 32oF 13.61 849
Mica, solid 2.88 180
Mica, broken 1.60 100
Milk, powdered 0.45 28
Molybdenum 10.19 636
Mortar, wet 2.40 150
Mud, packed 1.91 119
Mud, fluid 1.73 108
Nickel, rolled 8.67 541
Nickel silver 8.45 527
Nitric acid, 91% 1.51 94
Nitrogen 0.00 0.0784
Oak, live, dry 0.95 59
Oak, red 0.71 44
Oats 0.43 27
Oats, rolled 0.30 19
Oil cake 0.79 49
Oil, linseed 0.94 58.8
Oil, petroleum 0.88 55
Oxygen 0.00 0.0892
Oyster shells, ground 0.85 53
Paper, standard 1.20 75
Paraffin 0.72 45
Peanuts, shelled 0.64 40
Peanuts, not shelled 0.27 17
Peat, dry 0.40 25
Peat, moist 0.80 50
Peat, wet 1.12 70
Pecan wood 0.75 47
Phosphate rock, broken 1.76 110
Phosphorus 2.34 146
Pine, White, dry 0.42 26
Pine, Yellow Northern, dry 0.54 34
Pine, Yellow Southern, dry 0.72 45
Pitch 1.15 72
Plaster 0.85 53
Platinum 21.51 1342
Porcelain 2.40 150
Porphyry, solid 2.55 159
Porphyry, broken 1.65 103
Potash 1.28 80
Potassium chloride 2.00 125
Potatoes, white 0.77 48
Pumice, stone 0.64 40
Quartz, solid 2.64 165
Quartz, lump 1.55 97
Quartz sand 1.20 75
Redwood, California, dry 0.45 28
Resin, synthetic, crushed 0.56 35
Rice, hulled 0.75 47
Rice, rough 0.58 36
Rice grits 0.69 43
Rip-Rap 1.60 100
Rosin 1.07 67
Rubber, caoutchouc 0.95 59
Rubber, manufactured 1.52 95
Rubber, ground scrap 0.48 30
Rye 0.71 44
Salt cake 1.44 90
Salt, course 0.80 50
Salt, fine 1.20 75
Saltpeter 1.20 75
Sand, wet 1.92 120
Sand, wet, packed 2.08 130
Sand, dry 1.60 100
Sand, loose 1.44 90
Sand, rammed 1.68 105
Sand, water filled 1.92 120
Sand w/ Gravel, dry 1.73 108
Sand w/ Gravel, wet 2.00 125
Sandstone, solid 2.32 145
Sandstone, broken 1.51 94
Sawdust 0.27 17
Sewage, sludge 0.72 45
Shale, solid 2.68 167
Shale, broken 1.59 99
Silver 10.46 653
Slag, solid 2.12 132
Slag, broken 1.76 110
Slag, crushed, 1/4 inch 1.19 74
Slag, furn. granulated 0.96 60
Slate, solid 2.69 168
Slate, broken 1.67 104
Slate, pulverized 1.36 85
Snow, freshly fallen 0.16 10
Snow, compacted 0.48 30
Soap, solid 0.80 50
Soap, chips 0.16 10
Soap, flakes 0.16 10
Soap, powdered 0.37 23
Soda Ash, heavy 0.96 60
Soda Ash, light 0.43 27
Sodium 0.98 61
Sodium Aluminate, ground 1.15 72
Sodium Nitrate, ground 1.20 75
Soybeans, whole 0.75 47
Spruce, California, dry 0.45 28
Starch, powdered 0.56 35
Steel, cast 7.85 490
Steel, rolled 7.93 495
Stone, crushed 1.60 100
Sugar, brown 0.72 45
Sugar, powdered 0.80 50
Sugar, granulated 0.85 53
Sugar, raw cane 0.96 60
Sugarbeet pulp, dry 0.21 13
Sugarbeet pulp, wet 0.56 35
Sugarcane 0.27 17
Sulfur, solid 2.00 125
Sulfur, lump 1.31 82
Sulfur, pulverized 0.96 60
Sulfuric acid, 87% 1.79 112
Sycamore, dry 0.59 37
Taconite 2.80 175
Talc, solid 2.69 168
Talc, broken 1.75 109
Tanbark, ground 0.88 55
Tankage 0.96 60
Tar 1.15 72
Tin, cast 7.36 459
Tobacco 0.32 20
Trap rock, solid 2.88 180
Trap rock, broken 1.75 109
Tungsten 19.62 1224
Turf 0.40 25
Turpentine 0.87 54
Walnut, black, dry 0.61 38
Water, pure 1.00 62.4
Water, sea 1.03 64.08
Wheat 0.77 48
Wheat, cracked 0.67 42
Willow wood 0.42 26
Wool 1.31 82
Zinc, cast 7.05 440
Zinc oxide 0.40 25

Kylarra
2010-03-31, 01:42 PM
spoiler tag that list please. :smalltongue:

huttj509
2010-03-31, 01:46 PM
*generally good stuff*

Psst, 1 meter is 100 centimeters, not 1000, so 1 cubic meter is 1,000,000 cubic cm, not 1,000,000,000.

kilo = 1000
hecto = 100
deca = 10
deci = 1/10
centi = 1/100
milli = 1/1000

HenryHankovitch
2010-03-31, 01:47 PM
For boats, just don't shrink the air inside! You can get a decently sized boat shrunk that way.

"Okay, so I cast shrink item on the boat, but not the air inside."

"Your boat instantly shrinks to a tiny fraction of its former size. It then instantly explodes in your hand as the compressed air inside cannot escape fast enough. Let's see, the damage from that should be..."

I don't think I'd ever allow someone to ignore airspaces when figuring the volume of the item to be shrunk. But I may just be a jerk that way. The object has to fit within (2*CL) cu. ft. Otherwise you're just asking to argue with your player how much "solid" is inside, say, the Eiffel Tower. Or 500 suits of full plate.

rubycona
2010-03-31, 01:50 PM
{Scrubbed}

I think this makes more sense for the layman in context of an example:

Say, wood. I typed in Google, "Density of Pine," and of the results, I picked 530 (which this site clarifies is, 530kg/cubic meter.) Well, we have our spell in cubic feet, not meters. So let's convert to cubic meters. Say, we've got 20 cu feet for our spell.

I plug that into Google (20 cubic feet to cubic meters), and I get 0.566336 cubic meters. So, I multiply 0.566366 times 530kg/cubic meter, which gives me the result in kilograms, or 300.158 kgs. Say you don't like kilograms, so type into Google, 300.158 kg to pounds, which gets 661.735 pounds.

That's a light wood. So let's try again, a heavier one. Let's go with Oak, upwards of 930kg/cu meter. Let's do our math here:

20 cu feet -> cu meters = 0.566336. Multiply that by the 930 we got from the search result, for 526.69kgs. Plug in 526.69kg to lbs and you get 1,161 lbs.

2 minutes on Google and you know you can shrink, as a 10th level caster, 661 lbs of pine, and 1,161 lbs of oak. Not bad! By 20th level, that doubles, more if you've got CL increases.

Edit:

Psst, 1 meter is 100 centimeters, not 1000, so 1 cubic meter is 1,000,000 cubic cm, not 1,000,000,000.

kilo = 1000
hecto = 100
deca = 10
deci = 1/10
centi = 1/100
milli = 1/1000

ACK! Yes, gah, for some reason, I was thinking millimeters for that part XD Forgive me! I didn't plug it in, it was coming from memory. I'll go fix it.

jiriku
2010-03-31, 01:52 PM
"Okay, so I cast shrink item on the boat, but not the air inside."

"Your boat instantly shrinks to a tiny fraction of its former size. It then instantly explodes in your hand as the compressed air inside cannot escape fast enough. Let's see, the damage from that should be..."

I don't think I'd ever allow someone to ignore airspaces when figuring the volume of the item to be shrunk. But I may just be a jerk that way. The object has to fit within (2*CL) cu. ft. Otherwise you're just asking to argue with your player how much "solid" is inside, say, the Eiffel Tower. Or 500 suits of full plate.

That's easy. The Eiffel Tower is much too large to shrink. Steel weighs 490 pounds per cubic foot and a suit of full plate weights 50 pounds, therefore 500 suits of full plate are about 52 cubic feet, or perhaps somewhat more considering the lining is less dense.

HenryHankovitch
2010-03-31, 01:58 PM
That's easy. The Eiffel Tower is much too large to shrink. Steel weighs 490 pounds per cubic foot and a suit of full plate weights 50 pounds, therefore 500 suits of full plate are about 52 cubic feet, or perhaps somewhat more considering the lining is less dense.

But that's assuming that the spell is limited by mass, not volume--that 50 lbs of steel armor is indistinguishable from a 50-lb solid lump of steel.

You could interpret the spell that way, but I wouldn't. Particularly since the spell description is using a volume based measure. If you cast the spell at 3rd level, you can only shrink 6 cu. ft. of solid granite...or 6 cu. ft. of solid balsawood. So the spell is clearly limited by volume, not by mass: the cube of granite is far denser--has far more mass--than the cube of balsawood.

And arguing that spell ignores the geometry of the object touched, including interior spaces, also introduces its own set of problems. If I have two separate objects--a hollow beryllium sphere and a solid sphere of plutonium inside it--and I only shrink the outer sphere, what happens to the plutonium inside it? The answer, as far as I'm concerned, is "a dragon poops on your head, stop asking silly questions."

Going by mass just adds unnecessary math and argument to something which is plenty useful and powerful already, and gives the players about a cubic mile of wiggle room to argue over.

It's easier to say, "okay, the chair fits into a space 3' by 1.5' by 1.5'," than to try to figure out how much solid mass of wood is in this particular chair.

But like I said, I'm probably just mean that way.

rubycona
2010-03-31, 02:19 PM
But that's assuming that the spell is limited by mass, not volume--that 50 lbs of steel armor is indistinguishable from a 50-lb solid lump of steel.

You could interpret the spell that way, but I wouldn't. Particularly since the spell description is using a volume based measure. If you cast the spell at 3rd level, you can only shrink 6 cu. ft. of solid granite...or 6 cu. ft. of solid balsawood. So the spell is clearly limited by volume, not by mass: the cube of granite is far denser--has far more mass--than the cube of balsawood.

And arguing that spell ignores the geometry of the object touched, including interior spaces, also introduces its own set of problems. If I have two separate objects--a hollow beryllium sphere and a solid sphere of plutonium inside it--and I only shrink the outer sphere, what happens to the plutonium inside it? The answer, as far as I'm concerned, is "a dragon poops on your head, stop asking silly questions."

Going by mass just adds unnecessary math and argument to something which is plenty useful and powerful already, and gives the players about a cubic mile of wiggle room to argue over.

It's easier to say, "okay, the chair fits into a space 3' by 1.5' by 1.5'," than to try to figure out how much solid mass of wood is in this particular chair.

But like I said, I'm probably just mean that way.

Well, the spell does relate to volume, not mass... it's just easier to figure out the volume by turning mass into volume via density. (Mass unit / density (which is mass/volume) = volume unit)

Basically, I think of the spell as wrapping up the target in a shape-fitting bubble, and you've only got so much bubble.

While I wouldn't do it your way, fact is, D&D only exists through the DMs making (typically fairly arbitrary) judgement calls. It's only fun because the DMs make these judgement calls as quickly as they possibly can, while still striving for some level of accuracy, but generally, haste is preferable to accuracy.

If your game runs smoother, faster, and more fun by skimping on volume/mass/density elements, then definitely, that's how you should play it.

However, care should be taken about literally cubing a full spellcaster's already formidable might! Hence why the original question matters, and why understanding that 20 cubic feet does NOT equal a 20'*20'*20' cube. Once you realize that 20*1*1 = 20 cubic feet, how you adjudicate it from there is the DM's call.

Edit: It probably surprises absolutely no one that we Always have a calculator of some kind at our D&D table, and it's never used for dice :P

jiriku
2010-03-31, 03:17 PM
Woot for calculators! I will readily acknowledge that I am a massive, massive gaming geek, but tech is really the way to go. I develop games at the PC, store monster stats as document files, and build dungeon maps as more document files, using drawing tools. Frequently, if there's a contentious ruling, I just pull up my browser (which is already loaded with an online DM screen), open another tab and surf to the Playground, and start a thread with my rules question. We can generally get 2-4 opinions on the subject before the encounter is even over.

When you're that extensively wired, finding the answer to a simple question is trivial (Dear Google, "What is the weight of one cubic foot of steel?").

Vizzerdrix
2010-03-31, 03:25 PM
This topic makes my head hurt :smallfrown:

What about a re write of the spell based on sizes instead of feet?

rubycona
2010-03-31, 03:44 PM
This topic makes my head hurt :smallfrown:

What about a re write of the spell based on sizes instead of feet?

Thing is, while "size" works great with things like, I dunno, an ogre, it's less fantastic with things like water. How much is a "Huge" or "Large" amount of water, as opposed to "small"?

Ultimately, it breaks down to this: there will be DMs/players who care, and DMs/players who don't.

The DMs/players who don't care will look at "2 cubic feet / caster level" and go, "whatever, let's say you can shrink this amount."

The DMs/players who Do care, and actually want to try using these kinds of spells in a more precise way... it is Only for these people that this thread exists. And if you want to take care of these things in a more precise way, then the volume measurement is better than the arbitrary "size" measurement.

No doubt plenty of DMs decided it was 20*20*20, and ran with it, some did fine, others thought it was broken and nerfed it. Simple, fixed, done.

But for those of us who don't mind a little number crunching (or saying Hi to our beloved friend and comrade, Google) when the situation requires precision, and who want to actually Have that precision, then the whole "how do you determine exact volume" thing comes into play.

Even as a general rule, though, knowing what a cubic foot IS (which the original poster and his Math major buddy made a common mistake with) really helps, even for hastily half-randomly made judgement calls.

So all in all, I find the cubic feet thing to be best, even without the aid of the computer/internets.

As a side note, I am utterly thrilled to actually have a thread to which I can make a solid contribution! Who'd have guessed that my college chemistry classes would help in a D&D discussion? (Ok, when put that way, maybe it's not so surprising >.>)

jiriku
2010-03-31, 04:15 PM
As a side note, I am utterly thrilled to actually have a thread to which I can make a solid contribution! Who'd have guessed that my college chemistry classes would help in a D&D discussion? (Ok, when put that way, maybe it's not so surprising >.>)

If it is deadly to catgirls, then it must be good!

Renchard
2010-04-01, 04:04 PM
I think this makes more sense for the layman in context of an example:

Say, wood. I typed in Google, "Density of Pine," and of the results, I picked 530 (which this site clarifies is, 530kg/cubic meter.) Well, we have our spell in cubic feet, not meters. So let's convert to cubic meters. Say, we've got 20 cu feet for our spell.

I plug that into Google (20 cubic feet to cubic meters), and I get 0.566336 cubic meters. So, I multiply 0.566366 times 530kg/cubic meter, which gives me the result in kilograms, or 300.158 kgs. Say you don't like kilograms, so type into Google, 300.158 kg to pounds, which gets 661.735 pounds.

That's a light wood. So let's try again, a heavier one. Let's go with Oak, upwards of 930kg/cu meter. Let's do our math here:

20 cu feet -> cu meters = 0.566336. Multiply that by the 930 we got from the search result, for 526.69kgs. Plug in 526.69kg to lbs and you get 1,161 lbs.

2 minutes on Google and you know you can shrink, as a 10th level caster, 661 lbs of pine, and 1,161 lbs of oak. Not bad! By 20th level, that doubles, more if you've got CL increases.

The fact that some people consider this par for the course for their gaming more than adequately explains the difference between the 3.5 and 4e camps.

jiriku
2010-04-01, 04:09 PM
Heck yeah! 3.5 forever baby!

On a more realistic note, calculations of this nature mark you forever and anon as a powergamer. Regular gamers can get by quite fine by guestimating.

2010-04-01, 11:23 PM
"Okay, so I cast shrink item on the boat, but not the air inside."

"Your boat instantly shrinks to a tiny fraction of its former size. It then, having exceeded the speed of light, travels backwards in time, overlapping its past self. Nuclear fusion is initiated, resulting in the destruction of the boat and a large spray of radiation."

If you're bringing physics into it, you have to bring them all in

rubycona
2010-04-02, 12:36 AM
Heck yeah! 3.5 forever baby!

On a more realistic note, calculations of this nature mark you forever and anon as a powergamer. Regular gamers can get by quite fine by guestimating.

Haha! Actually, I'm not a powergamer at all. I really suck at feat-item-class-etc combinations for brokenness. (One of my players, mind you, DOES powergame, and it drives me nuts).

I am a very thorough DM, though, in the sense of the world. In one game, we spent about an hour arguing about how long standard lantern oil would burn when spread on the cliff face. Man, we looked up everything... types of lantern oil, volume of a barrel, trying to figure out the surface area of the cliff based on size and roughness, the amount of spread and splatter... we almost got into the viscosity of the oil when I said, screw it! It's lasting this long. Conversation over. No more arguing with the DM.

So it's not just that I'm a numbers-intensive DM (though, I'm the worst of the lot). My players happen to be a group that drags me into it XD

BobVosh
2010-04-02, 02:23 AM
Thing is, while "size" works great with things like, I dunno, an ogre, it's less fantastic with things like water. How much is a "Huge" or "Large" amount of water, as opposed to "small"?

Find the weight of the large, huge, and small water elementals. Find out how many gallons of water it takes to equal out these weights. Wa-la!

Probably the easiest way to do this is off weight rather than size anyway. So you can reduce 20 lbs. The object was 40 lbs. It is now half as large. Simplistic.

Tetsubo 57
2010-04-02, 05:20 AM
For me this is a fairly clear cut issue. Did the spell say 20 cubic feet OR a 20' cube? If it's the former, it's 20 cf. If it's the latter it's a cube 20' on a side. And if someone is trying to argue the latter when it is saying the former, they are being a ****.

Ravingdork
2010-04-02, 11:59 AM
Just thought of this, this morning:

Most everyone can agree that 1 cubic foot gives us a cube with 1 foot on a side.

12 cubic feet is NOT a 12x12x12 foot cube.

So answer me this: How come 12 cubic inches ISN'T a 12x12x12 inch cube?

Shouldn't 12 cubic inches give us the exact same cube as 1 cubic foot? Mathematically, doing it in inches gives us a much smaller cube. Why is that?

EDIT: Feel free to discuss the question, but I think I figured it out on my own.

Philistine
2010-04-02, 12:09 PM
Just thought of this, this morning:

Most everyone can agree that 1 cubic foot gives us a cube with 1 foot on a side.

12 cubic feet is NOT a 12x12x12 foot cube.

So answer me this: How come 12 cubic inches ISN'T a 12x12x12 inch cube?

Shouldn't 12 cubic inches give us the exact same cube as 1 cubic foot? Mathematically, doing it in inches gives us a much smaller cube. Why is that?
Because you've got the order of operations wrong.

EDIT: Perhaps it would be more helpful to first look at the case of area, rather than volume. A square foot is an area that is 1'X1', or 12" by 12". That gives us 1 sq ft as equal to 144 sq in. To get volume we multiply again: 1x1x1 = 1, and 12x12x12=1728, and so 1 cu ft = 1728 cu in.

EDIT 2: To try to clarify further, the 1 cu ft = a cube with sides of 1ft length is due to a unique property of the number '1' - namely, that is the multiplicative identity. When you use any number other than one, that no longer holds.

tyckspoon
2010-04-02, 12:12 PM
Just thought of this, this morning:

Most everyone can agree that 1 cubic foot gives us a cube with 1 foot on a side.

12 cubic feet is NOT a 12x12x12 foot cube.

So answer me this: How come 12 cubic inches ISN'T a 12x12x12 inch cube?

Shouldn't 12 cubic inches give us the exact same cube as 1 cubic foot? Mathematically, doing it in inches gives us a much smaller cube. Why is that?

For exactly the same reason that 12 cubic feet isn't the same size as a 12-foot cube. If you state it as 12-inches-cubed, then the units are equivalent, but if you're starting with a single cubic inch and then trying to stack together twelve of those to fill the same volume as a cubic foot.. well, you're doomed to failure.

Philistine
2010-04-02, 05:23 PM
The long form of my previous post...

The original question in the thread was, "Why isn't '20 cu ft' the same thing as 'a cube with sides of length 20 ft'?" The subsequent question about the number of cubic inches in a cubic foot is essentially a rehash of the same issue, and the two can be addressed as one problem.

To begin, consider the general case of the expression (x * y) ^ n. Standard rules for the order of operations dictate that this can be expanded as (x ^ n) * (y ^ n); expanding it as x * (y ^ n) is not correct.

If we have a cube with sides of length (x * y), then the volume of that cube will be calculated as (x * y) ^ 3, or (x ^ 3) * (y ^ 3). Now take our cube with sides of length 20 ft, whose volume is calculated as 20 ft * 20 ft * 20 ft, or (20 ft) ^ 3. Next, we expand the expression 20 ft to 20 * 1 ft, and substitute it back into our volume calculation, which now becomes (20 * 1 ft) ^ 3. Referring back to the general case, the proper expansion of this expression is (20 ^ 3) * (1 ft ^ 3); and since (1 ft) ^ 3 = 1 cu ft, this gives us our volume as 8000 cu ft. (Similarly, a cube with sides of 12 in has a volume of 1728 cu in, demonstrating that the relation 1 ft = 12 in is only valid for linear measurements; it does not hold for measurements of either area or volume.)

The argument in the original post, that '20 cu ft' (which can also be written as 20 (ft ^ 3)) should be the same as 'a 20 ft X 20 ft X 20 ft cube', is only achievable as the result of using the incorrect expansion for the general case as stated above, as it requires you to cube only one of the factors in the expression.

That said, there is one exceptional case: when the length of a side is 1 ft (or indeed one of whatever unit you happen to be using), you can get away with doing things the wrong way around. Basically, because 1 * 1 = 1, you still get the correct volume even if you forget to cube the first term - if and only if the length of a side is exactly 1. But it is important to remember that this is a special case, not the general case.

BOOM! Mathematician'd!

rubycona
2010-04-03, 02:37 PM
Accurate, high math stuff

While this may be correct, it bears the substantial problem of being very hard to understand if you're not familiar with the math already. I think I should try again to express this in simple terms, which should hopefully be understood without too much trouble.

Just thought of this, this morning:

Most everyone can agree that 1 cubic foot gives us a cube with 1 foot on a side.

12 cubic feet is NOT a 12x12x12 foot cube.

So answer me this: How come 12 cubic inches ISN'T a 12x12x12 inch cube?

Shouldn't 12 cubic inches give us the exact same cube as 1 cubic foot? Mathematically, doing it in inches gives us a much smaller cube. Why is that?

EDIT: Feel free to discuss the question, but I think I figured it out on my own.

12 cubic inches does not equal 1 cubic foot, because of the same thing I'd talked about already... 3D volume is an exponential (cubed, specifically) measurement, and straight distance (inches, feet, and so on) is linear.

Basically... inches/feet only refer to just one line, so if you increase the line, it just goes longer. Double the inches, and it's twice as long.

With 2D stuff, it goes longer AND wider. Double inches on both, and you double length AND width. Because you're increasing 2 measurements, not one, at the same time, it increases by squaring. (That's why a 2*2 square is 4 times as big, not twice as big as a 1*1 square)

With 3D stuff, it goes longer AND wider AND higher. Double inches (or feet) on all 3 measurements, and you increase it by cubing (specifically 23, the 2 is because you've got twice as many inches, and the 3 because it's 3 dimensions, and 23 is 8. That's why a 2*2*2 cube is 8 times as big as a 1*1*1 cube)

And finally, why 12 cubic inches don't equal 1 cubic foot. It's basically the same question you were asking in the first place (20*20*20 vs 20*1*1), but different terms.

Try to think of it in blocks. You've got a little block that's 1" by 1" by 1". You've got lots of them. Get 12 of them in a row, and it's 1 foot long, 1 inch high, and 1 inch wide, right? It takes all 12 cubic inches to increase 1 line of measurement to 1 foot.

[] -> [][][][][][][][][][][][]

How you do make a 1'*1' square with the little blocks? Well, you'll have to have them 12 blocks in another direction, too. Do that once, and you've basically got an L shape, and you've got to fill in all the empty space with more blocks.

[][][][][][][][][][][][]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]

How many will it take? Specifically, 122, or 144 total (12 blocks long by 12 blocks wide = 12*12 = 144)

So just to make a flat 1 foot by 1 foot by 1 inch square out of 1 inch blocks takes 144 blocks, so 144 cubic inches to fill just the bottom of the cube you're going for. How many will it take to make it into a full 1 foot cube, or 1 cubic foot?

Just do the same thing again. You'll have to stack those blocks 12 high, and each layer will take another 144 blocks. So that means, it'll take a total of 12*144, which is 1728. Another way of saying it is 12 times 12 times 12 = 1728. Another way of saying it is 123, which is also 1728. (Reason for the 12 is you've got 12 units. Reason for the 3 is you're increasing it in 3 dimensions, or directions (up/down, left/right, forward/back))

And that's why 12 cubic inches do not equal 1 cubic foot, because volume itself increases exponentially (3 directions), but when you add measurements together (like adding 12 cubic inches together) it adds linearly (1 direction).

So finally put, it's not 12 cubic inches to equal 1 cubic foot, it's 123 cubic inches (1728) to equal 1 cubic foot.

To relate it to your original question, it's not 20 cubic feet to equal the 20*20*20 cube, it's 203 (8,000) cubic feet to equal the 20*20*20 cube.

I hope I explained it in a way that a layman can follow. Sorry if it sounds patronizing to anyone, I'm trying to put it as simply as I possibly can. Hopefully, this post will clarify things once and for all.