How many hit points/hit dice does Neth the Living Plane have?

"Yeah, I once killed Bytopia. It had some mad lewtz. Still can't get the gnome out of my armor, though."
---Overheard in one of the many bubberhouses of Sigil

Okay, this is pretty bad, but I registered solely to do this.

Area of a sphere = four times pi times the radius squared.

You need to the area of a square mile, that's simple, 5,280 feet by 5,280 feet. When multiplied, you get 27,878,400 square feet. Now, you take that number and multiply it by 250, for the radius of 250 square miles. That is 6,969,600,000. Now that we have that, we can figure out the area of a sphere. We're going to use the approximation of 3.14 as pi for simplicity's sake.

A = 3.14*6969600000^2 You do the exponent first...
= 3.14*48,575,324,160,000,000,000 Times this by pi...
A = 152,526,517,862,400,000,000 That's only 152.5 quadrillions.

But wait! We're not done. Now you've got to divide that large number by 5, to find how many 5 square foot pieces are present. Finally, you multiply that number by 120 to find the total hitpoints.

HP = 120(152,526,517,862,400,000,000/5)
= 120(30,505,303,572,480,000,000)
HP = 3,660,636,428,697,600,000,000

And that tidy sum is only 3.660 septillions.

Oh, and hi.

If "If spread falt..." presumes a surface area of 500 miles in diameter, A=pi(rr) is accurate. Where 250 miles = 1,320,000 feet (250 mi * 5,280 ft/mi)
A=3.14159(1,320,000*1,320,000)
A=3.14159*1.7424e12
A=5.47e12 square feet.

Divide by 25 for the number of five foot square sections (A=lw, A=5*5, A = 25 square feet).
5.47e12 square feet / 25 square feet.
Total number of five foot squares = 2.189e11

Each 25 square foot section = 120 HP.
Total five foot squares, 2.189e11 * 120 HP per square.
2.6e13 HP

For the life of me Rargphlam, I am lost as to why you would multiply square feet (an area) by the raduis in miles. That third dimension (aside from mixed numeric increments) is already the volume of a cube.

That said:

If "If spread flat..." means looking at it from overhead.

Total surface area = 4pi(rr)
T = 4*3.14159(1,320,000*1,320,000)
T = 4*3.14159 *1.74e12
T = 2.1895e13 square feet.

Again, with 25 being the area of a five foot square, we divide.

2.1895e12 square feet / 25 square feet = 8.758e11 five foot squares.

Each five foot square has 120 HP, we multiply.

8.758e11 five foot squares * 120 HP per square = 1.05099e14 Hit Points.

Dhampire is correct -- he and I got the same answer.

Rargphlam, allow me to gently critique your math. Don't worry, I'm a math teacher, I don't bite. :^)

First, you've (correctly) found the number of square feet in a square mile, 27,878,400.

Your formula for the surface area of a sphere is correct, but incorrectly applied. 4 pi r^2 would be a useful formula if we had been told that Neth was roughly spherical, and had 120 hitpoints per 5-foot-square section of surface area. Instead, we are to imagine Neth as more of a many-times-folded membrane, which can be laid flat like a sheet of paper. This is very similar to many real biological structures, such as the folds of the human brain, or the wrinkles of our gut or lungs, or the inside of a mitochondrion; many biological processes (like gas exchange in the lungs) are more efficient if run over more surface area, and folding a membrane allows a lot of surface area to be packed into the same volume.

So we treat Neth as a flat membrane, and assume rough circularity since we're given a "diameter." As you note, radius r is half diameter d or 250 miles.

Now, here's where an important and common error gets made. You have found the conversion factor 27,878,400 "square feet per square mile", and then multiply this by 250 miles to get the number 69,696,000,000, in units of "(square feet / square miles) times miles," or, canceling a 'miles' in the numerator and denominator, "square feet per mile." Conceptually, "square feet per mile" doesn't really make any sense; "feet per mile" or "square feet per square mile" is a number you use to convert from one unit to another.

To correct this problem, remember this key concept, which will be very useful to you in all sorts of calculations: keep track of units. Units are our friends.

In this problem, we want an answer in the units "hitpoints." We are given the information "diameter is 500 (in miles)", and "120 hitpoints per 25 square feet of surface." Here's how we build up the answer, just with the units:

hitpoints = (hitpoints / sq.ft.) * (sq.ft. / sq.mi.) * (sq.mi. of surface area)
= (hitpoints / sq.ft.) * (5280 ft/mi)^2 * (pi * (diameter/2 in miles)^2).

See why units are our friends? You can look at the units-equation above and tell where each piece of information goes, and how each of the units cancels (square feet cancel, square miles cancel), so that you end up with the information (hit points) you know you're looking for. Now that we've got that equation, all that's left is to plug in the numbers:

Neth's HP in hitpoints = 120hp/(5ft)^2 * (5280ft/mi)^2 * (3.14 * (500 miles/2)^2)
= 120hp/25sqft * 27878400 sqft/sqmi * 3.14 * 250^2 sqmi
= 26,274,772,990,151 hitpoints, or about 26 trillion HP. (If Neth's Hit Die is a d8, he's a 5.8 trillion HD creature!)

Now, here's a second ingredient that's important in this kind of problem, which is knowing which formula to use. We used pi r^2 above since we were told Neth was basically a flat membrane. Had we been told that Neth was roughly spherical, and had been given HP per unit of surface area, we would have used

hitpoints = (hitpoints / sq.ft.) * (sq.ft. / sq.mi.) * (sq.mi. of surface area)
= (hitpoints / sq.ft.) * (5280 ft/mi)^2 * (4 pi * (diameter/2 in miles)^2).

Notice that the first equation is the same! The only difference in the second is the formula for the area of a different shape. Knowing when the problem calls for a certain formula is an important conceptual part of math and the sciences.

The answer we would have gotten in that case would differ by the extra factor of 4, giving us 4*26 trillion = 104 trillion HP.

Hope this clears up everything. I'm always happy to answer any math questions! :^)

I didn't realize that we had members of that strange little sect- the Mathematicians. I thought you spent all your time on Mechanus. They're spreading! They're spreading!!

Don't forget to apply Neth's size modifier to his hit bonus and AC

Shocking rules omission.

%^)

For idle reference, in GURPS Neth would have a Size Modifier of +39 (they have an infinite numerical scale... the Universe has a Size Modifier, I just can't recall what it is off the top of my head) which has the obvious effects such as +39 to hit (in DnD terms, -39 to AC, which means if you can't hit him you've probably been cursed).

Among the special rules for creatures that big, Neth auto-resists most afflictions (sorry, you're not infecting the Living Plane with mummy rot*) and while you might theoretically be able to cast a spell on him, you're going to need a whopping big lot of energy to augment the casting.

* Although damn, I suddenly wonder what would happen if there were infact an Undead Plane out there somewhere! ... maybe I should write that up.

Also, wouldn't the Massive Damage rules apply to Neth? If you can consistently dish out 50+ points of damage to Neth from a single source then you just have to wait for it to roll a 1 on its fortitude save.

-420

No, that's much too mundane for Planescape. Neth is the demiplane. The plane itself is aware. The landscape of the plane is flesh and fluid, but that's no more Neth than the mountains of Arcadia are Arcadia. That is to say, Neth's flesh is part of Neth, but even if it were all destroyed with spheres of annihilation, Neth would still exist. Neth is the the fabric of space-time, Neth is the Ethereal border, Neth is everything.

If there was a second Neth, could they mate? :shock:

To further this thought (or clarify it if you happen to be thinking on the same plane as I am) The 120 HP/25sq.ft is just the damage amount of that region to break through. This does not mean that this total actually reflects any part of Neth's actual HP.

This is like saying that it takes .1 HP of damage to break through a 1 sq.inch section of my skin and figuring out how many hit points my hide has. This is not inflicting damage to my heart, liver, lungs, or brain that would kill me in any conceivable way. Flesh heals over. Yeah, it hurts like a royal hag but, in small bits, it is not imminently lethal.

We have determined the HP of Neth's skin. Not how many HP or HD the living plane has because you really cannot kill Neth this way and it therefore becomes irrelevant.

You might be able to do grievous harm by finding out what part of his insides is vital but, I sure as Baator ain't going inside Neth to try and find out.

It's a lifeform consisting only of membranes. Therefore, destroying enough of those membranes should kill it.

Count Nethula... the vampire plane!

Well, Neth himself floats around in the Ethereal, although the amount he can perceive in the Ethereal itself is unclear. However, there aren't a lot of sites in the Ethereal other than other demiplanes.

To explore beyond his own borders, he creates Nethlings.

Neth might be interested in the phenomenon by which the Far Realms protrude parts of themselves onto material reality -- I forget what they're called, but part of the Far Realms manifests itself on the Prime Material or the Outer Planes, warping the locale. Information about such an interpenetration of spaces could pique Neth's interest, leading him to learn more about the phenomenon and attempt to copy it so that he could project himself into other planes. This is doubtless a very dangerous study, especially if Neth and Nethlings are making attempts to contact the Far Realms and summon bits of them into the normal multiverse, and could make a good plot.

I was thinking: there was this 9th level spell/psionic power oposite of spell "Demiplane seed" (wich creates demiplanes). This spell slowly destroys demiplanes.
So here is adventure seed: some villan (prehaps doomguard or some entity feeding on death and dying) has casted "Antigenesis" spell or psionic power on Neth, but spell has manifested in form of wasteing illness. Neth is slowly dying and PC must find cure, and if they save it they could get friend in living demiplane.

But not just any devourers but legendary "Eater of Hearts", mythical "beast" from egyptian mythology (looks like cross between lion, hippo and crocodile), wich dewours hearts (souls) of petitoners who does not deserve afterlife.
(Just imagine bloated undead monstrosity created from parts of 3 animals and eats souls for lunch, I allways liked old monsters with new twist).

Anyways this bloated monster became "unhappy" by meals (heh) provided by soul jugement so it turned rouge and wants to consume living demiplane.

Neth spell "antigenesis" is cast on Neth, and it is slowly dying, so "Eater of Hearts" is waiting for demiplane to be weak enough so it can be devoured in one gulp and hoping for such large meal to make him god of Devourers.

It just seemed as an good idea. Who knows, maybe Ammit was originaly first devourer, created to remove evil souls from circles of life and death so that that evil souls could not became fiends and spread their evil through the multiverse.

But road to hell is pawed by good intentions, maybe Ammit was corupted by evil she was consumed, or to make its job easier she tried to create others of her kind (now to think of it devourers look pretty much mummy like), but her children turned stag and instead of evil souls just devour anyone. (prehaps innocent and good souls taste sweet and evil souls are bitter while nautral are just bland).

Whew, this is lots of good ideas. And more are comming, I am having a storm.

You are wellcome.

I know that I have daviated this thread by this Ammit who want to eat Neth buisness, so I think I will open thread in her (I think it is she) name. With stats and picture and all. Who knows, maybe new advenure will be written in process. You are all invited to participate.

Hmmm, does Neth have a soul? If so where would it go when he/she/it dies?

Along these lines could you magic jar Neth or something similar? (can't remember the name of the spell/power that lets you body-swap, think it's something seed)
Becoming a demi-plane wouldn't be a bad objective for a villan who could then send out hordes of evil Nethlings to feed and grow the plane.

The Villan could trap & preserve his old body (and Neths mind) within himself to keep it safe from harm.

Or the sudden reduction in and change in his senses could drive Neth utterly barmy within hours of going out on walkabout like that - leaving the Villian in a rather precarious situation and forced to hire adventurers to go retrieve the now crazy and possibly a danger to himself demi-plane who absconded with his body...