More Accessing Infinity

A follow up to Accessing Infinity, with more numbers and region ideas. This brings the number list up to d20, for practical use.

d8	Number Title	What It Is...
1	Tattoo Arrow Niner	When trying to represent the biggest rational number, one must develop shorthanded systems. You can see some of them here: https://en.wikipedia.org/wiki/Large_numbers One continues to invent new notations to represent higher ordered calculations. (10↑↑↑10, 10→10→10…, etc.) The arrows-calculations representing other arrow-calculations get increasingly more complex, and take up increasingly more chalkboard room. Eventually you get to the point where you must use surface area on your skin to symbolize the arrows. This is the number written in the arrows encompassing the entirety of one’s skin, using 9’s (because 10’s are less time-efficient to write).
2	Mump’s Number	Nobody actually knows what this number is or what it represents, but it is apparently very very big.
3	Supertask Infinite Beta	An endotemporal being in a lower dimension begins counting upwards from 1 to infinity. We observe this as having been done in a finite amount of time. This is the number they achieve.
4	Flanck’s Number	The theoretical combinatorial analysis of all possible spatial configurations for everything in the universe.
5	Supertask Inverse Gamma	A god halts the person halfway to their destination. Because of this they cannot move. Inverse of the minimum distance they are uninhibited from taking.
6	Naughty Noght	The sum of all naughty numbers (2, 3, 18, 21, 47, 69, 3857, etc…)
7	Divergence Denominator	The number of possible universes, pending universes split at the most minute circumstances.
8	The Argentum Value	The value of a particular person, given in picograms of molten silver, by the Androsphinx of Argentum.

The Near Hotel

Count-Troll Country: It is well-known that Trolls are obsessed with counting. Bridge-trolls in particular, as the vast amounts of time between meals offer ample opportunity to count up hairs on their hands, or stones in a river, or flies in the air.

They hate it when they’re discovered counting, and frequently use their discovery as an excuse to eat a person. (Often, they’ll introduce a ‘riddle’ to offer the victim a chance. These will often be such things they’ve determined, such as “how many leaves are in this forest?”)

In the Infinity Hotel, a troll can start counting and never stop. It might start walking down the corridor and never return. Trolls encountered this way, moving from room to room, counting as they go, will often be extraordinarily famished and ready for a meal.

They’re found, sometimes, in the later sections of the Near Hotel, still trudging on, counting and eating as they go. Sometimes they’re found even further in. Sometimes they change. Those travelled furthest are the most dangerous: they have likely eaten dozens of people on their counting pilgrimage. Nothing compares to the ones that are coming back. But no troll could have possibly gotten to Infinity and back right? Right?!...

When encountered, they are likely to give you a riddle, usually related to some room number nearby. They’ll ask you to factor it, or ask in some convoluted way to divide it by 4. Fail, and they will eat you. Succeed, and they will probably still try to eat you.

Troll Speed without rest: 4mph

Average distance between rooms: 15ft

Troll Speed in terms of rooms: 1,408 rooms/hour

33,792 rooms/day

12,334,080 rooms/year

Count-Troll Country is around room 15 million. Here trolls start to reconsider their pilgrimages, and many stop to live out the rest of their days waylaying visitors and eating hotel mice. They don’t usually know how to use the Mystic Elevator. Heaven help us if they did.

The Last Restroom: This is the last bathroom before there are no more bathrooms… for the entire Hotel (theoretically, there should be an infinite number of restrooms, but nobody’s found any after this one). As it needs to alleviate some ni-infinite peoples, one can imagine it is quite busy.

To accommodate this, The Last Restroom was built on the Complex Plane, and as such it contains both components real and imaginary. This makes it incredibly efficient and useful at times, and impeccably infuriating at others. Hence the duality: 1) You can only imagine where the pee goes! 2) Nobody wants to deal with a mathematically “Complex” toilet.

The Far Hotel

Encrypted Algorithmic Rooms: One creates a variable-dependant algorithm which generates a constantly-shifting room number far into the hotel. Both the equation and the variable become factors in where the room will to be. These types of rooms are typically used for secret dealings.

Variables include:

How does the concierge greet you?

What number does the Goblin Prince wear on his crown today?

How many 9’s and how many arrows will the Human Calculator write between 5:17pm and 5:20pm?

What is the emotional state of the Atomic Bear?

Word Room Numbers: If you treat the alphabet as a base 26 number system, you can create room numbers by writing out words and sentences. A = 1; B = 2 ; … ; Y = 25 (equivalent for base 26 system) ;  Z = 0. These rooms tend to be quite far apart, as a difference in letters early in the sentence will equate to unconscionable distances. All of these numbers remain rational, however, and so they belong in the Far Hotel. Describing places by mnemonic sentences can be more useful than their numbers within certain ranges.

These rooms are frequented by Paromancers, who establish alcoves in effort to uncover the secrets of the Hotel and language.

Sentence Room Examples:

“Faraday”

6,1,18,1,4,1,25

“Derivatives Are Hardly Just That”

4,5,18,9,22,1,20,9,22,5,19,1,18,5,8,1,18,4,12,25,10,21,19,20,20,8,1,20

“The Wailing Bell of the Endless Hotel

Carries Far Indeed,

Though Strong as It May, As Loudly It Bay

None Will Hear It Plead”

20,8,5,23,1,9,12,9,14,7,2,5,12,12,15,6,20,8,5,5,14,4,12,5,19,19,8,15,20,5,12,3,1,18,18,9,5,19,6,1,18,9,14,4,5,5,4,20,8,15,21,7,8,19,20,18,15,14,7,1,19,9,20,13,1,25,1,19,12,15,21,4,12,25,9,20,2,1,25,14,15,14,5,23,9,12,12,8,5,1,18,9,20,16,12,5,1,4

Source: Charles Gilchrist

The Deep Hotel

The Mail Room: There may be an infinite space in the hotel, but somebody still needs to deliver the mail. Nobody is sure where the Mail Room came from, who runs it, or how it delivers the mail to every conceivable place within the hotel, but it does. Infinity finds a way.

It is a marvel of automation and magic - letters and packages sort themselves, flying through the air like swooping owls, or rolling along the ground like stomping automaton. A series of chutes, conveyor belts, fans, pulleys, levers, and tornados whisk the mail away to wherever it may.

It all makes use of the Mystic Elevator, with entire compartments stuffed to the seams with oblong packages and crisp letters to be whisked to who-knows-where. Many have surmised that the Mail Room is part of the organism of the Hotel, much like the Elevator itself.

More mystifying, however, are the addresses on the letters and packages. They are written in a number system completely alien to human understandings of mathematics. More so than that, they aren’t even written in a system used by other rooms of the Deep Hotel, giving rise to the belief that there are several incomprehensible alien systems of mathematics, some more convenient or alien than others.

The addresses are as strange and varied as can be: some hurt to look at, some smell strange, or must be licked to understand the address, or are very clearly modified demonic summoning circles. Does Yog-Sothoth run the Mail Room? The strange man in the Lobby says: “yes!”. Given the room’s size, it’s not impossible, like everything in the Hotel.

The Great Fold: Space gets strange in the Deep Hotel. Things stop being a neat linear algebra somewhere along the line and start being a very messy linear algebra. The Hotel still progresses in a line, mind you, but it is a line that folds and warps, that bends back upon itself and does several 360 spins before pirouetting to mad applause. In The Great Fold, this linearity is pushed to the limit.

To say this is confusing to newcomers is an understatement. They soon find that marching forward isn’t quite so, well… forward. They find that rooms don’t follow any logic they can understand, leaping plots of distance, speed, and time in ways that make them rather inaccessible.

Things found here are strange and inhospitable: they move about the hallway like video game glitches, darting in and out of higher dimensions without care to frivolous lower beings. They are facsimiles of being. Don’t touch them.

Home of the Gelatinous Tesseract. Or, at least, its main entry point into our reality. Its presence attracts multitudes of teleportation aficionados.

Counterspell

Looking back at this old post the other day, thinking about Counterspelling shenanigans. In the post I proposed a static d10 roll for counterspelling. Here's a second go at some counterspelling mechanics, to try and get something more integrated and less clunky.

Also, Betty Bacontime's comment for that post whetted my appetite for flavor, so let's make more of that.

Wizard City Counterspell

The idea is that you superimpose this template onto any system that uses a d20 saving throw (B/X, 5e, GLOG, etc.). Anytime you get a "critical hit" on the save, you may choose to Counterspell it, according to your class.

Numbers listed below are the minimum roll to "critically hit" the Save.

	Level
Class	1	2	3	4	5	6	7	8	9	10
AMWAT	19	19	18	18	17	17	16	16	15	15
Mo-RON	-	-	-	-	-	20	20	20	20	20
Spellshark	20/19*	20/19*	20/19*	20/19*	19/17*	19/17*	19/17*	19/17*	18/15*	18/15*
T-Man	-	-	-	20	20	20	20	20	20	19
Wizard	20	20	20	20	19	19	19	19	19	18

* Roll required if the target owes you money.

If your spells use attack rolls, then low ‘critical fail’ rolls apply. So a spell attack roll of a 1 on a level 1 wizard will produce a counterspell. A spell attack roll of 1-2 against a level 1 AMWAT will produce a counterspell.

Class Templates
Basically, you play the system you want with the class you want, and superimpose the above Counterspelling mechanic onto that system. I make no promises of balance.

Class	Old School Base Template (B/X, Labyrinth Lord, DCC)	New School Base Template (3.5/Pathfinder/5e)
AMWAT	Fighter	Barbarian/Fighter
Mo-RON**	Dwarf, Halfling, Fighter, any non-Elf demi-human.	Barbarian, Fighter, Monk, Ranger, Rogue, Warlock
Spellshark	Elf	Any Half/Third Caster, Sorcerer
T-Man	Thief	Rogue, Monk
Wizard	Magic-User/Wizard	Wizard

** Class used depends on what kind of chassis is currently equipped.

Counterspells

Big thanks to Betty Bacontime over at Paper Elemental for coming up with some of these, which were too good to iterate upon. For old school systems that don't have wizard schools, just pick the wizard counterspell that appeals most. Or hell, go with all of them. Have fun!

Class	Counterspell
AMWAT	Bat that spell right back at sender. If it was an area spell, the new spell area is centered on the caster.
Mo-RON	Absorb the spell, adding its spell level to your next chosen attack roll, skill check, or save. Only one spell may be stored this way.
Spellshark	Bank the spell, allowing you to recast it as your own within 24 hours, at which point the spell is lost.
T-Man	Sequester the spell for 1d4 Rounds. Spell effect happens on the exact space you’re in now upon expiration. Duration roll explodes. Every time they explode move the time up one time category: Rounds -> Minutes -> Hours -> Days -> Years -> etc.
Wizard, Abjuration	Utilize a spell magnet, pulling the spell towards the device. Chuck the device like a grenade. The spell will hit it instead. 30ft range on that sucker.
Wizard, Conjuration	Conjure a minor and possibly adorable creature to take the spell hit for you at any space between you and the caster. Pigeons are popular.
Wizard, Divination	Foresee an improbable outcome that foils the spell. The caster slips on an oil slick, two orphans on a sled come carringing through the battle and accidentally intercept the spell, a wagon full of cabbages falls from the sky. DM discretion.
Wizard, Enchantment	Charm the spell, making it think you’re an ally. The spell, being very confused, will mull about for 1d4 Rounds before chasing after the closest target.
Wizard, Evocation	Evoke an exact counter to the spell being cast at you. A fireball is met by a waterball. A summoned bear is met with a bear trap. DM discretion.
Wizard, Illusion	Haha! That was an illusion, fool! Spell hits illusory you. You get to teleport anywhere within 30ft and say that’s where you were when the spell went off.
Wizard, Necromancy	Kill the spell, then raise it from the dead. It is now a zombie spelll. It takes the form of a shimmering floating skull, lingering in a space near the caster. After one round it will unleash the spell on anybody who goes within 5ft of it, forever. It’s more or less a visible land mine now.
Wizard, Transmutation	Transmute the spell into something less or possibly quite more scary, like a cloud of glitter or an portrait of your mother.