INFINITE TERROR

Posted: Wed May 02, 2007 11:24 am

Okay so today's comic speculates about nesting ghosts like Matryoshka dolls (those Russian nesting dolls you've probably seen). The question is, can you really have arbitrarily-large TERROR in a finite volume?

I was intending the nesting doll metaphor to be kind of loose, figuring that if ghosts can walk through solid objects, then they can walk through other ghosts, which means you could have them all standing in the same space. But what if you do need a ghostly shell to keep the ghosts from merging together?

BN sent me this email that examines that possibility!

bn wrote:

so what t-rex is proposing is that the scary part of a
ghost is the surface area, rather than the volume. and
from this he deduces that a russian doll ghost could
possibly be INFINITELY scary. is this the case?

so i guess the question you should ask yourself is:
does a ghost "scare membrane" have depth?

if the curtain that is a ghost has depth e,
what is the surface area of a spherical nesting doll
ghost of radius R?

hmmm. what's the surface area of one ghost of radius
r?
=>4*pi*r^2
total surface area, where N=R/e

SUM{n from 1 to N} (4*pi*e^2 n^2}
=4*pi*e^2 SUM(n^2)
=FINITE

hm. so if the depth of a ghost scare membrane is
finite, then the scaryness of a nesting ghost is also
finite. but how big is it?

what's the volume of all these nesting sphere ghosts?
the volume of one spherical ghost is
4/3 *pi*( (r+e)^3-r^3)
=4*pi( er^2+r*e^2+(1/3)e^3)

so the total volume where N=R/e will be
=SUM{n from 1 to N} (4*pi* (
e(n*e)^2+(n*e)*e^2+(1/3)e^3) )
(recall that this =4/3*pi*R^3 )
>4*pi*e^3 SUM(n^2) (= surface area *e)

so the surface area is related to the volume by:
Volume / e = total surface area.

so at the limit of e->0, the finite volume will give
an infinite area and thus, be infinitely scary.

but is this a realistic assumption? hard to say:

in general relativity, once a star "dies" and is no
longer capable of maintaining fusion, one possible
end-state is a black hole. black holes are pretty much
ghosts of stars... in that, the position and
impression of the star still remains, though nothing
else of the star remains in place. further, in terms
of regular words, a black hole is characterized only
by a 2-dimensional boundary: the even horizon. the
event horizon has no depth, it's an infinitesimally
thin curtain separating the happy normal universe from
the horrors of gravitational crushing hell. Finally,
the scaryness of a black hole is relatable to its
area: the black hole of a baseball would be very small
indeed, and the black hole of the earth or the sun
would also be pretty small compared to the regular
world. uhhh... 2m=r-> as you increase the area
linearly the mass increases quadratically.

so t-rex's picture fits well, kind of. we're drawing
an intuitive analogy, and not saying that they are
equivalent, so i won't go into how the picture doesn't
fit.

on the other hand, in quantum mechanics, there is
generally assumed to be a fundamental length scale,
beyond which length is meaningless. thus, an
infinitesmally thin sheet cannot exist. at the very
smallest, the ghost would have the width e= plank
length. which is very small indeed. but it's not
zero. thus, a nesting ghost could be VERY SCARY, but
not infinitely scary.

finally, the universe has not existed for an infinite
amount of time, and so it's not obvious how an
infinite number of ghosts could nest together to be
infinitely scary.

this concludes my discussion on the subject.

bn

an addendum wrote:

oh, so lets suppose that ghost membranes have variable
widths, which they can make arbitrarily small.

the russian doll of ghosts would be a countably
infinite degree of scaryness at the very most.

on the other hand, if the ghosts are indeed
2-dimension, then the full-up russian doll of ghosts
would be uncountably infinite!
so when you see one, chances are YOUR SOUL IS ALREADY
SOMEWHERE INSIDE THE GHOST!!!!!!

awesome.

Joined: 24 Jan 2006 Posts: 2468 Location: Utah

Haha, bn is just far too awesome for words

Posted: Wed May 02, 2007 11:49 am

Do they teach a class on this somewhere? They should.

Joined: 15 Oct 2006 Posts: 278 Location: The Future

Do you mean the math stuff? Or the ghostology?

Posted: Wed May 02, 2007 2:03 pm

i think he obviously meant the ghostology. There are "real" academics who do work in para-studies, like measuring the physical effects of seances and whatnot.

Joined: 17 Jan 2006 Posts: 1019 Location: Finland

Like the doctors Egon Spengler, Raymond Stantz and Peter Venkman.

Joined: 02 May 2007 Posts: 1

You know what would be even scarier than nested ghosts? A fractal ghost!

Posted: Wed May 02, 2007 3:22 pm

I guess I meant a class on the math of ghosts.

Joined: 17 Nov 2006 Posts: 510

What bn didn't address is the limits of human scariness perception. Every human will only be able to distinguish a limited number of overlapping ghosts.

H = total horror
h = horror per ghost
n = number of ghosts present
m = maximum ghosts detectable

H = h * min( n, m )

Infinitely large values for n produce no more total horror (H) than when n = m. For the highest possible H values, you want to be increasing h, not n.

Also, linear growth requires infinite ghosts to approach infinite horror. T-Rex should work on is a method for making the horror of each ghost increase the scariness of all the other ghosts present, such that there is quadratic growth in scary. That way total horror (H) will be approaching infinity at a faster rate and T-Rex will achieve higher horror per ghost values.

---

Another idea would be a recursive ghost: the ghost of a person who's ghost killed him(or her)self. There you have an infinite number of ghosts and victims all in one entity.

true falcons will attack children · Posted: Wed May 02, 2007 4:29 pm

Joined: 08 Dec 2005 Posts: 9009 Location: SOMEWHERE EXTREME

Guys did you know that this is basically what Scientologists believe? That everyone is haunted by tons of ghosts and as people die their ghost, along with the ghosts haunting them, go out and find a baby to haunt? So as time goes on people are haunted by more and more ghosts and their lives get crappier?

I think they call them body thetans or something instead of ghosts, though.

Posted: Wed May 02, 2007 7:11 pm

Wow. I thought they were weird. I didn't know that they were TERRIFYING.

Posted: Wed May 02, 2007 7:16 pm

Also they are the ghosts of ancient humans who were teleported into a volcano by an alien space warlord.

Joined: 26 Apr 2007 Posts: 2500 Location: erie, pa

otie wrote:

Like the doctors Egon Spengler, Raymond Stantz and Peter Venkman.

I have to quote this because it's probably the best reply in the thread and nobody responded.

Posted: Wed May 02, 2007 7:30 pm

I think we should measure overlapping ghosts with a g-prefix. six ghost would be a g-g-g-g-g-ghost, and ovet time you'd end up with g^23host

Posted: Wed May 02, 2007 7:30 pm

six ghost

Joined: 17 Nov 2006 Posts: 510

Only Shaggy could discern the number of overlapping ghosts

Joined: 15 Oct 2006 Posts: 278 Location: The Future

Miles wrote:

I guess I meant a class on the math of ghosts.

Yeah, so klaw, you would be looking for a BOOlean algebra class, if you'll pardon my horrifying pun.

Posted: Thu May 03, 2007 12:43 am

Future Skeleton wrote:

Miles wrote:

I guess I meant a class on the math of ghosts.

Yeah, so klaw, you would be looking for a BOOlean algebra class, if you'll pardon my horrifying pun.

*makes joke about only DEAD people reading hex.*

Posted: Thu May 03, 2007 9:45 am

Half a Bee wrote:

Only Shaggy could discern the number of overlapping ghosts

hahaha awesome

this was a very awesome comic, ryan. very funny i thought.

Joined: 26 Apr 2007 Posts: 2500 Location: erie, pa

Future Skeleton wrote:

Miles wrote:

I guess I meant a class on the math of ghosts.

Yeah, so klaw, you would be looking for a BOOlean algebra class, if you'll pardon my horrifying pun.

DEAR GOD MY BRAIN

Posted: Thu May 03, 2007 12:56 pm

justinpie wrote:

I think we should measure overlapping ghosts with a g-prefix. six ghost would be a g-g-g-g-g-ghost, and ovet time you'd end up with g^23host

seconded

Posted: Thu May 03, 2007 3:20 pm

I think we really need to consider issues relating ghosts, singularities, and the holographic principle here.

Axiom 1: Ghosts are compact regions.
Axiom 2: Ghosts are, or have, some form of physical energy.

An infinitely nested ghost would have infinite energy density. But any compact region with energy density above a certain threshold will collapse into a singularity.

Could some ghosts be black holes? If a sufficiently terrifying ghost haunts you, would there be no return -- you simply join the ghost directly? Or perhaps it only takes part of you, leaving you to suffer as a terrified, empty shell.

According to Hawking Radiation, black holes evapourate without continued input of energy; a human-sized black hole would evapourate pretty quickly. Perhaps that is why it needs to haunt people -- the ghosthole must constantly add to itself to survive?

I mentioned the holographic principle because I thought I could mention something about only needing to understand the state of the shell but ... I can't think of anything anymore.

There is also the nagging issue that a finite universe could not produce an infinite ghost...