[Ar-list] mindrunning and the Matrix

[Carter Butts]

W Isaac Carroll wrote:


> Carter, I've read through the Mindrunning MRS and I have some questions and
> comments for you.
> 
> Hacking into the Matrix as it is portrayed in the movie seems qualitatively
> different from mindrunning described in the MRS. Conflict in the Matrix is
> between separate beings inside the mental world, rather than the conflict
> being between an intruder and the world itself. The Mindrunning MRS does not
> (yet) cover multiple recursive minds struggling within a paradigm which none
> of them directly controls, but can only influence to greater or lesser extent.
> 


Yes, that is true.  The Mindrunning MRS was really inspired by a more 
"psionic" model than was The Matrix, although it is obviously the case 
the man/machine interfaces are related to the former as well.  (Just in 
case anyone here is confused about this, the Mindrunning MRS doesn't 
have anything to do with The Matrix per se, and predates it by several 
years...it just happens to deal with some similar issues.)  The mental 
combat which took place as part of the backstory for the character of 
Hamash in The Phoenix Cycle (the first AR test campaign, later novelized 
in part by Karim) was an early template for the idea of mindrunning, 
although I was also inspired by a variety of other sources.  (The stuff 
on somatic markers, for instance, is loosely based on some work in 
neurobiology, although I've obviously glammed it up quite a bit.) 
Anyway, the current MRS focuses more on two-person interchanges, 
attempts to manipulate characters' behavior, and mental "programming" 
(for good or ill).  The action of The Matrix is really _netrunning_ 
rather than mindrunning, and hence there's not much support for it at 
present.  (Not that it can't be added, obviously.)


> From the movie I get the impression that an infiltrator's mind is actually
> transferred into the Matrix when he hacks in. The infiltrator's body is
> (mostly) inert for the duration, and if the link is broken prematurely, both
> mind and body die. This may need to be handled differently than the creation
> of a recursive copy.
> 


Yes, this is IMHO a silly thing about the movie which is happily and 
intentionally absent from the MRS.  :-)  Under the Mindrunning rules, 
you don't actually "go" anywhere when you engage in mindrunning, nor can 
your mind be "trapped" per se.  (Well, recursive copies _are_ trapped in 
a certain sense, but they're a rather different sort of beast.)  This 
isn't astral travel, after all!  But, in any event, to be faithful to 
the movie you should amend this so as to allow for more mind/body 
feedback (including the "pulling the plug" rule).  These kinds of things 
are pet peeves of mine, but then I was not consulted by the movie 
makers....  ;-)


> The next question is about basic AR mechanics. Is there a standard mechanism
> for a situation where a character wants to engage in a continuous form test
> until success is achieved? The continuous form test assumes that the character
> already has decided how long he will be performing the action.


The answer here is "no" (IIRC).  Ira's suggestion of using the inverse 
minimum SM seems quite clever...a bit cumbersome, perhaps, but I cannot 
help but think that it Partakes of the AR Nature.  I cannot remember 
whether Paul ever came up with a rule like this for his Melee MRS; since 
I can't find a copy of it on my hard drive, I can't check to be sure.

WARNING: Math-intensive digression follows!!!

Anyway, the way this "should" be done is something like the following. 
Assume, for the moment, that "opportunities" for success arise randomly 
via a Poisson process with rate r, and that each of these corresponds to 
a standard form test on attribute a.  Then it follows that the 
probability density of the time-to-success is given by a mixture of 
Gamma distributions, i.e.:

f(t) = Sum( Gamma(x | r,i) Geom(i | DRF(a)), i=1..Inf )
      = Sum( (x/r)^(i-1) exp(-x/r) (r(i-1)!)^-1 (1-p)^(i-1) p, i=1..Inf )
      = (DRF(a)/r) exp(-(x DRF(a))/r)
      = Exp(x | DRF(a)/r)

That is, the mixture turns out to be exponentially distributed with rate 
parameter DRF(a)/r.  Cool, yes?  Even cooler, I can tell you how to draw 
from this distribution using dice.  Generate a uniform deviate on the 
(0,1) interval using your percentile dice (or whatever), and call this 
quantity u.  Then

-(DRF(a)/r) ln(u) ~ Exp(DRF(a)/r)

i.e., logging the roll (expressed as a decimal) and multiplying it by 
the negative of your rolling target divided by the rate gives you the 
time taken for a success to be accomplished.

No, don't thank me yet.  There's more. :-)

The continuous test, itself, is not very well justified.  If we were 
doing this the _right_ way, we would think of "opportunities" as Poisson 
distributed with rate r, and then consider the number of successes 
within a given time interval as a Binomial mixture.  In particular

f(x) = Sum( Bin(x | i,DRF(a)) Poi(i | rt), i=0..Inf )
      = Sum( iCx p^x (1-p)^(i-x) exp(-rt) (rt)^i/i!, i=0..Inf )
      apx (DRF(a)rt)^x exp(-DRF(a)rt)/x!
      = Poi(x | DRF(a)rt)
      apx N(x | DRF(a)rt, DRF(a)rt)

That is, the result turns out to be approximately Poisson distributed 
with rate parameter DRF(a)rt, which is in turn approximately normal with 
mean and variance DRF(a)rt.  _If_ the DRF were a standard normal CDF 
(which it isn't, although it could be in the future), then we could 
simulate this by the expression

IDRF(u) Sqrt(DRF(a)rt) + DRF(a)rt

which, I admit, is a little cumbersome (that square root, in particular, 
is very annoying), but provides an excellent simulation of the 
underlying process.  The same idea, BTW, can be used to approximate the 
net successes/failures for a two-sided continuous form test (i.e., where 
your gains and losses _both_ count) by using the properties of normal 
sums, but I shan't go into that at present.

One more digression, and I shall attempt to get back to work.  :-)  An 
alternative to the current AR test mechanic would be to define the DRF 
to be the normal CDF, and to make the test algorithm as follows:

1. Find the attribute to be tested, a, including any modifiers.
2. Roll percentile dice, calling the result u.
3. If IDRF(u)+a>0, success occurs (else failure).
4. The "success factor" (rather than success margin) is equal to 
IDRF(u)+a; this would multiply some standard outcome variable (analagous 
to the ORN) to provide extent of success/failure.

The above is faintly cool in that it generates results which are on the 
real line, and which are always interpretable in terms of standard 
deviations.  OTOH, this would require us to put attributes in these 
terms as well, which would make a lot of other things more difficult. 
At any rate, I'm not advocating such a drastic change at the moment, but 
just thought I'd mention an interesting variant of the current strategy. 
  Ruminating on such things can be a useful way of finding potential 
game system improvements.....

-Carter