Statistical Probabilities - Factors and Equations

[Unimatrix Q]

What factors were used by Bashir and his thinktank? How did they use them? How would a paper of them look like?

 

[Marc Voorhees]

What factors were used by Bashir and his thinktank? How did they use them? How would a paper of them look like?

Well, I don't recall it being discussed, however:

1) it is possible to model a life expectancy of each class of ship the federation makes. (survivability models)
2) There are construction forecasts for how many ships can be built and replaced.
3) Would be easy enough to take the first two models and use them in conjunction with Dominion fleet movements to identify high probability targets and the necessary allied fleets numbers needed to defend or pull back to consolidate
4) Eventually, there are no more ships, no more defenses, and the death toll is higher than is sustainable.

Seems like it would be a fairly straightforward model on some level, with enough data, the entire war zone can probably be reduced to a dozen or so equations that nest inside of each other.

Source: I do the Maths sometimes.

 

[Unimatrix Q]

What factors were used by Bashir and his thinktank? How did they use them? How would a paper of them look like?

Well, I don't recall it being discussed, however:

1) it is possible to model a life expectancy of each class of ship the federation makes. (survivability models)
2) There are construction forecasts for how many ships can be built and replaced.
3) Would be easy enough to take the first two models and use them in conjunction with Dominion fleet movements to identify high probability targets and the necessary allied fleets numbers needed to defend or pull back to consolidate
4) Eventually, there are no more ships, no more defenses, and the death toll is higher than is sustainable.

Seems like it would be a fairly straightforward model on some level, with enough data, the entire war zone can probably be reduced to a dozen or so equations that nest inside of each other.

Source: I do the Maths sometimes.

Thank you. And how would the longterm developments ( Successful Rebellion against the Dominion for example) be predicted?

 

[Nebusj]

Thank you. And how would the longterm developments ( Successful Rebellion against the Dominion for example) be predicted?

Have you ever played the Europa Universalis line of games? It's great, for people who get into this sort of thing. It's this vast grand strategy game, with hundreds of nations in the world. It includes simulations of economic, diplomatic, scientific, and demographic developments.

Some of the games are incredibly fine-tuned, simulating the progress of the World War II era hour-by-hour. Some are broader but still breathtaking, simulating the world day-by-day from the time of the Hundred Years War through to the Napoleonic era. They're all fantastically complicated and if your head was exploded by playing Sid Meier's Civilization then the games aren't for you.

However. They create mock histories that are fascinating, and compelling. If you pick some insignificant little power and let the artificial intelligence play out the world powers you can create histories that echo what really happened, or that diverge from ours in ways that make sense. (My favorite was a 16th-to-18th century in which Europe congealed into several Great Powers early --- a Great Britain, a France-and-Spain, an Italy-and-Balkans, a Germany-and-Poland --- remarkably peacefully.)

Just a game? Sure. Of course. But the principle of modeling social interactions, and of building models of complicated and even unpredictable things out of simple models, is reasonably sound. It isn't very far, spiritually, from thermodynamics. (Indeed, J W Gibbs, who created much of the standard mathematical formulation of thermodynamics, thought a thermodynamics-of-history at least attainable in principle.)

Would such a thing work? For games, sure. For stories, magnificently, even if its science-fictional version of psychohistory is surprisingly under-explored. For actual history? ... I'm skeptical. In making short-term predictions, sure. It's not very different to the normal sorts of demographic forecast that any responsible planner will consider in working out what a city should look like twenty years hence.

For longer-term forecasts, or forecasts that have to include new philosophies or inventions? I doubt we could do that. Of course, they're working with a mathematics, and a philosophy of mathematics, several centuries beyond ours.

 

[Marc Voorhees]

TL;DR "Modeling this is all about figuring out when the Dominion woudl say screw it and kill everyone instead of trying to administer an occupying force"

Mostly right I would say. Love the introduction to that gaming world, have never really done that, so I may be spending some time fiddling with that. You are 100% correct that near term models are all that can probably realistically done, but I am not really sure that they are working with a higher thinking of mathematics than us.

Everything in Star Trek seems to be grounded in reality from a certain standpoint (Here I am now waiting to be lambasted about all the stupid shit they have done in various episodes) an I don’t think that the actual modeling process that they use is any different fundamentally than we do. Sure, they have a much…….different…….approach to physics, but when watching Geordi run modeling simulations in Booby Trap, seems well grounded in the same steps and calculations that we use today. Maybe I am wrong, but hey, welcome to the internet J

Now, to answer the question at hand; how do we model the success of a rebellion and their chances of success?

First things first, what is the objective of the rebellion? To overthrow? To disrupt to allow an outside ally to take out the invading party (Think Maquis in WWII or the Cardassian Resistance)? Or some other variation?

At this point in the war, assume that it ended immediately and Earth and the Federation were occupied. Well, there is more than likely no outside power to overthrow the dominion, therefor the terran rebellion would have to win on its own. This is where it starts to get a bit hairy.

Rebellion wise, it is necessary to create enough damage or disruption that it hurts the enemy, but not enough that they respond out of line. An example of this would be Dukat’s discussion in Waltz where he patted himself on the back when describing his response to terrorist attacks as being carefully tempered. If he eradicated all Bajorans after the first terrorist attack, then the rebellion failed big time.

Modeling wise, it is necessary for the rebellion to participate in activities x where the probability of detection is very very low and the probability of damage or disruption is high and the outcome expected damage is not high enough to trigger the “nuclear option”. These types of activities in reality are very low, especially given 1) not talking about a city or country, talking about multiple planets. Communication is traceable and P(success|number of planets to coordinate) is probably .0000000001 or smaller (guessing, but reasonable, and definitely a function of the number of planets).

So let’s look at the Nuclear Option as Eradicate a planet population. At what point does the Dominion use this? In my opinion, almost immediately. Weyoun was talking about eliminating all of Earth’s population as soon as they conquered it. Even if they showed mercy and gave it a shot, at the first sign of an organized uprising, Earth and other planets, would be barren as hell.

The long and short of it is that a rebellion is only successful if there is an advantage somewhere that the rebels could exploit to buy time for outside help to arrive or the other side to realize it isn’t worth it.

The Maquis: Hell of a thorn in the Vichy’s side, bought time to allow the Allies to have a pipeline into the country. Nazi Germany fighting a two front war/ The dominion would not have this distraction, or would be large enough to overcome it.

Cuban Rebels: Bay of pigs was a disaster. Waited for outside help that never really arrived, revolution failed

American Revolution: Advantage of distance from dominating force, time to travel was prohibitive, advantage of lay of the land and the base of the dominating power was concentrated elsewhere. Also, French outside help or the revolution would have failed.

Rebellions that succeeded were about cutting the head off of the leadership before the body knew what hit it (French revolution, Bolshevik revolution). The terran resistance would not likely be able to do this in our scenario.

Actually modeling this is all about the assumption of when The Dominion would use the Nuclear option.

I will stop rambling now

 

[Marc Voorhees]

Don't let this die! Combining my favorite hobbies Math and Star Trek has been a blast!

 

[Unimatrix Q]

Don't let this die! Combining my favorite hobbies Math and Star Trek has been a blast!

I concur! I would really really like to read a fanfic version of Bashir's report!

 

[Ember]

On that topic, I think he played some really advanced chess with the various factors as pawns, taking into account the usual behaviour and reactions of various galactic factions as well as individuals on various situations, extrapolating different scenarios and rating them by likelyhood.

They would have been better off being given unrestricted access to Starfleets archives and intelligence records, while being asked to build the ultimate rapid-response pocket battleship, or rather "Design us a ship that flies circles around the Jem'Hadar, has the firepower of a Romulan Warbird, the size of a Klingon Bird of Prey and design us a Von Neumann universal constructor for a drydock that builds us a few thousand of these ships before we lose the war."

 

[Timo]

The intriguing thing here is, Bashir and the Jack Pack would be at a really major disadvantage compared with the analysts of the real world. What enemy in the course of Earth history has been as unknown as the Dominion?

Say, the odds of a rebellion succeeding would depend on the anticipated Dominion response to such an event. Bashir has seen the Quickening, but he also ought to be aware that it is just one arrow in the big quiver of the imaginative Dominion that revels in its ability to quell resistance through deterrent. What good is modeling when a key parameter is known to vary within limits so vast the analysts can't even see the endpoints?

Timo Saloniemi

 

[Marc Voorhees]

The intriguing thing here is, Bashir and the Jack Pack would be at a really major disadvantage compared with the analysts of the real world. What enemy in the course of Earth history has been as unknown as the Dominion?

Say, the odds of a rebellion succeeding would depend on the anticipated Dominion response to such an event. Bashir has seen the Quickening, but he also ought to be aware that it is just one arrow in the big quiver of the imaginative Dominion that revels in its ability to quell resistance through deterrent. What good is modeling when a key parameter is known to vary within limits so vast the analysts can't even see the endpoints?

Timo Saloniemi

Modeling is all about assumptions. Sometimes you have to start with nothing more than a guess and go from there.In this case, you assume the worst at some threshold and then figure out how long it takes to get to that threshold. The modeling doesn't have to be particularly accurate in order to show that a revolution is not likely to be successful!

 

[Unimatrix Q]

Maybe Bashir took possible arrival of an unknown sympathetic species in Ex-Federation Space as a variable for a successful rebellion. Or internal changes of the dominion throuh outside or inside influences.

 

[Nebusj]

Maybe Bashir took possible arrival of an unknown sympathetic species in Ex-Federation Space as a variable for a successful rebellion. Or internal changes of the dominion throuh outside or inside influences.

Also, if Bashir was even the slightest bit genre-aware, he'd realize that if things ever got too dire it would turn out the situation was an alternate timeline, and some Hero would travel back in time to prevent it ever coming about. So the most dreadful futures could be ruled out right away.

Oh, something about future-predicting I had forgot to mention. There can be a fair bit of work done through the magic of game theory, the study of how people seeking to maximize some benefit will choose from among sets of actions. Game theory got a big burst of real-world application in the early Cold War as American strategic planners realized some chilling implications.

Specifically, since war with the Soviet Union was inevitable, and the Soviet Union was the weakest it could plausibly be at the end of World War II, and would only gain strength as it rebuilt, the conclusion is obvious. The war would be least bad --- least long, least costly, least destructive to all human and other life --- if it were fought as soon as possible. Certain flaws in the reasoning are now obvious.

The field is still a useful one, and mathematically quite fruitful. Applying it does require that the reasoning be tempered with psychology and with the challenges of having imperfect information. (Imperfect-information games are studied mathematically as well, of course, it's just usually easier in a theorem to say something about what is not known.)

 

[at Quark's]

To quote Bashir:

According to our analyses, there it is, they'll vote to abandon their non-aggression pact with the Dominion at next year's plenary session. By which time, internal pressures between the Cardassians and the Dominion will have erupted, and after three years six months and twenty seven days, we predict that

The way our statistical analysis works, the farther into the future you go, the more accurate the projection. It's based on a kind of non-linear dynamics, whereby small fluctuations tend to factor out over time.

I'm curious (no, let's be straightforward: skeptical) whether such mathematics could actually ever be developed. For bounded systems with limited inpredictability (and unknowns), I might believe a statistical approach might work. But for entire societies and still being able to come up with projections that are accurate to the day? Sounds akin to magical "psychohistory" to me ... and at least, in that series, Asimov had the good sense to mention margins of uncertainty (both in time and in probability) again and again...

 

[intrinsical]

The part about non-linear dynamics cancelling out is pretty much pure hogwash. When multiple random variables interact, especially when they are non-linear variables, the system is going to be mathematically chaotic. Meaning instead of large swaths of variables cancelling out each other, what's more likely to happen is each variable's starting condition becomes critically important. Any minor change in the starting values is likely to result in drastic changes in the future.

However I can say that even today, there are techniques such as Bayesian Graphical Models that can manage very sophisticated probabilistic/statistical inferences on several million random variables. With several hundred years of advances in computing technology, algorithms and mathematics, I can easily imagine an advanced version of Graphical Models being applied on trillions of random variables. Such a system *might* just be able to compute the outcome of the war, conditioned upon how accurately Bashir is able to model all the forces at play.

 

[Marc Voorhees]

To quote Bashir:

According to our analyses, there it is, they'll vote to abandon their non-aggression pact with the Dominion at next year's plenary session. By which time, internal pressures between the Cardassians and the Dominion will have erupted, and after three years six months and twenty seven days, we predict that

The way our statistical analysis works, the farther into the future you go, the more accurate the projection. It's based on a kind of non-linear dynamics, whereby small fluctuations tend to factor out over time.

I'm curious (no, let's be straightforward: skeptical) whether such mathematics could actually ever be developed. For bounded systems with limited inpredictability (and unknowns), I might believe a statistical approach might work. But for entire societies and still being able to come up with projections that are accurate to the day? Sounds akin to magical "psychohistory" to me ... and at least, in that series, Asimov had the good sense to mention margins of uncertainty (both in time and in probability) again and again...

Yeah, This is complete hogwash. Again though, you can model things that are pretty damned complex. Never seen a prediction to the day however.

The part about non-linear dynamics cancelling out is pretty much pure hogwash. When multiple random variables interact, especially when they are non-linear variables, the system is going to be mathematically chaotic. Meaning instead of large swaths of variables cancelling out each other, what's more likely to happen is each variable's starting condition becomes critically important. Any minor change in the starting values is likely to result in drastic changes in the future.

However I can say that even today, there are techniques such as Bayesian Graphical Models that can manage very sophisticated probabilistic/statistical inferences on several million random variables. With several hundred years of advances in computing technology, algorithms and mathematics, I can easily imagine an advanced version of Graphical Models being applied on trillions of random variables. Such a system *might* just be able to compute the outcome of the war, conditioned upon how accurately Bashir is able to model all the forces at play.

Predicting the outcome of a war or battle is conceptually straight forward, and has been done for decades. Calculating the probability and dates of uprisings and treaty violations is a bit beyond reality I think. The Bayesian methodologies have an interesting extension into the future with the vastly more powerful computers.

 

[kkt]

It's worth making the attempt to predict, but it's hogwash to think you can account for everything that might have an effect, and still more hogwash that it would get more accurate farther in the future. Did the Germans account for the possibility that some Brits might invent effective electromechanical computers and be reading all their Enigma coded messages? Did anyone account for the Manhattan Project? (Okay, didn't change the outcome, but changed the timetable and the postwar world.)

Earth's atmosphere is a whole lot more friendly to predictions than actions of intelligent beings across the galaxy, and even the 12-hour weather forecasts miss things at times, and any forecast farther ahead than three days is a wild guess.