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Subject: The Firing Squad Problem rss

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...should really be called the Line of Soldiers Management problem....but sensational titles sell.

That said:

The FS Problem is an automation/IT problem - but as I read it, this must have been something Frederick the Great and others had to think about and possibly write up.

http://www-cs-faculty.stanford.edu/~eroberts/courses/soco/pr...

It speaks to the issue of command and the reason why things don't happen and why things do happen, and how you make it more reliable and more efficient:

=====================

Picture a group of soldiers standing in a line, with a general at one end. Assume that all of the soldiers are mentally keeping track of time by counting at the same speed. In other words, after a certain signal, all soldiers should be counting out zero, one, two, and so forth, at the same time as everyone else. At every count, each soldier looks at their neighbors, considers what they themselves were already doing, and decides what to do next, completely according to what they see. Of course, the two soldiers on the ends have to act according to what themselves and their one neighbor is doing. In more mathematical terms, the actions, or state, of each soldier at time t+1 depend on the actions of itself and its neighbors at the previous time t. For all soldiers, there is a limited, or finite, amount of actions that can be done, and there are set rules for finding out which actions follow given observations. Using technical terms, the soldiers can be seen as synchronous, finite-state machines, whose states at any given time are dependant only upon themselves and their neighbors.

The concept of synchronization arises when the initial state of a machine is known or partially unknown, yet the task requires that the machine be brought to a specified final state. In this case, it is first necessary to bring the machine to a known, intermediate state, identified by a resulting output sequence. As soon as the intermediate state is identified, a second input sequence is selected, and the machine is sent to the desired final state. For some machines, it is possible to use one sequence to take the machine from the unknown initial state to the known final state. In this case, the input sequence is known as a synchronizing sequence, and the synchronizing problem is considered solvable.

The question begins when the general gives the signal to fire, and does not do anything else. Assume all of the soldiers start off in the same, inactive, state, called the quiescent state. After a count of time, the soldier closest to the general reacts to the signal by changing what its doing, equivalent to a machine changing its state. As time goes by, the signal propagates down the line, moving at most one soldier per count. Of course, each individual soldier might be changing their own state according to the states of themselves and their neighbors. Assuming that there is a fixed number of states, regardless of how many soldiers there are in the line, how can the states be defined such that all soldiers enter the same firing, or terminal, state at the exact same time? In other words, the same definitions for the states should still work even if the number of soldiers is dramatically increased.

======================

This mathematical problem helps illustrate why you have commands of soldiers in line chopped into small bits, in rank and file, and the evolution of those systems - and the importance of drill.

This machine needs practice to work.

The Keeping Time portion can be considered, in march for example, to be the obvious cadence of action, and then shifting orders on a line that it is trying to keep time with other members of that line.
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Roger Hobden
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One way to tackle this problem is through various theories of Motor Control.

See for instance the ISCM (international society of motor control)

http://www.i-s-m-c.org/ismc/News_and_Announcements/News_and_...

The Haken-Kelso-Bunz equation for instance is one of the ways that have been used to model phase stability and phase changes.

http://www.scholarpedia.org/article/Haken-Kelso-Bunz_model

The very big question, of course, is this one : is this a model that describes the phenomena, or is this a model that causes the phenomena.

A rock falls to the ground associated with a force F=m.a.

But the rock itself is not doing any of the calculating.
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Are any of the soldiers travelling in a train at a speed approaching that of light?
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Roger Hobden
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You can never be sure of the velocity of the soldier, if you know exactly his position, however,
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I'm confused. Are we talking about soldiers or cats?
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Oh my God They Banned Kenny
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Wilhammer wrote:
... this must have been something Frederick the Great and others had to think about and possibly write up....

There were quite detailed manuals on the steps that should be taken to load and fire their muskets. It was in fact about 'synchronizing' the soldiers actions, as well as providing a method for loading. Where the analogy fails is that the soldiers were to follow audible commands (audible to groups essentially simultaneously), so it wasn't like a command was issued to the nearest soldier and it then propagated down the line.
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Kluvon wrote:
I'm confused. Are we talking about soldiers or cats?

Cats or AT guns.
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Or cats manning AT guns.
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deadkenny wrote:
Wilhammer wrote:
... this must have been something Frederick the Great and others had to think about and possibly write up....

There were quite detailed manuals on the steps that should be taken to load and fire their muskets. It was in fact about 'synchronizing' the soldiers actions, as well as providing a method for loading. Where the analogy fails is that the soldiers were to follow audible commands (audible to groups essentially simultaneously), so it wasn't like a command was issued to the nearest soldier and it then propagated down the line.

At least within the constraints of the speed of sound and the audibility of the sergeant in battle.
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Gibberish? Try this one:

This dissertation addresses a major theoretical problem in performance studies: how to understand games (including play, sports, and so on) as a distinct mode of performance. It considers a wide variety of games across media and genres. Its central goal is to create critical frames that can help performance scholars analyze games alongside other types of performance (such as theater) without eliding their salient qualities, and conversely also help games scholars make use of performance as a way to address play. The first chapter explicates concepts of experience that describe unique and distinguishing qualities of play. It addresses ideas about experience from pragmatist philosophy, interaction design, and popular culture. It uses them to develop a framework for ludic experience that relates games to aesthetic performance, consumer electronics, narrative, efficacy, and affect. The second chapter describes performers other than players in games, which it describes as devices (such as sports equipment) and designs (such as rules). It uses perspectives from speech-act theory, theater criticism, design studies, and object-oriented ontology to help locate the performativity of nonhuman performers in play. It also considers how the device-design analytic merges and blurs in toys and videogames. The third and final chapter investigates how embodiment functions in games. Through further engagement with game studies, theater criticism, and gender theory, it develops constructs called the "game body" and "ludic subjectivity" that help describe how players create new bodies and identities through acts of play. By interpreting several distinct varieties of game practice -- from board games to play with avatars and puppets to tabletop roleplaying -- through the lens of the game body, it reveals a spectrum of modes of embodiment that become manifest in play. In doing so, it outlines a general critical method for examining how play transforms bodies and physical performance.
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The key learning point for me is this-

If I'm ever sentenced to death by firing squad, my last request should be that it be organised by a mathematician.

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Put a drummer at the head of a column of marching soldiers. If everyone marches to the beat of the drum, those toward the back of the column will be increasingly out of step with those in front. Well trained troops will learn to march in step with those far ahead of them, ignoring the audio cue and attending to the visual one.

I have no idea whether this is relevant to anything in that Poindexter's paper.

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Sunray11 wrote:
Put a drummer at the head of a column of marching soldiers. If everyone marches to the beat of the drum, those toward the back of the column will be increasingly out of step with those in front. Well trained troops will learn to march in step with those far ahead of them, ignoring the audio cue and attending to the visual one.

I have no idea whether this is relevant to anything in that Poindexter's paper.


Marching out of step will at least prevent the destruction of bridges by resonance.
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Michael Dorosh wrote:

That mostly reads as gibberish to me, unfortunately. Generals don't control tactical units, and the ones that do, don't stand at the ends of the lines [. . .]

It's a thought experiment to illustrate problems in "automation/IT"--not a descritpion of historical army practices...

But please continue with the pedantic explanation of how it is all wrong.
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the Big D said:

Quote:
"Generals don't control tactical units, and the ones that do, don't stand at the ends of the lines, they gain tactical control by acting as file-closers, placing themselves"


Pendantacism aside, consider the writer is a mathematician, and he does not know what a General does...identify your audience and you can avoid the embarrassment of your need to correct them.

The layperson knows Generals are in charge of soldiers, so....

Now we know who is talking about - the guy, under whatever title, lead the rank or the line or the unit.

===============

At to gibberish - well, if you don't study mathematics and automated systems, and just do a cursory look, yeah, its gibberish.


==============

I think that what the big D is not getting is that this a thread about systems and how mathematical models are used to describe automated systems and how in the PAST, we had very few machines, but HUMAN systems; machines being systems and not mechanical devices.

This mathematical theory/problem is very much like Freddie training troops.

And it is something to consider in simulations and this AGE OLD Wargaming argument:

"Why shouldn't all my troops obey me blindly?"

"They can all hear me and see me, and I them!"

The reason; there busy and this is why; or one reason why.

================

I do automation in IT, and I will tell one and all, moving bits and ordering them around is very much like moving troops and issuing orders - if you get the command wrong and in the wrong order, you are going to have a very bad day.

And my automation depends on other interactions - I cannot backup some files if they are in use, or if a system is down or its network clogged, or a plethora of other WTFwhyaintthisworkingdammits.
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Seriously, Wil, what is the thought problem about? The decay of data?
 
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Kluvon wrote:
Seriously, Wil, what is the thought problem about? The decay of data?

Whatever it brings you to think about.

The problem is everywhere.

'tis the kind of thing I am likely to bring up in conversation with other gamers FTF - I am a nerd.

And this place is full of fellow smart people...who also may like these things.
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Oh good. It's not just me who finds this to be gibberish.
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I trust my learned Greek slaves are competent enough to handle any abstract matters beyond good old Roman common sense. whistle
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Wilhammer wrote:
Kluvon wrote:
Seriously, Wil, what is the thought problem about? The decay of data?

Whatever it brings you to think about.

The problem is everywhere.

'tis the kind of thing I am likely to bring up in conversation with other gamers FTF - I am a nerd.

And this place is full of fellow smart people...who also may like these things.

My field was anthropology, though I am not all that bright. The problem brings to mind how we studied enculturation.
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sullafelix wrote:
I trust my learned Greek slaves are competent enough to handle any abstract matters beyond good old Roman common sense. whistle

So long as they scrape the olive oil off of you, right?
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Kluvon wrote:
Seriously, Wil, what is the thought problem about? The decay of data?

The timing of the flow and the interdependence of transfer of the flow from one part to another and the impact those parts have on the part you wish to influence, or how the whole acts based on the part getting the message.

Interesting on "Decay of Data" - it could be better considered "Decay of Relevance" - The Orders by the end they reach the last guy in the line because of all the other interactions may find the order meaningless, worthless and confusing, or impossible to carry out - or, perhaps that one soldier got 'removed' by another "process engine" and thus his sudden omission increases the complexity of the machine operation or renders it worthless.

ya see, these math-nerds are using a military metaphor to describe the gibberish to the non gibberish reader.

And I find that interesting - for all systems have this data/reception and timing issue.

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Kluvon wrote:
sullafelix wrote:
I trust my learned Greek slaves are competent enough to handle any abstract matters beyond good old Roman common sense. whistle

So long as they scrape the olive oil off of you, right?
I prefer the ones without beards.
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Kluvon wrote:
Are any of the soldiers travelling in a train at a speed approaching that of light?
I'd think it hard for them to keep their balance on a frictionless plane...
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Eric Brosius wrote:
Kluvon wrote:
Are any of the soldiers travelling in a train at a speed approaching that of light?
I'd think it hard for them to keep their balance on a frictionless plane...

In a vacuum.
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