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Thread: Hopefully a little more on-topic: the math of compromise

  1. #1
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    Doug Started an interesting thread about the limits of N-dimensional shapes asa proof that compromise cannot exist in complex relationships like society.

    However, he's got the wrong branch of math. N-dimensional shapes are a theoretical construct where first thedefining points are totally independent, andsecond the fact that no matter how many dimensions we live in, there are a finite number, is discounted (because this is theory). It also, being theoretical, requires a perfect solution, not merely an acceptable one.

    There is however a branch of computational mathematics called constraint satisfaction problems, or CSPs. It's the branch of computationthat could, for instance, calculate a train schedule, or solve a Sudoku puzzle, given the requirements of the solution, called constraints. In doing so, the algorithm must discover mutually exclusive contraints to determine "sanity" (the possibility that the problem can be solved), and for efficiency, determine bounds set by interdependent constraints called relations. For example, take a simplesolution set of variables X and Y on an infinite plane, and the following constraints: Y=.1X,Y> 5. This might correspond to, for instance, retirement planning, where you make X dollars, can contribute 10% and only 10% of earnings to retirement,and must save more than5 dollars (or 5 of a quantity of dollars like 5,000 or 50,000)to be able to retire as planned. The solution is simple; if Y > 5, X > 50. Any value of X less than 50 will not satisfy all constraints, while any X > 50 will. A smart algorithm will detect this relationship between the two constraints and discount values of X <= 50 as possibilities. Now, add a third constraint X < 40. The problem becomes unsolvable, as .1(40) = 4 and 4 < 5. A smart algorithm will detect this before running all possible values of X and Y.

    Let's put this in gun terms so this thread doesn't get locked as well :P.The constraints of a satisfactory solution for gun law might be as follows:


    1. Incidences of all criminal injury/death involving a firearm, A,reduced to less thanA' per year


    2. Incidences of all crime committed using a firearm, B, reduced to less than B' per year


    3. Incidences of all criminal possession of a firearmC less than C' per year


    4. Accidentalfirearm deathsDreduced to less than D' per year


    5. Purchase time for a firearmE less than E'


    6. Percentage of people in the U.S. not prohibited from owning a firearmF greater than f


    7. Percentage of people in the U.S. wholawfully owna firearm G greater than g (lawful here having the meaning of competent, non-malum in se users of firearms; the ideal is that malum prohibitum doesn't exist with regard to guns)


    8. Required time to ready a firearm from nominal carry state H less than H'


    9. Required time to ready a firearm from nominal storage state Iless than I'
    There are obviously others, but these are the major points of contention; gun activists want easy access to guns for lawful individuals, the ability for a lawful owner to quickly ready a weapon, and high percentage of gun ownership. Antis want low gun crime, low criminal access to handguns, and low incidences of accidental firearm deaths.

    To solve such a problem, we must definethe acceptable limits (minimums are the lowercase, maximums are the prime vars).The antis' ideal numbers for A' through D' is zero, and most would agree those arethe bestnumbers for those statistics. The gun rights activists' ideals for E' is zero, for f is 100, for g is 100, and H' and I' are infinitesimal (bound only by the ability of the handler). Most would agree those are alsothe best possible stats.

    However, we must consider correlations:

    • A and B are a function of Csuch that a change in C is directly proportional to a change in A and B. An increase in criminal gun ownership means an increase in crimes in which guns play a part, and vice versa.
    • D is directly proportional to G and inversely proportional to H and I. If gun ownership increases, or access time to stored/carried firearms decreases, accidental injury or death relating to firearms will increase.
    • As E increases, C decreases, but G decreases more.
    • Here's where it gets interesting:Increasedownership G reduces crime rates A and B, but increases criminal possession C through theft. Incidences of theftmust bea new variable, call it T.
    • It is possible forT to be greaterthan the number of gun owners or criminals, but let's assume T<=C and<= G based on reality, because even if G = 0, C > 0 through methods other than theft. Theft is inversely proportional to access time, thus as H and I increase, T decreases.
    • Even more interesting: Even though access times H and I decrease C via decreased T,an increase in access timeincreases A and B.
    • Lastly,we assume a zero C creates a zero A and B; a criminal must possess a weapon to use it. However, gun ownership is directly proportional to criminal activity because of the percentage of G that commits a crime. Call it P.0% < P < 100%; lawful gun owners commit crimes, no matter how few do so, but not every gun owner is a malum in se criminal. P is inversely proportional to wait time E, but never zero, and never 100% even if wait time is zero.
    Given these correlations, it is impossible for A, B and C to be zero if G is anything but zero. If G > 0,there will becriminal possession and gun crime because of theft andlawful owners turning criminal. On top of that, because P and T are not the only contributorsto C, even if G = 0, C > 0 and thus A > 0 and B > 0. On the flip side, even if G is 100% thus having its maximum effect on A and B, 100% gun ownership does not guarantee zero crime, and at 100% gun ownership, the contribution to P and T, and thus to C, is at its maximum. G of 100% is impossible anyway because G will always be less than F; not everyone who CAN have a gun WILL unless forced by law to do so (a condition the antis would CERTAINLY reject). Thus, A=B=C=0 is impossible strictly by controlling gun-related variables. Only D alone can be brought to effectively zero by increasing gun control.

    But you knew that already.


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    *I* don't have the 'wrong branch of math.' You have avoided the attribution to Al Schwartz, against his brilliance mine pales and Marilyn Vos Savant becomes an anile idiot-vos-savant.

    Either we are equal or we are not. Good people ought to be armed where they will, with wits and guns and the truth. NRA *******

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    Doug Huffman wrote:
    *I* don't have the 'wrong branch of math.' You have avoided the attribution to Al Schwartz
    Al was joking.

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    Uh huh.

    Either we are equal or we are not. Good people ought to be armed where they will, with wits and guns and the truth. NRA *******

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    Doug Huffman wrote:
    Uh huh.
    Well, the proof is either a very good joke or a very badly flawed piece of math. Based on all of the other excellent and witty humor on his site, I think he was joking.

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    Criticise his work to his face. His e-mail is visible and he has never failed to respond to me.

    There is more than humor there including http://www.google.com/search?q=guns+....com%2Funcleal

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    Please don't lock this thread. I love it. I even almost understand all of it.
    Colorado Gun Owners - COGO
    http://www.ColoradoGunOwners.com

    A discussion forum for Colorado Gun Owners.

    Colorado Firearm law.
    http://www.lexisnexis.com/hottopics/colorado/
    Lexis Nexis: Colorado law pertaining to firearms.
    Title 18, Article 12

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    Doug Huffman wrote:
    Criticise his work to his face.
    Why would I criticise? I think it's brilliant. The flaw (the unjustified limit) is just subtle enough to pass cursory review, yet the result is that if the proof demonstrates anything it demonstrates the exact opposite of what it claims.

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    Interesting. Quite interesting, but requiring more focus and thought than I have time for at the moment. Going to have to brush the cobwebs off a certain section of my brain and see if I can't parlay that math minor into a coherent, contributing response. I do wonder at the efficacy of such a mathematical model in a broader sense. I find it pretty well established that the psychology of the gun grabbers, just like the psychology of Code Pink, MADD, Millions Mom March for a few examples, lend almost exclusively to emotional reactions with little to no logical analysis of their belief system or consequences of their acts and beliefs, as they act on a self-perceived moral authority based on mutual fallacies. However, I wonder if certain members of academia tending towards leftist ideals, could be swayed by a complete mathematical model/proof of this argument. Regardless, it is always fascinating to see life reduced to mathematics.


    Bob Owens @ Bearing Arms (paraphrased): "These people aren't against violence; they're very much in favor of violence. They're against armed resistance."

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    Liko81 wrote:
    Doug Started an interesting thread about the limits of N-dimensional shapes asa proof that compromise cannot exist in complex relationships like society.

    However, he's got the wrong branch of math. N-dimensional shapes are a theoretical construct where first thedefining points are totally independent, andsecond the fact that no matter how many dimensions we live in, there are a finite number, is discounted (because this is theory). It also, being theoretical, requires a perfect solution, not merely an acceptable one.

    There is however a branch of computational mathematics called constraint satisfaction problems, or CSPs. It's the branch of computationthat could, for instance, calculate a train schedule, or solve a Sudoku puzzle, given the requirements of the solution, called constraints. In doing so, the algorithm must discover mutually exclusive contraints to determine "sanity" (the possibility that the problem can be solved), and for efficiency, determine bounds set by interdependent constraints called relations. For example, take a simplesolution set of variables X and Y on an infinite plane, and the following constraints: Y=.1X,Y> 5. This might correspond to, for instance, retirement planning, where you make X dollars, can contribute 10% and only 10% of earnings to retirement,and must save more than5 dollars (or 5 of a quantity of dollars like 5,000 or 50,000)to be able to retire as planned. The solution is simple; if Y > 5, X > 50. Any value of X less than 50 will not satisfy all constraints, while any X > 50 will. A smart algorithm will detect this relationship between the two constraints and discount values of X <= 50 as possibilities. Now, add a third constraint X < 40. The problem becomes unsolvable, as .1(40) = 4 and 4 < 5. A smart algorithm will detect this before running all possible values of X and Y.

    Let's put this in gun terms so this thread doesn't get locked as well :P.The constraints of a satisfactory solution for gun law might be as follows:


    1. Incidences of all criminal injury/death involving a firearm, A,reduced to less thanA' per year


    2. Incidences of all crime committed using a firearm, B, reduced to less than B' per year


    3. Incidences of all criminal possession of a firearmC less than C' per year


    4. Accidentalfirearm deathsDreduced to less than D' per year


    5. Purchase time for a firearmE less than E'


    6. Percentage of people in the U.S. not prohibited from owning a firearmF greater than f


    7. Percentage of people in the U.S. wholawfully owna firearm G greater than g (lawful here having the meaning of competent, non-malum in se users of firearms; the ideal is that malum prohibitum doesn't exist with regard to guns)


    8. Required time to ready a firearm from nominal carry state H less than H'


    9. Required time to ready a firearm from nominal storage state Iless than I'
    There are obviously others, but these are the major points of contention; gun activists want easy access to guns for lawful individuals, the ability for a lawful owner to quickly ready a weapon, and high percentage of gun ownership. Antis want low gun crime, low criminal access to handguns, and low incidences of accidental firearm deaths.

    To solve such a problem, we must definethe acceptable limits (minimums are the lowercase, maximums are the prime vars).The antis' ideal numbers for A' through D' is zero, and most would agree those arethe bestnumbers for those statistics. The gun rights activists' ideals for E' is zero, for f is 100, for g is 100, and H' and I' are infinitesimal (bound only by the ability of the handler). Most would agree those are alsothe best possible stats.

    However, we must consider correlations:

    • A and B are a function of Csuch that a change in C is directly proportional to a change in A and B. An increase in criminal gun ownership means an increase in crimes in which guns play a part, and vice versa.
    • D is directly proportional to G and inversely proportional to H and I. If gun ownership increases, or access time to stored/carried firearms decreases, accidental injury or death relating to firearms will increase.
    • As E increases, C decreases, but G decreases more.
    • Here's where it gets interesting:Increasedownership G reduces crime rates A and B, but increases criminal possession C through theft. Incidences of theftmust bea new variable, call it T.
    • It is possible forT to be greaterthan the number of gun owners or criminals, but let's assume T<=C and<= G based on reality, because even if G = 0, C > 0 through methods other than theft. Theft is inversely proportional to access time, thus as H and I increase, T decreases.
    • Even more interesting: Even though access times H and I decrease C via decreased T,an increase in access timeincreases A and B.
    • Lastly,we assume a zero C creates a zero A and B; a criminal must possess a weapon to use it. However, gun ownership is directly proportional to criminal activity because of the percentage of G that commits a crime. Call it P.0% < P < 100%; lawful gun owners commit crimes, no matter how few do so, but not every gun owner is a malum in se criminal. P is inversely proportional to wait time E, but never zero, and never 100% even if wait time is zero.
    Given these correlations, it is impossible for A, B and C to be zero if G is anything but zero. If G > 0,there will becriminal possession and gun crime because of theft andlawful owners turning criminal. On top of that, because P and T are not the only contributorsto C, even if G = 0, C > 0 and thus A > 0 and B > 0. On the flip side, even if G is 100% thus having its maximum effect on A and B, 100% gun ownership does not guarantee zero crime, and at 100% gun ownership, the contribution to P and T, and thus to C, is at its maximum. G of 100% is impossible anyway because G will always be less than F; not everyone who CAN have a gun WILL unless forced by law to do so (a condition the antis would CERTAINLY reject). Thus, A=B=C=0 is impossible strictly by controlling gun-related variables. Only D alone can be brought to effectively zero by increasing gun control.

    But you knew that already.
    I think you are making some pretty bold assumptions by calling any of those constants.

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    expvideo wrote:
    I think you are making some pretty bold assumptions by calling any of those constants.
    Well, the only constants in the problem are in defining the desired solution; the minimum and maximum bounds of the solution set must be specified, and the specification cannot change as a function of other variables in the model. I agree that if you find a workable solution when gun crime is capped at, say, 10 per 100,000, the antis will push for 5 per 100,000, and if you find a workable solution that results in 90% of the populationbeing eligible to buy a gun the gun-rights groups will push for 95%, but you first have to get to 10 per 100,000 or 90% before redefining the problem.

    I havealso already demonstrated, if not proven, that you can't have zero crime no matter how many eligible civilians exist, and if criminal possession is malum prohibitum then you'll never have 100% of the population eligible to own a gun without instating a permanently extreme method of criminal justice. That's the point; the closer to ideal perfection you get, the harder it is toget even closer,and the ideal may be impossible, especially if it is found as it is herethat two ideals (no crime, 100% eligibility) are mutually exclusive.

    Asingle solution to a mathematical model is by definition static; it is based on a snapshot of things as they are and produces a result that fits the snapshot. The real world is dynamic and based on far more variables than the library of available mathematical variable symbols. If you wanta fully realistic mathematical simulation of reality, rent "The Matrix".

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    Decent analysis.

    But unfortunately, it's entirely invalid because it is not exclusively about OCing.



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    Liko81 wrote:
    expvideo wrote:
    I think you are making some pretty bold assumptions by calling any of those constants.
    Well, the only constants in the problem are in defining the desired solution; the minimum and maximum bounds of the solution set must be specified, and the specification cannot change as a function of other variables in the model. I agree that if you find a workable solution when gun crime is capped at, say, 10 per 100,000, the antis will push for 5 per 100,000, and if you find a workable solution that results in 90% of the populationbeing eligible to buy a gun the gun-rights groups will push for 95%, but you first have to get to 10 per 100,000 or 90% before redefining the problem.

    I havealso already demonstrated, if not proven, that you can't have zero crime no matter how many eligible civilians exist, and if criminal possession is malum prohibitum then you'll never have 100% of the population eligible to own a gun without instating a permanently extreme method of criminal justice. That's the point; the closer to ideal perfection you get, the harder it is toget even closer,and the ideal may be impossible, especially if it is found as it is herethat two ideals (no crime, 100% eligibility) are mutually exclusive.

    Asingle solution to a mathematical model is by definition static; it is based on a snapshot of things as they are and produces a result that fits the snapshot. The real world is dynamic and based on far more variables than the library of available mathematical variable symbols. If you wanta fully realistic mathematical simulation of reality, rent "The Matrix".
    You're still assuming. Human nature is a static thing, not a constant thing. You can't set a limit of 10 per 100,000 murders. Things like Virginia Tech happen. Gang wars happen. Things out of the control of your statistics happen. Suddenly hundreds of people end up being killed in a single month, or no one is killed all year. These things happen and you can't control them. Do your statistics matter if, say for example, a group of white supremacist radicals captures a large building full of people that support Israel, and exeute them all? That would mess up your statistics pretty badly, wouldn't it. Do your statistics work for 9/11? I would say that those people in the towers were all victims of crime, but I wouldn't think that stricter gun laws or waiting periodshad any relationship with that crime.

    Also, you are making assumptions on what the causes and effects are of crime. Inflation, pop culture, and the disappearing middle class are much more likely to have an impact on crime than gun laws. For example the development of rap music happens to follow the same trends as gun control, so those murderstatistics are not necessarily related to each other.

    There are way too many variables for you to simplify it into a general math problem. You are looking at a short period of time in history, which bears no evidence on being anything more than coincidence, and you are only looking at gun laws versus gun crime with the assumption that the two are related.

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    expvideo wrote:
    Liko81 wrote:
    expvideo wrote:
    I think you are making some pretty bold assumptions by calling any of those constants.
    Well, the only constants in the problem are in defining the desired solution; the minimum and maximum bounds of the solution set must be specified, and the specification cannot change as a function of other variables in the model. I agree that if you find a workable solution when gun crime is capped at, say, 10 per 100,000, the antis will push for 5 per 100,000, and if you find a workable solution that results in 90% of the populationbeing eligible to buy a gun the gun-rights groups will push for 95%, but you first have to get to 10 per 100,000 or 90% before redefining the problem.

    I havealso already demonstrated, if not proven, that you can't have zero crime no matter how many eligible civilians exist, and if criminal possession is malum prohibitum then you'll never have 100% of the population eligible to own a gun without instating a permanently extreme method of criminal justice. That's the point; the closer to ideal perfection you get, the harder it is toget even closer,and the ideal may be impossible, especially if it is found as it is herethat two ideals (no crime, 100% eligibility) are mutually exclusive.

    Asingle solution to a mathematical model is by definition static; it is based on a snapshot of things as they are and produces a result that fits the snapshot. The real world is dynamic and based on far more variables than the library of available mathematical variable symbols. If you wanta fully realistic mathematical simulation of reality, rent "The Matrix".
    You're still assuming. Human nature is a static thing, not a constant thing. You can't set a limit of 10 per 100,000 murders. Things like Virginia Tech happen. Gang wars happen. Things out of the control of your statistics happen. Suddenly hundreds of people end up being killed in a single month, or no one is killed all year. These things happen and you can't control them. Do your statistics matter if, say for example, a group of white supremacist radicals captures a large building full of people that support Israel, and exeute them all? That would mess up your statistics pretty badly, wouldn't it. Do your statistics work for 9/11? I would say that those people in the towers were all victims of crime, but I wouldn't think that stricter gun laws or waiting periodshad any relationship with that crime.

    Also, you are making assumptions on what the causes and effects are of crime. Inflation, pop culture, and the disappearing middle class are much more likely to have an impact on crime than gun laws. For example the development of rap music happens to follow the same trends as gun control, so those murderstatistics are not necessarily related to each other.

    There are way too many variables for you to simplify it into a general math problem. You are looking at a short period of time in history, which bears no evidence on being anything more than coincidence, and you are only looking at gun laws versus gun crime with the assumption that the two are related.
    I think in your second sentence you meant "dynamic" rather than "static". If not please explain what you meant as I am confused otherwise.

    I think you are missing what Liko is saying. The limits he is discussing as constants are the desired outcome, not the actual outcome. He acknowledges what you argue, that the mathematical solution to the equation, with a given set of data is just a snapshot. There are numerous formulas to look at events over time though. This is done daily with statistical analysis of all manner of things. Your examples of large scale acts do not "mess up the statistics pretty badly" as they are statistical outliers. While they would effect the data, overall they will not be significant statistically unless one is looking at a very narrow time and geographical data set, or in other words, if the "snapshot" is limited to a time frame or geography in which those limited large scale events occur. Futhermore, for this discussion, the scale of the act doesn't necessarily need to be part of the data for a valid proof, but rather just the event. We have millions of instances in this country annually where firearms are used to both commit and defend against crime so even if the scale would be included, looking at the data over time, it will still become statistically insignificant due to the limited instances of mass crime compared to the huge data set of small scale events.

    The point under discussion which is being examined mathematically though is, as liko very nicely summed up, "the closer to [the] ideal... the harder it is toget even closer,and the ideal may be impossible, especially if it is found as it is herethat two ideals (no crime, 100% [firearm ownership] eligibility) are mutually exclusive." Your points about crimes not involving firearms simply support the arguments herein that banning guns or restrictive gun laws will not eliminate crime which is a conclusion with which I think we would all agree and here it is simply reduced to a mathematical perspective.
    Bob Owens @ Bearing Arms (paraphrased): "These people aren't against violence; they're very much in favor of violence. They're against armed resistance."

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    I really garbled that sentence. You are right, I meant that human nature is a dynamic thing, not a static thing. Must have been typing faster than I was thinking.

    That being said, I can agree that outlawing guns will not lower the crime rate, but I don't think that the math works. I believe that you could do the same thing for My Little Pony dolls and have the same outcome. There are too many assumptions being made about what causes and effects are or aren'trelated.

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