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  1. #1
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    Jun 2006
    Washington Island, across Death's Door, Wisconsin, USA

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    The supreme postulate of Liberalism, social engineering, social activism, social advocacy, rights movements, peace movements, the United Nations... is that compromise is possible. By crippling the able and enabling the crippled we can all get along. It is rigorously mathematically demonstrated that no compromises exist for complex multi-variable problems, even in theory. Zealot religions of tiny-minded fanatics know what they are doing. Diversity (a word grievously devalued in the manner of "gay") is mathematically guaranteed, irrevocable, inevitable disaster.

    Create a multidimensional compromise space. Choose a variable, normalize it on a scale of 1 through zero to -1 inclusive. Love thy neighbor, kill thy neighbor. Racial integration, racial segregation. Keep all that you earn, the State confiscates all that you earn. Every school kid gets automatic straight As in everything, Darwinian social evolution. United Nations, mean Mother Green. Sister Boom-Boom, Vlad the Impaler.

    Each normalized line is assigned its own dimension and is appended orthogonal to all prior lines. The zero centers of all lines coincide as a common origin. N variables then create a filled N-dimensional unit hypersphere, a closed N-hyperball, with each line being one of its diameters (each variable being wholly independent of all the others). The closed N-hyperball embraces every possible combination and magnitude of overall policy as the totality of single points on its surface and in its volume. Points near the center are maximally effete compromise. Points near the surface are the most draconian events possible.

    A hypercube with edge length 2 and volume 2N circumscribes about any unit N-hypersphere. The ratio of our N-hyperball's volume to its circumscribed hypercube monotonically decreases as the dimension N, the number of independent variables, increases. As a problem's complexity increases the closed N-hyperball of all possible solutions - of any kind - monotonically shrinks toward a zero volume point. The results are inescapable:
    1. As N, the number of variables, increases the number of compromise choices of all kinds shrinks toward zero. A large multi-variable problem has asymptotically no solutions at all much less a menu of nice compromise solutions.
    2. By N=10, 89.3% of the volume is within 20% radius of the surface. Almost every choice is a draconian imposition.
    3. By N=20, 98.8% of the volume is within 20% radius of the surface, and the overall volume - the summation of choices available - is essentially zero. There is no compromise possible. The few choices remaining are fanatic.
    A society exercising local decisions given limited choices can find optimum solutions. A society with central administration juggling hundreds of variables for each decision (social policy, economics, Congresscritters' appetites) will be a shambles at every scale of implementation. The USSR was doomed from the start; Washington ever more passionately seeks a death spiral.

    The Department of Education and the Department of Health and Human Services are mathematically constrained to fail. Abominable Neanderthal Drill Instructors on Parris Island will succeed. A kinder, gentler armed forces with girls and benign, fairly administered procedures is a hopeless farce.

    Fair business practices obeying multiple layers of reportage, regulation, affirmative social policies, and union negotiation wither and die. Monomaniacal robber barons succeed. Mighty, huge, and politically complex Imperial Rome fell to small bands of simpleton barbarians, each a one-man show. The Balkans are a disorganized bloodbath stable for 1000 years against every invader; the US is shaken to its core by the loss of two buildings (and still upchucking tens of $billions/year for "homeland security" seven years later).

    The solution to complex multi-variable social, economic, and political problems is not compromise. It cannot be compromise. It can never be compromise even in principle. Any attempt at compromise is a long voyage into wrong answers where traveling more is drowning deeper. Accomplishment is the exclusive providence of narrowly focussed individuals.

    1900s education worked because it was simple and direct. Every wretched immigrant kid learned English reading, English writing, and arithmetic without choice in buildings that were hardly more than shacks. Education in the 21st century is a dysfunctional bleeding ulcer not because we are not doing enough, spending enough, or lack compassion. Public education is a bleeding ulcer specifically because we are pursuing all those things with maximum vigor and budget in carpeted air-conditioned audio-visual multi-cultural pleasure domes for our delicate Adderall-gulping children. If public education is about anything but the narrowest least complex vision of education, it will fail.

    The Constitution grants broad undifferentiated swaths of individual rights, limitations upon State incursion, and then shuts up. Massive waves of immigration arrived on American shores and became part of the American dream one generation later. Actively interventionist centrally administered social policy since President Johnson's Great Society sought to please everybody. It created a nation of two working parents, shattered families, intractable slums, hyphenated Americans, and multi- lingual ballots. Lose the hyphens and locally target simple goals, or the closed N-hyperball will swallow you and shrink to a point. CRUNCH. Mathematics is implacable.

    As for Liberalism, social engineering, social activism, social advocacy, rights movements, peace movements, the United Nations... their failure is a necessity not an annoyance. "It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong." Richard Feynman.

    The non-monotonic behaviour of the numerical value of n-spheres as a function of n may seem strange at first glance. However, by assigning units of length to each dimension one can see it is meaningless to compare the unit-sphere volumes in different n's, just as it is meaningless to compare a length to an area in other contexts. A meaningful comparison is obtained by using a dimensionless measure of the volume, such as the ratio of the n-sphere and its circumscribed hypercube volumes. Using this measure restores the intuitively normal behavior of a monotonic decline in the volume as the dimension increases.
    Accept the premises and the conclusion is logically and mathematically inescapable.

    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 *******

  2. #2
    Regular Member
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    Feb 2007

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    How is this OC or gun related?

  3. #3
    Regular Member
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    Dec 2007
    Firestone, Colorado

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    Dang it, when I saw the title I thought there'd be something cool here.

    Doug Huffman wrote:
    As a problem's complexity increases the closed N-hyperball of all possible solutions - of any kind - monotonically shrinks toward a zero volume point.
    Assuming I understand the very poorly-defined terminology here, this is false, and since the rest of the argument (it's too vague to be called a proof) depends on this, the rest falls as well.

    Doug Huffman wrote:
    As N, the number of variables, increases the number of compromise choices of all kinds shrinks toward zero.
    This makes no sense. I think maybe the author forgot he's working in N-space? Since the number of dimensions is equal to the number of variables, any set of "compromise choices" can be chosen, and there exists a unique point within the hypersphere that corresponds to those particular choices.

    Doug Huffman wrote:
    By N=10, 89.3% of the volume is within 20% radius of the surface.
    Okay, I get it. It's a joke proof. Mathematicians pass a lot of these around.

    The flaw here is the use of an unjustifiable limiting argument. It's true that if you take the limit as N tends to infinity of the volume of an N-sphere of any radius (including 1), the volume goes to zero. Thus, it is true that if you actually had an infinite numer of linear compromise ranges, the ball would shrink to a point.

    That seems weird, but lots and lots of very bizarre things happen in infinite-dimensional space. People have a hard time getting their heads around four dimensions, and an infinite number of dimensions is just crazy. Even simple points can only be defined via generating functions!

    In fact, though, we probably live in a finite universe and certainly live on a finite planet, and for any finite N, no matter how large, the n-sphere and its enclosed hyperball does have a volume, containing an infinite number of points (assuming each dimension is either countably or uncontably infinite). Mapping this back to the "compromise space" that the proof is attempting to model, this means that for any given set of positions you want to choose, there does exist a point inside the compromise closed hyperball that expresses that set of choices.

    In other words, the proof actually demonstrates the exact opposite of what it claims to demonstrate (which is a common feature of really good joke proofs). It says that any compromise position is possible.

    That simple model neglects interactions between axes or, stated differently, that most compromise axes are themselves spaces, so it really falls apart from the get-go and ultimately tells us nothing one way or the other.

    Edited to remove a stray paste.

  4. #4
    Administrator John Pierce's Avatar
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    May 2006
    Bristol, VA

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    As noted elsewhere, I am going to start cutting down on mission creep and even the freedom and liberty topics on OCDO should be gun related in some fashion.

    As neat as it is to discuss Nth dimensional physics as it relates to societal and governmental theories, I think this one goes way off-topic.

    I am going to go ahead and close this thread and any others that seem to be too far off target. Please feel free to PM me if you think I am misfiring.

  5. #5
    Regular Member
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    Oct 2006
    Lynnwood, WA, ,

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    Wow Doug. You are a super-brain and apparently you have more in your bookcase than a thesaurus. We should all be humbled in your divine presence.

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