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.

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