Philosophy and Science for the Third Millennium

The Bernoulli Form

An Essay by Christopher Bek



Summary—The Bernoulli Form elucidates the notion of Platonic Forms in describing how a motley crew of Forms—including Delphi, forecasting, integration, utility, optimization, efficiency and complementary—come together to form The Bernoulli Model.


In 1952 a young graduate student named Harry Markowitz studying operations research demonstrated mathematically why putting all your eggs in one basket is an unacceptable strategy and why optimal diversification is the best one can do.  His revelation touched off an intellectual movement that has revolutionized Wall Street, corporate finance and decisionmaking of all kinds.  Its effects are still being felt today.

—Peter Bernstein


I do my best thinking in a warm bed.

—René Descartes


Paradigm shifts are not unpredictable, just unthinkable.

—Peter Bernstein


Some men never seem to grow old.  Always active in thought, always ready to adopt new ideas, they are never chargeable with foggyism.  Satisfied, yet ever dissatisfied, settled, yet ever unsettled, they always enjoy the best of what is, are the first to find the best of what will be.

—William Shakespeare


You have the look of a man who accepts what he sees because he is expecting to wake up.  And you are here because you know something.  What you know you can’t explain, but you feel it.  You’ve felt it your entire life.  That there’s something wrong with the world.  You don’t know what it is, but it’s there, like a splinter in your mind driving you mad.  It is the world that has been pulled over your eyes to blind you from the truth.  Like everyone you are a slave.  You were born into bondage, born into a prison you cannot smell or taste or touch—a prison for your mind.

—Morpheus from the 1999 movie Matrix



The Bernoulli Form


The Method of Moments elucidates the notion of Platonic Forms in describing how a motley crew of Forms—including Delphi, forecasting, integration, utility, optimization, efficiency and complementary—come together to form The Bernoulli Model.


The Efficient Frontier examines the notions of God, option theory, portfolio theory, faith, reason and Arab mathfinally arriving at the inescapable conclusion that all roads of sound decisionmaking lead to the efficient frontier.


The Unpardonable Sin charges all honourables and doctors in Canada with heresy, child abuse and the unpardonable sin that Christ spoke of—which is the deliberate refusal to follow the light when seen.


The Uncertainty Principle contrasts Einstein with Heisenberg, relativity with quantum theory, behavioralism with existentialism, certainty with uncertainty and philosophy with science—finally arriving at the inescapable Platonic conclusion that the true philosopher is always striving after Being and will not rest with those multitudinous phenomena whose existence are appearance only.


Twenty-Eight is a Perfect Number argues that the Canadian Government is systematically violating its citizens and—in that I am the unchallenged Canadian Sovereign and have formally requested intervention from the United States Government—the Canadian people now have the means and legal right to remove the Canadian Government.


A Formal Patient congratulates Alberta Health and Wellness for insisting on the accountability of due process in declaring individuals to be formal patients—and argues that I am being considered a formal patient as the result of an absence of due process elsewhere in Canada—and that I should not be considered a formal patient but that I should be declared disabled on account of being outside the cave of behaviorism.



Singularity identifies the trigger of the looming paradigm shift from the three-dimensionally conscioused Everyman to the four-dimensionally conscioused Superman as the 1935 Schrödinger's Cat though problem—which proves that consciousness is real.


The Great Cosmic Accounting Blunder compares the two physical fixedpoints in the universe—lightspeed and Planck’s constant—and argues that we have been guilty of double counting up until now and that in fact there is but one fixedpoint—which, as it turns out, is the boundary of the universe.


The Unified Field Theory counts down the Euclidean hits from five to one in categorically nailing the vast majority of this little thing I like to call cosmic pi.  At this point in spacetime I would like to pay special tribute to my excellent wingman Albert Einstein (18791955).


Closing the Liars Loophole identifies the malignant cancer within the healthcare system and society as the outwardly focusing behavioral psychological model, which denies the existence of consciousness—while the inwardly focusing existential model makes consciousness and the soul primordially important.

On 14 December 1900 Max Planck (1858-1947) told his son that he had just made a discovery as important as that of Newton.  Planck revealed why we are able to stand so close to a fire without being overwhelmed by radiation.  He realized the fact that energy is transferred in discrete packets or quanta defined by Planck’s constant puts a size restriction on escaping energy units thus causing a traffic jam.  In 1925 Planck’s constant formed the basis of quantum theory—which is the natural law of matter and explains the periodic table and is the foundation of electronics, chemistry, biology and medical science.  In 1905 Albert Einstein (1879-1955) produced three papers—The Photoelectric Effect, which applies Planck’s quantum concept to light—Brownian Motion, which delineates the stochastic process and is the basis of all riskmodeling—and Special Relativity, which is the natural law of spacetime.  In 1906 Planck wrote to the unknown Einstein and acknowledged the greatness of his discoveries.  In 1915 Einstein adapted the curved geometry of Bernhard Riemann (1826-66) as the underlying a priori Form for general relativity.  Special relativity refurbished Newtonian physics in respect of uniformly moving bodies traveling in straight lines—and general relativity upgraded special relativity to account for bodies traveling at varying speeds along curved lines.  On 28 May 1919 Sir Arthur Eddington led an expedition to the island of Principe off the coast of Africa to photograph an eclipse of the sun.  Analysis revealed a warping of spacetime consistent with general relativity thereby providing a posteriori validation.  Planck stayed up all night awaiting the results while Einstein slept like a baby.  When asked what he would have done had the results not confirmed his theory, Einstein responded by saying—Nothing, for the good Lord must have errored.

Platonic Forms.  The Greek Plato’s (427-347 BC) theories of knowledge and Forms holds that true or a priori knowledge must be certain and infallible, and it must be of real objects or Forms.  Thales and Pythagoras laid the foundation for Plato by founding geometry as the first mathematical discipline.  Mathematics is the systematic treatment of Forms and relationships between Forms.  It is the science of drawing conclusions and is the primordial foundation of all other science.  The Greeks synthesized elements from the Babylonians and Egyptians in developing the concepts of proofs, axioms and logical structure of definitions—which is mathematics—which when combined with a posteriori validation allows us to arrive at a priori knowledge.  While Thales introduced geometry, it was Pythagoras who first proved the Pythagorean theorem which establishes a priori knowledge that the square of the hypotenuse of a right-angle triangle is equal to the sum of the squares of the two sides.  Both Einstein’s relativity in 1905 and my theory of one in 2001 make use of the Pythagorean theorem as their underlying a priori Form.  Relativity derives its a posteriori validation from the 1881 Michelson and Morley experiment while the theory of one gets its a posteriori validation from the 1982 Aspect experiment.

Existence and Essence.  The term a priori refers to a four-dimensional mathematical essence while a posteriori refers to a three-dimensional commonsense existence.  Essence is the true kernel of a thing while existence simply refers to the sheer fact that a thing is.  The soul is an essence while the ego merely exists.  William Barrett wrote in his 1958 book Irrational Man that the history of Western philosophy has been one long conflict between existentialism and essentialism.  Jean-Paul Sartre (1905-80) defined existentialism as the philosophy for which existence precedes essence.  Conversely, essentialism asserts that essence precedes existence.  The problem is that precedence is a temporal operator and essence is outside time—meaning that the notion of precedence here is meaningless.  It is the age-old problem of the chicken and the egg.  As a fundamental attitude, The Bernoulli Model is existential—but based on a portfolio of empty Forms—with the faith being that the application of the model will animate the Forms thus realizing the essence of model.

The Delphi.  Existentialism is based on the self-verifying Form of the Cartesian cogito—I think, therefore I exist.  The Bernoulli Model employs the self-verifying Form of the Delphi method which is an iterative process intended to draw out executive values—and is named after the Socratic inscription on the oracle at Delphi—Know thyself—which is of course equivalent to the Cartesian cogito and also equates to the objective function from operations research.  The basic Delphi value pertains to allowable downside risk exposure for the portfolio distribution.

Forecasting.  The statistical distribution is one of the most beautiful Forms for the reason that it represents both the forecast of outcomes as well as the expected uncertainty.  Advanced forms of forecasting of The Bernoulli Model include intertemporal riskmodeling—which is able to accurately represent time-series data like energy prices and foreign exchange rates characterized by contemporaneous and intertemporal dependencies.  The approach deconstructs historical data into signal, wave and noise—each of which is then forecast separately.

Integration.  Integration is the process of aggregating or bringing together forecasts of outcomes and uncertainty.  The closed-form method of integration involves matrix algebra and applies strictly to the two-moment normal distribution.  The Bernoulli Model also employs the open-form method of Monte Carlo simulation with the four-moment Camus distribution in order to capture and integrate the full spectrum of heterogeneously distributed forecasts.

Utility.  Daniel Bernoulli (1700-82) founded utility theory by writing a paper entitled Exposition of a New Theory on the Measurement of Risk—with the theme being that the value of an asset is determined by the utility it yields rather than its market price.  His paper, one of the most profound ever written, delineates the all-pervasive relationship between empirical measurement and gut feel.  The Bernoulli Model employs utility theory by adjusting market returns to more accurately represent internal values.

Optimization.  Optimization is part of operations research that originated in World War II when militaries needed to allocate and deliver scarce resources to operations.  Optimization algorithms search either cost-function or risk-reward space to determine the optimal value for the objective function subject to Delphi constraints such as allowable downside risk exposure.  Local search algorithms include linear programming and hill-climbing algorithms while global search algorithms include genetic algorithms.

Efficiency.  In risk-reward space the process of optimization is carried-out for every level of risk with the result being the construction of the efficient frontier.  A similar process in cost-function space is known as data envelopment analysis.  The Bernoulli brothers, James (1654-1705) and John (1667-1748), set the roadmap for efficiency analysis by finding the curve for which a bead could be slide down in the shortest time.  The efficient frontier has come to form the bedrock of portfolio theory since its introduction in 1952 by Harry Markowitz.

Complementary.  Niels Bohr (1885-1962) defined the complementary principle as the coexistence of two necessary and seemingly incompatible descriptions of the same phenomenon.  One of its first realizations occurred in 1637 when Descartes revealed that algebra and geometry are the same thing.  In 1860 Maxwell revealed that electricity and magnetism are the same thing.  In 1915 Einstein revealed that gravity and inertia are the same thing.  The ability to contrast paradigms presents the invaluable feature of the complementary perspective.

The Agency Problem.  The agency problem is the pervasive predicament whereby agents select against organizations.  The first realization arose between tenant farmers and landowners.  A business manager who invests in marginal projects so he can reaps the benefits of being the manager of a larger portfolio is selecting against the organization.  The risk measuring concept of VaR originated because traders were playing the game of heads-I-win-tails-you-lose and exposing organizations to huge risks.  When gambles went south the traders simply moved on.  The problem now is that traders are gaming VaR.  Owing to its mathematical basis—The Bernoulli Model is made virtually impenetrable to the agency problem.

Conclusion.  The Harvard Business Review publication began in 1922 with the intention of connecting fundamental economic and business theory with everyday executive experience.  The Bernoulli Model represents a systematic realization of that very mandate.  The approach frees executives from political gridlock and offers the ability to either skim the surface of decision analysis or drill-down and examine the inner workings of decisions and asset valuations.  It affords a comprehensive overview and provides unequivocal confidence allowing executives to sleep like babies knowing what Einstein knew—when the math is good the math is good.


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