On the World
Neglected Degrees of Freedom in Sciences
NEVATHIR
January 25, 2017
Today we describe a fallacy committed by many scientists in almost every discipline that will prove their results deserve the same fate as alchemy. I have already proven the unreliability of hypothesis tests before, and the following discussion deals another heavy blow to modern sciences.
Without loss of generality, marginal analysis in economics is offered as a example to illuminate the topic without the need of comprehensive theoretical construction.
Marginal analysis claims that equilibrium market price occurs at the intersection of supply curve and demand curve. These curves are formed according to the relationship between price and supplied or demanded quantity. Thus generic equilibrium market price is a point or at most zero-dimensional quantity. Why curves and points, not surfaces and curves? The former assumption is not obviously or naturally justified, and lends us a argument against it.
Every ordinary businessman knows he can strike different market-clearing quantities with different customers at the same time. Like, buddies get extra services. Given a price, the quantity of supply is undetermined without knowing whether the customer is a buddy! For simplicity, suppose there are no other factors. The extra dimension called buddies has to be formed along with price so that supplied quantity may be determined. Similarly, customers determine the demanded quantity with price and the additional buddy criterion.
Thus, the generic relationship between price and supply or demand is a surface and equilibrium market price is a 1-dimensional object, like knots or braids.
Take into account that the buddy criterion is a simplification. Actual supply or demand schedule may be a n-dimensional quantity, and equilibrium market price a (n-1)-dimensional quantity.
Physicists are very familiar with the effect of dimensions. Quantization gives radically different objects for different dimensions. Graphene isn't diamond. Saturn is a ball, unlike its rings.
It's logical to speculate the effect of previously neglected degrees of freedom, in this case dimension, on the theory of marginal analysis, and more generally on all sciences. These neglected degrees of freedom likely will render previously held propositions nothing but alchemy. And real science may be done once scientists overcome their own negligence.
The argument presented here isn't a isolated piece. As before, my proposal to construct a unified theory of sciences builds upon my own research on the foundation of empirical sciences that discredited hypothesis tests, and neglected degrees of freedom are another topic to consider.
Scientific developments in previous centuries have made the construction of a unified theory of sciences possible. It's our intelligence and wisdom that constrain the scope and soundness of our sciences.