Three dimensions are needed to specify the centre of the object. Three more are required to specify location and position of the object in motion. Spin groups whose dimension are square root of that vector in n-dimensional space give four more dimensions.A particle is treated as of dimension 0 and  a brane as of dimension 1 as some dimensions curl up.There is a spending symmetry from degrees of freedom, then holding distributivity there is an impact grading with k* algebra. With affine space and no preferred origin, the gamma starts time flow and alpha is dimensionless, as in string theory.Applying to capital asset pricing , a positional scalar inhibits the length of vector and beta determines the risk and the range of shape of yield curves.

Events are grouped by  easy methods as of  mind or as of matter. This makes both just methods of convenience for grouping with increasing redundancy. Events and not particles make physics, hence, we look at particles merely as a series of events. The contribution of Quantum Physics lies in considering physical events as discontinuous. The causal chains are perceived in some degree due to the object so perceived.

Multi-layer perceptions can  be dealt with pseudo-random numbers which  are explained by beta minus expansivity and multiplicative linear congruent generators. The non-linear in data will require a hypothesis either of volatility feedback or leverage hypothesis when used for financial analysis. Volatility feedback essentially would mean the delta hedge is working and the market has a fine structure constant. The dimensions being added at edge we have embedding dimensions with n histories. As  the investors attitude towards risk and expected returns are non-linear there is a distinction between non-linearity in mean and in variance as it is a multiple moment analysis.

The empirical relevance of imperfect risk sharing for asset pricing requires separation of Risk Aversion and Inter-temporal Substitution. The elasticity of the inter temporal substitution could be taken as reciprocal of the co-efficient of relative risk aversion given by gamma which has a close connection to market catastrophe. The stochastic discount factor is the inter temporal marginal rate of substitution. i.e. the discounted ratio of marginal utility in two successive periods. In the psychological models of decision making people make choices that differ in several respects from expected utility theory. In a static context it can be prospects where instead of preferences over consumption there are gains or losses relative to a benchmark outcome, with losses given greater weight. Gamma 's become curvature parameters and lambda,( from market wave) measures loss aversion.

The mind has thoughts and no other object except ideas. In its memory what it knows is in the past yet the act of knowing is in the present. This is what philosophers say that there is an act of knowing and the object which is known. Perception and conception. Knowledge is then the awareness of the idea and perception of the inter-relationships between ideas. With a logical syntax we arrive at the notion that matter is a series of events or strings and these events can be collected and bundled. Quantum logic would treat physical phenomenon as discontinuous, hence, perception is an effect of the object perceived. Knowledge of the physical world is an abstract properties of structure, thus, images which form a loop. A non-perceived material object can be a conception as an image, the difference arising from being perceived and consciously perceived being of degree from loop theta.

With alteration in capital asset prices, the gains in each year of the expected life of an investment project requires a readjustment of the return rates and discount rates. The internal rate of return could make the stream of discounted net benefits equal to the initial capital cost. The projects with high net present value may not record high internal rate of return with adjusted market data while deriving an estimate of the social surplus associated with the project in determining net worth. It is the social rate of discount and the cost of capital which decides the allocation of resources between the public and private sector. The social time preference rate is to lead to the emergence of the modern state,  from the spallated hypothetical global state and the  time required for restoration of the third state which  is the proposition put forward in Legum Baccalaureus ( New Age Books) when the issue of uncertainty is dealt with. Neutrality, Political Robustness and compatibility appear as major considerations in collective decision making.

If knowledge has a triadic movement which begins with sense perception as awareness of the object, then vide critical faculties and sceptical criticism of senses it becomes subjective. The last stage being self-knowledge where object and subject are indistinct.

To discuss the theory of a firm in social choice framework, what is required is the axiom of completeness.  A set of alternative choices where A is  being preferred to B or B to A as the operator or as the generator there is indifference between A and B, there is completeness. The preferences are transitive. If A is preferred to B and B is preferred to C then A is preferred to C. Indifference's are quasi-transitive. If there is indifference between two or more alternatives any alternative can be chosen and this specific choice is indeterminate. Probability can be assigned. Risks are calculated with reasonable expectation considering all the three markets. Sufficiency is then a condition.

The optimal level of public expenditure would be a value which is closest to individual preferences contingent upon the specific set of property rights that exist. Individual indifference and preferences are about property right structure and mechanisms to change it as a generator operator behaviour. Social indifferences and the commonality of preferences being considered, Laws which effect group behaviour rendering many other behaviour redundant generate efficient reflection of individual preferences when market crystallizations are sufficient with bounded rationality.Optimality requires an emotional cost depending on the outcome of the decision and cognitive costs which is of the mental processing cost of coming to a decision. The time required for restoration of the third state is the measure of benefit obliquely.

While discussing Rousseau's rhetoric " Man is born free, but everywhere he is in chains" reference is made to Byron's  Corsair by Russel
             O'er the glad waters of the deep blue sea.
             Our thoughts as boundless and our hearts as free
This freedom of choice runs into trouble if we take into account the four kind of alienation's, Man from man, Man from the means of production, Man from the process of production, Man from the end product as laid out by Marx. Read Yahweh = dialectics, Church = Communist party, Messiah = Marx, Second Coming = Revolution. This is not the spiritual dialectic of Hegel but dialectical materialism. The individual choice from an indifference schedule and social choice from commonality of preferences, leads to the question of theory of the firm, state owned enterprises.

http://www.worldcat.org/title/cho-gyal/oclc/62598928&referer=brief_results
Ideas lead to opinion. Conception and perception

http://www.worldcat.org/title/legum-baccalaureus/oclc/297203511&referer=brief_results
Toplogical Jurisprudence. Topos has Greek roots and Jurisprudence Latin


http://www.worldcat.org/title/methodological-frame-of-the-field/oclc/69984201&referer=brief_results
Super String Theory