Economic Models' Math__Applies To Physics, As Well__& Vice-Versa...

(P.s. added Tim...)

http://en.wikipedia.org/wiki/Economic_model

"The economics/(physics) profession appears to have been unaware of the long build-up to the current worldwide financial/(mathematical physics) crisis and to have significantly underestimated its dimensions once it started to unfold. In our view, this lack of understanding is due to a misallocation of research efforts in economics/(physics). We trace the deeper roots of this failure to the profession’s focus on models that, by design, disregard key elements driving outcomes in real-world markets/(physics models). The economics/(physics) profession has failed in communicating the limitations, weaknesses, and even dangers of its preferred models to the public. This state of affairs makes clear the need for a major reorientation of focus in the research economists/(physicists) undertake, as well as for the establishment of an ethical/(scientific) code that would ask economists/(physicists) to understand and communicate the limitations and potential misuses of their models."

Tim, I think it quite important to read David Hestenes' entire paper, to see where this paragraph links the maths of any and all model constructs together, and which ones are invalid and useless, verses, the truly valid and useful maths and models... Remember, at the most and absolute fundamental level, all these maths__being one of the fundamentals of all models__are all fully isomorphic, at limits__That's the real 'Conformality' of the entire 'House of Cards...' I think Hestenes has much better captured these facts with humor, than any serious post I could possibly make... The most important thing to recognize, is the fact that all these maths and models absolutely must be grounded in real World and Universal facts, parts, pieces and motions(the 9 degrees of freedom motions, i.e., vectors of real asymmetric wave actions, of the real fs-field...)__1st and foremost...!!!

http://geocalc.clas.asu.edu/pdf-preAdobe8/MathViruses.pdf

Imo Tim, you are going to have to understand the asymmetric/achiral control of the entire Universe's fundamental wave mechanics control mechanisms, in order to see how a Bose-Einstein Condensate truly forms and decays__over time__The true four dimensional aspects of FS-Matter, through its most fundamental wave-mechanics__Pure Wave-Mechanics as Vector-Phase-State-Spaces through Scalar Time Factors... Imo Tim, this takes a full understanding of the achiral actions of opposite handedness(the 3rd state), in a far deeper model of understanding chirality(left and right symmetric states), than you are presently looking at... I hate to keep chasing you back to this well worn point, but until you see what this model represents, I know it's not possible to see the Universe's most fundamental wave and motion mechanics(it's like a self-polarizing triadic orthogonality of the most fundamental hydrodynamic forces__the least understood of the least actions...) When you finally see what I'm truly saying here, the whole world of your personal Universal understanding will explode anew... Build the wire models Tim, and see the true Boogie-Man, in the Universe__It's far more fundamental than the analog-digital models, as they are thus far, interpreted almost entirely dyadically, and I'm constantly speaking about the triadicity of the fundamental polarizations__necessitated by the time scalar waves altered distance actions, in relation to the fundamental orthogonal polarizations, of the FS-Waves... This is more easily understood through 'Tensor Mechanics', as first started by Leibniz, and followed all the way through to Levi-Civita and the many more moderns, like Hestenes'(Geometrical Algebra...) Imo, math is absolutely necessary, but it must be the proper maths, and the even more proper use of the maths, in relation to real World and Universal facts...

A few years back, I named it: 'The Relational Geometry & Algebra of Responsible Intelligence…' It still holds...

A related link:
http://en.wikipedia.org/wiki/Nine-point_circle

The Achiral Non-Conformality, Within The Chiral Conformality...
The Achiral Non-Symmetries, Within The Chiral Symmetries...
The Non-Conservation of Time, Within The Conservation of Space…???

And Tim's Theorem:
http://en.wikipedia.org/wiki/Lester%27s_theorem
http://mathworld.wolfram.com/LesterCircle.html
http://en.wikipedia.org/wiki/Fermat_point
http://en.wikipedia.org/wiki/Circumcenter

And:
http://en.wikipedia.org/wiki/Binary_Golay_code
http://en.wikipedia.org/wiki/Ternary_Golay_code
http://en.wikipedia.org/wiki/Jakob_Steiner
http://en.wikipedia.org/wiki/Steiner_system
http://en.wikipedia.org/wiki/Steiner_triple_system
http://en.wikipedia.org/wiki/Steiner_tree_problem
http://en.wikipedia.org/wiki/Geometric_median
http://en.wikipedia.org/wiki/Ernst_Witt
http://en.wikipedia.org/wiki/Leech_lattice
http://en.wikipedia.org/wiki/%C3%89mile_L%C3%A9onard_Mathieu
http://en.wikipedia.org/wiki/Mathieu_group

P.s.
A few more of the notes I'm working with, Tim:

The Symmetry Illusion…

The Mechanics of Long Wave to Short Wave Photons__Radio to Gamma…
Peirce__The Teleological Logician…
Teleology__The 1^st Beginnings of Knowledge Gives Ya The Ends of Knowledge__Primitive Logic…
Peirce__The Father of True Teleological Pragmatic Logic…
Only Teleological Intelligence__Exists…!!!
The teleological past, present and future of entropy__Gas shrinks upon losing all heat…
A living organism holds a continuum of ideas, to form real intelligence…
Peirce__The Teleological Genius…
Thought mechanics is outside-in__Not inside-out…
Archetype Thought Modes__Pure_Category_Model Logics…
Modal Teleological Epistemic Pragmatic Logic…
The False Vector/Scalar Models of Physics…

Sherrington's philosophy as a teacher can be seen in his response to the question of what was the real function of Oxford University in the world. Sherrington said:  "after some hundreds of years of experience we think that we have learned here in Oxford how to teach what is known. But now with the undeniable upsurge of scientific research, we cannot continue to rely on the mere fact that we have learned how to teach what is known. We must learn to teach the best attitude to what is not yet known. This also may take centuries to acquire but we cannot escape this new challenge, nor do we want to."

Peirce solved Cantor’s, Frege’s and Russell’s paradoxes, before they were ever created__Deep Relational Algebra__Foundations to Tensor Algebra…

‘The Axiom of Choice’ vs. ‘The Axiom of Determinacy…’
Both Geometry & Nature Necessitate ‘The Axiom of Choice’, or No Universe Could Ever Exist__Difference Necessitates ‘The Axiom of Choice/Action…’
‘The Axiom of Difference’ Mandates Choice, or Random Action, As Same…
‘The Axiom of Difference’ Makes Strong Determinism__Impossible…
The Universe Requires ‘The Axiom of Difference’ to Produce Different Quarks and Protons…
Factual Ideas & Goals force logic to actions, occurences and events__which change the world…
Iff granted absolute power, then & only then, can I emplace law to solve all the world’s problems…
Science = A Provable Concept…

Professor Hochberg’s book is best characterized by his own words from the preface: The book attempts to sketch, not work out in detail, an account of reference, meaning, truth and intentionality that stays within the “linguistic turn” characterizing twentieth century analytic philosophy. But it seeks to avoid following the contemporary variants of analytic philosophy that have turned from the analysis of things and facts to a preoccupation with and virtual worship of language and its use. The classical focus on ontology, combined with careful and precise formulations, that marked the writings of the early founders of the analytic tradition, has degenerated into the spinning of intricate verbal webs of analysis. The latter supposedly yield “theories of meaning” but more often signal the rebirth of idealism in the guises of “anti-realism” and “internal realism.” The focus on the world, as what words are about, is often lost as “analytic philosophers” concentrate on language itself—the world being “well lost,” in Nelson Goodman’s honest words… . We shall also note examples of a remarkable combination of arrogance towards and ignorance of the philosophical tradition that is displayed in some writings within the analytic tradition, including influential works.

The Complete/Incomplete “Distinction…”

His paper “Universals”, which denies any fundamental distinction between universals and particulars, surmounts serious objections to a realist view of universals and, at the same time, solves several long-standing problems about them, dismissing other venerable enigmas as nonsense. Ramsey

 

Various reasons for making the distinction between universals and particulars – psychological, physical and logical – can be advanced. Ramsey argues that logic justifies no such ontological distinction. Allusion to the grammatical subject-predicate distinction will not do, since “Socrates is wise”, with the subject “Socrates” and the predicate “wise”, “asserts the same fact and expresses the same proposition” (p. 12) as “Wisdom is a characteristic of Socrates”, with subject “wisdom” and predicate “Socrates”.3

Moreover, there is, he argues, no essential difference between the (in)completeness of universals and that of particulars. “Wise” can, for example, be used to generate propositions not only of the atomic form “Socrates is wise”, but also of the molecular form “Neither Socrates nor Plato is wise”. But “Socrates” can also be used to generate propositions of both these forms: e.g. “Socrates is wise” and “Socrates is neither wise nor just”.

There is therefore a complete symmetry in this respect between individuals and basic properties (qualities). As Ramsey succinctly puts it, the whole theory of particulars and universals is due to mistaking for a fundamental characteristic of reality what is merely a characteristic of language (p.13).

The Particular/Universal Distinction ¬…

One of his co-workers, Frank Ramsey, took Russell’s warning very much to heart. But Ramsey soon came to the conviction that philosophers had not only been misled by language to adopt and adhere to a subject-predicate logic and a denial of relations. Writing in his 1925 Mind paper “Universals” (hereafter U) Ramsey declared: “nearly all philosophers, including Mr Russell himself, have been misled by language in a far more far-reaching way than that; that the whole theory of particulars and universals is due to mistaking for a fundamental characteristic of reality, what is merely a characteristic of language.” (U: 13)

The Particular/Universal Distinction Illusion__The Language Illusion_At Limits…
“True” Is An Incomplete Symbol… Ramsey
Quantum Uncertainty & ‘The Axiom of Difference…’
Russell, Quine, Putnam, Chomsky__Purile Bastardizations of Peirce…
The Subjective Psychology & The Objective Philosophy…
Russell’s Phony Symbol Semiotics__A Logical Joke…
Language and Linguistic Non-Sense__A Running Series of Logical Jokes…
The Frege-Russell-Quine Psychological Era of Logic…
Russell’s False Symbol System__Confused and Conflated Semiotics…
The ‘One-Many’ ‘Universal-Particular’ Plays Out In Every Hand of Logic…
The ‘One-Many’ Central Logical Illusion… 
Russell’s Purile Tensor Logic…
The Mind Is A ‘One-Many Continuum’, Having To Interpret Both ‘Universals’ and ‘Particulars’__At Once__In Each Propositional Analysis…
The Central ‘One-Many Continuum’ Logic Problem Always Exists…
‘Formal Truth Formal Logic…’ Ramsey…
¬ () = X Is False…(let ¬ = the empty)
¬ {()} = X Is False…
1^st Methodological Tensor Choice Modality…
The Continuum of Triadic Choice Modalities…
All Knowledge Is Combinatoric From Its Initial State, Except Psychological Non-Knowledge Systems…
Psychology__The Modern-Day Anti-Knowledge System__Nietzsche On…
Psychology can not be added, subtracted, multiplied or divided…
Psychology, being non-mathematizable, must remain non-scientific…
Hard Knowledge vs. Soft Non-Knowledge…
The Methodology of Discovery__Science…
Weak Belief vs. Strong Knowledge…(from Hume on)
The Combinatoric Compositionality of All Real Hard Knowledge Systems…
Economics is primarily historically combinatoric, except for the slight and short anomalies of intermittent negative psychological events…
Modal Knowledge vs. Modal Belief…
‘The Difference Axiom’ of Knowledge vs. Belief…
The Continuum/s Obviously Create/s Difference…
Determinism requires symmetry, whereas the Universe is asymmetric, thus the asymmetric actual eliminates hard determinism…
Francis Bacon’s Eliminative Induction…
Eliminative Combinatoric Induction Mechanics…

http://en.wikipedia.org/wiki/Multinomial_theorem
This my help with this Tim:
The Universal Isomorphic Algorithm__UIA = ∑∫∏v -> IC:M Iff / ≡ ∑’s •…(The universal isomorphic algorithm equals the sum of the integral product variables, implying the isomorphic center of mass, if and only if divided identical to the sum’s center…)
Proof
This proof of the multinomial theorem uses the binomial theorem and induction on m.

First, for m = 1, both sides equal x₁ⁿ since there is only one term k₁ = n in the sum. For the induction step, suppose the multinomial theorem holds for m. Then

by the induction hypothesis. Applying the binomial theorem to the last factor,

which completes the induction. The last step follows because

as can easily be seen by writing the three coefficients using factorials as follows:

A related Pdf:
http://mathsci.kaist.ac.kr/~drake/pdf/towards-a-combinatorial-theory-of-multiple-orthogonal-polynomials.pdf

Best first source informations:
http://www.constitution.org/bacon/nov_org.htm
http://en.wikipedia.org/wiki/Pafnuty_Chebyshev
http://en.wikipedia.org/wiki/Andrey_Markov

And as Chebyshev's work relates analog to digital:
http://en.wikipedia.org/wiki/Chebyshev_filter
Chebyshev filters are analog or digital filters having a steeper roll-off and more passband ripple (type I) or stopband ripple (type II) than Butterworth filters. Chebyshev filters have the property that they minimize the error between the idealized and the actual filter characteristic over the range of the filter, but with ripples in the passband. This type of filter is named in honor of Pafnuty Chebyshev because their mathematical characteristics are derived from Chebyshev polynomials.