## Mis-use of math

m concoyle
*02 Jul 2013 16:55 GMT*

Alternatives to both formalized axiomatic math and to physical descriptions based on either indefinable randomness or non-linearity

(See scribd.com put m concoyle into the web-site’s search bar)

The failure of the entire social system…,

a system in which all of society focuses on “serving the needs of the ruling class,” a similar social structure as was the Roman-Empire, where Roman civilization was designed to serve the Roman emperor and his associated ruling-class in Rome,

…, system failures such as the failure of (as the media story goes) the money lending between banks (since the banks all know that financial transactions are now (at least since 2008) all based on fraud),

which was associated to failed investments [or the failure of the society to stop the destruction and poisoning of the earth, where this failure to stop the earth’s destruction is done by the political system in order to serve the selfish interests of the few bankers-oilmen-military people who own and rule society]…,

where the bank failures was, to some large-degree, brought about by failed calculations of risk, where this risk was determined by using the math methods developed concerning the random context of quantum physics, a method associated with indefinable randomness, where the distinguished states, whose probabilities are to be determined, are patterns which are either not stable (eg elementary-particles) or not calculable (eg the spectra of a general nucleus).

Now this failed math construct, concerning risk (or randomness), is becoming the basis for a (failed) probabilistic model of a future “crime perpetrator,” who is to be pre-emotively exterminated by the state, based on an easily manipulated model of an enemy, a model which can be easily manipulated by adjusting data or adjusting categories to which events belong, ie by adjusting an arbitrary definition (or arbitrary context) of an indefinable and unstable pattern, eg where an enemy might be defined to be “a person opposed to the interests of banking-oil ruling-class”

(where the protection of the ruling-class has defined the national security system).

Note: Because math has become based on axiomatic formalizations, much in modern math deals with descriptive contexts in which

either

measuring is not reliable, eg non-linear and/or chaotic contexts associated to the measuring constructs upon which the descriptions of patterns are based, as well as where the patterns being described are not stable patterns, eg from non-linear shapes to elementary-particles,

or

the basic events of random patterns are either not stable or not well-defined, ie no known math methods can be associated to a calculation which leads to the identification of an observed system’s events…, which are either not stable events or are not definable…., or to the determination of their probabilities,

…, (the [so called] failure of the money lending between banks, which was associated to failed investments, though more likely, the bank failures were associated to failed calculations of risks) where this set of failed investments was turned into an opportunity to…,

lie to…,

de-fraud…,

steal from…,

and then oppress…,

…, the public,

so that the ruling class was saved from ruin by their failed investments…, where this opportunity to save the ruling-class from its own induced failures was facilitated (caused, or set-up) by the media (or propaganda system) in the media-governing-military system in which we live, which is designed to serve the needs of the ruling-class.

This (same) Roman-model of civilization has repeatedly proven itself to be a failure.

Yet, this failed social structure has come to control the knowledge and creativity of the society.

This was the main point of power, which was central to Roman civilization, namely, the ruling class was served by the military, and the military was also where the central repository of knowledge and the basis upon which practical-creativity was instituted, ie the Roman legions built the water systems and sewers and roads for the towns in their newly acquired lands.

The narrow models of cities, agriculture, and finance (stable money) of the Roman civilization was built and organized around the engineering structures which the Roman armies built.

One sees that this is the same type of narrow context requiring ever more expansion and exploitation and destruction about which the banking-oil-military defined ruling-class also depends today.

Similarly, today, technological engineering is funded and designed to support the ruling class.

That is, today, the ruling class control the information channels and the (university) centers of learning within society, so that these structures are constructed and designed to serve the interests of the ruling class.

The failures of math and physics…,

[most notably that quantum physics and particle-physics both of which have no relation to practical creative development within society, note: micro-chips are built based on knowledge of thermal physics]

…, are related to a formalized axiomatic language, which was made fixed by the decree’s of the ruling-class (though instituted by the experts who serve the interests of the ruling class), this was around 1910, so that the descriptive constructs of math and physics are based on rigid axiomatic formalism, and as a result the described patterns of the professional mathematicians have come to be without any content, ie they cannot describe the observed patterns of general fundamental systems to sufficient precision (both in general quantum systems and in regard to the stable properties of the solar system) and they are unrelated to any form of practical creativity (except the solvable parts of classical physics, which are still the basis for nearly all of our “modern” technology).

The math statements made within the context of a formalized axiomatic structure form a formalized language which can be used to describe properties, which belong only to an illusionary world, and thus, these ideas (or patterns) can be manipulated so as to form a quantitative structure, which, if carefully constructed, can, nonetheless, be used to support arbitrary ideas, so that these arbitrary ideas appear to be based in an objective “quantitative set of measurements,” eg statistics being based on vague and unstable patterns used to define a random event space.

This manufactured quantitative relation to an illusionary world of false images is the result of math having come to be about expressions (of a system its containment and its measures) about relations which exist based on a formalized axiomatic basis, which it is believed “can be assumed to be present in regard to any measurable description, in regard to any (vague) pattern, and in a context where measuring is not reliable,” and, subsequently, this is a descriptive context, which has no practically useful content, other than creating illusions of measurable objectivity which are used in the media (to deceive the public). Nonetheless, it is a descriptive construct which allows for rigorous treatment concerning any invented illusionary world, so as to be based on the (this) formalized axiomatic basis (for a too technical language of formal mathematics).

New ideas come from people who are at the margins of society rather than coming from the class of peer-reviewed, professional science and math people. Referring to peer-review as if this makes an authentic truth, is similar to look to the media to describe the relationship which the public has to the actions and intents of the governing institutions, as the practically useless and failed math-physics constructs of: quantum physics, particle-physics, string theory, and non-linear based general relativity have shown.

The professionals are good at adjusting complicated instruments and gradually extending an instruments range of uses.

Furthermore, a professional math and science person, is a carefully selected particular personality type, and would be a person who is at a prestigious university, ie aggressive and competitive, who might best be characterized as being obsessed with (their own) memorized dogmas, which is mostly symbolic, and these symbolic dogmas would be without content, in regard to what the technical language (of such professionals) is trying to describe, eg particle-physics is not capable of describing the stable spectral properties of a general nucleus, but that is what it is supposed to be describing.

New ideas which are practically useful, come from people on the margins of society, where such people as: Faraday, Copernicus, Kepler, Tesla, the Wright brothers, Einstein (at first), etc existed (but Einstein was raised-up to become an “illuminati,” while the much more substantial, Tesla, was pushed aside [maybe because Tesla did not talk with academics, but rather talked to investors]).

On-the-other-hand, within the academic world Einstein axiomatized electromagnetism and special relativity, and he borrowed from E Noether, the symmetries between time and energy, to find [Energy = mass], but his general relativity, ie trying to axiomatize inertia, has been a disaster, ie trying to quantize a non-linear context where measuring is not reliable, and these efforts fit into the newly begun effort to formalize the axiomatic structure of math, eg the efforts of the Bourbaki professional mathematcian’s program of axiomatizing math.

Math as a technical descriptive language

(See scribd.com put m concoyle into the web-site’s search bar)

But math is about:

1. Quantity and shape

And

2. Where, there is reliable measuring, and there are stable patterns, where these stable patterns are both (a) to be described, and (b) there are stable patterns which are a part of the descriptive constructs.

These general math properties are more necessary, in regard to descriptions of stable measurable patterns, than are the frames defined in physics, where frames are concerned with the relative motions of the (physical) system-containing coordinate space, within which measuring is assumed to occur.

The frames of physics relate to both metric-stability, or metric-invariance, and the relation that these frames of coordinates have to the properties of a system defining (partial) differential equation, ie the laws of physics.

The idea that a physical system’s defining set of (partial) differential equations which are covariantly invariant…,

ie related to differential-forms (which should also, in turn, be related to an invariant definition of the containing space’s coordinates metric-function, ie not a general metric-function which defines an unreliable measuring context)

…, is not sufficient (ie Einstein’s principle of general relativity is not sufficient)…,

…, one also needs the math property of these equations being continuously commutative everywhere.

Note: An alternative containment context where “inertia might be defined due to the shape of the material containing space.” The geodesics defined in a metric-invariant context can be related to inertial dynamics, but only in the energy-space of a hyperbolic metric-space, if the material is contained within a discrete hyperbolic shape (which is also a metric-space).

A physical system’s defining set of (partial) differential equations which are covariantly invariant is modeled after the structure of the classical force-fields, F, of classical physics, where such force-fields are differential-forms which determine relations (by means of exterior derivatives) between material geometry and local linear geometric measures…,

(ie general covariance, but in classical physics there is metric-invariance),

…, which, when solved, can be placed into an inertial differential equation of, ma = F, which, in turn, when solvable, is both accurate to sufficient precision, and its description is stable, and the system can be controlled, which allows for practical usefulness in regard to this information’s use.

General relativity assumes that only local linear derivatives are fundamental, and a (general) metric-function for a coordinate space can be found in a context of general covariance, ie a partial differential equation pertaining to differential-forms, so that a solution to such an equation can determine

either

the coordinate space’s natural local linear measure for length, ie the coordinate space’s general metric-function,

or

the sets of local linear geometric measures consistent with the general metric-function.

In turn, the geodesics, which are determinable from the metric-function, determine the inertial properties of the system.

This is a circular relation between local coordinates and the model of the derivative as a “local linear measure” which cannot be unraveled.

The problem is that measuring requires both a metric-function and local linear derivatives to exist as stable patterns within the descriptive construct.

Otherwise the partial differential equation is non-linear and defines a descriptive context (or a set of containing coordinates) which are found from a non-linear differential equation, ie this is an unreliable context for measuring.

Thus, general relativity has only solved one problem; the one-body system which is assumed to possess spherical symmetry, a continuously commutative shape almost everywhere. But, try to put another piece of material into such a one-body construct, and an ensuing attempt to find a stable shape (eg a stable solar system) can never be resolved, the context does not allow measuring to be reliable, and the math patterns will always be chaotic. So using this descriptive context to describe the stable solar system is unthinkable.

There are two basic categories for physical description (having just dispensed with general relativity) classical description and quantum descriptions.

Classical physics

Classical physics is based on geometry and measuring and its laws about a physical system’s partial differential equation apply to general classical systems, when solvable they identify accurate measurable patterns for the system defined to sufficient precision (to be both verifiable and practically useful) and they are practically useful descriptions of the physical system’s measurable patterns. The descriptive structure goes from local measuring to a global solution function, and it depends on:

1. materialism,

2. a differential equation, and

3. a system-containing (metric-invariant) metric-space.

Non-linear systems of classical physics

However, most partial differential equations, which are related to the definition of classical systems (based on classical laws of physics) of a material system’s defining (partial) differential equation (which has been defined within a containment set and associated sets of measurable properties), are non-linear, and thus they are not (in general) solvable. However, the critical points of a non-linear (partial) differential equation…,

[ie zeros of the homogeneous non-linear differential equation, and boundary points, and points where the differential equation is not defined] {of such a non-linear partial differential equation}

…, determine different regions of the domain space where the dynamical properties of the interacting material (which composes the system) determine convergence properties, convergences to limit cycle boundaries of the different regions of the domain space.

Furthermore, some solutions to non-linear partial differential equations are related to geometric properties, eg the lower-dimensional boundary shapes associated to higher-dimensional geometries, ie cobordism. But if the shapes are non-linear then they are almost always unstable, and thus, they define a context where measuring is unreliable, and the patterns are not stable.

However, in the context of general (or non-linear) shapes, it has been shown that there do exist sets of very stable shapes, ie the discrete Euclidean shapes and the discrete hyperbolic shapes, but (even though they were derived from a general context concerning shapes) these stable shapes are: linear, metric-invariant, and continuously commutative everywhere (except, perhaps, at one point). This is the geometrization theorem of Thurston-Perlman.

But elementary considerations concerning “reliable measuring and requiring a descriptive basis in stable patterns” are sufficient to see that a: linear, metric-invariant, continuously commutative everywhere, context for measurable descriptions, wherein the stable reliable measuring shapes are: the line, the circle, and cubes, and circle-spaces, which all together form the proper context within which to consider these ideas about “reliable measuring and the existence of stable patterns” as being central to math descriptions concerning patterns about quantity and shape.

Quantum physics

Quantum physics is based on randomness (indefinable randomness) and a stable spectral set, which are concepts (which are supposedly) defined by both a quantum system’s function-space and a set of operators, which represent the quantum system’s measurable properties, but these sets of operators cannot be found for general quantum systems, (ie quantum system’s whose stable spectra can n be measured), and if this description is formulated, the description is neither accurate nor determined to sufficient precision in regard to the quantum system’s observed very stable, and distinctively precise, spectral properties, and, furthermore, the descriptive patterns have virtually no practical value, since it is usually a many-but-few-body quantum system which is described by probabilities (ie it is not a description which can be controlled). The descriptive flow, for the logic of quantum description, is from a set of local operators to a local solution function, which is a descriptive context which, in turn, implies that “measuring in the lab is sufficient for determining the quantum system’s properties.”

So the question is, “Why even try to describe its properties by means of physical laws of quantum systems?”

Is the main problem with quantum physics either,

(1) that “it is a probability based description”

or,

(2) it is a descriptive context which is local, and it [ie this “local to local” math construct] leads to (other) information which is also local, so the math process cannot lead to any further information about the quantum system (that cannot be collected in a local context)?

However, the quantum system is (can be) provided with a new model [eg the quantum system is a stable metric-space shape].

The quantum description also depends on the ideas of:

1. materialism (random material-point-particle-spectral events in space and time),

2. a set of spectral differential equations (or sets of spectral-operators defined on a function-space), where

3. the system containing domain space is a (metric-invariant) metric-space.

But in this function-space context the math structure is seldom continuously commutative everywhere, thus, the stable measurable properties of general quantum systems can (virtually) never be found (only a handful of exceptions, eg the main exception being the H-atom [a two-body system reduced to being a one-body system which is (in this one physical case): linear, metric-invariant, and continuously commutative, ie solvable]).

The only context in which either of these “descriptive constructs” is solvable (either classical or quantum) is when the partial differential equations are:

1. Linear,

2. Metric-invariant metric-space,

3. Continuously commutative everywhere,

The shapes which allow this set of conditions are the shapes which are also quantitatively consistent, and, in turn, these quantitatively consistent shapes are the lines and circles; and then the associated shapes of:

cubes,

cylinders, and

circle-spaces, eg tori and discrete hyperbolic shapes (which are composed of toral components attached to one another).

That is, the metric-invariant metric-spaces whose metric-functions have constant coefficients, and whose curvatures are constant and non-positive.

The descriptive context of:

1. materialism,

2. a differential equation, and

3. a system-containing (metric-invariant) metric-space.

Can be changed to:

1. Material equals an open-closed (within itself) metric-space shape

2. a differential equation, and

3. a system-containing (metric-invariant) metric-space, is an adjacent higher-dimension metric-space than the metric-space-shape model of material, and the material-component containing metric-space, now, also has a shape.

The descriptive context of quantum physics:

1. materialism (random material-point-particle-spectral events in space and time),

2. a set of spectral differential equations (or sets of spectral-operators defined on a function-space), where

3. the system containing domain space is a (metric-invariant) metric-space.

Can be changed to:

1. Material equals an open-closed (within itself) metric-space shape

2. a set of spectral differential equations (or sets of spectral-operators defined on a function-space but now the functions in the function-space are discrete hyperbolic shapes which model material), and

3. a system-containing (metric-invariant) metric-space, is an adjacent higher-dimension metric-space than the metric-space-shape model of material, and the material-component containing metric-space also has a shape.

Note: Even the math structure of particle-physics, 2-dimensional and 3-dimensional shapes in complex-coordinates (which are related, in particle-physics, to quarks and leptons), can be related to the (small) discrete hyperbolic and Euclidean shapes (of the same dimensions, just listed), upon which a new descriptive context for physical containment can be modeled.

In fact, these small shapes, in complex-coordinates, might be related to the energy partitions of a quantum system’s energy space, ie its relation to the quantum system’s quantum numbers (in regard to an energy-wave operator model of the quantum system).

This partition of the energy space’s volume by small fundamental domains of discrete hyperbolic shapes (which are metric-space shapes related to an energy space), into which charges naturally fit, is related to the entropy properties of thermal systems.

In the new structure of:

1. Material equals an open-closed (within itself) metric-space shape

2. a differential equation, or sets of spectral-differential operators acting on sets of discrete hyperbolic shapes which are functions (ie differential-forms), and

3. a system-containing (metric-invariant) metric-space, is an adjacent higher-dimension metric-space than the metric-space-shape model of material, and the material-component containing metric-space, now, also has a shape.

and

4. This (stable) pattern of lower-dimensional material being contained in an adjacent higher-dimensional metric-space, can continue in this dimensional-containment pattern up into higher (hyperbolic) dimensions, where the last known discrete hyperbolic shape has a dimension of ten, and thus this pattern of shapes of “a particular dimension being contained in an adjacent higher-dimensional metric-space” can be continued up to an 11-dimensional hyperbolic metric-space, which is an over-all containment space, so that each dimensional level is to be a discrete hyperbolic shape, which is an open-closed topology, and thus each dimensional level is separated, or is discontinuous, from the higher-dimensional metric-spaces. Within a metric-space of a given dimension the properties of the higher-dimensional metric-spaces are excluded, ie either not observed or difficult to understand how to observe these higher-dimensional properties. The relative sizes of adjacent different dimension metric-spaces can also affect what can be observed.

In this new way in which to organize physical description (I) new stable material components can form during collisions (due to resonance), and (II) stable orbits can be determined by condensed material, which is both interacting within a metric-space, but also being contained in a metric-space-shape, where the shape (and its geodesics) can define an envelop of orbital stability for the interacting condensed material components of the system (within a relatively large-sized metric-space shape), eg the planets interacting with the sun so as to form the stable solar system (where all the material components are contained in a metric-space shape).

I. Within this new structure of description the collision-dynamical-system (defined by a dynamic partial differential equation of material components contained in a metric-space) can result in a new stable discrete hyperbolic shape as a product of the collision,

if the collision has

both

the right range of energy, which allows a new material component to form (where it forms due to resonance),

and

if the original discrete hyperbolic shapes (which are colliding) and the final (new) discrete hyperbolic shape, of the lower dimensional material component shapes, have either the correct range of spectral values, or have the correct spectral values, so that the new (lower-dimension) discrete hyperbolic shape resonates with the finite spectral set of the over-all containment hyperbolic metric-space…,

which is defined within an 11-dimensional hyperbolic metric-space

[which, in turn, is partitioned into discrete hyperbolic shapes so that each subspace of each dimensional-value has a largest discrete hyperbolic shape associated to itself, so that this set of “largest shapes” (associated to all the different dimension subspaces) all together define the finite spectral set associated with the over-all containing 11-dimensional hyperbolic metric-space].

II. While on-the-other-hand the condensed material, which is contained in a metric-space [which possesses a shape], can dynamically (defined by a dynamic partial differential equation of material components contained in a metric-space) define an orbital structure which is related to an envelope of orbital stability, which the shape of the material-containing metric-space defines.

The dynamic structures associated to either the classical differential equations, or, in quantum description, to sets of differential operators (which are now acting on sets of functions which are differential-forms associated to discrete hyperbolic shapes) do not have enough of a relation to stable shapes so as to allow for their solution functions to be able to define the stable properties which are observed for such fundamental physical systems as: nuclei, general atoms, molecules, crystals, or the solar system (as well as dark matter), and thus new containment spaces need o be considered, for all of existence (ie and not simply maintaining the idea of materialism), but it also helps to use consistent math patterns which are measurably reliable and so that there exist patterns in the descriptive context which are stable.