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Meaning in math

Review of a review of a book, "Meaning in Mathematics" which is a book of essays about the philosophy of math, edited by J Polkinghorne, a physicist-theologian, and reviewed by M Heller a philosophy professor (and also a theologian), where this book review appeared in AMS Notices, May 2013
There is a book, "Meaning in Mathematics" which is a book of essays about the philosophy of math, edited by J Polkinghorne, a physicist-theologian, and reviewed by M Heller a philosophy professor (and also a theologian), where this book review appeared in AMS Notices, May 2013, where in order to form this book, a small set of "so called" "qualified experts" J Polkinghorne, R Penrose, M Leng, M Steiner, T Gowers etc (altogether about 15 authorities), who discussed, in the book, various things about math, including "the independent realm of mathematical reality," and some doctrinal subtleties about math, as well as other questions given below, as presented in the book review.
The review begins with the question about the dimensions needed to describe measurable patterns of "reality" vs. "the idea of materialism," and the question, "Are the dimensions of materialism incapable of describing the observed physical patterns?"
This would be a good question, if it were placed in an open context. However, it appears that these experts are concerned about the math structure of particle-physics, not in regard to open questions which invite the exploration of new math ideas. For example, new ways in which to mathematically organize a physical description, so that the new ways of organizing math patterns possess more dimensions than are allowed by the doctrine of materialism and its companion particle-physics (where particle-physics requires that the random particle-events be contained in 3-space, or in space-time).
But the reviewer indicates their bias toward "the interpretations which qualify them to be a member of an expert team," where the reviewer leaves the review with the idea that... ,
particle-physics is about how the phenomenon of the physical world all depends on a mathematical-model of the internal transition patterns in regard to both the internal states as well as the decay patterns of elementary-particles (where these patterns are modeled in terms of a set of internal-dimensions associated to elementary-particles),
... , but since there are no valid models of the spectra of a general nucleus based on the laws of particle-physics, it is difficult to see "how such a statement has any relation to truth," but nonetheless it is claimed that these patterns of transitions of internal particle-states are all defined mathematically, and imposed on the data of particle-collisions in particle-accelerators, so as to be done with great (math-pattern) consistency.
And then the final question of the reviewer is, "Does this tell us something about the nature of mathematics itself?"
[Answer from the author of this paper; that math patterns allow us to interpret our world of experience, but what is the correct interpretation of that experience, that unstable shapes in 3-space (or space-time) decay according to the patterns of U(1)( x SU(2) x SU(3), or that these patterns are involved in material interactions at the quantum level, but these interactions provide no valid descriptions of observed stable physical systems (they need to be widely applicable and provide descriptions to sufficient precision in regard to large sets of very stable systems [nuclei, general atoms, molecules, etc], but if these patterns are "to be true representations of the world" then they also need to be related to practical creativity {the stability of these physical systems implies they are solvable and they form in a causal context}.]
Though the philosophical questions put-forth by these experts, associated to the book "Meaning in Mathematics," could lead to new ideas, the experts prefer to organize them into an "envelop of fixed interpretations" which define the domain of the experts.
So this book is really about imposing the arbitrary thought of intellectual authorities, concerning the (regular) decay patterns of unstable shapes which are the products of high-energy particle-collisions, onto an educational endeavor, which is now focused on trying to understand physical phenomenon based on these regular decay patterns of elementary-particles (but physical phenomenon is unrelated to the decay patterns of these elementary particles)... , so that the educational endeavor cannot succeed in realizing a practically useful description of observed very stable physical properties.
Particle-physics has been around since the late 1940's and though it fills technical journals with complicated math patterns (actually logically inconsistent, and apparently in-comprehend-able, math patterns) the stable systems, which are supposed to be the focus of these descriptive structures, are not being related to sufficiently accurate descriptions nor to useful applications (other than being relatable to rates of nuclear reactions in the design of bombs).

A better philosophical discussion... , one not so beholden to a failed authoritative doctrine... , might go as follows:

Meaning in math is about how "precisely described patterns, concerning measurable-properties and shapes, can be related to practical creativity."
If math patterns cannot be related to practical creativity then such math patterns have no meaning.
Measuring deals with reliable comparisons, ie relating standards of measuring to stable systems so that the system's properties can be identified based on general law and these properties used in a carefully measured and put-together new systems which are controllable (or useful).

"The independent realm of math reality" is an idea which is about deception.

The main issue of math is about the stability of identified math patterns, and the context within which measuring is reliable (or stable).
When measuring is reliable, then a precise description of a pattern has a valid context, if the pattern is stable. If a describable (or measurable) pattern is stable then it can be used in a practically useful context.

Some of the questions posed by the contributors in the book "meaning in mathematics," and mentioned by the reviewer, in Notices, go as follows: Note: where the answers to these question given by the author of this paper are given in [ ]:

Are numbers objects?
[Only if they are used in a context where measuring is reliable.]
Can math patterns be compelling, (in that, if proven true then it is a pattern which will be found to exist objectively, ie in a measurable context)?
[This would be a true statement if the math context is stable and measuring is reliable, and if the pattern has useful practical creative value.]
Can consciousness be a factor which is applicable to math descriptions?
[Only if there is a valid, stable mathematical model of life and its consciousness.]

Does materialism define the context of existence, or does existence depend on higher-dimensions?

This is posed as an open question but it actually will be put into the traditional authoritative context of today's intellectual authorities, ie it will be related to particle-physics.

Another set of questions which could have been asked in the article, are:
What is material?
and
What about the different types of material (charge, mass)?
Are different types of material associated to different containment spaces?
For example, inertia belongs in Euclidean space, while charge and energy belong to hyperbolic space (or equivalently, space-time space).
Can a globally commutative function-space be best found by associating the individual functions of the function-space with discrete hyperbolic shapes (with certain set properties) and relating... . the usual commutativity (in regard to a pattern-defining set of operators acting on the function-space) of... . the global function-space, instead, to sets of continuous locally commutative (individual) discrete hyperbolic shapes which possess various properties of: size, dimension, and set-containment relations?
This is about the process of fitting stable shapes (ie discrete hyperbolic shapes) into various quantitative structures which are generated from a finite quantitative set.
That is, it is doubtful if both the observed properties of system stability and a reliable measuring context can exist simultaneously in a consistent math context (consistent both quantitatively and logically) unless a finitely generated set of stable shapes exist in a metric-invariant containment set.
That is, physical law, which is based on non-linearity, also requires an underlying context of stability and containment within a metric-invariant context, in order for both stable systems and reliable measuring to be observable attributes in a math containment context (or in a context of math descriptions). Furthermore, the operator constructs, in regard to the measurable properties of patterns (physical systems) within a quantitative containment-set, depend on the underlying stable shapes as a part of a discrete definition of such operators, which identify the measurable changes and/or measurable patterns, but with the set of stable shapes within the containment set are to be dominant in regard to what measurable patterns can exist in a stable context. That is, the discrete construct which becomes associated with local operators supports (and depends on) an underlying stable containment context.

These are very interesting questions about language-systems of math description,

But, unfortunately,
The point of the article (ie the book review, in Notices) is that abstract ideas about math and science can only be considered within the context of traditional math and science authority.

The article is about the dissection of math language into a fixed set of abstract categories, which are provided (to the [allowed] intellectual communities) by the traditional authorities of math and science... ,

... , and then "the identifiable set of learned (or authoritative) communities are" to study math patterns in such a narrow context.

This, dissection of the language of math into categories which have been mapped-out by the authorities, is similar to studying molecular properties of biological systems based on the narrow set of "detectable molecules" and basing descriptions on the correlations which can be made in this narrow context. Instead, one really needs a valid model of life, and since life is a highly controllable system and... . this property of being controllable... . implies that such living-systems actually exist in a solvable and causal math structure.
[Such a viewpoint (of living-systems needing to be associated to simpler math models) is never considered. However, geometrization allows new math contexts, which can be based on the idea of stability, to be considered, since such a formal authority for the idea of stability has now been formally established within the intellectual community. However, the formal structure of geometrization is not really needed to consider the idea of "reliable measuring and stable patterns" as being the central attribute of math descriptions]

In the conclusion, of this book-review in Notices, there is the statement that particle-physics is about how the phenomenon of the physical world all depends on the mathematical-model of the internal transition patterns in regard to both the internal states as well as the decay patterns of elementary-particles... ,
but these properties are not relatable in any valid way to the observed stable patterns of nuclei, atoms etc.
... , where it is claimed that these patterns are all defined mathematically and imposed on the data of particle-collisions obtained from particle-accelerators, so that these hidden math patterns allow us to classify and identify data from particle-collisions in particle-accelerators. But are these patterns simply the decay-patterns of unstable states which are transitioning to stable states, and thus, these patterns are of no value in regard to identifying the stable spectral-patterns of nuclei, general atoms, molecules etc?

This way of allowing fixed authority to set meaning concerning observed patterns and an associated set of math patterns, and their interpretations, is really about imposing the arbitrary thought of intellectual authorities, concerning the (regular) decay patterns of unstable shapes which are the products of high-energy particle-collisions, onto an educational endeavor, which is now focused on trying to understand physical phenomenon based on these regular decay patterns of elementary-particles (but physical phenomenon is unrelated to the decay patterns of these elementary particles), so that the educational endeavor cannot succeed in realizing a practically useful description of observed very stable physical properties.

One seldom finds such a stark characterization of elementary-particle properties as primarily being related to decay paths, namely... ,
particle-physics is about how the phenomenon of the physical world all depends on a mathematical-model of the internal transition patterns in regard to both the internal states as well as the decay patterns of elementary-particles
... , perhaps "because Polkinghorne is a theologist" the dogmas of useless models are weighing on his viewpoint... , if he knew that one could also considers the math structures of stability, essentially identified by the Thurston-Perleman geometrization, and he also saw that they lead to a much wider array of ideas and constructs which incorporate models of life and re-establish the context of "the ideal" (as opposed to the idea of materialism)... ., perhaps he would be someone who would be interested in considering the new context within which to describe our existence (based on many-dimensions but related to the math patterns of geometrization).
The art of communication is about how to acquire cheer-leaders, or about "how the owners of society abuse the culture, and manipulate people within a very controlled and narrow social context" for their own selfish advantages...

The academic professional is more or less a cheer-leader for the current academic dogmas, but the professionals (associated to the book "Meaning in Mathematics") whom are also theologians, one would expect that they would want an intellectual basis for the philosophical viewpoint of idealism... .,
but academics are known for their arrogance, which they are allowed to show-forth if they are associated with the current reigning intellectual dogmas, so it would not be expected that academic theologians to be any different
... , though an "ideal" viewpoint would be a better context for theology, but then again, theology is itself very dogmatic so an ideal viewpoint may-well not be something which a particular religious viewpoint would support.

The wage-slave and hierarchical nature of society and its organization of social-power cause havoc with both language and descriptive knowledge, since social-authority becomes such an integral a part of one's behavior in such a social context (ie a social context of hierarchy), wherein people compete and are manipulated at such a childish level.