The Unreasonable Effectiveness of Mathematics

Unreasonable Effectiveness of Mathematics

This article is posted for everyone to read but it targets those studying Elegant Reasonism. If the language below seems not quite right then you have homework to do. The links will resolve for registered users. If this article is your first encounter with any of this then its context will not make sense and you will need to register here, and then explore other articles and pages to bring this article into focus. Otherwise you may be wasting your time.

Common Ground

People do not expect the context of common ground of being human to change. Not ever. We do not exactly because we are all human and it is a shared experience. This shared experience and expectation is fundamentally the genesis of the Epistemology we call Empiricism.  Elegant Reasonism, as a framework supporting a new epistemology seeking truth as a function of the unified Universe was designed and created with exactly this situation in mind. What do we do when the predicate priority constructs establishing context do change?  The framework forces philosophical critical thinking relative to the predicate priority constructs employed by science questing unification with a specific objective of minimizing or eliminating Langer Epistemology Errors (LEEs).

Eugene Wigner once entitled an article The Unreasonable Effectiveness of Mathematics. Quoting Bertrund Russell he said: “Mathematics, rightly viewed, possesses not only truth, but supreme beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry. Wigner pointed out that someone once said that philosophy is the misuse of a terminology which was invented just for this purpose.[This statement is quoted here from W. Dubislav’s Die Philosophie der Mathematik in der Gegenwart (Berlin: Junker and Dunnhaupt Verlag, 1932), p. 1.] In the same vein, I would say that mathematics is the science of skillful operations with concepts and rules invented just for this purpose. The principal emphasis is on the invention of concepts. Mathematics would soon run out of interesting theorems if these had to be formulated in terms of the concepts which already appear in the axioms. Furthermore, whereas it is unquestionably true that the concepts of elementary mathematics and particularly elementary geometry were formulated to describe entities which are directly suggested by the actual world, the same does not seem to be true of the more advanced concepts, in particular the concepts which play such an important role in physics.

 

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What does not become saliently clear until one fully comprehends Elegant Reasonism is the role “context” philosophically plays out in these insights relative to science. When humans commit Langer Epistemology Errors (LEEs) the mathematics will have a greater affinity for the context erroneously believed to be nature will be. The simplex answer to the observation Wigner and others made is a clue to the commission of LEEs and a failure to recognize the mechanisms within human physiology manifesting abstractions furnished to our brains by our central nervous system. In essence we are all intrinsically wired to make this mistake. If you believe that those focusing on the natural sciences work directly with nature you are committing LEEs. However, that is not the subject here. What is the subject is how that mistake manifests the affinity for the mathematical effectiveness we experience.

When we realize the implications of M1‘s logical correctness we realize encapsulation of that model manifests the fundamental context against which all of the mathematics within that model execute. We must be able though to distinguish distinctions between the mathematics and the constants and variables generally associated with the natural sciences. To presume that those constants and variables represent actual real reality constitutes commission of LEEs. The realization of these relative and respective implications will wash over you with a liberating recognition of what the challenge has been all along precluding accomplishment of unification.

Unification aside, it is the failure to Philosophically place the core constructs of encapsulated interpretive models as predicate priority considerations across Science that is chiefly responsible for the ‘unreasonable‘, ‘uncanny‘, pick your phrase or word, that we all experience employing mathematics. Now, having said all this I will back up and say that the actual real unified Universe wants us to see its secrets. It has been leaving us clues almost everywhere. As one grows to wield Elegant Reasonism effectively so too will your skills in recognizing the distinctions between contextual alignment with a logically correct model and holistic alignment with the unified Universe and in that holistic ability to leverage those insights mathematics will remain steadfastly at your side. Its mechanics remain just as solid as they ever have. Only now they will help you discern truth as a function of the unified Universe.

Mode shifting the various ideas and constructs discussed in the above video is an interesting learning exercise across the plurality of models required by Elegant Reasonism on the path toward not just understanding The Emergence Model but wielding it in pursuit of any given investigation. Today what most often occurs is situational awareness of the implications due to complex composite architectural mass derived from M5. Where Einstein explained, for example, the inverse square law as a function of gravitational field interactions, M5 would employ fields of gravitons that are architectural mass in and of themselves. The net result is the same. Experiments would draw the same conclusions because the scenarios are simultaneously logically correct. What changes is why each is true and in order to understand those contextual distinctions one must comprehend what is being accomplished by mode shifting.

We discussed briefly the above video of Richard Feynman discussing Knowing vs Understanding from 1950 in our Open Letter to Science Professionals and where “Immutable Laws” were discussed. Anyone caught in the clutches of the logic trap that is M1 believes such laws are “of nature” rather than the logical correctness manifested by the context of M1‘s philosophical construct and such a belief constitutes a Langer Epistemology Error. They further believe that Science has departed from Philosophy, largely due to employment of laboratory experimentation and Empiricism. Such individuals fail to recognize LEEs Empiricism Trap.

The framework established by Elegant Reasonism employs mathematics both encapsulated within the various interpretive models and holistically across the analytical layers of tools like Translation Matrices. At every step and stage of the processes holistically employed seeks objectively to accomplish two essential tasks: Elimination of LEEs and seek truth as a function of the unified Universe which requires Philosophical predicate priority consideration of the criteria of unification which is in turn immersed in Science.

Hindsight, the proverbial ‘they’ say, is 20/20 (e.g. perfect vision). The Emergence Model, a product of an Elegant Reasonism based Systems Review we see that the intrinsic nature of its MBP construct leads inextricably to Knot Theory and its ‘rope segments’ therein correspond nicely with String Theory in M1. The critical insight therein is that these affinities are, in M5, fundamentally a function of the intrinsic nature of MBPs and not some other theory or hypothesis. The Emergence Model is simple to the point of elegance. Amazingly is the fully compliant holistic alignment it brings not just to a specific discipline of Science but in accomplishing holistic unification which describes the unified Universe Bang to Bang.

Consider Modeling Virtual Worlds

Have you ever played a game on a computer? Have you ever given any thought to what those programmers had to do in order to render that virtual world to you. Below is an excerpt from a paper linked by the section title here. The point is not to to discuss necessarily what they said but to get you to think about the differences between what any programmer does and actual scientists working in these various fields have to do. Consider then the implications of committing Langer Epistemology Errors (LEEs) by any of these people, scientist or programmer, or even information scientists. If we mistake the abstractions we employ for actual reality where and how do we draw the lines if all of the sensory input to our brains is provided by computers. Presumably you saw the movie triology or gaming environment: The Matrix. One of the distinctions is that programmers can arbitrarily chose not to follow natural laws within the worlds they create. Scientists don’t have that opportunity. Nature has a way of acting litmus to what it is they do. Consequently scientists are constantly seeking to establish experiments, which others can replication and presumably get the same results (e.g. via Empiricism). We all want to better understand reality, and while the unified Universe played something of a trick on us by having our central nervous systems (CNS) instantly furnish our brains abstractions in order to cope with the realm of our existence, it must too be noted that it gave us the intellect necessary to distinguish abstraction from reality. We need to use that intellect.

As you read through the next few paragraphs consider this:

What Albert Einstein created beginning in 1905 was absolutely 100% logically correct, and therein lay the strategic clue needed to accomplish unification. Susanne K Langer gave us Langer Epistemology Errors (LEEs) and provided the next few insights. Lev B Okun pointed out the need to segregate modern interpretation from original beliefs (e.g. M1 vs M2). The rest is now history, unification is here, now. – Charles C McGowen

Physics Level

A higher level is physical level. The laws of physics dominate here. The behavior of everything in this level should abide by basic laws of physics, or kinematics, narrowly speaking. Objects may have internal structures, and certain forces bind them together. In certain circumstances, these internal structures can corrupt under certain laws too. The environment must be modeled too. All subjects interact with the environment, and should follow the laws of physics. Virtual objects are modeled physically by specifying their mass, weight, inertia, surface texture (smooth or rough), compliance (hard or soft), deformation mode (elastic or plastic) etc. These features are merged with geometrical modeling and behavior laws to form a more realistic virtual model. Using fishes as an example movement should show the water resistance, the lighting condition should be different at different places of pool (depth, distance related), and so on. However, at this level, how fish swims is not defined, say, a fish can move either forward or backward, eat or vomit zooplanktons. Thermodynamics defines the time arrow, but it is not necessarily be used at this level. How fish acts to get the food and how zooplanktons reproduce themselves (or added by the VR engine) will not have an effect on the output. However, the real life experience requires a better virtual world be abided by the laws of biology, ecology, and more.

Biology Level

This level gives more restriction or rules to the virtual world. We have to obey laws of thermodynamics, chemistry, as well as biology and ecology. There should be a biological model of the fish, beside the physical model. Also we need an ecological model of the environment, in addition to the material model. For each live thing, we need to have the algorithm for its behavior. This can be obtained from the achievements of animal behavior research. This part is the hardest, and we may even don’t know exactly what the algorithm is — like what algorithm is for human behavior? But for lower intelligent animals, we do know a lot, and they can be used to program the behavior of these animals. The virtual world will be more complicated and there are more interactions within the virtual world itself. Much more computation power is required for each object in the model, and they need to be synchronized well to output to user. At this level, the fish won’t swim randomly, they will distribute themselves according to the distribution of food, and they won’t always swim, they have their own way of life. They are “really” – in a sense – a life form. Ecological rules will maintain the food chain, limit the population of fish, and do what you put into the model. User interaction will be better served at this level, because there are more restrictions to make it real. If user immerses into the system as a bigger fish, the other fishes will probably flee when seeing this monster. Then what the user sees will be a nicer virtual world, than what is in level 2.

Sociology Level

The ultimate virtual world is the real world we live. How to replicate a real world in computer requires ultimate understanding of human intelligence and the essential construction of human society and the laws governing our behaviors. This, in fact, is a high level biological thing, but since we, human beings, are also part of it, it makes the system distinguished from other biological systems that are purely the subjects under our observation and control. At this level, you can really construct a world that user cannot tell it from. However, at this stage of computer science and technology, it is just a sci-fi topic now. The four levels of modeling are not separate; each lower level is contained in higher levels by adding more restrictions, rules, and details of the object. Currently, we did pretty well at the geometry level, and there are some good jobs done at physics level, at least partially, we don’t have any good work done at the biology level. So, it’d be great to design and build a virtual world that lives at biology level, the user may feel hard to tell it’s true of not if it is beautifully done (like a virtual fish tank).

Software

There are currently hundreds of different programs that can be used to create virtual worlds and objects. Each one is slightly different, but they all perform the same task: to create virtual objects that may or may not have any basis in reality. This section will examine CAD packages, Virtual World Creators, 3D game development packages, and 3D/2D construction packages. All four genres of program can be used to make virtual objects and worlds, although the approach and end product will differ.

The Fine Line

There is something of a very fine line between characterizing/reflecting nature and outright declaring you think you are describing what nature actually is. Programmers creating virtual worlds don’t really care if that alignment happens or not. In fact they usually take great joy in schisms and incongruous behaviors because it makes the characters they create appear to have superpowers that can be used to battle each other or set up good vs evil story lines. Scientists and engineers working to understand or build something on which human life depends is an entirely different matter. There, in the real world alignment matters, or people can get hurt or die. Rhetorically ask if we truly understand nature then why is mathematics can not predict structural failures or answer Wigner’s point.

The distinction we are trying to draw out for illustrative purposes is not really about mathematics. It is about the abstractions with which mathematics must contend and the assumptions we make, often through commission of LEEs. What Elegant Reasonism brings to these discussions is the need to surround reality with reflections of it and insist those reflections close to unification. Think of it something like a filter. Once we accept the paradigm shift that M1 and M2 are both logical realms it really is quite a liberating experience. Even more so when we realize that even Erwin Schrödinger believed he was writing about reality in his treatise on Spacetime Structure. Not until his cat died did we begin to suspect the truth about the baubles we were playing with.

The fine line we must never cross is commission of Langer Epistemology Errors (LEEs). Once we understand that as we execute the utility process, enable the framework in support of the epistemology whose basis in truth is the unified Universe will navigating the Process Decision Checkpoint Flowchart be both conversational and much easier. In those conversations where all parties understand these various issues not only will communication tasks ease but justification for insights will become crystal clear. Global enterprise so enabled will transition through a revolution as a result and civilization will ultimately align with the unified Universe.

Encapsulated Interpretative Models (EIMs)

EIMs manifest fundamental context which changes the pattern parameters with which mathematics must deal. That was essentially the core message delivered in our presentation In Unification’s Wake, Part 02: Mathematical Proofs. Investigators of all sorts need to clearly understand that logical correctness is absolutely critical and vital (e.g. necessary) but it is also wholly insufficient > IF <, those considerations also do not also close to unification. Therein lay the benefit of the Elegant Reasonism utility process, framework, and epistemology. What is vital to recognize is that you can not calculate mathematics across encapsulation boundaries. The reason is simple, EIMs are distinct and generally have completely different manifestations from one another. That’s why they are encapsulated. The only way to calculate any analysis is down through the analytical layers of Translation Matrices comprising the framework. Another aspect vital to recognize, especially in context of Feynman’s points in the video above is that the litmus test is the unified Universe, not congruence with an EIM that can not philosophically close to unification.

 

 

 

 

 

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McGowen

By Charles McGowen

Charles C McGowen is a strategic business consultant. He studied Aerospace Engineering at Auburn University '76-'78. IBM hired him early in '79 where he worked until 2003. He is now Chairman & CEO of SolREI, Inc. ORCID: https://orcid.org/0000-0003-2439-1707