Logic Driven Science: Physics without Attributes

Lingam in sea

Physics, as it is presently construed, involves the study of physical phenomena.  This kind of science, I will call phenomenal physics.  Of central concern is the motion of physical bodies.  Classical Newtonian physics proposed the first version of the laws of motion of such bodies.  Einstein provided a second version that took relativity into account.  At the macro level, the laws of motion based on Special and General Relativity Theory are so accurate that for all intents and purposes they are generally considered as exact. However, at the quantum level of physical reality the deterministic laws of macro physics break down. The break down is dramatic. David Bohm remarks that at this level:

…there are no laws at all that apply in detail to the actual movements of individual particles and that only statistical predictions can be made about large aggregates of such particles. (Bohm, 1980)

The laws of motion for individual particles simply vanish at the quantum level. Quantum Mechanics takes up the challenge and provides the wave function as the necessary probabilistic way of predicting the phenomenon of individual particle behaviour.

At the level of elementary particles, phenomenal physics has virtually nothing to say about the state of affairs of any individual particle, except at the extreme instant of measurement.  The only two possible exceptions are at opposite ends of the phenomenal spectrum and are constants. These are rest mass and the speed of light which both appear to be stable measurables and are useful for scaling the system.  Any non- constant property of an individual particle is effectively quantifiably meaningless.  I will henceforth refer to these non- constant properties as attributes.

In this paper, I accept the scientific uselessness of the attributes of an individual particle. I then proceed to argue that it is useless to carry such burdensome luggage along in the formalism needed to understand elementary particles. Attributes only add unnecessary clutter to the science. After taking this dramatic step, we are naturally led to another kind of physics—physics without attributes. Physics without attributes is obviously a different breed of fish to traditional phenomenal physics.  For the want of a better name, I will call the science generic physics.

Generic Physics

Bohm argued that there
was another side to physics
– the Implicate Order.

The relationship between phenomenal physics and generic physics is somewhat like that imagined by Bohm in his Explicate Order and Implicate Order idea. The Explicate Order corresponds to traditional phenomenal physics which he saw as derivative of a higher, ultra-holistic , unifying  Implicate Order.  Bohm’s approach has many similarities with the one I have been developing in previous work. Like myself, he even refers to the left and right brain analogy.  In order to lighten the terminology, I will sometimes refer to the phenomenal,  “Explicate Order” as the “left side’ paradigm or point of view whilst  the generic,  “Implicative Order” side  as the “right side” paradigm. In this paper I will provide the necessary constructs to formalise the difference between the two paradigm and their formal nature, something that is missing from Bohm’s account.  As will be seen, my account of the right side paradigm is presented quite differently  to Bohm’s Explicate Order. 

For me, order is the affair of the left side paradigm, a paradigm shared by all the traditional sciences  including axiomatic mathematics. From an epistemological perspective, the left side “Explicate Order” sees reality as diachronic. The diachrony in mathematics is expressed at the elemental level as number. The diachrony of number is most forcibly expressed in Peano arithmetic in the form of five axioms essentially defining the successor function, the fundamental mathematical engine of diachrony. This was recognised by Russel and Whitehead in building their Principia Mathematica system, and equally by Gödel who brought it tumbling down. Intuitively, the diachronic nature of the left side paradigm can be thought of as a world view relating the a priori with the a posteriori.  The diachronic structure applies no matter what the science, or whether it is mathematics or logic.

Turning back to the much less familiar right side paradigm, Bohm sees this as a higher order form of organisation, his Implicate Order.  He still sees this holistic, unifying paradigm as an order, whatever that may mean. Moreover, he also still sees it as phenomenal physics albeit operating at a higher organisational level. The fragmented, localised perspective of the left side paradigm gives way to a flickering hologram[1] like image of reality.  Standing waves of interfering quantum fields determine what we see as particles, explains Bohm. The imagery has some merit but is missing in any rigorous formalising methodology.

My approach to the “Implicate Order” is not to see order at all, but its complete abolition. The diachrony gives way to a pure synchrony.  The perspective is that of the ancient Stoics who claimed that the only things that exist are those that exist synchronously with the subject. Objects in the past do not exist; neither do objects in the future. Only exist are the objects in the immediacy of now, relative to the subject,  To the materialist Stoics, the objects in existence must be material bodies being capable of acting or being acted upon.  From a Stoic perspective, Bohm’s Implicate Order takes place in the immediacy of a subject’s nowness.

How to get rid of attributes

Generic Physics is physics without attributes. Getting rid of attributes is one thing, but what can we replace attributes with? The answer to this little puzzle is surprising simple and as well as surprisingly profound.  We start by consider an entity which has a single attribute and examine the entity-attribute relationship.

First, take the diachronic traditional viewpoint of all the traditional sciences and axiomatic mathematics. According to the conventional wisdom of the left side doctrine, there is a distinct dichotomy between entities and attributes. No entity is ever an attribute nor any attribute ever an entity.  Then comes the problem of gleaning knowledge about the entity.  Conventional wisdom clearly would say that one cannot get to know the entity directly but only via its attribute. Thus any science pertaining to such entities must be attribute driven.  In other words, common sense declares that science, and hence physics, must be empirical in nature. This is the standard orthodoxy proclaimed by all left side science. There are no surprises there.

Now turn to the not so orthodox right side perspective.  This is the perspective that does away with the need for attributes.  In the left side scenario, the scene was occupied by an attribute with the corresponding entity hidden off-stage. Knowledge of the entity is gained by getting to know the antics of the on-stage attribute. In the right side scenario both the entity X and the attribute Y are on centre stage. The attribute is considered as an entity in its own right. Any specificity it may or may not convey is of no importance. What matters is the dialectical relationship between these two players.  This relationship is semantic.  The entity X will express its only known specificity, the fact that X has an attribute.  The entity Y will express its only known specificity, the fact that it is an attribute. To use expressions familiar in Computer Science, X expresses HAS-A semantics, whilst Y expresses IS-A semantics.  The basic idea in this right side science, is that one doesn’t care any more about the value of attributes. What matters is whether an entity is an attribute or has an attribute.

This IS-A, HAS-A construct leads to a generic way of typing entities. I call it the construct ontological  gender. An entity with HAS-A typing will be said to be of feminine gender and an entity with IS-A typing will be said to be of masculine gender.  Of fundamental importance is to realise that gender is not an attribute. Two entities of different attribute can be distinguished from each other by attribute comparison.   Two entities of different gender cannot be distinguished from each other by attribute comparison for the simple reason that there is only one attribute between them. One has it, the other is it. In what follows, I will show how this gender construct maps up with the ancient use of this construct in Stoic physics, and Stoic logic.

One use of the IS-A and HAS-A construct in computer science is in the design of Object Oriented programming languages. The early OO language C++ allowed open slather multiple inheritance of entities with IS-A and HAS-A semantics. This was found to lead to bad programming practice. In the next generation of OO languages such as JAVA and C#, the languages were designed to only allow the single inheritance of IS-A semantics. Inheritance should be limited to the masculine line. For example, a Cadillac IS-A Car.  Also, a Cadillac HAS-A CD player, HAS-A engine etc. Whilst it is perfectly reasonable that the class of Cadillacs inherit the common interface of the class of Cars, it doesn’t make much sense for the Cadillac to inherit the interface of CD players or engines.

It’s a bit like traditional societies where the family unit inherits the surname and clan membership (inherit the social interface) from the male IS-A line whilst the feminine turns up with the dowry of ten cows (HAS-A). I find that fascinating but will not dwell on it. This is good programming practice in OO!

In quantum mechanics the famous BELL experiment demonstrated that, at the micro level there are no hidden variables, no intrinsic attributes. Attributes are only accidental and have no place in universal science. What matters is the qualification in terms of the universal IS-A and HAS-A qualifications. Quantum mechanics based on is-A and HAS-A quantum states is the way to go. I will be developing this theme in later posts and in a paper I am writing

A computer illustration of gender would be the placeholder-value dichotomy. Consider a standard 32 bit computer. The computer would have 4 gigabytes of addressable memory. Each of the 32 bit memory locations can store a value ranging from zero to 4 “gig”. From an attribute perspective, this computer is a cruncher of 32 bit numbers and it is hard to understand how it works. However, ignoring the specificity of the numbers, one can look at a computer as being organised along gender lines.  A placeholder for a value can be thought of as feminine, and the value contained as masculine. Consider now the contents of a general purpose register in the computer. What is the gender of the number contained in the register?  From the register point of view, the number is a contained value, and hence masculine. However, this number could also be interpreted as a pointer to a memory placeholder, and hence be interpreted as feminine. Is it a pointer or a value? Is it feminine or masculine? In actual fact, without knowing the complete context, there is no way of telling the difference. The gender status of the general purpose register could be said to “be in superposition.” Nevertheless, despite the fleeting nature of gender when viewed by a third party, we do now know that a computer is a system involving the dynamic organisation of value and placeholder semantics. However, this gender structure is extremely shallow in computers for this somewhat desperate example to get the reader beginning to seriously grapple with the gender concept. This is more an allegory than an example.

In summary, the gender construct provides an alternative to attribute based semantics. Gender semantics provide a qualitative alternative to the traditional quantitative approach. Of course, entities typed as having a single masculine or feminine gender are too ephemeral to be considered as discernable entities. However, the situation changes in the case of entities with mixed gender. Rather than considering gendered monads as the building block of the science, consider dyads where the each end of the dyad is simply gender typed as masculine or feminine. This leads to four possible binary gendered dyads MF, FM, FF, and MM.

Because gender is an attribute free construct, it is not restricted to the attribute specificity of any particular problem domain. It is a truly universal construct and can literally apply to any problem domain whatever.  Of particular interest in this paper is to associate gender with logic. My overall strategy is to exploit this universal gender logic as the logical foundation for physics.  The proof of the pudding will be to show how this foundational logic naturally leads to a generative scheme that enumerates the elementary particles of a logical physical reality. The approach is generic and independent on any specific attribute system. The predicted elementary articles would apply to any phenomenal reality as long as it is “logical.”

What are the logical properties of gender? In this quest one is immediately led to Aristotles Term Logic, the Syllogistic. The formal structure of the syllogism is quite simple. Each syllogism is made up of three terms, a Major, a Minor, and a Conclusion. There are four elemental forms called terms. It is not difficult to discern the implicit gender typing in this syllogistic system. Each term is binary typed. Aristotle doesn’t use a masculine-feminine dichotomy but a Distributed-Undistributed dichotomy. A subject or predicate is either Distributed or Undistributed. Thus the four possible term types are typed as DU, YD, UU, and DD.  The textbook make valiant attempts to explain whether a subject or predicate is distributed or undistributed or not. The best way is to simply see the distributed subject or predicate as expressing IS-A semantics and the undistributed expressing HAS-A semantics. In other words the distributed corresponds to masculine typing and the undistributed to feminine.

For a rapid refresh of syllogistic logic in this context, I recommend that the reader spend a few minutes with my online syllogistic machine.

However, the logical platform that we need to generate the elementary constituents will not be Aristotle’s Syllogistic logic but rather the closely related Stoic logical system that came later.

[1] In previous work I explained how a weak version of the left and right side paradigms can be found in Heaviside’s Operational Calculus. On the left “time domain” side can be found time series and complicated calculus of differential equations. On the right “frequency domain” side can be found a simple algebra of functions of a complex variable calculable by Laplace Transforms.  Note that the Laplace transform F(s) of a continuous function f(t) has the “holiographic” mathematical property that given a finite sample of F(s), no matter how small, the rest of F(s) can be perfectly reconstructed.

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