Over the last several centuries, science has discovered objects in the world along a continuum of scale. In one direction, we have found planets and stars, galaxies, and galaxy clusters. In the other direction we have found cells and proteins, atoms, and neutrinos. In order to locate and model this world, we use the 3 traditional directions of length, width and height. However inherent in all our measurements is the scale of what we are measuring – a continuum we do not directly see with our eyes. We need to include this continuum in a full model of the natural universe. However, we do not understand how to measure along this continuum and may lack the mathematical tools to do so. Those tools could require a new numeric representational system with more power than our traditional decimal or positional based numerals.

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    This "scale dimension" sounds interesting and plays a role in fractal theory. However, it is taken into account in usual theories in the form of "interaction energy" in dynamic equations, which originates from smaller scales (and then may be transmitted to larger ones). It's not a physical object that can really move along the scale axis but a hierarchy of emerging interactions (and objects) or respective events/processes. In cases where they form a distinct avalanche of growing-scale changes, one may have an impression of a certain dynamics, but in reality it's interaction energy that is transmitted through scales (often due to previously accumulated instabilities). So, it's not about any new "coordinate" expressing a "dimension" with respective "motion" in it, it's about interaction or complexity levels progressively emerging, one could say, along the scale axis. Things may become complicated when those levels are very close to each other and become dynamically mixed, as in turbulent processes or actually in some fractal structure dynamics...

    Donald Palmer
    Very important topic and ideas.
    You write:
    <<Nature operates as a cohesive whole.>>
    Agree. The holistic paradigm, the universe as an holistic process of generation, should come to the aid of the "paradigm of the part" that dominates science.
    Next you write:
    <<The suggestion is to expand space to four dimensions and then we could tack time onto these four spatial dimensions –conceivably modeled as a five dimensional ‘space-time’.>>

    Carlo Rovelli in the article “Physics Needs Philosophy / Philosophy Needs Physics” (2017) outlined a list of issues and topics currently being discussed in theoretical physics. It can be seen that most of the questions relate to the sphere of philosophical ontology. And this list is not complete. The first question on the list is "What is space?" Second: "What is time?".

    The mathematician and philosopher Pavel Florensky left a philosophical testament to mathematicians and theoretical physicists:
    “The problem of space lies at the center of world understanding in all emerging systems of thought and predetermines the composition of the entire system. With certain limitations and clarifications, one could even recognize space as a proper and primary subject of philosophy, in relation to which all other philosophical topics have to be evaluated as derivatives. And, the more closely this or that system of thought is worked out, the more definite the peculiar interpretation of space becomes as its core. We repeat: worldunderstanding is spaceunderstanding."

    In order to establish the ontological status of "space" and "time", theoretical physicists must "dig" deeper into ontology to the most remote semantically distinguishable depths and develop the ideas of Whitehead's metaphysics of the process and rethink all dialectical ideas from Heraclitus to Hegel and Losev.
    More than a quarter of a century ago, mathematician and philosopher Vasily Nalimov set the super-task of building a "super-unified field theory that describes both physical and semantic manifestations of the World" - the creation of a model of a "Self- Aware Universe".
    Therefore, one must first determine the ontological dimension of space, and then - the gnoseological dimension. To do this, you need to "grasp" (understand) the new matter as an eternal integral process of generating more and more new meanings, forms and structures.

    Here we must recall the philosophical testament of A. Einstein:
    “I like to experience the universe as one harmonious whole. Every cell has life. Matter, too, has life; it is energy solidified."

    The dialectics and ontology of development as an eternal holistic generating process give us a new understanding of matter and a methodology for the dialectical-ontological construction of the "the universe as one harmonious whole" model.
    There are three and only three absolute forms of existence of matter (absolute states): absolute rest (linear state, Continuum) + absolute motion (vortical, circular, Discretuum) = absolute becoming (absolute wave, Dis-Continuum). What is especially important: each absolute form of the existence of matter has its own ONTOLOGICAL PATH (bivector of the absolute state). Accordingly, SPACE (absolute, ontological, existential) has three ontological dimensions and nine gnoseological dimensions. It is necessary to “dig” deeper into ontology in order to “grasp” the MetaNoumenon — ONTOLOGICAL (structural, cosmic) MEMORY, “soul of matter”, its measure. Ontological (structural, cosmic) memory is that "nothing" that holds, preserves, develops and directs matter (enteleschia, nous, Aristotelian mind, "prime mover").

    That is, the Big Ontological Revolution is needed in the foundations of knowledge. Physics must move from the stage "Phenomenological physics" to the stage "Ontological physics".
    A.N. Whitehead: “A precise language must await a completed metaphysical knowledge.”
    John A. Wheeler: "Philosophy is too important to be left to philosophers."

      Vladimir Rogozhin

      I couch my essay as an heuristic requirement, rather than posing it as an ontological one (I believe there are others who have done this as well in the past). I cannot argue the importance of the ontological question - however, I do believe we are far from understanding the true underlying nature of reality and thus do not pretend to provide an answer to this question.
      It would seem to me that considering the multiple levels of objects in scale as lying along a continuum defines a dimension. Is this the 'last' dimension - I doubt it. The perception of objects at multiple levels of scale does conform to our concept of observational science and therefore should overrule the current pure reductionist philosophy of physics (and I believe a number biologists would agree). So I also agree with the need for philosophical reflection, which is what has led me to the belief that we are missing a mathematical concept that prevents current thinking from understanding scale as a dimension. If we cannot measure something (distance in scale), due to limitations of our mathematical representations, then we are unable to build it into our scientific theories. This puts the real issue in mathematics and not physics.
      It also appears to me that identifying 'time' as a dimension is particularly heuristic for modeling purposes only. Time does not act like the a physical dimension and therefore should not be considered one - it just works well to model it as such.

        6 days later

        Continuous vs. discrete was discussed in an eartier FQXi contest.
        In order to demonstrate my opinion that there is no standstill, not even in the "deepest" fundamentals of science, I made aware of Dedekind's cut as a perfect number system.

        "As we move toward digitally modeling entire bodies in the universe, we will find the need for
        locating objects in scale, in addition to locating objects in three-dimensional space. This will
        require a four-dimensional scientific model of space, which will require some distance measure
        and units that cross non-linear scale. "
        The 4-th dimension in space we need is the energy dimension converted as fixed time dimension. There is an universal constant to convert energy to fixed time and the energy of a corpuscle change than its coordinate in fixed time change. Ordinary time is absolute in any theory and it signify changes. We have the following equations:
        4-vector momentum= universal constant times 4-vector wave-vector
        4-vector momentum= universal constant times 4-vector identity
        4-vector identity=(speed of light times fixed time coordinate, speed of the corpuscle times fixed time coordinate)
        4-vector wave-vector= universal constant times 4-vector identity
        fixed time coordinate=universal cosntant times energy of the corpuscle.
        There is a good article here in th FQXI competition 2023 speaking about Identity vector (ApriCorn or ApriHot article).

        "Constant movement in scale would appear to be moving
        exponentially (e.g., first 1 unit, then 10 units, then 100 units). In other words, the objects in
        motion in scale would appear to be accelerating. This is an important consideration, as a
        constant velocity in only scale would appear to an object at rest (in our three dimensions) as
        moving at a constant acceleration on us. Using F=ma, this would indicate we should measure a
        force on an object moving in scale. Since the object is not moving in the dimensions we directly
        perceive, it would appear as an undefined force on the object and might be indistinguishable to a
        known accelerative force."
        Moving exponentially is well described in Max Planck theory about Black Body radiation. The mean energy of an oscillator is an exponentially function: when the frequency of the oscillator is very high than its mean energy tends to zero in Planck model & when the frequency of the oscillator is so low than its mean energy tends to a constant value equal to "kT" the Boltzmann classical energy.
        The same model for mean energy oscillator can be applicable for space. A corpuscle have a mean position in space but compared to a reference position or scale position: when the position of the corpuscle is so great than it collapse to zero compared to a scale reference and when the position of the corpuscle is so precise (so low) than it tends to a constant value which is "the Boltzmann value".
        This is possible when only there is a unique absolute system of unities to measure space, time and energy: in fact time is absolute in a given frame and it transduce changes only.
        I had read your article twice and I think it is important.

        4 days later

        VermillionGoldfish
        I thought you expressed very important ideas. There clearly are times when it is more helpful to limit the scope of our inquiries. However, since meaning is context or scale dependent, findings at one level may not apply to a deeper perspective and may even be misleading, obscuring connections into more fundamental levels. This applies not just to the physical and biological sciences; our failure to recognize its relevance to all social interactions is sadly noted in our failure to learn from history!

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