Essay Abstract

Many mathematicians are Platonists in the sense of believing that their major concepts and theorems are discovered rather than invented. It is claimed here that the initial foundational source of those apparently spaceless and timeless mathematical ideas is the invariant Vacuum of physical space-time. This constitutes a non-classical yet "real" Form Heaven for fundamental physics and is a storehouse for all the knowledge of the physical constants, laws, and particles of physics. The intricate structure of the Vacuum is common to all intelligences in our universe and helps to constrain the reality of their emergent knowledge. A reductionist view begins with the basic set of quantum fields living in the Vacuum leading to more complex forms emerging from these fundamentals (protons, nuclei, atoms, molecules). These entities are quantum, and their nature along with the fundamental fields might be said to live in an unusual "square-root of reality." Mathematics applies logic, intelligence and abstraction to world patterns and then gener- alizes at will forming abstractions of abstractions. But the field of mathematical-physics continually cross-fertilizes math and physics modestly limiting their divergence.

Author Bio

David Peterson holds a BS and MS in Physics from the University of Colorado, Boulder, with further graduate studies in the departments of Biophysics and in Mathematics. He worked as an Engineer and mathematical modeler in magnetic data storage for tape and hard disk for thirty years with publications mainly in the IEEE Transactions on Magnetics and the Computer Measurement Group (CMG). He is now retired but still has an active interest in physics and cosmology.

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Dear David,

I read with great interest your essay. I fully agree with your conclusion:

"What motivates mathematicians and physicists to devote their lives essentially to the study of these Forms? Transcendence and connectedness. We sense that we are participating in a huge world beyond our own limited experiences. We sense that the intelligences in the universe might discover the same truths we value; so we have a cosmic sharing. Without overtly expressing it, the physicist senses Einstein's "Cosmic Religious Feeling" which can be essentially summarized as rational "Deep Nature Appreciation."

I think we need a new interpretation of the ideas and eidoses of Plato taking into account all the accumulated knowledge for 2.5 thousand years. And even more, beginning with the first strike on the rock of our ancestor, the first fire and the first weapons. We need to understand the absolute forms of existence of matter (absolute states) to come to the new unifying paradigm . This requires a total unification of matter on all levels of existence of the Universe as a whole.

Here it is necessary to trace the dialectical line in knowledge, beginning with Heraclitus. We have a good idea of Bourbaki in the spirit of Plato - "les structures mere". John Wheeler left the physicists and mathematicians good philosophical covenant: "Philosophy is too important to be left to the philosophers".

I remember the words of the poet Alexander Vvedensky:

"We do not see the world in detail,

All insignificant and fractional ...

Sadness takes me from all this."(1930)

Physics, mathematics, biologists and poets should have unifying picture of the world, filled with all the senses of the "LifeWorld" (E.Husserl). And what is your opinion?

Kind regards,

Vladimir

You're very classical as your essay with many perceptions filling the gaps between space-time.

Great indeed!

Sincerely,

Miss. Sujatha Jagannathan

Hello David,

You make your point very clearly in your essay. There is not much to quarrel with except to make or ask one or two questions or statements.

First, in your description of "physical entities were said to 'exist'", you mentioned the defining properties as mass or energy equivalence. If some measurable locus that was massless, and 'cannot deliver energy', but measurable in the sense that we can say the volume is 100 cubic metres, does it exist? In my opinion and according to Leibniz, I think in his Monadology, the defining property of what exists is the occupation of some locus.

You discussed in some detail the Platonic world, which is the road our mathematics and physics have in the main followed. Historically, there was a fork in the road, which led to the Platonic one and a less favoured one, which I discussed in my 2013 Essay, 'On the road not taken'. Aristotle, Proclus and others opposed the Platonic route with good reasons for doing so. You may take a look.

As you near the end of your essay, ideas like Frank Wilczek's Grid are introduced as a possible replacement to the old ideas of aether, plenum, substance, vacuum, spacetime, or world-stuff. If the Platonic route was followed but in a questioning rather than unquestioning manner perhaps there would have been no need now for this search for a replacement, as Space itself would have been able to do the job, with the smallest units of the grid being the non-zero dimensional point. This is the focus of my essay this year, essentially a continuation from the theme of the 2013 essay.

You may wish to read and comment. Thanks.

All the best in the competition.

Akinbo

    Dear Akinbo,

    I like history of philosophy, so I enjoyed your two essays and the difference between ideal points and ``extended points'' or monads. In the world of physics, distance measurement depends on massive detectors (or massive rods and clocks) and on detection of end-points as events (like tiny firecracker explosions or light flashes in space and time). We wouldn't discuss pure volumes without some of these classical references. And for all practical purposes (FAPP), being ultimately discrete or ideally continuous wouldn't make any difference. I suspect that it is likely that we will never ultimately know. And discussions of space (above nano-space) depend on understandings of special and general relativity to compensate for relative movement or curvatures. For truly tiny intervals, quantum mechanics plays a blocking role. Smallest units of the Grid are likely undefined and operationally un-measurable. I notice you used ``Space" with a capital as I use ``Vacuum'' also with a capital letter.

    Regards,

    Dave.

    Dear Sir,

    Though we understand the reason for your asking the question "Does pi (= C/D) exist before we discover it", it can be misleading. The ratio implies the existence of circular objects. Thus, the question can mean "whether circular objects (and by extension; any object) exist before an observer observes it" - the famous observer created reality. As evidence and experience show; the moon will exist even when we are not looking at it. The use of pi in mathematical equations is often manipulated, as its precise value is not yet known - hence probabilistic; and mathematics is a science of exactitude.

    In ancient Indian literature (before 800 BC), a word was meant to convey "this (object or form) is like that (the concept or information conveyed by the word). Hence it is that". Thus, perception required prior information (hence existence) about the object or form. Since mathematics describes the quantitative aspect of Nature, it would be universal - even for aliens, because the validity of a mathematical statement is judged by its logical consistency. But the same may not be true for the constants, as most of them depend on local factors. For example; the value of G changes every time with precision measurement. It may be different if measured from an alien planet.

    Mathematics is not independent of human experience nor reality or forms; as numbers are perceived as a property of objects by which we differentiate between similars. If there are no similars, it is one. If there are similars, it is many; which can be 2,3....n, depending upon the sequence of perception of 'one's. This has been experienced as true - hence accepted as the quantitative description of reality. We have discussed the fallacies of mathematics used in relativity and the views of Wigner in our essay in this forum.

    One problem with modern physics and mathematics is divesting numbers from reality to abstract imagination. The other is superstitious belief in 'established theories', even when they are known to be wrong based on current information. Space, Time and coordinates arise from our concept of interval and sequence. When the interval is related to objects, we call it space. When the interval is related to events, we call it time. When we describe inter-relationship of objects or events, we describe the sequence by coordinates. Directions are arrangements of the sequences of intervals of objects in space. Dimension is the perception of differentiation between the internal structural space and external relational space of objects. Since we perceive through electromagnetic interaction, where the electric and magnetic fields are perpendicular to each other and both move perpendicularly, we have three mutually perpendicular dimensions. These are invariant under mutual transformation (if we treat length as breadth or height, the object is not affected) and can be resolved into 10 different combinations. But even after more than a century of failures to find extra-large or compact dimensions; almost all scientists superstitiously subscribe to such fiction perpetuated by the novel FLAT LANDS. There is a need to review modern science based on current information and rewrite it.

    Regards,

    basudeba

    12 days later

    Dear Mr. Peterson,

    You quoted Alexia Auffeves and Phillipe Grainger's guess that: "The goal of physics is to study entities of the natural world, existing independently from any particular observer's perception, and obeying universal and intelligible rules."

    Please behold my reality Mr. Peterson: Proof exists that every real astronomer looking through a real telescope has failed to notice that each of the real galaxies he has observed is unique as to its structure and its perceived distance from all other real galaxies. Each real star is unique as to its structure and its perceived distance apart from all other real stars. Every real scientist who has peered at real snowflakes through a real microscope has concluded that each real snowflake is unique as to its structure. Real structure is unique, once. Unique, once does not consist of abstract amounts of abstract quanta. Based on one's normal observation, one must conclude that all of the stars, all of the planets, all of the asteroids, all of the comets, all of the meteors, all of the specks of astral dust and all real objects have only one real thing in common. Each real object has a real material surface that seems to be attached to a material sub-surface. All surfaces, no matter the apparent degree of separation, must travel at the same constant speed. No matter in which direction one looks, one will only ever see a plethora of real surfaces and those surfaces must all be traveling at the same constant speed or else it would be physically impossible for one to observe them instantly and simultaneously. Real surfaces are easy to spot because they are well lighted. Real light does not travel far from its source as can be confirmed by looking at the real stars, or a real lightning bolt. Reflected light needs to adhere to a surface in order for it to be observed, which means that real light cannot have a surface of its own. Real light must be the only stationary substance in the real Universe. The stars remain in place due to astral radiation. The planets orbit because of atmospheric accumulation. There is no space.

    Warm regards,

    Joe Fisher