SPACE AND ITS LINE-UP OF EMINENT EXPERT WITNESSES
Here, I list a number of contentious ideas and provide testimonies from expert witnesses, human and non-human to illuminate them. Some of the quotes here have been paraphrased from the original in order to emphasize some of the possible interpretations of them. I can point the reader to the original quotes for reference if necessary.
1. Space has parts, which ultimate parts (points) have no further parts.
*Euclid - Elements, book 1, definition 1, A point is that of which there is no part.
*Leibniz - Monadology, Something that has no parts ...can't be split up. So extended points (monads) are the true atoms of Nature - the elements out of which everything is made.
2. The parts (points) of Space are not dimensionless.
To varying degrees of consensus,
*Proclus - points really exist and have the attribute of position as I commented in Proclus: A Commentary on the First Book of Euclid's Elements, translated by Morrow, G.R., Princeton: Princeton University Press (1992).
*Aristotle - There are reasons why space must be something, although there are difficulties that may be raised about its essential nature. However, if lines exist, points must also exist.
*Pythagoreans - points are extended objects and we prefer to use the term, 'monads' for them.
*Plato - points are not fictitious geometric objects but I prefer to refer to them as the beginning of lines or indivisible lines.
3. Space cannot be infinitely divisible.
*Zeno - Through my 'Dichotomy Argument' I have demonstrated the practical impossibility of moving from one place to another destination, if there are an infinite number of positions to be traversed between origin and destination.
4. Space is substance, IF its parts can "move".
*Newton - In De Gravitatione, I made it clear that philosophers would cheerfully allow space to be substance, just as body is, if only parts of space could move as body can. Space is capable of having some substantial reality. Indeed, if its parts could move, ...then there would be no question about it - parts of space would be corporeal substance.
*Descartes - There's no real difference between space and corporeal substance. It's easy for us to see that the extension that constitutes the nature of a body is exactly the same as the extension that constitutes the nature of a space. This I have borne witness to in my Principles of Philosophy, Part 2: The principles of material things, section 11.
5. A part of Space, whether it be of body or of extension cannot move in the manner of leaving its place for another place.
*Zeno - In my 'Arrow paradox' centuries ago, I demonstrated and still stand by my testimony then that "what is in motion moves neither in the place it is, nor in one in which it is not". An arrow is a place! And a place cannot abscond from its place to take up another place. Motion definitely exists but it must have a different underlying basis different from the way it is commonly conceived. It is our duty to find out how the impression of motion is manifested when places cannot leave their place for another place.
*Newton - A body is a place and a part of space. Unless we are postulating that there are two places in one place, a moving one and another one that is at rest there is no way the moving part of space can be translated out of itself. A body cannot leave a property intrinsic to it behind when it moves.
*Descartes - For a body to 'move', in the strict sense, is for there to be a change in what bodies it is in immediate contact with. NOT IN LEAVING ONE PLACE FOR ANOTHER. In my definition I specified that the transfer takes the moving body from immediate contact with some bodies to immediate contact with others. I did not say that the transfer takes the moving body from one place to another. That is because, as I explained in sections 10 - 14 of Part 2 in my Principles of Philosophy, the term 'place' has various meanings, so that the question of whether and how a given body is moving at a given time may have no unique answer if 'motion' is defined in terms of change of place. But when we understand a body's motion as its transfer from being in immediate contact with certain other bodies, we have a single determinate account of whether it is moving, because the notion of 'bodies that are in immediate contact with x' is fixed, not floating and indeterminate like the notion of 'the place x is in'. All these I have already said in section 28.
6. Space and its parts do not eternally exist.
*Cosmologists (opposed to the steady-state model) - Big Bang and Big Crunch are events respectively describing emergence and annihilation of space. Both events bear witness that space can appear and disappear.
*Hawking and Penrose - In 1970, we showed from our singularity theorems that there are initial and final singularities. Singularities are characterized by zero volume, i.e. no space. As far as the singularity theorems go, ultimate destruction of all matter and space-time is therefore inevitable, likewise the reverse creation of same.
7. Space cannot be cut.
*Dedekind - Firstly, I find that there must be a point at the incident of cutting. Secondly, if I go ahead with cutting, this point must belong to one or other segment. This leaves one of the segments not having a point at its extremity, a contravention of Euclid's book 1, definition 3 ("If all points of the straight line fall into two classes such that every point of the first class lies to the left of every point of the second class, then there exists one and only one point which produces this division of all points into two classes, this (point) severing the straight line into two portions", Essays on the Theory of Numbers by Richard Dedekind, p.5). I have tried unsuccessfully to cut space without contravening Euclid's axioms.
*C.S. Peirce - Whenever, I attempt to cut a line into two portions, the point at which the cut takes place actually becomes two points and I ask myself, does this mean 'the point at which the cut takes place' can have two parts? And if so, would this not contradict Euclid's axiom on the definition of a point stated in book 1, definition 1? (In Lecture 3 of my Cambridge Conferences Lectures of 1898, published as Reasoning and the Logic of Things, I observed that, if a line is cut into two portions, the point at which the cut takes place actually becomes two points... This approach may contain hidden but real contradictions, and it is a problem that has not yet been solved by researchers into my logic and mathematics). If a point cannot be divided, then Space cannot be cut.
8. Space can vibrate and in doing this the magnitude of extension between two points oscillates.
*Einstein - Space as part of an amalgam I call space-time can vibrate as gravitational waves. Thus space can 'move', for whatever can vibrate has parts that can move. It may be instructive to note here that hypothesized gravitational waves, apart from having the same speed as light are also transverse waves. This therefore compels that the medium requirements for wave propagation are same as for light, i.e. an 'elastic solid' medium is required.
*Bondi, Hermann - "Place several beads on a rough stick and let a gravitational wave pass - the wave will push the beads back and forth on the stick, heating it. Surely, if the wave can heat a stick, it must carry energy" - Bondi, H. (1957), Nature, 179, 1072. In other words, the length between the beads oscillates due to the passage of the wave. If points are not dimensionless, then the number of points on a length can vary. This is also a first hint of the way points "move" (i.e. by annihilation and emergence). A length constituted of an infinite number of dimensionless points cannot vary in magnitude due to the passage of a gravitational wave since the number of points remains infinite.
9. A fundamental unit of space cannot be deformed since it has no parts. It cannot be twisted or undergo any deformation that preserves its volume. It is therefore RIGID.
*Leibniz - "Something that has no parts can't be stretched, can't be shaped, and can't be split up" as can be interpreted from my Monadology. That is, it is extremely rigid.
10. A fundamental unit of space can only undergo deformation that involves a complete change of volume to nothing, not by shape. Now, if parts of something ONLY move by such volume change to nothing (annihilation) or volume change from nothing to a volume (emergence), this implies they have a quality of being extremely elastic, shrinking at the slightest necessity, and inflating without effort when required by some law of nature.
*Leibniz - "It doesn't make sense to suppose that a fundamental unit of space can be altered or re-arranged internally. Within it there's nothing to re-arrange, and there is no conceivable internal motion in it that could be started, steered, sped up, or slowed down, as can happen in a composite thing that has parts that can change in relation to one another". As can therefore be inferred from paragraph 6 of my Monadology, "we can say that the only way for non-zero dimensional, extended points to begin or end - to come into existence or go out of existence - is instantaneously, being created or annihilated all at once". In other words, the only change they can undergo is elastic in nature, this in spite of being extremely rigid and resistant to volume-preserving changes as stated in the preceding paragraph. This appears an uncommon nature, that a substance be receptive to deformations that result in volume loss/gain (elastic), while very resistant to deformations that preserve volume change (characteristic of rigid solids).
*Wheeler - If what Leibniz is saying makes sense, then reality can be expressed in two binary states and this information in terms of expressed binary choices will underlie reality. I said before that, "... even the SPACE continuum itself - derives its function, its meaning, its very existence entirely - from ... binary choices, bits". A thing that can be expressed as binary choices must therefore be capable of change of nature, which is fundamentally motion. Take a listen, "Why, because the one, if it were moved, would be either moved in place or changed in nature; for these are the only kinds of motion" - Parmenides by Plato 370 B.C.E. The expression of these binary choices in terms of existence/ non-existence could then be the fundamental event in this universe. All other events are secondary patterns to this, no matter how seemingly complexly contrived and expressed. It is therefore obvious that a universe such as this would be digital, with each state of its physical reality representable by the digits 0 and 1.
11. Space and its parts are irrotational meaning the parts do not move by rotation. As has been pointed out the only possible motion is from 'nowhere' to 'somewhere' (emergence) and from 'somewhere' to 'nowhere' (annihilation). Parts cannot move from one place to another, as by definition a 'part' is itself a 'place'.
12. What is body, i.e. what is substance?
*René Descartes: In addition to what Leibniz said that points are the atoms of Nature (both body and space), and Wheeler's concurrence that binary choices is what primarily underlies and is expressed as body, I have already stated in section 11 in my paper and in paragraph 4 here that there's no real difference between space and corporeal substance. Let me add here as I did in section 23 of my paper, that "All the variety in matter, all the different forms it takes, depend on motion. So the universe contains the very same matter all through, and it's always recognized as matter simply in virtue of its being extended. All the different properties that we vividly perceive in it come down to its being divisible into parts that move, so that it can have all the different states that we perceive as derivable from the movement of the parts. No change in a portion of matter comes from our dividing it merely in our thought; all qualitative variety in matter comes from differences in how its parts move. The inference from this then is that what we call a particular place, an electron, a proton a distance, etc depends on the pattern of motion in that place".
If we consider together all these expert witness testimonies, we can clearly arrive at my postulate that:
The non-zero dimensional point does not have an eternal existence, but can appear and disappear spontaneously, or when induced to do so by physical law.
With this postulate I can now call on Light, our eminent and most important star witness to take the stand and testify.
