(7)
What is the true nature of physical reality? We perceive reality through our senses. Human senses are unique to our species and other species have completely different ways to perceive their surroundings. Variations exist among humans, women in general have a more complex sense of color than men and some women have extra color rods in their eyes while color blindness is much more common in men. What we call reality is both an illusion and not an illusion. An illusion in that it is a manufactured product of our brains and not an illusion since this outside reality has enough consistency to allow us exist within it. Humans have been able to expand our senses and with experimental science and the descriptive analogies of mathematical logic, are able to not just understand but manipulate our surroundings. Still, this is like the parable of the blind men and the elephant (1), reality is much too big and complex to get more than a distorted view. There is a basic antitheses, physical reality vs psychological reality. Physical and psychological reality have two main components, space and time. This essay is about physical and psychological space.
The idea of physical space vs. psychological space is a fairly recent issue. A longer running controversy has been about the underlying structure of space. Is space absolute or relative? What does this mean? O’Keefe and Nadel define absolute space as:
"… the notion of a framework or container within which material objects can be located but which is conceived as existing independently of particular objects or objects in general. Objects are located relative to the places of the framework and only indirectly, via this framework, to other objects. Movement of a body (including the observer) changes its position within the framework but does not alter the framework or the relationship of other objects to the framework …" (3)
and relative space as:
"… set of relations amongst objects or sensory inputs which in themselves are inherently non-spatial. Objects are located relative to other objects and relative space does not exist independent of the existence of objects …" (3)
Notice the key word “non-spatial.” In relative space the idea of distance is either missing or secondary. In mathematics this idea of distance define a measure. Euclidean geometry is a 2 measure defined by three properties:
In other words:
Distance between objects is positive. Distance between the same object is zero
The distance from one object to the next doesn’t change with the direction traveled.
The so-called triangle inequality. There is always a shortest distance between two objects.
Relations have been mathematically defined as a Graph, sets of connected points (nodes) and lines (edges.) The visual component of a Graph is termed a network and modern parlance uses network for both.
Puluwat Star Chart (4)
Etak (4)
In the western Pacific are the Carolinas, a string of small islands running east to west for almost 2,200 miles. Near the center is the island of Puluwat whose inhabitants are famous for their sea faring skills piloting small canoes to this day all over the region. Their society contains a class of highly trained and respected navigators who mange the journeys with impressive safety. Navigators use star charts of the rising and setting stars, the sun, knowledge of ocean waves, water color, wind and weather patterns, and habits of sea birds and other ocean life. In addition, they have a system of matching star positions to reference islands called etak that is purely relative. Etak has no relation to time or distance just to fixed landmarks relative to the canoe and to the stars. Etak is not a system of measure but a network. It must be noted that this whole body of navigator knowledge is memorized and handed down, there is no written record except by a few modern researchers. Here is a more familiar example. On the freeway are milepost markers that count out distance from a start point. This system is spatial and part of what is called a linear reference system. In addition there is a set of interchanges on the freeway which creates a simple network. It is non-spatial, the distance between interchange A and B can only be calculated using the linear reference system, it doesn’t have to be a property of the network.
In 1687, Sir Isaac Newton published The Mathematical Principles of Natural Philosophy in Latin. In this work he came out against the notion, mainly from Rene Descartes, that absolute space cannot exist. This notion is exemplified by the so-called Bucket Argument (6), which Newton used to create modern physics:
"If a vessel, hung by a long cord, is so often turned about that the cord is strongly twisted, then filled with water, and held at rest together with the water; after, by the sudden action of another force, it is whirled about in the contrary way, and while the cord is untwisting itself, the vessel continues for some time this motion; the surface of the water will at first be plain, as before the vessel began to move; but the vessel by gradually communicating its motion to the water, will make it begin sensibly to revolve, and recede by little and little, and ascend to the sides of the vessel, forming itself into a concave figure...This ascent of the water shows its endeavour to recede from the axis of its motion; and the true and absolute circular motion of the water, which is here directly contrary to the relative, discovers itself, and may be measured by this endeavour. ... And therefore, this endeavour does not depend upon any translation of the water in respect to ambient bodies, nor can true circular motion be defined by such translation. ...; but relative motions...are altogether destitute of any real effect. ...It is indeed a matter of great difficulty to discover, and effectually to distinguish, the true motions of particular bodies from the apparent; because the parts of that immovable space in which these motions are performed, do by no means come under the observations of our senses."(5)
Notice the final part of this quote: “do by no means come under the observations of our senses.” Newton considered physiological space relative and physical space something that could only be known through experiment, logic and mathematics. This has been a controversy to this day. In 1714 Leibniz, the co-discoverer of the calculus, published The Monadology (8). In this short article Leibniz lays out a purely relational structure to reality based on entities he calls Monads. The Monadology seems weird and fantastical but it is considered an important philosophical work and is still influential today because it can be seen as describing quantum entanglement. In 1710 George Berkeley published A Treatise Concerning the Principles of Human Knowledge (9). Berkeley rejects physical space altogether and takes a mind only approach to reality. Our only way of understanding reality is through human perception. This human perception is strictly relational. Although Berkeley’s views on physical space can be thought of as being church reactionary, his insights into human perception are today thought to be the start of the science of human perception. The basic ideas of Berkekey, Newton and Leibniz are summed up by O’Keefe:
"Newton's advocacy of absolute physical space rested on the role this concept played in his physics, and the empirical success of that physics. Berkeley's epistemological analysis cast grave doubts on the ability of conscious beings to know anything about the existence or nature of the external world. Finally, Leibniz provided one example of how notions applicable to the external world, such as space and objects, could be manufactured by conscious entities totally isolated from that world." (3)
In 1787 Kant published Critique of Pure Reason. Kant originally believed that physical space is relative but changed his mind by 1787:
"… absolute space has a reality of its own, independent of the existence of all matter, and indeed as the first ground of the possibility of the compositeness of matter …" (10)
Kant’s unique notion was that psychological space must also be absolute. Historically, this has always been a minority opinion. In 1883 Ernst Mach published The Science Of Mechanics, a strong critique of Newton’s absolute space, a return to the Bucket Argument (11) and a strong influence on Einstein. Einstein’s Special Theory of Relativity is considered a completely relational theory, banishing the frame of reference. (12) Unfortunately this was superseded by his General Theory of Relativity (13). I’m still not clear about the details but it is generally thought that this more powerful theory failed to banish absolute space. (14)(15) The general consensus among physicists is that physical space is relational but that this is still an open question. Some physicists like Lee Smolin, are looking back to Leibniz for inspiration for a purely relational theory. (16) This questioning of Einstein’s banishing of absolute space didn’t happen right away and both Behaviorism in the United States and Structuralism in Europe readily adopted a relational view of psychological space. Unfortunately experiments done on rats and other mammals didn’t agree. In 1978, John O’Keefe and Lynn Nadel published The Hippocampus as a Cognitive Map (3). In 2014 O’Keefe and two other researchers won the Nobel prize for their work. Psychological space is Euclidean and absolute and is represented in the brain as a cognitive map. This cognitive map is implicated in the formation of memory and maybe even human intelligence. These notions of absolute and relative space have had a profound and continuing influence on both our understanding of physical space and the inner workings of the human mind.
“Blind Men and an Elephant.” In Wikipedia, November 29, 2020. https://en.wikipedia.org/w/index.php?title=Blind_men_and_an_elephant&oldid=991292336.
Gladwin, Thomas. East Is a Big Bird: Navigation and Logic on Puluwat Atoll. Harvard University Press, 1970. https://www.jstor.org/stable/j.ctvjsf6g9.
O’Keefe, John, and Lynn Nadel. The Hippocampus as a Cognitive Map. Oxford : New York: Clarendon Press ; Oxford University Press, 1978.
Knight, Gerald R. “Traditional Navigation on Puluwat.” Gerald R. Knight, March 22, 2020. https://geraldrknight.com/2020/03/22/traditional-navigation-on-puluwat/
Newton, Isaac, N. W. Life of Sir Isaac Newton Chittenden, Daniel Adee, Andrew Motte, and Theodore Preston Early American mathematics books CU-BANC Hill. Newton’s Principia : The Mathematical Principles of Natural Philosophy. New-York : Published by Daniel Adee, c1846. http://archive.org/details/newtonspmathema00newtrich.
Wikipedia. “Bucket Argument.” In Wikipedia, August 21, 2020. https://en.wikipedia.org/w/index.php?title=Bucket_argument&oldid=974081025.
Thomas, Steve, “Sailing - 22,”UHM Library Digital Image Collections, accessed December 9, 2020, https://digital.library.manoa.hawaii.edu/items/show/10175.
Leibnitz, Gotfried. “The Monadology,” 1714, 15.
Berkeley, George. “A Treatise Concerning the Principles of Human Knowledge,” 1710, 63.
Kant, Immanuel, Paul Guyer, Allen W. Wood, and Immanuel Kant. Critique of Pure Reason 1787. The Cambridge Edition of the Works of Immanuel Kant. Cambridge ; New York: Cambridge University Press, 1998.
Dr. Ernst Mach. The Science Of Mechanics. The Open Court Publishing Co., 1919. http://archive.org/details/scienceofmechani005860mbp.
Einstein, Albert. “On the Electrodynamics of Moving Bodies,” 1905.
Einstein, Albert. “On the Influence of Gravitation on the Propagation of Light,” 1911.
Grünbaum, Adolf. “Has the General Theory of Relativity Repudiated Absolute Space?” In Philosophical Problems of Space and Time, edited by Adolf Grünbaum, 418–24. Boston Studies in the Philosophy of Science. Dordrecht: Springer Netherlands, 1973. https://doi.org/10.1007/978-94-010-2622-2_14.
Huggett, Nick, and Carl Hoefer. “Absolute and Relational Theories of Space and Motion.” In The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta, Spring 2018. Metaphysics Research Lab, Stanford University, 2018. https://plato.stanford.edu/archives/spr2018/entries/spacetime-theories/.
Smolin, Lee. Einstein’s Unfinished Revolution: The Search for What Lies Beyond the Quantum. Illustrated edition. New York: Penguin Press, 2019.
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