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FQXi FORUM
CATEGORY: Essay Contest
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TOPIC: Temporal Platonic Metaphysics by Aleksandar Mikovic
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The voting deadline has been extended to January 1, 2009.
Please vote for your favorite essays soon!
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Essay Abstract
In this essay we describe a platonic metaphysics where time is a fundamental idea such that the passage of time is independent of observers and the laws of physics. Furthermore, time serves to distinguish between a real and an abstract universe, where a real universe is an appropriatelly ordered set of ideas in time, while an abstract universe is such a set outside of time. We allow for non-computable and non-mathematical ideas to be part of our model of the universe in order to include intelligent observers. The part of the universe which can be described by mathematics corresponds to a mathematical structure in Tegmark's sense, while the non-mathematical part can be described by a human language. We describe the mind-brain connection in our framework, and show that it resolves the problem of obtaining abstract knowledge in platonism. We briefly discuss how different interpretations of Quantum Mechanics can be implemented in our framework and point out some physics implications, most notably that the time travel would be impossible.
Author Bio
Aleksandar Mikovic is a professor of mathematics at Lusofona University in Lisbon and a member of the Mathematical Physics Group of the Lisbon University. He obtained his PhD in theoretical physics from the University of Maryland in 1990. From 1990 till 1994 was a postdoc in string theory and quantum gravity at SUNY-Stony Brook, Queen Mary College, and Imperial College in London. He was a researcher at the Institute of Physics in Belgrade from 1995 till 1999. Since 1999 lives and works in Portugal. He has written over 50 papers on string theory, quantum gravity and spin foam models.
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Empiricism that drives today Science is still derivating from Plato. Einstein for example is not describing or explaining the Universe, he is stating it.
Algebraic Geometry is Empiricism and Empiricism is poetry.
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Dear Dr. Mikovic,
I enjoyed your essay, especially because you proposed an original platonic vision. Interesting the idea of time Universe, the representation of the increase of knowledge of the observers, and your resolution of the epistemological problem in Platonism.
Best regards,
Cristi Stoica
Flowing with a Frozen River
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Professor Mikovic,
I was heartened to read your essay ‘Temporal Platonic Metaphysics’ as you were one of the few to delve into the Platonic realm. As I am a Platonist at heart, I would like to repeat back the gist of your ideas in my own words to see if I have understood them, then add a few observations of my own that would not have occurred to me had it not been for your essay.
Time is independent of any observer. It is embedded in the abstract relationships of sequence. It is physically manifested in the movement or flow of mass-energy through a sequence of adjacent points in space. Adjacency is an interesting and non-trivial consideration in light of the possibility and likelihood that the manifestations in our familiar 3+1 (McGuckens’ 3 + ict) -dimensions are projections from higher, compactified, brain-like and/or imaginary dimensions. Your D-dimensional manifold with its temporal D - 1 -dimensional sub-manifold fits perfectly with this. I would argue for a D - N sub-manifold to get back to the familiar 3 + 1 -dimensions from a yet to be determined D. I am drawn intuitively to the special case where D = 8 and N = 4 yielding four regular and four imaginary dimensions. There may very well be mappings onto that from higher levels yet.
The only homogeneous (non-differentiated) thing is non-existence. The first thing to arise, discretely and discontinuously, is the existence of non existence. Here, I would distinguish the abstract entity ‘existence’ from the physical attribute of ‘being.’ The first abstract relationship (the fundamental or primal relationship) in the Platonic Realm of Mathematics (PRM) is this duality of existence and non-existence. The PRM is nothing more or less than all abstract relationships. These abstract relationships have existence independent of a physical medium or a consciousness to contemplate them. All other relationships spring forth from the primal duality. They are heterogeneous (differentiated into two parts), and can be discrete and discontinuous or continuous. It strikes me as a conjecture that there is a foliation for each following duality where it can be considered to be a primary relationship when considered against a background of all others. In that sense, I would agree with you that T is irreducible to a sub-duality. But yet, I can see that there are different possible foliations of relationships where T is a compound of others.
From the primal duality some of the relationships spring forth sequentially and others spring forth simultaneously. The sequential relationship: from nothing to the empty set to the set of nothing and the empty set, and so on, generates the integers in sequence. From the N ^ N matrix comes N –dimensional space, with each point existing simultaneously but also being related to all others in space as a sequence by adjacency. The sub-set of all relationships that relate to these points in sequence produce order; those that relate to the points out of sequence produce chaos. Time springs quite naturally from these sequential relationships. At this point it can be appreciated that the vast preponderance (orders of infinities!) of sequential relationships fall into the second category and produce chaos or are simply unfruitful. The simplest and most orderly sets are not sufficiently complex to allow a universe to spring into being.
Are you using H as the set of all possible Histories which comprise the block and our specific instance U(H,T) is but one particular sequence picked out from the possible Eigenstates remaining in superposition? That is to say, consistent with the specific U(H,T) which is partially determined globally by H in terms of sequential events due to mechanisms such as decoherence, entropy and self organized criticality, and partially determined locally by the actions of an observer (with consciousness).
My quantum mechanical interpretation would be a virtual forest of trees all decorated in different ways, forming a subset of all possibilities in superposition from the total set of all relationships in the PRM. One of the decorations is responsible for the tree catching on fire. The relationships that lead to the block (simultaneous) time of GR and also those that lead to real (sequential) time, which lock in as history at the collapse of the wave function, both exist side by side in the PRM. Could they not exist as future and past in our unfolding universe.
I equate Nature as that subset of relations in the PRM that are holographically fruitful; those relationships that reinforce in an interferometric sense to produce our physical universe. A sum over histories of all possible virtual universes.
In your description of the Platonic Realm you use the word idea (I know this is the classic description). Are you intimating that a consciousness to hold that idea is contained within the PRM? I guess I like the word relationship because it is more neutral and non-committal as to where consciousness resides. But one must remember that even the word relationship is just a symbol that allows a thinking mind to encode and contemplate that abstract entity which has existence independent of that symbol and that mind.
Also, your division of ideas (relationships) into mathematical and non-mathematical is helpful because it opens the discussion to include the emergent and non-reducible aspects of being, such as psychology, sociology, philosophy and the biggie, consciousness itself. It is the conjectured foliation of relationships where consciousness is considered against all other relationships as basic. Whether the PRM is the ground of consciousness (my feeling) or the other way around is the ultimate conjecture, not reducible to any logic, only to be arrived at by an intuitive, discontinuous leap of faith.
Again, I want to say how much I enjoyed your essay. It catalyzed many new thoughts for me.
Your last paragraph sums it up perfectly.
Jim Stanfield
http://www.fqxi.org/community/forum/topic/366
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Dear Dr Stansfield,
Thank you for your comments, since they shed light on my proposal from a different angle. Let me try to answer your questions:
The objects of the Platonic Realm, I call ideas. Hence I use the name World of Ideas for PR. The PR can be split into mathematical part (PRM) and everything else (non-mathematical ideas). The mathematical ideas can be thought of as graphs, i.e. relations among some elementary objects, like natural numbers. How to specify non-mathematical ideas is an interesting problem, but the simplest approach is to use a human language to describe their relations to other ideas.
In the case of time, or the idea of passage of time T,
given a sequence of ideas H, which I call a history, then
U(H,T) would be a universe which we would perceive as the one where the instant of now is moving along the levels of H. An analogy which I like is that H is a DVD and U(H,T) is a movie played by a DVD player T.
As far as the consciousness is concerned, it is a temporal sequence C of ideas contained in U(H,T), which are attached to a particular brain. C contains both mathematical and non-mathematical ideas. Therefore I beleive that C is not a subset of PRM, since we can imagine T, and T is a non-mathematical idea. On the other hand I beleive that the brain is a part of PRM. In other words, mind contains mathematical and non-mathematical ideas, while the matter is mathematical.
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Hello Prof. Mikovic,
while i'm particularly sympathetic to the general premise here, because i am sympathetic to the cause, there are a couple of aspects here i think i'd like to see taken a little more deeply in their consideration.
re:
The ideas stored in our brain can be of two types: the ideas which are records of our interactions with the environment and the ideas which are not this, i.e. the abstract ideas.
while i may be misinterpreting the intent here, this strikes me as slightly facile. we're part of the environment, cannot be separated from it (try as we may, and we do indeed try mightily to achieve this these days). any thoughts occurring, even abstractions, are a subset of 'environment'. even our abstractions have arisen in some way from interactions with the environment and constitute further interaction with the intimate environmental subset we call 'self'.
even mathematics cannot actually isolate itself from the context from which it emerges.
perhaps taking it backward:
abstract thought not describable in mathematical terms is a capacity of consciousness in human beings.
human beings are a feature in the universe.
some aspects of the universe are not describable in mathematical terms.
in your discussion with Dr. Stanfield above, re: "How to specify non-mathematical ideas is an interesting problem, but the simplest approach is to use a human language to describe their relations to other ideas."
ya. very interesting problem. even language falls short. we only have so many words, we become dependent on them, they come to limit our perceptions - if we can't name it, we have a hard time acknowledging its existence. "table" for an elaborately carved and inlaid Louis XIV piece of furniture hardly cuts it. not to mention the dynamics that lead to the table being used as a work bench in a shed in southern Illinois. the topic of 'requirements of infinite computational resources' came up in a paper elsewhere here. it's part of what got me interested in fine arts years ago - as a communications medium with a potentially much broader spectrum of expression.
in differing cultures, there have been different ways of communicating some very ethereal concepts.
in Zen, there is a mind state of which it is said, "however you describe it, that's not it."
yet it has been communicated in fidelity down through the generations and can't be faked.
the above paragraph is both entirely true and patently false.
such abstractions beyond expression in terms of systematized symbolic language of any sort are typically considered as 'nonexistent' in physics or math.
that's a problem.
re:
The ideas in observer’s brain could be then pictured as colored graphs attached to the hooks.
The number of ideas on a hook is increasing with time(2), corresponding to our increasing
memory and knowledge.
well, "increasing"... this is an anthropocentric convention for the depiction of the process, but it may not be entirely accurate to say 'increasing', so much as a continuously varying frame of reference.
within a couple of days, my conscious recollection of having written this and your recollection of ever having read it will likely be gone forever. but there may be left a faint 'something' like a hint of the aroma of a cup of coffee lingering in the air.
if one could actually recollect in detail all of one's experiences, 'increasing' might be appropriate, but this does not appear to be what actually happens.
re:
In theories with global time, the conflict with relativity can be avoided if one postulates that the label t is not the same as a clock reading and that a clock reading
depends on the clock trajectory.
yes. this would help a lot.
re:
On the other hand, it is clear that t is related to the age of the universe. Since t always increases,
this is not so clear here.
't' always 'increases' because this is the convention of how we 'count' 't' (on occasion, 't' actually diminishes. i remember watching launches of astronauts when it was a novel thing - "four, three, two, one, ignition, lift-off), not necessarily an inherent quality of 't' itself. increase or decrease coupled with the word 'time' is largely a subjective valuation. it might be much more appropriate to say that the age of the universe is related to 't' rather than the other way around. i'm far from convinced of any commutative property involved in this relationship between time and events -in- time. it is clear from most of the papers here that time frequently gets confused with the metric. akin to taking measurements of the front entrance to the Taj Mahal, presenting the measurements as a set of numbers on a sheet of paper and saying, 'This is the Taj Mahal'.
"That's the Taj Mahal?" "Well, I only had an hour before the tour bus left and they wouldn't let me go up on the roof or inside." "What color is it?" "Oh. That's right here... 6."
re:
then the time travel will be impossible within our framework.
i'd appreciate it if this were a little more specific. time travel in consciousness is indeed demonstrably possible. using a very simple technique for minimizing imaginative interference, it is more than likely that you yourself could experience perception and verifiable data acquisition of distant past, future and distant elsewhere now events in explicit violation of the speed of light information transmission limitation. this has some very interesting implications for our concept of the nature of time, suggestive of a very space-like quality. while physically verifiable feedback for very great distances in time or space is obviously problematic, clock time and physical distance are apparently irrelevant in that it doesn't seem to take any more or less time to access the intended target if it is far away in time or space than if it is more close at hand. this suggests an 'i'-like quality involved in both time and consciousness.
thanks for your paper,
glad to meet you,
:-)
matt kolasinski
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