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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. ...

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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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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...

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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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Dear Dr. Mikovic’

I read with interest your essay since it deals with questions that I have worked on and have been interested for some time. I would like to offer you a number of observations which, though, avowedly critical, remain sympathetic and may help you sharpen up your interesting and estimable undertaking.

Tegmark’s Mathematical Universe Hypothesis is not so much a...

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Dear Dr. Mikovic’

I read with interest your essay since it deals with questions that I have worked on and have been interested for some time. I would like to offer you a number of observations which, though, avowedly critical, remain sympathetic and may help you sharpen up your interesting and estimable undertaking.

Tegmark’s Mathematical Universe Hypothesis is not so much a platonic proposal as a pythagorian one since he is reviving the notion of a “world-made-of-math”. I believe he has finally acknowledge this in his latest papers on the subject (e.g. arXiv:0704.0646). It is important to have in mind that “all is number” does not quite amount to a full developed metaphysics while Plato had quite an elaborate one and it surely takes a bit more effort (and sophistication) to be a committed platonist than a pythagorian.

Plato did not propose “an abstract and a real universe” as you state, but a “Real World of Ideas (Forms)” and a “False World of Appearance” and the distinction is crucial for the platonist since appearance is composed of changing and perishable images eventual participants of the real ideas. Recall that in the Timaeus time is defined as the “moving image of eternity” and that definition circumscribes most of one can say about time in a platonic context. It seems to me that instead of engaging this definition (pregnant with relativistic meaning, by the way) you choose, unwisely, to revive an entirely newtonian, absolute, invariantly flowing, observer-independent concept orthogonal to your stated platonic departure and, I am afraid, quite inconsequential to your purpose (next point)! Furthermore and unlike Plato, you want to make this absolute time “a fundamental concept, not reducible to other simpler concepts” that is, you want to force it into the Realm of Ideas which could not possibly take note of it since they are eternal. In Platonic terms, if you excuse the pun, Time cannot ever pass... for an Idea!

Because you get the reality/appearance distinction wrong your ontology is handicapped from the beginning: “real objects in spacetime” cannot be ideas since they are merely (corrupt) images of Ideas as these, according to Plato exist outside of space and time. Yes, this is a major obstacle to building a platonic theory of time since Plato, as his disciples Barbour and Rovelli, believed that time does not exist. But unlike them he was kind enough to provide a hint, in the above definition, for why time must appear to us. I regret that you did not take him up on this instead of trying to force Newton down his throat!

Finally I must take issue with your erroneous and outrageous statement that “all interpretations (of Quantum Mechanics) share a common feature: one needs multiple universes in order to accommodate the probabilistic nature of QM, as well as the existence of states which are linear combinations of two or more classically different states”. This is wrong in more Universes than I surely can count! First no other interpretation than Everett’s invokes multiple universes and it is debatable whether even Everett requires that invokation. Furthermore the main argument against Everett (e.g. by Adrian Kent) is exactly that it does not produce a consistent assignment of probabilities to branches of the wavefunction. Apparently, you do not seem to know that there are other interpretations of QM besides Everett’s and Bohm-deBroglie (!?) but I can assure you that any of the defenders of the later would also take issue with your statement on the subject.

Beyond the shortcomings I detect in your essay I appreciate the basic thrust of your project and encourage you to reassess it since the platonic point-of-view has much more to recommend it, in my view, than the refurbished pythagorianism of Tegmark and the string theory landscape.

Best regards,

Joao Leao

Cambridge, MA

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