February 9, 2013

The Trinity, Simultaneity, Temporality, and Riemannian Geometry


Bernhard Riemann rocked nineteenth-century mathematics by smashing the boundaries of Euclidian geometry. He developed geometric models with a possible infinite number of curved dimensions. The Riemannian geometry laid a foundation for physics theories that include special relativity, general relativity, the Big Bang, and speculative physics models of an infinite multiverse.1 Previous articles of mine refer to special relativity and define God as the Trinity who is originally atemporal with infinite simultaneity and temporal since the beginning of temporality.2 This essay briefly explains how a possible infinite number of dimensions in Riemannian geometry help to model the paradoxical relationship between infinite simultaneity and temporality.

Classical theism says that God atemporally self-exists without change. Trinitarian classical theists attempt to explain how the unchanging God manifests in temporal theophanies such as the outpouring of the Holy Spirit and the Incarnation who physically aged and temporarily died.3 Various contemporary Christian philosophers and theologians shifted from belief in divine atemporality to unqualified divine temporality that means God always existed and exists in temporality without origin.4 However, William Lane Craig saw the problems of classical theism and unqualified divine temporality. 5 For example, proponents of unqualified divine temporality never overcame the obstacles of John Philoponus's discovery that the completed passage of an infinite temporal succession is impossible, except when unqualified temporality includes ill-defined temporal succession. Craig embraced the best of both views and concluded that God existed atemporally apart from creation and temporally since the beginning of creation. This article supports Craig's view and ill-defined unqualified temporality by developing an analogy of Riemannian geometry that models atemporailty as an infinite simultaneous dimensionality and models the emergence of temporal succession in new parallel dimensionality.
1. Roberto Torretti, "Nineteenth Century Geometry," Stanford Encyclopedia of Philosophy, 2010, http://plato.stanford.edu/archives/sum2010/entries/geometry-19th.
2. James Goetz, "The Atemporal Immutability of the Trinity and Conditional Providence," TheoPerspective, 2012, http://theoperspectives.blogspot.com/2012/10/the-atemporal-immutability-of-trinity.html; "Love and Special Relativity in the Atemporal and Temporal Trinity," TheoPerspective, 2012, http://theoperspectives.blogspot.com/2012/09/love-and-special-relativity-in.html.
3. Thomas Aquinas, Summa Theologica, 3:2:1.
4. Gregory E. Ganssle, "Introduction: Thinking about God and Time," in God & Time: Four Views, ed. Gregory E. Ganssle (Downers Grove, Illinois: InterVarsity, 2001), chapter 1.
5. William Lane Craig, "Timelessness and Omnitemporality," in God & Time: Four Views, chapter 4.

Definitions for this essay include:
A. Simultaneity means "dimensionality with no distinction between the past, present, and future."
B. Atemporality and timelessness mean "dimensionality apart from or without succession that could include a time dimension with infinite simultaneity."
C. Temporality and time mean "within a succession going from past to present to future" except when the context indicates simultaneity.

Classical theists such as Aquinas teach that God is completely atemporal. For example, Aquinas said that God alone exists in eternity while eternity is a simultaneous whole with no succession.6 This compares to the atemporality in the materialistic models of Zeno and the philosophical concept of eternalism. Zeno proposed that the observable universe is motionless and an undivided whole.7 Eternalism similarly proposes that the observable universe is absolutely simultaneous with no distinction between the past, present, and future.8

Eternalism developed from Einstein's theory of special relativity that predicts relative simultaneity. Relative simultaneity means there is no absolute simultaneity of distant events, which indicates that there is no absolute time frame. This lack of absolute time frame from relative simultaneity ironically supports the radical simultaneity of all events in an infinite time dimension with no distinction between the past, present, and future. The absolute simultaneity of all events also indicates that the set of all events in the universe is uncaused and likewise self-existent while all apparent evidence of causation and time's arrow in scientific observations and human experience is merely an illusion.

Incidentally, McTaggart proposed two models of eternalism. First, McTaggart proposed the B-theory of time that says the time dimension has no distinction between the past, present, and future while all appearance of temporality is an illusion. Second, McTaggart ultimately rejected both his A-theory and B-theory while proposing that all appearance of a time dimension (A-theory or B-theory) is an illusion and there is no distinction between the, past, present and future.

In the case of atemporality in classical theism, God is uncaused, self-existent, and immutable. Similarly, in the case of eternalism, the observable universe is uncaused, self-existent, and immutable.
6. Thomas Aquinas, Summa Theologica, 1:10:1.
7. Nick Huggett, "Zeno's Paradoxes," Stanford Encyclopedia of Philosophy, 2010, http://plato.stanford.edu/archives/win2010/entries/paradox-zeno/.
8. Ned Markosian, "Time," Stanford Encyclopedia of Philosophy, 2010, http://plato.stanford.edu/archives/win2010/entries/time/.

Aquinas clearly distinguished between eternity and temporality. He said that eternity exists with no beginning, no succession, and no end while temporality has a beginning, succession, and an end.9 However, Aquinas's view of temporality faces conflict with contemporary evidence of a flat universe that has a finite origin and a succession that will never end. For example, the observable universe presumably has a beginning while space-time and respective vacuum energy will continuously expand without an end and always approach zero degrees Kelvin. Also, despite the lack of an end in the continuous expansion of a flat universe, any possible measurement of temporality would always equal a finite age.

Temporality in the observable universe always involves entropy, which is the inevitable increase of disorder. However, perhaps there are created regions non-subjected to entropy. Such regions might be thought of as atemporal because nothing is subject to age, but such a region is temporal if there could be succession of activity, regardless of apparent reversibility. Also, some created regions might involve no succession of activity apart from their origin. These regions might appear atemporal except for their beginning, which makes them quasi-atemporal.
9. Thomas Aquinas, Summa Theologica, 1:44—46.

Biblical scholars dispute the biblical definition of time. Here is an example. On one hand, Psalm 90:2 says that God is from everlasting to everlasting, which appears to say that God always existed in an infinite succession of time. On the other hand, 1 Corinthians 2:7 says that God existed before the ages, which arguably refers to divine existence prior to the beginning of successive time and implies divine atemporality. These verses and others lead many to the conclusion that the Bible does not focus on delineating philosophical and scientific definitions of time. This leads to philosophical considerations when trying to understand the relationship between God and time.10

As previously mentioned, Aquinas's classical theism saw God as atemporal and creation as temporal. This strains the concept of God relating to temporal creatures and some contemporary classical theists such as Paul Helm try to resolve this strain by proposing that creation is not temporal but atemporal.11 Helm proposes an atemporal relationship between an atemporal Creator and an atemporal creation, which is consistent with eternalism. But the biggest strain with eternalism is that it reduces all appearance of temporal succession to an illusion. Objects such as humans appear to exist after nonexistence while eternalism indicates that every such object actually has always simultaneously non-existed and existed. Also, the concept of cause and effect requires temporal succession while eternalism also reduces cause and effect to an illusion. In this case, statistical studies have nothing but an illusionary basis while the scientific method is based of repeatable experiments that typically involve statistical analysis. Likewise, eternalism reduces science to an illusion. Moreover, in the case of theism, the observable universe always non-existed and existed, which blurs the reality of the Creator.

Another proposal of God and time says that God has immeasurable relative time while creation has a finite origin and measurable time. Alan Padgett and Nicholas Wolterstorff take different directions with this proposal.12 Padgett says that God always exists in immeasurable relative time while Wolterstorff says that God originally existed in immeasurable relative time and then entered measurable time upon creation. The biggest problem with these views is that their immeasurable relative time is indistinguishable from the simultaneity in eternalism. For example, the reduction of Padgett's view compares to Aquinas's view of an infinite simultaneous atemporal God somehow relating to a finite temporal creation. Also, the reduction of Wolterstorff's compares to Craig's view, which as previously mentioned proposes an originally atemporal God who enters temporality upon creation. The next section models Wolterstorff's and Craig's view with an analogy of Riemannian geometry.
10. Gregory E. Ganssle, "Introduction: Thinking about God & Time," in God & Time: Four Views, ed. Gregory E. Ganssle (Downers Grove, Illinois: InterVarsity, 2001), chapter 1.
11. Paul Helm, "Divine Timeless Eternity," in God & Time: Four Views, chapter 2.
12. Alan G. Padgett, "Eternity as Relative Timelessness," in God & Time: Four Views, chapter 3; Nicholas Wolterstorff, "Unqualified Divine Temporality," in God & Time: Four Views, chapter 5.

This essay proposes that God originally exists in infinite simultaneous dimensionality and God generated new dimensionality with successive temporality while divine omnipresence likewise entered the new dimensionality. Riemann's geometry with a possible infinite number of dimensions and manifolds help to picture this. Similarly, Andrei Linde's speculative physics model of steady-state eternal inflation with an infinite number of parallel universes in a multiverse that continues to develop new universes helps to picture a model of infinite simultaneous dimensionality that generates yet new parallel dimensionality. Linde's steady-state eternal inflation model evidently includes a drawback of a zero probability for generating universes that produce galaxies,13 but the geometry nevertheless helps to picture the parallel coexistence of infinite simultaneity and the emergence of succession.

In this theological model, the Trinity self-exists in infinite simultaneous dimensionality. The three divine persons infinitely love each other in indivisible infinite dimensionality and experience infinite pleasure. Divine omniscience knows all reality and all possibilities, which indicates self-consciousness. Divine power includes inexhaustible capacity to create new dimensionality. Infinite time within the original dimensionality involves no distinction of past, present, and future. This original dimensionality is internally simple without change. There are no elementary particles and no vacuum energy that generate movement. God lovingly and freely decides to generate new dimensionality with succession. The first new dimensionality might have involved only inter-Trinitarian relationship. Regardless if that was the first new dimensionality, God lovingly and freely decided to create new dimensionality with successive time for the habitation of creaturely free will agents while God wanted to cultivate new loving relationships. God remains omnipresent in the original simultaneous dimensionality and continues omnipresence in all new successive dimensionality.

God's omniscience and inexhaustible creative capacity could have completely determined the outcome of all created dimensionality. However, God's omniscience and inexhaustible creative capacity could have decided to forbear complete determinism and enable boundaries of freedom for contingencies such as genuine stochastic processes and creaturely free will decisions that could go in more than one direction. A model with complete determinism is called meticulous providence while a model with partial determinism is called general providence.
13. Alan H. Guth, "Eternal Inflation and Its Implications," 2007, http://arxiv.org/abs/hep-th/0702178v1.

Aquinas referred to the Incarnation as the union of God's essential nature and God's nonessential created nature.14 This model refers to God's original simultaneous dimensionality as God's essential nature and God's temporal dimensionality as God's nonessential nature. However, the term nonessential in this context in no way implies unimportant or inadvertent.

The central nonessential experience of God in Christian doctrine is the Incarnation. Christ is the second person of God who remained one hundred percent God and also became one hundred percent human, which according to the Fourth Ecumenical Council is the divine-human hypostatic union. The hypostatic union was a manifestation of Christ who originally existed in essential mode, developed a nonessential mode at the beginning of temporality, and eventually developed into the Incarnation. Likewise, Christ possessed at least two nonessential modes while each mode was one hundred percent the second person of God.

Another divine nonessential mode in basic Christian doctrine is the outpouring and manifestation of the Holy Spirit, the third person of God. The essential mode and the nonessential mode of the Holy Spirit are completely God in the same way the essential mode and nonessential modes of Christ are completely God.

An example of a manifest nonessential mode of the Father was at the baptism of Christ. The Father spoke an audible declaration: "You are my Son, the Beloved; with you I am well pleased."15

The three divine persons relate to each other both in essential nature and nonessential nature. Also, no created person can possibly perceive the essential nature of God, but God reveals nonessential divine manifestations to angels and humans while cultivating loving relationships.
14. Thomas Aquinas, Summa Theologica, 3:2; 3:25:1.
15. Luke 3:22.

Temporal succession results in continuous development of new reality. This leads to questions about divine omniscience and foreknowledge. Ancient church fathers evidently unanimously believed that God possesses static foreknowledge, which means that God has always exhaustively foreknown the definite outcome of all events. This meticulously includes for example the formation of all dust bunnies. However, some ancient church fathers believed in general providence while asserting divine static foreknowledge.16 Regardless, this divine model of parallel dimensionality could only possess static foreknowledge in the case of meticulous providence. Any range of unpredictability in general providence results in dynamic omniscience, which is a major component of open theism.17

This model of divine parallel dimensionality in the case of meticulous providence resembles Thomism. The divine essence possesses simplicity, immutability, omnibenevolence, and static omniscience. God's omnipotence is limited only by non-contradiction.18 Divine foreordination completely determines all activity. God meticulously orchestrates all appearance of contingencies such as all genuinely stochastic processes and free will decisions that could go in more than one direction, which means that no detail is unpredictable to God. Also, all divine relationship to creation is nonessential.

In the case of God granting creation a range of unpredictability in general providence, then the divine essence possesses simplicity, immutability, omnibenevolence, and omniscience while omniscience is the knowledge of all reality and possibilities. God's omnipotence is limited only by non-contradiction. In the case of divine foreordination, divine omniscience has always known the range of omnibenevolent responses to every possible circumstance. Also, all divine relationship to creation is nonessential.
16. Irenaeus, Against Heresies, 4:39:4.
17. Clark, Pinnock. et al. The Openness of God: A Biblical Challenge to the Traditional Understanding of God, (Downers Grove, Illinois: IVP Academic, 1994).
18. Thomas Aquinas, Summa Theologica, 1:25:4.

Immanuel Kant in Critique of Pure Reason struggled with the mysteries of an infinite universe. For example, an infinite passage of measurable temporality could never completely occur. This logically indicates the emergence of measurable temporality. But absolute nothingness that by definition never changes from nothingness could never cause the emergence of measurable temporality. Or how could an atemporal nature that by definition never changes cause the emergence of measurable temporality?

The emergence of temporal succession is perhaps the greatest partial negative mystery in philosophy and theology. I previously mused the possibility that God's atemporal creative capacity had compelled God to make an initial unspecified creative decision that by definition began temporal succession, but I now reject that anything compelled God. Most open theist scholars in personal communication assert that God needed immeasurable temporality to make the first creative decision. But open theist philosopher Alan Rhoda in personal communication disagrees and says that God needs no temporal succession to deliberate a decision despite that all finite humans need temporality for deliberation. I consider the impossibility for the passage of infinite measurable temporality and that omniscient God needs no measurable temporality for deliberation. I assert the partial negative mystery that God in infinite simultaneity freely made his first creative decision that necessarily included the emergence of temporal succession.

This essay briefly introduces a new academic model of God and time. This leads to many questions that I plan to answer in a scholarly book. I also plan to illustrate the concepts in popular books. I would greatly appreciate any thoughtful feedback from blog comments or email.

Perhaps the most sensitive questions instigated by this model involve the coexistence of God and temporary evil. I began answering these questions in my blog essay "Divine Love, the Problem of Evil, and Theodicy."19
19. James Goetz, "Divine Love, the Problem of Evil, and Theodicy", TheoPerspective, 2013, http://theoperspectives.blogspot.com/2013/02/divine-love-problem-of-evil-and-theodicy.html.

Copyright © 2013 James Edward Goetz

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