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“Those who go forth weeping, carrying sacks of seed,

Will return with cries of joy, carrying their bundled sheaves.”

According to the standard model, we live in a universe of three spatial dimensions and one temporal dimension: a four dimensional space-time. The spatial dimensions serve to order events according to ‘proximity’, the temporal dimension according to ‘sequence’.

In classical physics, the temporal dimension behaves just like the three spatial dimensions: we can move back and forth along the time ‘line’ at will. Past and future are symmetrical.

But that is not how we experience time. Science fiction notwithstanding, we do not move back and forth at will and past and future are certainly not symmetrical. For us, time moves in just one direction and ‘sequences’ events along just one trajectory. Time is apparently not a line but a vector.

Even so, the temporal ‘vector’ could theoretically sequence events in any imaginable order…but it doesn’t. In real life, time sequences events in one very specific order: from states of lower entropy to states of higher entropy (i.e. from more ordered states to less ordered states). So far as the laws of probability, statistical mechanics and thermodynamics allow, the arrow always points along the path of increasing entropy.

Is this a fundamental feature of time…or something else? In his Brief History of Time, Stephen Hawking theorized that the mind is only able to recognize events if those events are correlated with an increase in entropy. With this speculation, Hawking joined a tradition of thinkers who argue that reality is neither the world nor the mind but the interface between the two. The French Existentialist, Albert Camus, for example, defined the fundamental nature of being as L’absurde and he located ‘the absurd’ precisely at the interface of mind and world.

Hawking went on to note that, mathematically speaking, temporal values behave just like spatial values, provided that we measure them in “imaginary” units rather than “real” units. An ‘imaginary unit’ is simply a unit that has the square root of negative one as one of its factors.

Hawking’s mathematical insight ‘squares’ with our everyday insight. We get that there is something odd about time: it only flows in one direction and it only flows along a single trajectory. But what if the ‘time’ we experience is just the ‘square root’ of actual time?

If so, to get actual time, we’d just need to ‘square’ the imaginary numbers we use to measure time. That would do two things: (1) it would convert the one dimensional ‘time line’ to a two dimensional ‘time plane’ and (2) it would change the unit of measurement from an imaginary number to a negative number (the product of two imaginary numbers is always a negative number).

Space expands in positive real units while time extends in negative real units. Regardless of the number of spatial or temporal dimensions involved, extension is always ultimately linear (Pythagorean Theorem). Therefore, negative scalar units of time balance positive scalar units of space. So time and space cancel each other out, mathematically speaking.

This is an extremely fortuitous result from a cosmological perspective. It eliminates the need to somehow import energy in order to account for an extensive universe. Plus, if the time we experience is really just the square root of actual time and if can restore actual time by squaring experienced time, we get a huge added bonus: time can now link events in any imaginable sequence without regard to the relative entropy of adjacent states and one such sequence would be the exact reverse of the time vector as we experience it.

This brings us back to Psalm 126: we “go forth weeping” (along the traditional time line) to “scatter seed” (increasing entropy) but we return (following the reverse trajectory) with “cries of joy” and “bundled sheaves” (reduced entropy). As above, in Psalm 126 events are re-sequenced…from states of higher entropy to states of lower entropy.

But why the weeping? This world has been called a “vale of tears”. We are overwhelmed by pain, illness and finally death. We are surrounded by injustice, cruelty and greed. The inexorable increase in entropy forms the backdrop, if not the cause, of all human suffering. Loss, illness and ultimately death are all related to entropy.

Order is not synonymous with Good…but the concepts are certainly related. All manifestations of Beauty, Truth, Justice and Love (four faces of Good) require a certain amount of order. Nevertheless, our lives do include pockets of adventure, beauty, tenderness and charity; but these appear as welcome but temporary eddies in a river rushing toward annihilation.

Yet these eddies play a crucial role. They represent temporary, local increases in order. They are permitted by the laws of probability, statistical mechanics and thermodynamics. They are essential because they give us a vision of how the world might look if order was increasing (or steady) rather than decreasing.

These eddies of order are windows onto a different world. The predominant reality is one of steadily increasing entropy with all that that entails. This state of affairs gives rise to what is sometimes called ‘The Problem of Evil’: how could a world created and/or directed by an All-Good, All-Powerful God possibly include adversity in such abundance? But if the world is inexorably progressing from higher ordered states to lower ordered states, what else could you expect?

But what if our experience of the world is only a subset of what’s actually happening in the world…it’s ‘square root’? What if the world’s headlong rush toward maximal entropy is perfectly balanced by a steady climb toward a minimal entropy? As in Psalm 126, on one level we ‘go forth weeping’ to ‘scatter seed’ but on another level, we ‘return with cries of joy’, carrying ‘bundled sheaves’.

“Ok,” you say, “This is mildly interesting. But it’s beginning to sound a bit dualistic, even Gnostic. How does that help us?”

This is ‘the beauty part’! According to Roger Penrose and others, the state of maximal entropy also known as ‘heat death’ is actually a state of non-being. The world of our experience is a world hurtling toward its own annihilation. Good riddance! At the same time that this world is ‘coming undone’, another world, also our world but a world of minimal entropy, is coming to be. We just can’t see it directly…at least not yet. (We do see it indirectly when we experience beauty, truth, justice, love, etc…)

What can we say about a world of minimal entropy? It will have maximal order and therefore support optimal Beauty, Truth, Justice and Love. Maximal order is not perfect order; there would still be enough residual entropy in the system to avoid stasis and to permit ‘process’ to continue. Such a living world of optimal Good is what we call the Kingdom of God.

“But,” you object, “When we look back to the state of the universe immediately after Big Bang, we don’t see Beauty, Truth, Justice or Love. So how is a world of minimal entropy of any value to us?”

This critique assumes that what we see from our entropic perspective as minimal entropy is the same thing we’d see as minimal entropy from a negentropic perspective. There is no reason to suppose that this is so. Roger Penrose, for example, says that Heat Death and Big Bang are mathematically equivalent. They may even be the same event seen from different perspectives.

From our entropic perspective, our only glimpse of how the world might look from a negentropic perspective is contained in those eddies of order we identified earlier. Instances of beauty, truth, justice and love are oases in the entropic desert. They function like icons, windows that open onto the Kingdom of Heaven.

So our world may be much more amazing than we ever imagined. Events are simultaneously moving toward maximal entropy and minimal entropy along a reclaimed time line. The maximal entropy path leads to self-annihilation which effectively erases its existence; we are left then with an eternal state of minimal entropy which is the Kingdom of God.


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