The Significance of Paradox

THE SIGNIFICANCE OF PARADOX

By Roland Watson

In the last article, where I reviewed different theories about the universe as a whole, I mentioned the role of gravity. I want to begin this article by looking at it in more detail; specifically, at the nature of its energy.

Is gravity the will of god?

Gravity, when it is considered in relation to the expansion of the universe, reveals a paradox. One of the implications of entropy, the movement from order to disorder, is that in the past the universe was more ordered than it is now. Indeed, the point of maximum order would have been at the Big Bang itself. I might add, this - on its own - is odd, because this is also where - or when - at least as we understand them, the laws of physics break down.

Following the Big Bang, the universe inflated extremely rapidly into a near-featureless soup of particles, at which point, under the force of gravity, the particles began to accumulate. But, this aggregation was in effect a reversal, towards increasing order, since it took place while the universe continued to expand and move towards increasing disorder. Gravity has therefore been viewed as "negative" energy, and it also had to be stronger that the force of the Big Bang, its residual force, which survived the period of initial inflation. However, the relative advantage of gravity is only temporary, since ultimately it will be overwhelmed.

Gravity holds everything together, but it has a limited duration. The elimination of available energy will end it. At that point, no space-time distortions will remain. Indeed, if the universe is alive, gravity can be viewed as its will. But, it will be overcome by entropy. Gravity, the will of the universe, and the universe itself, will die.

I can also add, if the universe is god - or even just the product of god - then gravity may be viewed as the will of god.

Dynamic and static time

To return to the different perspectives that exist on time, I should mention that the linkage of time with universal expansion is a "dynamic" argument. However, there is another possibility as well, in which time is "static." We may appear to be, or think we are, moving forward in time - do we move in time, or does time move in us? - but from another perspective perhaps there is no movement. Past, present and future are simultaneous. From this viewpoint there would be no causes and effects - no actions have consequences! Further, it implies that everything would be determined. But, of course, there is much evidence that argues against this. Therefore, if such a perspective does exist, it would appear to be necessarily excluded from anything that occupies the universe. Also, it would imply that there is the possibility of simultaneity coexisting with chance and choice.

This is also what leads to the idea - the fantasy - that it might be possible to navigate in time, to travel through it at other than a normal relativistic velocity, and in both directions, and also that it might be possible to "jump" through "folds" in space. Space is not only curved; it has twists, folds and other topological features. Indeed, the laws of physics - some of them - are time reversible. There is no reason why they wouldn't continue to function if time changed direction. However, the phenomena of reality are not. The chance element that exists, and which time reversal would not eliminate, precludes the possibility of an exact unfolding.

The boundary of the universe

Finally, there is the problem that if the universe is expanding, it presumably must be expanding into something. What is this something? Is it "potential" space-time? Also, we imagine it to be infinite, but what is infinite? This in turn raises another question. What is the nature of the universe's boundary, the point where its finite reality meets its infinite potential?

I said earlier that an implicit assumption of physics is that the universe must be infinite. This represents a possible refinement of that assumption. The universe as it exists now is finite, but it has infinite potential.

Actually, another idea, known as the Holographic Principle, and quoting Brian Greene, says that "everything that occurs in the 'interior' of the universe is merely a reflection of data and equations defined on a distant, bonding surface." If this is true, it serves as proof of my analogy about the ant farm, that there is a fundamental limit to our knowledge, since such a boundary is, by definition, inaccessible to us.

The problem of infinity

Said another way, our limitations are clearest when we consider the concept of infinity. What is infinity? Is it a measurement of scale, as in really, really big, or small, or fast, or hot - but not cold! - there is an "absolute" zero. Or, is it something else entirely, something that we do not, and cannot, understand?

Regarding space, and considering infinitesimal, or infinitely small, we do have some ability to grasp this, both tangibly and intellectually. For example, when our eyes adjust to a completely dark room, when the irises open as wide as possible, they can sense - see - a single photon, or particle of light. And this, while it is not infinitesimal, is very, very small. Also, through the language of mathematics, of calculus, we can determine the value of an exact point on a curve, an infinitesimal point, with an infinite number of other such points extending away from it in each direction along the curve.

At the other end of the continuum, we have considered some very large numbers: one quadrillion synapses in the brain; and the astronomical number of potential linkages between them. But, these amounts, while very, very large, are by no means infinite.

Indeed, you could take the number "9," typed on a piece of paper in a small font - its actual size including depth - fill up all the space in the entire universe with such nines, then string them out in a line - in imaginary space - and make it, the resulting number, a factorial, and calculate it, all - every single one - of the possible combinations, and the result would still be so small, relative to real infinity, as to be next to nothing: even, effectively, zero.

Infinity appears to be, or at least it may be, a measure of scale, but it also seems to be something else as well, something which is excluded from us because we are finite. I can add, it may also be a fantasy - like time travel - a human conception having no, and no possible, objective reality.

Because of this, infinity is a paradox, and it leads to many derivative paradoxes as well, as in, how can we possibly reconcile:

- something out of nothing, as with the universe, and life.
- more generally, the idea of boundaries, both in time and space. This includes, for the universe and for time, its beginning and prospective end, and for space, at its edge. For life, it includes birth and death, and also its own spatial self-containment.
- the issue of movement and no movement, meaning the movement that exists within the universe, compared to its probable lack of movement, its expansion notwithstanding, as a whole.
- time and no time, meaning that while time within the universe is sequential, there is the possibility of a simultaneous perspective from without.
- and that there are such things as limits - as of velocity, as defined by the speed of light.
- and the distinctions between particles and waves.
- discontinuous and continuous.
- and parts and a whole.

What is paradox?

Paradox is often viewed as a mental - or language - construction that fails to grasp reality completely, and which therefore leaves us with an implicit contradiction. Also, in some cases, as with good and evil, love and hate, and winning and losing, it arises from the idea that one cannot exist without the other. However, the underlying suggestion that is itself implicit in paradox is that it can be resolved. Reality can be grasped completely. The subjective can be "transcended." We can eliminate our separateness.

From the Manifestoes of Surrealism, by André Breton. "Everything tends to make us believe that there exists a certain point in the mind at which life and death, the real and the imagined, past and future, the communicable and the incommunicable, high and low, cease to be perceived as contradictions. Now, search as one may one will never find any other motivating force in the activities of the surrealists than the hope of finding and fixing this point."

In this website, I have reviewed numerous social paradoxes, such as equality versus freedom, and also ideas for their resolution. Existential paradoxes, though, and the search of the surrealists and the supposed ability to solve Zen koans - paradoxical puzzles - notwithstanding, are of a different quality, as in unresolvable. For instance, if reality does constitute a whole, this means that in some way it is continuous. It must be completely interconnected. Any division or separation necessarily is artificial. Even such seemingly tangible things as quanta of energy, particles, atoms, and people, cannot be distinct or separate in a fundamental sense.

But, the basic paradox is that we experience and describe them as if they are. However, we can now see that there is a fault in our reason. As we seek to interpret life, we break the inseparable into the separate. Through doing this, we add a bias, a judgment and its underlying value system, which actually is not there. But, if there is no separate interpretation, there is no paradox.

(Here's another paradox: nothing lasts forever, but life goes on.)

This is the same type of trap that occurs with language. Without us, such distinctions as good and evil, love and hate, and pleasure and pain, cease to exist. I can also add, if all of the bad people in the world disappeared, this would not change the fact that the rest are good.

Of course, the paradox, or rather the irony, is that we need these judgments. They do serve a purpose. As "parts" of the universe ourselves, we relate to other parts using the mechanism of self-consciousness and the tool of language. Without this perspective, we could not live! But, while language serves a purpose, it is also flawed. It is always a subjective representation.

For example, it is impossible to consider the above paradoxes without introducing the ideas of space and time. Indeed, they are paradoxes of space and time. But, space and time, which all language incorporate, may have no independent existence. Self-consciousness and language enable us to have "relationships," so they are useful, but they are also regularly a misleading and artificial construct.

More generally, our predisposition is that there cannot be an "all," including one of infinite magnitude. Anytime we conceive or are told of such a thing, we ask: but isn't there anything else - and wasn't something before? And, because we view ourselves as separate from "all," we will always think this way.

Why is there paradox?

The problem is much more than language. Even if we are not, fundamentally, a separable part, that is how we see ourselves. Also, while there may not be time, or even chance, to the whole, there certainly are to us, to the parts.

Is there any way to resolve completely these paradoxes, starting with infinity: any perspective from which it makes sense, and constitutes a whole? The answer appears to be: not for humans. But then the question becomes, what about for non-humans, meaning, for our supposed creator?

Through physics and mathematics we have developed explanations, and a structure, of how things are, which is more and more consistent with what we experience, in other words, which "correlates" experience. But, at a fundamental level we have no knowledge at all of what it is, exactly, that we are experiencing. Physics doesn't describe the world, only our interactions with it.

This is because we do not have objectivity. We cannot eliminate our subjective perspective. There is a greater reality, which includes us and which is invariant, but anytime we think about it and study it, we cannot escape the fact that this is nature studying itself. Is the world complex, or is this just the way we see it?

We have language limitations, which represent perceptual limitations, which in turn represent knowledge limitations, including what we have yet to understand, but also what it is not possible - for us - to know. In other words, we are back to the ant-farm - our basic epistemological condition - once again. We are in fact bumping up against it in many different ways, as we unearth more and more of what it is possible to know through physics, mathematics, and other fields of science.

Our view of life and the universe, that they are consequences with no predicate actions, is quite possibly a fault of our perception; evidence of our limitations. It only means that we cannot see the larger picture, not that there isn't one.