On Paradoxes and Discontinuity

We might compare the impossibility of separating numbers inside a bigger one (of showing where the five starts and ends inside of the eight, which contains the five) with reality in general. At a deeper level, reality might be considered an all-encompassing unity. Then, despite the tremendous diversity of spatial things, the latter would exist within the same all-encompassing space, which places them in continuity with each other and with itself too. 

The human mind cannot think of this continuity, which is why we get into all kinds of paradoxes when we try to do it, like the famous paradox of Achilles and the tortoise. 

According to this paradox, Achilles, known in antiquity for how fast he ran, could not catch up with a tortoise moving slowly a few meters in front of him because he had to go through an infinite number of smaller spaces. 

These spaces resulted from the potentially infinite division of any length. The logical conclusion was a paradox, that you cannot go through an infinite number of spaces in a finite time. 

It is obvious that Achilles easily catches up with any tortoise in reality, and we see all the time things and people, while moving in space, also overtaking each other. 

Although rational arguments might force us to think that reality is continuous, it is a fact that we witness discontinuity everywhere: that the tree in the garden is separate and different from the house in front of it, that the Sun and the Earth are two distinct cosmic bodies and that a cat is separate and different from a dog or a human being. 

And modern mechanical science is based on this practical reality, which can be verified, whereas continuity can be confirmed, at the most, only for living beings. In their case, if you cut off parts of their bodies, you can kill them. 

The same is true – or even truer – for the continuity of time, except that the separation in time is much harder to establish: whereas you can repeatedly check your measurements in space, you cannot do this in time. Only if events can repeat, is measurement possible.

(Undoubtedly, nowadays, when we can record things happening in time, we can also rewind  the recording and measure the process quite accurately. However, this is rather uncommon.)

This common-sense understanding of things as being separated in space and time led to the materialist modern scientific approach. Although continuity was acknowledged, it was rather seen as an oddity, as something that could not have any place in science. Newton considered space a ‘sensorium Dei,’ but this idea had a metaphysical meaning rather than a rigorous scientific one. 

How continuity could transform into discontinuity seems to amount to the question of how God created the world, i.e., it is something one cannot comprehend. We might say that the ‘Bing Bang’ – which is considered a singularity because one cannot comprehend how from the initial dimensionless point the whole magnitude of the present universe arose – is the present-day scientific and atheistic correspondent to the perplexity of the human spirit when faced with this problem.  

We may compare the fact that we perceive all around us the discontinuity of things with the analytical operation through which we subtract one number from another. As with the initial numeric unity of a number from which we subtract smaller numbers, we could imagine that our mind and body, while interacting with reality, cut it into all kinds of pieces, transforming them into separate entities. 

Certainly, both natural perception and intellectual activity proceed in this way. At first, we see the forest and only subsequently the individual trees. Or, first, the sea and then the individual waves. It happens similarly with any other concrete thing, whose details come to the foreground only when we examine it closer.

As for concepts, the greatest part of philosophy consists of analyzing words, that is to say, of showing their meanings, of which we are unaware while we are using those words. 

Natural transformations are also continuous: where and when exactly does an embryo start? What is the first internal component of a seed that initiates the process of germination? In the past, one thought that such processes happened identically, leading to identical results. One thought that there could not occur a different embryo from the same type of parents.

Meanwhile, the concept of ‘type’ changed. Type is no longer an immutable entity but rather an extremely slowly changing one. In this transformation of the type, one could say that new aspects emerge from the past continuity depending on the way organisms interact with their environment.

These new features allow organisms to grasp qualities of their environment that their ancestors could not seize. The opposite is also true, namely that new types of organisms cease to see qualities that the old types were able to do. 

In this process of cutting out features of reality, our memory proceeds in the same way. Memory is selective; it does not retain everything that happened in the past but only small fragments that are somehow relevant to us. And, of course, the process of memorizing changes over time according to the changes in our personality: we retain things that we ignored in the past and forget those that were meaningful to us when we were younger. 

We thus see in reality everywhere the symphony of emerging and receding features, similar to the waves that grow and vanish on the surface of the sea. Of course, this is a metaphysical proposition, since no one can verify it: ‘everywhere’ is unreachable.

Still, it seems we cannot think otherwise. Even our science is based on it through the principles of mass conservation and conservation in general. A very intuitive formula of it is: ‘Nothing is lost, nothing is created, everything is transformed.’

However, rarely are we aware of the premise that grounds it, namely that we must think of reality as continuous in order to think that transformation is ubiquitous. We operate with the results of transformations while, more or less, voluntarily ignoring what lies beyond the threshold of discontinuity. 

However, this might change in the future. The new proofs of quantum entanglement might open new directions of research and thought that reckon on continuity instead of discontinuity.

Then, we will learn to handle continuity the same way we already handle the otherwise-inconceivable quantum processes. And when continuity descends from the realm of metaphysics into the realm of science, we can expect a never-before-seen spiritual revolution.  

Leave a Reply

Your email address will not be published. Required fields are marked *