Zeno's Paradoxes and the Reality of Motion under Ibn al-Arabi's Re-creation Principle
This paper was delivered at the First International Conference on the Concept of Time in Science, Philosophy and Theology", AlAin, UAE University, 24/2-4/3/2012.
Ibn al-‘Arabî (1165-1240 AD) has a unique and challenging view of time and creation that has never been discussed by any other philosopher or scientist. We have explained this view in other publications. One of the major principles of this eccentric view is the so called “re-creation principle” which postulates that the cosmos is being re-created every instant of time. This outlandish view may have tremendous consequences on our understanding of many basic natural phenomena and particularly motion on which all physics theories and cosmological models are based.
Unlike most Greek philosophers who tried to understand the cosmos based on their observations of the motion of different earthly and celestial objects, Zeno (b. ~488 BC) alone questioned the mere phenomena of motion and he doubted that it has any intrinsic reality. He formulated some ‘thought experiments’ which lead to various kinds of infinity paradoxes whether we adopt either the atomic or the continuum view of space-time. Despite long centuries of research and despite the apparent success of modern physics and cosmology, these paradoxes still puzzle scientists and philosophers until now.
This paper studies the reality of motion under Ibn al-‘Arabî's re-creation principle and how these Zeno's paradoxes of motion may be potentially resolved based on this new cosmological model.
It has been shown before that Ibn al-‘Arabî (560-638 AH/1165-1240 AD) has a unique view of time that has never been suggested or discussed before or since. He clearly advocates a discrete nature of time, but in a very complicated and unprecedented manner which may unlock the way for promising new cosmological theory. He considers the divine creative ‘Week’ as the basic cyclical unit of time, and he shows that this perpetually renewed Week of creation corresponds to both space and time, with the world being created as space in six Days (from Sunday to Friday) and then manifested on Saturday (‘the Day of eternity’) in time. It has been also shown that this Week does in fact correspond to the moment which is the quanta of space-time together. This means that in every moment of our time-frame the world is re-created in this divine Week in ever new forms. For this reason Ibn al-‘Arabî takes great pains to explain the relation between this original Week and our normal week and he shows that the Days of this Week are equal to but intertwined with our normal week-days, and that the daytimes of these original Days are taken-out from their own Nights and separated from them by three Daytimes and three Nights, which for him underlines the three-dimensional structure of the world.
Based on the above hypothesis, Ibn al-‘Arabî affirms that, despite the apparent multiplicity, in reality there is only one single ontological entity that is repeatedly manifested in different forms, creating all this diversity and multitude of entities in the cosmos. This ultimate entity, immediately beneath the Real, the Creator, is what he calls the ‘Single Monad’. According to Ibn al-‘Arabî's cosmological model, the Single Monad recurrently appears in the forms of physical and spiritual entities; one form at a time on each instantaneous divine ‘Day’; thus it takes a full divine Week to scan all the states of the world both spiritual and material, or hidden and manifest. But because this creative process is done in sequence, each created entity only feels the time when it really exists, so this divine Week is witnessed as only a moment for each entity in the world. Therefore, in the normal earthly week that we encounter, each entity in the world is created many times, as many as there are moments in this normal week. The normal, observable week is thus a collection of many other moments of those divine original Weeks forming a structure of complicated intertwining.
In this way the world and its constant re-creation resembles the underlying reality of a movie displayed on a computer screen: it is composed of series of still pictures, each of which is composed of many individually generated pixels, which are like the created forms in which the Single Monad appears at every instant of time.
Based on that, we can explain various basic concepts of physics such as motion and causality in a new and fundamentally different manner. For example, there is no real motion in the sense that the object gradually moves between its starting and destination points; instead, it is re-created every moment in a slightly new position, just like the motion of the images and characters displayed on the computer monitor screen. This also means that at this deeper ontological level, there is no direct link between causes and results, because they appear in different frames, though this at the end doesn't deny causality but also provides an alternative explanation in full agreement with the principles of Quantum Mechanics.
Therefore, according to these novel views, it is possible to understand Zeno's famous paradoxes of motion, as well as the EPR paradox which underlines the apparent discrepancies between the two major modern physics theories of Quantum Mechanics and Relativity. In this paper we shall focus on Zeno's paradoxes and we will leave out the EPR for a separate article.
2. The Re-Creation Principle:
Ibn al-‘Arabî's affirms that the ‘forms’ [i.e., the particular forms taken by creation in all the different levels of existence at each moment] become nonexistent in the second instant-of-time after the instant of their coming into existence. He also makes it clear that this continuously renewed ‘return to non-existence’ is an intrinsic condition of all the created forms, and not due to any external force. Typically Ibn al-‘Arabî relates this fundamental insight to the Qur’anic verse: but they are unaware of a(n ever-)new creation, which he frequently quotes—along with the famous verse concerning the ‘Day of the divine Task or event’ that he cites in relation to his intimately related concept of the quantisation of time.
Therefore the existence of things in the world is not continuous, as we may imagine and observe, because the Creator is continuously and perpetually creating everything whatsoever—at every level and domain of existence—at every instant of time and space, or in every single ‘Day of event’. This means that, just as time (for Ibn al-‘Arabî) may exist only as one atomic instant at a time, so also space and whatever it may contain also exists only one instant at a time.
Thus, Ibn al-‘Arabî explained that: ‘the world exists between the circumference and the point’. The ‘point’ here refers to the Real (the ‘Necessary Being’) while the ‘circumference’ is the circle of creations (the ‘possible things’ or the contingent entities) whose existence depends on the Real. However, Ibn al-‘Arabî was well aware that this paradoxical relation between the Creator and all manifestation is in clear apparent contradiction with the widely accepted philosophical maxim—a central assumption in the prevailing contemporary philosophical cosmology of Avicenna and his followers—that ‘from the One only one may emerge (or proceed)’.
The problem encountered by philosophers and theologians when they want to explain how the Creator created the world is that the Creator is One while the world is many, because logically it is not possible to imagine a relation between the One and the many without affecting the unique Oneness and Unicity of the One. In Ibn al-‘Arabî's view, however, every individual entity in the world always has a direct creative relation with the Creator, and that is how it exists and its existence is maintained. If The Creator would not maintain this creative ‘special face’ between Himself and each entity, it would cease to exist instantly. So in order to solve the problem of unicity-multiplicity relation, Ibn al-‘Arabî actually asserts that this interface between the One and all the many existent things does not happen all at once. Rather, at any instant, there is in reality a single relation or interface—a unique divine ‘with-ness’ between the One and only ‘one’ of the entities of the world. But what happens at this particular instant with the other entities in the world, since their existence is also preserved only through this unique creative relation between them and their Creator, the unique One? The answer is: they do cease to exist, and then they are re-created again and again.
Therefore, in order to understand the relation between the unique Oneness of the Real and the multiplicity of the creatures, Ibn al-‘Arabî adds time to the previous philosophical statement, which can be then reformulated as: “from the One there can emerge only one at a time”. This re-statement is indeed the key to understanding Ibn al-‘Arabî's unique views of time and the oneness of being and to solving the mystery of the relation between the Real and His creation. In this way the world is created by The Creator ‘in series’, and not just one single time, just as the repeated images of a movie are created one pixel at a time and then displayed in sequence on the screen. The meaning of this principle is in fact derived directly from the well-known verse in the Qur’an that we have already mentioned in earlier context: each Day He is upon some (one, single) task. So since The Creator is One, He does only one single creative task each ‘Day’—of course not this normal observable day that we encounter, in which an almost infinite number of tasks or events are happening but the actual Days of events which are equal but intertwined with those normal days as we mentioned above.
One of the most important consequences of this view concerns the concept of simultaneity which shall be given an even more relativistic sense than it gained after the advent of Relativity. Many classical theories considered time as an absolute linear quantity. This coped very well with the common concept of simultaneity, where events which occur simultaneously in one frame of reference were considered to have occurred simultaneously also in all other frames. In Special Relativity, the fact that light travels at a finite speed in all directions and in all frames of reference changed this piece of common sense. According to this new theory, simultaneous events in one frame of reference aren't necessarily considered simultaneous with regard to another frame of reference moving at a relatively high speed with regard to the first.
According to Ibn al-‘Arabî's view of time and his model of the cosmos that we have briefly summarised above and explained in detail elsewhere, the concept of simultaneity will have an even more relative aspect. With regard to us—i.e., considered as partial monads or entities present on the level of multiplicity—it is possible to have simultaneous events. The reason is simply because we only exist at one single location of the whole momentary ‘Day of event’. For us, therefore, at every single moment of re-creation there is a still picture (that contains maybe infinitely many events) displayed in the world, in any given frame of reference. All these events are considered for us simultaneous, but according to the sequential creation of the re-creation principle summarised above there can be no two cosmic ‘events’ actually happening at the same time. Therefore, in reality there is no such thing as ‘simultaneity’ with regard to the Single Monad who is creating the real flow of time.
Simultaneity, and therefore multiplicity, appears to occur only because of the re-creation that is spread over space and time. In reality there are no any two separate ‘events’ happening at the same created instant of time.
Thus, this extremely significant conclusion might be the key to resolve Zeno's paradoxes as well as the EPR paradox which we shall discuss in another coming article.
4. Zeno's Paradoxes:
Motion, as a manifestation of causality, is the main concern behind all the theories of physics, from the pre-Socratics through Newton's theory of gravity to the most recent theories of quantum mechanics and quantum gravity. Yet there are a number of famous philosophers who have doubted that there could be any motion at all, despite our daily experience. Most notably, Parmenides of Elea (b. 510 BC) affirmed cosmological conceptions remarkably similar to Ibn al-‘Arabî's doctrine of the oneness of being: he held 'the One' unchanging existence to be alone true, while multitude and change were said to be an appearance without reality. This doctrine was defended by his pupil Zeno (b. ~488 BC) whose philosophy of monism claimed that the many things which appear to exist are merely a single eternal reality which he called Being (a term Ibn al-‘Arabî also applies to the Single Monad). The complex and rigorous adaptation of Parmenides' hypotheses in Plato's Parmenides—constantly elaborated by the later Neoplatonists—offer even closer analogies to Ibn al-‘Arabî's overall ontological system. Zeno wrote a book containing forty paradoxes, and although his book was lost, four of those paradoxes managed to reach us through Aristotle who discussed them in his Physics: the Dichotomy, the Achilles, the Arrow, and the Stadium. Each of those four paradoxes challenge all claims that there is real motion!
The Dichotomy paradox concludes that there is no motion because that which is moved must arrive at the middle of its course before it arrives at the end. In order to traverse a line segment it is necessary to reach its midpoint. To do this, one must reach the one-fourth point; to do this, one must reach the one-eighth point, and so on ad infinitum. Hence motion can never be completed, because the sum 1/2 + 1/4 + 1/8 + ... equals one, but only after infinite number of additions, and therefore it actually approaches one but never reaches it. Even more perplexing to the human mind is the attempt to sum 1/2 + 1/4 + 1/8 + ... backwards: for we can never get started, since we are trying to build up this infinite sum from the wrong end!
The paradox of Achilles attempts to show that even though Achilles runs faster than the tortoise, he will never catch her! Let us suppose that Achilles runs at ten meters per second and the tortoise at only one meter per second, and that when the race started the tortoise was ten meters ahead. After one second Achilles would arrive at the point where the tortoise was when the race started, but the tortoise would have moved one meter further—so that by the time the Achilles covers this one meter, the tortoise would have advanced again 0.1 meter, and so on. Thus the Achilles can never catch the tortoise.
Zeno bases the above two arguments on the fact that once a thing (i.e. distance) is divisible, then it is infinitely divisible. One could counter the above two paradoxes by postulating an atomic theory in which matter (or space) is composed of many small indivisible elements. However the remaining two paradoxes cause problems only if we consider that space is made up of indivisible elements that may be cut in indivisible durations of time.
Turning to the third paradox of the Arrow: if we consider the path of an arrow in flight where at each instant of its path the arrow occupies some particular defined position in space; this is what it means to say that space is discrete. But to occupy some position in space is to be at rest in this position. So throughout the entire path of the arrow through space, it is in fact at rest, or else, if in an indivisible instant of time the arrow moved, then indeed this instant of time would be divisible (for example, in a smaller instant of time the arrow would have moved half that distance). So how can the arrow reach its destination point if it is actually at rest in every point on the path?
The fourth paradox of the Stadium is a little bit more complicated, but it leads to the same result as the above—i.e., that time and space can not be discrete, while on the contrary, we have seen that the first two paradoxes may only be resolved if we assume that time and space are not continuous.
The above four paradoxes not only challenge all scientific theories of motion, but also our everyday experience. For this reason they have been often dismissed as logical nonsense. Many attempts, however, have also been made to dispose of them by means of mathematical theorems, such as the theory of convergent series or the theory of sets. Aristotle did not fully appreciate the significance of Zeno's arguments, since he called them ‘fallacies’, without actually being able to refute them. Many modern scientists like to believe that axiomatic mathematics has dispelled Zeno's paradoxes, where now it is possible to talk about limits and infinity without reaching any mathematical contradiction and it can be proven that the sum of an infinite number of halving intervals is finite. But some recent philosophers such as Bertrand Russell persisted with such arguments, and recently similar puzzling phenomena (called the ‘quantum Zeno effect’) have been observed in radioactive atoms.
5. Discreteness and Continuousness:
There is no doubt that Zeno has presented a deep problem which, despite centuries of efforts to resolve it, still seems to lack a truly satisfactory solution. As Frankel wrote:
The human mind, when trying to give itself an accurate account of motion, finds itself confronted with two aspects of the phenomenon. Both are inevitable but at the same time they are mutually exclusive. Either we look at the continuous flow of motion; then it will be impossible for us to think of the object in any particular position. Or we think of the object as occupying any of the positions through which its course is leading it; and while fixing our thought on that particular position we can't help fixing the object itself and putting it at rest for one short instant.
This basic dilemma of discreteness and continuousness has kept coming up in various guises, but most clearly in the long historical debate on the nature of light; whether it is particles or waves. With the success of the wave theory in the nineteenth century, the continuum seemed to have won. But in 1899, when Max Planck solved the ‘black body problem’ by postulating that atoms could absorb or emit energy only in discrete amounts, the age of quantum theory began. Soon after that, Bohr used the concept of quantisation to construct the first successful atomic model, and Einstein was able to analyse the photoelectric effect only by adopting the quantum nature of light. However, the quantum theory was not able to solve the question of motion and change, where the continuous theory of relativity was more successful.
So the human mind is accustomed to classifying quantities as either countable or uncountable, or either discrete or continuous; there is no other way. This is inevitable on the level of multiplicity. But on the level of oneness, in that highest ontological level, there would be no meaning for such terms. A first look at Ibn al-‘Arabî's model could conclude that, on the level of multiplicity, the world should be certainly discrete, but it isn't easy to judge—even on the multiplicity level—whether the world is ultimately continuous or discrete because, although there are discrete events happening in discrete times, still the change from one event to another looks continuous, just like the flow of normal days; there is no abrupt change. Although we can easily divide events over days and classify them according to the date, actually the relation between any two consecutive events that happened during the day is not different from those which happened also consecutively but on different days—for example, right before and after day or night. In other words, the motion of the earth around its axis, though generating the appearance of different distinct days, it is itself a continuous process. Likewise, the all-creative ‘motion’ of the Single Monad is also a continuous process in everlasting alteration between ‘daytimes’ and ‘night-times’, manifestation and being hidden, material and spiritual—yet there is no point of separation or abrupt transformation between any two periods or states. That is why Ibn al-‘Arabî calls the terms of discreteness and continuousness ‘disconnection’ and ‘connection’, because for him the actual process of change (re-creation) it is like a one-dimensional flow of divine manifestation. So if there is an apparent continuity or discontinuity that would only be in our imagination or abstract consideration, but not in reality.
6. The Reality of Motion:
There is no doubt that Zeno was not trying to deny motion altogether, because it is clearly occurring; objects reach their destinations, Achilles does run faster than the tortoise and the arrow does move in space. What Zeno was trying to say is that our understanding of motion, and hence space and time as containers of events, is completely wrong.
We have to admit that physicists habitually accept a very naive concept of motion, usually expressed by the formula ‘velocity is distance per time’. Such a simplified concept of motion has been working nicely for many centuries and although modern theories slightly corrected these classical (Newtonian) equations, they did not address the more philosophical question about the nature of motion itself. To answer this question, one has to verify whether space and time are discrete or continuous, an issue that is still persisting and unsettled even in the latest theories, as we have seen above.
With Ibn al-‘Arabî's re-creation principle, we would have no difficulty at all in resolving Zeno's paradoxes and reconciling his conclusion that there is no real motion with our daily perceptions. When we watch a movie we have no doubt that nothing really moves on the screen, but it is only a succession of different frames. According to Ibn al-‘Arabî's cosmological perspective, the whole world runs exactly like the movie. As we noted above, Ibn al-‘Arabî plainly stated that the object that we see moving actually is re-created in the distinct places between its start and destination one after another and does not really move between them, so there is never any real motion in such a way that the object gradually moves along its path. Therefore there is no real motion like that which we habitually perceive in the human common sense; in reality there is only a ‘change of place’: i.e., the thing that is the subject of motion is being re-created in different places and not moved between them.
7. Causality and Induction:
At the end of his short book al-Durrat al-Baydâ’ ('The White Pearl', which is another name for the Single Monad), Ibn al-‘Arabî wonders how (the general) people (not to mention physicists and philosophers) do not so easily realise the delusion of motion and space. He says that everything that moves does not move in occupied space, but it can only move into a void, thus the thing may not move into a new place until this new place is emptied. So by simple logic, this (false) assumption would lead to the conclusion that the result of an action would occur before the action itself. For example when you fill a cup with water, the air already in the cup will have to be gradually evacuated as water pours in. At any instance, before the water (the cause) can replace the air, the air has to be displaced or evacuated (the result). So the result happens before the cause. One may argue that in this case both the cause and the result could happen at the same time. This, however, will lead to all events, that are essentially continuous series of causes and results, happening at the same time.
So the mere concept of motion apparently violates causality, the most fundamental principle of physics, and common sense. Actually, Ibn al-‘Arabî affirms that the things are created next to the causes and not by them. Though this does not deny causality itself, it does suggest a radically new type of strictly divine causality, based on the same re-creation principle explained above. This new understanding can be shown to be in complete coherence with the principles of quantum mechanics.
References and Notes:
 For more information about Ibn ‘Arabî's life and intellectual background, see: Claude Addas, Quest for Red Sulphur: The Life of Ibn ‘Arabî (Cambridge: Islamic Texts Society, 1993). See also: Stephen Hirtenstein, The Unlimited Mercifier - The spiritual life and thought of Ibn ‘Arabî (Oxford: Anqa Publishing/Oregon: White Cloud Press, 1999).
 We shall indicate the original Week by capital letter and the normal week by small letter, likewise the original Days are indicated by capital letter and normal days by small letter.
 Most of the references from Ibn al-‘Arabî's literature are taken from his most famous and influential work of al-Futûhât al-Makkiyya ('The Meccan Illuminations'), which is an encyclopaedic discussion of Islamic wisdom. The standard edition of this book is the old four volumes edition of Bulaq 1329/1911 widely available and reproduced by many Arab publishers. I will use a short reference style similar to that used by William Chittick: [X 000.00] which means: [volume page.line]. [II 208.27]
 [II 385.4]
 All references to Qur'an are given according to the standard format [x:y], where x is the chapter number and y is the verse number. [50:15]
 For a more detailed account of the central role of these two verses in Ibn al-‘Arabî's view of time and creation, see chapters II and V of the thesis (pp. 87, 102, 108, 191, 209-210).
 [II 454.21, II 384.30]
 [I 154.22]
 Ibn ‘Arabî quotes this expression and comments on it very often in his books, and he ascribes it to al-hakîm ('the philosopher-sage') [II 458.20]. Though it is not very clear who he exactly means by al-hakîm, it is possible that he refers to Plotinus, who was known in several Arabic translations of his writings as 'the Greek sage' (al-hakîm al-yunânî). Based on Davidson (H.A. Davidson, Alfarabi, Avicenna and Averroes: Their Cosmology, Theories of the Active Intellect, and Theories of the Human Intellect. New York, Oxford University Press, 1992.), William Chittick asserts that this maxim was apparently first used by Avicenna [See: William Chittick, The Self-Disclosure of God: Principles of Ibn al-‘Arabi's Cosmology (Albany: State University of New York, 1997), p. 17]. This maxim is certainly the basis of Avicenna's cosmological schema of emanationism (fayd) [See: EP, 'Emanationism', I, pp. 473-4, and also The Cambridge Dictionary of Philosophy (Cambridge University Press, 1995, ed. Robert Audi,), pp. 258, 604-6, 714.], and it was possibly used by early Christian and ancient religions as the basis of the concept of the holy Trinity [See: Maurice Lachâtre, Nouveau Dictionnaire Universel (New Universal Dictionary) vol. 1 (Paris, n.d.), p. 1467. See also: Hopkins, E. Washburn, Origin and Evolution of Religions (New Haven: Yale University Press, 1930), [chapter XX: The Christian Trinity, chapter XVII: The Triad, chapter XVIII: The Hindu Trinity, chapter XIX: The Buddhistic Trinity]].
 Ibn ‘Arabî, 'al-Durrat al-Baydâ’', in Rasâ’il Ibn ‘Arabî (Beirut: Mu’assasat al-Intishâr al-‘Arabi, 2002), ed. Sa‘îd ‘Abd al-Fattâh, vol. II (131-145), p. 133.
 [II 385.4]
 Al-Durrat al-Baydâ’, p. 139.
 T. L. Heath, A History of Greek Mathematics From Thales to Euclid (Dover Publications, 1981), pp. 273-83. See also: Roy Sorensen, A Brief History of the Paradox: Philosophy and the Labyrinths of the Mind (Oxford University Press, 2003), p. 44-57; David Darling, The Universal Book of Mathematics: From Abracadabra to Zeno's Paradoxes (Wiley, 2004), p. 351; and: Justin Leiber, Paradoxes Interpretations, (Duckworth Publishing, 1993), p. 77, and also: Erickson, G. W. and Fossa, J. A. Dictionary of Paradox (Lanham, MD: University Press of America, 1998), pp. 218-220.
 See: B. Misra, ECG Sudarshan, ‘The Zeno's Paradox in Quantum Theory’, Journal of Mathematical Physics 18, 756 (1977); and Corey S. Powell, ‘Can't Get There from Here; Quantum Physics Puts a New Twist on Zeno's Paradox’, Scientific American, May 1990; and also: W. M. Itano, D. J. Heinzen, J. J. Bollinger, D. J. Wineland, 'Quantum Zeno Effect', National Institute of Standards and Technology, Boulder, Colorado, 1989, and: G. Grossing, A. Zeilinger, 'Zeno Paradox in Quantum Cellular Automata', Physica D 50(3):321-326, July 1991.
 H. Frankel, ‘Zeno of Elea's Attacks on Plurality’, Amer. J. Philology 63 (1942), pp. 1-25, 193-206.
 The black body problem was raised by the observation that certain materials (especially black bodies) can absorb all frequencies or wavelengths of light. So when heated it should then radiate all frequencies of light equally—at least theoretically. But the distribution of energy radiated in real life experiments never matched up with the predictions of classical physics.
 [III 324.35-325.18]
 [II 457.31]
 Published in: Rasâ’il Ibn ‘Arabî (Mu’assasat al-Intishâr al-‘Arabî: Beirut, 2002-4), ed. Sa‘îd ‘Abd al-Fattâh, p. 142.
 [II 204.13]