It’s well known that the act of observation affects that which is observed. In physics it’s called the observer effect, and it can be demonstrated in most other areas of existence – things that happen in physics have a habit of being the deep patterns that philosophy and religion are always looking for. Not so much the grand unified theory of physics, but the commonplace, everyday theories of daily life.
Having noticed such a deep physical principle in life, it has historically been tempting to extend such thoughts into metaphysics, whether the mundane, everyday metaphysics of ‘A watched pot never boils,’ or the more exotic paradoxes of Zeno. Of course, a watched pot will eventually boil, but it seems to take longer than if you go about preparing the ingredients for the forthcoming meal for which the pot is being boiled in the first place.
Even though the idiom ‘a watched pot never boils’ is momentarily arresting, and even intuitively true, to an extent, it is likewise intuitively not true. We’re quite capable of holding these two contradictory interpretations of something without ever really experiencing a contradiction. This is probably because the hyperbole of ‘never’ speaks to our felt experience of mild exasperation, but few people are likely to suggest that such a statement is actually true. So it’s strange that Zeno’s paradoxes, which speak to the same basic effect, took so much longer to unravel.
Zeno’s ‘Achilles and the Tortoise’ paradox portrays Achilles giving the Tortoise a head start in a foot race. It takes Achilles a certain amount of time to cover the distance of the head start, in which time the Tortoise has covered some small distance. It takes Achilles a lesser amount of time to cover this distance, in which time, of course, the Tortoise has covered yet more ground. The question being: can Achilles ever pass the Tortoise? The answer is of course yes, but one can, and many people did, get sidetracked into an infinite loop of shorter and shorter distances that you can mentally conjure up and that Achilles had to therefore run, and the Tortoise was forever in the lead.
So why, if you explain the “paradox,” can most people say that of course Achilles will pass the Tortoise, even if they can’t provide the mathematical proof as to the distance covered and the time elapsed? Well, the intuitive correct answer was never the point – explaining why the formulation of the paradox is wrong, was. Just as we know that the watched pot does indeed boil… eventually.
If you make the act of measurement as real as the race, for example, if you had a particularly large and obstructive individual measuring the distances, and remaining permanently in the way of Achilles, then, indeed, the act of measurement has affected that which is being measured and Achilles may well never pass the Tortoise, or will only do so after bundling the official measurer into the bushes, which will serve to delay Achilles’ passing the Tortoise, and give no clear measurement of when and where this occurred.
The problem is that we can virtualise the problem in mental space and mental time, but whilst our brain can do this, as with many things that our brain does that seem flawless to us, as observers of our own mental phenomena, there are in fact flaws. A very large part of our brain is given over to visual processing, and so our virtualisations of the visual aspects of this puzzle are quite acceptable to us. But we’re not quite so good with time, which is fairly important to solving the puzzle. We’ve established that the mere fact of doing something whilst waiting for the pot to boil seems to make the pot boil faster. Of course, it doesn’t boil faster, we are merely less aware of the intervening time. If space and time become detached in consideration of a ‘real world’ problem, the chances seem good that we won’t come up with a ‘real world’ answer.
The so-called paradox seems to rely on a dissociation of the elements. We can virtualise all of the elements in our minds, but it’s less easy to maintain an accurate relationship between these constituent elements. Indeed, part of the difficulty with the problem is that the third ‘protagonist’ is never mentioned, merely implied – but it is pivotal to the story – the space in which the race takes place, and the behaviour of time between the start of the race and the point at which Achilles passes the Tortoise; in other words, context. We intuitively know that the race is set in our time and approximate space, but we ignore the attendant properties of local time and space in focusing on Achilles and the Tortoise. Further, it takes as much mental time to contemplate each key point in the race (when Achilles reaches a point that the Tortoise was measured as being at), despite the increasing rapidity with which those points would be generated. Ultimately, as the story purportedly takes place in real world space (and time) the moment the distance between Achilles and the Tortoise is less than one Achilles-sized stride the mental gymnastics of measuring is no longer necessary, unless you want to know exactly when, to the micrometer, Achilles passes the Tortoise, and that’s what mathematics is for.
A more modern paradox of similar type is Thomson’s Lamp. Here the idea is that at the start of the story the lamp is on. After one second it is turned off. After a further one half of a second it is turned back on. After a quarter of a second has elapsed it is turned off. And so on, and so on. After each period of time has elapsed, being half that of the time that elapsed in the previous condition, the lamp is switched to the opposite position. The questions are, then: Is the lamp switch on or off at exactly two minutes? And would this be different if the lamp had started in the ‘off’ position?
As with Achilles and the Tortoise, we can imagine the time halving and halving, and with each halving the lamp switching, but switching itself takes time, so as soon as the time between switches is less than the time taken to switch, the question becomes redundant. This is true, even if the switching is carried out by a superfast computer, we just end up dealing with smaller increments of time. Some period of time elapses in the act of switching, so once the measured time is less than that time, the question becomes redundant. Further, once our ability to measure the increment of time has been surpassed the commonsense mathematical attitude is to round up to two.
Yes, we can contemplate the foot race or the lamp switching continuing on into some kind of infinity, but we can only do so by shedding some of the elements of the story. The deeper into these paradoxes we go the less the elements that make up Achilles, the Tortoise, and the Racetrack, or the lamp, with its bulb and switching device, are present, and the more they are merely labels divested of their elements. This is not our fault, this is how things that we label as a single thing are made up in our minds; by their constituent elements. These elements may have labels, themselves, but the key point here is that whilst we’re focusing on the label of ‘Achilles’, ‘Tortoise’ or ‘Racetrack’, we’re bad at maintaining all of the embedded elements that those labels imply, so the deeper we go into the paradox the more meaningless the labels ‘Achilles’, ‘Tortoise’ and ‘Racetrack’ become – in much the same way that they will lose meaning if I continue to use the words ‘Achilles’, ‘Tortoise’ and ‘Racetrack’ at the current rate.
So we can manipulate objects and constituent elements in our minds. Indeed this is the very virtualising process that our minds are most useful for, and that which underwrites our success on this planet. At some point, when manipulating virtualised objects with embedded characteristics, we end up manipulating only the labels, or at least not the full complexity of the embedded elements implied by the label, and thus not really the objects that those labels represent.
I would submit that this is exactly how actual physics lead to metaphysics, but it’s also why so many metaphysicians are leaping on to the quantum physics bandwagon – the actual abstraction into the counter-intuitive that is quantum physics, at a certain level of abstraction, does seem like the intuitive abstraction from the ‘real world’ that is metaphysics. Quantum physics starts, to all intents and purposes at the microscopic (sub-atomic) level, with known and established labels for the particles under consideration. Metaphysics starts at the macroscopic and gets to the faux quantum by divesting real world facts of the embedded elements of context and descends into actual absurdity rather than mere counter-intuition.