Time and Infinity


Zeno the philospher, not Xenu beloved of crazy people

I’ve been reading some good books lately.  At the moment I’m just finishing off an exploration of the nature of infinity as expressed in mathematics, physics and philosophy and written by John D. Barrow, a research professor of mathematical sciences at Cambridge.

john barrow

Professor John Barrow

The understandings of infinity that mathematicians, physicists and philosophers have are often at odds with one another and are certainly at odds with the universe as most of us experience it.

One of the most irritating (for want of a better word) problems is Zeno’s first Paradox.  This by the way is the Greek philosopher Zeno of Elea and not Xenu, despotic ruler of a galactic confederacy some 75 million years ago who exists primarily in the unfathomable minds of Scientologists.

Zeno’s paradoxes concern infinity in the context of motion, the first proposing that you can never walk from A to B because you must first travel half the distance, then a quarter, an eighth, a sixteenth and so forth.  By infinitely subdividing the remaining distance you can argue that the traveller will never complete the journey, becoming trapped in the ever increasing fractionality of his or her journey.

Zeno’s second paradox plays on almost exactly the same idea positing a race between Achilles (an interesting choice given his tendon troubles) and a tortoise where the tortoise has a head start of, say, a thousand yards.

Achilles, being of an athletic disposition, runs ten times as fast as the tortoise.  So by the time Achilles has run a thousand yards the tortoise has covered one hundred.  By the time Achilles has run that hundred yards the tortoise has covered a further ten. By the time Achilles has covered that ten the tortoise has shuffled one.  By infinitely subdividing the outstanding distance in this way Achilles can never overtake the tortoise.

It’s obvious to most of us that the universe doesn’t work in this way.  It’s a philosophical and not a practical problem. Even empiricist philosophers learn to look both ways when they cross the road.

What Zeno fails to do is to treat time as inexorable and a constant in an otherwise constant environment.  Of course time can be relative to the speed of the objects observed and the observer (as Einstein suggested) and time can pass at different speeds for two objects if they’re travelling at radically different speeds where one is accelerating unfeasibly fast.  However neither the speed of Achilles nor the tortoise act here to distoort space and time in a way that impinges on the paradox.  However Zeno’s process of infinite subdivision effectively treats time as malleable, at least for the purposes of the problem. You’re either working faster and faster with your temporal knife to slice time into ever smaller chunks, or you’re slowing down the reel of film (perhaps the better analogy) to such a degree that time all but stops.

So let us argue that you have filmed (using physical film at either a finite or an infinite frame rate) the race between the tortoise and Achilles and that after 1000 frames you halve the speed of the film, after the next 100 you halve the speed yet again and so forth.  By the same token Achilles never overtakes the tortoise.  Yet if you film the race in real time and you let the film roll then Achilles indeed overtakes the tortoise and wins.  As you slow the frames of the film you reach a point at which you all but stop. Yet regardless of whether you’re working with a finite or an infinite series of frames if you look ahead of those frames that are crawling past the heads, further down the film strip, you can still see Achilles racing past the tortoise. You haven’t changed the flow of events, you’ve merely changed the way you interact with them. You have chosen to slow the process of observation/analysis, by degrees, infinitely.

You could equally suggest that by slowing, to an infinitely slow crawl, the movie ‘The Empire Strikes Back’ three quarters of the way through you prevent the final showdown between Luke Skywalker and Darth Vader.  We all know that the force moves inexorably towards that confrontation. Not even Zeno could stop it.

We can theoretically choose to alter our perception of time (because in practice we cannot slow our perception of the passage of time infinitely, only finitely, so we can’t truly experience smaller and smaller divisions of time, we experience time as an unstoppable continuuum) but that doesn’t affect the underlying fundamental.

However perception of time is interesting in itself. My friend Rupert Read, a philosopher at the University of East Anglia, and drawing on Wittgenstein (his field of study) suggests that our perception of time changes as we age and that we measure a period of time, say a year, against the passage of time in our lives as a whole; our eternity.  Thus for a three year old a year is a third of eternity, for a twenty year old it’s a twentieth, for a forty year old a fortieth and for a centenarian it’s a mere hundredth.  It’s a neat explanation of the fact that for most of us time seems to pass faster as we age.

Students of the workings of the human brain confirm this in a different way by suggesting that as we age the brain processes information differently – essentially acting in a similar way to digital compression – it only records new bits of information. It doesn’t re-record the old.

This is why routine kills time.  Travel, and apparently meditation, both over-ride this tendency, the former by presenting us with so much new information that our brains have to work harder to process it and we perceive time as slowing.

However I’m also interested in how our senses affect our experience of time, place and, having read Barrow’s book, the infinite.  Our primary sense is sight so our visual experience of time almost defines our wider experience of it.  Einstein’s theory of relativity gives us the speed of light as a constant and thus a reference point for time, which makes perfect sense if you’re sighted. But what if you’re blind?


Bloodhound, eyes shut…

Moreover suppose that you’re blind and your primary sense is smell – a blind dog for instance.  If you smell someone before they enter a room, while they’re there and well after they’ve left then what is your experience of their being?  It’s certainly different from one’s experience when it’s primarily enjoyed through sight.

In the latter case a creature enters and leaves the room and because the experience of it is through the medium of light then you’re aware of their presence or absence as close to instantaneously as makes no difference to human beings.

If you possess the sense of smell of a bloodhound, which has the most sensitive schnozz known to man (10-100,000,000 times more sensitive than ours) then you experience your environment in a different way. The presence of other beings through scent is both anticipatory and persistent. Events unfold differently. In visual terms it’s as though every encounter takes place within a far horizon so you see people approach and retreat from a great distance.

So does the speed of light as an absolute in any way shape the experience of time of a blind bloodhound?

And how does a blind bloodhound conceive of infinity? Of course we can count through touch and we could arrive at the concept of infinity by extrapolating from what we can touch to what we can’t, but if your primary sense is smell would you think about number in quite the same way? Might you not rather have a concept of multiple aspects of a singular environment given that scents merge in ways that objects tend not to (unless they’re liquid or gaseous of course).

Rather than diverge towards the infinite might not creatures whose perceptions are mainly olofactory converge towards the finite and singular?

This blog isn’t very good at answers, but I can supply all sorts of questions…

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3 Responses to Time and Infinity

  1. Sometimes when I eat a chocolate cake, the taste is still on my tongue quite a bit later. I can say that does prolong the enjoyment for a short while. Something like durian on the other hand….three days later…

  2. Andy Lancaster says:

    I wonder whether Zeno`s thesis was prompted by a journey on the M25 where the road signs suggest one is edging nearer to ones destination but the experience of time screams the opposite?
    I love your final sentence but would personally replace the word blog with the words, Father and Husband.
    On a different note, I would be interested at some point in the future to hear your views on the way Nov 5th is celebrated in Sussex!

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