sumit/blogs

I’ve always found it curious that we’re compelled to perceive continuous forward motion in time, but not in space. I know that, absent any external impulse, we’re actually moving along geodesics in four-dimensional spacetime. That means the simple (but easily visualised) picture in which we move continuously along the “t-axis” of spacetime is misleading. But it’s not that easy to visualise what it means to move along curves determined by the topology of local spacetime.

Going skiing a few weeks ago provided me with a halfway-decent metaphor — for probably the first time in the decade since I last seriously studied general relativity. Granted, time doesn’t actually ebb and flow as you slalom and snowplow, but still. It’s the very nature of skiing to follow gravitationally-constrained paths through space and time; and it takes a major external impulse – the skis on the snow, a backside on the floor, or a pylon on the piste – to effect a dramatic change of path.

That’s not something I appreciated the first time I went, for the simple reason that I never got to follow an uninterrupted path for long enough. (I tried and failed to insert a godawful pun about “Minkowskiing” here, so you’ll have to make up your own). This time, not only did I get to geek out on the slopes but, as it turned out, my reading matter included three really interesting articles exploring the illusory nature of the passage of time – from remarkably different angles.

The first article, by Oliver Sacks, in the January 15 issue of the New York Review of Books introduces the idea that the stream of consciousness can slow to a trickle or even freeze altogether:

The normal flow of consciousness, it seemed, could not only be fragmented, broken into small, snapshot-like bits, but could be suspended intermittently, for hours at a time. I found this even more puzzling and uncanny than cinematic vision, for it has been accepted almost axiomatically since the time of William James that consciousness, in its very nature, is ever-changing and ever-flowing; but now my own clinical experience had to cast doubt on even this.

That, suggests Sacks, is empirical evidence that consciousness isn’t a thing, but a process – the melding together of a sequence of blurred, overlapping “snapshots” of reality. Sacks covers a lot of ground in his essay, too much for easy summary here: but one intriguing implication is its clues as to how we might construct, rather than directly perceive, the passage of time.

The second article (dug up for some reason I’ve now forgotten because of this post), from the Dec 2000 issue of Discover, is the hardcore physics analogue of Sacks’ piece: a profile of theoretical physicist Julian Barbour, who believes that time and motion are both illusions. Barbour postulates a kind of variant on the “many-minds” interpretation of quantum mechanics, in which our minds simultaneously gather “snapshots” from many different worlds. Those snapshots — or “Nows”, as Barbour calls them — don’t exist in succession, but simultaneously – the perception of time is constructed somehow by our minds roving over them. Edge has a good interview with Barbour, who’s also interesting because he’s a credible independent physicist — an endangered species whose ecological niche has been almost overrun by crackpots.

The last article, by Stephen Battersby in the 20 Dec issue of New Scientist, was an exploration of the work of Metod Saniga. (Only available to subscribers, alas, but there’s a shorter account available from the Times). Saniga’s a Slovakian astrophysicist who’s sought to understand our perception of time by looking at the experiences of people in altered states: in other words, on drugs. (And some experiencing psychotic and near-death episodes, for good measure). Taking their reports seriously — feelings that time was standing still, or that many events were taking place simultaneously, say — allowed Saniga to construct a startling geometric model of spacetime and how the perceptions of time might change according to the observer’s position in it. It’s arguable that Saniga has actually constructed a model of what happens to your brain on drugs, but it’s a great article nonetheless.

Put together, the three pieces encouraged me to think that maybe the next manifestation of the Copernican principle will be the dismantling of the idea of the passage of time – whether for psychological, physiological or physical reasons. Perhaps motion through spacetime really is an illusion … but it sure didn’t feel like that coming down the piste.

Update: Why does time fly when you’re having fun? Apparently because the brain doesn’t have enough processing capacity to keep track of time and many other tasks simultaneously. There’s apparently also a big overlap between the areas of the brain that estimate time and those that control movement:

[Lead researcher Dr Jennifer Coull] said this overlap suggests that the brain may make sense of time as intervals between movements, in much the same way as a musician marks time with his foot, or an athlete anticipates the sound of a starter’s pistol.

Which sets up a seductive (if specious) correspondence between physical and mental models of time: the relativistic interpretation of time as the interval between events and the mental representation of time as the interval between movements. Time dilation: time flying.

Matt Webb’s inspired light cone project struck a chord, given its resemblance to the space-probe metaphor I posted about a month back. The basic idea: counting off the stars that light from the Earth could have reached since you were born – which is to say, everywhere that you could possibly have affected in your lifetime. Or conversely, the furthest points that could have affected you.

One of the first things that occured to me was that the rate at which stars enter the “lifecone” (see what I did there?) will increase with age, in accordance with the square-cube law. The volume of your personal causality sphere will increase as the cube of your lifetime, and so will the number of stars contained in that sphere (assuming no local voids or clusters). So you’d expect stars to enter at a ever-greater rate as you got older.

That seems to hold reasonably true. It takes just under five years for the first star other than the Sun to enter the lifecone, another five years for the third – but after another ten years, the number jumps to 18. Another ten, and it jumps to 45, then reaches 78 at forty years and 129 at the half-century boundary. The pick-up’s not quite cubic, probably because the underlying dataset includes only stars visible with the naked eye – which is related to distance.

Stars visible with the naked eye amount to less than one in ten of all stars within fifty light-years of Earth. I don’t know if it was a deliberate choice to omit the fainter objects, but it seems a reasonable one, because there’s not much emotional resonance to being told that yet another invisible red dwarf has just passed into your ambit. (They keep discovering new ones, too). It does counts out some old favourites. Barnard’s Star, third-closest to Earth and an early candidate for extra-solar planets, isn’t on the list. Nor is Wolf 359, which might come as a disappointment to Trekkies.

Anyway, the exact relationship with distance turns out to be a non-trivial problem that’s fairly intractable without decent population and brightness statistics for stars. My attempt to generalise it turned into a variation on Olber’s paradox, the old astronomical puzzler that asks “why is the night sky black?” There might be a decent shortcut available (or Googlable), but in my recuperative state I’m not up to the job. In any case, our Sun would only just be visible at fifty light-years’ distance, and as a moderate Main Sequence star it seems a reasonable benchmark.

In which case we’d expect the rate at which stars enter the lightcone to peak somewhere in that neighbourhood, plus or minus a few light-decades. That makes the lifecone seem like quite a good metaphor for our personal experience of the progression of time, illusory though it might be – slow at first, during childhood, then accelerating through adulthood until, in our dotage, discrete events start to blur into a continuum.

Perhaps also a reasonable one for our social networks, which are initially very limited, explode during early adulthood years and then dwindle away again as we approach senescence. (Or on a more compressed scale in media spaces). If we liken stellar luminosity to human celebrity, we get the implication that most of us can’t be seen beyond a relatively small horizon – which helps to illustrate how I can live in a small world only a few causal steps removed from George W Bush, but he still can’t see me. And they say relativity has no relevance to everyday life …

Well, my self-image might be unhealthily confused with that of a spaceship, but at least I’m not as far gone as Richard Hoagland, most famous for his part in elevating the Face on Mars from an astronomical curiosity to a cosmic conspiracy artifact. For the uninitiated, Hoagland makes a slew of contentious claims to have advanced planetary science; many of his suggestions fall well beyond the fringe.

Anyway, Hoagland’s latest hobby-horse (although he didn’t invent it) is the suggestion that Galileo’s suicidal plunge into Jupiter actually ended up in a catastrophic nuclear explosion, based on the basis that:

plutonium = nuclear bomb
Jupiter = hydrogen = nuclear bomb

I paraphrase, but lots of things are very wrong with this idea, as enumerated over on Bad Astronomy. Hoagland admits as much on his site, although he constructs the usual concatenation of obscure what-ifs to build his scenario and blames the usual cover-up for the lack of supporting evidence.

At least he’s not crazy enough to endorse the idea that it’s a deliberate plot to turn Arthur C Clarke’s 2010 into reality. This bandwagon gained momentum with the appearance, a month later, of an unusual dark spot on Jupiter’s face – just like (cough) the one in 2010. Such spots aren’t all that unusual, but try explaining that to the conspiracists. And Clarke suggested that such a monumental task would have to be completed by alien von Neumann machines, to which today’s battered and bruised National Air and Space Administration bears little comparison. Sometimes, fiction really is stranger than fact …