Considering measurement: a meme
Let’s take this at a snail’s pace. You are familiar with the liar’s paradox, in which the claim of a statement that it is a lie is either lying and therefore true or else it is true and a lie: in short, an impossible confabulation. Coleridge’s poem ‘Kubla Khan’[1], a pretty piece of exotica that gives the lie, lures us into ‘caverns measureless to man’, depths of unfathomability. I tell you, the imagination knows not where to turn: sheer involution. Easier to grasp is the fact that there are no stepping stones between the individual letters t-o-p and the meaning of the word top. Beyond that, there is no exact top to the word top or the word w-o-r-l-d, it extends as high as you might wish or dream it to go. Pity the poor snail. Or consider Gödel’s Incompleteness Theorems, which hold that a true self-consistent theory is not able to be fully boxed in.[2] As Donald Hoffman states, there are unavoidable assumptions at play in any theory that are necessary and non-interrogable. As there is no top to the word top there are also neither sides nor bottoms that stay put long enough or else refuse to be shifted around. To say you accept something or that it is true is not sufficient. Hence the reference to the snail with which we began—a snail’s pace, or the shapeliness that that movement suggests, implies a wandering that will not always obey the traffic signals. As Hoffman elaborates, measurements in time and space have no operational bearing beyond 10-43secs and 10-33m at the Planck Scale:[3] past the most utter tininess, we’re still in a pickle, a veritable void. You may smirk, but what do you say is the humour quotient in the Planck Scale? Measurement is leaky. If you observe the black swans at Te Wai Ōrea Western Springs, you can see that their long quizzical necks are fluid and indefinable in the very way they are held aloft or allowed to dip in the water or tangle with another swan, black or white. Indeed, even the water welling up from below the surface to form the lake knows not from whence it arises to form it knows not what. Until you become the new thing you don’t know what it entails and when you arrive you no longer know what it was that you were and what brought you here. Float here a moment, with the swans.[4] I’ve come to view the process of shaping (think of ‘Kubla Khan’) as a better measure than either space or time made to perform under our instrumental gaze, my darling. Lurking anticipation, that’s what draws the mind. In the end (if there is one) the one and only thing that science measures is its own measuring. Otherwise any unit of perception is a fabulous decorum rather than a package or the content it holds. There is nothing to weigh up. Life is a squiggly squiggle!
notes
[1] Alliteration carries from the poet’s name to that of the poem’s title: K3. In crucial ways, signification is a weave.
[2] Two Gödel incompleteness statements: ‘In any consistent formal system that can express basic arithmetic, there are true statements that cannot be proven within that system’ and ‘No consistent system can prove its own consistency’.
[3] The resolving wave lengths of light required to make the measurement at that point become too small and the mass of the object being measured increases exponentially until you find yourself in a black hole. Right there: deep meaning!
[4] Have I married the snail to the swan? I’m reminded of Jana Levin’s Klein Bottle: endless inbound material possibility.j