What can we learn from tying a rope around the world?

Dunes at Wells-next-the-Sea, Norfolk

What you have here in the readings is a juxtaposition of pictures concerning our idea of foundations and the foundation of our ideas. Today, for this address to have its greatest impact I'd like you to be aware, not so much of the different pictures themselves but rather upon the act of juxtaposition itself.

So, on the one hand, Jesus said:

Matthew 7:24-27

Jesus said: “Everyone then who hears these words of mine and acts on them will be like a wise man who built his house on rock. The rain fell, the floods came, and the winds blew and beat on that house, but it did not fall, because it had been founded on rock. And everyone who hears these words of mine and does not act on them will be like a foolish man who built his house on sand. The rain fell, and the floods came, and the winds blew and beat against that house, and it fell—and great was its fall!”

And, on the other hand, Archie Ammons said:

“Dunes” by A. R. Ammons 

Taking root in windy sand
    is not an easy
to go about
    finding a place to stay.

A ditchbank or wood's-edge
    has firmer ground.

In a loose world though
    something can be started—
a root touch water,
    a tip break sand—

Mounds from that can rise
    on held mounds,
a gesture of building, keeping,
    a trapping
into shape.

Firm ground is not available ground.
on them will be like a wise man who built his house on


What can we learn from tying a rope around the world?


(Grateful acknowledgments to the Center for Public Philosophy at the University of California, Santa Cruz and AEON magazine for the short film called: “What wrapping a rope around the Earth reveals about the limits of human intuition” upon which this address extensively draws. Do click this link and take a look if you have time. It's a lovely, fun and helpfully provocative piece of work.)


In one of Wittgenstein’s weekly ‘at-homes’ with his Cambridge students on Saturday afternoons from five to seven during term-time during the academic year of 1946-47, he asked his students to imagine they were at the equator standing by a rope lying flat on the ground and which was tied all around the world. For the purposes of this little thought experiment one also needs to imagine that the earth is a perfect sphere and that there are no hills nor water in the way. Now, were we to cut the rope somewhere along its length and sew in an extra yard of rope so it was one yard longer than it was before, when we evenly pull it out around the earth’s surface once again to make a perfect circle, the question is, how far off the ground is the new rope? Is it a mile off the ground; is it a yard off the ground; an inch or hardly anything at all?

Almost all of us when we first hear this question reply, as did Wittgenstein’s students, “hardly anything”. If the rope came off the ground at all nearly all of us think that we wouldn’t even see the space in-between the surface of the earth and the rope. The earth is so big what difference would a yard make across the entire circumference of the earth? Almost nothing.

Well, it turns out that the rope would be almost six inches off the ground, 5.73” inches to be exact. Adding just one yard would create a tripwire all around the entire circumference of the earth. How can that possibly be!? — Most people, on a first hearing this feel that this simply can’t be right!

In his at home, Wittgenstein said that this was “the kind of mistake that occurs in philosophy. It consists in being misled by a picture (Norman Malcolm, Ludwig Wittgenstein: A Memoir, OUP, 1984, p. 46).

In the case of the rope around the earth, the picture we have in mind is that when we spread something small all over something much, much bigger — for example pouring a gallon of water into the ocean — the effect is negligible to us. In the case of the gallon of water in the ocean, the sea would hardly rise and so, in this instance, the picture we have in our mind works.

But, in the case of the rope things are astonishingly different because the picture in our heads just mentioned — that when we spread something small all over something much, much bigger the effect is often negligible — simply doesn’t work.

To realise this we only have to go back to our school maths days and recall the equation C=2πR. The circumference (the distance around the circle) always equals 2π x the radius. Now, with the rope at the equator, we’re adding a yard to the circumference and asking how much the radius increases when we do that. Since a circle’s radius is always exactly 2π, or 6.28 x its radius, then, if you add 1 unit to a circumference, you’ll always be adding 1 over 2π units to the radius. In other words, how much the radius increases remarkably has nothing to do with how big the circle is.

But the picture we have in our head is so strong that for some of us, especially those like me who are somewhat numerical challenged and rather frightened by numbers, even with the proof before us, we continue to feel certain that the rope cannot now be nearly six inches off the ground. No, no, no . . .

OK but so what? None of you will have come to church this morning expecting an elementary maths lesson so what on earth has this to do with church and religion? Well, some kind of answer to this comes in part two of this address.



Everything hinges on the fact that something which seems completely obvious to us can be totally and completely wrong. Not only this but, even when we are offered an irrefutable proof of some description (such as C=2πR) that we can intellectually work our way through, we can still often find ourselves feeling certain that this proof cannot be right. But we are fortunate that, in certain areas of life, we have access to various proofs which can help us see how a picture has been misleading us and this, in turn, can serve to release us from being held captive by that same picture. We now know that although we can safely use the picture “when we spread something small all over something much, much bigger the effect is often negligible” to think about adding water to the ocean we cannot, indeed must not, use it to think about apparently tiny additions to large circumferences.

But, alas, what is true in the example of the rope around the earth is not for the most part true in the realms of religion, philosophy and politics. In these areas of human life, we have found it impossible to access any pithy, knock-down dead proofs of the C=2πR kind.

This means we are all, to greater or lesser extents, living by various unproven (and unprovable) religious, philosophical and political pictures of how the world is (or should be) and our place in it. These pictures are what deliver up to us those things we daily, for the most part, unquestioningly live by and take for granted, those things which seem obviously true to us. In our own European Christian and Enlightenment-derived traditions these obviously true pictures have included (and do still include for some) that an omnipotent, omnipresent, omniscient creator God exists; that good, ultimately, will always win over evil; that the good people will go to heaven and the evil ones will go to hell; that humanity is the apex and epicentre of the created world; that matter is inert and not itself vibrant and affective and so on and so forth.

However, all of the things I have just mentioned — none of which I, personally, take as being true — are incapable of being proved or disproved in the manner of C=2πR. I can cite all kinds of reasons for why I believe as I do but what I cannot do is offer you anything like a knock-down dead proof of the C=2πR kind. Naturally, were you so motivated, neither could you offer up any proofs to the contrary (though you could, of course, provide arguments to the contrary).

Given this, what on earth can we, should we, do in our religion, philosophy and politics? Do we just throw up our hands and say well, since there’s nothing we can prove let’s just allow all people (including ourselves) simply believe what they’d prefer to believe? In this scenario, for example, fascism would as unprovably bad as modern, liberal social-democracy is unprovably better. Whilst I personally remain unconvinced that not everything about modern, liberal social-democracy is wholly good I have absolutely no problem in saying — and fully believing that — fascism is wrong and I am able, I think, plausibly to claim that in forming this opinion I’ve genuinely been very careful about my reasoning and truly honest with myself.

But now here’s the problem: the truth is that were I making mistakes here I probably wouldn’t know about it. Why? Well, think about the rope again. The only thing that convinces people about the rope is the proof from the formula: 1 yard over 2π = 5.73. The intuition to the contrary is so strong that nothing but the proof could get a person to see they were wrong. Indeed, I don’t think I would believe it without the proof. But with many things in life — and this is the crucial point relevant to us in church today — there just aren’t available these kinds of proofs in the fields of religion, philosophy and politics. In these cases, were we ever to be in the grip of a misleading and wholly captivating picture it would be very difficult for us to ever see that we were because no proof or formula would be there to convince us otherwise. If I can be so wrong about the rope might I not be equally as wrong about the wrongness of fascism?

Now, even though I find I can still stand here say that I am certain I’m right about the utter wrongness of fascism and say I’ll go to my grave fighting it, all the foregoing reminds me of two important things:

1) I’m sometimes certain, but wrong and

2) there are many examples where, were this happening to me, it would be unlikely I’d ever realise it.

Given that we cannot turn to equivalents of C=2πR to prove the truth of the rightness or wrongness of so many of the important pictures we consciously or unconsciously live by, the only critical tool we have available to us is constantly to be interrogating our own current pictures of reality by considering, comparing and contrasting with them with other possible pictures of reality that occur to us thanks both to our poetic and mythological endeavours and those we carry out the natural and social sciences. In the realms of religion, philosophy and politics the closest thing we can get to “proof” (although it is not really a proof as is C=2πR) — is in the pudding, and the eating thereof. But we have to be willing to “taste” these other pictures and see what new things they help us see (or taste what we taste).

Let’s begin with a fairly comprehensible if possibly trivial example. Think of how you might set about “proving” to a friend who, for some reason, has got it into their head that Beethoven’s fifth symphony would be immeasurably improved by beginning on the downbeat with four quavers and a minim instead of beginning with a quaver rest followed by three quavers and a minim.

In this instance, you obviously can’t produce out your hat something akin C=2πR. What you have to do is sit down at the piano or sing various alternatives until your friend does or doesn’t say, “Aha, I see what you mean!” Alternatively, it can be imagined and certainly should be left open as a possibility (although it hasn’t happened to me yet) that you suddenly feel your friend is right and so it is you who says “Aha, I see what you mean!”

Of course, not much of global consequence depends on the way we picture the best possible way Beethoven might have begun his Fifth Symphony but a great deal of global consequence does depend upon the religions, philosophical and political pictures we live by.

Now, I’m of the opinion that, on the one hand, the supernaturalist picture and, on the other hand, an overly crude materialist picture of the world which sees matter as simply inert stuff run by wholly deterministic rules, are fundamentally misleading pictures about how the world is and they are holding us problematically captive. In their different but overlapping ways, I think both these pictures are contributing to the deepening of our climate emergency and adding hugely to our general feelings of anxiety, despair and anomie. New pictures (metaphors) really do seem to me urgently to be needed before we can get around to making meaningfully different new (what we believe will prove to be) ameliorating actions and policies.

My strong feeling — which, even though it is based on what I believe to be careful reasoning and being truly honest with myself, I know may be wrong — is that many of current religious, philosophical and political problems would at least be significantly improved by living our lives by different pictures (metaphors). By now you know what my preferred new picture is: it is one which holds that we best understand our world as being founded, not upon some central, static, eternal rock-like foundation (such as the God of Monotheism, the Platonic Forms), but upon eternally moving and indeterministic natural, flows, folds and fields of matter/energy that resemble shifting sand dunes more than they do rock. Regular attenders will know that for me this poetic picture is best found in the poetry of the Roman poet Lucretius, the work of the twentieth-century American poet A. R. Ammons — most pithily in his short poem “Dunes” which you heard at the beginning of the service — and in the work of philosophers such as Spinoza and Nietzsche, and certain modern new materialist philosophers such as Jane Bennett, Thomas Nail and Emanuele Coccia.

This allows me to want to say — quite strongly — I think that, although Jesus famous picture about the efficacy of building a house on the rock rather than the sand remains true (enough) when you are building an actual house, when it comes to how we should be creating religious, philosophical and political foundations suitable for our own age, Jesus picture is seriously misleading and is merely serving to hold us captive to a wrong-headed view of the world because, to quote Ammons, “firm ground is not available ground.” As far as I’m concerned a decent, proper modern religion, philosophy and politics can no longer be something over-confidently and hubristically erected on an eternal, unchanging rock of ages but only humbly, gently and provisionally erecting our dwellings knowingly and carefully on the ever-shifting, transient sand dunes of moving matter/energy.

But the problem is I cannot prove this to you in the fashion of something analogous to C=2πR. The best I can do is something similar to what I’d have to do with a mate who is wedded to a picture of Beethoven’s Fifth Symphony that would have been best begun with four quavers and not three. All I can do is continue to be prepared to compare, contrast, juxtapose different pictures (metaphors) with you perhaps ideally whilst walking along some quickly eroding, sandy, East Anglian coastline until an “Aha!” moment does (or doesn’t) come to you (or to me).

And it seems to me that this is what, at our best, we try to do here each week we meet. We gather to juxtapose and interrogate the (pictures) metaphors by which we have lived, are living and might live to see if we can ascertain, firstly, if and how they might be misleading us and holding us captive in problematic ways and, if that does seem to us to be the case, then to see if we can either improve in subtle ways the pictures we already live by or whether we can, and perhaps should, find a completely new one that seems more appropriate to our present condition. (This is what I’m trying to do in my recent suggestion that perhaps a better way to picture what it is to be a human being most fully and fruitfully alive in this shifting world is by considering carefully the astonishing life of plants).

BUT, in all cases, although we will all always have no choice but to live as best we can with the pictures (beliefs) about the world we do come to hold, as we do this, we’d be wise to remember we should always be a lot less certain about our current beliefs than perhaps we’d like to be because, in the end, and to put it bluntly, we may be wrong a lot more often than we realise.

This is a burden we must honestly take on board and live with.