The Parable of the Cube

This is an extract from the book, showing the relevance of mathematics to the argument.

It is a perennial problem with theology that I say one thing and you say another and… what do we do next? The things we say can’t both be true, so what is it to be? Compromise, anathema or despair? Here is a down-to-earth, practical example from mathematics to show how sometimes two eyes can be better than one. It is best done with a friend, but if you are on your own then you only need to use a little imagination.

  • On the table in front of us there is an object.
  • You pick it up and hold it up to the light and you say, ‘It has four sides.’
  • I pick it up in my turn. I hold it up to the light and I say, ‘It has six sides.’

Where do we go from here? How many sides does the object really have? You say four, I say six, so which of us is wrong? Who wins and who loses?

If you leave the maths out of it and think about disagreements in general, you will know the kinds of answers that people give at this point. Some will say we ought to be respectful of diversity and I am being needlessly confrontational in talking about ‘right’ and ‘wrong’ at all. Politicians might encourage us to split the difference and agree that the object has five sides. A broad-minded churchman of a certain kind might tell us that in a very real sense four and six are the same thing.

You and I both listen politely to these answers, but none of them makes sense. We may not agree on everything, but we do definitely agree that four is not six, six is not four, and neither of them equals five. We may have got hold of opposite ends of the stick, but at least we know that it is a stick, and the same stick, and that sticks matter. These easy ways out are not ways out at all: on that, we most definitely agree.

There is another way of dealing with this disagreement without sinking into meaninglessness. It is not a way out, but a way through. It will enlighten us both.

In my initial statement of the story I carefully withheld one vital fact. Here is the story again, with that fact put back in.

  • On the table in front of us there is a cube.
  • Pick up the cube and hold it up to the light with its face towards you. Squint at it with one eye shut, and you will see a square silhouette against the light. That makes it four sides.
  • Now hold the same cube at a different angle, this time with one corner pointing directly towards you. When you squint again, you will see a hexagon: six sides.

We are both right, and we have both won. That is not because we have given in to ‘four equals six’ or ‘they both equal five’ or whatever other nonsense the spectators have been urging on us. We have won not because we both see exactly the same but because our observations, though different, are observations of the same thing. It is a thing that cannot be summed up in one single silhouetted view. A cube, which is a three-dimensional object, makes one shape if you project it one way onto two dimensions and another shape if you project it another way.

Mathematically, this enlightenment has come from discovering that there is a geometry beyond the two dimensions of silhouettes and shadows. The ‘four’ and ‘six’ of our individual experiences are only shadows of the true cubical reality, which is a solid object, not a bare outline. It is a solid object with six faces, eight corners and twelve edges.

The moral of the story is not just mathematical. What it has just told us is this: No eye has ever seen a cube and no eye ever will. That is not a paradox, but the strict and precise truth. The eye cannot see the cube in itself, the cube in its full glory of cubicality. All the eye can see is shadows, not realities.

Given those shadows, our minds can put together what two eyes have seen, to give us knowledge of something the eye alone cannot see. Or, to put it another way, the eye without the brain is as blind as the brain without the eye. Or to put it another way still: we see the world best, in its solidity, in its reality, when the left eye and the right eye see it in different ways.

As with mathematics, so too with theology and with the Creed. If in this book I show you something from a direction that you don’t expect, I am not saying that the direction you are seeing it from is wrong, and I am not claiming for my own point of view anything more than the status of a shadow. All I claim is that my shadow is a truthful one. I am saying that if we can somehow perceive the truth from two directions at once, we have a chance of perceiving it better. ‘Four sides’ and ‘six sides’ are both equally wrong, but they both equally lead us towards the truth.

The sound bites

In the run-up to the publication of The Creed in Slow Motion the Universalis apps and programs gave a brief daily one-minute sound bite – one chapter each day – to whet people’s appetites. Some people liked them so much that they were disappointed when the series ended.

Accordingly, for future reference, here is the whole series to listen to whenever you feel like it.

Publication day!

The Creed in Slow Motion is published today. This blog tells you all about the book.

How to get it

The printed book

UK etc

The Creed in Slow Motion comes out on Thursday 30 June 2022 in the UK, Europe and India.

If you have a local bookshop, support it by ordering the book from them. We need to support our bookshops! If the book isn’t in stock they will have it for you in a day or two.

  • Bookshop.org is a web site which donates a proportion of each purchase to local bookshops.
  • Amazon.co.uk has the book in stock.

To find the book in other countries, search for its ISBN, which is 9781399801546. Many online bookshops list it, especially Scandinavian ones; and so of course do Amazon’s various European sites.

If you are a bookseller and want to order copies of the book, please see the Publishers’ Contacts page.

Americas and Australasia

The publication date is October 2022.

There are some international booksellers who will probably ship to you now (and at least one of them claims not to charge postage). This Google search will find them.

Other parts of the world

Please get in touch and let us know where you are, and we will make suggestions.

The e-book

Unlike the printed book, the e-book is published on the same date all over the world, on Thursday 30 June 2022.

Here are the commonest Amazon links: amazon.co.uk amazon.com amazon.com.au. In the other Amazon sites, searching for their code B09MK56GPT is a good way of finding the book.

In Apple Books, searching for Kochanski Creed will find the book.

The ISBN of the e-book is 9781399801553, and this Google search will find it.

Sample chapters

Read the Introduction and Chapter 1 online.

Hear about the book

A short introduction to the book for potential readers (audio and video).

Booksellers – why you should stock this book! (audio and video).

One-minute sound bites – one per chapter, originally broadcast in the run-up to publication. 

Press and bookseller contacts

Here is the list of contacts at Hodder & Stoughton.

 

The three sciences

In The Creed in Slow Motion I refer to the three great sciences of Mathematics, Physics and Theology. To some people this is such an obvious division that it needs no explaining; but to others it sounds provoking and deeply suspicious. So it is worth taking some time to explain what I mean by it.

What the sciences have in common

A science is a discipline which seeks the truth. It has rules and methods and a community of practitioners. 

As there are different kinds of truth, so there are different kinds of science. The three great sciences are mathematics, physics and theology. Everything else is built on these three. For instance: chemistry comes from the physics of electron clouds, biology from the chemistry of big molecules. Once the truths of any given science are established, they can be applied. So accountancy can be seen as a kind of applied mathematics; engineering a kind of applied physics; religion a kind of applied theology. 

Each science seeks the truth and, having found it, seeks to hold on to it. So the first two ingredients of every science are reason and authority: reason to find and understand truths and authority to preserve them when found, from one generation to the next. There is a constant interplay between reason and authority: we can’t work everything out for ourselves every time, so authority is needed; but nothing is true because authority says so, so authority must always be ready to be prodded and challenged by reason. The dialogue between reason and authority – sometimes a conflict – is part of what gives each science its character; but the existence of such a dialogue is a feature that all sciences share.

The place of faith in science

There is a third ingredient to every science, and that is faith. Faith is not unreason. It is reason transposed into a different key.

Faith steadies a science. It helps us to keep believing the truths the science has reasonably and rationally told us, even at a time when they temporarily feel unbelievable. Faith is also a foundation of the science itself: it lays down the rules of the game and tells us which game we are playing. 

Here is an example. When a chemist in Italy found that a certain manufacturing process did not work properly on Wednesdays, it was by faith that he rejected the obvious conclusion that the “Wednesdayness” of Wednesdays was responsible. He turned instead to other things that might be happening every week at that time, and there he eventually found the cause of the trouble. That days of the week do not matter in the physical sciences, times of day do not matter, the location of the experiment does not matter and neither does the name of the experimenter – these are fundamental articles of physical faith. Everyone believes them; they cannot be proved physically; and yet although they cannot be proved by reason, belief in them is not irrational.

Another example: we all hope that mathematics is a science which will never contradict itself – that it will never happen that some clever person, using the tools of mathematics in a new way, will one day prove that two and two make three. That is a good hope to have: but it is a hope and not a certainty. Nobody will ever be able to prove that mathematics is non-self-contradictory in this sense. It is rational to believe in mathematics but at bottom it is faith, not reason, that keeps us believing in it. 

Theologians have a nice simple way of expressing it. Reason leads you into belief; faith keeps you there even at times when you aren’t certain of your footing.

The place of myth in science

There is one more ingredient the sciences have in common which sounds even more disreputable than faith. It is myth. 

Superior people like to say that myth is nonsense, fantasy, untruth. It is not. It is truth conveyed in a different way. 

The creation myths in Genesis are there to make a particular statement – that the world is contingent, intended, structured and above all very, very good – all without using the words I have just used, because abstract words change their meaning over the centuries. 

Physics has its myths as well: for instance, that an atom is a central nucleus with a lot of electrons orbiting round it. This is as literally untrue as compressing the origins of everything into six twenty-four-hour days. Electrons do not orbit. And yet beyond the falsity of the surface meaning, a valid truth is being taught – a truth which could only be literally expressed by the complex equations of quantum mechanics, which nobody would understand.

The sciences share defects as well as ingredients: perhaps because all sciences are conducted by fallen human beings. The worst of them is prostitution. A fallen science sells its authority to the powers of the world so that they can make use of it. In return its practitioners receive rewards of power and wealth. But the rewards have their price. The integrity of scientific enquiry is challenged on all sides by “what the sponsors want”, and the methods of enquiry native to the science are obscured by the methods of the world: politics, bribery, coercion and the criminal law. Looking at stringism, climatism and racial hygiene shows the process in action. So (looking further back) does looking at the question of the dual nature of Christ, which so quickly tangled itself up with power, influence and ecclesiastical revenues.

The prostitution of any given science is an embarrassment; but looking at the phenomenon across the sciences two consolations appear. First, you are not the only sufferer because other sciences are affected too. Second, despite all the perversity and corruption, somehow the truth does in the end get found and recognised.

The three sciences

I have named three great sciences. Why three? Because the sciences can be categorised according to how they deal with existence. 

Physics studies the existent world. For it, the existence of everything is a given. Existence itself is not a physical attribute the way (say) temperature or density are. There is no such thing as an ontometer to measure it. Physics does not study existence but presupposes it. 

Theology, by contrast, studies existence itself. Does anything exist? Does it (must it?) have a cause? What, if anything, can we say about that cause? How, if at all, can we relate to it? It will be seen that none of these questions presuppose God. “There is no God” is a perfectly valid statement in the language of the science of theology. Valid, yes: but is it as true as the valid mathematical statement “2+2=3”, or as the valid mathematical statement “2+2=4”? That is a theological question, and the methods to be used on it are the methods of theology. 

Meanwhile, mathematics doesn’t care about existence at all. It ignores it. You could say that mathematics is the study of “what would be left if nothing existed”. For if nothing at all existed, six sixes would still make thirty-six. This is, ultimately, the reason for the overwhelming authority of mathematics. It is why everyone believes in it. And yet even mathematics is not self-sufficient. It depends ultimately on truth, and it cannot itself define truth. Like every other science, it must remain dependent on something outside itself. Properly viewed, that is not a failure but a liberation.

I tell you about the book (for booksellers)

Creed_in_Slow_Motion_hb_blue_S“Here is an exciting new book,” the bookseller says. “Where should it go? On the table or on a shelf? Who will be interested? Who will be buying it, and why?”

Here is a quick two-minute talk about The Creed in Slow Motion which gives some answers to these questions. Even if you aren’t a bookseller, you may find it enlightening.

Listen

 

 

Watch on YouTube

“I am a mathematician”

When people wonder what makes me write the way I do, I want to explain it all in four words: “I am a mathematician.”

I want to say this because it explains everything. But it also risks meaning the opposite of what I want it to mean. That is because there are two kinds of mathematician, and they are opposites. 

There are two ways of loving mathematics. One is because it teaches absolute truth and if you remember what you have been taught then you will always be right. The other way is to love maths is because it talks about truth. Truth is truth is truth. No truth is true because mathematics says it is. Mathematics has revealed it and described it: it has not made it true.

This is of course the age-old dichotomy between authority and reason, in slightly different clothes. It works itself out in various ways. If you love authority, you need to memorise what authority tells you. If you love reason, you need remember nothing. You only need to be able to work out truths as and when you need them.

I am the second kind of mathematician. I love reason. When I am told something that is true, I love knowing that it is true for a reason, and I love knowing that if I ever questioned it, I would have a chance of discovering what the reason is, rather than just being told “it is true because somebody says so“.

To examine the Creed with the eyes of a mathematician of the first kind would be strange and a little bit ridiculous. The authority of mathematics is not theological authority and the statements of the Creed are not mathematical theorems. But with the eyes of a mathematician of the second kind, the Creed opens vistas of delight. The Creed is full of truths, and since all truths make sense, these truths must make sense too. 

It is a joy to be able to look forward to seeing what sense they make. The attempt may be successful or it may not be; but it is delightful in itself. Both success and failure are good, because whether one succeeds or whether one fails, one is following the basic principle that the truth of God, like all other truth, makes sense.