“Can God make a rock so heavy that even God can’t lift it?” This age-old question has been long debated by philosophers and theologians. For some, it ridicules the idea that God can be “all-powerful” – but for others, it’s a warning to be careful with language.

The Bible clearly presents God as the greatest. I was tempted to say “the greatest being” but philosophers would argue that God is not a “being” because God is the One who gives being to all things which exist. Some texts in the Hebrew Bible (Deuteronomy 4, Psalms 95-97) are torn between recognising the true God as unique or suggesting that each nation has their own god but the God of Israel is the best!

As the Old Testament gives way to the New, so God reveals more about Himself. The greatness of God is that God knows everything (Isaiah 40), including every human thought (I Chronicles 28, Acts 1, I John 3), the fall of every sparrow (Matthew 10), and how many hairs are on your head (Luke 12). Jesus taught (Matthew 19) and the Archangel Gabriel also said to Mary (Luke 1) that nothing is impossible for God. Should we try to measure God, we will find that God is before all things (Colossians 1) and is everlasting (Isaiah 26). Psalm 139 – the inspiration for Dan Schutte’s popular hymn You are Near – affirms that whether we go to the depths of the underworld, the heights of heaven, or the furthest shores, we will still find God – and St Paul affirms that nothing in any of those places, no distance and no drama, can ever separate us from the love of God (Romans 8).

Scientists and mathematicians know we have to take extreme care once we start talking about the “greatest” things. What’s the biggest number you can think of? Add one to it, and you’ve got a bigger number. But perhaps you answered, “infinity”. Very well – what size of infinity?

Mind-boggling though it may sound, there are actually different sizes of infinity. Mathematicians compare infinities by trying to match each item in two infinitely long lists. One famous example is “Hilbert’s Hotel”, named after the German mathematician David Hilbert. In this hotel, the rooms are numbered 1, 2, 3, and so on without end. The hotel is infinitely large, with the “size” of the infinity being all the positive numbers. Every room is occupied by a guest. But what does the management do when a new guest wants a room? They ask each guest to move up one, from room N to room N+1. So the guest in Room 1 moves to Room 2 and now Room 1 is vacant for the new arrival.

Actually, there’s an identical hotel next door, but it has to close and all its infinitely many guests have to be accommodated. This isn’t a problem. Each current guest is asked to move from room N to room 2N. So now all the original guests are in the even-numbered rooms, and there’s an infinite number of odd rooms available for the guests from next door. You could imagine that the closed hotel had rooms numbered -1, -2, all the way down to minus infinity. This shows that the span from “minus infinity” to “plus infinity” is the same size as the span from +1 to infinity.

Some infinities are “larger” than this. A simple demonstration was given by the Russian/German mathematician Georg Cantor. Suppose you write down an infinitely long list of decimal fractions. Each entry in the list is a decimal fraction which itself goes on for ever, like 0.3141592653… and you now have a list of infinitely many of them. Does your list contain every possible decimal fraction? No, said Cantor. You can always create a new fraction that’s not on the list. For its first digit, choose something different from the first digit on the first line. That was 0.3… so let’s start off with 0.4… and for the second digit choose something different from the second digit on the second line in your table. Keep doing this for every digit and the number you eventually create will be different from every other number in the list. Because you can always create a decimal fraction that’s not on your infinitely long list, this proves that the infinite number of decimal fractions is a bigger infinity than the size of the infinitely long list of numbers you can write down.

So if God is going to pit an infinitely powerful force against an infinitely heavy rock, we may have to ask, “Are the infinities the same size?”

Mathematics can conceive of different infinities and compare them. But physics deals with things which actually exist. When infinities start showing up in our physics, it’s a sign that we’ve done something wrong. We pretend that everything in the universe obeys simple rules, but real things follow different rules at different scales. We can think of one billiard ball bouncing off another as a perfect and instantaneous collision, but the reality is that as they come together, the negatively charged electrons on the atoms repel those on the other ball as the two come together. That clean ‘click’ that we hear is actually a gentle ramping up and ramping down of repulsion at a micro-scale far too short for us to hear. It’s not possible for there to be something infinitesimally small (a thing made of atoms can’t be smaller than atoms) – but what limits large things?

Albert Einstein realised one way to avoid infinities was to propose that the Universe is governed by a maximum speed – the speed of light. Only pure energy can travel in our Universe at this speed. Anything which actually has mass must go slower. And trying to accelerate a massive object close to light speed will result in the object getting heavier rather than faster – the extra energy manifests as mass (that’s the meaning of E = mc²).

When we say that God is “great”, might we really mean that God is maximally great the way that light takes the maximum speed – but God is not infinitely great? There is a fundamental difference between us creatures of flesh and God who is pure spirit. We can “approach” God but never “become” God, just as no physical object can ever attain the speed of light.

As a physicist and a mathematician, then, I am well aware that there are multiple interpretations of the idea of the “biggest” or “greatest” of anything. When it comes to the Lord Almighty, I am reminded of the preface of the Hitch-Hiker’s Guide to the Galaxy: “Space is big. You just won’t believe how vastly, hugely, mind-bogglingly big it is.” In the same vein, Scripture declares God to be the One who fills the heavens and the Earth (Jeremiah 23), who stretches from everlasting to everlasting (Psalm 90). As a scientific description this is far from precise, but as poetry, it is majestic. In Psalm 145 we read:

Great is the Lord, and greatly to be praised,
and his greatness is unsearchable…
On the glorious splendour of your majesty,
and on your wondrous works, I will meditate.
They shall speak of the might of your awesome deeds,
and I will declare your greatness.

An all-powerful God is not required to be able to do things which are nonsensical, like create a square circle. Such a God could suspend the laws of physics to work a miracle, but questions about lifting rocks imply that we know what a rock is, and what it means to lift something. If a rock is a physical object, obeying all the usual laws of physics, then Einstein’s relativity tells us what happens when a physical object gets too large. All dense objects, when made too large, will collapse and become black holes, gravitational traps which pull in and crush all nearby matter.

We’ll take granite to be our typical rock. What if God were to make a sphere of granite with a radius greater than about 244 million kilometres? “Lifting” (rather than moving) an object implies it’s resting on the Earth. Or rather, the Earth would be resting on this enormous granite planet, whose diameter could be spanned by more than 38,000 Earths in a row. Such a sphere would be large enough to encompass the Sun and all the planets out to beyond the orbit of Mars. Suffice it to say that since the laws of physics force this miraculous rock to immediately become a black hole, it not only couldn’t be lifted, but this wouldn’t end well for Planet Earth, either. So yes, God could make a rock too heavy to lift. Let’s be grateful that He hasn’t!

Revd Dr Gareth Leyshon is a parish priest in the South Wales Valleys, who read physics at Oxford and completed a doctorate at Cardiff (a study of the structure of distant galaxies) before entering seminary.

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