Eternity is central to our Christian beliefs, and infinity is so important in mathematics that it has gained a symbol of its own. Although most mathematicians since Sir Isaac Newton regard infinity as an essential mathematical concept, it is difficult to find any place for it in the physical universe. Astronomers tell us that our universe is finite and quantum physics tells us that nothing is infinitely small. Even eternal time is a physical absurdity because time is measured by change, and every universe we can imagine is governed by entropy, which eventually results in cold stillness. Infinity or eternity, therefore, appears to have no foothold in reality.
The Bible certainly refers to the infinity of eternal life, although this is very hard to find in the Old Testament, and many Jews in Jesus’ day (including the Sadducees) concluded that there was no afterlife. However, the Pharisees did believe in eternity and tried to convince their rivals of this with the words of Exodus 15:18: ‘[He] will reign for ever and ever’ (ESV). They inserted this phrase into the start of their daily prayers, although they said it in a low voice (perhaps enjoying irritating the Sadducees, who happened to be standing near them!) and still to this day Jews say it more quietly than the rest of their prayers.
New Testament Christians and subsequent church liturgies adopted this phrase and popularised the translation ‘for ever and ever’. I think ‘for ever and ever’ inadequately expresses the original Hebrew, le’olam va’ed. I much prefer Buzz Lightyear’s version: ‘To infinity and beyond!’
MOST PEOPLE WOULD USE THE CONCEPT OF INFINITY TO DESCRIBE THE CREATOR
It might seem that this biblical phrase is a proof of the mathematics of infinity, but we do have to be careful when using the Bible to infer any mathematical or scientific principles. For example, if we calculated the number Pi (circumference divided by diameter) from the measurement of the huge circular brass bowl in Solomon’s Temple called the ‘Sea’, Pi would be three, because according to 1 Kings 7:23 this bowl was 30 cubits round and 10 across. So does that mean mathematicians are wrong when they say that Pi is 3.14? The answer depends on how we regard biblical inspiration and the accuracy of ancient measurements. We shouldn’t dismiss ancient mathematicians too quickly. After all, some of their buildings will still be standing when all of ours have fallen down.
THE PRE-EMINENT ZERO
The number zero is the key to calculations, and to infinity. It was invented by the Sumerians in about 5000 BC, but when Alexander conquered the world it was mostly forgotten. Greek philosophers loved the purity of algebra, and left numbers and calculations to non-scholars. This meant that zero became a secret known only by tradesmen and Islamic scholars.
Although zero was lost to Christendom for a millennium, when Europe eventually rediscovered it, Newton used zero to solve the problem of Zeno’s paradoxes by merging infinitesimally small movements into a single formula. To do this, he created calculus: a new branch of mathematics that describes the complex elliptical movements of the planets with exact precision.
When Newton discovered the mathematics of gravity and planetary motion, he came to a startling conclusion that was almost entirely rejected by his generation: that the universe runs on mathematical equations. It was a weird concept. Why should a system of numbers and other symbols, which humans have invented, describe how God runs creation?
Earlier mathematicians had helped to build things or predicted when an eclipse would happen, but that merely showed that maths approximated to God’s order. Previously, people had believed that angels moved the planets, but Newton’s calculations predicted the workings of the universe so exactly that it was clear they were controlled by mathematically determined forces.
CREATION BY NUMBERS
Newton was a keen Christian who studied the Bible as much as maths, but his work was seen by some to make God redundant by explaining even the beauty of creation. His calculations revealed the reasons for the colours of the rainbow, and now we can explain the hues and shapes of autumn leaves by fractal formulae and use quantum light formulae to describe the shimmering colours of a soap bubble. However, Newton’s conclusions didn’t mean that God was superfluous: he regarded them as proof that God is consistent and perfect in all his dealings with creation, as well as with humans.
The universe is undoubtedly ordered mathematically. It is now normal for mathematicians to predict new particles that physicists will discover, the reactions that chemists will observe or the shape that a tree branch will grow. New abstract mathematical ideas may initially appear to have nothing to do with reality, yet they often help us understand previously puzzling phenomena. For example, chaos theory helps us understand weather systems and imaginary numbers (those based on the square root of minus one) help to calculate currents in electrical circuits.
However, this happy marriage between the sciences and mathematics breaks down in respect to infinity. Since nothing in this universe reflects infinity or eternity, this appears to be a meaningless branch of mathematics.
But could we be looking in the wrong place for the reality revealed by this mathematical concept? After all, most people would use the concept of infinity to describe the creator. Since most other types of mathematics we have invented (or discovered) have eventually revealed different areas of reality that we didn’t understand before, maybe the mathematics of infinity will do likewise. Perhaps, in the end, the mathematics of infinity will lead us into new insights about the eternal reality that the Bible describes: the reality of the God who is all-powerful, all-knowing and with whom we will exist for ever and ever.