The next post in our series on numbers covers Infinity. Is it a number or just a concept? How can we even start to discuss infinity when we live in a finite universe? What is infinity? And what happens when we break something finite down into arbitrarily small (infinitesimal) parts?
The ancient Greeks were discussing the boundless and infinite even back in 600 BC so the concept has been around for a long time. Zeno famously described some paradoxes that challenged our notion of the finite everyday world by looking at motion as a series of infinitesimally small segments.
Infinity remained a philosophical sideline until Georg Cantor put it on firmer mathematical footing in the 19th century. By the use of some clever conceptual arguments he showed that there are (at least) two types of infinity. Aleph-zero is the infinity of the counting numbers and Beth-zero is the number of points on a line (a much bigger number).
Most of the engineering mathematics of today relies on the fact that we are allowed to break down every problem into an arbitrarily large number (not quite infinity) of arbitrarily small pieces and the result is still valid. We have Isaac Newton and Gottfried Liebniz to thank for some of the pioneering work in this domain.
Some other fascinating ideas about infinity are that it is possible to describe an infinitely long line that surrounds a finite area, and, that the number one can be created from the sum of infinitely many diminishing fractions.
Infinity leads us to consider the possibility of eternity or ever-lasting life. This is an important spiritual concept as human beings are affronted by their earthly mortality and many believe that there must be life after death. Evidence gleaned from the experiences of people who have died and been resuscitated suggests that there is an afterlife where time and space take on new dimensions.
The Hebrew/Greek sacred text supports the possibility of eternal life:
‘God has planted eternity in the hearts of all human beings’ and ‘is not willing that any should perish but that all would turn towards Him/Her’.
In turning towards the Divine One, we receive unconditional love, ever-lasting life and constant companionship. This belief is at the heart of Christian faith.
‘I came that you may have life, and have it abundantly’ are words that Christ spoke two thousand years ago. God’s intention is that all humans would have a quality of life that is satisfying and abundant and eternal. It reminds me to pray ‘Your will be done on earth as it is in heaven’ and to work/give towards helping make this ‘life’ a reality for all people.
So, as Buzz Lightyear would say: ‘To infinity … and beyond!’