The Existence of God

God and the Parable of Infinity


Ahmed Khan, USA

God’s attributes are eternal.

This is a central tenet of Islam, as explained by God in the Holy Qur‘an when it states:

‘He is the First and the Last, and the Manifest and the Hidden, and He knows all things full well.’ [1]

This helps to understand God: He is a being without limit, and His attributes are the principle methods by which we understand Him.

Granted, infinity in all its grandeur is difficult to grasp; it is an abstract notion to a human’s empirical mind; minds which understand everything in units and limits. It is impossible for these finite minds to encapsulate infinity. Thus, the subject of infinity must be approached while understanding that humans are very limited.

For example, perhaps one can know how far the sun is, but he cannot truly understand the distance of 93 million miles in the same way he understands a meter ruler; that which is small can be understood. This is why our minds try to grasp distances by virtue of small things; a blue whale must be X number of cars long, or the moon is a 3 days journey.

This is the paradigm through which infinity must be examined: we cannot have perfect knowledge of it, but we can understand it better.

The Mathematician’s Attempt

In the pursuit of all the largest calculable numbers, Graham’s Number is known to many. It arose as a solution to a complex mathematical problem. It is a number so massive, it is impossible to even write out how many digits it has.

The first iteration of the calculation of Graham’s Number is more than the number of atoms in the visible universe by a large amount. Furthermore, the calculated size of the number of each iteration thereafter is so much more than the previous iteration – a total of 64[10]. The final number cannot be comparable to anything we know of in our physical universe.

This number is the largest theoretically calculated number known to man. Perhaps we may understand the vastness of infinity a bit better if we understand this number. With this understanding, God in all His infiniteness would be understood a little bit better.

So how do we go about understating the biggest number conceivable? Why, by starting with the smallest distance conceivable, of course. The smallest measurable distance in the universe is called Planck’s volume. This volume is so small, that an atom is many times bigger than Planck’s volume.

Now, if every digit in Graham’s Number was the size of Planck’s volume (quite literally the smallest ‘thing’ ever), it still wouldn’t fit within the entire observable universe.               

Stunning as these values may be, they pale in comparison to the utterly immeasurable vastness of infinity, a fundamental characteristic of God.

Is it fascinating; every number known to man must be infinitely smaller compared to infinity, because all numbers can be measured, but infinity is immeasurable. If we attempt to understand endlessness by contemplating God Himself, this becomes circular in reasoning. 

Thus, the concept of God gives us the perception of endlessness, but we do not necessarily have a way of comprehending this infinitude of God.

Understanding the Vastness of God Through the Holy Qur’an

Allah has given us a path to try to understand Himself and infinity. The Holy Qur‘an uses a parable that can demonstrate the unfathomable magnitude of Graham’s Number, and how that can elucidate the size of God’s infinite status.

It states:

And if all the trees that are in the earth were pens, and the oceans were ink, with seven oceans swelling it thereafter, the words of Allah would not be exhausted.’ [2] 

In its own literary fashion, this parable represents an analogy of Graham’s Number. It illustrates an extremely large number to ponder over: the number of trees in the entire world must be multiplied by the number of pens that can be made from these trees.

This is then multiplied by the amount of water in all of the oceans combined as ink to be used for these pens. Finally, multiplying it by the increase of the size of the oceanic water (represented as ink for the pens) over many orders-of-magnitudes.

The final number in the analogy above shows us a glimmer of the vastness and infiniteness of God, indicated by the words ‘the words of Allah would not be exhausted’.

In a thought experiment, one can actualize the final order-of-magnitude the analogy above is alluding us towards.

A study led by Yale scholars estimated the number of trees on earth to be 3.04 trillion or 3 with 12 zeros. According to the organization TreeHugger, it is estimated that an average-sized tree can produce 170,000 pencils. This equals 516,800,000,000,000,000 pens.

The total amount of oceanic water on earth is 1,260,000,000,000,000,000,000 litres.

A ballpoint pen uses around 0.27 ml of ink, and writes 100 pages. [3] Thus, the amount of pens used per litre is 3703 pens. Each pen writes 100 pages, so that equals 370,300 pages of words. On average, there are 500 words on a page, so one litre can write 185,150,000 words. This, multiplied by the number of litres on earth, comes out to:

233,289,000,000,000,000,000,000,000,000 words written by the world’s oceans. This number is much too big for a mind to comprehend.

The Quranic example then multiplies this by another factor from the words ‘seven oceans swelling it thereafter‘ which alludes to a final gargantuan order-of-magnitude.

The Holy Qur‘an indicates that the word ‘saba’, literally translated as seven here, to be a very large order-of-magnitude, greater than the magnitude of the number with 30 digits above. This is because the linguistic use of the word seven has always alluded to incomprehensible infinity in Quranic prose.

Thus, the Quranic parable corroborates the mathematical fact through the understanding of Graham’s number that nothing can ever come close to God’s infinite status.

Both the Quranic Parable and Graham’s Number state that large numbers like theirs cannot physically be displayed or represented in any way within the physical limitation of this universe.

In other words, this helps us to realize why we cannot physically behold or fathom God either, since his infiniteness is beyond the limitation of this universe as well.     

However, when we calculate Graham’s Number (beyond the scope of this article) we can definitively know the final digit is a 7 in our calculations. This is a strange outcome as well since the Quranic parable uses the word ‘saba’ which literally means 7 as well in Arabic to indicate the ‘seven oceans’.

Thus, the Holy Qur‘an simply states that God’s infinite status is unfathomable by us and it can never be physically portrayed within this limited universe. Similarly, Graham’s number can never be physically portrayed either, but it does give a small picture for us to imagine the vastness of God in our otherwise limited minds.

About the Author: Ahmed Khan is the Outreach Director for the Ahmadiyya Muslim Community in Oshkosh and is also a member of the Muslim Writers Guild of America


[1] The Holy Quran, 57:4

[2] The Holy Quran, 31:28