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Infinity is one of the most intriguing concepts that has intellectually challenged philosophers throughout history. In its simplest of definitions, it is the largest number possible, however, therein lies the catch. If, theoretically, we were to describe the largest number that exists, we could always add one to achieve a number greater than the so-called largest number. Hence, infinity can be imagined as a continuous moving target that never rests, or an endless iteration that keeps going and growing without an end.
Infinity as a number is gigantic beyond our wildest imaginations. To understand its enormity, we could attempt to benchmark it with a very large number called googol, which is 10 to the power of 100. This number is so big that according to some estimates, if we were to write numbers from 1 to googol in a book, the weight of the book will be greater than the weight of our entire milky way! Fascinating, isn’t it? In this era of big data, this number can be classified as humungous data at scale. Still, googol despite its enormity, is relatively miniscule when compared to infinity.
The sheer magnitude of infinity when combined with the theory of probability leads to startling and mind-boggling possibilities which never fail to marvel scientists and philosophers.
The basics of probability theory are commonly taught through the example of a bucket containing different coloured balls. Consider a bucket with one red ball and 99 blue balls. Now, if we were to randomly draw 100 balls, one at a time with replacement, how many times do we expect to draw a red ball? The answer obviously is one since the odds of drawing a red ball are 1 to 100, although in real life it could vary, but to keep it simple, we’ll consider the statistically likelihood scenario.
However, what would happen if instead of drawing 100 balls, we draw an infinite number of balls one at a time randomly with replacement? How many red balls can we expect to draw? Well, after every 100 drawings we are likely to pick one red ball, but as the drawing of the ball goes on forever, we will end up drawing infinite number of red balls!
This outcome is profound and holds for all scenarios, such as a hypothetical bucket with 1 red ball and googol blue balls.
Therefore, in an infinite number of trials, any event, despite having remotest of odds, will occur infinite number of times. This happens because infinity is so very large compared to any other conceivable number, that eventually even the unlikeliest of possibilities tend to occur repeatedly.
In short, implausible becomes plausible, unlikely become likely, and impossible becomes very much possible in infinity.
Talking about improbable scenarios, an example is to one day run into our own precise genetic copy. The human genome project highlights why the possibility of that happening is very unlikely except in case of born twins. The latest estimates by scientists is that our chromosome consists of 20,000 genes which provides the structure for the unique signature for each one of us. Even if we were to simplistically assume that every gene can take on a binary value with equal likelihood of occurring, the odds of finding another copy of ourselves comes to 1 in 220,000. These odds are miniscule beyond comprehension, just by way of example, the odds for 1 in 230 translates to 1 in a billion!
The power of infinity ensures that there will be infinite instances when the lowest of the low odds will come out in our favour.
Hence, it is unlikely to run into our own genetic copy in our finite lifespan due to negligible odds, however, in an infinite timescale, even the rarest of probabilities occur multiple times. So, in fact, as generations go by till infinity and as new chromosomes are sampled endlessly, our twin (genetic copy) will also exist countless times in the future and has perhaps also occurred multiple times in the past. More interestingly, amongst our countless repeated existences, there will be a repeat of our current life many times over despite it having the unimaginably low probability.
Moving beyond our world, the cosmic theory of inflation describes the exponential growth of the universe which continues to expand. As it spreads, new planets and solar systems are created as the result of this expansion. The probability of an exact replica of our solar system with life and having gone through an evolution exactly as we did is too small to measure. However, considering the infinite timescale, the creation of such a solar system will happen endless times. In other words, we can find our cosmic twins somewhere out there in faraway galaxies, some of them leading the same life as we do now and doing exactly what we are doing at this very minute.
Current day physicist Max Tegmark from the MIT has calculated the distance between us and our nearest cosmic twin. Renowned philosopher, Friedrich Nietzsche, has championed the theory of ‘eternal return’ highlighting our cyclic re-emergence as described, and Albert Camus has compared ‘eternal return’ to the King of Ephyra, Sisyphus, in Greek mythology. Additionally, both Indian and Egyptian cultures speak about rebirth and reincarnation in metaphorical as well as factual terms.
Thinking about the countless number of combinations of worlds that potentially exist in our cosmos, I wonder about a world that is not burdened by its history. As we live our lives, we are reminded of the horrors of history, both past and present. The International Holocaust Remembrance Day serves as a reminder of the worst atrocities committed by people based on religion; The Slavery Remembrance Day commemorates the pain and misery endured by millions under bonded labour; and the Islamic month of Muharram reminds us of the sufferings endured at Karbala. The list is endless, and no culture or society is immune from it.
On starry nights, it is tempting to look to the sky and imagine a world which is at peace with itself and reflects how Martin Luther King described in his ‘I have a dream’ speech. It can feel comforting to visualise our cosmic twin in that environment which is free and just for all. During such moments, I often lose touch of my surroundings as I find myself deeply immersed in that world, thinking about their trials, evolution, and journey towards their current state of nirvana.
The probability of such a society to ever exist, and for my cosmic twin to be a part of it seems improbable. However, infinity has the power to convert improbable to probable and thereby making it viable for such a world to occur.
As I come out of my trance, I feel a sense of optimism. I am confident about our future despite the historical burden we must all bear. Our lives may have a lot of hardships, yet we should never despair even if the odds are heavily stacked up against us. The power of infinity ensures that there will be infinite instances when the lowest of the low odds will come out in our favour. This life could be that very instance when that happens. Therefore, as individuals we should never give up on outcomes with meagre chances, since scaling to infinity ensures that our time to experience miracles will surely come one day.
Vaqar Khamisani is based in London and works as a Global Director of Insights for a leading information-based analytics company.
