Infinity is a very fancy word, isn't it? Many corporations use the term as part of their branding strategies. Many scientific paradigms rely on the concept of infinity for their descriptions. It's almost inseparable from art. Yet, what does the very term actually mean? Without bounds? Without limits? Unending? Indeed all these point to it. But for someone trying to understand infinity, I thought it's better to tell him what it is rather than what it isn't it. So let's attempt to explain what it is.
In our bid to explain infinity, probably we'd
be better served by tracing the evolution that our own understanding of the
term undergoes right from the time that we first encounter it. So, when do we
first get introduced to the concept of infinity in our lives? Quite obviously,
it should be in primary school mathematics, isn't it? As we get to know the
natural numbers 1,2,3..., we are told that the series never ends and 'infinity'
represents the never ending sea of bigger numbers that we'd encounter if we
were to count forever. A little later into high school we are told that
anything divided by zero becomes infinite. I have never really fully understood
what dividing by zero means? If at all dividing by zero is going to give you an
entity as a result, be it 'infinity' or whatever, then zero multiplied by that
entity should get you back the original number right? What? Multiplying zero to
get a number? I thought zero is going to stay zero if you multiply it i.e., add
it to itself once, twice,.... a trillion times or yeah, an 'infinite' number of
times.
0 + 0 + 0 + ......... (infinity) should equal
0, isn't it? Before we can assert that, can we ever complete the calculation on
the left side? Indeed the fastest of supercomputers is going to work on finding
the sum on the left side for eternity. So while we know that zero is not going
to get any bigger how many ever times you add itself to it, we are not able to
assert that the statement in the previous paragraph is false since we are not
in a position to complete the calculation on the left hand side of the above
equation. Ah! we are beginning to see the profundity of the eight letter term
that we are discussing. If at all we were to prove that anything divided by
zero can't possibly yield infinity, we'd probably be shaking up the foundations
of mathematics! Little surprise that celebrated men in history like Zeno
craftily used the idea behind the conception to dish out uncanny paradoxes that
are now world famous.
Mathematics indeed does well to introduce us
to infinity with a well defined set of rules around it. But is it really our
first encounter with the concept? We, or at least most of us, actually get a
feel for the idea even before we first set foot in school. As we complete 1 or
2 years from the time we appear in this world as an infant, the idea behind the
eight letter term reaches us when we are told at home about a still bigger
three letter term (oxymorons are expected when we ponder on something like
this). The three letter term is 'God'. Irrespective of the faith that we may
adhere to, what is the typical definition of God that we get to hear when we
are told about Him for the first time by possibly our parents? A super being
who is so powerful that he is capable of doing anything at will...who is
present everywhere and knows everything......who always does what is morally
right and consequently favours people who do the right things.....who is
compassionate in general....who is capable of delivering you out of any kind of
trouble or problem....who punishes the wrong doers and consequently invokes the
fear of being punished if at all we were to tread the path of committing sinful
activities. You are probably beginning to see that the definition borders on
the idea of infinite power. We should consider ourselves fortunate that we are
told about 'God' when we are about 2 or 3 years old. The state of consciousness
is unalloyed at this stage and hence we are able to absorb the idea quite
readily and retain it for the rest of our lifetimes. If we were to grow all the
way upto being 20 years of age without any introduction
to the idea of divinity, we'd probably have a hard time understanding
who 'God' is, if we were told about Him at that age. We'd probably be thinking
about Him in terms of someone who can travel faster than an airplane (or maybe
faster than light if you are scientifically inclined), someone who is more
capable than a Superman or a Spiderman, someone who is bigger and stronger than
the dinosaurs, someone who is capable of composing better tunes than Mozart,
someone who is capable of time travel and consequently can travel between the
past and the future at will. Yet these conceptual ideas get nowhere near the
conception of 'God' that a 2 year old forms when he is first told about God.
Having seen Infinity from the mathematical
and theological perspectives, is there more to it beyond these abstract
conceptions? Is there something more 'real' about infinity? (This certainly
isn't to say God isn't real for I do firmly believe in divinity as that's the
only way the miraculous wonder called Life can be explained.) What I'm trying
to ask is that is it possible to perceive infinity as part of the observable
physical reality around us? That could well turn out to be a search in vain as
just about everything that constitutes the physical reality around us is finite
in nature. Not surprising, since a physical object, by definition, is got to be
finite in nature whether you're considering its dimensions, colour or whatever.
If it's red in colour, it's got to be of a particular shade of red. In fact,
human mind, by its very nature, can have only finite perceptions. It's these
finite objects that help us have a perception of physical reality around us.
That does leave us with a bit of a void.
Having got a feel for the glorious conception of infinity, we do yearn to have
a glimpse of it in the observable world around us. However, that seems to be a
case of hoping against hope indeed. But what about the totality of the physical
reality around us, the Universe? Is it finite or infinite? Since the Universe
too is, by definition, something that physically exists, it's got to be finite
in its extent, by the same argument as above. Now, imagine that you are at the
outer edge of this finite Universe. How does this physical limit exist? As some
solid structure? If so, what exists beyond it? By definition, there can't be
anything beyond it for you are already at the outer edge of the finite
Universe. But such an absolute physical limit is hard to imagine for the mind
does intuitively feel something's got to be there beyond it. Since that
contradicts our initial understanding of a finite Universe, does that mean the
Universe is infinite? The mind, so used to finite conceptions, cannot conceive
of an infinite Universe either. Hmmm, infinity does leave us with a profound
dilemma here.
Infinity thus establishes itself as an awe
inspiring idea by its uncanny manifestations in the various realms of human
thought. At the start of this post, we had set out trying to understand what
infinity is. While we may not have completely succeeded in our mission, we do
seem to have pondered on a profound subject. Infinity can never really be
defined in its entirety for anything that’s defined to be something
automatically becomes finite. At the most, we can have abstract descriptions
that point to it. As elusive as it may be, it's this elusive nature of infinity
that has inspired generations of artists, musicians, scientists, etc. to
constantly raise the bar and seek it in the form of greater expressions in
their endeavors. We may never really get to it but the promise it holds for
constant upliftment does make infinity an eternal source of inspiration for
mankind indeed.
