death, infinity, and the story we tell ourselves
As much as we tend not to take great delight in acknowledging the fact that physically we are meats wrapped around skeletons on our path to decomposition (and, in many cases, cremation) and amuse ourselves by visualising what that will be like, we are not physiologically wired to appreciate the transient nature of life. It takes great efforts for our reptilian mind to accept and embrace mortality without distantiating the realistic notion of death with imaginary abstractions. As a product of natural evolution akin to all other life forms on Earth, we operate on wetware fine-tuned for survive-and-reproduce. Intelligence is a by-product. And so are our appreciation for arts and our craving for meaning and purposes and cat videos.
Life is short, as Paul Graham would tell you. We have a finite window of time in which we get to interact with this world, and with all these people whose windows of time overlap with ours. And then we are gone. Unless you believe in an afterlife there will presumedly be nothing afterwards. It will be truly a transition into infinity in the sense of an eternal void. Nothing. No muse befriends; no invention, no hope; no notion of time; no notion of the future; no notion of the past. A static equilibrium due to the absence of brain activities. Brain dead. Consciousness ceases.
It is as much as an escape from this world into nothingness as it is the surreal ending that promises nothing for eternity. This by definition renders life intrinsically meaningless in that the end goal of life is none-existent. As humans we often have troubles with this notion of death in one way or another. Perhaps we are too used to continuation. Perhaps we are too used to having goals. Perhaps we are too used to meanings and abstractions. The absence of an afterlife, i.e. a complete and non-negotiable termination, can feel very unsettling even when we try our best to accept and embrace it. After all, we are obsessed with infinity. When the concept of infinity is mixed with nothingness, it has this unpleasant connotation to it (though it can be an enormous relief at times when the notion of nothingness is appreciated like during the experience of intense agony). Either way, the mystery of death is unnerving as much as it is fascinating because it is the actualisation of infinity and nothingness. A termination that continues the discontinuation forever. In this sense, the concept of an afterlife or rebirth reflects the denial of an infinite void but not at the expense of infinity itself. We are indeed really obsessed with infinity.
The same way that functional programmers, i.e. programmers who are secretly mathematicians, know the value of everything but the cost of nothing, our obsession (or meta-obsession) with infinity is the by-product of the very nature of conceptualisation which tends to detach us from physical reality and the cost structure of things in that the concept of a cat encapsulates infinitely many cats but really there can only exist a finite number of cats in this universe, let alone encountered in one’s self-contained existence of finite time (and with a finite amount of efforts and resources; encountering cats is hard work). Indeed, a brief look into the history of mathematical formalisation starting in the 1900s (e.g. Cantor’s work) would give us a sense of how fragile the intuition-based approach to infinity can turn out even for machines that turn coffee into theorems i.e. master mathematicians. The first time we truly catch a glimpse into the flaws unto the concept of infinity is in Gödel’s work (i.e. his proof of the incompleteness theorems), which is really more about the limitation of infinity (as observed in a formal language with the capability to construct infinitely many clauses which as Gödel demonstrated undermines the completeness of its modelling of a none-inconsistent system of infinitely many things) than many believed to be the limitation of formalisation, considering that any useful formalisation of systems in every day life (or to this world) are designed and constructed to be constrained in a finite manner to ever run into anything remotely resembling the incompleteness depicted in the theorems in the same way that the halting problem doesn’t stop compiler to check for infinite loops in programs, and any valuable formalisation of mathematical concepts and amusement with regard to infinity or any infinite system (such as the incompleteness proof itself) can always be appreciated in a finite amount of time requiring a finite amount of mental resources, or they will not be wholeheartedly appreciated.
That leaves the abc conjecture somewhat still an open question even assuming no errors in Shinichi Mochizuki’s theory presuming the structural complexity and mind-numbingly elegance of his work will take most of us more than a finite amount of time to appreciate the same way that some classes of Turing machines simply don’t halt on a certain input string.
Indeed. Infinity has always been a human construct. As we study and learn about the physical realm we grow a little bit more appreciation for the impossibilism in the physical actualisation of infinity. There can exist not infinitely many things for the number of atoms in this universe at any moment in time is finite. We can’t go infinitesimally small the way Zeno’s paradoxes play out because we are confined within the Planck constant. In this world no transfer of information of any possible mean is able to exceed 299792458m/s. (In this case, looking into the instantaneous collapse of entangled particle superimposition at a distance under measurement should perhaps be interpreted as poking into a very fundamental property about this world than the studying of a correlation which in physics often implies an interaction in some way, or a spooky action at a distant as Einstein would put it.) Either way the physical reality is itself finitely bounded. But this finiteness is derived from the scrutinisation of reality under a framework developed from the notion of quantifying measurements and each measurement corresponds nicely to a finite numerical value which under any sensible operations will only give rise to more finite numerical values, and in this way the reality we talk about is physical, and in this way the results from studying the physical reality is useful in terms of the applications to construct/maintain physical systems, especially as technology advances and higher precision in measurements can be obtained with a lower cost, and tremendously more pragmatic as compared to the once popular disciplines of alchemy which emphasise a great deal on the quality notions in things in this world, that which can’t be measured but felt (i.e. qualitification, as different from quantification in what would be annotated as sciences today).
This pragmatism deserts the notion of infinity. Anything infinity-related can never be experimentally verified by the own axiomatisation of the scientific methods (though may be theoretically inferred e.g. in String theory). There is a nice correspondence in real life too in that anything pragmatic is ultimately considered within the framework of finite resource allocation and the more finite (or limited) we consider of the pool of resources the less work we would expect to be done (e.g. less things in the sprint backlog for the first week please) and the closer we get to how things will actually end up, realistically, and the better the project management becomes, while anything spiralling unto romanticism or approaching infinity in one way or another is often none-accomplishable and will (though not always the case) lead to unfavorable consequences e.g. falling deeply in love with someone and end up broken-hearted because reality is a lot harsher than your idealism the same way that physical systems are coarse under high resolution while our mental representation of things always encode approximations of them akin to viewing a regular polygon with efficiently large number of vertices as a circle (since a circle is pretty much a regular polygon as the limit of the number of its vertices approaches infinity).
In this sense, conceptually (or meta-conceptually) we are always performing infinity-based (and highly category-theoretic, and amidst fuzziness) operations with the characteristic of lossy compression, and, instead of giving rise to more entropies, successfully performed operations give rise to more rounded generalisation/categorisation, often in a granular manner, capturing what we deemed as the essence of things but in a low resolution i.e. a simpler but the same time more encapsulating representation of the senses, feelings, emotions, concepts, etc (as we upscale the abstraction layers meta-conceptually), attesting to the limitation in the brain’s physical ability to encode a significantly large amount of details the same way it attests to the structural wondrousness and elegance that arose from this very limitation/finiteness that entails infinities and beyond. Such is the combinatorial beauty of the brain.
And it is indeed precisely things with the very infinite-ish attributes or connotations that we value the most in life. And these are often the things from which meanings and purposes can be derived and felt e.g. spiritual experiences, love, mystical states of consciousness, human connections in a deep and profound level, religions, the notion of leaving a legacy or making the world a better place, the profoundness of the cosmos, synchronicity, the beauties in mathematics, believing in The Book, etc. We are indeed truly obsessed with infinity. Infinity makes us feel great. Or perhaps feeling great is infinity. When you feel really great and you feel like you have seldom been this level of great before, this level of great is perceptively infinite in the same way that when you have a number line marked with 0 and 1 at both ends and you will ever only go into values on this line and there is no way to instantaneously jump from one value to another once a value has been selected (as constrained by continuity or to sustain the topology of the space), 1 takes the place of infinity. Conceptually you can go into 0 or 1. But practically you can’t. And perceptively you do from times to times i.e. the furthest point you have gone and of which you know not of going beyond will feel like it is the furthest point (i.e. 1), especially in a system environment where significance of existed things decay as memories get corrupted and dilute themselves through the passage of time. This is why practising mindfulness is great. In every deep and profound appreciation of the present presents itself the feeling of getting closer to both 0 and 1.
After all, this very immediate conscious experience of reality is akin to a recursive function call, perhaps in continuation-passing style . We are all voids stuck in an infinite loop of continuations, for the lack of a better word, corresponding to the state of a biochemical entity that is physically finite which, under computation, constitutes the notion of a self in a little made-believed world that reflects the stories we tell ourselves as we age and deteriorate, and encountered and remembered things in the past from which reality and this mathematically consistent world can be inferred. But the past doesn’t exist the same way perfect circles don’t. Neither does reality nor this mathematically consistent world inferred. All there is is this recursive function call and we are the infinite voids within.