For a while now the concept of infinity has been bothering me. Not because I have encountered it in my studies and unable to get rid of it, as is sometimes the case with physicist/meta-physicists (c.f. the history of Quantum Electro Dynamics for example). But, rather, specifically because others have, and decided to circumvent the issue. In this first in a series post, I shall try to explore the nature of that which is seldom explored out of fear and uneasiness...
Most people, including scientists, the so called leaders of knowledge of our time, feel uneasy when talking about infinity. I know some of my fellow philosophers who are usually unafraid to delve into deep philosophical rants about anything, are wary of infinity. This leads to a rather interesting effect, wherein infinity becomes more of a legendary creature that no one dare approach or stay with for a long time, lest they loose their sanity. Most believe infinity to be an ugly side effect of our ever increasing mathematical field and thought. And even worse, is the fact that, today unlike before, the leaders of knowledge are the scientists and not the philosophers, which means that the ones who are at the forefront are NOT those who are unafraid of overstepping thier boundaries, or being a little insane in order to try and find out the truth. Science, as we all know, is a rather controlled dogmatic version of philosophy, nothing wrong in that, thats probably why science can get somewhere (computers technology etc) and philosophy cannot, but that might be our undoing, for no scientist in his right mind would try to analyse a concept so crazy as the nature of the non-finite. How can you, science is all about finite mathematics...
Types of Infinity
Of course, as a concept, it was not merely a side effect of certain mathematical calculations, an inevitability to our ever growing thoughts. Originally it was a rather deliberately constructed concept to describe the ultimate reality as an ancient culture saw it. (more on this later).
Regardless a lot of people I fear, misunderstand the concept of infinity. And whenever it is encountered even within math formulaes it is usually ignored (c.f. history of QED). Most of what is said in this and the next posts in this series, is my own personal opinion, formed from studying both physics as well as metaphysics of those cultures who were unafraid to go beyond the framework set by logic and science.
Infinity comes in many varieties, anyone who studied it agrees on that much, from the ancient indians who gave us modern numbering system and 0 and the infinity, to modern mathematicians and number theorists. At least this much is agreed upon, here are what i feel are the basic kinds:
- असंख्य (asankhya): means ennemarable, however असंख्येय [asankhyeya] (another form of the same root word) is actually 10^140, in Buddhist mathematics (Basically an improvement on vedic math). So this can be seen as essentially a very very large number. Not truly infinity of course, but usually what you would encounter when I am talking about infinity in say Optics. An infinite distance in optics is often just a very very long distance in comparison to the size of the lens.
- अनन्त (ananth): the endless, this may be closer to what we think of as infinity, a number that is endless. And could be possibly taken to represent the concept of a mathematical infinity. In mathematics infinity is usually used to denote a unbounded number (i.e. a process that keep on growing).
- अदिति (aditi)/पूर्णम (purnam) : aditi originally means boundless and unbroken, and purnam means "full-(ness)". These two concepts are slightly different from a modern mathematical defenition of infinity, since as far as I know modern mathematics does not strictly define infinity in any way. However depending on you interpretation and field or mathematics, this can be taken as a mathematical infinity. However the thing with this number, that makes it different from all the rest, is that, this number is an "open infinity" i.e. it is boundless both ways. This gives rise to this rather interesting formulae:
पूर्णमद: पूर्णमिदं , पूर्णात् पूर्णमुदाच्याते
पूर्णस्य पूर्णमादाय, पूर्णमेवावशिष्यते
(That is) whole (This is) whole, (From that) whole (this) whole arises/comes out of
when (this) whole is (thusly) taken from (that) whole, (what remains is still) that whole.
- This is basically the following mathematical concept:∞ - ∞ ≠ 0. Where 0, is defined as the number that the result of subtracting any finite number from itself. However (i feel) that the last form of infinity would suffice for this concept of a number or idea that when taken from itself, would still remain as if untouched. The last numeber is better defined, as the buddhists did, by negation rather than an actual defenition, i.e. it is NOT a finite thing, take everything you know and can know, the true infinite is none of those.
There are of course many other kinds of infinities, by the 4th centuary AD the indians had at least 6-9 different kinds/words floating around to describe infinity, in conceptually different ways.
The truly infinite....
The most important one is the last kind, the truly infinite. A rather interesting side effect of being boundless, is that by definition it is boundless, which means that there can be no boundaries or conditions (since conditions set a limit on the conditioned) of any kinds set on this concept. The Vedic sages, called this "unconditioned", in other words, any condition put on the boundless/true infinity would yield it being less than truly infinite (or boundless). Which in turn means that there is nothing greater. The concept of greater come from the lesser being lacking in some way (i.e. it is lacking something in other words is bound in some way). For example, I am bound by my young age, whereas the earth is not. But both are bound by age, i.e. both will at some point perish, the fate of anything finite.
Now the funniest thing about true infinity, comes from the fact that it is unlike any finite number, i.e. it does not, no matter how many times you divide it, yield anything lesser than itself. Infinitesimally diving up the truly infinite will do you absolutely no good in terms of getting you somewhere. The other interesting thing comes up when you consider an object with such a property, of being truly infinite.
A finite object has a finite number of properties, and as such, MUST have a finite number of possibilities and properties. There are only so many ways of thinking about it etc. Being a finite object we are bound by its finitude. One simply cannot have a finite object that is infinitely big, or infinitely good, that is bogus, since then the object would be infinite (not necessarily truly infinite though). Interestingly enough, a truly infinite object, is bound by its infinitude. Since a truly infinite object is necessarily boundless and infinite (by definition), as a whole it must retain such a state, putting conditions of any kind on a truly infinite object will yield in it becoming less than truly infinite (for example a truly infinite object with a beginning is merely endless not truly infinite). Note here that there is "infinite object" and then there is "truly infinite" object. keeping in line with the definitions of the different kinds of infinity above.
What it all means
Why does this matter? Well it doesn't for now. But this is often an overlooked thing about the nature of infinity. For example how can God (assuming he exists) a truly infinite being, be bounded by the nature of good? That would make him less than truly infinite. Akin to Descartes' own argument about the necessity of the existence of an infinite being, a god who is not bound by good is greater (in a way) than one that is, for the latter is smaller at least in that the latter cannot do things that the former can (for example things that are outside the realm of "good"). So while the latter (god that is bound) may be considered to be infinite (using the loose definition of the term, he may be endless and without beginning etc.), he cannot be considered to be truly infinite, since there can by defenition be nothing outside/greater than the truly infinite, since that would imply you found something that bounded the truly infinite, making the thing that is greater greater due to it not having said bound. This becomes even more important when you consider the possibilities of quantum superpositions for an infinite object. More on that on part 3, or possibly part 4.
Next Time
For now I shall leave you with this. Next time: the possible anti-thesis of today's topic....and an even more misunderstood creature...NOTHING.
