Wednesday, January 20, 2010

Anything must be something, except for nothing ...

We all have encountered and enjoyed seemingly mind convoluting statements like:
"This statement is false" or "I am a liar", such statements are basically 'unprovable'.

I have been reading about this while investigating logic and it's roots, mathematics, number theory, Goedel .... Some older posts are related to this.

Recently I decided to write down one such sentence that comes pretty naturally whenever you start thinking about what 'something' is.

Here is the complete sentence:
"Anything (any 'thing') must be 'something', except for nothing, which is of course also 'something', but on a different level of thingness, which goes up and down into itself to infinity."

The sentence flows pretty naturally when you are making it up, you start with:
"Anything must be something"
But then your mind remembers that there is an exception to that so you add:
"Except for nothing"
Again your mind jumps in, it cannot accept the void, this 'nothing' also fits the mind's intuitive notion of 'something', in the end, we just mentioned it, so it must be something, and this is where the fun starts, so you add:
"Nothing is also some kind of 'something'"
But then you fell uncomfortable, now nothing is nothing and something at the same time, but let's simply go on trying to explain how we feel about that:
"But on a different level of thingness"
The mind is trying to say that this nothing on one level (of 'thingness') is 'something', yes, but not on that same level), but now we have two levels, we needed those to resolve the paradox of nothing, but that's a problem, because on that new level we can probably do the same, and we can also think that the lower level is an upper level for some other level which has a 'nothing'. So we add:
"which goes up and down into itself to infinity."

So here we have it, nothing, something, a paradox and infinity all at the same time, plus the inability to make logical sense out of even the simplest everyday construct.

If you have been reading some Set theory, Number theory, Russel, Hilbert, Whitehead, Turing and friends all this would seem all too familiar: nothing could be the more formal 'Empty Set {}' ... and it's a long ride after that. So this is my layman's version of what all these geniuses and many others spent years thinking about, if that makes you interested, I suggest you read the most excellent book: "Godel, Escher, Bach: An Eternal Golden Braid"

I also found it interesting that this multi-level hierarchy of rules that we make up to reflect on a lower system from a higher system (escaping to the meta level as some colleagues would say) is inherent in the way we think, it is even mentioned in a seemingly unrelated game design book "Theory of Fun" and also a recurrent topic in our AI related discussions.

Next I will be investigating in more detailed the 'Completeness' part of this whole topic coming from Goedel's famous "Incompleteness theorem" that seems to be touching the physical limits of our brain and melting them in the core. More specifically completeness relative to what? Logic itself? probably, but, but ....