UPDATE: An epilogue and a meta-epilogue were added

Is there a state in which a civilization can say "we know everything there is to know"? Is the chain of discoveries and inventions an endless one? Or is there a point where it all stops, and there will be nothing left in the universe that can surprise us?

At first it seems that knowledge has no bounds, because when we invent/discover something, the new information can be combined with older building blocks - thus something new is obtained. The more elements you have, the more ways there are to combine them - so there is clearly no bound.

Here is a simple example, we only have 10 digits: {0, 1, 2 ,3, 4, 5, 6, 7, 8, 9} - but we can write an infinite number of numbers with these 10 digits; i.e. the number of things we can do is infinite, while the number of building blocks is finite.

Follow up:

Currently science evolves in two ways:

1. discovering new elements (smaller particles, new materials, etc. From now on these will be referred to as "atoms" and "rules of the game")
   
2. combining elements and obtaining new technologies, or improving existing ones (let us call this "playing with atoms")
   

I will now make the following assertions:

• #1 is finite, i.e. there is a point we can reach, once there - we know we know all the atoms of the universe (note: by "atom" I mean "something that cannot be further divided", and not "that what molecules are made of")
  
• #2 is infinite, i.e. with all the knowledge about all the primitive elements we can build derived elements, and then new derivatives based on the "first level" derivatives, and so on
  
• a civilization becomes "omnignostic" if
  
  • they're done with #1 (discover all the atoms and all the rules of the game)
    
  • they can correctly predict the outcome of any experiment and simulate it
    

So, primitive knowledge (atoms) is finite, derived knowledge is infinite. However, we can master infinity if we learn all the rules of the game.  

How is this useful?
If I am right:

• If knowledge is finite, therefore it can be mastered.
  
• If it can be mastered, the state of "mastership" can be achieved.
  
• If this state can be achieved, a sufficiently advanced civilization (given enough time to develop) will do it.
  
• Therefore god (if any) is nothing but a very developed civilization (i.e. nothing super-natural, just an entity with enough time on its hands and the will to learn).
  

If I am wrong:

• If knowledge is infinite (i.e. the number of atoms is infinite), it cannot be mastered.
  
• If it cannot be mastered, the state of "mastership" cannot be achieved, thus there cannot be a civilization or entity that can correctly predict the outcome of any experiment (simulation, phenomenon, etc).
  
• Thus the best result we can get is an entity that represents all the knowledge and information of the universe.
  
• The only such entity is a 1:1 map of the universe itself.
  
• This entity has no conscience, because it cannot run a specific simulation or tweak its parameters and then watch the outcome; it's just there (here)
  
• Therefore
  
  • god (if any) has no conscience, no purpose, no drive, no will, etc
    
  • most likely this means there is no god at all (the universe is just a bunch of rocks [some hot, some cold] with space between them, what's so special about that? are we back to worshipping rocks? :-)
    

In either case: god is nothing special

• it is either a state that can be achieved by any sufficiently advanced civilization
  
• or a state of no particular interest to us - "if we didn't exist, there would be no one to care about it", says each civilization out there
  

 

How do you know you know everything, what if you're limited by your sensors' resolution?

It is true that one can only see as far as their eyes (and devices) allow them to. A civilization can continue improving their sensors and methods, up to the point where they cannot come up with anything better. But does the fact that nothing new is discovered mean that there is nothing else to discover?

A civilization has the potential to know everything there is to know, but be unaware of that (since they continue looking because there is no guarantee they know it all). Thus we can have two types of omnignostic civilizations:

1. Aware omnignostic
   
2. Unaware omnignostic
   

Assertion

• god (if any) is an unaware omnignostic, and the purpose is to become an aware omnignostic
  

Hey, at least this way god has a reason to exist ;-)  

Further thoughts, is mathematics discovered or invented?

We can try to tackle the problem of the finitude of knowledge from another angle, using mathematics, by figuring out whether it is invented (invent = "come up with a new concept") or discovered (discover = "find something that was there").

If it is discovered, it means there is a finite number of atoms and rules of the game, therefore one can know all mathematics.
If it is invented, it means the number of atoms and rules of the game is infinite.

Note: one should refine the definitions for 'invent' and 'discover' before engaging into such a debate, because otherwise it is reduced to playing with words.

Epilogue

A highly-advanced future human race finally created a sentient device out of massive resources, linked from across every corner of humanity. They asked it one question to test it: "Is there a god?" The computer replied: "There is... now."

Meta-epilogue

Most people, assume that the computer is asserting its own divinity. But, when asked who god is these same people reply "He is my creator." And to the computer, humans are the creator.

Further reading

• a discussion about mathematics on Slashdot
• a previously posted hint on the finitude of knowledge