Is possible knowledge infinite, and does it grow exponentially?

[ItWillNeverWork]

If a new idea is conceived of as a combination of already-existing ideas that produces novelty, and these new ideas can in turn be combined with both each other and the older ones, then every new discovery opens up the way for yet further discoveries. But does this process of idea formation ever stop, or does it go on forever with knowledge increasing at an exponential rate?

If only I knew the answer.

 

[Firky]

Are you saying knowledge has a mobius loop effect?

I think ideas and knowledge are t wo separate things but I am not quite sure how to go about explaining what I mean.

 

[ItWillNeverWork]

Are you saying knowledge has a mobius loop effect?

I think ideas and knowledge are to separate things but I am not quite sure how to go about explaining what I mean.

Well if it is of any comfort, I don't know what you mean either. I had to Google mobius loop and it doesn't seem to link into what I'm thinking about. What I'm trying to get at is the way in which it is possible to combine two separate ideas to create a completely new one, and how many combinations it is possible to perform. For example, say there are 2 ideas that exist in the world. You can combine idea1 + idea2 to make idea3; you can combine idea1 + idea3 to make idea4; idea2 + idea3 = idea5; idea3 + idea4 = idea6; etc etc. Every time a new idea is created, there is an increase in the number of possible further ideas, and so knowledge grows exponentially.

The only problem I can see with this is that it is talking about knowledge in the abstract rather than a knowledge of something. There are a finite number of objective 'things' out there in reality, and so our ideas are obviously limited by the the number of things that we can have ideas about.

 

[goldenecitrone]

The only problem I can see with this is that it is talking about knowledge in the abstract rather than a knowledge of something. There are a finite number of objective 'things' out there in reality, and so our ideas are obviously limited by the the number of things that we can have ideas about.

Ideas are infinite. For example, have you ever considered the bowler hat with sleeves?

 

[EastEnder]

Infinite in possibility, finite in extent. Knowledge requires a physical substrate for its persistence. Assuming the universe is finite, at least with respect to a single instant in time, then its knowledge carrying capacity is also finite. The range of possibilities may be infinite, but only a finite subset can be manifest at any single instant. That set can change constantly over time, but at any given temporal snapshot, the ultimate limit of knowledge is the ultimate limit of the information carrying capacity of the accessible universe.

 

[ItWillNeverWork]

Ideas are infinite. For example, have you ever considered the bowler hat with sleeves?

Haha, that's brilliant. I want one. It still doesn't prove that ideas are infinite though, just that some ideas are obscure, useless, or as yet unknown to us.

 

[ItWillNeverWork]

Infinite in possibility, finite in extent. Knowledge requires a physical substrate for its persistence. Assuming the universe is finite, at least with respect to a single instant in time, then its knowledge carrying capacity is also finite. The range of possibilities may be infinite, but only a finite subset can be manifest at any single instant. That set can change constantly over time, but at any given temporal snapshot, the ultimate limit of knowledge is the ultimate limit of the information carrying capacity of the accessible universe.

How would someone compute this carrying capacity? What in practical terms does that mean?

 

[littlebabyjesus]

The number of expressions language is capable of is infinite.

This is due to its recursive nature:

I kicked the dog, which was dribbling saliva, which is a sticky liquid produced by the mouth, which is a part of the body used for eating, which is a process by which animals take in food, which is...

There is no limit to this series of embedded clauses - every time you say something, you can qualify the elements within the statement to say more about them. For you to have run out of things to say would require you to have said everything there is to say about everything in the universe and its relationship to everything else. It is a function that doesn't stop. And given that the statement itself has to be formulated from within the universe, by the time you've reached the end of saying everything there was to say about the universe at the point where you started saying it, time has moved on in such a way that there is a whole load more to say.

Perfect knowledge of the universe cannot exist within the universe - so, as far as we can tell, we can never identify bounds to potential knowledge. We may describe this situation as 'infinite', but the problem with the concept of infinity is that it isn't fully defined.

 

[EastEnder]

How would someone compute this carrying capacity? What in practical terms does that mean?

It's all a question of states, or at least, measurable states. Consider the totality of every measurable element in existence - the spin of each electron, the polarisation of every photon, the frequency of every electromagnetic wave, and so on. Ostensibly quantum uncertainty suggests infinitely more states, however if one assumes knowledge to be that which is measurable (hence, knowable), then quantum states must collapse into classical states in order to be considered as definitive. They can of course form a part of infinite knowledge - in the sense that quantum states collectively can represent infinite states, but as soon as you measure them - in order to know them - their multiplicity vanishes. Clever physics bods have in fact calculated the total information carrying capacity of the universe - estimated, of course - and iirc, the answer is "shitloads". Interestingly, they consider knowledge in the same vein as energy - it cannot be created or destroyed, merely transformed from one state to another. In practical terms, much of it will be forever beyond our ability to discern, but an inability to know something does not preclude the existence of the knowledge. I think, as far as we mere humans are concerned, knowledge may as well be infinite - it would seem improbable that we'd ever manage to exhaust the universe's information carrying capacity, no matter how long our ultimate descendants exist for.

 

[littlebabyjesus]

The ultimate carrying capacity of the universe is universe-sized. Some physicists and mathematicians, such as Roger Penrose, are starting to consider the universe as a quantum computer. I think you can pretty much define it as such. And in that case, you could theoretically create a quantum computer that would calculate everything that the universe does, but that quantum computer would itself need to be exactly the same size as the universe.

 

[goldenecitrone]

How would someone compute this carrying capacity? What in practical terms does that mean?

Have a read.

http://poincare.matf.bg.ac.rs/nastavno/viktor/Channel_Capacity.pdf