[anonytrary]

The space of inventions increases exponentially with every new piece of knowledge, insight, or tool we produce. Are you asserting that this space becomes so sparse that we will no longer have any useful inventions?

If this is the case, why have we seen an explosion in inventions? Is there some critical turning point? When is the critical point? It's a lot of speculation.

As depressed and lonely as I am, I live because I believe the future is worth living for, mainly because there's stuff left to do. If there's nothing left to do, we may as well all die today.

[coldtea]

>The space of inventions increases exponentially with every new piece of knowledge, insight, or tool we produce. Are you asserting that this space becomes so sparse that we will no longer have any useful inventions?

I'm saying that the previous assertion is more religious speaking than valid reasoning.

We can find new knowledge, insight, and/or tool without increasing the "space of inventions", much less exponentially increasing it.

Some fundamental types of new knowledge do increase the space of inventions (e.g. the discovery of fire, or the discovery of electricity, or the discovery of dna, etc), but not all.

>The space of inventions increases exponentially with every new piece of knowledge, insight, or tool we produce. Are you asserting that this space becomes so sparse that we will no longer have any useful inventions?

If we are just living because there's stuff to invent, we might as well, as this means inventions are inherently useless (else what we have already invented would be enough to make life worth). Life should be celebrated (or not) for itself, not because we can create new gizmos and find new natural laws.

[anonytrary]

Suppose you have a list of N things you know, and we define an invention as being any subset of those things. There would be 2^N possible combinations, or the size of the set of all subsets, or the size of the set of all inventions.

That's my toy-definition of an invention. Not very good, but it's a start. Let's take it further and say that each item in the list of knowledge is actually a basis vector, and that an invention is simply a vector in the space spanned by the basis set.

> We can find new knowledge, insight, and/or tool without increasing the "space of inventions", much less exponentially increasing it.

In my model, I will prove this is impossible. The dimension before finding the new vector is N. Suppose we find a new knowledge vector k'. If it is truly new, then it will be orthogonal to the other knowledge vectors, and the new basis will span N+1 dimensions, meaning the "space of inventions" increased. The only way for the dimension to remain the same is if k' could be written as a linear combination of k_i, which would imply that our assumption that k' is new was false.

ENOUGH METAPHYSICS!