Is there a constant time search function that works on an infinite set?
Or Let's ask it this way?
Can a human or any entity ever acquire the infinitely large repository of knowledge on this existence?
Or in a more practical question, can an AI ever comprehend the seemingly infinite amount of knowledge a Human has, for at one point to become like a human??
These are some questions I have been pondering upon for a few days now. Obviously the Infinite is very relative in these terms but I definitely don't want a clear answer yet, but I wanted to explore this. I am brainstorming on ways to proceed with this, maybe scientifically if its ever possible.
Lets start with some observation. There is seemingly infinite things to learn about in this reality or all of the existence. The apparatus we use to get information about the world are our sensory input. Be it any sensors natural or artificial there is a maximum bandwidth with which it can capture information. Even if all our senses are 100% active every minute of our life, there is still a doubt whether we can capture the infinite, because again the sensor bandwidth is finite. If we are reading from text, then obviously there is another bottleneck of the amount of concepts you can get per sentence and the time it requires to read and comprehend all that. So, is this ever possible ?
My initial intuitions are,
1. Can we bypass the finite apparatus ? Is there a more direct way to all the repository of knowledge in this existence ? Maybe something like what the Spiritual Gurus say. This concept maybe translated to a constant time search function that can work on an open domain.
2. Another way is to take out Time from the equation, the finite amount of time of our life is one bottleneck that makes our apparatus finite, and its time with which we define a rate. If it takes no time to get information or let's say everything happens simultaneously then we are left with an infinite capability apparatus as well, so we can hypothesise that it can capture the infinite as well.
These are very speculative ideas, but that's how I like it. The process of exploration can start with a definition then constantly updating it to the point that the definition is clear and self-expressive. This is the way spiritually or scientifically. Also the mathematical question I posed is expected to have some past explorations on it. As you might know the idea of Turing Machine and universal computation. People were generally curious of the infinite unknown from time immemorial. I am going to do some research on the ideas of infinite domains now. And at the same time also look at spiritual ideas or whatever it is for a motivation for the answer now.
