Well lets begin with semantics. "Understanding the Nature of the World" What do you mean by this? I take it as the totality of knowlege about all that is real. By implication, if I know all that is real, then anything that falls outside that knowlege is by definition false. This requires at least 2 things. Perfect knowlege, and perfect reasoning. I maintain that to have perfect knowlege would require knowing the current state of all things. Perfect reasoning then gives the correct answers to whatever question is asked drawing from this aforementioned perfect knowlege. Let's stop here and breathe. Let's go back a bit to Kurt Godel. At the risk of oversimplification, he stated that there are both unknowable truths and falsehoods. The key word is unknowable. Now this says our knowlege is imperfect. If so, then our knowlege of current conditions is incomplete. If that is true, then what we think we know is real and true can be wrong. Now we may have the correct answer to a question on any number of questions, but the TOTALLITY of knowlege eludes us. So we examine, we test, but the "Nature of the world" always has something new to reveal.
If you think my definition is too stringent, or in error, then I suggest you consider this. I remember a bible story about God confounding the language of men at the tower of Babel. Something to the effect of "Let us go down and confound their language else they will be able to do whatever they imagine." Not an exact quote, but quite like it I think. Lets assume for arguments sake that we can do just that, by reason and imagination, we learn all that is knowable. Lets take this and run with it a bit.
Animals.
Yep animals. Mammals in particular. You can train a rat to find food in a maze. After enough trials, it remembers where it's food is. Further if you change the maze a little, it can figure out a path to the food. It drew upon its knowlege and found a path to its lunch. Rats have intelligence. Not much by our standards.
Now take an ape. An ape can also do this trick, but much better. In fact apes can use tools, carry out complex interactions. They can predict future events based on past events. In other words they can REASON. It seems that that ability is limited. Can an ape imagine space flight? If so they are keeping it a great secret. Rats then? I doubt it. So what can a rat or a monkey do? Most likely what it can imagine, however primitively. So is it a fault in ourselves that we cannot teach a rat about Newtons Laws, or a chimp QED? Or is the animal at fault for being uncooperative? No, "fault" is a type mismatch. You cannot apply it here no more than you can ask about the marital status of the number 5. It is the nature of the creatures involved. Any adequate language or symbolism is forever beyond them. Remember an infinite number of monkeys typing forever may produce all the works of Shakespere, but NONE of the monkeys would grasp their meaning, at least not in our context. This leads to-
Axiom- A creature may not understand more than it can understand.
It therefore follows.
An ant can know what an ant can know.
A rat can know what a rat can know
An ape can know what an ape can know.
A human can know what a human can know.
Lets stop a moment. What correlates with what and how much a creature knows? The complexity of its central nervous system. I don't think this is contraversial, so I will proceed.
Rats know more than ants because rats are more complex neurologically
Apes- same as above.
Humans- same as above.
Now is there no evidence to suggest that human brains are inherently the last possible step in complexity.
So.. to go on a hypothetical limb, suppose there were a creature that was as neurologically advanced compared to us as we are to the rat. What would it be typing in its ATOT? Nothing we could comprehend. How long would it take to teach us what it knows? How many times do we have to talk to that dang rat before it gets the principles of internal combustion. So I will call this new creature a Grue.
Grues know more than humans ever can. So they know everything? Hey what about Bleems? Oh I forgot to mention them. They have a nervous system 5 orders of magnitude greater than the Grue.
so
Humans can know what humans can know
Grues can know what Grues can know
Bleems can know what Bleems can know
They all follow the Axiom.
Now this question- What level does a creature have to attain to know more than it can know?
It never happens. Therefore there is always a potential mind that can know more than any given mind. That mind can imagine more, it can reason more and most importantly be AWARE of more than us. We look through a glass, darkly.