It's the ultimate mindbreaker.
There are certain problems that humans can't grasp, let alone transcend: the mystery of awareness (AI), the fourth dimension and all higher dimensions, the phenomenon of existence itself, or even the notion of non-existence.
A similar problem is infinity and the number of possible structures, including all minds.
Mathematically speaking, almost all possible minds should be infinite.
A completely alien state of existence, such a mind would not have awareness as we know it.
Since it's infinite, its self-description would be exactly as large as the mind itself - even if the description is infinitely smaller. It would look down upon a hierarchy of simplifications as complex as itself.
Unable to simplify itself any further, it would not perceive its own limits.
Its thoughts might be the most meaningful true statement about such a mind at any moment; but there would be an unlimited number of such statements.
How are we supposed to think about all possible minds at once?
If an infinite number of minds exist, expanding in size and complexity without limit, there will always be an infinite number of even grander, more advanced minds.
This is the limit problem. Instead of a rational convergence as we go along, all the trends deconverge.
It's an unsolvable paradox: normally when considering infinite systems, things get easier as the system gets bigger. The universe gets smoother at larger scales. At the largest scale, it resembles a gas of galaxies. All the small differences, the details and opposing possibilities, cancel out.
As the energy or speed of an object increases, the required time to complete a task decreases.
Zeno's Arrow has to cover ever more fractional distances, but we know it will inevitably reach its destination.
In normal human experience, exponential phenomena tend to run out fast.
Thinking about infinite minds, the possibilities only expand with the mind size, becoming ever more spectacular and immense, higher and wider, an endless accelerating ascent into the unknown, until the unknown is all there is.
No matter how impressive the possible minds may appear, they're like nothing compared to the next level, which leads to still grander potentialities, and so on forever.
Unable to visualize further, we reach a state of absolute ignorance, a blinding mystery that seems to erase itself.
At least some of this grandeur should 'leak' down to our mundane level, but apparently it doesn't.
To understand any process, we have to at least dimly see how it ends, but how can we do that if the process has never even truly begun?
The totality of truth may transcend logic itself.
Probably the best hard SF novel ever written: Infinite Thunder by Jack Arcalon.
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