The Uncertainty Principle limits our knowledge in physics: We can never know a particle's location and momentum with arbitrary precision, the product of both uncertainties has a lower bound. This is a problem if you want (at least in principle) to calculate a particle's trajectory in the future, to say nothing of the entire universe.
This is not a limitation but an understanding of the universe's physical engine of cause and effect and the role that absolute chaos plays in it. However, we
may eventually learn that it is not chaos but the very realm that a creative intelligence works within to adjust the normally cause and effect naturally 'running' program of the universe whenever it sees fit.
Gödel's Incompleteness Theorems limit our knowledge in Mathematics: Even a rather simple part of Mathematics like Arithmetics can never be completely proven without resorting to "outside knowledge", that is, knowledge outside of Arithmetics. What this means for Mathematics as a whole is not entirely clear.
It sounds like they are basically saying that even the Divine would have to have a limit, in that mathematics is a natural structure of logic as opposed to a system that can even be created or manipulated - it IS and cannot be anything other than what it is without destruction of logical cause and effect based reality. Therefore, if the world IS actually rational, and not just temporarily so as some religions have argued (I'm referring to Aboriginal Dreamtime theory here) then mathematics is a hard fact and all acts of creation and intervention must operate within that structure of pre-existing fact. Eventually scientific observation should be able to confirm or deny this.
Rice's Theorem limits our knowledge in Computer Science: All non-trivial, semantic properties of programs are undecidable. Non-trivial in this case rules out the properties "all programs" and "no programs". [Edit: Semantic properties are properties of meaning, something you infer from what is there.] You cannot construct an algorithm that "knows" a certain property and checks other algorithms for having that property. A special case of this is the Halting Problem, which I mentioned because it's much better known than the general case. Even a simple sounding property like "Is this algorithm a sorting algorithm" cannot be decided automatically. This is a severe limitation of Turing Machines in general, and a reason why some people think the human brain might not be one.
I'll have to research this but I'm not really seeing how it's so impossible on an initial read-through of the concept at least. However, this comes across as relative to our current limits of understanding rather than forming an absolute wall that cannot be overcome or solved.
The Laws of Thermodynamics (especially the first and the second) mean that energy cannot be created out of nothing (so there should be an upper bound to energy available to us) and even the energy we have cannot be transformed into the form we need with 100% efficiency.
A full understanding and capturing of Zero Point Energy, I believe, will pretty much prove this to be just a 'usual' limitation and not a hard law.
Unified Field theory, I'd like to point out, would, if we achieve it, have us very close to, if not completely understanding whether there is a Divine or not and a lot regarding it's nature.
Sadly no people were ever kept from a killing spree because they lacked justification.
I see this the other way around. Nobody has ever been able to commit evil without doing a tremendous amount of mental gymnastics to enable them to bypass the boundaries of control that exist naturally inside their own minds. Justification has always been required, but we're all quite good at manufacturing these justifications when needed and more often than not religion becomes a tool by which we twist it's intent into enabling dark behavior rather than letting us help to create a reason not to. That's kinda the point of Genesis and the fruit of the tree of knowledge of good and evil... that we are MORE likely to commit an act we know we shouldn't, simply because there's a prohibition, whether internal or external, against it. Thus if we are to move forward to learn about right and wrong, we must first understand that as we learn about it, wrong acts will become a natural draw for us to explore. A fairly good message for a beginning to a religious text that will attempt to tell you a perspective on right and wrong don't you think?
One problem is that most religions are quite old, which means their message may have become less compatible with modern life. Which may be one of the reasons for their decline in popularity.
This is exactly a reason that I have a problem with religion on principle. If it is TRUE, and the FAITH it asks of us to commit to it is to be completely rewarded, then should it not ONLY instruct us in a manner that can never be more or less compatible with modern life? Does it not suggest that some modern views of human rights and our developing views on morality in this regard, when conflicting with religion, are either WRONG or the religion is a farce in its absolute entirety? When asked to rely on Faith to believe something, I would think a perfect creator would have known about these emerging conflicts to come and have worked all that out... or perhaps the more likely answer is that a religion is just a system of public control and manipulation thought out by very very intelligent human beings that could never have predicted future scenarios that would erode the ability to maintain that blind faith thanks to paradoxes with emerging social understandings of right and wrong that come not from an ancient text but from a social collective realization of what is and what is not fair. Nothing in the Bible, for example, states that slavery is wrong directly, but we have certainly come to understand that if we are to adhere to the Golden Rule, it's pretty much a glaring violation.
