Collatz Conjecture Parallel to Manic Thought Process

I have been pondering the Collatz Conjecture recently (start with a number, if odd, 3x+1; if even, /2. Is there any starting number that will never reduce to 1?). I have looked into the proofs and pathways on it and it seems that it is the type of puzzle with no solution, because a functionally infinite field of numbers could hypothetically be checked, but as of yet doing so provides no confirmed solution, or proof that it can not be done. I feel like this is similar to the thought process described as manic, because depending on your starting position you can become significantly entrenched in a problem (starting number), driving to its solution without stopping, at the cost of everything else. Eventually, it seems, you will end up back at square one (1: "normalized" position), but you will feel driven to try it again. For most things this means a strong focused push, stronger than those who don't think like you can generally muster, but for some things this will end up unbalancing. 

The keys seem to be knowing when to let this equation push a level deeper in your mind. By our nature, we cannot just drop the problem, but by pushing it to the subconscious we can "get off the train" and the subconscious mind will process it more quickly and with fewer actions taken, actions which could derail our lives if actually carried out. Assuming the problem has a solution, this method, if done consciously and deliberately, should work to allow the options to resolve without any damage, while still operating correctly within the confines of the operator's program (manic= driven to solve a problem here). 

The inverse can also be used, if no direct cause of the issue can be identified. This as of yet seems more difficult, but if you can identify that your subconscious is making you manic, you can focus your efforts on identifying the source, or more likely separating the source from other problems. Once separated, you may find it is a problem worth pursuing consciously, at which point you can drive to its conclusion. You may also find it is too large to handle that way, at which point you "jump off the train" once more, and return the problem in its new clarified state to your subconscious brain. 

I imagine that the more often that you perform these handoffs, the more successful they will become, until eventually being manic becomes the problem solving, focus finding, advantage it is meant to be. There will still be those outliers of course, but hopefully they are few and far between, and represent significant issues that should derail anyone that can see them clearly, rather than molehills acting like mountains to climb. In these cases hopefully you have someone to lean on, who thinks in a different enough way to "complicate" your problem just enough to turn one without a solution into a complex problem with a solution you can live with. In this way, getting stuck in an infinite loop can be avoided, without losing these techniques or everything you had built.

Also, regarding the Collatz Conjecture, and certainly this must be known already, the key would be finding a closed loop that does not involve 1, 2^x, or any numbers already confirmed to lead to 1. If you do that, then the conjecture (all strings end in one) is disproven. While this may seem obvious, if not already done, testing the number field in this way could lead to more efficient searching as a whole, and from a processor perspective could eliminate the need to reach 1 on any given attempt, as soon as any previously flagged failure number is landed on. Additionally if the geometry of this shape within the field of numbers can become known, then it can help direct the picking of the starting numbers. As an example of the "geometry" to do this, working backwards the starting number would need to either be reached by 3x+1 (from a smaller odd number) or /2 (a larger even number). By moving backward each step, both the operation and the odd/even status of the number are known, rather than just the operation as when moving forward. If a closed loop is the goal, then this would be the path to take, quickly eliminating either path to arrive at that singular position in the loop, while testing several related strings at once. You may also find a pattern with this that can be used to prove the conjecture true, because it will give more shape to the infinite solution. It could be that the only possible solution has been proven to be an infinite staircase (approaching infinity), I have not looked into the problem enough to know this or not.