All the puzzles and logical posers presented here have implicitly used a common assumption. This assumption is so basic we seldom even think about it. In fact, you would likely think me odd if I ignored it. The assumption is simply that something either exists or does not exist. When Hamlet says “To be or not to be, that is the question,” no one corrects him to point out he could both be and not be at the same time.
In the macro world around us, that seems like a reasonable starting point for a logical progression. In fact, we might feel that it is critical for any rational thinking. Imagine the shock of scientists when they discovered that this common assumption is only an approximation!
The truth was discovered in studying the world of very small particles. Things are not limited to being or not, they can actually occupy all possible states at the same time. One outcome of this observation is that the common concept of a bit (1 or 0) must be generalized in the microscopic world to a “qubit,” or quantum bit. This peculiar thing is not limited to being in one state or the other, but takes on all probabilities. Note that this is different from saying a qubit can have an analog value between 0 and 1, with a definite value. The point is that the state of a qubit is not either a distinct value or a point on a line.
What does that mean for decision making and problem solving? Not much — at least not much if we stick to macro world puzzles and normal Boolean logic. The probability that you will experience a spooky quantum effect in your normal course of events is much smaller than the probability that you had a hallucination. But it does happen for very small objects and that opens the door to novel computing. After all, digital computers use bits. What if you built a computer based on qubits? For reasons that are too complex to go into here, such a computer (which people are working furiously to design with some success) would be many times faster than normal computers. Some types of problems could be solved extremely quickly with a quantum computer. Breaking security codes is one of those types of problems that would suddenly become easy.
All this leads us to a future discussion on what is a random event, but for now let us update Hamlet: “To be and not to be simultaneously, that is the answer.”