My first preference for solving the UFO mystery is via Graham Hancock, who pointed out that the ratio of shamans in primitive (?) societies is the same as the ratio of Americans who claim to have seen UFOs, roughly 1%. That suggests that 1% of people are prone to hallucinations, or are in touch with other dimensions, or spirit beings, or somewhere in-between.
My second preference is that a UFO is a 4D object passing through our 3D world. Imagine living in a 2D world (flatland). All you can see is what occurs on a flat surface, for example one side of a sheet of paper.
Throw a ball hard enough to crash through a sheet of paper, and watch it from the 2D world of the sheet itself. As the ball first enters the sheet, it appears as a single dot. As it passes through, the dot expands to be a circle. Midway through, that circle is at its largest, and then it subsides down to a dot, then back to nothing. It has totally disappeared, and we cannot see where it went.
Similarly, a 4D object passing through our world will magically appear out of nowhere. It will grow in 3 dimensions, then reduce, then be gone without a trace.
UFOs are typically reported to defy the laws of our world. Most interestingly they change direction without slowing down. In the above sphere illustration, flatlanders would see an object change size in a way that is alien to them… UFOs get bigger and smaller, AND change direction. The directional change is how a 4th-dimension movement appears in our world.
If 4th-dimensional beings were studying us, whenever they get too close they could appear as UFOs, just as a finger pointing at an insect floating in water might sometimes break the surface.
Something perhaps telling is the entry points. Do UFOs appear in the sky because most of our visible world is above us? If they came from the north horizon, and left via the south horizon, they wouldn’t change size, but they would appear to grow in size as they approached us, and diminish as they left. But this is normal for us when we watch an aircraft fly by – our brains adjust this for us.
If UFOs entered our 3D world from random directions, then we should see that the vast majority are high above us, and they grow and shrink dramatically. The few that move from horizon to horizon would change shape less. This is perhaps testable by looking at all recorded accounts. The higher they are in the sky, the more they grow and shrink.
Of course they could send us a message if they wanted to. We could send a message to Flatland by passing a set of pipes through their world that appeared to them as something like braille on the horizon. So they could definitely create a 4D object that spelled a message in our 3D sky, if they chose to.
Or they could give us a 4D impossible object in 3D. I know they can, because we can make a 3D impossible object in 2D:
What would it look like? Not a Klein bottle, because that is a 4D possible object:
The impossible object could look like these – but for it to ever exist we will need a really good mathematician in our world, or intelligence in the 4D world (and it is quite likely there isn’t…)