It's interesting to consider illustrations for the Incarnation. Let me say at the outset that I don't use "mystery" and "paradox" as synonyms. A paradox is a particular kind of relation: an apparent contradiction. I often mention things that are paradoxical at first glance, but consistent if you think about it more deeply.
Although a paradox may be mysterious, a mystery needn't be paradoxical. Something can be mysterious without seeming to be contradictory. I think the Trinity and the Incarnation are mysterious, but not paradoxical.
Unitarians scoff at "mystery". And from their standpoint, that makes sense. For instance, the unitarian gosling of Dale Tuggy is basically a human being with superhero powers. A very anthropomorphic god like Zeus. A god of finite knowledge. A god who exists in time. Naturally there's nothing mysterious about a god like that! It's all too human. A difference of degree rather than kind.
By contrast, the God of Christian theism has a mind of infinite complexity. By the same token, his intentions are nearly infinite, when you consider the number of intended events, and how one event is coordinated with another.
Any God worthy of the name is going to be mysterious. The average adult can understand a math problem that the average child cannot. A math teacher can understand a math problem that the average adult cannot. A math genius can understand a math problem that the average math teacher cannot. Yet even those are finite differences.
Because the Incarnation is unique, there are no direct parallels in human experience. But we can explore analogies. Here's one I thought about recently. Consider a lucid dream. Dreams are the product of the subconscious. When dreaming, the dreamer is normally unaware of the fact that it's a dream. But on rare occasions, the dreamer becomes lucid.
At that point the same person has two different, interrelated, and simultaneous mental states. The dreamer becomes conscious, or self-conscious, of the fact that the setting is just a dream. At the same time, his subconscious is still producing the dreamscape.
Once he becomes lucid, it's possible for him to take charge of the dream. To consciously direct the dream. But lucid dreams are unstable because the dreamer is on the cusp of wakefulness. It's hard for him to both be lucid and remain asleep.
But I'm concentrating on the initial moment of lucidity. The sudden realization that it's a dream. That's one mental state, yet that takes place in tandem with another mental state: the ongoing subliminal production of the dreamscape. Both mental states belong to the same person at the same time. The dreamer becomes the conscious observer of his unconscious imagination. The conscious mind knows far less than the subconscious mind. Conversely, the subconscious mind is unaware of what it knows.
If even a finite human thinker can have two different, interrelated, and simultaneous mental states, what justification is there to rule out dual psychology in the greater case of Christ?