What does it mean to take Jung seriously when he says that we "continue to dream in the unconscious while awake?"
Two principles, one ancient oriental, the other modern and at least quasi western may help situate this question
Vedantic axiom: The world we (perceive ourselves to) live in is Maya
(Old fashioned inadequate translation of Maya is illusion. Nowadays we can say Matrix or Simulation)
What they (humans!) call consciousness is just a fictitious thing. When they finally discovered their real consciousness they called it "subconsciousness"
Paraphrased and simplified from Gurdjieff's Beelzebubs Tales
To operationalize this into a meaningful life-process another Jung statement that may help:
He who looks outward dreams. He who looks inward awakens.
In simple terms : a program to conclusively answer yes/no may be impossible to construct. But a program to answer yes when true and hang (crash) for no may be possible.
Applied to "Is this world a dream?"
If I awaken I know it is (was) true.
If not I can (at most) keep asking
Testimony of Sages
When you think that everything is someone else's fault you will suffer a lot. When you realize that everything springs only from yourself you will know peace and happiness.
There is only one mistake you are making: you take the inner for the outer and the outer for the inner. What is in you, you take to be outside you and what is outside, you take to be in you. The mind and feelings are external, but you take them to be intimate. You believe the world to be objective, while it is entirely a projection of your psyche. That is the basic confusion and no new explosion will set it right! You have to think yourself out of it. There is no other way.
Q: How are we to treat others?
Ramana Maharshi: There are no others.