In Human Action, Mises considers a curious hypothetical scenario:
If the memory of all prices of the past were to fade away, the pricing process would become more troublesome, but not impossible as far as the mutual exchange ratios between various commodities are concerned.
It would be harder for the entrepreneurs to adjust production to the demand of the public, but it could be done nonetheless.
It would be necessary for them to assemble anew all the data they need as the basis of their operations.
They would not avoid mistakes which they now evade on account of experience at their disposal. Price fluctuations would be more violent at the beginning, factors of production would be wasted, want-satisfaction would be impaired.
But finally, having paid dearly, people would again have acquired the experience needed for a smooth working of the market process. (337)
Apparently, even a complex market like ours could recover after a wound as grievous as the destruction of the knowledge of all present / immediate past prices.
But can a socialist dictator also solve his many millions of simultaneous equations to determine the "shadow" equilibrium prices of the factors of production if similarly afflicted? I think not; this problem is too hard computationally.
And this is just the first part of the socialist calculation problem. Even if one has a fully solved system, the next task is how to improve it, to re-configure the entirety of the structure of production upon introductions of novelties into the system and inventions of new technologies and methods of production, and to do so every day.
This second problem is, in my view, completely intractable with a complex economy.