Comment: another angle to consider

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another angle to consider

Could it be that God wasn't punishing the builders of the tower for constructing a tower to heaven but that he was punishing them for their arrogance and their own exaltation?

They seemed like brilliant people and if they had one language - I wonder what those people would've accomplished had God allowed them to continue?

In order to break up their union he confounded the languages so that the people could no longer communicate effectively with one another and thus thwarting their own abilities - sort of like dowsing a fire with water.

So with that said - to the OP's question it's not that God is against us going to space - if that were the case there would be some calamity or roadblock that keeps us from leaving the atmosphere of earth.
I believe one cannot factor that logic into the question of the Tower of Babel. There was obviously some other factor as to why God confounded the languages and I believe it was due to their arrogance and NOT because God was/is against man going to space.