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This question is adressed to the older versions where farlands like the following image exists. Beta 1.7.3.
My question is not about how big is a Minecraft world, my question is about what can happens if you keep flying through the farlands for a lot of time.
Will the game crash due to the HUGE data values?
Also, does the world size depends about if a computer is 64 or 32 bits?
Per the Minecraft Wiki's entry on Far Lands:
As the player journeys even deeper into the Far Lands, the effects worsen to the point where the game is unplayable. At X/Z ±32,000,000,[5] block physics stop functioning correctly. Lighting doesn't work and the blocks, although they appear to be there, aren't solid. If the player tries to walk on these blocks, he or she will fall into the Void. At excessive X/Z positions, world renderer no longer works, or takes incredibly long times and uses most, if not all CPU usage. It then becomes almost impossible to close Minecraft without a task manager.
So, yes - eventually, if you go far enough into the Far Lands, Minecraft becomes less and less responsive to the point of the only solution being to kill the process.
As for whether a 64-bit processor vs 32-bit changes anything? Doubtful, although the trivia section does include this bit of info:
The highest signed value for 64-bit machines is X/Z ±9,223,372,036,854,775,807. However, despite this being the limit any machine can go, it may not be possible to reach anywhere near this point, since the vast majority of people experience instant client freeze, followed by the client crashing. If teleported there, the screen will display completely black with no sun and oddly glowing clouds.
So while it sounds like it is conceivable to go that far, Minecraft would probably cease responding long before.
