A Perfect subject for the Rome-haters, and other people frustrated that they are using latin alphabet, living in states with judicial systems based on roman law, etc.
Putting aside all the annoying "barbaropolis must be destroyed" and other symptoms of inferiority syndrome, if Alexander would invade Italy instead of Persia, hewould face various peoples determined to firght for their freedom instead of an ill-motivated army of minor-asia satraps. Still, i think Rome was not strong enough yet to hold off Alexander in the 330s.
In the 280s, however, Alexander would probably share the fate of Pyrrhus (countrary to what he thought, Alexander was not a god).
And after 200 BC the vastly superior Roman army would cut Alexander's army to pieces, like they did it with every other "hellenistic" army of that time.
If Alexander would attack Italy after Hydaspes and India, the great empire and it's resources would rather turn to his disadvantage...
The soldiers from different corners ofthe empire would have trouble in guessing what would they be fighting for.
And even if he would win, his Italian conquests would be impossible to hold on to for any longer than a few short years - a state based in Babylonia cannot reach further than Asia minor, i think even wiki knows that, hehehe.
Bookmarks