The ‘mundane’ observation that caused Joseph-Michel Montgolfier (1740 –1810 CE) to invent the hot air balloon was just as accessible to the Romans of ~400 BCE, as were the materials and technologies required to construct human carrying hot air balloons. Certainly, the same motivations were present in both cultures at both times: Joseph Montgolfier was contemplating how to successfully assault the British fortress of Gibraltar, which had proved impregnable to the French by both sea and land, when he noticed how floating embers from a fire he was laying next to were carried aloft and over great distances; giving him the idea of lighter than air flight. The Romans, a military people with similar problems, as well as a love of spectacle and a penchant for technological innovation in war, could just as easily have developed lighter than air manned flight – and yet they did not. There are no Roman frescoes of hot air balloons, whether for war or celebration, drifting over the Empire’s capital.He uses this to springboard into a much larger discussion about technological progress. The post is well worth reading in its entirety. But I disagree with the certainty Mike expresses here. We don't know that the Romans lacked hot air balloons, only that there's no surviving evidence they did. And evidence from that time is sparse at best.
The Antikythera Mechanism which Mike mentions in the post is a good example of just how little we know. As he says:
The Antikythera Mechanism has forced a complete re-evaluation of the technology of the ancient world. The device contained 32 gears, assembled into a mechanism that accurately reproduced the motion of the sun and the moon against the background of fixed stars, with a differential drive giving their relative position, and thus the phases of the moon.4 More recently, it has been discovered that device also integrates eclipse prediction with cycles of human institutions, most notably the Olympics!The Antikythera Mechanism was only discovered very recently. Furthermore, it's entirely singular in age and complexity. An entire industry of mathematicians, astronomers, and craftsmen must have existed in order to build such a machine. Of that industry, only one device survives to the present day. If we never found the Antikythera Mechanism then we would be entirely ignorant of the advanced industry that must have existed around 80 BC.
The technology used to produce the Antikythera Mechanism rivals that used in the best 16th century clocks, and the understanding of planetary motions embodied in the workings of the device suggest that some form of the calculus may have been in use by its makers. It is also clear from the complexity and precision of the device that it was not a prototype, but rather represents a well developed, and arguably a mature technology, which must have had other applications.
The Antikythera Mechanism doesn't imply that the Romans had hot air balloons, but it does underscore our inadequate knowledge of ancient technology. And I still think it would be damn cool if the Egyptians had hot air balloons.