Of course, there is no really good reason to assume the sails in Archimedes’ era were white…
So, to recap:
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It may be possible to aim a large number of mirrors at a single target. Or it may not. This has not yet been demonstrated in a practical system against a moving target using technology that would have been available to the ancients.
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There is little to no historical record of this having in fact been done in the battle between Syracuse and the Romans.
As an aside, can anyone offer a military technology that was successfully deployed once in antiquity, but never again fielded by that same culture or independently developed by another culture? This is not a “gotcha” question - I’m really interested in what technical/sociological characteristics such a system would have.
As a further aside - the ignition, even in the system demonstrated by MIT, would not have been near-instantaneous. To initiate and sustain combustion until the ship’s timbers will continue to burn will take quite a bit of time (this is not kindling, but heavy boards with low surface area to mass ratio); in the MIT demonstration this was on the order of minutes, if I recall correctly.