[SquarishTriangle (OP)]

In light of the currently flooding situation in Queensland, Australia:

If I were to stand in a given location during biblical times and the land around me began to flood in a circular pattern, what sort of area would the floodwater have to cover before I would be convinced that the entire world had flooded? Assuming I were a fairly reasonable person with good eyesight and an ability to float...

[Mazurka]

I think to be literally of biblical proportions it would need to exceed the 5000m (above sea level) heightof Mount Ararat, upon which Noah's ark came to rest...

From a perception point of view, from sea level, the horizon is about 10 miles or so.

[CliffordK]

You know, stories get passed down from year to year, generation to generation, it is hard to know exactly what happened.  Certainly details can be exaggerated for effect.  I have to doubt that Noah would have actually loaded his boat with any more than his own pets and farm animals.

I doubt that a truly global flood as presented in the 2012 movie (can I say that here?) could occur.  You essentially have to have a conservation of land/water.  So unless the continents suddenly sunk, there would be no way for the oceans to suddenly completely cover the land masses.

However, it is believed at the end of the most recent glacial period, and the beginning of the Holocene Interglacial Period that the sea levels increased by 120 meters or so.  I think the evidence is indicating that it may have been over a period of a few millennia.  However, with such a sea level rise, whole fishing villages would have been flooded, and the coast lines could have receded for miles.

Land bridges might have disappeared....  and if you were stuck in the middle of the land bridge, everything would be gone.  And, it is likely that many islands eventually succumbed to the sea level rise.

Some people have also suggested cataclysmic events such as an earthquake that could cause an island to sink very quickly.

There could also be rapid sea level changes if some kind of a natural dam existed, for example the straight of Gibraltar may have been plugged, then suddenly opened to the Atlantic due to tectonic shifts or sea level rises.  It still would take days or weeks for the Mediterranean to fill up.  But, changes could be much more rapid than millennia. 

The floods may not extend to the horizon (a bit of literary license here).  Or, perhaps if the flood was caused by a sudden filling of the Mediterranean basin, it might cause a circular current that would take a person away from the familiar shore lines.

Even a tidal wave (tsunami) can flood for several hours...  and leave complete destruction in its wake.  That could certainly be seen as an act by the gods.  And, again, if you were in a boat, the currents would tend to drag a person out to open sea.  And without proper compasses and sextants, navigation in the open sea can be particularly perilous.