Mr E you say ( To the ancients time was not linear, it was circular. And they marked time by observation and not calculation. ) Mr E me does think they used both. As to calculation they certainly had linear counting methods as shown through many clay tablets and Papyrus. We find accounting, commerce, currency, capital and private transactions all through their histories. They calculated extremely well even having calculation tools such as Abacus which enabled them to subtract use multiplications and divisions. we only have to look upon their many architecture structures of magnificence that do look down upon us from millenniums past unto this very today. Their precision of measurements be as precise as ours if not better in some regards. We have only to evaluate the great pyramid of Giza the tallest structure until the coming of the Empire State Building which only succeeded the Great pyramid in the 20th century. So their linear calculations would certainly have been on par when it came to evaluating the heavenly abode. Though you are correct that observation certainly played a big part in how the ancients viewed their world and the universe around them right up to this very day. Observation is as important today as it was back than. But were the ancient ones so wrong in their understanding in evaluating their world as a geocentric one ? What be the final authority when worlds do collide. Is it the ever changing world of science with its many anti biblical stances that continue to grace the hallways of the scientific world at a alarming rate. And who do seem very much hell bent on denying a very special creation and replacing the God entirely out of the picture, be that with some form of bacterial life that hitched a ride upon a meteorite from somewhere in far deepest space from so long ago. All heliocentricity ever seemed to do was replace a very special creation from the centre piece of Gods creation. Which now has been sent to the vast array of furniture and endless boxes coated over with cobwebs of time to the backwoods of some forgotten storage depo. Mr E yes all those things be true the daily week the monthly calendar and yearly cycle of the sun. But all days still do adhere to a 24 duration at least in our world anyway. Mr E It be the time of blowing the horn in Jerusalem. The feast of trumpets a new cycle of time and of life. May the full fruition of the head go well with their start to a new year.