So let us suppose that, at the end of the thirteenth century, the mechanical clock was unknown and was not subsequently invented. This does not mean that there were no timekeeping devices, or that there were no geared devices of any sort. There were sundials and water clocks (clepsydras), as there had been since ancient times. There were time candles, known at least as far back as the ninth century. There may or may not have been sandglasses. One of the curious things about the history of timekeeping is that mechanical clocks and sandglasses appear in the record at about the same time. For short timings, the sorts of things we might use an egg timer for today, Europeans would recite a given number of Paternosters (Lord's Prayers).
Of these methods, the sandglass and the time candle were the only ones to keep constant time with equal minutes or hours. Both were used more for timing than for telling time, though sandglasses would be used by ships for centuries to time a watch, which normally consisted of eight "glasses" turned every half-hour. Time candles seem to have been rare. They maintained a constant time by the simple expedient of marking them at fixed intervals.
Sundials were incapable of keeping equal hours as they were in fact based on the unequal hours of the sun itself. Clepsydras could be geared to work with an escapement, like a mechanical clock in fact, and so could be made to keep standard hours if desired. The Chinese had in fact created at least one water clock of this sort, but they had not followed up on it. Most water clocks were far simpler, and while they could be made to ring an alarm, like a mechanical clock, they were based on how much water would flow through an opening in a given time, thus moving a float. They were not given to unequal hours in the same way as a sundial, but they were unequal due to temperature fluctuations that affected the flow of water, particularly in winter.
It seems unlikely that equal hours would have caught on, or would have taken much longer to catch on, without the mechanical clock. Conceivably some form of clepsydra, like the one known Chinese example, might have been used for monastic or town clocks, but it would have been awkward in a bell tower and useless in much of northern Europe. Without equal hours, time would have continued to move according to the natural rhythms of the sun and the seasons. Work routines would not have been disrupted in the 1380s and after.
Quite possibly the idea of standardized measurements would have been weakened. I may be mistaken, but standard hours were the first measurement to have been constant over a long period across most of Europe. There were no time zones, so the actual time varied from place to place, according to when noon occurred, but the length of an hour became fixed long before other international measurements.
The sciences would have progressed more slowly, or followed a different path. As the accuracy of mechanical clocks increased, fine timing became vital both to astronomy and experimental science. By the end of the seventeenth century, seconds had become critical and for a few experiments, very accurate clocks that measured one one-thousandth of a minute were in use. If the examples of standardized minutes had not been available, would other kinds of standardized measurements have been postponed as well? Would scientists today still be making mistakes in converting English, French, and German inches, feet, and pounds back and forth?
The implications of not having equal seconds, hours, and minutes do not end there. No digital electronic device, and many analog ones, including televisions, would work. Telecommunications as we know it could not exist. Railway and flight schedules would be a nightmare, as varying lengths of hours at different longitudes and a lack of uniform time zones would mean that timetables would have to be recalculated constantly for a myriad of departure locations and destinations. Of course navigation would be just as hard, for while it is possible to go north or south without knowing the time, all east-west travel (moving from one longitude to another) requires knowing the time as precisely as possible. A few minutes error can be catastrophic, as Sir Cloudesley Shovell and his men discovered when their ships were lost due to the inability of the navigators to correctly calculate the longitude in 1707. They found themselves in the Scilly Isles, rather than off the coast of Brittany, in a storm. Only after chronometers were introduced was this sort of thing avoidable. Sailing ships only travelled at a few miles per hour. Imagine the navigational errors in a jet flying a hundred times as fast.
We would simply not have the modern world in any recognizable form without mechanical clocks. They are one of those central inventions that not only had a direct effect on civilization, but had a tremendous knock-on effect (like a cue-ball sending billiard balls in several directions) as well. I have only scratched the surface of the possibilities here, and barely mentioned the cognitive effects, which might have been even more profound.
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