Columbus did not have an accurate calendar either but he crossed the Atlantic successfully several times. The Manilla Galleons of the 16th Century didn't have calendars either but they knew that land lay to the East of them. So they would bear due East. Yes, their landfall was often unpredictable and they often made land in Oregon or even British Columbia. They could tell by the flora that Mexico lay South of them so they would hug the coast southward. Magellan and Drake circumnavigated the Globe. When they returned home, their dates were askew but they still made it.
I once viewed a show on Micronesian navigation. Since they used small boats and all the islands were tiny, it was vital that they hit the island they were going to, dead on. The old time navigators were able to do this by learning the signatures of the currents. The navigators claimed they could sense how the current was being affected by the nearness to land and that every part of the ocean had different signatures of currents and countercurrents. The ability to read them took years and is now a defunct art.
The Chinese probably used the same methods that the early Spanish employed. They may have also employed methods developed by people like the Micronesians. It looks like some Chinese didn't make it back. When the fleet was disbanded, some of the colonies just withered away.
One could argue that a calendar is man's earliest computer - for it can tell both date and time . Modern 8.5x11 pieces of paper are based on modern assumptions which medieval/ancient man did not have.
day length I already talked about it in a previous post.
good theories on the shape of the Earth, help In previous posts, I never mentioned Columbus. Columbus was off in the diameter of the Earth and in his writings, he convinced himself that the earth was NOT larger than he initially believed, but that the earth was in fact the shape of a pear, and that he had just sailed the "stem" part of the pear. Kepler would have had a good belly laugh at the flaw in that thinking.
Go back in time, and forget your digital watch, forget your GPS, how do you figure out where you are? When you jump on a plane and travel East, you'll have to adjust your watch to adjust for the position of the sun. But what do you do in your boat, particularly when you don't have a watch? hugging the coast is NOT exploring ANYONE can do that!
If all you've ever studied is the sun and the earth-sun-angle based on your position, what do you do when the sun goes down? How do you know where you are in a vast ocean? Ok, you'll decide to study the stars. So what stars do you learn? The north star? Not much good to you if you cross the equator. What do you do, if you're fixing your position based on a constellation (such as Orion) and it is not up? What do you do if you have to wait for months for it to come up? How do you calculate rise/set times of your favorite stellar object?
In summary - A calendar is a computation of date/time and position. For example, astronomers don't talk about "calendar" dates-- January 1, 2003 is: 2452640.5 (GMT midnight). Ancient explorers used ephemeris tables based on complex astro-navigation theory. 2452640.5 is very much a "calendar" output.
Anyone can jump in a boat and crash land some where. Knowing how to get back is the real art. The last great navigational challenge that man faced was returning from the moon. We knew how to get there. Getting back was the trick.
If the Chinese did crash land somewhere (I truly doubt it), they sure as heck couldn't get back. Their science wasn't sophisticated enough. The Chinese lacked the math to do predictable overseas navigation. The Vikings and the Mayans had this.
A calendar is a methematical solution of time and space. Understanding the components of the solution are what comprise navigation. Bear in mind is that the author is proposing that the Chinese accomplished the navigational feat of all time, exeeding all civilizations. There is no basis in history to even suggest that the Chinese had the science required for complex navigation and calendar creation.