 Greetings and welcome to the Introduction to Astronomy. In today's lecture, we are going to be looking at Babylonian astronomy and specifically concentrating on their use of numbers and the calendar that was developed by the Babylonians long, long ago. So let's go ahead and start with numbers. Now, the Babylonians gave us what is called the sex-adjustable numbering system, which is a base 60. Now, we normally count 1 through 10, and that is base 10. And you can also use things like binary, and there are others that use a base 8 and other different numbering systems, and in fact, you can use any base you like. 10 happens to be what we have developed over the years. But there's no reason that any other numbering system doesn't work just as well. And in fact, the sex-adjustable system is still used today in many ways. And in fact, we measure things like time. We have hours, minutes, and seconds. And we know that there are 60 minutes in one hour. So 60 minutes is one hour. Well, why? Why are there 60 minutes in an hour? It's because of the sex-adjustable numbering system. That's what we're using. 60 minutes in an hour. And of course, there's also 60 seconds in one minute. Exactly the same that we are using here. So this is all tied into the sex-adjustable system. We also use this for angles. When we break up a degree, there are 60 minutes of arc in one degree, and 60 seconds of arc in one minute of arc. So we use these for both time and angle measurements today. So we use roughly the same system that has been used since the time of the Babylonians in fact is a carry-over from what the work that the early Babylonians did. Now, the other thing I want to look at briefly here is the Babylonian calendar. Now, the calendar is a lunar-solar calendar, meaning it uses both the moon and the sun. And in fact, each month there are 12 months and they begin when the new moon is visible. The crescent moon, I should say, is visible after sunset. So the first time you can see the crescent moon in the sky as shown here, the first time you can see that very thin crescent, that was the beginning of the new month. And then the month would run through the entire cycle of the moon, 29 and a half days until you again saw that very thin crescent moon in the sky right after sunset. Now, you can't see the new moon, so you wouldn't start the month at new moon simply because you could not see it. But you could then use this for when you could first find the moon. And that's actually a challenge to be able to find it and you can imagine that weather would be an issue here. What if it was cloudy for a few days? You might miss the beginning of the month. But this is again how the month was actually determined here. Now, the day also began at sunset, so we have our days begin at midnight here, the days began at sunset. And in fact, the first day of the month would then begin as soon as that crescent moon was seen. Now, if we figure this out, 12 lunar months gives us 354 days. Now, we know there's 365 days in a year because of the orbit of Earth around our sun and the rotation of Earth on its axis. But because those two are not related to each other, the number of months and days will not fit evenly into a year. So, what you do to keep things from falling out of sync is to add an extra month every few years. This is, what, about 11 days off? So, if you added an extra month of about 30 days every three years, that would bring you about into sync and keep everything from traveling off too far. Now, unlike our year, which begins in wintertime for the Northern Hemisphere, the year began in the spring and was broken up into three seasons of four months each, not like our current year of four of three months for four seasons. And it was a very observational calendar. Now, this, they actually eventually, by about 500 BC, had refined it a little bit more. So, this 12 months to 354 days, it was figured out that a 19-year cycle came out almost exactly to 235 months. So, you could split up exactly when you were going to need those extra months over the course of those 19 years to make everything balance out at the end. So, a very complex and accurate calendar that was developed many thousands of years ago. So, let's go ahead and summarize what we've looked at here. And what we've looked at is that the Babylonians gave us a numbering system used today for time and angles. We also looked at the calendar, which was a lunar solar calendar, looking at the motions of the sun and the moon. And we also discussed how the Babylonian day begins at night and the month began when the crescent moon was first visible in the evening sky right after sunset. So, that concludes this lecture on time in the calendar from the Babylonians. We'll be back again next time for another lecture. So, until then, have a great day, everyone, and I will see you in class.