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WashMe

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Everyday I go on wikipedia for about 20-30 minutes and learn about something completely unrelated to any classes or anything like that. I learned about the Julian calendar this morning.

If anyone is interested in a history lesson (somewhat inaccurate probably, as I'm just writing what I remember), read on.

So...

Julius Caesar instituted a calendar with 365 days, just like the Gregorian one we have today. This calendar even had leap years every four years, as does ours. In 325 CE, the council of Nicea arranged Easter to fall on a certain date relative to the vernal equinox. No problem, except that the Julian calendar (averaging 365.25 years) is eleven minutes off compared to the solar year. Every 136 years or so, this adds up to being a whole day off. By the early 16th century (maybe 1536, I forget), this problem resulted in a discrepancy of ten days between the solar year and the calendar year (the equinox and solstice dates were off). A change was made to the Gregorian calendar, and an instantaneous shift of 10 calendar days occurred. To those taking notes, this affects geneology charts including age if a person was born on Julian (Old) time and died on Gregorian (New) time.

That's the tidbit.

Now, the Gregorian calendar and the Julian calendar both average 365.25 days (w/ leap years); how did the new calendar solve the problem of the extra 11 minutes? Here's what I thought was really cool:

Since ~136 years of calendar time results in 1 day of shift, then we would be off by 3 days approximately every 400 years. In our calendar, leap years do not occur on century years that are not divisible by 400. We had a leap year in 2000, but there wasn't one in 1900, 1800, 1700. There was one in 1600, and the next on on a century year will be in 2400. The way this works is that every 4 centuries (400 years) we ignore 3 of the leap days and the calendar lines back up with solar time! Pretty neat if you ask me.

This whole thing raises a more interesting issue though...

If we were off by eleven minutes, then isn't our concept of a "second" somehow inherently wrong? I haven't looked into it, but I imagine it is defined by the period of a pendulum of a certain length. In more recent times, it has been defined as the half life of some atom (too lazy to do the research); this is, however, irrelevant, as it was instituted because it was the same duration of time as a "second" was already known to be. Why can't each second be marginally longer, thus making up the time discrepancy over the course of a year? I don't think that anyone would notice if each second were merely...

31558260 (w/ 11 more min to = solar yr) / 31557600 (sec/yr currently)

= 1.00002091

= 0.00002091% longer...

I do think the Gregorian solution is pretty smart though.

edit: I was vague in indicating which way the solar/calendar years are off. See below.

A calendar year is 365 days and 6 hours
A solar year is 365 days, 5 hours, 49 minutes, and 12 seconds.
 
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You should totally post this in the MCAT subforum and say that it's a sample problem from the MCAT :meanie:

Then you'll get a bunch of people trying to answer your question.
 
Since ~136 years of calendar time results in 1 day of shift, then we would be off by 3 days approximately every 400 years. In our calendar, leap years do not occur on century years that are not divisible by 400. We had a leap year in 2000, but there wasn't one in 1900, 1800, 1700. There was one in 1600, and the next on on a century year will be in 2400. The way this works is that every 4 centuries (400 years) we ignore 3 of the leap days and the calendar lines back up with solar time! Pretty neat if you ask me.

this is the coolest thing i've read in a while - i had no idea!
 
You should totally post this in the MCAT subforum and say that it's a sample problem from the MCAT :meanie:

Then you'll get a bunch of people trying to answer your question.

haha I really should! now, to think of some questions to grill them with... :laugh:
 
i love this kinda stuff. Thanks.

Wiki forever!!! hahaha
 
Changing the amount of time in a second wouldn't break more than it would solve. Calendars are based on days, and there's no way to change the length of a day... it's one sun rise to another. If we change the amount of time in a second (therefore changing how long a minute, an hour, and a day is), the calendar would no longer be synchronized to the rising of the sun, meaning everywhere around the world would undergo a cycle where the amount of daylight in one day would be progressively less, until it was complete night, and the cycle would reverse.

It would work to correct the discrepancy in time, but it wouldn't synchronize each calendar day to each solar day. Does that make sense? I know I'm not explaining myself well but I hope you get the point.
 
I've heard a lot about this stuff. I leaned a lot about it when I wrote a computer program to implement the zeller equation. It gives you the day of the week given the date of the year. Granted I did this before wikipedia existed.

As for the definition of a second, it's based on the vibrations of a cesium atom somehow. Here's why a second isn't just slightly longer. We would end up defining our day length differently. Longer second = longer minute = longer hour... Then our days would slowly drift off. At the end of the year , we'd be ~ 6 hours off. The sun would rise at noon or so.

The way we do it now, the sun always rises at the right time, and all we have to do is add a day to the year on years divisible by 4, excluding centuries, but including melinia... Etc.
 
Wait, I just thought about that a little more. I need to read over the original post again in the morning when I'm more awake.
 
I spend about a half hour a day on wiki as well just reading random stuff. Great way to pass time in a boring lab.
 
Changing the amount of time in a second wouldn't break more than it would solve. Calendars are based on days, and there's no way to change the length of a day... it's one sun rise to another. If we change the amount of time in a second (therefore changing how long a minute, an hour, and a day is), the calendar would no longer be synchronized to the rising of the sun, meaning everywhere around the world would undergo a cycle where the amount of daylight in one day would be progressively less, until it was complete night, and the cycle would reverse.

It would work to correct the discrepancy in time, but it wouldn't synchronize each calendar day to each solar day. Does that make sense? I know I'm not explaining myself well but I hope you get the point.
👍

that's right. seconds come from day (cesium oscillation is there just to keep accurate record of it) and

1 day = 1 earth rotation time

and

1 solar year = earth orbit time

each is independently defined so you can't just change the length of either.
 
Seriously, if it wasn't for Wikipedia and SDN, my life would be so boring.😛
 
Glad you enjoyed this, guys.

For those paying attention, I couldn't initially remember if a solar year was longer or shorter; it is shorter than a calendar year, so the "second" would need to be slightly shorter (not longer is previously proposed).

I understand the dissociation b/w earth's rotation (a day) and its orbit (a year), however I don't think making up 11 minutes will have any real difference throughout one year. I understand the argument about the start/end of days eventually being out of sync with sunrise/sunset, however we work off of fixed time already; we don't get up when we hear the rooster outside. The scale is arbitrary no matter what; when you think about it, leap years and daylight savings time are as "confusing" as what I was suggesting.
 
The Gregorian calendar will have one too many days every 3333 years.

"In the Soviet Union, however, they use an even more accurate calendar, introduced in October 1923. All years are ordinary years except those which when divided by 9 leave either 2 or 6 as remainder. This calendar contains one day too many after 45,000 years."

Penguin Dictionary of Curious and Interseting Numbers, by David Wells, a great book is now tattered and split from all my enjoying it as a youth. =)
 
I understand the dissociation b/w earth's rotation (a day) and its orbit (a year), however I don't think making up 11 minutes will have any real difference throughout one year. I understand the argument about the start/end of days eventually being out of sync with sunrise/sunset, however we work off of fixed time already; we don't get up when we hear the rooster outside. The scale is arbitrary no matter what; when you think about it, leap years and daylight savings time are as "confusing" as what I was suggesting.

I thought about it a little more. If we changed the length of seconds/days, we'd end up with 11 extra minutes right? We'd have to set our clocks forward 11 minutes every year. That would be more sane than all these Gregorian rules, but if we didn't set clocks forward 11 min every year, the sunrise would slowly drift through the day. I do disagree with the whole sunrise point though. I don't think we could motivate a whole society to work from 8-5 in the dark (and some jobs need light, like landscaping, or construction).

We could always just think up some extreme engineering solution. Here are two:
1. Attach rockets to the ground meant to slow down or speed up the rotation of the earth. Then we could match the number of rotations per revolution to a number much closer to 365.
2. Use some sort of propulsion to push the earth's orbit farther out or closer in to match the revolution time to 365 rotations. Maybe we could build a big volcano or something.
 
I thought about it a little more. If we changed the length of seconds/days, we'd end up with 11 extra minutes right? We'd have to set our clocks forward 11 minutes every year. That would be more sane than all these Gregorian rules,

i think if back in the days they could do this as efficiently as we could now, (we have much more accurate clocks commercially available to measure exactly 11 minutes; communication is also better to make sure everybody does it), they would have probably set up the calendar this way. just maybe...

1. Attach rockets to the ground meant to slow down or speed up the rotation of the earth. Then we could match the number of rotations per revolution to a number much closer to 365.
2. Use some sort of propulsion to push the earth's orbit farther out or closer in to match the revolution time to 365 rotations. Maybe we could build a big volcano or something.

lol... i think the earth's rotation is already slowing down due to friction from tides. but that'll take a while.
 
i didn't know this one!!

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