Day Million

[retina]

Originally Posted by jasong

the millionth day of our calendar

It also depend on what you mean by "our". There are so many calendars used around the world and I think it is safe to say that this forum crosses many countries and cultures.

I have always liked to think of year 0 (or day 0) as beginning the day the solar system formed, i.e. ~4.5Gy ago for this solar system. So in that case, on day 1M life on Earth would not be existent as we currently know it (although it may have been in another form).

However, there is also another twist. If we go with the original intent of the question and use the Gregorian Calendrical system, what would life be like on day 1M then?

Well my answer would be life would in an infinite variety of forms (just like now) because I think there is life not just here on planet Earth but also in lots of other places throughout the Universe.

Okay, I know, I didn't even answer the original query of just when is day 1M. Sorry, but I got distracted.

[gd_barnes]

Originally Posted by alpertron

Dividing 1000000 by 365.25 in order to find an approximate year we obtain 2737.85.., which is near 2738, so the date should be near 1/1/2739.

So now we will find the number of days between 1/1/1 and 1/1/2739 and then adjust.

First we will need to know how many leap years are between these two dates.

There are 2738/4 = 684 years multiple of 4, but 27 of them are multiple of 100 and 6 multiple of 400. So we have 684-27+6 = 663 leap years.

So we have 365*2738+663 = 1000033 days between 1/1/1 and 1/1/2739.

Between 1/1/1 and 12/1/2738 we have 1000033 - 31 = 1000002 days.
Between 1/1/1 and 11/29/2738 we have 1000002 - 2 = 1000000 days.

So the millionth day of the Gregorian Calendar is November 28th, 2738

This is definitely right on. I like playing around with dates so if you're a non-math type but you know some Excel basics, here is an interesting way to get at the same result:

1. Excel uses an integer for each day that is the # of days since 1/1/1900. Unfortunately it has a bug where it doesn't recognize that 1900 is not a leap year whereas it knows that all other years > 1900 divisible by 100 are non-leap years unless they're divisible by 400.

2. Based on #1 and the fact that we need a starting date where the year is an exact multiple of 400 years different from the date of 1/1/1, type 1/1/2001 into a cell.

3. Change the cell in #2 to 'format general' and you'll see an integer value of 36,892.

4. In another cell, since the integer value in #3 is day 1, add 999,999 to that value to get the 1,000,000th day, which to Excel is the value 1,036,891.

5. Change the cell in #4 to 'format date' in mm/dd/ccyy (or ccyy/mm/dd, etc.) format.

6. The value in #5 will be 2000 years too great since we started from the year 2001 so just subtract 2000 years from it and you have your answer, which is just as Alpertron calculated...11/28/2738.

I've used this method to get days between dates in the past where at least one year was < 1901. Adding 2000 to the beginning and ending year is the easiest way.

Here's a constraint note: Excel can only display dates up to 12/31/9999 although it can still do internal arithmetic on integers for dates that are greater. The final answer just needs to be 1900 < year < 10000. It allows a year of 1900 but has the leap-year bug in only that year so I don't suggest using it.

Alpertron, are you the person who wrote the ECPP factoring program at the website that bares the same name? I use it constantly.


Gary


Edit:
BTW, 11/28/2738 is a Monday, which means that the U.S. Thanksgiving that year would be on 11/24. I think it would be a good day to take off work and have a 5-day weekend! :-)

[jasong]

Originally Posted by gd_barnes

BTW, 11/28/2738 is a Monday, which means that the U.S. Thanksgiving that year would be on 11/24. I think it would be a good day to take off work and have a 5-day weekend! :-)

Now, that's what I call planning ahead!!!

I would be 764 if I were to live that long, meaning that dying of old age would have been vanquished sometime before the 22nd century, or at least tamed considerably.

What I'd like to know is whether or not the world(as opposed to, say, Linus Torvalds ;) ) would still have trouble with viruses, botnets, and all the other nasties associated with insecure operating systems.

[gd_barnes]

Originally Posted by roger

I found the website http://www.timeanddate.com/date/dateadd.html which gives what alpertron worked out for himself (I'm just too lazy ):

Alpertron,

A couple of things are confusing me on your date website here. If you plug in January 1st, 0001 and add 1,000,000 days to it; like Roger showed above, it comes back with Sunday, November 27th, 2738. Yet you said earlier and I calculated later through Excel that the 1,000,000th day is Monday, November 28th, 2738. Therefore it appears that your date website is off 2 days somewhere.

For example:
Day 1: Saturday, January 1st, 0001
Day 1,000,000: Monday, November 28th, 2738
Day 1,000,001: Tuesday, November 29th, 2738

Day 1,000,001 would also be the day obtained by adding 1,000,000 days to January 1st, 0001 so shouldn't your site return 11/29/2738 instead of 11/27/2738?

I also noticed in the link for 'Calendar for any year' that on your calenders for all years ending in 00 prior to 1800 that February has 29 days in all of them. Based on the way you calculated the 1,000,000th day above, February would only have 28 days in years ending in 00 unless they were evenly divisible by 400. It has also always been my understanding that the '3 times every 400 years' adjustment to leap years applies to both past and future dates.

The same type of problem that is in the calendars appears to permiate the addition of dates in the past. If I plug in January 1st, 0001 and add 36,525 days to it, I should get January 2nd, 0101 because year 0100 is not a leap year yet the site return January 1st, 0101. I kept doing this for every 100 years and it had the same problem (when the century was not divisible by 400).

BUT...the big problem came when I plugged in January 1st, 1700 and added 36,525 days to it. It returned January 12th, 1800?? Since 1700 is not a leap year, like above, it should have returned January 2nd, 1800. But when I plug in January 1st, 1800 and add 36,525 days, it correctly returns January 2nd, 1900. It also returned correct calculations for dates starting with 1900 and 2000.

I think I see what is happening. You attempted to correct the problem with leap years on centuries prior to 1800 by adding 10 days during the 1700's somewhere. This is where the history may elude me and perhaps your site is correct afterall. Weren't adjustments for prior leap years determined during the 1700's?

Someone correct me on my history of leap year adjustments or if I'm off base anywhere else here. What would still confuse me though is why adding 1,000,000 days to 1/1/0001 comes up 2 days different than what we determined to be the 1,000,001st day here.


Thanks,
Gary

[cheesehead]

Originally Posted by MS63

Do any of these calculations take into account the 'lost' ten days in October 1582 when the Gregorian calendar was introduced?

Do they need to?

No, because no days were "lost". There was a 10-day difference between the Julian and Gregorian calendars then, but each calendar contained all days, with none missing.

Since there was a change in which calendar was official between Julian October 4, 1582 and Gregorian October 15, 1582, the italicized dates in the following table were unofficial (within the countries that converted in October 1582, that is), but the days corresponding to those dates did exist.

E.g.,

Julian September 24, 1582 = Gregorian October 4, 1582
Julian September 25, 1582 = Gregorian October 5, 1582
Julian September 26, 1582 = Gregorian October 6, 1582
Julian September 27, 1582 = Gregorian October 7, 1582
Julian September 28, 1582 = Gregorian October 8, 1582
Julian September 29, 1582 = Gregorian October 9, 1582
Julian September 30, 1582 = Gregorian October 10, 1582
Julian October 1, 1582 = Gregorian October 11, 1582
Julian October 2, 1582 = Gregorian October 12, 1582
Julian October 3, 1582 = Gregorian October 13, 1582
Julian October 4, 1582 = Gregorian October 14, 1582
Julian October 5, 1582 = Gregorian October 15, 1582
Julian October 6, 1582 = Gregorian October 16, 1582
Julian October 7, 1582 = Gregorian October 17, 1582
Julian October 8, 1582 = Gregorian October 18, 1582
Julian October 9, 1582 = Gregorian October 19, 1582
Julian October 10, 1582 = Gregorian October 20, 1582
Julian October 11, 1582 = Gregorian October 21, 1582
Julian October 12, 1582 = Gregorian October 22, 1582
Julian October 13, 1582 = Gregorian October 23, 1582
Julian October 14, 1582 = Gregorian October 24, 1582

...

Julian February 17, 1700 = Gregorian February 27, 1700 (note 10-day difference in day-of-month)
Julian February 18, 1700 = Gregorian February 28, 1700
Julian February 19, 1700 = Gregorian March 1, 1700
Julian February 20, 1700 = Gregorian March 2, 1700
...
Julian February 28, 1700 = Gregorian March 10, 1700
Julian February 29, 1700 = Gregorian March 11, 1700
Julian March 1, 1700 = Gregorian March 12, 1700 (note 11-day difference in day-of-month)

and so on ...

Each calendar date is just a label for a particular day. Different labels in different calendars, but the corresponding day is just itself.