Origins of "lucky" numbers.
July 21st, 2010 at 7:50:34 AM
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Why is the number 7 considered lucky?
My simple answer:
There are seven bright heavenly bodies which also describe a path through the heavens. They are the Sun, Moon, Mars, Mercury, Jupiter, Venus and Saturn. These are also known as the Seven Traditional Planets (of course not all of them are planets by modern definition).
Throughout history they've had a alrge influence over human cultures. They're the reason the week has seven days, all at one time named after one of the Seven (the naming of days deserves a thread of its own, as it involves mythology, etimology and several languages).
Seven thus is a heavenly number, backed by seven deities. That should guarantee "luck," right?
Briefly the deities associated with each "planet" are:
Helios/Sol god fo the Sun
Selene/Luna goddess of the Moon (later the Moon became associated with Diana, goddess of the hunt)
Ares/Mars god of war
Hermes/Mercury messenger of the gods
Zeus/Jupiter chief of the gods
Aphrodite/Venus goddess of love and beauty
Chronos/Saturn best known as Zeus' cannibalistic father, formerly head of the Titans.
My simple answer:
There are seven bright heavenly bodies which also describe a path through the heavens. They are the Sun, Moon, Mars, Mercury, Jupiter, Venus and Saturn. These are also known as the Seven Traditional Planets (of course not all of them are planets by modern definition).
Throughout history they've had a alrge influence over human cultures. They're the reason the week has seven days, all at one time named after one of the Seven (the naming of days deserves a thread of its own, as it involves mythology, etimology and several languages).
Seven thus is a heavenly number, backed by seven deities. That should guarantee "luck," right?
Briefly the deities associated with each "planet" are:
Helios/Sol god fo the Sun
Selene/Luna goddess of the Moon (later the Moon became associated with Diana, goddess of the hunt)
Ares/Mars god of war
Hermes/Mercury messenger of the gods
Zeus/Jupiter chief of the gods
Aphrodite/Venus goddess of love and beauty
Chronos/Saturn best known as Zeus' cannibalistic father, formerly head of the Titans.
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July 21st, 2010 at 8:33:59 AM
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I have heard that it is God's perfect number.
Possibly coming from verses in the Bible:
Genesis 2:1-3 (NKJ)
1 Thus the heavens and the earth, and all the host of them, were finished.
2 And on the seventh day God ended His work which He had done, and He rested
on the seventh day from all His work which He had done. 3 Then God blessed the
seventh day and sanctified it, because in it He rested from all His work which
God had created and made.
Possibly coming from verses in the Bible:
Genesis 2:1-3 (NKJ)
1 Thus the heavens and the earth, and all the host of them, were finished.
2 And on the seventh day God ended His work which He had done, and He rested
on the seventh day from all His work which He had done. 3 Then God blessed the
seventh day and sanctified it, because in it He rested from all His work which
God had created and made.
There is a flip side to that coin.
July 21st, 2010 at 8:39:29 AM
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Quote: trinityI have heard that it is God's perfect number.
Possibly coming from verses in the Bible:
No doubt the Bible does say it. It would be surprising if it didn't.
But where did the notion come from? From older civilizations, naturally. I don't know enough to say where exactly, but possibly from the early civilizations along the Tigris and Euphrates rivers. Ur, Chaldea, Babylon, etc. Teh seven day week was decised there.
Naturally the Hebrews cleaned it up and adapted it to their own belifs, like monotheism. But the origin is in the seven heavenly bodies.
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July 21st, 2010 at 9:43:12 AM
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Quote: NareedThere are seven bright heavenly bodies which also describe a path through the heavens. They are the Sun, Moon, Mars, Mercury, Jupiter, Venus and Saturn. These are also known as the Seven Traditional Planets (of course not all of them are planets by modern definition).
I have heard this traditional description of the origin of lucky 7. My problem with this is that it's too convenient. Obviously, there are other heavenly bodies, and certain stars can appear to be brighter than some of the planets. These 7 bodies may move through the heavens, but they do not do so in exactly similar paths. And some move very rarely, much as many stars.
My feeling is that the number 7 was already considered sacred and/or lucky for some reason, and thus 7 heavenly bodies were found to match this tradition.
Thus, my question has always been, why was 7 considered lucky/sacred prior to the "discovery" of the 7 heavenly bodies?
July 21st, 2010 at 10:04:38 AM
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Quote: konceptumI have heard this traditional description of the origin of lucky 7. My problem with this is that it's too convenient. Obviously, there are other heavenly bodies, and certain stars can appear to be brighter than some of the planets. These 7 bodies may move through the heavens, but they do not do so in exactly similar paths. And some move very rarely, much as many stars.
I believe Sirius outshines Venus. It is brighter than all the other planets on the list for certain. But it stays put against the background stars (actually it has a small parallax because it's very close, but that's hard to notice). It does not move noticeably from day to day as the planets do.
But there is one other planet that's visible to the naked eye and which moves: Uranus. Except it's faint and it's motion's too slow, therefore it wasn't recognized as a planet until the telescope era. Even then, most early telescopes only showed it as a bright star. It took William Herschell, who made his own instruments, to make a scope good enough to resolve Uranus as a disk. He stumbled upon it as he tried to compile a map of the heavens.
Of course there is a group of constellations that line the Earth's ecliptic (the apparent path followed by the Sun). There are 12 of them (12 months in a year, imagine that!) and we call them The Zodiac. They form the basis for astrology, which is bogus and hokum, but at one point required accurate and detailed observations of the skies.
When casting horscopes or making predictions, astrologers noted where the seven "planets", which also line the ecliptic, were in relation to the Zodiac.
I maintain the seven traditional planets came first, then the lucky number 7
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July 21st, 2010 at 10:15:43 AM
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In Vegas, and especially Macau, the dominant lucky number is 8. This is because the word for 8 in Chinese sounds similar to the word for "rich" or "lucky," I can't remember which one. Likewise, 4 is unlucky, because in Chinese it sounds like the word for "death."
I'm think that 13 is unlucky in western culture because there were 13 people at the Last Supper. Where 7 comes from as a lucky number, I have no idea. The astrology theory sounds very plausible.
I'm think that 13 is unlucky in western culture because there were 13 people at the Last Supper. Where 7 comes from as a lucky number, I have no idea. The astrology theory sounds very plausible.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 21st, 2010 at 10:25:22 AM
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Quote: konceptumI have heard this traditional description of the origin of lucky 7. My problem with this is that it's too convenient. Obviously, there are other heavenly bodies, and certain stars can appear to be brighter than some of the planets. These 7 bodies may move through the heavens, but they do not do so in exactly similar paths. And some move very rarely, much as many stars.
My feeling is that the number 7 was already considered sacred and/or lucky for some reason, and thus 7 heavenly bodies were found to match this tradition.
Thus, my question has always been, why was 7 considered lucky/sacred prior to the "discovery" of the 7 heavenly bodies?
All the planets, and the sun and the moon move along the elliptic, in the same plane. The seven traditional planets do all move, and quite quickly. The stars do not move (at least not to the naked eye). I've tracked both Jupiter and Saturn moving night after night. The 5 wandering stars (or "asteres planetai") are noticeable even more if your not suffering from light pollution.. Venus is brighter than Sirius when it's at it's peak (futherest away from the sun as viewed from earth) and Jupiter is also very bright.
Just a quick search shows that the 7 heavenly objects were known in many different cultures, and referred to in Alchemy, mythology, astrology and astronomy across the world. I would suspect that 7 comes from the number of heavenly objects rather than 7 being a lucky number and the objects fitting the pattern.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
July 21st, 2010 at 10:30:38 AM
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Quote: WizardIn Vegas, and especially Macau, the dominant lucky number is 8. This is because the word for 8 in Chinese sounds similar to the word for "rich" or "lucky," I can't remember which one. Likewise, 4 is unlucky, because in Chinese it sounds like the word for "death."
I'm think that 13 is unlucky in western culture because there were 13 people at the Last Supper. Where 7 comes from as a lucky number, I have no idea. The astrology theory sounds very plausible.
12 is a nice complete number. It divides many ways. 13 is a pain in the back side :)
5 and 23 are also significant numbers... if you are a Discordian. 5 is the number of human, and it's the sum of the first two primes. 23 or the Enigma of 23 is the 'theory' that 23 turns up far more often than it should. And it does, as soon as you start looking for it.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
July 21st, 2010 at 10:56:43 AM
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Always interested to hear about astrology/astronomy. Didn't know about the planets in the zodiac. Is that why that song goes, "When the moon is in the seventh house...etc.?"
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What are the most unlucky numbers? I always thought 5 was a f---ing evil number. Something to do with the five fingers makes it more "manual" than transcendent for me. One and two are also unlucky. They are more binaries than numbers. Three is lucky. Nine should be the default lucky number in my opinion, instead of seven. Think about it. The best total in baccarat and Pai Gow Tiles is nine. The number nobody wants to see most of the time in a dice game is seven. I vote to change the "lucky number" to nine.
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What are the most unlucky numbers? I always thought 5 was a f---ing evil number. Something to do with the five fingers makes it more "manual" than transcendent for me. One and two are also unlucky. They are more binaries than numbers. Three is lucky. Nine should be the default lucky number in my opinion, instead of seven. Think about it. The best total in baccarat and Pai Gow Tiles is nine. The number nobody wants to see most of the time in a dice game is seven. I vote to change the "lucky number" to nine.
"Dice, verily, are armed with goads and driving-hooks, deceiving and tormenting, causing grievous woe." -Rig Veda 10.34.4
July 21st, 2010 at 11:20:00 AM
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Quote: teddysAlways interested to hear about astrology/astronomy.
Would that I'd known that. Anyway, for interesting astronomy stories look up Isaac Asimov.
Quote:Didn't know about the planets in the zodiac. Is that why that song goes, "When the moon is in the seventh house...etc.?"
Yes. I've no idea what a house is supposed to be, but the references are always to some of the seven traditional planets being there.
Had Uranus been brighter it might have been noticed despite its glacial pace. Then the lucky number would be 8.
5 is the easy number. It's easy to multiply and divide by 5, we have five fingers in each hand, and it's about as high a number as people grasp.
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July 21st, 2010 at 12:25:41 PM
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Quote: Nareedit's about as high a number as people grasp.
LOL!
"Dice, verily, are armed with goads and driving-hooks, deceiving and tormenting, causing grievous woe." -Rig Veda 10.34.4
July 21st, 2010 at 12:35:54 PM
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Quote: thecesspit
5 and 23 are also significant numbers... if you are a Discordian. 5 is the number of human, and it's the sum of the first two primes. 23 or the Enigma of 23 is the 'theory' that 23 turns up far more often than it should. And it does, as soon as you start looking for it.
Interesting! I was born on May 23, at 5:23 PM.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 21st, 2010 at 12:45:50 PM
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So is that evidence that the 5 shows up more than it should or the 23? Guess it depends on which random number you are looking for.Quote: WizardInteresting! I was born on May 23, at 5:23 PM.
July 21st, 2010 at 1:27:50 PM
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Quote: WizardInteresting! I was born on May 23, at 5:23 PM.
You should have waited two days to post that information ;)
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July 21st, 2010 at 2:44:07 PM
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The houses of the zodiac are just the signs. The astrological houses divided the elliptical into 12 even sections. Astronomers don't do any of that, and some of the constellations that cross the elliptical cover more of it than others. Virgo covers 5 times more space in the elliptical than Scorpio, meaning that for astronomers, 'Jupiter can been seen in Virgo' will happen more often than 'Jupiter can be seen in Scorpio'.
Also Orion, Perseus and Auriga (the Charioteer) also cover a little bit of the ellipitical (Jupiter off the shoulder of Orion...). Cancer, the Crab is a really dull looking constellation, whereas Leo really does look a bit like a Lion.
Also Orion, Perseus and Auriga (the Charioteer) also cover a little bit of the ellipitical (Jupiter off the shoulder of Orion...). Cancer, the Crab is a really dull looking constellation, whereas Leo really does look a bit like a Lion.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
July 22nd, 2010 at 10:02:43 AM
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Quote: NareedI believe Sirius outshines Venus. It is brighter than all the other planets on the list for certain. But it stays put against the background stars (actually it has a small parallax because it's very close, but that's hard to notice). It does not move noticeably from day to day as the planets do.
The Sun, the Moon, Venus (-4.7), Mars (-2.9), Jupiter (-2.8), and Mercury (-1.9) all outshine Sirius (magnitude -1.4). Saturn, at magnitude -0.5, is the only one of the "seven heavenly bodies" that do not outshine Sirius. The magnitudes of the "heavenly" bodies change of course depending on their position in the sky.
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July 22nd, 2010 at 1:14:12 PM
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The Metonic Cycle discovered in the 5th century BCE states that 19 solar years equals almost exactly 235 lunar months. The easiest way to get this correlation is on a calendar is with 12 years with 12 lunar months (12*12=144 months), and 7 years with 13 lunar months (7*13=91 months) (as in a Jewish calendar or Islamic calendar). You will then get 12+7=19 solar years equal to 144+91=235 lunar months.
These extra month numbered 13 was seen as portentious, and gave rise to the idea of 13 as a lucky number. The idea of friday the 13th being very unlucky is not in written history until the 19th century, but the superstition could be a lot older.
These extra month numbered 13 was seen as portentious, and gave rise to the idea of 13 as a lucky number. The idea of friday the 13th being very unlucky is not in written history until the 19th century, but the superstition could be a lot older.
July 22nd, 2010 at 2:14:58 PM
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Quote: pacomartinThe idea of friday the 13th being very unlucky is ....
Just can't pass on the chance to post this slightly-related puzzle:
The story goes that some people believed that Friday the 13th was unlucky because it seemed the 13th of the month occurred more often on Friday than on any other day of the week. Does the 13th really occur on Friday most often or not? For whichever answer you choose, prove that it is the correct one.
I first heard that puzzle in 1968, I think. I thought I knew which was correct, but I couldn't prove it. Finally in about 1984 or 1985 I figured out a method. Once I did, I found that I had been wrong all those years! Can you folks come up with both a correct answer and proof?
July 22nd, 2010 at 3:14:26 PM
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Quote: boymimboThe Sun, the Moon, Venus (-4.7), Mars (-2.9), Jupiter (-2.8), and Mercury (-1.9) all outshine Sirius (magnitude -1.4). Saturn, at magnitude -0.5, is the only one of the "seven heavenly bodies" that do not outshine Sirius. The magnitudes of the "heavenly" bodies change of course depending on their position in the sky.
My bad.
I must have been thinking that Sirius outshines all other stars, except the Sun.
BTW, a common trick to trip someone up regarding stars is to ask "What is the second star closest to the Earth?" Make sure you stress the word "second." The answer most people, who know some basic astronomy, will give is Barnard's Star. The rigth answer is Proxima Centauri.
Discuss.
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July 23rd, 2010 at 6:40:56 AM
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Quote: Nareed
BTW, a common trick to trip someone up regarding stars is to ask "What is the second star closest to the Earth?" Make sure you stress the word "second." The answer most people, who know some basic astronomy, will give is Barnard's Star. The rigth answer is Proxima Centauri.
Discuss.
You could trip up the tripper! According to Wikipedia (I know, I know), Alpha Centauri is two stars that together appear as one. And what about the Sun? That's technically a star, so Alpha Centauri could be right again.
I think the percentage of people who know Alpha Centauri is the closest non-Sun star to Earth is minuscule. I've never even heard of Barnard's Star. Actually, I would like to see the Wizard use that as his next cocktail waitress trivia question.
"Dice, verily, are armed with goads and driving-hooks, deceiving and tormenting, causing grievous woe." -Rig Veda 10.34.4
July 23rd, 2010 at 9:56:51 AM
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Quote: teddysYou could trip up the tripper! According to Wikipedia (I know, I know), Alpha Centauri is two stars that together appear as one.
The Centauri System, a more appropriate name, si made up of three stars: Alfa Centauri, Beta Centauri and Proxima Centauri. The latter is "nearest" to the Solar System, and it is a red dwarf. In a telescope you can spot all three. Without instruments, they all look as a pinpoint source.
Quote:And what about the Sun? That's technically a star, so Alpha Centauri could be right again.
That's the whole point. The star closest to the Earth is the Sun, the second closest is the Centauri System (or Alpha Centauri, as is traditionally known), and the third closest is Barnard's Star.
Most times the question is posed as "What's the star closest to the Sun?" And lots of poeple know it's Alpha Centauri. When you ask for the second closest, not many poeple know the answer. By changing "Sun" for "Earth," you trip more knowledgeable people.
Quote:I think the percentage of people who know Alpha Centauri is the closest non-Sun star to Earth is minuscule. I've never even heard of Barnard's Star. Actually, I would like to see the Wizard use that as his next cocktail waitress trivia question.
Back in elementary school everyone knew it. But who knows what they teach kids these days.
Barnard's (named for astronomer E.E. Barnard) is an oterhwise unremarkable red dwarf star (the Galaxy, and likely the universe, is lousy with red dwarves). But it's very close to the Earth, only about 6 light years away, and it has the largest known propper motion in relation to the Sun. You need a telescope to see it, though, because red dwarves are very dim in visible light. If you could see infrared light, it would be visible without a telescope, perhaps.
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July 23rd, 2010 at 2:16:13 PM
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Quote: WizardLikewise, 4 is unlucky, because in Chinese it sounds like the word for "death."
Thats why you won't see a number 4 spot on a bac table. But the number 4 spot is still there, duh! Just because you don't have a 13th floor in a building, the 13th floor doesn't go anywhere, its still there. It shows you how ridiculous superstitions are.
"It's not called gambling if the math is on your side."
April 25th, 2011 at 3:37:06 PM
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Quote: DocThe story goes that some people believed that Friday the 13th was unlucky because it seemed the 13th of the month occurred more often on Friday than
on any other day of the week. Does the 13th really occur on Friday most often or not? For whichever answer you choose, prove that it is the correct one.
I say that the 13th falls on a Friday 1/7 of the time over a long period of time. There are only 14 possible calendars, and every 28 years they should go through a cycle, ignoring the rule that years that are divisible by 100, but not 400, are not leap years. In other words, if you didn't write on your calendars, a set of 14 would last you forever. A set of just 7 would work for the non-leap years. I'm quite sure that if you looked at all 12*14=168 months that in 24 of them the 13th would fall on a Friday.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
April 25th, 2011 at 4:36:02 PM
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Quote: WizardI say that the 13th falls on a Friday 1/7 of the time over a long period of time. There are only 14 possible calendars, and every 28 years they should go through a cycle, ignoring the rule that years that are divisible by 100, but not 400, are not leap years. In other words, if you didn't write on your calendars, a set of 14 would last you forever. A set of just 7 would work for the non-leap years. I'm quite sure that if you looked at all 12*14=168 months that in 24 of them the 13th would fall on a Friday.
Nice start, and similar to my start back in 1968. Unfortunately, you have assumed an answer rather than proving it. The proof is not trivial, and your assumption just might not be correct. That "ignoring the rule..." phrase could get you into trouble, but even if you did, do you really believe that each of the 14 calendars is used twice each 28 years? How many of those calendars are specifically for leap years?
Here's another bit of a hint: 1/7 is not the correct answer, not for Friday or for any other day of the week.
April 25th, 2011 at 6:30:02 PM
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Edit: Ooops! I posted the comments below in response to a post from the Wizard. But that post is now gone! (I don't think people have been double-flagging the Wizard's posts, have they?) I don't know where it went, and I didn't copy it in my reply, but honest, the comments below related to what the Wizard said.
Excellent progress! Yes, I am talking about the long term, and there is indeed a cycle that is important, but it is not 28 nor 700 nor 2800 years. (Well, 2800 years might work for a proof, but you don't need to look over that long a period.) I agree that a spreadsheet is an excellent aid. I use one now when repeating my proof, though I don't think I had ever seen one back when I first worked out my solution.
But I think you may have a calculation error in your spreadsheet. In part 3, I am not certain what you meant when you said "any given date will advance by 1 day after 100 years". Did you mean that the date that started on Monday in year #1 of your example would be on Tuesday in year #101? If so, look at your table of the 28 years in your part 2. Repeat that to year 101. I think that suggests Sunday rather than Tuesday. Did I read that incorrectly? And you only get to adjust by one day for the 100-year rule. There might be a similar error in your part 4; at least I have the same uncertainty.
There are a couple of other factors that haven't come up yet that make the spreadsheet a little more complicated, but I think we first need to resolve this point of my misunderstanding of your "solution".
Excellent progress! Yes, I am talking about the long term, and there is indeed a cycle that is important, but it is not 28 nor 700 nor 2800 years. (Well, 2800 years might work for a proof, but you don't need to look over that long a period.) I agree that a spreadsheet is an excellent aid. I use one now when repeating my proof, though I don't think I had ever seen one back when I first worked out my solution.
But I think you may have a calculation error in your spreadsheet. In part 3, I am not certain what you meant when you said "any given date will advance by 1 day after 100 years". Did you mean that the date that started on Monday in year #1 of your example would be on Tuesday in year #101? If so, look at your table of the 28 years in your part 2. Repeat that to year 101. I think that suggests Sunday rather than Tuesday. Did I read that incorrectly? And you only get to adjust by one day for the 100-year rule. There might be a similar error in your part 4; at least I have the same uncertainty.
There are a couple of other factors that haven't come up yet that make the spreadsheet a little more complicated, but I think we first need to resolve this point of my misunderstanding of your "solution".
April 25th, 2011 at 8:21:28 PM
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I'm not sure how this relates to the Friday the 13th issue, but...Quote: Doc...do you really believe that each of the 14 calendars is used twice each 28 years? How many of those calendars are specifically for leap years?
There are 14 calendars. Seven, one each for 1/1 being on each day of the week for non-leap years (and these are each used three times in 28 years), another seven, one each for 1/1 being on each day of the week for leap years (and these are used once each in 28 years).
While the divisible by 100 thing does throw things off, and the except divisible by 400 further screws up the sequence, add "usually" in there. I.E., The 14 calendars rotate in a cycle that usually lasts 28 years.
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Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
April 25th, 2011 at 8:30:51 PM
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Quote: DocEdit: Ooops! I posted the comments below in response to a post from the Wizard. But that post is now gone!
I deleted that post because I realized there was a mistake somewhere in it. So I hope you're happy, I just got back from vacation, have a ton of catching up to do, and I've spent much of the day on this. So, here is my thinking at this point.
1. Forgetting the 100- and 400-year rules for a moment, a century would have 25 leap years, so 75*365 + 25*366 = 36,525 days. That is 5,217 weeks and 6 days. So, for example, today is a Monday, so in 100 years it would be a Sunday, which is 6 days later in the weekly cycle.
2. Now let's add the 100 year rule, still leaving out the 400 year rule. Every 100 years a leap year turns into a 365-day year, so there are now 36,524 days in a century. That is 5,217 weeks and 5 days. So, if today is a Monday, in 100 years it would be a Saturday, which is 5 days later in the weekly cycle.
3. Now let's add the 400 year rule. For those that don't know, this overrides rule 2, making years divisible by 400 leap years. Here is the day of the week by date:
4/25/2011: Monday
4/25/2111: Saturday
4/25/2211: Thursday
4/25/2311: Tuesday
4/25/2411: Monday
The reason 4/25/2411 is a Monday is 2400 was a leap year, giving one extra day since 4/25/2311. So we advance 6 days in the weekly cycle rather than the usual 5. So, we're back to Monday too early.
As it turns out the kinds of years that happen more frequently have more Friday the 13ths. To be specific, here is a distribution of day of the week by each month in a 2800-year cycle.
Sunday 4809
Monday 4795
Tuesday 4795
Wednesday 4809
Thursday 4788
Friday 4816
Saturday 4788
Note the most common is Friday.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
April 25th, 2011 at 8:31:19 PM
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Sigh. My mother-in-law used to do that.Quote: Wizard...In other words, if you didn't write on your calendars, a set of 14 would last you forever. A set of just 7 would work for the non-leap years.
She had a set of seven of the fabric wall-hanging type calendars. She would simply change them an extra time on 3/1 if it's a leap year.
She finally got rid of them when she discovered the local Chinese take out restaurant gives a bamboo version away.
I invented a few casino games. Info:
http://www.DaveMillerGaming.com/ —————————————————————————————————————
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
April 25th, 2011 at 8:34:49 PM
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Back up the gravy train....Quote: Wizard1. Forgetting the 100- and 400-year rules for a moment, a century would have 25 leap years, so 75*365 + 25*366 = 36,525 days....
I didn't run all the math, but I don't need a calculator to know that 100 does not divide by 28 evenly.
I invented a few casino games. Info:
http://www.DaveMillerGaming.com/ —————————————————————————————————————
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
April 25th, 2011 at 8:52:24 PM
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Quote: WizardInteresting! I was born on May 23, at 5:23 PM.
Then whoever put your birthday into the Wikipedia article needs to go edit...
Each of us is entitled to his own opinion, but not to his own facts.
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April 25th, 2011 at 9:34:20 PM
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It is only 400 years for a complete cycle. There are 146097 days in 400 years (365*400 plus 97 leap days) which is exactly divisible by 7.
Here is my 400 year cycle chart for how many dates are on what date.
Here is my 400 year cycle chart for how many dates are on what date.
| date | Sat | Sun | Mon | Tue | Wed | Thu | fri | total |
|---|---|---|---|---|---|---|---|---|
| 1 | 684 | 688 | 684 | 687 | 685 | 685 | 687 | 4800 |
| 2 | 687 | 684 | 688 | 684 | 687 | 685 | 685 | 4800 |
| 3 | 685 | 687 | 684 | 688 | 684 | 687 | 685 | 4800 |
| 4 | 685 | 685 | 687 | 684 | 688 | 684 | 687 | 4800 |
| 5 | 687 | 685 | 685 | 687 | 684 | 688 | 684 | 4800 |
| 6 | 684 | 687 | 685 | 685 | 687 | 684 | 688 | 4800 |
| 7 | 688 | 684 | 687 | 685 | 685 | 687 | 684 | 4800 |
| 8 | 684 | 688 | 684 | 687 | 685 | 685 | 687 | 4800 |
| 9 | 687 | 684 | 688 | 684 | 687 | 685 | 685 | 4800 |
| 10 | 685 | 687 | 684 | 688 | 684 | 687 | 685 | 4800 |
| 11 | 685 | 685 | 687 | 684 | 688 | 684 | 687 | 4800 |
| 12 | 687 | 685 | 685 | 687 | 684 | 688 | 684 | 4800 |
| 13 | 684 | 687 | 685 | 685 | 687 | 684 | 688 | 4800 |
| 14 | 688 | 684 | 687 | 685 | 685 | 687 | 684 | 4800 |
| 15 | 684 | 688 | 684 | 687 | 685 | 685 | 687 | 4800 |
| 16 | 687 | 684 | 688 | 684 | 687 | 685 | 685 | 4800 |
| 17 | 685 | 687 | 684 | 688 | 684 | 687 | 685 | 4800 |
| 18 | 685 | 685 | 687 | 684 | 688 | 684 | 687 | 4800 |
| 19 | 687 | 685 | 685 | 687 | 684 | 688 | 684 | 4800 |
| 20 | 684 | 687 | 685 | 685 | 687 | 684 | 688 | 4800 |
| 21 | 688 | 684 | 687 | 685 | 685 | 687 | 684 | 4800 |
| 22 | 684 | 688 | 684 | 687 | 685 | 685 | 687 | 4800 |
| 23 | 687 | 684 | 688 | 684 | 687 | 685 | 685 | 4800 |
| 24 | 685 | 687 | 684 | 688 | 684 | 687 | 685 | 4800 |
| 25 | 685 | 685 | 687 | 684 | 688 | 684 | 687 | 4800 |
| 26 | 687 | 685 | 685 | 687 | 684 | 688 | 684 | 4800 |
| 27 | 684 | 687 | 685 | 685 | 687 | 684 | 688 | 4800 |
| 28 | 688 | 684 | 687 | 685 | 685 | 687 | 684 | 4800 |
| 29 | 641 | 644 | 641 | 644 | 642 | 642 | 643 | 4497 |
| 30 | 629 | 627 | 631 | 626 | 631 | 627 | 629 | 4400 |
| 31 | 401 | 400 | 399 | 401 | 398 | 402 | 399 | 2800 |
“Man Babes” #AxelFabulous
April 25th, 2011 at 9:43:15 PM
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Quote: mipletIt is only 400 years for a complete cycle.
You're right.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
April 26th, 2011 at 6:37:51 AM
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Quote: Wizard... So I hope you're happy, I just got back from vacation, have a ton of catching up to do, and I've spent much of the day on this.
Yes, I'm happy that you found the puzzle that intriguing. ;-) And excellent work! It took almost a year for me to get anyone on this forum to give it a try.
Quote: Wizard... As it turns out the kinds of years that happen more frequently have more Friday the 13ths. To be specific, here is a distribution of day of the week by each month in a 2800-year cycle.
Sunday 4809
Monday 4795
Tuesday 4795
Wednesday 4809
Thursday 4788
Friday 4816
Saturday 4788
Note the most common is Friday.
Yes, just as the puzzle suggested as the source of the superstition, the 13th of the month occurs more often on Friday than on any other day of the week. But the cycle of calendars recurs every 400 years, so it is only necessary to look at how often each of the 14 calendars occurs in any 400 consecutive years and how often the 13th of a month occurs on each day of the week in each of those calendars.
Edit: Ooops again! I hadn't seen miplet's and the Wizard's latest posts when I typed the sentence above.
Yes, it's a bit tedious to calculate, but the key is recognizing that there is a cycle in the usage of calendars and that things don't "average out to 1/7 of the time on each day of the week in the long run." If I had recognized that back in 1968 when I first saw the puzzle, I don't know how I would have done the tedious calculations. Back then, I just made the common, erroneous assumption. By the time I figured out how to solve it in the early 1980s, microcomputers were around, and I programmed it in Basic. Later, I discovered spreadsheets.
So it took me ~15 years to find a solution, and the Wizard worked it out on his first day back from vacation. Guess that says something.
April 26th, 2011 at 12:01:17 PM
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Quote: mipletIt is only 400 years for a complete cycle. There are 146097 days in 400 years (365*400 plus 97 leap days) which is exactly divisible by 7.
Here is my 400 year cycle chart for how many dates are on what date.
...
miplet:
Back in the '80s, I was stuck in a commuter traffic jam. In dealing with the boredom, I did that days-in-400-years calculation in my head. When I recognized the "exactly divisible by 7", I knew I had stumbled onto a solution to the old problem and turned to the computer the next day.
Your table, of course, provides much more info than is required by the basic puzzle and exceeds anything I ever generated. Either you are a glutton for drudgery, or you must have a more efficient method than what I used. May I inquire as to your technique?
April 26th, 2011 at 12:27:22 PM
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I've always figured 7 was lucky because it's the winning number in craps on a coming out roll. 13 is generally condiered unlucky because it is the first 2 digit prime number that is unlucky.
April 26th, 2011 at 12:43:46 PM
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Very interesting read. May I ask is this contingent on "Day 1" of your cycle falling on a certain day? i.e. if April 26, 2011 was a wednesday instead of tuesday would your answer be different?
April 26th, 2011 at 1:02:29 PM
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Quote: gogVery interesting read. May I ask is this contingent on "Day 1" of your cycle falling on a certain day? i.e. if April 26, 2011 was a wednesday instead of tuesday would your answer be different?
The answer is that you don't get to choose the day of the week for 4/26/2011. That was determined when the Gregorian calendar was first implemented. If they had shifted the calendar by two days way back then, the 13th of the month would occur more often on Wednesday (or Sunday) than on any other day of the week. But the exact pattern of the 400-year cycle of calendars has been set for centuries, and the way they chose it back then, the 13th falls most often on Friday. We don't get to pick which day of the week we like a date to fall on.
April 26th, 2011 at 1:08:09 PM
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Quote: mipletHere is my 400 year cycle chart for how many dates are on what date.
Column totals would be nice.
April 26th, 2011 at 1:18:07 PM
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Quote: kpColumn totals would be nice.
The 400 years include 146,097 days, or exactly 20,871 weeks. Every day of the week occurs a total of exactly 20,871 times in the table.
April 26th, 2011 at 1:19:41 PM
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20871 for each. edit: I type really slow.
“Man Babes” #AxelFabulous
April 26th, 2011 at 1:49:35 PM
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Quote: DocSo it took me ~15 years to find a solution, and the Wizard worked it out on his first day back from vacation. Guess that says something.
Thanks for the compliment, but it took some correcting by others to get it right. I bet Miplet did it right the first time within 15 minutes.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
April 26th, 2011 at 4:17:40 PM
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Quote: WizardInteresting! I was born on May 23, at 5:23 PM.
Quote: FarFromVegasThen whoever put your birthday into the Wikipedia article needs to go edit...
I updated the Wikipedia article. You were in Hawaii and someone said you were born the same week that I Dream of Jeannie came on the air which was 18 September 1965.
On your birthday the 70th episode of My Favorite Martian was airing in black and white.
The Martian's Fair Hobo
Martin is trying to contact a Martian scouting ship via long wave radio, but in reality he contacts a Earth based rocket - the "Martian Scout". As per central control instructions, Martian Scout states that they should contact Shorty Smith. Martin has no idea what that means (in actuality, Shorty works in space command's Australian tracking station), so looks for a Shorty Smith in the Los Angeles area, thinking that Shorty will be his ticket home to Mars. There is no Shorty Smith in the telephone book, but Martin does find a hobo named Shorty Smith.
