According to your knowledge of mathematics, what is 2010 - 2010?

[ZombieHorde]

You may use a calculator if you wish.

[SemiCharmedQuark]

1. There is no year zero according to the Gregorian calendar, if that is what you are getting at.

It goes directly from 1 BCE/BC to 1 CE/AD.

[ZombieHorde]

2. Then the Gregorian calendar is not based on mathematics.

The Gregorian calendar is strictly a convenient social convention.

[SemiCharmedQuark]

3. It's the social convention that we use.

I don't understand your point. Are you arguing that there *should* be a year 0?

[ZombieHorde]

6. I am arguing 2010 is a new decade because our calendar is based on social convention, not math. nt

[SemiCharmedQuark]

7. Ahh, yes. I see what you are saying.

It's a new decade because most of society regards it as a new decade and since the whole system is based on social convention, this is adequate.

Gotcha

:)

[sendero]

12. And I agree with you...

... as does just about everybody.

[tonysam]

18. It's not. It's the fault of stupid journalists who don't know

that the twenty-first century started on January 1, 2001, not January 1, 2000, and that the millenium started on January 1, 2001, not January 1, 2000.

It's this laziness which drives me up the wall. The first decade of the 21st century still has another year to go before it is over.

[ZombieHorde]

20. No, the 21st century began on 2000.

The calendar has nothing to do with math.

[Raineyb]

25. Thank you.

The argument that we're supposed to accept this faulty reasoning based on what the media, which often can't find its ass with both hands, say is ludicrous.

[ZombieHorde]

28. The reasoning is not faulty, the reasoning is perfect.

You are trying to use math with a system which is not based on mathematics. The Gregorian calendar is merely inspired by math. The Gregorian calendar is strictly a social convention.

A year is not 365.25 days long, but we call a year this length because of social convention.

2010 - 2010 = 0, but with years, we claim 2010 - 2010 = -1 because of social convention.

The Gregorian calendar is just a convenience.

[Jim__]

80. No, a year is not 365.25 days long by social convention.

That's as bad as the congressmen who want to make a law that the value of pi is 3 (this is the implied value in the Bible). But the value of pi is determined by the relationship of the circumference of a circle to its diameter. That's not a social convention.

A year is the length of time it takes the earth to complete one orbit of the sun. That's an astronomical fact, not a social convention. Now 365.25 days is an approximation, but that's an approximation due to rounding.

Yes, language is a form of social convention, so the fact that we use the word "year" to denote the time it takes the earth to orbit the sun can be called a "social convention." But the actual time it takes the earth to orbit the sun is not a social convention; and it is this length of time that people are interested in when designing a calendar.

[ZombieHorde]

81. I realize a solar year is not a social convention, but a solar year is not the same as a

calender year. The calender year is a social convention.

2000 years ago is one day in solar years, but another day in calendar years. The calender is supposed to be based on astronomy, but the numbers do not add up. The Gregorian calender is merely inspired by astronomy.

Now 365.25 days is an approximation, but that's an approximation due to rounding.

365.242199, rounded to the hundredths place, is 365.24, not 365.25.

[Jim__]

83. Once again, you're identifying the calculations you're used to, as a universal rule.

365.242199, rounded to the hundredths place, is 365.24, not 365.25.

It is a perfectly valid rounding procedure to round 365.24<delta> where delta is any digit between 1 and 9 to 325. These are the rounding procedures allowed for the JAVA BigDecimal class (if you browse the class, scroll down to the field definition - I'm not sure if you're used to looking at Java class definitions). They are allowed because different applications want to use different rounding procedures.

Besides all that, the Gregorian Calendar does not specify a year as 365.25 days long. That's only a rough average of the average length in days of a Gregorian year - there is actually compensation for this at 100 and 400 year marks. Ignoring the special cases of 100 years and 400 years, the Gregorian Calendar has a year of 365 days unless the year is evenly divisible by 4 and then it has a 366 day year.

Now think about it. After 100 complete years, then number of days is 365 * 100 + 24 for the 24 leap years, and we know that for the 100th year, it is not a leap year, giving a 100 year cycle of 36524 days or 365.24 days a year. Then for a 400 year cyle we have 36524 * 4 + 1 for the leap year that is the 400th year; which is 146,097 days in the 400 year cycle (with some error factor due to my possible math mistakes), for an average year of 365.2425 days/year.

Notice that by mathematical design, not social convention, the 400 year cycle of the Gregorian Calendar is within .0004 days of the number of astronomical days in a 400 year cycle.

[ZombieHorde]

87. The 400 year rule helps, but the numbers still don't add up.

The Gregorian calender is close to accurate, but the numbers are still wrong.

On a side note, one thing I have learned in math classes is a number is accurate only if the teacher says the number is accurate. 365.2425 can be right in one math class and wrong in the next.

365.2425 is a lot closer to 365.242199 than 365.25, but it is still not 365.242199.

a perfectly valid rounding procedure to round 365.24<delta> where delta is any digit between 1 and 9 to 325. These are the rounding procedures allowed for the JAVA BigDecimal class

JAVA and time are very different things. If a bus comes at 5:24, and I show up at 5:30, I will probably miss my bus.

there is actually compensation for this at 100 and 400 year marks.

Doesn't affect your argument, but technically, the 100 year marks don't factor into leap years.

[Jim__]

89. The bus example is a good analogy.

The real purpose of a calendar is to track time so that we can accurately predict seasons and measure dates from year to year. Given the variables that are present, the length of 1 day (1 solar day), the number of days in one orbit of the sun (there is no exact integral answer to this; and the time is not the same from year to year), and the length of a lunar cycle also factor in.

The Gregorian calendar manages to balance all these variables in such a way, that we may lose a day every 2500 years; but subsecond adjustments are periodically made to account for this, and our easy to use calendars give us an extremely reliable measure of time.

The solution is mathematically accurate to within a predicted error bound. Most measures are only accurate to within a predicted error bound. The error bound here being .0004 of a day every 146097 days is far better than most.

So, in analogy to your bus example, if the measuring device is designed with the understanding that it needs to always be accurate in predicting the arrival of the bus, and the resultant device does this, then it's a successful device, even if it's occasionally, say, predicts the bus 30 seconds before it actually arrives.

As to the number of rounding procedures, different people use different rounding based on their needs. That's why not everyone always rounds using the method that you are familiar with.

Your point about teachers is really a problem with the education system. You should be able to use a reliable method that is accurate for the precision you require. Either the problem should let you figure this out, or the teacher should specifically tell you. Give the radius of a circle, for instance, you can't (in general) figure the exact circumference.

technically, the 100 year marks don't factor into leap years.

They factor into the length of the average gregorian year in days, changing it from 365.25 to 365.24.

[Warren DeMontague]

67. You can argue until you're blue in the face that 1970 was part of the "60s"

you'll still sound like someone with WAY too much time on his or her hands, and I'm not sure what it is you think you'll accomplish.

[Raineyb]

24. No it's not.

I don't care what the social conventions say. They're wrong. We start counting at 1 that makes a decade starts with 1 and ends with 0 making 2010 the end of the first decade of the millennium which started on January 1, 2001.

[ZombieHorde]

27. The Gregorian calendar is not based on mathematics, the Gregorian calendar is inspired by math.

Evidence 1) 2010 - 2010 = 0, yet year 2010 - 2010 years does not equal = 0.

Evidence 2) The solar year is not 365.25 days long, the solar year is 365.242199 days long.

Souce: http://www.britannica.com/clockworks/article2.html

[Ghost in the Machine]

56. When we start counting at 1 it's because we are already at zero...

It's not that hard to understand, really. You don't say a newborn, or a 6 month old, is 1, do you?


Jan 1, 0000 to Jan 1, 0001 = 1 year
Jan 1, 0001 to Jan 1, 0002 = 2 years
Jan 1, 0002 to Jan 1, 0003 = 3 years
Jan 1, 0003 to Jan 1, 0004 = 4 years
Jan 1, 0004 to Jan 1, 0005 = 5 years
Jan 1, 0005 to Jan 1, 0006 = 6 years
Jan 1, 0006 to Jan 1, 0007 = 7 years
Jan 1, 0007 to Jan 1, 0008 = 8 years
Jan 1, 0008 to Jan 1, 0009 = 9 years
Jan 1, 0009 to Jan 1, 0010 = 10 years

What's so hard for people to grasp about this?

:shrug:

[HuckleB]

48. Then we'll need to change all the years since the calendar began, and we're really in 2009.

[ZombieHorde]

51. The calander would still be mathematically wrong because

a solar year is not 365.25 days long, a solar year is 365.242199 days long. http://www.britannica.com/clockworks/article2.html

We don't need to change the calendar because the calendar's purpose is convenience, and it serves this purpose well.

[HuckleB]

74. Duh.

That does not address the point of my post, however.

[ZombieHorde]

75. I thought the point of your post was to make the calender accurate.

If not for accuracy, why do you want to subtract a year from the Gregorian calender?

[Jim__]

10. The Gregorian Calendar is mainly based on astronomy, but also on math.

If you are counting apples, do you start with 0 or 1? The set of natural numbers, {1, 2, 3, ...}, is a perfectly valid mathematical set, and that is the set (with the addition operation defined over it) that is being used for counting years in the Gregorian Calendar.

[HereSince1628]

14. Exactly, more than 1 scale of measurement exists. Folks should read "The Biography of Zero"

Excellent book if you are the sort of person that would post the OP.

Different scales of measurement may limit mathematical operations that can be defined for that scale, but it doesn't make the scales unmathematical.

[ZombieHorde]

21. You have 3 apples. Now remove 3 apples. How many apples do you have?

The answer is 0 apples.

The year is 3. Now subtract 3 years. What year is it? The answer is 1 B.C.

These are two different systems.

astronomy, but also on math

The Gregorian calendar is inspired by astronomy and math, but it based on either. A solar year is not exactly 365.25 days long. The math does not add up. The Gregorian calendar is strictly a social convention.

[Jim__]

79. OK, you have 1 year, now remove a year ... uhhh ... wait a minute ...

0 is not in the set of counting numbers. The calendar is not using the full set of integers that we normally use. But that does not make it mathematically incorrect. The counting numbers, {1, 2, 3, ...} are a perfectly valid mathematical set; and you can define an addition over them - note the set is not closed under the normal rules of substraction. This is easily handled by defining subtraction differently from normal subtraction. This is done all the time for date processing with software. The algorithms are not straight arithemtic processes, they have to handle dates specifically under a date processing algorithm. This is not unusual processing under mathematics where a function can have different definitions for different values of the independent variable(s), and so, different computations have to be run for these different values.

It's not the arithmetic that you are used to, but it is perfectly valid mathematics.

[ZombieHorde]

82. OK, I will accept this argument against my number line argument, but the Gregorian has another flaw.

The Gregorian Calender uses the wrong numbers.

A year is the length of time the Earth travels around the Sun. This journey takes 365.242199 days. The Gregorian calender uses the number 365.25 instead of the number 365.242199, or even 365.24. This means 2000 years ago, accurate math will give us one day, while using Gregorian calender math will give us a different day. The Gregorian calender is not mathematically sound because it does not give us an "accurate reading."

This flaw can be corrected by considering the Gregorian calender a convenient social convention, as opposed to an accurate mathematical tool.

[Jim__]

85. See post #83 above - the Gregorian Calendar has a 400 year cycle - that matters. - n/t

[Unvanguard]

46. That presumes a certain interpretation of "2010."

Namely, the view that it signifies that 2010 years have passed since something.

But in fact it is a counting number: it signifies that this year is 2010 in the count, that it is the 2010th year (since Jesus was supposedly born).

It is based on mathematics. The problem is that you are using the wrong math.

[ZombieHorde]

50. The Gregorian calendar uses the wrong math.

A solar year is 365.242199 days, not 365.25 days. This means the whole basis of the calendar is mathematically incorrect, yet still very convenient for social reasons.

Additionally, 1-1=0 according to mathematics, yet 1-1=-1 according to the Gregorian calendar.

In mathematics, number lines include the number the zero. ...-3,-2,-1,0,1,2,3... In the Gregorian calendar, the number line does not include zero. ...-3,-2,-1,1,2,3...

[Unvanguard]

57. Actually, the modern version of the Gregorian calendar corrects for that.

Not every four years is a leap year.

And you are just confused about the math. True, 1 - 1 = 0. But one year before some time during the first year (year 1) is indeed some time in the last year before (year -1). You're confusing two very different uses of numbers. Your logic would only work if years worked like age, if the year number counted the number of years that have already elapsed since the starting point. But this is not how years work; it is not what their numbers signify. They are counting labels: they are ways to order a set, not measures of a quantity, and can more helpfully be thought of as ordinal than cardinal.

[ZombieHorde]

58. "Not every four years is a leap year."

That sounds interesting, I will have to look into that, but the past dates will still be mathematically inaccurate.

"They are counting labels, like exit numbers on a highway, or street addresses: they are ways to order a set, not measures of a quantity, and can more helpfully be thought of as ordinal than cardinal"

That makes a lot of sense, but aren't labels more of a social convention than a mathematical convention? In mathematics, ordinal numbers include the number zero on number lines.

[harun]

62. Who said it was?

[ZombieHorde]

64. I made two different claims in that post, and I don't know which one you are referring too.

Claim #1 = The Gregorian calendar is not based on mathematics.

If this was the claim you were referring too, then the answer would be those who use math back the claim the year 2000 is part of the 1990s. 1 + 10 = 11.

Claim #2 = The Gregorian calendar is strictly a social convention.

If this was the claim you were referring too, then the answer is ZombieHorde.

[LastLiberal in PalmSprings]

4. The problem doesn't specify dates, just two integers.

Zero. If the numbers are supposed to be dates, your answer is the best one.

[ZombieHorde]

5. The numbers represent numbers, but make a point about dates not being based on numbers.

[Toots]

16. Fourteen full moons

rarely does that happen in a single year. Full moons come every 29.5 days and 2010 has fourteen of them. Most years have only twelve.

[ZombieHorde]

23. Wiccans should be delighted. nt

[LooseWilly]

8. My ads won't let me answer in your poll... but 0 is the answer.

And yes, there was plenty of politics involved in the switch to the Gregorian from the Julian calendar, as I understand it... It was also controversial because it was a part of John Dee's attempts to convert the English system from the old Roman Numerical system to the "new" Arabic decimal system, complete with all that new-fangled algebra... (imagine Queen Elizabeth's poor scribes working out the English Empire's finances using the Roman Numerical System - MMIX = 2009 ... rather than using the "base ten" decimal system invented by the Arabs... and introduced by John Dee... court Magus, and supporter of the "Mathematics" which were, at the time, equated with Satan...)

And by the by... a decimal number system runs from 0-9, then repeats with a numeral prefix (10-19, 20-29, etc.) To think otherwise is to fail to acknowledge both the etymology ("twenty" is more related to "twenty one" than it is to "nineteen"...) as well as the anthropological evidence (of which I'm only passingly familiar) of cultures that use such things as a base 20 number system... in which numbers run 0-19, and then there is a "twenty" with an addition of 0-19...

The notion that the "oughts" began with "ought one" is easy to fall prey to, as "0" = "nothing"... but algebraically it is very significant ("fucking Arabs" :sarcasm:)

[whyverne]

9. I surrender. By popular acclaim, decades run from 9 to 9.

There's no use in arguing or trying to change that fact.

[ZombieHorde]

31. An 11 year decade? Few will go for that. nt

[TheCowsCameHome]

11. Lazio, Italy postal code + 4

:shrug:

[rampart]

13. 1969 was in the 60s .

1970 was in the 70s.

[ZombieHorde]

22. I agree. nt

[ChairmanAgnostic]

29. You sure? It seems even longer ago.

[snagglepuss]

15. Interesting and informative thread. Thanks for posting.

[H2O Man]

17. Other.

It is a measure of time, best used to organize meaninful activity.

[OffWithTheirHeads]

19. It's not Bush

That's all that really matters.

[johnnie]

26. Today is really yesterday...

...until midnight.

[Iggo]

30. What calendar were they using...

...in The Year 1?

In other words, in what year did they decide The Year 1 was The Year 1?

[ZombieHorde]

34. A copy/paste from Wikipedia... (the bold is mine)

The Gregorian calendar is the internationally accepted civil calendar.<1><2><3> It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter gravissimas. The reformed calendar was adopted later that year by a handful of countries, with other countries adopting it over the following centuries.

http://en.wikipedia.org/wiki/Gregorian_calendar

[Iggo]

41. Ah, okay.

So then nobody ever started counting at The Year One.

That shoots down a bunch of these arguments.

Okay (and bear with me, I'm trying to learn here) is a decade a measurement of ten years only counting from zero to nine or is a decade a measurement of any ten years? If I've been engaging in an activity from 1996 thru 2005, can I say I've been at it for a decade? Can decades be arbitrary?

If so, that'd shoot down a bunch of the rest of the arguments, wouldn't it?

[ZombieHorde]

42. A decade is 10 years, but when we start counting decades is a matter of social conventions.

Right now, the decades run from 0 to 9, but in the future, they may run from 1 to 0, or two other numbers.

[Iggo]

44. Sounds good to me.

It goes from zero to nine because we say it does.

[ZombieHorde]

47. Yes. nt

[Vickers]

32. Dumbest. Poll. EVAR. n/t

[ZombieHorde]

36. You don't have to use your calculator if you don't want to. nt

[Vickers]

39. Tell me more about the year Zero.

:rofl::rofl::rofl::rofl::rofl::rofl::rofl::rofl::rofl::rofl::rofl::rofl:

[Ikonoklast]

40. There was panic in it.

Ask Ray Milland.



Here's a scene where Ray and his movie son, Rick (played by Frankie Avalon) do a little shopping at the hardware store, using armed persuasion as a mode of exchange for goods.

[ZombieHorde]

43. You are trying to insert mathematics into a system which is not based on mathemathics.

The Gregorian calendar is not based on math at all, it is merely inspired by math and astronomy.

Evidence 1) 2010 - 2010 = 0, yet year 2010 - 2010 years does not equal = 0.

Evidence 2) The solar year is not 365.25 days long, the solar year is 365.242199 days long.

Souce: http://www.britannica.com/clockworks/article2.html

The Gregorian calendar is strictly a convenient social construct, and therefore, the decades are whatever most people consider them to be in any particular society.

[Vickers]

60. *I'm* trying to insert math?

:rofl::rofl::rofl::rofl::rofl:

Yer funny!

[ZombieHorde]

63. If you are not trying to insert math, why are you concerned about a year zero?

Use logic and critical thinking. Explain your answers. This exercise will help you.

[Vickers]

65. YOU started the thread about The Year Zero!!! YOU used math in the OP!!!

Hey, at least you aren't on the Greatest Page with this ridiculous bullshit!!! I reckon you're at about negative 100 with this pathetic asswipe of a thread!

:rofl::rofl::rofl::rofl::rofl::rofl::rofl::rofl::rofl:

[ZombieHorde]

69. No, you misread and became deeply confused. My thread is not about the year zero.

My thread contrasts mathematics with the Gregorian calendar to demonstrate the fact the Gregorian calendar is not based on mathematics. Do you understand the difference?

I stated you were trying to insert math into the Gregorian calendar, which is different than using math in other aspects, such as an OP. Do you understand the difference?

Mathematics and calendars are two different things. Do you understand the difference?

[Name removed]

71. Deleted message

Message removed by moderator. Click here to review the message board rules.

[Onceuponalife]

33. Major OP FAIL on this one

You're giving atheists a bad name. Not to mention zombies.

[ZombieHorde]

35. Explain your logic. nt

[Onceuponalife]

77. It's been explained by many posters here

You just aren't listening. (Hint: it has to do with counting 1-10). That's counting, not mathematics. If you tried to dazzle us all with boring lectures about the Gregorian calendar, you failed.

[ZombieHorde]

78. Do you believe the Gregorian calender is based on mathematics,

and if so, do you believe the mathematics involved are accurate?

[caitxrawks]

37. o.o zeeee....ro?

Is this a trick question? I'm scared.

[lunatica]

38. When you start counting you never start with zero

"If you don't stop that in 3 seconds I'm stopping the car right here and now!" "One....", "Two...", "Three..."

See parents never start with "Zero..."

[ZombieHorde]

45. Does not matter. You can start with the number 7.3 and the decades would still be 0 to 9.

The Gregorian calendar is not based on mathematics, it is strictly a social convention.

[lunatica]

49. A decade is 1 to 10 or 15 to 25

ten years. When someone says 'for a decade' or the 'in the last decade' they're talking about a ten year period or the last ten years.

[ZombieHorde]

52. I agree when considering "a decade," but the year 2000 is not a part of the "90's."

This is what I was trying to claim.

[Mari333]

53. well according to Quantum Physics there is no 'time' so its a moot point

[ZombieHorde]

54. Well obviously the Gregorian calendar is not based on quantum physics. nt

[Mari333]

55. I know, the sillies....

:P

[REP]

59. 2001, the first movie. Duh. 2010 is the sequel

[ZombieHorde]

61. Sci-Fi authors were overly optimistic about our developing technology.

[Vickers]

66. It was called 2001 because the person who wrote it KNEW the next century

started in 2001.

DUH!

[ZombieHorde]

70. Why do you believe the century started in 2001? Can you explain your logic? nt

[Name removed]

72. Deleted message

Message removed by moderator. Click here to review the message board rules.

[ramblin_dave]

73. The logic is simple but depends on what is meant by "the century"

We have two ways of designating centuries.

One way is by enumerating them - 5th century, 18th century, etc. The first century AD was from year 1 to year 100, the second century was from 101 to 200. This leads logically to only one conclusion: the 20th century was from 1901 to 2000 and the 21st century started with 2001.

The second way is based on the the first two digits being the same - the 1600's, the 1900's, etc. The 1900's would be 1900 to 1999. Note that the 1900's is not one and the same as the 20th century which is 1901 to 2000. The two time spans are shifted by one year relative to each other.

These two ways leads to confusion if you don't explain what you mean by "the century".

[GreatCaesarsGhost]

68. i don't know, but 2010 is on at 8.

tcm est.

[Igel]

76. Let's assume it's just a social convention.

Not that social conventions and mathematics are obligatorily mutually exclusive.

Math was used to formulate the decadal system and the calendar. Just not the math that you want to apply. This is specious. If you don't understand, don't assume. It looks foolish.

Now, actually using this particular math is a social convention. We didn't need to use tjos math. We did for a long time. However, language provides labels, and we can find useful ways to generalize from those labels and form social conventions from that generalization. Then it's possible to actually use *both* conventions and for them to interact badly. That's abstract. Let's exemplify it.

English counts using simplex numerals from 1-10. At 11 it looks simplex, and is. But historically it's "one left over"--you count using your fingers and if there's one left uncounted you've got 11. 12 is "two left over". Apparently "three left over" was a bit much for the Common Germanics, so it's "3 added to 10", threotene or some such form, which we've inherited as "thirteen". Same for 14-19. That "tene", now "teen", is handy. We generalize 13-19 and get teens. Translating "teenager" to other languages is a bitch because the word is based on a peculiarity of English, one that most languages don't have and we only have because some people living in N. Europe in 500 BCE decided to count 11 and 12 oddly. Still, having "teens" is a useful social convention, at least in English. I asked my wife earlier today if she thought of 18 and 19 year olds as teenagers. She knows a bit of semantics, and they're not prototypical teenagers. She said "no, not really". Then she said they are anyway. That sums it up nicely.

We have another convention. At age 18 you become responsible for yourself. You can marry at 18 and 19, own property, do all kinds of things. You're not a minor anymore, you've reached your majority. Or, since that's a bit old fashioned sounding, you're an adult.

So a couple of years ago the CDC published the teen birthrate and noted a spike in infants born to teens in the US. It was easy to assume that meant out of wedlock births, but it didn't; it was easy to assume it meant "babies having babies," but it didn't. Enough 18- and 19-year-olds married and had kids (whether or not conception occurred pre-nuptials is beside the point) that it made for misleading statistics. The category "teen births" had to be kept for practical reasons. The prototypical teen should not be having kids because that, statistically, had nasty correlations with future problems for the kids; to say that a married 19-year-old woman shouldn't have kids is a stretch, the correlations fail to hold so neatly. Still, it's usually a useful convention to track things by teen versus 20s. And usually better than using the minor/adult classification. Two conventions, and the usually useful one failed to be useful briefly.

So we can have two conventions in use at the same time to cover the same ground. One is rooted in something other than informal social conventions--the minor/adult distinction is grounded in law--and the other is rooted in superficial linguistic forms (note that the legal one is still a social convention, but not as quirky as the language-idiosyncratic idea of "teens").

Let's look at time.

First, we enumerate things. I have 3 apples, let's say I number them in the order I received them, apple 1, apple 2, apple 3. (We don't do this with ages, but who needs consistency?) Let's say I'm hungry. If I eat 3 apples out of the 3 (eating the 3rd first, the 2nd second, and the first last), i.e., 3 - 3, I have zero apples. Crucially, I do *not* have apple 0 after eating my three apples. I'm subtracting things and counting what's left; I'm not subtracting numbers. Oddly, try this: 3 - 2.5. What do I have left? Half of apple 1. So I still have something I can point to and say "this is apple 1, my first apple." I do not say I have "apple 1/2". If it's easier, think of "apple 1" as a formal way of writing "first apple", "year 2010" as writing "two thousand tenth year".

I could write "QED" and stop. There's math involved. Just not your math. Using it is a social convention, of course, and I'm not done with this in any event. Not by a long shot, because there's a useful social point to be made after all the falderol about social conventions and mathematics.

When I have no apples, I have no apples. If I extend it to years, it's "2010 years - 2010 years", so I don't have year 0. I have zero years. Zero years at the most? Isn't that a bit nonsensical? Time existed before year 1, surely. But time doesn't come in discrete units that started at 12:00 a.m. in 1/1/1. But let's keep using apples.

If I have 0 apples and suddenly want to nibble an apple I can borrow one. Do I call it apple 0? No. It's an apple owed. I'm in the hole for an apple. If I'm going to document it, number it, list it on my fruit ledger, it's apple -1. Whether all or part is consumed, it's apple -1 that I have, that I owe back to somebody. There is no apple 0, unless I'm in a computer science class or otherwise indexing numbers consciously trying to label my first 10 apples using just one digit. (Then I'm also likely to count 8, 9, a, b, c, d, e, f, as well.)

Shifting back to time, if I'm at a hypothetical 12:01 am on 1/1/1 and want to move back to that moment just before midnight, where I'm forced to be if I force the clock backwards to remove every last bit of year 1 (since time is continuous, or at least appears so in normal life), where am I? I'm before year 1 but I'm still in a year--I haven't fallen out of time--and so that year has to be counted. I don't count 0, as a rule. It's the same as with apples: I'm a bit in the hole, taken a bite out of a piece of time not in positive territory. If 1 is "common era", the first year of the common era is year 1, then I've moved to "before common era". Simply because I'm counting things. If 12:01 a.m. on 1/1/1 is year 1 because it's in year 1, then the 11:59 p.m. 2 seconds earlier has to be 11:59 p.m. on 12/31/"-1" or 1 BCE/BC. 0 is where there is no time and, because of the nature of reality (one tends to choose one's math to suit what one's modelling), there is no point at which I can say, Aha, zero! Unlike when I can say I have no apples.

0 is what you have, the quantity you have, when you have none. But after moving a fraction of a second before 1 CE/AD starts I'm still in some year. And that year gets counted. That's the way *that* kind of math works. In all fairness, numbering things 0 really is a recent kind of thing. And, think about it: if you number your first apple "apple 0", then if you take away that apple you get nothing. You'd probably want to write it "0 - 1 = 0".

So the lack of year 0 isn't a problem. It's entailed, actually, by the way we number things. And that nasty 0 - 1 = 0 business. (Yeah, I know it's mixing different kinds of terms as though you could perform a mathematical operation on them, but it's funny to look at.)

Let's keep going. Now, it's a social convention to group years in sets of 10. That's a decade. A trite definition, to be sure. Let's assume that we start with 2010 as the first year in a decade. It's not hard to see that 20 is two decades, 200 is 20 decades, and 2000 is 200 decades. So if 2010 starts a decade, we zap out 200 decades and wind up with the year 10 starting a decade. No problem, in principle.

Do we want to exhaustively include all years in decades? I mean, what about the "rump" years of 1-9? They're not a decade; they're a nonad. Do we have a social convention that we start grouping the years into decades from 1 or from, say, 2010? Which do you want to do *mathematically*? I'd start with 1 and count exhaustively. Then 2010 ends a decade, because the first decade was 1-10. A lot of people like that convention. It's simple: you start counting and every 10 you say, "Ah, the end of a decade." If we do that, though, saying 2010 starts a decade *is* a problem. It's a useful social convention because every year is in a decade, with no 9-year decades there to screw up the count. (I mean, if the first decade is odd, why not the 198th? Then 2009 would start "the" decade.)

On the other hand, just as we have oddities with "teens" based on the superficialities of language mapping in some useful way with adolescence and adolescents, so we have our numbering system where 20s, 30s, 40s, 50s... all form neat kinds of similar units. And, not accidentically, they're all decades--units of 10, and all based on the penultimate digit in the year designation. They form a handy class. All of the "nulevye" in Russian, all the "zeroeths", for instance; the "ninetieths", i.e., the '90s. Russian's consistent because you can just as easily talk about the antepenultimate digit and refer, say, to the eight-hundredths (i.e., the 1800s) or use two digits and refer to the eight-hundred-seventieths (1870s). It's a handy social convention. Russian nicely has "10ths", so they can refer to the period of, say, 2010-2019 in a consistent way (they don't have the eleven/twelve vs. 13-19 split in linguistic form). English doesn't handle those numbers consistently, so that's going to be interesting: Will 2010-2019 be the "pre-teens" or "tweens", while 2013-2019 are the "teens"? Will we oddly refer to 2010-2019 as the "tens"? (Note that we skipped from the "gay '90s" to the "roaring '20s" probably not by accident, lacking handy terms for 1900-1919.)

Of course, this is a *different* social convention. As with the teen/20s versus minor/adult contrasting conventions there are two distinct and competing conventions or definitions at play here.

The question that's usually posed is infelicitous, the word used in discourse pragmatics for "ill-formed" or, well, improper: "When does *the* decade start?" That "the" presupposes that we have a common frame of reference, that we know that "the decade" refers to even as we ask what it refers to. It, in this case, presupposes that we have the same definition, i.e., the social convention, in play. But there are two. One starts decades at year 1 and insists that all years be part of a well-formed decade, the other bases decade division on surface linguistic forms or a labeling scheme forced by decades that can be easily so labeled.

The question imposes an absolute unity on an obvious dichotomy, and forces a "if you're not with me you're against me" mentality that's inappropriate. Then it compels us to try to force reason and things like mathematics to rally to our side, as though forcing things that way made any kind of sense. Really, "2010 - 2010 = 0". (Even look at your graph: ok, 0 to 1 is the first unit greater than 0, 0 to -1 is, I guess, the -1th unit, the first unit less than zero--now, find me the zeroeth unit, the one, I guess, between 0 and -0? Yep, as though forcing things that way made any kind of sense.)

For some purposes, by one social convention, 1990, i.e., 12/31/1990, concluded the decade that began on 1/1/1980. For other purposes, by a different social convention, 1/1/1990 started the decade that (presumably) started the decade that ended on 12/31/1999.

Without context, without definitions and some background, there is no "the decade". It's a bit like like talking about "Dave"--surely you know one and when I say, "Hey, did Dave call you?" a particular Dave comes to mind. If I continue, "If he calls again, tell him and his wife Carmelita hi and ask if he still has a viszla" it's likely to be a bit jarring. It's improbable we know any of the same Daves. It would be silly to assume we have some "shared Dave."


Arguing about which is the One True Social Convention is pointless, as well--it's like asking which of us knows the "real" Dave. We live with the quirkiness of acting like teenagers are all minors yet being forced to call an adult 19-year-old a teenager. And yet most people are convinced that *their* social convention must necessarily be everybody else's social convention.

Diversity's fine, and to be encouraged, as long as we're all of my opinion.

Meh.

[ZombieHorde]

84. An excellent argument against my number line argument. Now consider this...

Let's pretend Dave owns a store and every day Dave receives a shipment of 24 apples. Dave doesn't like to work with the number 24 because he believes the number is inconvenient and he hates the show. Dave decides will call his 24 apple shipment a 25 apple shipment in his books.

After one week Dave has no apples and he decides he wants to figure out how many apples he has sold versus how many apples he has wasted. Dave, and his wife Carmelita who runs the store's bakery, look over the books. They both decide the store sold 162 out of 175 apples.

"We only wasted 13 apples," says Dave.

"A mere dozen, not bad at all," says Carmelita.

"You are mistaken Carmelita, we wasted 13 apples, not a dozen apples."

"Thirteen is a dozen."

"Maybe for stupid bakers."

"You Asshole! Ahhhhhh!"

"Ahhhhhh!"

Dave and Carmelita did not actually waste 13 apples. 24 * 7 = 168. They actually wasted 6 apples.

The married couple fought over the definition of the word "dozen," which you basically addressed already in your reply, but the couple did not have 13 wasted apples, they were fighting over imaginary apples due to using the wrong numbers in the mathematical equations.

A solar year 365.242199 days long, but the Gregorian calender claims a solar year is 365.25 days long. "Gregory" used the wrong numbers in his "books."

Dave claims 12/31/2010 is the last day in the decade.

Carmelita claims 12/31/2010 is the last day of the first year in the decade.

Neither are technically right. The math does not add up. Many or most of us know the numbers are not completely accurate, but we use the numbers anyway. These false numbers are really convenient. To me, this means the Gregorian calender is more of a social convention than a mathematical convention. We know it is wrong, but we use it anyway.

[ramblin_dave]

86. The Gregorian calendar is not based on a year being 365.25 days

In fact the Gregorian calendar replaced the Julian calendar that assumed a year was 365.25 days long and which added a leap day every 4 years. Under the Gregorian calendar the convention for determining leap years is more refined as explained here...

http://en.wikipedia.org/wiki/Leap_year

The scholars working for Pope Gregory did not get their numbers wrong. The leap year adjustments instituted by the Gregorian calendar will work for a few thousand more years without any further adjustments.

[ZombieHorde]

88. The numbers are wrong, but the 400 year rule does help considerably. nt