# Mine goes to 11 11 11

By Phil Plait | November 11, 2011 1:11 am

Geeks across teh intertubez are giddy with delight today. Why? Because it’s November 11, 2011, of course! And if you’re in the US, you’d write this as 11/11/11, so of course this tickles the heart of any true mathematically-inclined nerd such as me. now, in the US we put the month first — MM/DD/YY — which is somewhat silly; in England and other realms they write it more logically with the units getting bigger left-to-right, so for them it’s DD/MM/YY, or, contrary to us yanks, 11/11/11.

OK, so anyway, it’s all ones. Why is that cool?

Well, it just is. Duh. But deep down, this goes to the root ("root"! HAHA! Oh man, I’m a math riot) of how we count. And I am never one to miss a chance to lecture on nerdalicious topics, so stick with me for a bit.

The power of ten compels you!

On the web, which consists of 87% dorks (look it up!), this date is special because it looks binary. For those of you unfamiliar with this, we humans tend to use the number ten as the basis of our counting. Our numbers reflect this: we break things down into powers of ten when we write out a number.

For example, the number 1234 — one thousand, two hundred, thirty-four — has four digits, each representing a power of ten. On the right, we have the "ones" place, where 1 = 100. For our example, there are four of them.

Next, moving left, is the "tens" place, and 10 = 101. For 1234, we have three tens, or thirty.

See how this works? Next is the "hundreds" place, and 100 = 102. Two of those is two hundred.

Last, all the way to the left is the " thousands" place, or 103. We have one of those, for one thousand.

Add ’em together, and you get 1 thousand, 2 hundred, thirty four. This is actually a very clever way to write down a number. Compact, efficient, and makes simple arithmetic possible. It’s not that hard to learn how to add fairly large numbers in your head due to this notation. Try that in Roman numerals!

An important note: we use single digits to represent numbers from 0 – 9, then two digits for 10 – 99. Obvious, right? But if you think about it, you’ll see there’s a reason: you don’t need a one digit numeral for "ten", because it has its own column. Counting up from 0, once you reach the base number of ten you just put a 1 in the next column to the left and a 0 in the column on the right. Simple, neat, and efficient.

I’d even say it’s a brilliant innovation in notation, and is what allows us to represent huge numbers simply. Roman numerals use symbols for certain numbers, and you just mash them together to represent a bigger number (sometimes subtracting them, too, which is truly awful). Our number 1234 would be MCCXXXIV, which is unwieldy. And adding a number to that is completely nonintuitive. It’s more like a code than a system of notation for numbers. Our current method is way, way better. In fact, I’m not really sure why Roman notation is even taught anymore. Seriously, who needs it? Movie copyrighters and SuperBowl fans. That’s about it.

All your base are belong 2 us

But it turns out, you don’t have to use base 10. We have ten fingers, so it’s somewhat natural for us. But in fact other bases are possible, and sometimes even preferred. Like binary.

Binary is the simplest system. It’s base 2. So when you write a number, you use powers of two in the places, not ten. So the columns go from right to left like this:

20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32

and so on. You can only use a 0 and 1 in this case, and that makes sense. Why? Because, like base 10, you use a two-digit numeral to represent your base. What we think of as "2" in base ten becomes 10 in binary. It’s the base to the power of 1, just like it is in base 10 (which is called decimal, by the way). I’ll add that when you use the number 10 in decimal you call it "ten", but when you use 10 in binary you call it " one zero" to avoid confusion. If you call it "ten" then all the math people will laugh and make fun of you, and not invite you to their Star Trek marathon*.

In binary, just like in base 10, we add the columns together to make a number. So let’s pick an arbitrary number, like 42. If we look to the powers of 2, we see it’s 25 (32) + 23 (8) + 21. So we’d write it in base 2 as 101010. You have to put in the zeroes as place holders, or else you can’t see what power is what. But that makes sense: it’s 1 x 25 + 0 x 24 + 1 x 23 + 0 x 22 + 1 x 21 + 0 x 20: 101010.

It may seem more cumbersome than base 10, since 42 is only two digits in decimal but 6 in binary. True, but it’s really easy to represent numbers in base 2, since a 0 and 1 can be represented in lots of ways, like an arrow pointing up or down, or a section of a DVD with a tiny laser-burned microscopic pit or no tiny laser-burned microscopic pit, and so on. Anything that exists in two states (on/off, filled/empty) can be used to count in binary. Electric circuits do that, they can be made small and fast, and hey, don’t computers run on electricity?

So yeah. That’s why binary is used in computers.

Will you still need me, will you still feed me, when I’m sixty-three?

And finally, that brings us back to the date! November 11, 2011 is 11/11/11 or just 111111. And that looks like a binary number!

So what is binary 111111 in decimal form?

It’s 1 x 20 + 1 x 21 + 1 x 22 + 1 x 23 + 1 x 24 + 1 x 25 = 1 + 2 + 4 + 8 + 16 + 32 = 63.

That’s just one less than the next higher power of two, 64 (26). In binary, a number full of 1s is like a decimal number full of 9s. Add one to it, and you bump up to the next power of your base.

And that’s why some dorks people think today is cool. It’s the last binary number this year, and in fact we can’t get another date that looks like a binary number until 01/01/00, or January 1, 2100! That’s the first day of the last year of the 21st century. It’s a long wait.

And? That date will be 010100, or 20 in decimal.

I don’t know if people will hold binary parties tonight (you can either go or not go) or how they will celebrate — one person on Twitter said he’s getting married today, and I have to admire that — but for me, it’s just fun to think about the numbers.

But then, I’m a dork too.

The Ramans do everything in threes…

So I’ll leave you with a quiz. Base 3 (called ternary) is fun as well, and I don’t want to leave it out!

In base 3, you can use the numerals 0, 1 and 2. As it happens, today’s date consists of those numerals! So we can write out our entire date in ternary, including the full year: 11/11/2011. I ask you: what’s that in decimal? (Those of you who are in other parts of the world, where you’d say it’s 2011/11/11, you’re invited too). You could cheat and look it up online, but that’s no fun. Being a dork means doing it long hand sometimes!

And fun fun fun, as it happens, that ability to use a 2 means more dates in ternary are coming soon. So here’s a semi-trick question: when’s the next all-ternary date?

And, of course: Happy binary 63 day!

Image credits: The Flickr streams of Kichigai Mentat, Joe Shlabotnik, goldberg, and sgilliesm all licensed under Creative Commons.

* Spare me the nerd rage, please. I’ll be watching Stargate.

OK, so it’s not arbitrary. It’s a pronic number!

CATEGORIZED UNDER: Cool stuff, Geekery

1. » Happy 63 (binary) day :: Granite Geek :: NashuaTelegraph.com | November 11, 2011
1. Aaron

Anyone else feel a sense of loss knowing 2013 will eventually happen?

2. Teaching Roman Numberals

I think when they teach Roman Numerals they should teach their origin. ie. representation of numbers with fingers. You can count to 99 with your fingers using a system similar to them, with out the strange minus notation.

3. Javier

“I’ll add that when you use the number 10 in decimal you call it “ten”, but when you use 10 in binary you call it ” one zero” to avoid confusion. If you call it “ten” then all the math people will laugh and make fun of you, and not invite you to their Star Trek marathon”

I do use “ten” for ’10’ in binary. Also, “f-ty-five” for ‘F5’ hexadecimal ( or “d-hundred-and-e-ty-six” for ‘DE6’). Star Wars fans do it this way.

PS: 11/11/2011(b3) = 3298(b10)

Next ternary date? Tomorrow: 12/11/2011 (4027) or 11/12/2011 (3379) in USA.

4. Patrick

“So here’s a semi-trick question: when’s the next all-ternary date?”

Tomorrow: 11/12/2011

5. Messier Tidy Upper

Thanks BA – well written and noted.

Over here in Oz it’s been ’11 / 11 / 11 for nineteen hours already.

6. Brian

So yeah. That’s why binary is used in computers.

That’s certainly one reason, but I personally would say that the real reason binary is used in computers is that binary has the simplest processes for doing basic arithmetic. The times table, for example, has only four entries (instead of 100 for base 10), and it couldn’t be simpler: 1×1 = 1, and everything else equals zero. Imagine a world where you never have to carry when doing long multiplication! (Well, except that you have to do carrying in the final stage where you add all the partial products. But still.)

In short, using binary is a trade-off of having simpler recipes for doing math at the expense of having more digits per number — a trade-off that pays out very well indeed.

7. KimS

Actually, in the UK we write dates DD/MM/YYYY – so it’s technically not all 1s for us, as it’s not usual to leave out the 20 in 2011.

8. Great article.
One comment though about the briliant innovation of power of ten counting. Even though this is indeed very handy and neat, there are still languages that mess it up.
In almost all languages the number ‘1234’ is also read out from left to right. But in some languages such as my own Flemish, but also Dutch and German for instance, this is read out as ‘1243’. In short, we say “four and thirty” instead of “fourty-three”. Illogical, but then again, who ever said language was logical?

9. Oded

In my timezone – http://twitpic.com/7czu0h

10. Other Paul

Speaking from UK, I’m not so sure that the the US practice of putting the month before the day, to form a date, is as daft as it looks. It’s all a matter of context. Within a year, month first then day makes date sorting (with two digits each) easy and natural.

Having the most significant component on the left – as is done with positionally notated numerals – makes alphabetical sorting a breeze – providing you left-pad adequately with zeros of course. The same argument would obtain in languages reading right to left, if dates were also rejigged. [Not sure about in ancient greek boustrophedon, but there you go].

It’s when you add the year that it goes pear-shaped. Of course you should have followed the pattern and pre-fixed, rather than suffixed it. Then you’d’ve ended up with the eminently text-sortable ISO 8601 standard yyyy-mm-dd before the Swedes and way ahead of anybody else.

Who knows – had you done that, you may even have ended up dominat .. ing … the … plan … oh, wait.

11. Damn, someone beat me to the answer.

@Sereniteit Yeah, it’s the same in Afrikaans and also presumably Dutch.

12. DrFlimmer

11/11/2011. I ask you: what’s that in decimal?

3298

when’s the next all-ternary date?

Yeah, that would be tomorrow.

13. JB of Brisbane

Don’t forget, the USA gave us, for example “November 11″ or November 11th”, whereas it was more fashionable in the rest of the English-speaking world to say “the eleventh of November”.
Or am I mistaken?

It’s even better, at 11:11:11 11/11/11 it’ll be 4096 second.

Also next year we’ll have 12:12:12 12/12/12 and that’s the last datetime like that this century.

15. PayasYouStargaze

There are 10 types of people in the world, those that understand binary and those that don’t.

I’ll get my coat.

16. Other Paul

@JB:

The USA also gave us Niney-Leven. Elevenine would be – poetically – more appropriately sombre.

17. Bigfoot

And why do vulcans have pointy ears? So they can count to twelve.

18. Nigel Depledge

The BA said:

So let’s pick an arbitrary number, like 42

OK, so it’s not arbitrary. It’s a pronic number!

It may well be a pronic number (in decimal notation at least), but it is non-arbitrary for a much more significant reason – it is the Answer to the Ultimate Question of Life, the Universe and Everything.

Incidentally, in base 13, 6 x 9 = 42.

Just sayin’.

19. Don F

And because we use a 12-hour clock, we get to have 11:11:11 11/11/11 TWICE!

(We will be listening to Spinal Tap at the second occurrence of 11:11:11 11/11/11.)

20. Unashamed

@Bigfoot: to thirteen.

21. I’d also like to point out that our base 10 number system is also called denary.

22. PayasYouStargaze

Why do mathematicians confuse Halloween and Christmas?

Because 31 Oct = 25 Dec.

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I’m really going now.

23. KimS

@ JB – yes, I’d never say ‘it’s November eleventh’ if asked the date, I’d always say ‘it’s the eleventh of November’ (modified with the actual date, of course!). The only time that wouldn’t happen was if I were referring to the events of September Eleventh, which is now more of a title than a date.

We have our own 11 11 11 every year in the UK as it’s Armistice Day and we have a two minutes silence on the eleventh hour of the eleventh day of the eleventh month, to commemorate our war dead. I think you do the same thing in the US, though, as well as NZ and Australia and most of Europe?

24. Jeremy

I would have to argue that YYYY/MM/DD makes the most sense, at least for sorting purposes. I’ll often just do YYYY/MMM/DD though to avoid any confusion at all (ie. 2011-Nov-11)

25. Tarrkid

“The Ramans do everything in threes…”

Greatest. Final. Sentence. Of a book. Ever.

26. Pete Jackson

Happy XI/XI/XI

27. Pete Jackson

@PayasYouStargaze: And 34 Sept as well!

28. Musical Lottie

Wow, if any of my maths teachers had explained binary as being base 2, I’d have understood it – instead, I got a D when we did a module on binary at the age of 11 or 12 (and now I’m no longer ashamed to admit it). But it’s so simple, thanks Phil!

29. Mike Torr

I think that 42 in binary being 101010 is doubtless the origin of the words “And i-o-i-o-i-o by priest and people sungen” in the carol “Ding Dong Merrily On High”. 😐

Also I think yyyymmdd should be adopted by the entire world. But then, I also think that clocks should have 0 instead of 12 on them, that an octave should be called a heptive, the inside lane on a road should be the outside lane etc. etc. Maybe it’s just me, but so many of our conventions seem so illogical! Captain.

I notice nobody has commented on Phil’s controversial (yes it is, I’m sorry!) assertion about centuries. The only reason to say that a century ends on Dec 31 ’00 instead of Dec 31 ’99 is that you must believe Jesus Christ was born around the start of 1AD. In other words, Christians have a good reason for adopting the rather ugly “99 and the following 00 are in the same century” convention – but not atheists, who, I submit, should be opting the elegance of letting the century begin when the digits tick over. Why not? 1AD to an atheist (or indeed, a non-Christian of any kind) is just a year like all the others…

30. Erik

May I humbly recommend the date format recommended by the International Organization for Standardization, called ISO 8601? Today’s date is:

2011-11-11

Using the standard has several advantages:
1. It is unambiguous, whereas DD/MM/YY and MM/DD/YY can get mixed up easily.
2. There’s no confusion with century.
3. Files named by date are automatically sorted in chronological order.
4. The date string is always the same length, making it easier for the eye to scan columns of dates.
5. All numbers are in descending order: Millennium-century-decade-year-month-day.

31. Joe G.

There are 10 types of people in the world: Those who understand binary and those who do not.

32. PayasYouStargaze

@18 Pete Jackson:

But isn’t 34 Sept just 4 Oct?

@21 Joe G:

Too late. I made that joke in comment 10. (That’s comment ten not comment two)

33. Bill3

@Mike Torr

I don’t think the rationale for the centuries ending and beginning when they do has to have any religious connection. It’s the simple fact that we begin counting at 1, rather than at 0. Centuries have 100 years – you’d be shorting the first century 1 of its years if you claimed the year 100 was in the 2nd century.

If you had 100 apples and were asked to number them, would you number them 0-99 or 1-100?

I don’t believe it’s controversial, I just think there are people that count wrong.

34. Kato

I was planning on picking apart some completely nonsense claims in this article but it turns out my phone was not properly rendering the “power” notation so I was seeing this: “Next, moving left, is the ‘tens’ place, and 10 = 101.”

Anyway, today is also Nigel Tufnel day. “Look, look, who’s in here? No one!”

35. Pete Jackson

@22PayasYouStargaze: Yes, 34 Sept is indeed 4 Oct. It’s called buffer overflow.

36. Digital Atheist

For you, it may be 11/11/11, but for me it is 11NOV11, or 11NOV2011… 😉

37. IW

“Binary is the simplest system’

It’s not as simple as unary….

38. How is writing bigger left to right logical? Standard numbering has it bigger right to left. take 2011 for example, 2 is 2000 which is the bigger unit, and it goes big to small, left to right, so I tend to write my dates in this order: YYYYMMDD.HHMM. That way it looks like a stardate 😀

39. Dunc

Happy binary 63 day!

AKA Nigel Tufnell Day.

I personally would say that the real reason binary is used in computers is that binary has the simplest processes for doing basic arithmetic.

That’s certainly a useful point, but I would say that it’s really because anything other than binary is a real bitch to implement electronically. It’s very easy to implement binary with a transistor, or even a valve – anything below a set threshold is 0, anything above it is 1. Ternary or higher is very much more difficult to implement, requiring multiple logic elements and threshold values.

And why do vulcans have pointy ears? So they can count to twelve.

If you know your 12 times table, you can count up to 156 on your fingers – count each phalanx on the fingers of the right hand as ones (using your thumb as a cursor) and each phalanx of the left hand as 12s.

40. Mike Torr

@Bill3 – I don’t dispute what you say. I think we just have different values I value the “tripping over” of the digits to a new hundreds value higher than I value the fact that a multiple of a hundred years has passed. Hence, I prefer to begin at 0.

I would count the apples from 1 to 100, obviously: but apples are not like years, because I started with no apples. Years extend back way further than our species, so are as good as infinite in their previous extent.

Everyone’s different, and I don’t say others are wrong, but I do stand by my statement that it’s controversial

41. Dunc

@27: Also, if you use a year-month-day date format, it sorts alphabetically into date order. Very handy.

42. Anne

I thought it was a spinal tap reference.

43. The Lonely Sand Person

11112011 in ternary is 3298 in decimal.
The next ternary date is tomorrow!

44. Tara Li

The current date can also be interpreted as a trinary number – so *TODAY*.

45. Atheist Panda

And there I was, thinking I was the only person who did this sort of thing…..
I remember working nightshift on my 25th Birthday, and watching the digital clock in our crew room, as the time displayed was 01:23:45 6/7/89, (GMT).

AP

46. STEVE

But what happened 1/9th of a second after 11:11:11 this morning?

47. I was a bit saddened to see no mention of Nigel Tufnel day, but the Arthur C. Clarke quote definitely earned a cheer from me!

48. Forget 11:11:11 on 11-11-11.
Some 45 minutes ago it was 1111:11111 on 11-11-11 😉

49. An oldie, but a goodie: There are 10 types of people in the world… Those who understand binary, and those who don’t. Edit: (Darn. Joe G. beat me to it.)

But deep down, this goes to the root (“root”! HAHA! Oh man, I’m a math riot) of how we count.

A math joke, or a Unix joke? (Or was it both?)

Anything that exists in two states (on/off, filled/empty) can be used to count in binary.

I thought it was TRUE, FALSE, and FILE_NOT_FOUND?

50. Crosis101

Interestingly enough, you mention that we have ten fingers, which makes counting in base ten easy.

in Childhood’s End by Arthur C. Clarke the Overlords have 5 fingers on each hand and two thumbs. One of the main characters remarks, “I am thankful for our ten fingers and toes…the concept of thinking in BASE 14 makes my ehad hurt” Also thank you for explaining a concept that didn’t make a lick of sense to me in High School.

Secondarily, in the US, the US Armed Forces do use DD/MM/YYYY notation and a 24 hour clock. In the US that has become known as “Military Time”

51. gdave

@KimS:

In the U.S., “Armistice Day” is now Veterans’ Day, to honor U.S. veterans of all wars. Services are still usually held at the eleventh hour of the eleventh day of the eleventh month, though. In fact, as soon as I’m done typing this, I’m off to a local national cemetery to attend Veterans’ Day services.

52. Chris

@34: Your text bought back memories of my childhood. I was a bit too young to see any relevance in 5/5/55 but I do remember vividly my excitement at being able to write 6/6/66 in my school excercise books and of clock watching that very evening a little after 6pm.

53. DrFlimmer

@ KimS

We have our own 11 11 11 every year in the UK as it’s Armistice Day and we have a two minutes silence on the eleventh hour of the eleventh day of the eleventh month, to commemorate our war dead. I think you do the same thing in the US, though, as well as NZ and Australia and most of Europe?

Interesting. In Germany on 11.11. (the German way to name dates) at 1111hours the fifth season begins, i.e. carnival. So, here is nothing like a mourning the dead… here the crazy folks begin to party for the next 3 months or so.

54. Nigel Depledge

Mike Torr (29) said:

I notice nobody has commented on Phil’s controversial (yes it is, I’m sorry!) assertion about centuries. The only reason to say that a century ends on Dec 31 ’00 instead of Dec 31 ’99 is that you must believe Jesus Christ was born around the start of 1AD. In other words, Christians have a good reason for adopting the rather ugly “99 and the following 00 are in the same century” convention – but not atheists, who, I submit, should be opting the elegance of letting the century begin when the digits tick over. Why not? 1AD to an atheist (or indeed, a non-Christian of any kind) is just a year like all the others…

What utter nonsense.

There are 100 years in a century.

Therefore, the century ends at the end of the 100th year, not at the start of that year. If you allow a century to end at the start of its 100th year, you are assigning only 99 years to a century, which is plainly wrong.

We number our years. The system we use did not start at 1, as it was only invented some time in the 5th century (IIUC), but each year is assigned a number. Each new year increments the count by 1. Thus, 1965 was year number one thousand, nine hundred and sixty-five. Irrespective of the origin of the system, that year was given that number.

If you accept the year number 2000 (irrespective of the origin of the counting system), then the 2nd millenium ends at the end of 2000 and the third millenium begins at the start of 2001. By the same token, the 20th century ended at the end of year number 2000 and the 21st century began at the start of year number 2001.

It’s nothing to do with the origin of the calendar, it’s to do with the meaning of the words.

55. Nigel Depledge

Ah. Bill3 (33) beat me to it.

56. J5

Last year, my wife and I were trying to decide when we should get married. We’re both rather nerdy so we wanted to have some fun with the date. 11/11/11 was a definite candidate, but we decided against it because of it’s solemn importance here in Canada and in other countries as Remembrance/Armistice/Veteran’s day.

We settled on February 11. We use dd/mm/yyyy, so it’s 11/02/2011.

Not only is it a palindrome, but Feb 11 is the 42nd day of the year!

57. Nigel Depledge

Noel (39) said:

How is writing bigger left to right logical?

Erm, because each pair of digits represents a bigger unit than the preceding pair of digits?

It may be less logical than YY/MM/DD (or, if not less logical, less consistent with other conventions), but the US system of MM/DD/YY has no logic to it at all.

58. Nigel Depledge

Mike Torr (41) said:

@Bill3 – I don’t dispute what you say. I think we just have different values I value the “tripping over” of the digits to a new hundreds value higher than I value the fact that a multiple of a hundred years has passed. Hence, I prefer to begin at 0.

Eh?

This is not a matter of choice.

99 apples (to stay with the same example) is never a century of apples. As I stated in a preceding post, if you accept that the year 2000 was year number 2000, the definition of the words century and millenium constyrain when one ends and a new one starts. The terminology used of decades is wrong, too (because the last number of a decade must be a multiple of ten) but I’ve given up on that one.

59. Yote1112

Apples and years — and the debate about the beginnings and ends of centuries
Take an apple: you have one apple, and it’s the first apple you have taken. Apples are “atomic” in this counting example – don’t get me started on fruit salad. Take another apple, and you have a second apple and two apples in total.
Years can be like apples for counting: Take a year, say 1066, you have one year, and it’s the first one you’ve chosen. Take another year, say 2012, it’s the second year you’ve chosen, and you have two years in your collection of years.
Years can be experienced differently than apples because they measure something — in this case: time. [Distance can be experienced in a similar way, so this is not a time-specific operation.]
You can pick a starting point and call it zero. As time passes you are in the first year since picking the starting point. At the end of the first year, you can say that you have experienced one year since t=0, but if you continue measuring until you experience another year, you can only say that you have experienced one full year, even though you are in the process of experiencing the second year. [Pick a starting point, call it zero, until you move in a line one inch you have zero full inches, but you are in the first inch of the distance you’re measuring.]
Thus, the debate about the end of centuries is a debate between referring to years with cardinal numbers (1, 2, 3 . . .) and referring to them with ordinal numbers (1st, 2nd, 3rd . . .). It’s not like comparing apples and oranges; it’s like comparing apples and linear quantities like time and distance. For ordinals, you do, indeed, start numbering with zero; for counting with cardinals, you start with one.

60. Richard Woods

@Mike Torr #41

Our Gregorian calendar, which by default is the calendar used in conversation in Western countries when no other calendar is specified, had no year numbered 0. The first year of the first century was year 1.

If the last year of the first century had been year 99, then the first “century” would have had only 99 years, not 100 years — and that _would_ be wrong.

The last year of the first century was the year 100. Get used to it.

61. Naked Bunny with a Whip

each pair of digits represents a bigger unit than the preceding pair of digits?

How is that “more logical”? It might please your sense of aesthetics, but it doesn’t confer any objective benefits. It’s not easier to read. It’s not easier to calculate the difference between two dates. It’s actually worse for sorting.

Sorting numbers by unit size only confers an advantage (i.e. is “more logical”) when the units use the same scale so that you can do math on them directly. Until we have a regularized calendar that allows you to perform algebra on dates directly, any format you choose will require interpretation into a more amenable format, so the layout becomes essentially arbitrary. It’s the agreement on a standard that matters, and arguing over competing standards essentially boils down to personal preference. Trying to give your preference more weight by claiming it’s “more logical” is disingenuous.

62. Pete Jackson

@53Nigel, and others: Yes, the counting of centuries doesn’t agree with the way we normally think of numbering a continuous string in our digital age. But the Romans had no symbol for zero, and so naturally started counting the years at 1. Now, we would start the first year of the Common (Gregorian) Era at 0 if we were do do it over.

But there are way too many date references to change now, so I would say keep years 1 and later as they are now, but make year 1 BCE as year 0 CE. Then year 2 BCE would be year -0 CE, year 3 BCE would be year -1 CE. In other words, all years X BCE , where X>1, would now be written as -(X-2) CE. The negative number in front of a year would denote the new style.

Centuries would then revert to the intuitive form: The first century CE would be years 0 to 99, the 21st century would be years 2000 to 2099, the first century BCE would be the years -0 to -99, the 21st century BCE would be the years -2000 to -2099 and so on.

63. Special One

The last year of the first century was the year 100

Or the year 1 (BCE). Depends on which 1st century.

It would be nice if today were B/B/B in duodecimal, but alas it is B/B/B7. Although that is *11*B7 for the year.

64. Cool. What I can’t wait for is the year 2048. Because then you could write the year as 100000000000 in binary, then I can stand all akimbo and declare “I live in the amazing of year one hundred billion!”.

Point of interest, in 2048, I just calculated I’ll be 63! Coincidence?…

…well probably…

65. BJN

Apophenia, apophenia, apophenia! And this thread just contributes to the nonsense.

66. Joseph G

Hah. When I clicked on the post, there were 63 comments

Very cool! I’m a sucker for binary math. There are 10 types of people in the world, etc etc.

67. Joseph G

@66 BJN: Apophenia? Uh oh, is 99942 Apophis in the news again? 😛

68. Jess Tauber

…we humans tend to use the number ten as the basis of our counting…

Wanna bet? Lots of cultures had counting systems that didn’t use ten as basis. The latter has often spread because of conquests and cultural interchanges by and with more dominant peoples. Formal number sets are an innovation- and in the past the norm may have been quite different. Yahgans for example have a ‘ten’ that is ambivalently also ‘five’, yet all terms above three weren’t numbers per se.

69. Well, I celebrated the geeky date by releasing a novel – and I did one on 10.10.10, and will have another ready to go on 12.12.12. And THEN we run out of cool dates…

The only hitch of course is that like all numerology, it’s simply wrong. After all, 2011 is nothing like 11. There’s got to be another end of the world date in there somewhere.

71. Today reminds me of Chapter 28 of _My Immortal_, the worst piece of Harry Potter fanfiction ever written.

http://www.fanfiction.net/s/4719325/28/My_Immortal_REPOST

Why?

Because the Author’s Note for this chapter says “rraven u rok gurl!11111111111111111111”

72. @ Pete Jackson: You wrote:

“make year 1 BCE as year 0 CE. Then year 2 BCE would be year -0 CE, year 3 BCE would be year -1 CE.”

Um … you do realize that 0 and -0 are the same number, right?

73. Aaron

I usually write my all-numeric dates in YYYY-MM-DD format, because it follows the place value of the numbers themselves (handy for dated filenames), and it avoids ambiguity with low day numbers when I use it online. It’s also similar to (and more logical than) the M/D/(YY)YY format I grew up with as an American.

74. Alan(UK)

What a load of old nonsense. The time now is….

But it all depends. The SI unit of time is the second and we can measure it to a zillion decimal places. Then it all goes pear shaped. There are 60 seconds, or perhaps 61, or even 59, in a minute. There are 60, variable length minutes in an hour, and, 23 or 24 or 25 of these hours in a day (alternatively this may be considered as two parts, one of 12 hours and one of 11, 12, or 13 hours). The numbering scheme involves either missing out an hour or counting it twice for the short and the long day respectively. When, or if, the extra hour is added or subtracted depends on your location.

There are 28, 29, 30 or 31 of these days in a month and 12 of these months in a year.

Notice that, so far, we have not encountered anything to the base 10 except that all the digits are converted to decimal rather like a (v4) IP address.

A year consists of 365 or 366 days except for one year when the calendar was changed and several days were missed out. How many days and what year depends on where you were (don’t get me started on Sweden).

Years are counted to the base 10 but starting at 1 rather than 0. It may be expressed as modulo 100.

The numbering of hours and consequently days, months and years, depends on your time zone. This might depend on the country you are located in and, in some cases, what State or other administrative division, what County, what half of a County or whether you are on an Indian Reservation, in which case it may depend on what tribe.

So what does 11-11-11 11:11:11 signify?

75. Bob_In_Wales

Unless I have been misinformed educated people over the last few centuries have always counted the new century as starting with the 1, i.e 1901, 1801, etc. So the argument over which year the century starts on has to take into account whether or not you want to change an existing system. I seem to recall also that this is why censuses are always taken in a year ending in a 1.

So the question becomes, are we going to go for a “short” 20th century of 99 years or not?

76. Lennart

About date notations: Sweden (and Japan I have heard) are more or less the only countries using the ISO 8601 standard for date and time notation, namely the YYYY-MM-DD hh:mm:ss format with zero padding, which sorts dates and times the way you excpect (e.g. by use of the C language library method strcmp). Why is everyone else so keen on writing dates in every other order than the only sensible one ? A date is just a number, so why not just write it from left to right like all other numbers? Yes I know, this is a little off topic, but I could not resist the oppurtunity, since I’m never able to interpret the “best before” date on groceries from diffeernt countries.

77. Chris

You obviously didn’t see the episode where Bart Simpson needed to know roman numerals to avoid being eaten by lions.
“Caution: Exit through Door 7 only. All other rooms contain man-eating tigers.”
Roman numerals?! They never even tried to teach us that in school…. OK, think, Bart. Where have you seen Roman numerals before? I know: Rocky V. That was the fifth one! So, Rocky 5 [points to V], plus Rocky 2 [points to II], equals Rocky 7 [points to VII], Adrian’s Revenge!

78. Pete Jackson

@73Tracer: But 0 and -0 here are labels, 0 represents 0.000 to 1.000 and -0 represents 0.000 to -1.000. After all dates are labels and can be converted to numbers but the conversions are non-trivial as any programmer knows.

79. WJM

I would count the apples from 1 to 100, obviously: but apples are not like years, because I started with no apples.

= = =

Apples, in this case, are exactly like years. You are counting the apples, just as calendars count the years. You start with 1.

If you are measuring an elapse of time, that’s different: you start at zero. But that’s not what a calendar is doing.

80. WJM

Our Gregorian calendar, which by default is the calendar used in conversation in Western countries when no other calendar is specified, had no year numbered 0.

= = =

Nor would it: you don’t start counting things at zero. A calendar is a count.

81. Joseph G

@77 Lennart: About date notations: Sweden (and Japan I have heard) are more or less the only countries using the ISO 8601 standard for date and time notation, namely the YYYY-MM-DD hh:mm:ss format with zero padding, which sorts dates and times the way you excpect (e.g. by use of the C language library method strcmp). Why is everyone else so keen on writing dates in every other order than the only sensible one ? A date is just a number, so why not just write it from left to right like all other numbers? Yes I know, this is a little off topic, but I could not resist the oppurtunity, since I’m never able to interpret the “best before” date on groceries from diffeernt countries.

Fascinating, I never knew that Sweden and Japan use that format. I agree, though; that does make the most sense. After all, digital clocks aren’t read
min:sec:hour 😛

82. MPG

@WJM #81

you don’t start counting things at zero. A calendar is a count.

But you do though. Sticking with a calendar example, you don’t describe a baby as being “1” during the first year of its life; only after a year has passed is the child described as being “1”.

83. pettypi

Did you know that computers can sort things other than the order set in the ASCII table?

Date notation should not be dictated by the fact the a machine can sort them easier, or that your operating system of choice gives you limited options. Computers can sort things any way we tell them. If you’re writing the code to sort the date in an arbitrary way, then yes, you can’t just use strcmp(). Boo hoo. I also write my file names in YYYYMMDD format, but that’s because of a limitation of my OS, not because it’s superior.

Any notation you choose should be based on culture, history and what makes sense as a society. Don’t submit to your robotic overlords!! Personally, I’d like to do away with the MM numeric and use a three-letter abbreviation. Of course, that’s language-dependent. Oh well, we’ll all be speaking the same language eventually.

Although a world-wide standard would be nice, it’s completely arbitrary which one it is.

84. Jim Baerg

How can you mention ternary without mentioning the clever variation which rather than using 0 1 2, uses -1 0 +1?

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

85. WJM

But you do though. Sticking with a calendar example, you don’t describe a baby as being “1″ during the first year of its life; only after a year has passed is the child described as being “1″.

= = =

Exactly.

“First year of its life” = counting = calendar = 1. Not “zeroth year of its life”. When you “are 1”, you are in the second year of your life. Counting.

“only after a year has passed is the child described as being “1″.” = measuring (age, in years) = 1. != calendar. When you are in the first year of your life (counting) you are on your way to one year of life elapsing (measuring).

This is the same reason you describe a less-than-one-year-old child in terms of their days/weeks/months of age. Measuring, and we tend not to measure such workaday things in fractional or decimal years.

86. Mary

I REALLY wanted to get my postmark for 11/11/11. Since 2000. I have sent cards to myself so I would be sure of having postmarks with specific dates–like 02/02/02, 10/10/10 etc. I will not have a complete set as some of the dates were on weekends. This year. although not a weekend, was a holiday. Not everything was closed, but the Post Office is always closed on Remembrance Day. Oh, how I would have loved a 11/11/11.

87. Teshi

I taught binary to an “upper set” Year 5 maths class and not only did they pick it up super quickly, they were thrilled by it and all its uses. We talked very generally about transmission of data and for weeks afterwards I had kids asking me about things like, “Could I send a code by having each alphabet letter represented by a number?” “Is it binary going down this wire from my drum kit?”

I showed them “there are 10 types of people in the world” joke as well.

I learnt binary as a teenager because I went to dorky computer camps, but I don’t understand why I didn’t learn it in middle school. It’s so useful and gives you a much deeper understanding of place value. For me, it was learning binary and that Tom Lehrer song that solves a problem in base eight that finally liberated my understanding of place value from just knowing what each place stood for to actually groking it.

And that’s what we want kids to do with maths, surely. It’s also a thousand more times more interesting to truly understand mathematics than it is to simply be able to use algorithms.

The more I learn about the maths (including the uses and history) I could have easily learned as a kid the more I wish I had been taught it.

88. Lennart

pettypi said: “Did you know that computers can sort things other than the order set in the ASCII table?”

My point was that it is a nuisance we have all these different date notations, leading to mistakes easily being made. What does 01/02/03 mean? 2:nd of January 2003, or 1:st of February 2001, or 2:nd of March 2001? My second point was that having the most significant digits to the left makes sense (should we ever arrive at an international standard), since that is what we do with most other numbers. The sort order of the characters in the ASCII table was not important. But it is worth noting that the inventors of ASCII code made the character codes ascend in the same order as the “digits” they represent. Arbitrary choice and just a coincidence? Don’t think so.

89. Gunnar

My first thought after reading this post was “I wonder how many commenters will mention that old ‘there are only 10 types of people in the world’ joke'”?

90. There is an alternative ternary notation in which the digits are -1, 0 and 1. I think it’s called balanced ternary. I believe that a computer using this system was constructed in the Soviet Union in the late 60’s or early 70’s. The advantages include an unambiguous notation for negative numbers and rounding is a doddle.

91. There would be no dispute about dates if people were taught ordinal numbers. All dates are ordinal numbers. The first day of the month is day one, not day zero. The first month of the year is month one, not month zero. The first year of the common era is year one, not year zero. The numbers are not a measure of elapsed time. The elapsed time at the beginning of the first year of the common era was zero years. At the end of the first year, the elapsed time was one year.

OK, I will admit that astronomers have a zeroth of January, or a minus-first or minus-second and so on, but they are cheating and those dates have more conventional names. But even so, they are still ordinal numbers.

92. DaveN

You know, this beats the heck out of 11/11/11/ as “Curduroy Appreciation Day,” I have to say…
http://www.npr.org/2011/11/11/142235914/friday-is-corduroy-appreciation-day

93. Nigel Depledge

Yote1112 (60) said:

Apples and years — and the debate about the beginnings and ends of centuries
Take an apple: you have one apple, and it’s the first apple you have taken. Apples are “atomic” in this counting example – don’t get me started on fruit salad. Take another apple, and you have a second apple and two apples in total.
Years can be like apples for counting: Take a year, say 1066, you have one year, and it’s the first one you’ve chosen. Take another year, say 2012, it’s the second year you’ve chosen, and you have two years in your collection of years.
Years can be experienced differently than apples because they measure something — in this case: time. [Distance can be experienced in a similar way, so this is not a time-specific operation.]
You can pick a starting point and call it zero. As time passes you are in the first year since picking the starting point. At the end of the first year, you can say that you have experienced one year since t=0, but if you continue measuring until you experience another year, you can only say that you have experienced one full year, even though you are in the process of experiencing the second year. [Pick a starting point, call it zero, until you move in a line one inch you have zero full inches, but you are in the first inch of the distance you’re measuring.]
Thus, the debate about the end of centuries is a debate between referring to years with cardinal numbers (1, 2, 3 . . .) and referring to them with ordinal numbers (1st, 2nd, 3rd . . .). It’s not like comparing apples and oranges; it’s like comparing apples and linear quantities like time and distance. For ordinals, you do, indeed, start numbering with zero; for counting with cardinals, you start with one.

You have a valid point insofar as time is not directly comparable to apples.

But you are wrong that the difference is the difference between cardinal and ordinal numbers. We do not label years with ordinal numbers, we label them with cardinals.

When I reached my first birthday, I was one year old. The day after that, I entered my second year, but that did not make me 2 years old. I was not 2 years old until my 2nd birthday.

This is exactly parallel to the end-of-century point. You don’t get to the end of a century until 100 complete years have passed. Recording the first day of the 100th year does not mean you have recorded 100 years.

Many people celebrated the 21st century at the start of the 100th year of the 20th century.

2000 years is 20 centuries. Year number 2000 was the 100th year of the 20th of those centuries. The 21st century began on the first day of the first year after the end of the 20th century, i.e. 01 Jan 2001.

94. Nigel Depledge

Naked Bunny with a whip (62) said:

each pair of digits represents a bigger unit than the preceding pair of digits?

How is that “more logical”?

It isn’t.

Did I claim it was more logical? No. (Go back and read my post #58) I claimed only that it was logical, not that it was more logical than any other system.

In fact the international standard system is more logical, because it runs year – month – day – hour – minute – second, so the date and time follow the same structure.

It might please your sense of aesthetics, but it doesn’t confer any objective benefits. It’s not easier to read.

It’s easy enough.

It’s not easier to calculate the difference between two dates. It’s actually worse for sorting.

Sorting was never an issue when date formats were decided upon. If you want to sort by date, use the international standard date format.

Sorting numbers by unit size only confers an advantage (i.e. is “more logical”) when the units use the same scale so that you can do math on them directly. Until we have a regularized calendar that allows you to perform algebra on dates directly, any format you choose will require interpretation into a more amenable format, so the layout becomes essentially arbitrary. It’s the agreement on a standard that matters, and arguing over competing standards essentially boils down to personal preference.

Yes. So what?

Trying to give your preference more weight by claiming it’s “more logical” is disingenuous.

I did not do this, so your accusation is false.

I said (58):

Noel (39) said:

How is writing bigger left to right logical?

Erm, because each pair of digits represents a bigger unit than the preceding pair of digits?

It may be less logical than YY/MM/DD (or, if not less logical, less consistent with other conventions), but the US system of MM/DD/YY has no logic to it at all.

95. Nigel Depledge

Pete Jackson (63) said:

Centuries would then revert to the intuitive form: The first century CE would be years 0 to 99, the 21st century would be years 2000 to 2099, the first century BCE would be the years -0 to -99, the 21st century BCE would be the years -2000 to -2099 and so on.

Eh?

How is having years 1 – 100 making a century and years 1 – 1000 making a millenium not intuitive? No-one has this trouble when it comes to cricket (no batsman celebrates their century at the beginning of their 100th run!).

I submit that the hoo-hah over the year 2000 / 21st century point is one of human nature at its worst.

It seems to me that no argument made in defence of this error withstands scrutiny. And yet many people persist in adhering to the error. I think it is – in most cases – merely a stubborn unwillingness to admit to error.

Why then should we retroactively “fix” the counting system to fit in with the error?

96. Nigel Depledge

Alan (UK) (75) said:

So what does 11-11-11 11:11:11 signify?

The “1” key got stuck?

97. Nigel Depledge

MPG (83) said:

But you do though. Sticking with a calendar example, you don’t describe a baby as being “1″ during the first year of its life; only after a year has passed is the child described as being “1″.

Well, precisely the opposite in fact.

A child is only 1 year old (i.e. “1”) after he/she has lived one full year. You only count that year at its completion.

So, you count the child’s first year as “1”, not as “0”. But you can only count that year when it is a full year (as opposed to, say, 20 weeks). You would never say that a child is “o years old”, you would always express the child’s age in some non-zero unit of time (such as 20 seconds, or 4 days, or 16 weeks, or 8 months).

In other words, you don’t – as you assert – use zero in counting the passage of time.

98. Nigel Depledge

Lennart (89) said:

My second point was that having the most significant digits to the left makes sense (should we ever arrive at an international standard),

There is an international standard: YYYY/MM/DD

99. WJM

@98

In other words, you don’t – as you assert – use zero in counting the passage of time.

= = =

You do when you are measuring time: that’s why timed races start at 0:00:00.00

You don’t use zero when you are counting units of time. Thus, the marathon starts at 0:00:00.00, whence you measure the time of the eventual winner (and all other participants.) But you will also note that N of those racers dropped out in the first (second, third) hour, not zeroth.

100. Tracer:

Um … you do realize that 0 and -0 are the same number, right?

Not necessarily. In computers and mathematics, there is such a concept as “negative zero”.

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

101. kansel

@Aaron (#1) – I for one am looking forward to 2013. April 5 will be the first date in over 25 years without any repeating digits. (Not counting leading zeroes.) The last date with no repeating digits was June 5, 1987.

102. Lennart

Nigel Depledge (99) said:

There is an international standard: YYYY/MM/DD

Yes, I know (ISO 8601), but unfortunatly it does not seem to be used very much, at least not in every day life. Take a can of vegetables for instance and tell me what “best before date” 10/11/12 means.

103. Joseph G

Who’d have thought something so basic could generate such a wide range of deeply held opinions?

104. The year numbers are, and always have been, ordinal numbers. For example, the Black Death entered England in the thirteenth hundredth and forty eighth year of Our Lord. Switching from AD to CE doesn’t magically turn them into cardinals.

105. Nigel Depledge

WJM (100) said:

You do when you are measuring time: that’s why timed races start at 0:00:00.00

You don’t use zero when you are counting units of time. Thus, the marathon starts at 0:00:00.00, whence you measure the time of the eventual winner (and all other participants.) But you will also note that N of those racers dropped out in the first (second, third) hour, not zeroth.

Yes. So tell me, how many years are there in a century? And when is a century complete – at the end of its 99th year or at the end of its 100th year?

106. Nigel Depledge

Keith Harwood (105) said:

The year numbers are, and always have been, ordinal numbers. For example, the Black Death entered England in the thirteenth hundredth and forty eighth year of Our Lord. Switching from AD to CE doesn’t magically turn them into cardinals.

I don’t think anyone said it did.

What turns a year into a cardinal number is when you consider how many of them there are in any given period.

The year you mention, 1348, was indeed the one thousand, three hundred and forty-eighth year of the system, but there had only been 1348 years since the arbitrary beginning of the system at the end of 1348, not at the beginning of 1348.

107. WJM

@106. Yes. So tell me, how many years are there in a century? And when is a century complete – at the end of its 99th year or at the end of its 100th year?

= = =

There are 100 years in a century of any given calendar. Assuming the calendar starts, as most do, with Year 1, those years are Years 1 through 100 inclusive. The century is complete at the end of Year 100, the 100th year.

This is counting. A calendar is a count.

A century as a measure of time is a different beast. If you start running an uberhypermegamarathon, whose distance can be anything as long as you keep running for 100 full years, the measure (not the count, which is a calendar) starts at 0000, (years) 000 (days) 00:00:00.00. That’s a measure, not a count.

If you start this race on January 1, in Year 1 of Our Flying Spaghetti Monster, you will finish when they drop the ball at midnight on December 31, in Year 100 of Our Flying Spaghetti Monster, when your stopwatch will roll over from 099, 364 23:59:59.99 to 100, 0 00:00:00.00.

108. Infinite123Lifer

Personally, I nominate this post as:

The Greatest Thread Ever Written on the BA!

109. Nigel Depledge

WJM (108) said:

A century as a measure of time is a different beast. If you start running an uberhypermegamarathon, whose distance can be anything as long as you keep running for 100 full years, the measure (not the count, which is a calendar) starts at 0000, (years) 000 (days) 00:00:00.00. That’s a measure, not a count.

And in your marathon, once you have completed the first year of running, you have been running for 1 year.

Thus, at the end of the Year 1, 1 year has passed. Thus, the first year ends at the end of Year 1.

At the end of the first decade (Decade 1), 10 years have passed. Thus, the first decade ends at the end of Year 10.

At the end of the first century (Century 1), 100 years have passed. Thus, the first century ends at the end of Year 100,

So, how many years have passed at the end of the twentieth century? One thousand, nine hundred and ninety-nine, or two thousand?

110. Nigel Depledge

@ WJM (108) –

In even simpler terminology, the twentieth century is (by definition) Century number 20. Thus, to have 20 complete centuries, there have to be 2000 complete years.

This did not stop the 20th century from beginning at the beginning of 1901.

The definition of the word “century” pretty much demands this.

111. tom

this is an old note i posted on facebook two years ago…

Binary, Faux-Binary and Ternary Dates
by Tom Schicker on Monday, January 11, 2010 at 4:59pm

binary dates will include only the digits 0 and 1.

faux-binary dates include 0 and 1 when we follow the convention of considering only the 2 least significant digits of the date.

ternary dates include only 0, 1, and 2.

if we assume the western calendar has remained constant throughout the AD period (it has not) we can say the following…i think…i welcome corrections to my arithmetic:

there have been only 135 binary dates. the next one will be in 7990 years…that is 01.01.10000

we have enjoyed 3 faux-binary dates in 2010…there will be 9 such dates every year one is possible. including these three days, there have been 732 of these dates. #733 will be in 262 days…that is 01 October, 2010.

Today, January 11, 2010 is the fourth TERNARY DATE of 2010, and the 2244th such date AD. There are 40 such days every year they are possible and the next one (#5 of 2010, #2245 AD) is tomorrow! that is

01.12.2010 or 12.01.2010

then we will have 955 more ternary dates until December 22, 2222, which will be # 3200, then # 3201 will be January 1, 10000!

here’s a little problem: there will always be more ternary dates in the past than true binary dates in the past. will there ever be more past faux-binary dates than past ternary dates? will that be the case forever?

happy 2010!

112. I made sure to look at my watch at 11/11/11 11:11:11, but I forgot my watch is set 28 years ahead, so it wasn’t as nice-looking as it should have been. I have my watch set that way so that the days of the week are the same for my (foreseeable) lifetime, but I get to live in the future.

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