Recently, there has been much debate about when the old decade ends and the new one begins. Some say this decade ends on December 31, 2019, and the start of the new one begins January 1, 2020. For others, the new decade doesn’t start until January 1, 2021; the old one concluding on December 31, 2020.

But which is correct?

As you think about New Year’s resolutions, here’s one we should all make together: resolve to insist that **decades begin with the year ending in the numeral 1 and finish with a 0.** For a decade to begin, we must start with the year ending with 1 (2021) and finish with 10, or so far as chronology is concerned, a year ending in 0 (2030).

For example, January 1, 2001, opened the 21st century and the start of the new millennium, just as the year 1 A.D. marked the beginning of the Christian era. Of course, many of us will remember the wild celebrations that were touched off at midnight on December 31, 1999. But was that a year too soon? Yes!

That fact was known even to comedian Jerry Seinfeld. And if at the stroke of midnight on December 31st, you think you’ll be celebrating the start of a new decade, guess again. As was the case 20 years ago, you’ll be one year early, for the new decade will actually start in the year 2021.

### Calendrical Confusion

If you want to criticize anybody for this confusion, you can point the finger of blame at two men: Dionysius Exiguus, also known in some reference works as “Dennis the Short,” and the Northumbrian monk Bede, also known as the “Venerable Bede.”

Dionysius was born in what we now call Romania around the year 470 and was the first to suggest counting the passage of the years from the date of the birth of Jesus Christ; the beginning of the a*nno Domini* (which means “Year of Our Lord” in Latin) era, or A.D.

According to the contemporary historians of the time, Jesus was born during the 28th year of the reign of the Roman Emperor, Caesar Augustus. There is, however, considerable confusion about exactly when Augustus’ reign began, so the year Dionysius called 1 A.D. was not accurately placed in history; in fact, most religious scholars now think that Jesus might actually have been born several years earlier.

When Dionysius finished his computations, he figured that the year Christ was living in was 525 A.D. But he never bothered to number the years prior to Christ’s birth.

We would have to wait until 731 A.D. when the Venerable Bede popularized the *anno Domini* era in Anglo-Saxon England and extended the counting of years before the birth of Christ – the “B.C. era.”

Most unfortunately, however, Bede did not account for the year zero in his calculations. So 1 A.D. was immediately preceded not by a 0, but by 1 B.C.

### The Elevator Analogy

As an analogy, think of going into a building in which the ground floor is listed not as the first floor, but as the lobby. So the first floor is actually one flight above you.

So if you were to go into an elevator located in the lobby and wanted to go 10-flights up, you would actually end up on the ninth floor (if you were to assume that the lobby as the “zero” floor).

But if you assume the lobby as the “first” floor and went 10-flights up, you would end up on the tenth floor.

In essence, on our calendars, 2021 is the equivalent of a “first-floor lobby,” and after going up ten flights (or years), we’ll arrive at the tenth floor. Or in this case, the year 2030—when that decade ends.

**Fun Fact: The origin of the word decade goes back to the Greek word Deka meaning ten and dates from the early 17th century.**

### A “Punny” Year Ahead

So let’s face it, from a mathematical point of view, a new decade is still a year away, in the year 2021. But that doesn’t mean you can’t celebrate the arrival of 2020. For one thing, it’s going to be a year filled with many puns about perfect vision. How do I know?

*Eye saw it coming, thanks to my 2020 vision!*

And 2021 and beyond will be worse because… *hindsight is 2020.*

*How eye-ronic!*

people refer 2000 year as 21st century, which isn’t correct from mathematical point of view

If we had like decimal notation to each month, then it would be easier, but not for all

Like 0.1 year 0.2 year

Then jan 31 2020 would be jan 31 2019.1

(why? cuz 2019.1 donates running year 2020)

So to end the decade it has to reach ..2019.9 then 2020.0

Likewise jan 31 in year 1 (AD) would be 0.1 year(AD)

Well, now I guess that this all depends on whether you want the new decade to begin, or end with the coronavirus. I suppose that, because it started on the last day of 2019, it should come on the end of the current decade.

If the decade is the 2020’s it can’t have outside 2020

This is erroneous. Decades are not centuries. They are not counted by ordinal numbers. 1990 was not part of the 80s. Note that name “the 80s”, not “the 8th decade”.

Wrong, the 80s are from 1981 through 1990 because a decade is a full 10 years. The 1st decade was not from the year 0 through 9, it was from 1 through 10. Actually, a decade can be from 2008 through 2017 because that is a 10 year period. In other words, a decade (a 10 year period) can start with any year.

Except you didn’t refute what I said at all. The decades are not named or counted like the centuries. The year 2020 is part of a decade called the 20s, not the 10s, because it is literally part of the group of ten years that have a number with 2 in the tens place.

Ok so if the ground floor of a building is called the lobby, and the floor above is called the first floor.

Start in Lobby

Go one flight up — floor 1

Go two flights up — floor 2

…

Go 10 flights up — floor 10

If you count the ground floor as floor 1. .. go 10 flights up you are on floor 11.

So what you said in the elevator analogy was wrong.

That said … 2020 is the first year of

“The Barking 20’s”

There I named the decade — go forth and spread the word.

Illogical, if you enter a building on the ground (1st) floor, you only go up 9 floors to get to the 10th floor. In a 10 story building the elevator buttons are marked Lobby, 2, 3, 4, 5, 6, 7, 8, 9, 10.

This is so simple. Nothing starts at zero. You could have a billion trillion zeros and it’s still zero. The start of everything is naturally one. Go to the end of one and so on until the end of ten, then you have a decade. Who knows what comes after ten? That’s right, eleven, up to the end of twenty for another decade. The only reason for referring to , for example, the beginning of 2020 to the end of 2029 is because it’s a convenient way of referring to a period of time. 2020 has to end before the next decade actually begins. The beginning of 2000 was just a nice round figure to look to but for 2000 years to end, the year 2000 has to end. Isn’t it so simple? Gordon

Yes, but people refer 2000 year as 21st century, which isn’t correct from mathematical point of view

If we had like decimal notation to each month, then it would be easier, but not for all

Like 0.1 year 0.2 year

Then jan 31 2020 would be jan 31 2019.1

(why? cuz 2019.1 donates running year 2020)

So to end the decade it has to reach ..2019.9 then 2020.0

Likewise jan 31 in year 1 (AD) would be 0.1 year(AD)

oaQMVXLHU

For people to say that the new decade has not started yet is incorrect. When a child is born they are not one year old, they become one year old after living through the first year of life. Likewise with the decade, it starts at zero, when we get to 2021 the decade will be one year old the same as the child.

Michael

You made my point, a child is not 1 year old until he/she has lived 365 days. Therefore, a decade has to be 10 completed years and it starts from year 1 not year 0. In your way of thinking, the 1st day in all of earths history would be 00/00/0000, the next day would be 01/00/0000.

January 1, 2021, the decade will already be 365 days (or 8760 hours) old.

Edit: “… starting its year-0 at 1 AD coming forward, the other at BC 1 going backward,” should read starting its year-0 at 1 AD going backward, the other at BC 1 coming forward.

Well, I couldn’t resist being post sixty-six, ha. And, we have 66 = 11*6 —> 911 when reversed in both directions.

With two separate calendars, one starting its year-0 at 1 AD coming forward, the other at BC 1 going backward, the overall calendar with the two separate ones overlapping starts/ends at 1/2 either way.

We should be looking for July 2nd babies, in the middle of that day, in the middle of the year, instead of where an old year turns into a the new one. Celebrating, then, perhaps.

Isn’t it always the case that while everyone is “fighting it out”, someone comes up the middle from nowhere? Anyway.

The 2020s (a.k.a. The New 20s) have begun. The 203rd decade A.D. will not begin until 1 January 2021.

Yep. The inability of people here to distinguish between ordinal and cardinal numbers in an effort to sound smarter than everyone else is obnoxious, to be honest.

To Derick of ‘Simple Logic’. 01/01/2010 + 10 years = 01/01/2020. Or, simply start your chart from 01/02/201 – 01/02/2011 = one year. Or, start on 12/31/2010 – 12/30/2011 = one year. One day early or one day later. So it’s just another way of looking at it. Plus, people don’t say ‘One year ago today’ and actually mean the ‘day before’. as you are demonstrating.

Heck, for that matter, your explanation means ; (Using 0 as the 0 in 2010)

0-1=1

1-2=2

2-3=3

3-4=4

4-5=5

5-6=6

6-7=7

7-8=8

8-9=9

9-10=10

Gee, it ends in a 0, not a 9……??

It only works your way if you manipulate the numbers to favor your argument.

Hi Rick, But see what you did was start at 0-1 =1. Because there was no year 0, the counting starts at 1.

1

2

3

4

5

6

7

8

9

10

But decades are not ordinal, so you can absolutely start counting at a number ending in zero. They’re “the twenties”, meaning the years whose tens place is a 2, not the “twentieths”.

Is the number 30 in “the twenties”? No.

When I turn 50, am I still “in my forties”? No.

Then why would 1990 be in “the eighties”?

This has nothing to do with whether we start counting at 1 or 0: when we say “the twenties,” we specifically mean those numbers with “twenty” in them, in the 10s place, so that you say “twenty” when you read the number out loud. Two-thousand-thirty is simply not in the twenties, period.

“You seem intractably attached to multiples of ten”, I thought this was a discussion on decades? 10 seems pretty important there.

I said semi-palindromic attempting to coin a term who’s meaning I hoped would be obvious without realising it is already used for something else. What I meant is that 73 x 137 is only kind of a palindrome, if you remove the multiplication sign. I mean you chose the order of numbers too, so 137 x 73 is just as valid and not a palindrome.

Anyway, I might end this here on my end. I’m finding I can’t use examples in my arguments without them becoming a way too in depth discussion on their own. The dimensionality or whether or not the big bang was the true origin of time were not related to my point.

A couple of final simple thoughts that came to me on their own. The reason for working with definite or one-time strings of ideas such as digits of numerals is so that once you find a good fit in specific, the thing continues on in general, eg, with numbers of the form 11, 101, 1001, 10001, etc. Secondly, one may as well take the so-called 10’s to be 10 to 1, working backward from 10, instead of ahead from 0. Ie, just as there is the 10’s taken as the 0 to 9, there could be the 10’s from 10 to 1, starting with 1, and, the 20’s as the 20 to 11. What a simple way to bridge the gap here, for the pedantic-at-heart either way! Ha, I noticed, just noticed from 365 = 101101101 in base-two that there are a variety of ways to spit it up across the middle 0, but it does have an 11 in it. Of course, only a fanciful observation.

Well, I inserted the explanations in “quotes” from the internet to clear up your own sprawling comments about those things. As for 1 not being the “origin of all time”, eg, theoretical physicists no longer take the “big bang” to be a 0-dimensional phenomenon, but, instead to be something still 4-dimensional, and, hence a one something. Remarkably, this was something that I reasoned out on my own, long before I read it in print. You may check this sort of thing out for yourself at the physics stackexchange site, for professional physicists as well as for mathematicians and others.

That sounds pretty mathematical, etc, to me. But, the people around the time of Jesus had no clue of such things, at least not per se. If I recall, and correctly read the little piece Einstein wrote about dimensionless constants such as the fine-structure ones, he noted that everything had to have some physical or other explanation aside from the mathematical because, otherwise, any number could be any other number. Fundamentally, I, myself, don’t see how, in general, the numbers could be stripped of the physics, etc, or, in specific, how after numbers and the numerals that represent them describe physics, etc, in such astounding detail.

Do you know what a semi-palindromic number is? Not the example that you provided. Nor is 73137 semi-palindromic, which is neither strobogrammatic. Perhaps, palindromic things can be said to be subsumed by the semi-palindromic, strictly speaking. Regardless, the very few examples of coincidences in my posts are of the exactness to reflect the type and degree to which things must align in any conventional physical or mathematical theory. I didn’t ask for the odds of any old number coming along, but something like 73137, or 13731. If I had waited for you to write 137, and, then, I insisted that you wrote one of the three, or four I had just written, then who cares. For sure, some coincidences are less likely than other, but, I doubt that you will admit to this, either. I tried to show an example of how quickly such coincidences can become very, very hard to find, let alone stumble on, by way of a number theorist, who would better know than either of us. I just pointed out here how a number like 137, which isn’t supposed to have anything to do with anything, except for someone who related it, however, to the fine-structure constant, which is about the basic measurable properties of space and time, soon ended up here in an only slightly altered form in a mundane discussion of how we perceive time. Pretty darn cool, if you ask me. You randomly picked the one of a handful, and, one related to some “significant” time.

You seem intractably attached to multiples of ten. That’s perfectly fine because it’s definitely one way to count. However, there are a level of infinity of others, and then some, each just as suitable in its own isolated (pretend) way. Why would I take one digit over another? I expressly already wrote there can be no “theory of everything” in the usual paradoxical sense because no one anything can really supersede everything else. Speaking of base-2, “365 is 101101101 in base 2 (binary). It is 555 in base 8.” As cool as also this is, it remains as isolated until someone connects it to everything else. Want a “theory of everything”? Go connect it.

Thanks to everyone in this thread. There is always something to learn/review. Thanks to the Almanac, which I recall reading while growing up, early on, on the family farm. In those days, it was surely a “breath of fresh air” to the creative mind.

Hi Mark, coincidences are cool, but they are usually just that, coincidences. And in this case not really even that. There are a LOT of palindromic numbers, the fact that one of them has a semi palindromic set of prime factors is almost a mathematical certainty. I mean by manipulating your numbers I just created one:

40004 = 2 x 73 x 137 x 2

The numbers we use are just representations of scale, the digits involved aren’t that special. If we worked only in base-2 numbers (aka binary) would you be convinced that 1 is more special than 0?

Again, this is besides the point. My argument is that mathematics has no place in this discussion of start and end years for decades (besides that they be 10 years apart). A decade is just a period of 10 years, and society marks the significance of a “new” decade when the 3rd digit in the calendar year changes. If we are to mark decades at all, this is a useful way to do it, and going from eg, 21 to 30 has no added utility besides being less symbolic. I mean think of the “new millennium” discussion. Who gives a **** if the year goes from 2000 to 2001… 1999 to 2000 is way more significant, in so far as any year change can be significant.

Also, you didn’t need to explain temperature scales. I used them as examples of scales that use non-zero values to be their origins. Just like how the year 1 wasn’t the origin of all time, 0 degrees (F/C) isn’t zero heat.

Oh, one thing I overlooked. There are only five ways to punctuate with X the prime-number factorization of 10001 = 73 X 137, which, in its purest form, is the digits of 137 mirrored on itself. Five places to put the X, with, conceivably, a leading 1 inserted. Honestly, as well, what are the odds that any of the “fun numbers” I had already listed would explicitly show up in the one relatively large number you threw out? The “cult number” of physics – with many of its leading proponents in on the game – mirrored on itself as a palindromic number in some five-digit number thrown out almost randomly in some layperson conversation about calendars.

Is it so far-fetched to wonder that we all had everything backward, ie, that all begins with a few simple integers like 137 worked the other way around with its accuracy lost in the translation? That we are left with bit and pieces that never seem to match up.

Hi, Robert. It’s all okay. I don’t mind talking about anything that comes up that catches my eye. To this end, I like to set some definite boundaries, and, then, gradually work my way inward, especially so that it doesn’t look like I’m making it up as I go. It may sound a little scary, or fascinating, but w/o a working “theory of everything”, all we can express are our experiences and opinions, and those of others. We can only perceive reality whether we do so objectively, or subjectively; if there is even a reality at all. Which reminds me of an applied math professor with first name, Fogg, who told us on more than one occasion that the only rule is there are no rules. Again, things like this don’t actually sink in until discovered at none other than the School of Hard Knocks (with its Graduate school called Banging Your Own Head Against The Wall). If mankind were ever to find one thing for real, then wouldn’t everything else follow effortlessly? Science doesn’t work this way, although it’s ultimate purpose is a mathematical and physical “theory of everything”. I don’t mean the already old “new” line that everything boils down to math because math is everywhere. Nothing piecemeal-vague like that. Now neither I pretend to have such a theory. Contrary to popular belief, I think that the historical evidence shows that more of the well-known scientists believe/believed in some form of deity or an equivalent expressed in another manner. I think that you would be hard pressed to find many that have/would admit to a conclusion of the absence of such. Heck, for Relativity Theory to be correct, we can never actually know which things are actually doing the moving. Quantum Theory is even less helpful, and, the two seem totally irreconcilable. The two main theories of our time. (It’s been stated that if you really understand QT, then you don’t know what you are talking about.)

First, to clean up a couple of things.

“Daniel Fahrenheit did not use the freezing point of water as a basis for developing his scale. He called the temperature of an ice/salt/water mixture ‘zero degrees’, as this was the lowest temperature he could conveniently attain in his lab. He called his own body temperature ’96 degrees’, and then divided the scale into single degrees between 0 and 96. On this scale, the freezing point of pure water happens to occur at 32 (and the boiling point at 212). The Celsius scale has more convenient values for these phase transition points (0 and 100 degrees) because Anders Celsius DID use water as a basis for his scale.”

“The Celsius scale remains a centigrade scale in which there are 100 degrees from the freezing point (0°C) and boiling point (100°C) of water, though the size of the degree has been more precisely defined. A degree Celsius (or a Kelvin) is what you get when divide the thermodynamic range between absolute zero and the triple point of a specific type of water into 273.16 equal parts. There is a 0.01°C difference between the triple point of water and the freezing point of water at standard pressure.”

“So, while 10 degrees is not twice as warm as 5 degrees, when planning your swimming a reasonable rule of thumb might be to assume that it is.”

These quotes may be googled. I hope that this last one isn’t perceived to be some sort of “spam” out of bounds. It’s from a once popular “gambling math” forum, which once had a lot of advanced ad hoc science and math talk, but, is now for all intents and purposes, defunct. I used to be only a visitor, and infrequent contributor. The first question is from a retired physics professor; the reply from a retired number theorist, a field of math that, apparently, has relatively few members.

Physicist: “I wonder how many numerical coincidences could be generated to show that “XXXXXX of XXXX” is somehow equivalent to “Michael XXXXXXXXXXX” and prove that his developing/evolving into that identity was part of the grand divine plan of some higher power?”

Number theorist: “Please, you go first. I think you may find that these “coincidences” are not so easy.”

As far as the numbers go, I am truly fascinated only insofar as the numbers may be used to verify a “theory of everything”. The hard part here is to get past enough of the physics (along with numbers purely of that sort, I would say the boring stuff absorbed over the decades) to begin to see where things like the electromagnetic, and gravitational fine-structure constants fit in numerically, the latter of which is so much harder to figure experimentally, in any event. There’s not even supposed to be a way to interpret such things outside of empirical measurement, but, that’s not the type of “theory of everything” that holds my interest. At some point, eg, even the odd numbers become more distinguished from even. The idea with eventually getting the physics away from the physics is to find and try the numbers that are independent of all that. To find numbers to test that aren’t already in some manner biased by one’s own thought patterns. Numbers from completely different systems or (mathematics) fields. I expect that with a true “theory of everything”, however defined, that the numbers part of it would at least line up in all the numerical bases, and, in strikingly different manners. This is what fascinates me about the numbers. The sense that can then really begin to get somewhere with the numbers per se.

I have no qualms with counting in terms of any of the ten possible decades in that digit’s spot. However, the so-called 80’s, and, then also the so-called 81’s, up to the so-called 89’s as long as another nine years are tacked to each of these possible starts. We just have to open up our definition of counting integer things the remainder of the way. Each year in this interval then belongs to ten thus possible decades. (Lol, if I counted right. I often type before I think, especially when I am thinking about something.) There must be lots of mathematical integer number theory proofs that use just this extreme sort of counting. Constant cardinality sets of consecutive integers that are stepped one-by-one.

“In mathematics, the cardinality of a set is a measure of the “number of elements of the set”. For example, the set contains 3 elements, and therefore has a cardinality of 3.”

Mark, sorry I don’t mean to be dismissive, but I feel like your comment goes way into depth that isn’t relevant for the issue being discussed. My point about “The numbers themselves only really have relevance in relation to each other” really refers to the fact that the origin of the year numbering system (year 1) is arbitrarily placed. I mean the creator of the currently popular year numbering system aimed for an event of significance to him, but to most it’s just a point in time. A good comparison is the Celsius/Centigrade/Fahrenheit temperature systems versus Kelvin. 0 in those first 3 systems is chosen for significance to our lives, but means that there are certain things we can’t do with those numbers. 20 degrees isn’t twice as hot as 10 degrees. Likewise discussions of where a decadegree starts and ends mathematically would not really be that meaningful if it differed from the statement “the temperature is in the high 20’s”.

This means that if we wanted to talk about “mathematically meaningful” decades, the only way would be to reckon them from the beginning of time, but we don’t exactly know that to within even a few million years, and even then they would be even more arbitrary to our lives. The point is the reason we talk about decades at all is because of how the labels we give to years work. It’s that constant 3 digit prefix to all 10 years that makes it significant and nothing else. Any discussion whether the 80s’ started in 1981 and ran until the end of 1990 are wrong. 80s’ is a label referring to a specific period of 10 years, mathematical proofs are irrelevant.

Just to quickly address your seeming fascination with the numbers 1, 3, 5 and 7. I mean… maths is powerful. You’d be surprised how many variations of numbers you can break another number into with the right mathematical operators. You should watch the British game show Countdown, it’s impressive with a few randomly selected numbers what you can make fit. And the length of a year is approximately 365.25 days and is constantly changing. I don’t think you can draw any significance from a rounded value and then doing some arbitrary maths with it.

Yes, Robert, “The numbers themselves only really have relevance in relation to each other. ” This cries out for a bit of explanation. I wrote something very similar, only a few months ago. A mathematician asked me that a “theory of everything” could be based on particular numbers, or systems of numbers. Ultimately, no number is any more important than any other. Some may be more prevalent, at least appear so, but only to differentiate between themselves. Another simplistic argument here is that nothing could happen were everything a matter of fact(s). Mistakes, themselves, exist as much as any of the facts. We must “look away”, eg, lose precision of measurement, for something to happen for us to observe it anew. We can not know precisely when anything starts and ends, let alone days on calendars. And, what about that point in between, a zeroish point?

I agree with also the type of decades that we relate to when we think of our lives as a whole, but, this, too, may be more a function of circumstances both private and public. Each of us has different “good and bad years” that shape who we are. Eg, “Generally, the age of majority is designated sometime between age 18 and 21 in the U.S.” As well, it’s hard to compare the same periods of years but at different physical and mental ages, so, this may be a bit of a misleading approach, to suggest that we should measure ourselves by such decades.

I read, just this evening, that too many mathematical freedoms/rules can lead to results that are as boring as from too few. I tend to prefer numbers that are a bit more atypical than rounded numbers. Eg, 10001 is a palindromic number. Guess what, we have also that it equals 1(73) X 137. Incidentally, another manner to express the (bad approximation for) the number of days in a year, 365 = (-1 + 53)7 + 1, again with 153 on 173 with one of the number’s digits in reverse order.

Seriously, though, years ago, people still seemed quite puzzled and/or mystified by the paradoxical number zero. Internet searches now tend to confirm that the zeroth of something may mean the best of it, as ahead of first, as the quintessence or original of something. (I guess, too, that five may have something to do with zero in base-ten numbers.) What can zeroth really mean so that we can consider what is further beneath? Going by mathematical formulas, if I recall, a “unit ball” in the zeroth dimension has volume, but no surface area. But, I still prefer to call dimension-0 the first dimension, and to take things from there. This way seems to fit my own thinking and work. Certainly, to strictly match the cardinal with the ordinal numbers would squeeze these into the same thing when brought to extremes? It could be that a simple zeroth day or year might not pan out.

As far as Jesus goes, it’s probable that with so many possible religions that one or two of them hits on something more than the religious. I used to be amazed at the complexity of some of the religious philosophical writings, at a time before I become more mentally aware later on. It takes a lot of those decades of life to begin to clue in to something. For sure, even without considering any religions at all – although, I think, we unknowingly substitute other things for it now – there is still the possibility for an almost infinite number of real such mysteries out there. Eg, as humans we may not be at the center in the grand scheme of things, but, maybe, eg, we are at the middle of the evolutionary process. What could this mean? As well, numbers like 333, 911, 13, and, say, 7 don’t mean much on a macro level, but who’s to say that it’s not worth wondering at least how we come to view, and write about such numbers. These sorts of meme-like – maybe not the word for it – numbers can show up in the strangest places, even in the number 365, and, not in ways that require a lot of effort. Life can’t spring from nothing, so, it must already be written into the atoms, etc, for those to know where to go. Fascinating stuff from where the physical point undefined meets the mathematical point defined.

Thanks for the word, decamillennium.