You need 11 columns to keep track of 10 years.

[athenian200]

This is a weird math thing that is an example of why I find the subject frustrating, even with some of the most basic things like addition or counting.

What I was trying to do at the time was divide what I assumed was a 10-year span of time into two 5-year segments. Specifically, 1994-2004. I used a calculator to check, subtracting 10 from 2004, and even using a date calculator to measure from January 1 to January 1, and the result was still exactly 10 years. As long as I stayed with the calculator and didn't try counting myself, everything worked as I expected.

The first thing I noticed was that whenever I counted on my hand from 1994 to 1999, I would end up with 6 years instead of 5. The second segment would come out okay, from 2000-2004. I thought I was losing my mind or something, so I pulled up a spreadsheet and created this:

math.png

So I found it was impossible to divide a 10-year span of time evenly when dealing with it in this fashion, because you need 11 columns to keep track of all those years. It can get even weirder if you start late in 1994 and end early in 2004. You still need 11 columns if you're listing one event associated with each year, even if the actual span of time you are covering is closer to 9 years.

There may seem to be no practical implications from this, but suppose you make it a bit more concrete, like what I was planning to do and list a game I like that came out in each year.

1994 - Final Fantasy VI - 1
1995 - Chrono Trigger - 2
1996 - Super Mario RPG: Legend of the Seven Stars - 3
1997 - Final Fantasy VII - 4
1998 - The Legend of Zelda: Ocarina of Time - 5
1999 - Pokémon Yellow - 6
2000 - The Legend of Zelda: Majora's Mask - 7
2001 - Paper Mario - 8
2002 - Star Fox Adventures - 9
2003 - The Legend of Zelda: The Wind Waker - 10
2004 - Tales of Symphonia - 11

This means that you cannot make a list of 10 games on a nice, even-sounding range like 1994-2004, or 1990-2000, even if it seems like intuitively that should be possible. After thinking about it more, though, I thought this seemed familiar, and I realized this is a real-life example of an array index that starts from 0. Start counting from 0 instead of 1, and you get a result more like what you'd expect, ending with 10. I thought I only had to worry about that when programming, but apparently the arrays that start from an index of zero and trip you up are real things that you can encounter out in the world, and not just a bizarre quirk of computers that a programmer might encounter like I thought.

But we're in the physical world and 0 isn't a thing you can count, right? In the case of these real objects though, it started making more sense when I tried turning each number into a range to make it clear why there have to be 11.

1994-1995 - 1
1995-1996 - 2
1996-1997 - 3
1997-1998 - 4
1998-1999 - 5
1999-2000 - 6
2000-2001 - 7
2001-2002 - 8
2002-2003 - 9
2003-2004 - 10
2004-2005 - 11

That is to say, keeping track of values between 0 and 1, or between 1994 and 1995... requires a unit, regardless of the index starting at zero. Continue this all the way down the line, and eventually you see that although by the 10th number you're keeping track of values between 2003 and 2004, you can't keep track of any values within 2004 unless you add the ability to track values between 2004 and 2005... between 10 and 11.

It seems like I always have weird problems with zero... when I was younger, I was really confused by place value, and how you could go from 9 to a 10 but have a bigger value, simply because of the 1 being in front of the zero. Took me forever to figure that one out.

[Moonchild]

When you don't have a period of time explicitly ending/starting exactly at the edge of one of your periods/units of measurement, you always need one more. This is the "sliding window" issue, and has in fact been the cause of more than a few security issues causing overflows because of off-by-one size allocations due to this easily wrong assumption of the human brain to think it's 10 years when you include both end years. Numbers have a unit size of zero - they are exact. Years have a unit size of non-zero, they are not exact and span a time in themselves. The same goes for distance and anything else that is non-zero. They behave differently.
I.e.: if your start/end is somewhere "inside" a unit of measurement, anything over a period-1 range can need period+1 units depending on where the start of the range lies (even if you're wanting to measure from December 1994 to January 2004, which is 9 years and 1 month "time passed", you'll need 11 "calendars" to mark it all out)

[van p]

Uh, whut?!?!?!?!

Using your own numbers, 1994-2004 is 11, obviously. And adding 6 to 1993 gives 1999, starting of course with 1994. And your graphic lays out the whole thing perfectly.

Not only is this not rocket surgery, it's not even high math. Don't know why it's an issue. There may be something "weird" here, but it's not a "math thing."

Good luck with your next project.

[Moonchild]

It's a perception thing.
The problem is:

adding 6 to 1993 gives 1999, starting of course with 1994

i.e.: starting with +1. If you start with 1993, you need one more.
the "0" element is not included, but the period from 1993 to 1994 is still there, i.e. it is a time period itself. That's where the confusion comes from.

It's not rocket science, at all, but it requires you to reconcile 2 different concepts that are both represented the same way (with numbers) which can be tricky for your brain to learn.

[athenian200]

Uh, whut?!?!?!?!

Using your own numbers, 1994-2004 is 11, obviously. And adding 6 to 1993 gives 1999, starting of course with 1994. And your graphic lays out the whole thing perfectly.

Why are we talking about 1993? That's what I don't get. EDIT: (Oh, wait, I do get it... you're talking about starting from 1993 without including it.) The first span of time I am thinking of was starting at the beginning of 1994 and lasting to the start of 1995, so 1993 shouldn't be in there at all. Though it does appear that I would have to go all the way up to 2005 (without including it) to keep track of 2004-2005, and that's where the 11 comes from.

If 1993 was in there, then I would need 12 calendars.

The thing that was driving me crazy was that I needed 11 calendars to keep track of what was actually just under 10 years in terms of time passed. 1994-2004 is 10 years, but you need 11 calendars to keep track of what happens in each of those years, even if the amount of time you are tracking is something like 9 years and one month.

Like, I had encountered problems like this with programming before and knew to watch out for it, but I didn't know it could happen with real things and assumed it was a quirk of microprocessor/language design. But here, even if I took the computer out of the equation, I would still need 11 physical paper calendars to keep track of that number of years. It's a real-life instance of an issue I thought I only had to worry about when writing code.

[Moonchild]

If you think about it in the smallest time where this is a problem (2 days), it may help you.
Say you have an appointment that lasts 2 days. You'd assume that that is less than a year in length, and you'd be correct. So how many years can 2 days span? 2. If you start Dec 31st it will cross a year and you need 2 calendars to mark your appointment for the duration
(this is also why calendars tend to have extra days start/end of the months on one month's sheet, so you can mark periods that would cross the month boundary, and many actually have january of the next year as well. That's not just "being nice", it's a practical consideration.)

Either way it's the problem with numbers. what is the difference between events in 1994 and 2004? it's only 10 years exactly if you are exactly at the same day, otherwise it isn't and can be from 9.01 to 10.99 for any given pair of days (simplified to if a year was 100 days for the sake of ease). Obviously for anything more than 10.00, you'd need more than 10 years to fit it all.

[athenian200]

If you think about it in the smallest time where this is a problem (2 days), it may help you.
Say you have an appointment that lasts 2 days. You'd assume that that is less than a year in length, and you'd be correct. So how many years can 2 days span? 2. If you start Dec 31st it will cross a year and you need 2 calendars to mark your appointment for the duration

Yeah, that does help a bit with trying to visualize it. Thanks. I'm reminded of how on New Year's Day, I always tell people I saw yesterday that I haven't seen them since last year, and we laugh about it because it's technically true.

It also kind of makes sense if you think about how before your birthday in a given year, you aren't considered a year older yet, even though you are in the next calendar year.

[RealityRipple]

It's the "not starting from zero" problem; the same thing that made it so the 20th century was the 1900s and the 21st century is the 2000s, because 0-99 AD was the first century AD instead of the "zeroth AD".

While physical objects tend to not count from zero, time, iterations, and ranges of values should. Having "one" of something is not ever the initial state - having "zero" is. But having "one" is the first time we care about that state.

[athenian200]

It's the "not starting from zero" problem; the same thing that made it so the 20th century was the 1900s and the 21st century is the 2000s, because 0-99 AD was the first century AD instead of the "zeroth AD".

While physical objects tend to not count from zero, time, iterations, and ranges of values should. Having "one" of something is not ever the initial state - having "zero" is. But having "one" is the first time we care about that state.

Yeah, it's like... I knew this was a problem with programming, the zero-indexed array and "off by one" issues you can see, but it kind of blew my mind to see I hit that "bug" in real life. Even when I'm not programming, I run into bugs.

https://en.wikipedia.org/wiki/Julian_ca ... Year's_Day

This paragraph also really fascinated me, about calendar switching...

To reduce misunderstandings on the date, it was not uncommon for a date between 1 January and 24 March to be written as "1661/62". This was to explain to the reader that the year was 1661 counting from March and 1662 counting from January as the start of the year.[89] (For more detail, see Dual dating).

Apparently it becomes really important to specify your ranges when there is a chance of ambiguity on the start/end points, and this isn't a new problem...

[mr tribute]

I couldn't create an application if my life depended on it, but I don't understand this thread. It seems obvious.

You need 10 columns to keep track of 10 years.
For example: 1990 to 1999.

0 to 9 = 10 years
1 to 10 = 10 years

In the physical world you don't start counting apples saying the first apple is apple number 0. However, when counting years the first year is number 0 and the last year in a decade is number 9.

[The Squash]

Off-topic:

0-99 AD was the first century AD

Actually, the "epoch year" of the Julian / Gregorian calendar is 1 AD; there is no 0 AD. (https://en.wikipedia.org/wiki/AD_1) The Romans couldn't even conceptualize the zero; that was up to, ultimately, the Indians to invent later. (https://en.wikipedia.org/wiki/0#India)

That also means that, when everybody partied in 2000 due to the "new millennium", guess what: They were partying over a nearly-exhausted one instead! 2001 was the start of the new millennium. And, for example, 1970 was not the start of a new decade -- 1971 was.

OK, I didn't need to say that, it's a bit confusing at first, and it's only pedantry, but if you ever see an old book about, say, coins from a particular century (like 1701-1800), now you'll know why the numbering looks weird. It's because it's technically accurate.

[RealityRipple]

Off-topic:

0-99 AD was the first century AD

Actually, the "epoch year" of the Julian / Gregorian calendar is 1 AD; there is no 0 AD. (https://en.wikipedia.org/wiki/AD_1) The Romans couldn't even conceptualize the zero; that was up to, ultimately, the Indians to invent later. (https://en.wikipedia.org/wiki/0#India)

That also means that, when everybody partied in 2000 due to the "new millennium", guess what: They were partying over a nearly-exhausted one instead! 2001 was the start of the new millennium. And, for example, 1970 was not the start of a new decade -- 1971 was.

OK, I didn't need to say that, it's a bit confusing at first, and it's only pedantry, but if you ever see an old book about, say, coins from a particular century (like 1701-1800), now you'll know why the numbering looks weird. It's because it's technically accurate.

Off-topic:
The calendar was set up around the year 525, so all the years before then wouldn't actually be be the years we refer to them as when they happened anyway. They used the date of the founding of Rome (AUC) instead. They would have been the years ~754 to ~1277 AUC, then 525 - 2022 AD. Of course, that also starts from 1 AUC, not 0. And certainly not +0 and -0, which there technically also ought to be.

[athenian200]

I couldn't create an application if my life depended on it, but I don't understand this thread. It seems obvious.

You need 10 columns to keep track of 10 years.
For example: 1990 to 1999.

Except that 1990 to 1999 is only 9 years. You would need 10 calendars to keep track of it, true, but it's not 10 years.

[mr tribute]

OK. Then maybe Moonchild said it best. If you want to keep track of 10 years plus 1 day, then you need 11 columns.
Just for clarity: A year starts January 1 and ends December 31.

[athenian200]

OK. Then maybe Moonchild said it best. If you want to keep track of 10 years plus 1 day, then you need 11 columns.

Yeah, I would agree. The only way it actually stays within the span of time that seems right is if you don't include any part of the last year in your range, and actually stop before you get to the last year listed in the range.

[van p]

Except that 1990 to 1999 is only 9 years. You would need 10 calendars to keep track of it, true, but it's not 10 years.

In date/time duration situations, people usually say "to" when they should say "through." 1990 to 1999 is 10 years unless you really mean "1990 through 1998." For example, a local business had a sale that ended on May 31. By the business' terminology, the sale should have ended as soon as it became May 31, midnight or right after, with the rest of the day (May 31) still ahead. In fact, of course, the sale ended on June 1. Not sure how this fits exactly into this discussion, but when I read "1990 to 1999 is only 9 years," I was ready to declare war on your mathematical acumen; then I realized what you meant. Precision of expression is always better than not, I think.

[athenian200]

In date/time duration situations, people usually say "to" when they should say "through." 1990 to 1999 is 10 years unless you really mean "1990 through 1998." For example, a local business had a sale that ended on May 31. By the business' terminology, the sale should have ended as soon as it became May 31, midnight or right after, with the rest of the day (May 31) still ahead. In fact, of course, the sale ended on June 1. Not sure how this fits exactly into this discussion, but when I read "1990 to 1999 is only 9 years," I was ready to declare war on your mathematical acumen; then I realized what you meant. Precision of expression is always better than not, I think.

The thing is... you will never reach 10 years within 1999. You will get very, very close to 10 years, pretty much to 9.9, but it will never be 10 until the first day of 2000. So it only becomes 10 years after 1999 has completely passed.

[van p]

The thing is... you will never reach 10 years within 1999. You will get very, very close to 10 years, pretty much to 9.9, but it will never be 10 until the first day of 2000. So it only becomes 10 years after 1999 has completely passed.

If the objective is, for example, 10 years, then stop counting/calculating the nanosecond the 10th year has ended. It's true that you're in year 11, but ignore it; I don't think it's relevant to what you're trying to accomplish (although I admit I didn't delve into every detail of what you said; maybe you're trying to make something out of nothing--I don't know).

[Moonchild]

The thing is... you will never reach 10 years within 1999. You will get very, very close to 10 years, pretty much to 9.9, but it will never be 10 until the first day of 2000. So it only becomes 10 years after 1999 has completely passed.

You're focusing on the inverse of the problem there.

If you take that exact same time length of time (9.9 years) and start on a different day than the 1st of January, you will still start in 1990, but the end of it will "spill over" into 2000. And that's why you need an extra year. You're still < 10 years, but still need 11 calendar years to record it all.

Code: Select all

[O]=optional, MAYBE you need it.
[O][ ][ ][ ][ ][ ][ ][ ][ ][ ][O]
All of the [ ] squares is exactly 9.0 length combined.
The moment you go over a length of 9.0 exactly, you need at least one of the [O] optional squares, but maybe both, depending on where you start.

So you will need 10 or 11 for anything larger than 9.

Or... the moment you have -anything at all- you will need at least 1 whole square.
Maybe it helps if you draw 11 equal squares, then make a strip of paper exactly 10 squares long, and try to place it under the boxes. You'll find it extremely difficult to place it anywhere that it doesn't overlap all 11 squares. Then cut off half a square of length and do it again, and you'll find there are still situations where you need all 11.

[athenian200]

That visual aid does help a lot.

I think at this point, we can all agree that the number of calendars needed to record a given number of years, is greater than the number of years that has actually passed at any given time.

What I'm noticing is that there is never really a solid whole number of years, and we're always keeping track of incomplete progress with a calendar. The moment you start a year, you've gone past 0. And until the year has ended, you can't pass 1, but by that point you've started on the next year and are still tracking the incomplete progress of a year. Progress that will never be finished or reach a comfortable stopping point because the whole cycle just begins again right at the point you logically would want it to stop so you could have a nice whole integer.

The timing of a year is interesting, because the 0 point is at the very last second of last year's calendar (Dec 31st at 23:59:59), and 1 is the very first second of next year's calendar (Jan 1st at 12:00:00). So you never have a calendar for a given year display the point at which you are 0 days into the year, nor the first point at which the year has passed. Even if you are only one second short of midnight, you are still on last year's calendar, and even if you are only one second into January, you're still in January and thus in next year's calendar. So you could reasonably need three calendars to keep track of a year, if you need to account for a single second before it, and a single second after it. You never have a nice whole number of years for any meaningful length of time, and you spend the majority of your time always measuring the incomplete progress of a year towards the next integer, at which point it promptly goes over that and you start tracking progress towards the next whole number.

I mean, it makes sense when you think about it, but it really puts the whole idea of New Year's Resolutions and celebrating birthdays into perspective, and how minor they are compared to the huge amount of time where you are just past one whole number and not quite at the next one.