That's why I specifically added numbers, not numerals. Numerals are symbol used to express a number, while numbers are universal. 年は2017年です is "The year is 2017 in Japanese, and this follows almost every culture. Here's simplified Chinese, 今年是2017年, and traditional Chinese isn't much different. However this is not in the answer, so I'll add a bit about it.

You only need your own frame of reference, and a commonality between your timeframe and theirs. Most people don't type three-thousand, one hundred and eighty two, as that is the english numerals for the number. They would just type 3182, and in official documents, these don't change. All languages use numbers when doing math, so approach it with a mathematical mindset rather than a linguistic mindset and you'll understand that knowing the numerals is irrelevant. For instance using Chinese, take a look at the Ming Pao newspaper. Right at the top is today's date.

Even if Alice doesn't use the same numerals, the numbers don't change. Daisuke can determine (roughly) what time period she is from by her understanding of items and bodily language. If you provide someone with paper and they look at you quizically, chances are they didn't exist. Go further back with items and you'll get a rough estimate for time frame. As for numbers from 6000 years ago, the numbers 1,2,3,4 are easily recognized. They are I, II, III, IIII, numerals even Alice would understand being well-learned. Also, TWO downvotes? Some people just really don't like my answer I guess.

OP mentioned a cataclysm and civilization rebuilt afterwards (thus lacking modern technology). It's quite possible that they don't use the same calendar system, thus your reference of using a date on a newspaper wouldn't work.

I don't need to. Even roman numerals (which people as far back as Ancient Rome were familiar with) are commonplace, and translate easily to current arabic numerals. The conversion from there isn't as difficult as going from say Egyptian heiroglyphics to numbers, but mathematics have existed even before that. Using III + II = 5 is a valid way to show what each symbol means without needing her understanding, and the name Alice was derived from Old French, at the least in the 8th century as Alis.

@eques You don't need to. You need your frame of reference, and to determine their time period based on that.

@Jorgel Base 10 went even further back than the Romans, so please see my comment regarding Roman Numerals to do the conversion.

@shufflepants Also, keep in mind that Old French's cardinal numbers are current Arabic numbers, so there's not really much of a difference.

@Anoplexian suppose they number the years from some event after the catacylsm? Then for them it could be the year 476. How would someone from the 1900s recognize that 476 means hundreds of years in the future?

Roman numerals and Arabic numerals both have existed for a long time, but 1) they aren't the only numerals that have ever existed and aren't the only ones currently 2) that presumes that they are still in existence then which depending on the degree of cataclysm may not be true and 3) recognizing that CX means 110 doesn't tell you what that 110 means.

@eques Like I said, you don't need THEIR timeframe, you need yours. Providing them with an understanding of current numbers (and Alice being learned already knows maths), showing them the difference in their time frame (see answer) and the current timeframe can show them regardless of point in history. For instance, time didn't magically start at 0 on the Gregorian Calendar, it went BC and AD.

@Eques You don't need arabic numerals at all, you just need to compare your numbers to something they'd be familiar with. For instance, if they used arabic numbers and you use Roman, 1 still equals 1, and 2 still equals two. Even in base 12, with a learned person, having understood their current base of number, it's not hard to say "Your old 12 = my new ^".

This is easily the most controversial answer I've ever created, but if someone could explain the downvotes, I'd be happy to explain exactly why and hows this works, although I am personally partial to JeffUK's answer.

@Anoplexian which is predicated on you actually knowing when she is from. If all you know is that she's from some number of centuries ago, conveying to her the current year is 476 (for example) however that might be represented won't help her figure out that she's centuries in the future, let alone how many. That would require her to be able to convey what year she thought it was AND exactly knowledge between the two of them of when the calendar was altered (may not exist).

@Anoplexian which requires you to know she uses base 10 (not established he knows that). And still doesn't help determine that ~1900 Alice is now in year 476 of new system.

@Anoplexian Controversial would mean lots of up and downvotes. But it seems you have far more negatives than positives. I downvoted because a) your answer doesn't adequate explain how that helps and b) there are a number of issues about why that doesn't work.

Not really. Using her system, it's easy to determine if she's before the cataclysm. Provided they have the same level of knowledge, which OP said they did on terms of knowledge, they both have the historical knowledge. Think LCD between the two, and go from there. Even if you used base 12, and she used base 10, there's easy conversions between the two, as the maths had already been done to determine that different bases even existed.

@eques Also, I have no idea where you're getting the voting information from, because it says I have more upvotes than downvotes (by a factor of 25%), so yes, it's controversial.

@Anoplexian And how does he know her system? The question also isn't whether she is before the cataclysm but how much before the current time she is.

@Anoplexian meant negatives also including lots of comments finding issue with your answer (as opposed to comments requesting clarification or providing additional information to include)

@Anoplexian if he thinks it's 476 and she thinks it's 1912 (they would likely have the same year-length in mind unless the new calendar is not based upon the same astronomical events -- like a lunar calendar), how do you propose they determine it's been (for example), 1412 years?

History. If I know that the airplane was invented in 1908, and that's the latest thing she knows (by picture), I can say OK, that was invented on 1908, and it's been X number of years since the invention of this object, using the newspaper to validate it actually is the date.

It's more showing her the math than showing her the date.

She's not looking at the date, she's actually doing the math. You provide the frame of reference to say "We're in 476 AC, you're from X BC (for instance), and have her do the math in either your or her numerals.

@Anoplexian It's her knowledge level presumably because she is from around then.

@Anoplexian and so even with a catacylsm resulting in no modern technology, he has precise information that the airplane was in existence in 1908?

@Anoplexian Catacylsm could quite possibly mean a total breakdown in society to the degree that most of the records were scattered, damaged and lost. Maybe some things were pieced together later.

@Anoplexian That would be feasible only if he knew exactly when she's from, but given OP is asking about century-precision and indicates he doesn't know exactly when she's from, that still won't work.

You can only say you are from X BC if you know what X is

They may not even know exactly how long ago or for how long the cataclysm was

"Daisuke would be able to provide maps, solar system drawings and models." Given that the new civilisation has access to solar system models and drawings, it's not a stretch to assume they have archaeological information on historical objects, regardless of state of being (dinosaur fossils are millions of years old!). It's not hard to say using archaeology that "Airplanes were around about X number of years ago, and that's what Alice recognizes. She must be from around that time".

"An explanation that involves objects from her time in a aged state is borderline, as Daisuke doesn't know her exact departure time. "

It'd be similar to saying "We don't know everything about Mayans, but we know that their culture was like this or that from archaeological finds". Same thing, but Alice becomes a living Mayan from that time period.

He doesn't need to.

Like I said in the question, he shows her pictures from further and further back.

Considering pictures have been around from her knowledge period, and they have around the same knowledge level, providing records for these items is not problematic.

If the cataclysm happened to erase everything is a story issue, and not within the scope of the answers (any of them). It's an oversimplification to say "She's from 1908, but how?", when rather it's like "Shes from a time period with airplanes but without televisions".

@Anoplexian Actually archeology is a stretch. Maps and basic understanding of the stars requires less advanced knowledge to be accurate. You can easily dig up bones, vases, etc but determining how old they are, etc requires a lot of knowledge around material science, history, radiation, etc.

@Anoplexian which you are assuming they have with an accurate determination of which came first within some degree. i.e. the airplane was very early 20th century, the radio a few decades later, the TV a few after that, but compared to a thousand plus years, those are quite close.

@Anoplexian your "pictures" theory is better; the newspaper point is questionable and essentially falls back onto the language barrier issue.

Not at all. 1900s in archaeology was well documented, and the popularisation of archaeology was about the time frame of her knowledge (still confused why 1900....). Even now, we have a good idea of the exact years of the ballistae, so giving a rough estimate of timeframe (within a generous century) isn't difficult only a thousand years later, considering we're almost 2000 years from the invention.

Honestly the question was significantly changed with the authors most recent edits, so NOW pictures seem like a better idea. At the time of posting however, it significantly changes the question to add those details so it's not as applicable.

@Anoplexian "still confused why 1900...." Presumably because OP is writing a story where a early 1900s educated woman ends up in the future somehow (sorta like the Time Machine)

I can't however completely change the answer, as doing so would invalidate any discussion or upvotes/downvotes on it.

@Anoplexian You can change it quite a bit.

@Anoplexian It depends quite a bit on the degree of the cataclysm. Plenty of things archeologically we date to ranges of centuries, not close to < 100 years.

Yeah, but in 1900, she would be able to understand basic linguistic difference, and would know better than instant gratification on her time period is the least of her concerns. If it were in the 8th century, that provides a bit more of an issue linguistically, but for someone from the 1900s, understanding a different language wasn't so uncommon as to be impossibly for him to teach her.

@Anoplexian people in the 8th century understood the ideas of multiple languages, especially if they were educated. Even then, one OP indicated that language barrier would later be approached and two, OP wants to determine how time travel of some centuries could be conveyed before then, that's all that really matters

That's true, but we can narrow it down using her frame of reference on items. If I know that the airplane (1908) was in the same century as the television (1927) is enough. If she knows one, and doesn't know the other, then I know her time period is somewhere in the 1900s, as I know that they both existed during the same time period.

Yes, but the question inherently changes with a 1900s knowledge. The title says to tell her that she's traveled in time, but the question details ask for specifics.

@Anoplexian but you also have to factor in degree of knowledge. OP indicates that both of them are similarly educated and reasonably educated, but not necessarily extremely educated (like top of a field). Plenty of reasonably educated people could tell you that the airplane was invented in the early 20th or the TV was invented in the 20th century but be nowhere as precise as the decade.

How does Daisuke communicate the long passage of time to Alice? is the question.

@Anoplexian Yes, I know. Your point?

We're not trying to say that "It's been 1942 years since you remember.

It's "You don't recognize this technology, but you recognize (enter old technology here)." Time has passed.

@Anoplexian right, more like "It's been 19 centuries" or at least "it's been many centuries"

Right.

If I show you a TV, and you say 20th century, and and airplane and you say also 20th century.

@Anoplexian supposing the last thing she recognizes is the airplane, how does she know it's centuries as opposed to decades?

If you know one and not the other, I can reasonably assume you're from the 20th century.

She won't recognize anything after

She doesn't need to. Daisuke does. He's the one with the knowledge she traveled back in time, so if he knows "She's from the 20th century (in his units)", he can show her the math to show how many years has passed since that time.

If I say "Your year is in the 1900s, so using your time, we're now in 3051, 1100~ years have passed." Point to her number to tell her when she's from, point to yours for you.

@Anoplexian so all your pictures thing does is establish with greater detail what Daisuke already knew (premise already was that he knew she was from the "long lost past"), back to square one.

He knew, but she didn't. they both understand and know maths, so it's reasonable to say "Here Alice, this is the math."

@Anoplexian She knew she was from the 20th century. That's obvious. The picture thing doesn't establish anything for Alice, only for Daisuke. So it doesn't change the parameters of the question. So we're left with the math bit only.

It does for Daisuke, because otherwise he can't provide the knowledge to do the math. providing the newspaper (which existed in both period presumably), shows the date right on it. If he knows she's from a long time ago, and she recognizes the math in Daisuke's language to be x years, showing the newspaper with Daisuke's date proves the time passing, which is the answer to the question,.

If I can see "2501 AC" on a newspaper, and my host just showed me that in his time period, I'm from "-1100 AC (1100 BC)" then it's easy to get to 0, then to 2501. It works the exact same as going to 456 versus 1900.

@Anoplexian he already knew she was from a "long lost past". The use of "lost" implies limited knowledge by Diasuke about that past.

@Anoplexian and so you think it's possible to teach math without using any language, only gestures?

They know math.

They don't know time periods, but Daisuke can easily get his hands on archaeological photos from the time period. It's not like the world exploded, wiping everything from the Earth on a clean slate. Historical relics would still exist.

@Anoplexian by "teach math" I mean, come to a common understanding of what the symbols in use are.

Yes, easily. If she understands that he's using a different language which she does, any reasonable person can say that if "#" = 3 for me, and "%" = 5 for me, then #-%=-2 for me.

and that is still predicated upon Daisuke's ability to pinpoint her to at least a century (which is considered desirable by OP, but OP doesn't indicate whether Daisuke has the actual knowledge of Alice's time period and before to determine that -- e.g. does he know that airplanes are from the 20the century? or does he only know that there used to be airplanes before the cataclysm)

can I join in?

@Anoplexian "is also relying on body language and handsignals" not clear that writing is permissible. And still that only really works if a) calendar is still a solar calendar, years are still in base 10 (trying to explain different bases would be complex if you don't know what base she uses) and c) you know precisely enough what century she is from to be able to subtract back to

@EveryBitHelps of course

thanks. first off. OF COURSE writing and drawing are allowed. both parties just won't be able to decipher each other's written language.

Funnily enough, I actually have to go, I'll continue this when I get home (I'm at work ;P)

no problem :)

@EveryBitHelps won't be able to decipher? totally impossible as in "X = %" wouldn't be sensible?

that would be decipherable. but if you write "hello, this is the 20th century" that won't work. also, you would first have to establish that you both understand the "=" sign with some visual pantomime...

hold up an orange, write down "=" hold up another orange. hold up an apple, wirte down "=" and hold up another apple. hold up an orange write "=/" hold up and apple shake your head.

@EveryBitHelps how much knowledge does Daisuke have about the time before the catacylsm? e.g. would he know that a particular object was invented in a rough time period or just that it existed, etc?

Archaeology my friend. xD

he would know the rough time period like both airplanes, TV were 20th century and pre cataclysm.

thankfully he is actually well studied in precataclysmic history so he would know the broad strokes. he wouldn't really be able to say aeroplane 1908 and TV 1920!

@Anoplexian I was asking OP. The existence of Archeology doesn't mean certain conclusions were made nor that he personally would be aware of them

@EveryBitHelps Is the catacylsm well understood?

the mechanisms of the cataclysm yes. pretty much. they may have missed recording/misrecorded a few years during the immediate aftermath...which is why I'm not fussed about an exact date.

@Anoplexian e.g. for future archeology to determine the TV was invented around the early 20th century, it would require sufficient intact pieces to be found to determine actual use (which in the case of a TV would probably require also bits around antennae and transmitters), it would also require the right technology to determine how old those pieces were.

they know that there is a 20/30 year period that is a bit fussy, they know the date in the old calendar of the event happening

That makes things even easier using the newspaper method then.

regarding archaeology if you combine it with historical records you would find plenty of reference to TV in many surviving records...

Also, giving them both similar knowledge levels mage sense.

@EveryBitHelps 20-30 < 100. in other words, there's no chance there's a gap of record to the degree they don't know how long ago pre-cataclysm was?

@Anoplexian only if you overcome the language problem.

sorry, what do you mean "gap of record"

they know it's say 1100 since the end of the fussy part of the cataclysm. they know the fussy part was about 20/30 years. and they know the old calendar date of the start of the cataclysm.

@EveryBitHelps the "fussy" part may be the gap. "gap of record" a time period where records are sparse or incomplete and so it might be actually much longer than they though, etc

so if it the cataclysm happened in 1900 AD, Daisuke could know that is 3020-3030 AD. even though he himself, knows the year as 760 of the New Ming dynasty (or somesuch)

@eques

yes, the gap could be longer than they thought (gives me something to play around with story wise) but not vitally important in figuring out the time..i don't think.

getting back to your answer with the newspaper.

@EveryBitHelps so the only real gap is that he doesn't know what time Alice is from? I find it hard to believe he knows things like the airplane was invented in the 20th century, but doesn't know what objects he has which might help figure out the long time.

@EveryBitHelps it would start to affect things if he was supposed to be precise. e.g. if he tried to say she was from 15 centuries ago, it might actually be 20 centuries because there's a 500 year gap

@EveryBitHelps to what extent are records surviving?

if Alice had woken up say 200 years earlier when knowledge of the cataclysm was less then the gap in knowledge may have been so big and may have caused such an issue. but knowledge of the stars and archaeological techniques, the study of the records and environment (even tree rings etc) would have helped reduce the uncertainty of the gap period down to 20/30 years maybe 50 year gap in Daisuke time.

@EveryBitHelps This is starting to seem like a very minor cataclysm which leaves intact most of what came before it as far as records go.

But you do have a point that if it is such a small period, he should be able to provide more objects.

I think I came up with that restriction when the gap was still centuries in my head and I never mentally edited that ruling :)

@EveryBitHelps more so that if his knowledge of pre-cataclysm civilization is so good, he knows enough about the objects that someone would recognize to be able to pin point a time period.

If on the other hand, the historical record was fragmentary and a lot of the artifacts were in pieces, buildings from before the cataclysm destroyed, etc he'd have a lot harder time figuring it out.

It does seem odd that he would be able with 1900s knowledge know a lot about something 1100 years before him, when most reasonably educated people today would know not much detail about someone from the 9th century

but your newspaper answer. (1) alice sees a date on the newspaper and can immediately tell herself something has happened timewise (or at least location wise).

(2) she determines she is in a place she knows via a map but then doesn't understand the map

(3) they talk and figure out the "=" sign

@EveryBitHelps so the calendar is the same, the years just are numbered differently? She can recognize the numbers? but letters and math symbols are totally foreign?

(4) the calendar is numbered differently. crap...you messed with my head again...

(1) alices sees a newspaper and recognises what it is, she can recognise where the date is, but doesn't understand it (different numerals and looks shorter than it should (3 digits not 4)

(3) they have the "=" sign and then (4) work on assigning numerals to each other...

(5) but this still only provides Alice with Daisukes date. not how long it has been since she was last awake.

they would have to talk more to get to the point that there has been more time. hence, the frames of reference.

@EveryBitHelps but still 12 months, with a mix of 30-31 days, tied to the Sun, etc. as opposed to a Lunar calendar, etc

sorry, hence saying that you were awake in 1900 AD and now it's 750 New Ming dynasty isn't going to help.

you have to refer and say that it's been 1100 years since today's date....

the calendar is similar yes

not exact...but close enough to be recogniseable

@EveryBitHelps the more dissimilar, the more work required to explain "long time".

yes. that's why for now, I'm happy to consider somewhat similar calenders with different numbering of the years. I think communicating different calendar types may be a different question :)

@EveryBitHelps or at least easier once some common language has been establish

so I agree, the newspaper idea is cliché and could work, but I think in the end it would bring a whole other idea to be communicated via sign language and potentially confuse both Alice and Daisuke...

definitely easier after a few months and they know each others language.

I'm still partial to JohnUK's answer, but mine would work in a pinch.

you mean JeffUK?

yeah. it is good. Think I will be combining a few answers together to use myself, but it does answer the question on it's own merits.