Oh, I was confused. I was trying to find how to determine when equinox happens.
For solstice, finding the northernmost point of the horizon where the Sun rises is easy and less cloud-prone then the highest/lowest point at noon. Well, when is noon exactly?
Fun related point: the full moon rises highest during the winter, when the Sun rises lowest.
Why? Counting/subtraction. If you cast it before the solstice's sunrise a year earlier and it lasts until the new solstice, then it has lasted one entire year plus however much extra time there was between when you finished and when the earlier sunrise happened. If you cast it after sunrise, then the same thing but it's one entire year less however much time passed after sunrise. Only if the ritual is perfectly timed is it one entire year. Or are we willing to accept the common parlance version of an entire year instead?
And, of course, even if you time it perfectly with the sunrises, it's still not necessarily one entire year if you define the years astronomically via solstice, for instance, since the sunrises shift relative to the solstices. So if we're going with astronomical over solar as the important measurement for a year, where does that put us?
Actually, if you take the singular entire year very precisely (as you seem to want to), then the rules aren't quite aligned with themselves, as shown above. If you read it as common parlance (as I would like to) as how my wife said "entire year," then the rules are internally consistent and what I'm saying is perfectly aligned with them. Personally, I feel that when there are two interpretations like this (precise vs. common parlance) and one makes the rules internally inconsistent while the other doesn't, then the one that keeps things consistent is the better choice.
If you want to extend this, there is another interpretation of that Aegis that could be valid. You cast it at the solstice and it lasts the entire calendar year. Notice the year type is not specified. Why do we not take that interpretation into account? Things would become internally inconsistent.
This is only specifically true using certain definitions of the solstice. If the day(time) is the solstice (which does fit some definitions), then the winter solstice is absolutely perfectly timed with sunrise/sunset. You seem absolutely wedded to the idea that a solstice must be a moment in time. This is the narrow definition. There is also a broad definition which has it as the day, not the moment. Which definition is the book using??? This is why I asked the questions about why Year would work so differently from Sun and Moon instead of working in the same fashion. I don't think it's at all clear that the book uses the narrow definition. The broader definition seems to be more consistent with the other durations, though that certainly doesn't lock it down.
You are again tinkering with medieval calendars here
[/quote]
No, I'm not. I'm making a logical statement that does not require any calendar at all, just a measurement of a year and measurements of the length of daylight. That's it. I'm saying that if the solstice is the day(time) that is the longest (or shortest) in a year, then when the day(time) that is the longest (or shortest) has begun, then the solstice has begun. It's just a mathematical substitution and only requires the two measurements mentioned, completely independent of any calendar at all.
Meanwhile, if you go with the sunrise after the moment of a solstice, you'll commonly end up using the second-longest/shortest day of the year as the day on which the solstice is effectively counted in ArM5. That feels really odd to me. For instance, let's say the moment of solstice happens 15 minutes after sunrise on the longest/shortest day(time) of the year. The following day would end up being the second-longest/shortest of the year, and that's the day Hermetic magic would count as the sunrise on the solstice. That seems really wacky to me.
Chris
Yes, I was wondering about some of the same measurements as well. I know we've known about the time-zone issue (different sun timing at different locations) for millenia. Noon itself isn't so hard with a stick and its shadow if you measure carefully enough, but it's still a pain. As you said, northernmost sunrise is much, much easier. The equinox seems a lot harder to figure out unless you live on the equator or have great time-keeping equipment. Even then, unless you know about the size of the moon and refraction in the atmosphere, it seems it would be hard to figure out the equinox easily just with great time-keeping equipment. I would tend to think it was measured from the solstices first.
Chris
I guess I finally see what you are arguing. But it is completely besides the point. If we read, that a spell effect "lasts for the entire next year", we find no implication at all that the spell ends immediately after it has lasted a precise year.
At the very simple fact - with solar or sidereal year - that a spell with Duration: Year can last a little longer than a year.
A weird assumption on your side. I hope I have it dispelled above.
It's the default definition, rather. See en.wikipedia.org/wiki/Solstice . When claiming that a contemporary text uses another, you should give a reason.
From the perspective of a magus, a player, a SG or an author the Durations from ArM5 p. 112 look homogeneous. Your try to differentiate solstices/equinoxes from new moon/full moon uses categories quite foreign to the text's purpose.
Your statement requires a convention to use a specific definition of solstice - which still has to be given, has to come from somewhere and needs to be justified. It is not the common one. Sometimes - typically when handling practical, agricultural calendar issues - such definitions are used also in the middle ages. To my knowledge scholars (and in-game hence magi) would keep away from them otherwise. For the base of the scholarly concepts you might look here: en.wikipedia.org/wiki/Armillary_sphere . On an armillary sphere a magus can very easily show the positions of the sun during equinoxes and solstices to an apprentice.
Well, it makes the rules internally consistent, consistent with the game setting and with the examples I found in the ArM5 world. It uses the common definitions of the terminology used, and finds the common speech patterns around that terminology. And it is simple to boot. So all criteria for a good, correct reading of a text are fulfilled.
Cheers
In my mind, "next year" starts January 1st and ends on December 31th. That's 10 days later than the solstice.
I would have used "lasts for a full year" had the meaning been until the next winter solstice.
I am always weary of the fluff added to descriptions, as it often paraphrase in a manner inconsistent with the original rule. All this to say that the Aegis fluff about winter solstice is nonsense, rulewise.
yeah, that convention is from 24 February 1582
D: year is well-defined, as mentioned elsewhere in the thread.
First, you do realize that your own method also violates your own interpretation of the Aegis comment, though not necessarily always, right? An astronomically defined year lasts approximately 365.2425 solar days (a solar day is longer than a sidereal day). For example, let's say the moment of a given solstice happens exactly 6 hours (all hours solar here) before sunrise. We cast the ritual between the moment of solstice and the moment of sunrise. Let's give our team some leeway since they don't want to goof: they start the ritual 2 hours after the moment of solstice and end 2 hours before sunrise. This spell then runs out after only about 365 days and 2 hours. But to last an entire year it should have lasted 365 days, 5 hours, and about 49 minutes. Oops.
So we're left with two options. Read "the entire year" more as common parlance and accept that either of our methods work for this, or read "the entire year" as precise and accept that neither of our methods work. I say use common parlance, which leaves both of ours as equally valid vis-a-vis "the entire year" instead of neither one being valid.
And if you want to deal with the wording, the precision of the year depends on how you want to read it. If you choose to read it as very precise, then you need to note is says "for the entire year," not "for at least the entire year." For the precise language to work, the spell would have to end immediately after a precise year. If we don't like that, then we are saying we don't like using a precise reading. But if we get ride of the precise reading and turn to common parlance, then mine lasts just as much an entire year as yours. Your argument using the precision of "for the entire year" over common parlance to show what I'm saying doesn't fit requires the interpretation for which you say "we find no implication at all."
Though you have to swap definitions in the middle of that statement without telling anyone to make the statement hold true. The equivalent also holds for Sun and Moon. But if you use a measurement method that matches the method that triggers the effects, this is not true.
Yes, I already checked that for confirmation, after having checked elsewhere. Did you read it thoroughly? Here is what it says about what you call "the default definition": "Of the many ways in which solstice can be defined, one of the most common" is the one you state. Not only does the article not state yours is the default for the term "solstice," it states it is only one of many ways and more than one of these is very common. The article also mentions several times another use of the same term being what I said it could be. So why again should I be so sure it's supposed to be your "default definition" rather than another one of the most common definitions?
Ummm... backwards. For several posts now I have quite specifically pointed out that I would like to keep the durations homogeneous. A few posts back I even asked why your method would be used because it would remove homogeneity, and you said I should ask the authors why the lack of homogeneity to use your method was intended. Meanwhile I've been pointing out how my method preserves homogeneity. Let's look at a few specifics. Using the terminology above Diameter, Sun, and Moon are use solar determinations, not astronomical determinations - what I suggest for Year. Sun and Moon can last at most a daytime (nighttime) or lunar month if they are cast immediately after the trigger that causes the spell to fail - what I suggest for Year.
Also, how do you play Moon? Do you truly try to preserve homogeneity with your Year? Meaning, do you use the moment of opposition or what is known as the full moon? Note that "full moon" is a lunar phase based on earth-based observation while "opposition" is the astronomical equivalent. (Yay for different terms!) But we'll accept flexibility here and say "full moon" could mean either (and the equivalent for "new moon") for the duration. But here for clarity I'm going to stick with "full moon" and "opposition." Let's say for some observer opposition happens just a few minutes after the full moon sets. Do you consider the setting of the full moon to be roughly at the following dawn?
Let's look at the specifics, using the solar/astronomical identifier from before:
No, that is not true. The statement is internally consistent and complete. The only convention it requires is the understanding of how a conditional statement works as well as a basic grasp of the transitive property. Regardless of how you want to interpret "solstice," the statement can be properly read independent of that. Look at the part I left above. It contains the definition, so the definition does not still have to be given.
Read your own quoted article. It specifies your use is not the common one, just one of the common ones (plural). It also mentions my suggestion. I'm not saying mine is equally common, just an equally valid possibility.
I'm not disagreeing with that. However, if almost everything about the durations follow a solar method, then why would this one be different. Also, if the astronomical method is so important, why is it sunrise that acts as the trigger instead of the event itself? I could also argue that a magus could very easily use a sun dial or standing stones or something else to show and apprentice the northernmost/southernmost sunrise and to show how sunrise shifts in general.
Only if you read the night of the full moon being the night following the night of opposition and change how your interpreting the Aegis statement. And you're still left with why the astronomical method is important and yet the trigger uses sunrise (varies by location on earth) instead of an astronomical trigger.
So does mine. But mine actually keeps the rules internally consistent.
Chris
Yes, but I think Tugdual's point is that if you use the Aegis comment as making a determination about the duration, you could get some really odd behavior out of a normal reading of the Aegis. That is still true with other calendars.
Chris
First, you'd have to go back to the roman calendar to change that, and it'd still be from March first to February last.
Second, the 10 day drift of 1582 would put the solstice around December 15th in the 1200s, compounding the problem.
Third, I'd expect the rules to be written for the players, with the modern day expectations we have.
I therefore have no idea how your point could relate in any way with the concept of "next year" meaning "a year-long period starting on the solstice".
After three posts of hinting, I think I need to be more blunt. Ars Magica is a game of let's pretend - and in it we pretend, among other things, that the Ptolemaic model is true. So the earth resides at the center of the universe delimited by the fixed star sphere against the empyreum, and is circled by the sun along the ecliptic. So we also pretend - following the ancient and medieval scholars - that a year is the time the sun needs to perform that circle once, and that there is no distinction between the sidereal or solar/tropical year. Hence in-game the roughly 20 minutes of difference between the two do not exist. It is honorable to not be able to pretend a dated, falsified cosmology and in a game system fully follow through with it. But I will not make it my problem if a forum member just cannot do it, and will skip your further comments on the difference of solar and sidereal years.
I answered that already, but will do once more. The full phrase to interpret is "and the Aegis then lasts for the entire year" (underscore mine). If I tell somebody, that a battery will last for the entire year, I obviously do not promise him in that phrase that it will fail immediately after.
If you read the article in question even more closely, you will find, that it starts with the definition of the topic:
That's it, there you have the default definition of the term.
Some lines further into the article, we find:
So your alternatives are duely treated before the Wiki article begins to treat historical developments and cultural differences in definition, role and meaning.
Cheers
You are really confused. I don't want to say that 20-minute difference has nothing to do with what I was talking about, but it is essentially irrelevant. If you would prefer, I could write 365.2(4) instead. That 20-minute difference could drop to nothing and the problem would remain essentially unchanged. I'll continue to not worry about it, as you would like and as had done. The issue is that the earth's orbital period around the sun is not an integer multiple of its rotational period. Leaving out a ratio of 1 (tidal locking) or less for simplicity (and assuming an axial tilt under 90 degrees), this ratio describes the number of days in a planet's perspective per year in that planet's perspective. For the earth, since it's not an integer multiple, this means that a year isn't an integer number of days long. This is the reason for leap years working as they do. However, leap years do not need to have been invented as this simply exists (assuming you're playing Ars Magica in the last few millenia - go back long enough and you'll sometimes hit integer multiples when the earth was spinning faster).
When it comes down to it, your system has an Aegis last an entire year more often than mine does. But neither system always makes sure the Aegis lasts an entire year. So if not guaranteeing the Aegis lasting an entire year is the reason my system is faulty, then the same must be said of yours.
So, let me get this straight. You are really worried and fussy about this one line in Aegis of the Hearth's description. Yet you are totally willing to sweep away the sidereal/solar distinction? Even though the sidereal/solar distinction is not only explicitly part of canon, there are rules about durations in canon that depend upon it explicitly?
Now, if it helps we could make up a new term. (Maybe there is one, but I don't know it.) I was hoping to avoid this. Let's call it "rising/setting" and compare it to "solar" and "sidereal." Here "rising/setting" times are based on the celestial body being seen to pass the horizon. "Solar" can return to its proper use, and "sidereal" remains so. So, for instance, a rising/setting year is either 365 solar days or 366 solar days, depending on the year. Meanwhile both the solar year and the sidereal year are roughly 365.2(4) solar days. Note that rising/setting times depend highly on location and the others do not. Let's see which of the three are being used:
Diameter - rising/setting (depends on location)
Sun - rising/setting (depends on location)
Moon - triggers off rising/setting (depends on location); specific date could use any system
Year - triggers off rising/setting (depends on location); specific date could use any system
For those last two variable parts, which system would be most consistent with the other four things that are pretty specifically set?
So, if I say "Aegis of the Hearth lasts one entire day," you consider that a normal use of "last," right? My statement would not be misleading? If a hockey player asks how much longer the penalty will last while 45 seconds remain to it, would it be correct for the referee to reply "it will last 10 more seconds"? Or would that be misleading? What if your professor gives you a test and says "this test will last one hour" and tries to collect the test from you when an hour is up?
Your comment has an assumed "at least" in it. That's fine; it's colloquial. But if you're willing to accept that as colloquial (an assumed "at least"), then how can you not be willing to accept the colloquial "entire." Why is one assumption more valid than the other?
Yes, it starts that way. But what does it say about that start? The article explicitly says that it's own statement is only one of the common definitions. In fact, it mentions there are many ways and other ones are also common. I have no idea how many common ones there are, but apparently a few. The only other one I have specifically seen mentioned in this article is the one I'm using. If you want to find a source that actually says this is the default definition in non-scientific English, go for it.
Chris
If I just ignore the 365.2(4), which looks very jumbled, that would resolve the issue. Unfortunately you are looking for a new problem below, partly with homegrown terminology, and never really find it, or spell it out.
This is the reason, why medieval scholars and astronomers (and in-game Hermetic magi) do define a year by the period of the full circle of the sun around the earth along the ecliptic. In modern terminology this is the solar year. This is also the year the Ars Magica rules consistently speak of. (No RPG I know of distinguishes in its rules between solar and sidereal years - but as we have seen, in particular Ars does not need to because that difference in its cosmology does not exist.) The counting issues of the calendars derived from the Julian are best left to the churchmen who need to determine Easter. But we can skip these here, I hope.
My reading makes sure that an Aegis cast at the right times – on or rather a little after the solstices and equinoxes – always lasts until the sunrise after the fourth following solstice or equinox, that is an entire year. I grant you, that a magus may be taxed to cast the Aegis at the right time, if a sunrise follows the astronomical event very closely (say, within a few seconds or minutes) – but that is another issue I already addressed in the thread.
We have seen that a distinction between solar and sidereal years does not exist in Ars Magica. What you now understand by the 'solar / sidereal distinction', and how it relates to our topic, I cannot find out by your post – but maybe is not critical anyway.
Luckily we will never use that “rising/setting year’ in the following, so I will just pass it over.
Well, Duration Diameter does not depend of time or location of casting, in particular not in the Ptolemaic model - where the sun always maintains the same distance to the earth, and moves along the eclipse with constant speed.
Apparently, your new term "rising/setting" has overridden your concern about the 'solar / sidereal distinction' a paragraph before. But I still don't see any problems with the spell duration definitions as are, and the role of Duration Year in them.
EDIT: You are not actually proposing here to use your homegrown "rising/setting" year as the reading of 'year' somewhere in Ars Magica ... or are you?
As our combined efforts at finding examples have shown (and a little sense would have shown as well), the meaning of phrases depends on their contexts, and the expectations of those uttering or hearing them. So, what is the context of "and the Aegis then lasts for the entire year", and what are the expectations of author and reader? The reader expects to understand the ramifications for his magus to cast an Aegis. And the author needs to explain that to him. So the author would mislead the reader when telling him that the Aegis "lasts for the entire year" if cast under certain conditions, but indeed the rules would stipulate that it could expire before: because of that information the organization of the reader's campaign depends. It would not concern the reader if it would last a few hours longer though - just like the buyer of the battery.
Very much. Wikipedia is an encyclopedia. And if an article in an encyclopedia defines a term immediately in the first phrase, that is the definition, as far as the encyclopedia is concerned. If it later states "The term solstice can also be used in a broader sense", it just lists other uses to later be able to put them into technical, historical and cultural perpective.
Cheers
That's a standard format for recording measured values.
I hope you see the contradiction above. You say the year is defined by the full circle. Then to get your Aegis to last an entire year you had to switch to a year as defined by sunrise/sunset. Had you remained consistent in your definition in the second case, your Aegis would not always last an entire year.
Also, as I explained, using the solar year versus the sidereal year does not get rid of the leap year issue.
Yes, it absolutely does.
I left it open as a question because it seems to work most consistently. And it's not my homegrown use of a year, it's actually the everyday western calendar use of a year - a very common use of year. You decided yourself to adopt it above for half your argument. Why were you so quick to use it yourself to try to make your case that it shouldn't be used?
Except the article explicitly says this is not the definition, but only one of many.
Chris
That would be your 'rising/setting year'? No.
Why would I? I would not touch that thing with a rabble when physical or magical durations are involved - and neither would medieval scholars or Hermetic magi, who know the mess of medieval calendars first hand. Medieval calendars are rather the domain of laws, contracts, work obligations and holidays.
So lets take it really slowly.
How much time expires between one winter solstice - the astronomical event - and the next? Exactly one (solar) year Y. So if I cast a Duration: Year Ritual on or a short time T after winter solstice, and if that T is smaller than the time T' between the next winter solstice and the sunrise on it, then the overall duration of my Duration: Year Ritual is: Y-T+T' > Y. OK?
Because I saw somebody dangerously veering towards it. 
It is the definition of Wikipedia for solstice.
Cheers
EDIT: It looks like we were driving a carousel all the way from Saturday December 15th ( catnip & garlic ) - when your 'rising/setting year' was still just a calendar year - through sidereal years and back here. I wouldn't like this to become the second round.
You say this, and yet you did:
It's not so surprising that someone would use this idea for a year. It is, after all, the colloquial (and generally assumed in non-scientific circles) standard in English (and I suspect in most European languages). Certainly, I don't celebrate my birthday on different dates from year to year depending on the time of day I was born and when the dates are in comparison to leap years. The only ones I know of who do this regularly in western culture are the ones born on February 29 because they don't have a choice.
Similarly, do you, for Year+1, bother to figure out what time of day the spell was cast to figure out what date is a year later (and then add a day)? Or do you go to the same calendar date a year later (and then add a day)? I suspect most players would use the latter, not that it can't be done either way.
Good. So now you do see that casting the spell after the astronomical solstice and before sunrise is not sufficient to guarantee it lasting a year. You have to do so within certain extra constraints. So, as I said, using your method also does not guarantee the spell lasting a year if it cast at the time stated in the Aegis of the Hearth description. Since that was the point that was so bothersome about using my method and since neither one holds up to it consistently, either we must read the Aegis of the Hearth description a little more colloquially or throw out both interpretations and search for one that actually fits such a strict reading. I prefer allowing both your method and my method to having to throw both out.
Chris
PS: Forgot this:
Yes, it does; the distinction it is even stated. Ars Magica specifies working off sidereal years for some durations but goes on to, in essence, state that sidereal and solar years are so close that for game play we can estimate both of them similarly (the estimate being 1 month = 1/12 year, even though months vary).
That is quite irrelevant for the topic at hand - but certainly depends on the campaign, and the current SG's ideas to cause problems. I would at least give characters an easy Artes Liberales roll, if it is important for them to notice that scheduling their Aegis by their chaplain's calendar is a lousy idea.
Of course casting the spell after the astronomical solstice and before sunrise is not sufficient to guarantee it lasting a year. I don't recall to have ever said that, either. Casting it before sunrise is very important, though, because it is the condition to have the new Aegis come up while the current one is still in place - and thus to avoid the cumbersome pest hunt or worse.
So can we agree now, that the part of my reasoning which you quoted above is correct also from your point of view? In that case we can stop this exchange.
In the Aegis of the hearth description, we read "The Aegis is typically cast on the winter solstice, ... , and the Aegis then lasts for the entire next year." (Underscore mine as usual.) So there T = 0, while the case we just discussed - Aegis being cast sometime after the winter solstice - means T > 0.
That's interesting! Where is this stated?
Cheers
It's in TMRE. Look at the astrological stuff. There are several comments on the difference between the solar values and the sidereal values, and the sidereal ones are the ones used for the astrological stuff. I'm not sure the book ever says "sidereal." But They describe it. For example, the Sign duration is (for Hermetic magi) 1/12 of the time it takes the earth to complete a year with respect to the "fixed" (never really liked that term) stars. That is, Sign is a twelfth of a sidereal year. So the magi technically care about it. However, let's make it easy for the players, let's just estimate that as one month (which is not even consistently 1/12 of a solar year). But they do suggest making that estimate instead of dealing with what the magi actually deal with.
Chris
I walked through it again. In particular the chapters on Astrological Durations (p. 49f) and the Armillary Sphere (p.51ff), which both relate to this thread, were interesting to read once more. Weird is, how AstrologicaI Time (box on p. 49) is made location dependent with handwaving. I did not find any reference to sidereal years or values there, though.
Cheers
Look at how the measurements are made for Sign and the like. This is the easiest way to describe how someone can measure the difference between a sidereal year and a solar year or a sidereal day and a solar day. I don't believe the word "sidereal" is ever used there, but the sidereal periods are.
Interestingly, I considered the 20-minute difference and the lifetime of a magus. Assuming an average magus lives to be somewhere around 100, or roughly 75 years after gauntlet, things will have shifted about one calendar day during his lifetime. Magi who are interested actually live long enough to really notice this shift.
Chris
Of course the measurements described are 'sidereal' - by the very nature of astrological measurements.
So player character magi - if really interested - could by experience in their lifetime actually falsify the Ptolemaic model, if they found the 20 minutes difference per year. Of course, if they found the difference they would have also falsified the ArM5 rules: like those in ArM5 p.80 'The Limit of the Lunar Sphere' or A&A p. 16ff.
But it is anyway more likely that during their lifetime they have followed the general academic development and become observant Aristotelian magi, eschewing experience where it doesn't fit (A&A p. 10 upper box).
Cheers