After quite a bit of reading, I realized it's apparently really hard to have something that measures time with 1-second accuracy on the timescale of a day. This is sophisticated technology well beyond what people in the middle ages had or could even conceive of.
Basically, it seems that the best accuracy on that time scale would still be provided by sundials, and for several centuries after 1220. So, roughly speaking, a 1-minute accuracy (then again, if you think of it, 0.1% or so is pretty impressive). Even getting 10-minute accuracy on a day timescale (so, of the order of 1%) with a waterclock or sandglass is an astonishing feat. The more I think of it the more I'm convinced that magic, if used to measure/cause mundane events, should not be able to beat this.
So, what if you want to know time elapsed since the last solstice with 0.1 second accuracy? My best guess would be the following. Summon a minor aspect of the Kosmokrator of time, and keep it around, keeping track of time. No meagre feat, but if you want quality, you have to pay for it You can then sell to other interested covenants and magi Imaginem effects (including small, portable ones in bracelets) allowing them to observe said daimon ... in real time!
I think that one is firmly SG discretion.
I've said before I prefer magic as an art, not a science. It is not consistent. If people want to test a spell, a magi could test the same spell over and over, and sometimes the voice range spell would work at 52 paces, and sometimes fail at 48. That's magic. Others may not like that interpretation. My earlier example spell was going for a generous SG.
With that caveat, I think even a less generous SG would accept a magi getting accuracy within seconds if measuring under a day, within minutes measuring under a month, and within a day measuring anything longer.
Mm, I thought the same until an hour ago, and I've changed my mind. I would not allow the "average" magus to determine time with simple magics with better than 1-minute accuracy on the timescale of a day. That's about 0.1% accuracy; it seems very hard to set up any local (i.e. non-astrological) process to be that precise. And if you are looking at how the celestial spheres move ... well, then you are effectively translating a time measurement into a distance/angle measurement, and a 0.1% time accuracy means a 0.1% space accuracy (less than 5cm over 50 paces!); again, very hard to beat.
I looked at the Hermetic Astrology chapter in TMRE, and I only found what might be a very indirect hint: the astrological time is "the same" over an interval about 1000 paces long, which is the distance the Earth rotates (at the latitude of Western Europe) over about 4 seconds. But while you can't tell the time better than that, it's not obvious to me that you can tell the time with that accuracy. In fact, a spell such as Divine Heaven’s Aspect that "Reports all aspects of the astrological conditions" reports "minute, hour, day, sign, planets" suggesting (to me) that minute is roughly the best resolution you can get within a timescale of a day.
(In fact, the astrological "minute" according to TMRE is Diameter, so 2 "standard" minutes, but that's fairly minor).
(Hmmm. Now that I think of it: those 4 seconds or 1000 paces, are roughly one minute of arc at Western Europe's latitude. Hmm. Strange coincidence).
You've seen the guidelines. I think you just miscalculated or misread. The circumference of the world is about 43825760 paces at the equator. You need to be within 500 paces to be at the same time according to TMRE p.49. Let's divide that circumference up into 24 hour increments: 1826073. Now let's chop that into 60 intervals to get to a minute: 30435. So let's divide that again into 60 parts for seconds: 507. So the being at the same ArM5 astrological time is being roughly within 1s at the equator, a bit more in Europe. Yes, that's right, 1s. Now look at things like Sight of the Astrological Hour, which is enough to tell you if you're within a second or two or so, and we can see this guideline can tell you if you're within a second or two or so. So I ballparked 6s, as that's a round. So if you want to object to my 6s, you'll really want to say I should have narrowed that further.
Not really. I ran basically the same calculations as you, but
a) noted that if all objects within 500 paces of you are on the same time, objects within 1000 paces of each other are on the same time.
b) looked at stuff at the latitude of Western Europe, rather than the equator, which increases the time by roughly 50%.
So your 1-2 seconds become 4 or so.
However, as I said, I do not agree with your line of reasoning. The fact that stuff more than 1000 paces apart is - or can be - not "on the same time", does not automatically mean you can learn the time accurately with that resolution. Basically, your "astrological clock" might provide you with a measurement that's slightly off - say, by 40 seconds - but it's more or less slightly off by the same amount for all stuff within 500 paces, so your magic can work cohesively on that stuff.
In other words we might be in a situation where, after correcting for the local position so as to get a Universal Time, any pair of astrological clocks within 500 paces of each other differ by at most 1 second, astrological clocks further away can differ by up to 1 minute. Or perhaps all astrological clocks in the world are always perfectly synchronized after correcting for location, but they can, at any given time, be (all) off by up to one minute. Then everything still works as in the book, but you have no way of telling what the "real" time is with more than 1 minute accuracy. Does that make sense?
Ya, that's logically invalid here, and we know for sure the book disagrees on this. Object 1000 pace from you are far enough away that astrological stuff fails due to the times being different.
Or, more properly if you read what I wrote, my 1s becomes 2s, which is why I wrote 1-2s.
Except that you can measure the time well enough so that the astrological stuff that must distinguish between these times can work. If the astrological stuff must distinguish between these and the spells work to provide such distinguishment, then the spells must distinguish this well, too.
Well, this works in the sense of things like astrological v. solar time and not knowing which one you're using. But since the measurements must be able to distinguish between each second or two for the astrological spells to work and since these detections can work for this purpose, they must be able to distinguish one astrological time from another much better than that.
I would disagree: astrological stuff can fail if you try to affect simultaneously two objects 550 paces one way, and 550 paces the other way, from you. But we know it works if you only involve two objects 450 paces one way, and 450 paces the other, from you, so 900 paces from each other. But this is really a minor point not worth discussing further.
Not really. Again, let's assume for simplicity everything is corrected for location, so two astrological clocks in two far-away places show roughly (within a minute) the same time.
Your astrological clocks all over the world are providing you with what is effectively a measured-time-field. Now, you can have pretty big distortions in this time field, of a minute or more, as you move through space or time - even if the local gradient of those distortions is small, so that you never see a relative error of more than 1 second for two points within 1000 paces and/or 15 minutes from each other.
What's more, even if the distortion gradient is steeper, you might never really learn time with an accuracy better than 1 minute. Think of "real time" as a hidden variable. Your spells will provide you with a rough approximation of this hidden variable, which can correctly guide your actions even if it's somewhat wrong. But if your astrological magic ever tries to affect simultaneously two points where the hidden variable is different (even if the approximation is the same) it will (or maybe just might) break.
I think this is all compatible with what's in TMRE, and still with a magus not being able to learn the time with resolution better than one minute via spells such as Divine Heaven’s Aspect.
That doesn't mean they're at the same time. What it's saying is that everything must be within 500 paces of the measurement point. That way the times from the measurement point are within the 1s (equatorial). If your measurement point is one of the two, it will fail for the other one because their times are too far apart from each other. So they are at different times, but neither time is too far away from a central measurement time.
Look at this with something physical. Let's say I have a disk measuring 500 paces in radius. If I drop it on a central location, two points nearly 500 paces away on opposite sites can both be hit because the positions are close enough to the central point. But if I drop it centered on one of them, I totally miss the other, because they are not close enough to each other to be considered about the same point.
I really isn't. Let me give you a more concrete example to make it more obvious. You fly (to avoid horizon issues and the like) and multi-cast Sight of the Astrological Hour on a whole bunch of spots, each a few thousand paces from any of the others. You know the time at all these locations. Any one of those will allow you to hit things at about that location, but will fail against all the other locations. But you know the values for all these other locations, too. So you have clear distinguishment between the values at these points, even though the times will only differ by a few seconds from one to the next.
Now, I do understand what you're trying to get at between the gradient and the actual value. However, the guidelines don't say they give you the gradient. They say they give you the value itself. You would have to calculate the gradient from these. The guideline specifically says we can "discern and measure" this astrological value, not that we are told how different it is from another value. The book even goes into noting that you can use calculations with the gradient to figure out the actual value, which is what is needed. But the gradient is given by Artes Liberales, while the actual value you start with is from the spell. So it's really not a hidden variable at all, unless you want to change the guidelines and the rules for astrological spells.
Let's try to make it clear one last time, recapping what I read in the book.
Divine Heaven's Aspect gives you a whole lot of astrological information for a given point of space-time. Among other things, it gives you the (local, astrological) hour and minute; crucially, time information is not provided with finer resolution. Minute is specifically described as an interval equal to Diameter. So, we can think that the spell is giving you an hh:mm:ss number, plus or minus 60 seconds. You "read" 12:55:39, and you know you are between 12:54:39 and 12:56:39. That's your "minute interval".
You can use this information (which includes not only time, but other factors as well) to cast an astrological spell that will affect anything within roughly 500 paces of the reading point, because "for the purpose of Hermetic spells, conditions are essentially identical over an area extending approximately 500 paces in all directions from the point of measurement."
Note that this does not say that you get exactly the same reading for time. It means that if two points are within 500 paces, you might get two different readings, but they'll both be good enough for spellcasting, because the underlying conditions are "essentially identical" for hermetic purposes.
So, you might have two points X and Y that are at 50 paces from each other, and should be less than 1 second apart, and you still might read astrological time as 12:55:39 (+-60s) for X, and 12:54:57(+-60s) for Y. Nothing wrong with that. But what's the real time? Well, maybe 12:55:39, or 12:55:21, or 12:55:00, or 12:54:50. You have no way of knowing which one is exactly right. You do know they are all right within 1 minute, though obviously not within 10 seconds.
Note that it may still be that your reading for a point Z, 3000 paces away from X, is 12:55:30 (+-60s): a closer reading than for point Y. This does not mean that trying to use the same spell on points X and Z will still work. First, because there are other astrological parameters beyond time. Second, because the underlying time conditions might be sufficiently different to break the magic, even if they are not sufficiently far apart that the respective readings will be substantially different (i.e. the two intervals will be non-overlapping). These are two subtle points that I might not have managed to get across.
The above affects distortions of time readings over space. Basically, if you have two InIm spells active, each showing you the time at two different points in time, the readings might be closer or further (by up to a minute) than what you'd expect given the distance between the two points.
But there may well be distortions over time too. Suppose you repeatedly cast Divine Heaven's Aspect, once a round, eleven times. You might get:
12:54:57
12:55:01
12:55:44
12:55:45
12:55:46
12:55:48
12:55:50
12:55:51
12:55:55
12:55:56
12:55:57
This is perfectly compatible with what's written in TMRE. The readings are, or at least could be, all correct, if you take into account that each should be read as +-60s. Of course, you know that it's impossible that between between your second or third casting you could have waited enough time to cast not one, but seven spells... and that you have then managed to cast seven spell over the time you'd usually manage two.
Summarizing: it seems to me that nothing in TMRE contradicts the hypothesis that the finest resolution at which you can magically observe astrological time via Divine Heaven's Aspect is 1 minute rather than a few seconds.
OK, let's assume you are correct and see what happens. I'll use all east-west since north-south is a non-time issue.
Scenario: You work at one location and you're clever, knowing you only know the time down to the minute but you only need to be within a minute. You cast your InVi spell. No you repeatedly cast an astrological spell at the location using that time until it fails. The moment you hit a failure, you know the time you measured is now just outside a minute off, so you know the exact time down to the amount of time it takes to cast a spell. That means you know the time down to about 6s, or even better if you can fast-cast the spell well. So even given that one of these spells will only get you down to a minute, you can still use Hermetic magic to narrow the time down significantly further. That means even given this variation, Hermetic magic can detect things down to just a few seconds.
So, given that Hermetic magic can detect this true time down to a few seconds, why would it be that Hermetic InVi to detect the time cannot do it?
.
Also, do note that the book uses things like knowing the "hour" to mean knowing what hour down to fractions, not just whole hours. Given this, assuming a statement of learning a "minute" cannot give you fractions but only whole minutes does not follow.
No one said that your astrological data works unchanged for exactly one minute, and then "breaks". In fact:
Beyond modest limits, neither Daily Horoscopes nor astrological times can be applied
consistently. However, the steady increment in time as the day progresses in a single place is a natural part of astrological calculations and is already included in calculations: a Daily Horoscope lasts for one day in the place it is calculated for.
Remember that time is combined with many other factors - astrological information is heavily multidimensional. So, it's not obvious at all that your search algorithm can narrow down the "real time" to a few seconds using only astrological observations.
Well, if something is supposed to give me the hour and the minute of an event, I tend to assume it's not going to give me the nanosecond.
But please note that I never said that the book explicitly denies a time resolution finer than one minute is possible. I said that the book never says or implies it's possible, and that (see above) when you are told you can get the hour and the minute of an event, the language suggests that's more or less the resolution limit.
Also, I said I would dislike the idea of anything finer than that, because it seems that any type of mundane observation over the scale of a day was just unfeasible with a better resolution in the with the intellectual machinery of the middle ages. More in general, direct measurements accurate to 0.01% seem ... not quite what the Art of magic would give you, I don't know if I manage to make myself clear. (Getting 0.01% with lots of individual measurements and lots of computation is ok, of course, as well as asking to some powerful entity). This is just setting aesthetics for me.
Now, this discussion was a lot of fun, but it's starting to be distressingly similar to work for me. So I hope you don't mind if I bail out!
That's dependent on how one chooses to determine randomness and margin of error.
I do not have the book with "divine Heaven's aspect" so my apologies if I have an interpretation error here. If it gives the minute, if it always rounds perfectly, yes, one can get clearer detail.
For example -The spell tells the magi it is 6:51. The magi knows it is somewhere between 6:50:30 and 6:51:29. The magi keeps casting and when it tells the magi it's 6:52, yes, the magi know now it's somewhere between 6:51:30 and 6:51:36. I'm pretty sure I'm just saying what you said, just want to make sure we are on the same page.
If the SG wants that level of detail, great. If not, the SG randomises. At 6:51:20, the magi might get 6:51, or 6:52. This could mean the spell tells the magi it's 6:51, and 6 seconds later tells the magi it's 6:52. If the SG wants imperfect measurements with Hermetic magic, it's easy to do.
Correct. I didn't show this, but this is true as well.
Sure, but I just showed above how totally random returns within a minute still give you roughly 6s precision. So either of these ways we're getting 6s precision.
Yes, but all the other factors must necessarily remain locked to geometrical constants because if you know the time well enough at one place, all you need to know is the geographical location of another place compared to that first place and you know all the details there as well (assuming decent Artes Liberales to do the calculations). So if you don't vary the location, the only issue is the time, and that's how you can do what I showed.
Realize, we have things like InTe that can count grains of sand in a large pile in a moment or InHe to count the number of needles on an evergreen, and we can't even come close to those with any device today. Should it really be so unexpected that magic could advance some technology to count something else a few hundred years when I can so easily provide examples of how it can beat out stuff about twice as far into the future? Brahe was measuring with seconds prior to 1600 with just the technology of the time, no magical assistance. Within about a century of there we were about to measuring a day within 6s.
You can then sell to other interested covenants and magi Imaginem effects (including small, portable ones in bracelets) allowing them to observe said daimon ... in real time!