The Speed of Magic?

I can't check Byrhtferth (no command of Anglo-Saxon, so no try to find the text even), but I understood so far, that both Bede and Byrhtferth were involved with the symbolism of numbers in their computus. This might explain their interest in 'atoms' of time, and their later occasional recurrence.

Using such symbolism of numbers for time in current Hermetic magic would certainly help explaining some difficulties in achieving (A&A p.11) Aristotelian Magic Theory and/or Platonic Magic Theory. :nerd_face:

I don't have access to Byrhtferth in English either but I did track down the passage from Bede:

"The smallest time of all, and one which cannot be divided by any reckoning, they call by the Greek word ‘‘atom’’, that is, ‘‘indivisible’’ or ‘‘that which cannot be cut’’. Because of its tiny size, it is more readily apparent to grammarians than to computists, for when they divide a verse into words, words into feet, feet into syllables, and syllables into quantities [tempora], and give double quantity to the long [foot] and single to the short, they are pleased to call this an atomus, as they had nothing more beyond this which they could divide.

In exploring the nativities of men, astrologers likewise claim to arrive at the atom when they divide the zodiacal circle into 12 signs, each sign into 30 partes, each pars into 12 puncti, each punctus into 40 momenta, and each momentum into 60 ostenta...

...The Apostle uses the term for this kind of time in a better sense, to suggest the swiftness of the Resurrection, stating, We shall all rise, but we shall not all be changed, in a moment, in the twinkling of an eye, at the last trumpet. This deserves our attention, because although computists make a strict distinction [between these terms], many writers indiscriminately call that tiniest interval of time in which the lids of our eyes move when a blow is launched [against them], and which cannot be divided or distributed, either a momentum, a punctus or an atom"

The word translated as "moment" in the passage Bede quotes (1 Corinthians 51-52) is "atomō" in the Greek but was "momento" in the Vulgate which Bede probably was himself using, which is where the confusion in terms he complains about probably originates.

Bede definitely uses "atom" as a more general philosophical idea of an indivisible unit (for any given thing which can be measured) rather than specifically as a practical unit of time. I'm not sure where the value listed for an atom of time in later works comes from, possibly from trying to put a number to the reaction time of a flinch as Bede suggests (any such number would be a complete guess of course, impossible to measure at the time).

This is the problem: mixing measuring and divisibility.

As you quote:

If there is a rythm, there is of course a smallest unit, the unit of the meter. That may be called 'atomus'. But just by speeding up the tact and thereby shortening the meter, it is quite obvious that this is not an indivisible unit of time, but of a rythmical text.

The same with the partitions of a circle or zodiac: the smallest units are units of a scale, not of the circle proper. Latest Hippasos knew, that there existed incommensurable numbers, which could not be rationally expressed in terms of a specific scale.

In his allusion to Paulus (1 Corinthians 15, 52), Bede tries to describe the 'point in time' of resurrection with metaphors. But with Paulus he appears to imply, that this point in time has no duration at all - time ends there.

So I would conclude, that Bede indeed does not even care to define the smallest unit of time in this text. What Byrhtferth does with it, I don't know.

But

Is just rethoric.

This is precisely what I was saying, Bede doesn't try (or seem to think it useful to try) to define an "atom" of time. Bede is quoted a lot by later writers, but the value of an "atom" as a unit of time comes from some other source (Byrhtferth is the first to use that value, but may not be the originator of it). Maybe in Mythic Europe Byrhtferth learnt that value from a magus, who had made a strange observation involving a magical cube...

An atom as Bede explains it is really just some theoretical indivisible lowest possible unit. Not of time specifically, just of a quantity. An atom of time is some amount of time which cannot be divided further. An atom of meter is some amount of the meter which cannot be divided further. An atom of matter is some amount of matter which cannot be divided further. All unrelated units to one another except in the sense that they are indivisible. And really, that's just Bede parroting Atomist ideas - even if it was pretty much abandoned as a philosophy atomism still survived into the middle ages in quotations and refutations of their ideas, and some of their ideas inevitably bubbled up here and there.

Whether such an indivisible unit actually exists in regards to time in reality is a whole other question, and not one Bede bothers to examine.

I'm not arguing in favour of the existence of an atom of time as a specific quantity (or even in theory) in Mythic Europe. It's a possibility, but so is the Aristotelean view of infinite divisibility. I just thought the quote from Bede might be of some interest.

4 Likes

My suggestion was not that the box is "cloned" simply that it exists in two places at the same time. If you remove the box from either location the other box vanishes. Basically quantum superposition.

My reaction to this would be:

When the magus finishes enchanting effect #2 (which teleports in a specific direction when the cube enters a magical aura), the effect immediately triggers. And keeps triggering again and again every round, moving away until it teleports into a solid object (at which point the cube is destroyed) or it disappears into infinity.

No explanation. Let the player/character make up his own. :smiling_imp:

EDIT: Or some variation on that. The cube might stop right outside of the aura. When the magus tries to bring it back inside, it triggers again until it is outside. In short, he is never able to bring it back to his lab to enchant effect #3. Every time it is moved, that increases the likelyhood of it teleporting inside something or someone. Particularly since every time it teleports, it then falls down to the ground. At some point it will be at the lowest point possible and the next teleport will bring it into a solid object.

How's this:

If you look at Greek text of 1 Corinthians 15, 52, you find 'ἐν ἀτόμῳ' - en atomo.

ἐν ἀτόμῳ, ἐν ῥιπῇ ὀφθαλμοῦ, ἐν τῇ ἐσχάτῃ σάλπιγγι

There it means quite literally 'in an instant' - and in the Vulgata becomes

In momento, in ictu oculi, in novissima tuba

Your translator of Beda makes of it

in a moment, in the twinkling of an eye, at the last trumpet

Old schoolmaster Bede - full of his Greek - then harps on that 'ἀτόμῳ' he has found, as he has some idea of atoms of matter, likely from the Timaios - and comes up with 'atoms of time'.
When compiling the Epilogus, Byrhferth sees the need to further elaborate and attach quantitites to these 'atoms of time'.

The term " ἄτομος" comes from the atomist school of philosophy and so does the idea of atomic divisions of other quantities (time, motion, matter). The very early atomists, as far as we know from surviving fragments, only proposed atoms as a fundamental division of matter but later atomists (in response to critique from thinkers like Aristotle) also proposed that time and motion broke down into indivisible units - at least since the time of Epicurus. A summary of a lost part of Epicurus' works was later described by Simplicius of Cilicia in a commentary on Aristotle:

"...the Epicureans, who came along later, said that this is precisely how motion does occur. For they say that motion, magnitude and time have part-less constituents..."

So atoms of matter, but also time, motion, and potentially other quantities were a part of later atomist thinking, rather than being something Bede comes up with himself (though it's also possible Bede hasn't read any of these writings and is independently coming up with the idea, I suppose.). It reads to me more like Bede is explaining an idea he has read (possibly in a commentary by someone else) but which he himself doesn't necessarily find terribly sound. Atomism had fallen out of favour even by Bede's time, but the ideas were still floating around even if mostly in people trying to refute them.

The momentum/atomos/punctus confusion Bede complains about is pretty understandable imo. You have the Greek derived "atomos" meaning "indivisible, uncuttable" which is intuitive for matter, but then is being applied to time and motion too. You have the loanword "atomus" in Latin, but also "momentum" which can mean "[a] motion", "something which happens very fast/in a short span of time", or "a point" among other things. And then also in use as a time unit is "punctus" which literally means "a point" in medieval Latin. I can see how people might have gotten wires crossed...

Very likely, or if not Byrhferth then someone else a little earlier whose work didn't get transmitted. I certainly can't see any way for the value given to have originated other than "pulled out of thin air". Maybe there's some symbolic reason for the number 47 that I'm not seeing.

ἄτομος existed in philosophy as a terminus technicus at the time of Paulus. Field, manifold, series and variety do so in mathematics today. But this does not mean, that in every occurrence of these words they are used as termini technici.

I assume, that the authors of the Vulgata (a little before 400 AD) were more familiar with the Koine than we are: and they translate "ἐν ἀτόμῳ" as "in a moment". So does my GEMOLL Greek Dictionary.
To expect a philosophical terminus technicus in a letter of Paulus to a christian community also makes little sense to me. Even less so in a phrase, which treats resurrection with some poetical spirit.

The problem is here indeed, which texts on this thinking Bede had likely access to in the early 8th century. The Timaios in the partial translation to Latin by Calcidius in the 4th century (which stops in the middle of the theory of the elements) was most likely available to him, as was the still more fragmentary translation of the Timaios by Cicero.
I cannot exclude further inspirations, of course - but would like to see at least some explanations, which texts in which manuscripts at which places these might have been.
I certainly do not see any in Bede's text above - and honestly do not see any by the Timaios either. He just explains the term ἄτομος / atomus as a philosophical terminus technicus correctly in the first phrase.

EDIT: A plausible source for this definition could also be book XIII of the Etymologiae.

The difference, I think, is that all of those terms have other meanings and don't originate in Mathematics, whereas atomos is a term that originates in philosophy and filtered out into more general usage. There is no usage of the word which doesn't derive from atomism (even if by the time of Paul you didn't necessarily need to have studied philosophy to have heard of the idea). In that sense it's more like the word "karma" in English. An idea that is rooted in the ideas of certain religions and philosophies but that's entered common use.

I just find it more plausible that Bede had read the idea somewhere, rather than independently coming to the same idea as the atomists. Enough of the church fathers quoted Epicurean ideas (in order to dispute them) that I would be more surprised if Bede hadn't ever been exposed to the basic ideas of atomism. And you're 100% correct that Isidore does have a quite comprehensive definition of an atom, with a subsection on time even:

"With reference to time, the atom is understood in this way: you may divide a year, for example, into months, months into days, days into hours. The parts of hours still admit division until you come to a point of time and a speck of an instant such that it cannot be extended through any small interval,
and thus can no longer be divided. This is an atom of time"

And in that translation where it says "a point of time and a speck of an instant" the original actually read "punctum et quandam momenti stillam" which is the same sort of terminology that Bede uses (punti and moments and atoms etc.).

Anyway as interesting as it is (well I find it interesting at least) this has gotten a bit off track, so back to in-game stuff. It occurs to me that if you decide there is an atom of time in your saga (whatever the value might be) then a device like this is effectively magical clockwork (assuming it works consistently that is, which it might not). Connect another effect to the linked trigger and you have something which repeats a fixed number of times per day indefinitely.

Hook that up to something which can trigger other items and you could build quite a complex little system... It could possibly make a good "dungeon crawl" type adventure, exploring a mysterious ruined covenant once controlled by an elaborate system of enchantments which all mysteriously failed - the failure being because the whole thing was based on a cube like this until the aura boundary shifted too far (perhaps from the formation of a regio) and stopped the cube dead. There's a kernel of an idea there.

1 Like

Are you sure? ἄτομος is ἄ - τομος from τέμνω 'I cut'. Hence it means first: uncut, unmowed - and is used as such. See the GEMOLL here, which follows use in classical literature. It then becomes: not to be cut, impossible to cut. And then: the instant, the moment and finally the atom. So I see the typical development of a terminus technicus from commonly used words.

I think we both agree, that the Etymologiae, due to their popularity in Bede's time, are a pretty plausible inspiration for Bede's basic idea. I reckon, that we will not get any further here.

Perhaps 47 was simply the largest prime number he could come up with, or perhaps he simply added the biblically significant numbers of 40 and 7...
personally if 1) were using atoms of time and 2) my players came up with a way to discern how many of these there were in a diameter and 3) the results of this were in fact consistent, then my answer would be 172,800, but that assumes the 3 very improbable assumptions stated. (for those not wanting to do the math that is 1440 'atoms' of time per second- for reference modern science has shown the shortest amount of time a human being can process is roughly 1/10 of a second) Plank time, for the curious, is 5.39×10−44 seconds, but is not actually a quantization of time. However it also works as a nice anachronistic answer... (and why would a question about the atomization or quantization of time not have an anachronistic- literally without time- answer)

Do you have a reference for that? It mostly surprises me as 24 fps is considered the minimal frame rate to be used to have things look realistic. That slower than 20 fps is problematic seems to imply we process images faster than 10 fps. It also surprises me as I've seen people press start and stop on a stop watch in under 0.1 s, which requires multiple shifts in motion within that 0.1 s. From significant experience, a typical person can hit start followed by stop in a little under 0.2 s, and with some practice can commonly get below 0.15 s. I expect with better-designed buttons, it could well be faster; this is just with cheap stopwatches. But there can be issues between the difference in a bunch of coordinated things in a small amount of time and multiple disparate things in a small amount of time.

Are you referring to the older studies that found > 100 ms to process an image? Newer studies have shown otherwise. A 2014 MIT study found > 13 ms (though it may be lower due to computer limitations), which was consistent with the ~14 ms a 2001 University of Parma / University of St. Andrews study found with monkeys. But performing actions requires more time than processing images.

My understanding (and admittedly this was from educational television shows from 5-6 years ago, so more up to date information may be available) is that it relates not to processing a single sense but rather a delay in processing so that everything that is simultaneous seems to happen simultaneously, rather than say processing visual information in 13ms and receiving a signal from your foot in 97 ms. Reflexes of course would not be subject to these limitations, which may relate to things such as double pushing a button which may involve multiple physical movements in a single conscious thought. I do know from my background in electrical engineering that audio signals require twice the sampling/playback rate as the frequency being produced to produce clear sound, 24fps sounds to me like a 100ms perception rate with double frequency and a 20% margin, which falls within standard engineering practices.

Well, yes.

However, an effect triggered by an environmental or linked trigger doesn't need an action.

So, if a maga uses an invested item in combat, triggering it by herself would require an action, and thus would occur once per round at most. Even if the item is triggered by a linked trigger (like mind reading the maga), I would say targeting count as an action. Perhaps like a fast cast though, and thus only possible as long as the quickness roll is a success? But that's only my ruling there.

Other than that, I cannot find any rule limiting the number of effects activated in a round by a device. Perhaps I'm wrong?

So... for the proposed cube, I would say the frequency is higher than 1/6th of a hertz. And you proposed many interesting ideas. Thanks! :slight_smile:

technicality- 1/6 second would be the period. 6/second would be the frequency. For frequency the time interval should be in the denominator instead of the numerator.

Ahah! Indeed. I mixed two sentences. Thanks for pointing it out. I'll fix it.

regarding an effect triggered by a spell, there is nothing that indicates 1) that information from the InVi spell is instantaneous to the degree this is suggesting or 2)that having effects linked to a trigger somehow circumvents the rule on p100 of the core book that one effect may be triggered per action.

That's a valid answer to the "what happens?" question. If the sensing isn't instantaneous then the effects can't trigger faster than that delay - but then the question has become "what is the sensing delay, and why does it exist?". Are items with constant magical senses slower to react than a person or animal would be to something impacting a sense? If so, why? These are the kind of questions I imagine that Bonisagi lose sleep over.

This is saga dependent, but I've always viewed that rule as a game convention rather than an intrinsic law of nature in Mythic Europe. That said if this limitation were actually an intrinsic part of the world (that just happens to conveniently also be good for gameplay) that's an interesting answer too and raises all sorts of interesting implications. What exactly is an action, to a mindless item? If I link two effects to one trigger but only one can be triggered per "action" which happens first, and how long is the delay before the second happens? Why is the delay that length? And so on...

1 Like

If I'm not mistaken, there is nothing in the rules on this point. I tend to agree on the fact that it shouldn't be instantaneous. So it is a possible limitation of the frequency.

On this point, I disagree. Page 100 describes the activation by a person. In this case the action is done by the person, it's a trigger action. The object is not taking any action. The person is limited by one activation a round.

First sentence p.99 says "Any number of effects can be linked to a single triggering, and may depend in different ways on the result of that effect". So I understand that if you link three effects to another one with the same result, when the trigger is pulled, all three effects fire at once. The object is not limited by actions.

For me the real limitation is how many results a triggering spell can return in one round, that is your first point.