Engineers tend (IME) to have a somewhat superficial understanding of Entropy - and of physics in general.
Exceptions exist, obviously.
I think you are reading too much in the word "full". What we have is a full description of the end result of the enchantment/invention process, the actual creation. What we do not necessarily have is a full description of is the process by which it was obtained; we obviously do not know, for example, exactly what bonus the experimentation roll yielded.
Note the same use of circular logic as before. You write: "Thus the descriptions of their creation would not be full descriptions if they lacked notes about abnormalities due to experimentation; changes due to experimentation are considered part of a "full description," as evidenced by specific notes when there are abnormalities." I've underlined the point where the fallacy hides: you are using "when" to mean "in all cases when", while the logically correct reading should be "in some cases when". It's like saying that someone who owns only the ArM5 corebook owns the entire ArM5 line, because since he obviously owns a book when it's part of the line, there cannot be books in the line he does not own.
I am not sure hermetic magic can affect probability
but they can learn the arts of learned magicians who have one art affecting luck
Here is the reasoning:
- Spell descriptions include design.
- These are full spell descriptions, meaning they lack nothing from a spell description.
- Therefore they include all design information, not just some of it.
Where is the circle, please?
I think you just misread a couple things. I wrote "evidenced," not "proven," for a reason. If my interpretation is correct, based on the number of seasons of experimentation, we should see a certain number of side effects. If we do not see an appropriate number, my interpretation is likely incorrect. Only "some" of Scipio's spells were created using experimentation. Two of them show up with notes. We know there are more, though we don't know which spells. Odds are that roughly 2-3 of the spells should have side effects. So the number of written side effects is consistent with all side effects being listed.
Why did I write "when"? Because notes at other times would not be evidence of it, though we do see notes when Virtues are used, such as Glamour. Did I use it to mean in all cases? No, that's not at all what I wrote. For example, there is a law in my state for protecting emergency personnel, as evidenced by cars pulling over a lane when approaching emergency vehicles. Yes, I used "when," because cars pulling over for other reasons such as to pass another car are irrelevant to the law. However, not all cars pull over as they should; but the statement is still correct, so "when" doesn't mean in all cases in such a statement. Thus "when" used here does not imply what you say it does; that's just your misreading.
"Design" is one of "several factors that describe [a spell] for game use" (ArM5 p.115-116), and items just fire off spells. Lab total is not listed as part of the description. Neither is the number of seasons an individual used to make the item.
Now, results of experimentation and similar are not explicitly necessary as part of the description. But "design" is one of the "factors that describe it for game use." Only the parenthetical note at the end is explicitly required. So if my logic is in error, it's here. Now let's see the consequences of such design notes not being part of the full description...
Note that one of the purposes of the "full description" is so that player's may have their magi develop these effects from scratch. No, I'm not just guessing at that being a purpose; we're told that explicitly. If we don't have the details on how the spell is made, we can't replicate it. Let's continue with that. Many of Scipio's spells were created with experimentation, but far from all. The only ones we specifically know of are the two whose side effects are listed. So any of the others could be. With your interpretation, no one may use any of these except the two with listed side effects as guides to make spells from scratch because we don't know what the experimentation did. And those two only work out of you get exactly the same experimentation oddities. Concientia experimented some, but we don't know how much. So we can't use any of her spells. And she doesn't even list using experimentation in the years' summary. So if it's not listed there and not necessarily listed in spells, that could be true of the other magi's spells as well. So we can't use any spells in the entire book for a player to follow to make them from scratch. So your contention is that in writing "full descriptions" with the intention of allowing players to use those "full descriptions" to develop such spells from scratch, the authors failed.
It gets worse. Many example magi in different books have spells not published elsewhere without notes about not using experimentation. Same problem: we can't use them to make new spells.
It gets even worse. Some spells in the core book come from non-Hermetic sources or special research, and that can stop magi from making variants of them. See Aegis of the Hearth and probably Whispering Winds for examples. Most spells have no such notes. So now we can't use most spells in the core book to make them from scratch. For instance, is Lungs of the Fish a special oddity from something non-Hermetic or from research, or is that just the way MuAq(Au) should work? Do we let magi invent Pilum of Fire or variants of it on their own? Should it not be +10 damage, put perhaps the shape was a side effect from experimentation instead of being "purely cosmetic"? What about Arc of Fiery Ribbons and its shape(s)?
My contention is that the authors of MoH did not fail at one of the explicit purposes of writing "full descriptions," or, in other words, that what is explicitly written in the book is correct about the very same book. In order for this to be the case, design modifications due to experimentation (and Virtues, etc.) must be part of the "full description."
No, you can't do that. In Mythic Europe, the physical world gains it reality with its connection to Platonic Forms. What you are describing as ideas are in Mythic Europe Platonic Forms. You can't change a Platonic Form, because its essential nature is unchanging.
what exactly would a "deeper" understanding even mean? Is there some greater significance or meaning to laws of motion beyond them being laws of motion?
As to thermodynamics, it began as a study of engines- as in engineering. I'm not sure what your experience is in this, but the statement seems to me to reek of ignorance.
In my experience - from conversations with the engineers I play with, or otherwise interact with - engineers tend to mostly care about classical, macroscopic physics. Or more specifically, the area of physics that are directly involved in their area of expertice/practice. I have no doubt that they know stuff I don't, but in general, their knowledge of physics (and math) tends to focus on application, rather than theory.
I'm perfectly aware that there are exceptions. Engineers within the space industry undoubtedly have a deep and thorough understanding of the theory of relativity - but again, that's their area of expertice and practice.
Even more so, I've had some contact with a professor of Surface Science who was originally trained as en engineer. I have no doubts at all about his skills and comptences. But he's not your typical engineer in my experience.
Please understand, I'm not throwing shade at engineers. In many ways, I think their approach is probably more sensible than my own. But I do not expect engineering classes to offer the whole truth.
I'm aware of this. Our first-year book of thermodynamics was the same one used at the enginnering school, indeed it was written by engineers for engineers - or at least engineering students.
The same concept also see a lot of use in chemistry (no engines there), and indeed I have argued that all modern physics could be boiled down to an attempt to minimize the Gibb's Free Energy. My academic superviser at the time was (unbeknownst to me) standing right behind me at the time. He thought a bit about it, then said something like "Mnyeah... but that simplifies it too much to but particularly useful...", which I obviously agreed with.
My only academic degree is in physics, roughly equivalent to a master's degree with honours if I understand the US system correctly. The actual title is Cand. Scient. (or Candidatus scientiarum, but no-one ever uses the full term). I wrote my thesis in material science, which I had "committed" upon strained silicon. I spent a number of years there, and found no short simple definition of entropy that didn't make someone cringe and go "Yeah, that's not wrong, but it's not the whole story...", though admittedly I decided not to take the advanced statistical physics course, which might have provided such a very thing.
Now, I agree that, classically and macroscopically, your definition is useful. But since the same concept appears in other contexts (chemistry, nanoscience, etc) where it is less useful, I must admit I'd tend to go for a definition based on populated vs available micro-states. And I know for a fact that my understanding of entropy as a concept is not complete.
Which is one reason why I always cringe when people drag out that concept.
EDIT: Either way, I don't see how any of this is relevant. I'm all but certain that our discussion of the deeply anachronistic RL concept of entropy has little or nothing to do with the original poster's comment about entropy, which appears to be more closely related to the Mage the Ascension Sphere of Entropy.
Both of which are almost equaly irrelevant is ars Magica's medieval paradigm. (Yes, I used the P-word, intentionally).
And is there experimental evidence for microstates? Because if, for example, you release different gasses into a container in microgravity the eventual result tends not to be many microstates but a homogenous state. From one perspective there are always infinite microstates, whether gradation is detected or not, from another the idea of entropy as microstates can be disproved through simple experimentation.
Also entropy as being thermodynamic is the only model which does relate to AM, as it could make for excellent tractatus or summae on ignem in a more modern (or anachronistic) setting...
fairly significant evidence, yes.
microstates is another name for quantum mechanical energy states. not "pockets of gas".
So what you're saying is that you don't believe in quantum mechanics. 
1850 AD.... not that relevant.
I used intermixing gasses because it was the example of microstates definition that was used in my college physics textbook. Take from that what you will, I do believe that it is a fair conclusion that there are definitions of entropy being taught which do not hold up. If it has a secondary meaning for quantum mechanics I am of the opinion they should go find their own word, they have certainly done so with quarks, leptons, bosons, and other terms.
However, back to ars magica, it occur to me that what is mis-labeled entropy in common parlance did have medieval analogs- notably "chance", "luck" and yes "chaos"- though aside from chance these tended to be personalities- the word itself comes from a Greek proto-deity who preceded the titans. "Luck" would be a positive quality personified in a number of ways from minor gods, spirits, down to the modern "lady luck" and was something which brought good fortune. Of course any of these would be outside the hermetic arts, more likely an aspect of some form of conjuration than probability alteration...
wait is there a platonic form called"venice silk merchant guild"?
also is there any rule that says that the greater limits(at least that of essential nature) can't be broken with a breakthrough? perhaps after all the lesser ones are broken
A magus can attempt to achieve an HoH:TL p.27 Hermetic Breakthrough overcoming an ArM5 p.80 Lesser Limit of Hermetic magic.
The ArM5 p.79 Limit of the Divine and Limit of Essential Nature can however only ever be broken by - hopefully thoroughly and well discussed - troupe fiat and fundamental changes in Mythic Europe. Nobody says this is impossible or verboten, but there is no rules mechanism like the HoH:TL p.26ff Original Research for it.
Cheers
There are some hints in RoP:M that this sort of thing can be done through direct manipulation of the Magic Realm but these are never developed in other works and are certainly outside of the scope of the system of Hermetic Magic (spells/enchantments) presented in the core book.
In general this sort of reality-bending seems outside the genre of Ars Magica. Magic, and particularly Hermetic Magic, is much more concrete and less conceptual in this game.
The fact that every magus of house Diedne was supposedly targeted through a ritual suggests that it is in theory a possibility, in so much as House Didne was a concept whose manifestation could be attacked.
It might require the use of blood rituals, unusual magics or multiple breakthroughs however...