You are lacking basic reading comprehension.

There was more than one question. The reason why variable vs. binary was phrased as it was is because there are around 4 different versions of variable magical power. So first people had to be divided between their belief in binary or variable, then the survey moved on to identify which version of variable power people believe in. And crucially (and quite explicitly and unambiguously, such that only a dolt would miss it) those follow up questions identified the version of variable magical power in which those factors - knowledge, intelligence, skill etc - determine that variable magical power (in the basic vs complex attribute question).

Even if the survey was not so clear, the OP of this thread sets it all out in precise detail, so the plea to ignorance rings somewhat hollow. To be honest it seems like you just read the thread title and jumped straight into the comments without familiarising yourself with the concepts.

And despite subsequent explanation you still don't seem to understand it because your posts are still all pretending that basic attribute variable power is the only version and arguing against that as a straw man.

For the avoidance of doubt, no one is defending magical cores. As stated in the OP you didn't read, magical cores correspond to variable + quantity + basic attribute, a rare combination of answers on the survey and not one anyone has defended in this thread. Even aAlouda I think is defending variable + quantity + complex attribute.

 

You see @Taure the problem is you make up convoluted systems to base your expansion of cannon on and then bitch about people not understanding what you are proposing. And the "complex" proposal contains intrinsic elements (intelligence, personality to a degree) and acquired ones (knowledge, experience, world view), but how do those factor together...it's quite abstract and ~~ill~~ non defined. And your examples are just bad. Give a concrete example of how your notions would apply in the magical world.

a) complex variable magical power

b) binary magical power

To me it seems like with "complex variable magical power" a powerful wizard in the real world would translate to something like an excellent athlete. Intrinsic factors & acquired ones result in great physique (quantifiable & measurable strength/speed/etc). And an excellent athlete is bound to perform quite above average in most sports.

Whereas with binary magical power I picture someone like a great mathematician. Intrinsic elements (intelligence & aptitude) coupled with study & effort. These inherent qualities they possess do not change over time even though their understanding deepens and their thinking process perhaps changes, or they develop logical intuition. But if handed a problem outside of their area of expertise their abilities certainly would make a difference.

I don't get why you want to wrap up intelligence, intuition, personality, experience, knowledge etc into one package and call it "magical power". A package that can then be different in some quantifiable (bigger) or qualitative (...harder?) way.

And why if magic exists in binary, a wizard's intelligence, intuition, personality, experience, knowledge wouldn't make one iota of difference in the outcome of spells they're bad at or why it would mean that extraordinary wizards like Dumbledore wouldn't be able to exude a sense of power. He is powerful, just don't take everything so literally.

The truth is, apart from Dumbledore, in the books really it is binary magical power we see. That's what JKR is defending and that's how she's mostly written her world. And I'd argue she wants it so because it makes for a simpler and fairer world, easier to escape into.

 

@Skeletaure So you ask a question, open the floor for discussion, give your thoughts on why it’s a certain way…then accuse others of bad reading comp when they reject your premise.

I read your post and reject your argument for variable magical power. The basis for the thread is the survey question which others have interpreted and read in a similar manner to myself. You say I’m arguing against a straw man but you specifically set the guidelines of what was a binary and what was a variable in your OP question. It was never agreed upon that your post in this thread changed the nature of the question itself.

It feels like you’re just moving goalposts now so you can be right, but I thought the purpose was to discus the questions and results and debate the answers, not add on newer details or changing the framework of the discussion.

Based on how you worded the original question, I don’t see a strong Canon argument for a magical power variable as an input. We all agree there’s a variable output, but the framing of the question and most seek to agree we’re discussing input.

 

Okay, since I'm obviously smarter than everyone else who answered, let's put an end to the debate with some facts and magic =)

(note: this was sarcasm)

There's a lot of people who reduce this thread to Binary vs Magical Core, which is very annoying because I disagree with both, so let's take the questions in order.

Question 1: does magical power exist?​

aAlouda's quote from HBP kinda answers that. Dumbledore clearly says the boat measures the amount of magical power aboard, and that Harry's doesn't register next to his. Therefore, 1) magical power exists as a person's characteristic, 2) it varies enough from one individual to another that some wizards can be negligible to others, and 3) it's measurable outside of any magic being cast.

At the very least, it makes the distinction between Underage and Adult. Meaning, adding the Magicless (Muggle/Squib if you don't make the distinction) you have 3 categories wrt to magic power, which disqualifies the Binary answer (it would be at least Ternary). Unless you want to argue that Dumbledore is dumbing down concepts to make sure Harry understands, but then you're just arguing canon isn't canon.

As for the quote that there is no such thing as "magical enough", see the context: JKR was talking about acceptation in Hogwarts. That means Hogwarts accepts students whatever their power, as long as they do have magic. To make a number analogy (I don't like those but it works here), "natural numbers can either be positive, or not." That doesn't mean 1 is the only non-zero number. The same way, muggles are 0 and wizards are not, which doesn't mean they're equal, so the quote doesn't contradict varying power at all.

Question 2: does magical power vary in quantity or quality?​

Main argument against quantity is that no wizard in canon is ever shown short on magic, or even just worried about being short on magic. Absence of proof isn't proof of absence, but in the highly tensed events of canon it would be likely to come into play if it was a thing. So it's likely not.

Quantity might also influence "how much" magic is put into a spell, but really is the "reservoir" is infinite it's exactly the same as making spells better, therefore quality.

The HBP quote also somewhat answers that. Dumbledore, while being vastly more powerful than Harry, still registers only as one wizard, therefore he doesn't have "more" power, but "better" power.
As for why Harry still doesn't register, I like a lamp analogy: Dumbledore is a top-quality LED, while Harry is a low-quality incandescent bulb not yet warmed up. Even if they have the same consumption (= have "1 wizard worth" of magic), put both together and Harry just looks switched off.

Question 3: is magical power intrinsic or dependent on other factors?​

Well, this one is a bit trickier. Clearly there are extrinsic factors to magical performance, like knowledge of theory (hence the very existence of magic schools), mental health (see Tonks nearly losing her Metamorphmagic when she's depressed, or Dementors sometimes depriving wizards of their powers), character, etc. (what Taure calls "personality").
These factors could affect only a wizard's skill, not his power, but then it's a coincidence that the only wizard shown with tangible power, Dumbledore, is also the most skilled. It's much simpler to assume his personality enhances his general power AND his skill when using that power (meaning, for e.g., that even when he's unfocused or diminished and can't make full use of his skills he still has his latent power to compensate).

However, I do believe there is an inborn part to someone's magic power. It's seen when some people are born with magic gifts they don't need to understand or work on, like Parseltongue or Metamorphmagic. These could be (binary) characteristics independent of magical power, but then you have Queenie Goldstein's natural legilimency. I haven't seen the FB movies so don't quote me on that, but I believe she was born with a level of skill that normally takes years to reach, but that other people without the gift are able to reach. So it's not a switch independent from power, but still independent from her "personality" since she never had to work for it.

So yeah, I'd tentatively go with magic power depending on both intrinsic and "personality" factors, but with the intrinsic part being quite limited. After all, we never see a wizard's power being disconnected from their "personality", so other factors can't be predominant. It's possible that outside fringe cases like Queenie (which is of debatable canonicity to begin with), the intrinsic part of one's magic only dictates which special gifts you're born with and doesn't affect other kinds of magic.

Or, people are born with various degrees of, let's say affinity, to learning different kinds of magic, like some people naturally learn maths easier than others.
There are already many forms of intelligence IRL (logic, linguistic, emotional, etc.), I don't think it's a stretch that there would be a magic intelligence (i.e. some people understand magic more easily than others). Or even separate into Transfiguration intelligence, Charms intelligence, etc. since they don't work with the same principles, so someone's affinity for them wouldn't necessarily be the same.

Have you ever made an experimental measure of anything? Measure instruments are never perfect, they have a non-zero precision, and any variation below this precision is basically invisible to them.
And even assuming that Voldemort's spell IS a perfect measurement of magic power (because it's magic, so why couldn't perfection exist?), "negligible" has a variable meaning. In Physics class, you regularly neglect factors which influence a result for less than 1% (and sometimes up to 10%), so Dumbledore doesn't need to be infinite to make Harry negligible.

 

To be honest, the whole discussion seems to have been made confusingly complex by the language involved. Specifically, the blanket use of the term 'magical power', and the desire to use practical magic as a measure of said power.

There are two factors at play, but the way that the further questions are phrased tends to result in the two being conflated together. First, we have what you might call 'Magical Potential' (which I think is what these questions are aimed at), and the second is 'Magical Proficiency' which is what is really muddying the waters.

Questions around binary or variable magical proficiency would seem to be fairly pointless. It is obvious from even a cursory reading of the books that different people have different levels of competence when it comes to the actual act of performing magic. The precise factors that go into one's magical proficiency, aren't what's up for debate, but presumably include things like education, experience, intelligence, etc, in addition to the key factor being driven at in the poll:

Magical Potential.

Now, to be proficient at magic, obviously you need to have the potential to perform magic, at the very least. The question here is if Magical Potential is purely Yes/No, or if there are shades of grey. This is my understanding of the binary/variable question.

If magical potential is purely binary, then a practitioner's magical proficiency may still be variable, as it is at this point that their intelligence/education/etc comes into play.

But if magical potential is some independent variable (by that I mean a variable which is not influenced by anything else), then I guess some further questions do make sense. Then again, the specific questions do have me scratching my chin. I find it hard to conceptualise a meaningful, but still general enough to be sensible, difference between 'quantity' and 'quality' of magic in such a system.

For example, if we suppose a specific spell costs 100 'Thaums' to cast, a quantitively superior wizard has more Thaums in the tank with which to cast, while a qualitatively superior wizard may only need to use 50 Thaums to cast the spell. The end result is identical, and I'm not sure it's all that interesting a discussion.

Or perhaps I'm thinking about this wrong. Perhaps it's not about the size of the reservoir, but the flow rate of the input/output. Perhaps a quantitively superior wizard has a greater than average 'inflow' into their reservoir of power, while a qualitatively superior wizard has a greater than average 'outflow', with 'both' meaning a superior wizard has a larger inflow and outflow. But there's still three variables here, not two. Inflow, outflow, and capacity. Ultimately, this question feels hard to map into my own imagination.

The third question is where things start to go really sideways, though. It seems to contradict the first one? In the first question, it specifically states that 'variable magical power... is not just shorthand for a collection of other attributes'. The second question then asks if variable magic power is a 'complex product of other attributes'.

I understand what is meant here. The most obvious, magical core-based example would be expanding your 'core' as you learn new spells and practice more complex ones. On the other hand, a 'basic' variable system is one where no amount of learning or effort can improve the size of the 'core' (with the possible exception of dark and forbidden rituals with absolutely no downsides whatsoever which for some reason people still don't use). The issue is that this distinction really isn't clear in the wording of the actual question.

Where confusion really starts to seep in, however, is in how each of us describe our preferred systems to ourselves.

Say you believe in a complex, variable system. Well, it's entirely possible you actually consider it a binary system. Why?

Well, it's obvious that muggles can't become wizards by trying really hard. As variable as the magical core might be, you still have to actually have one to improve it. So in this magical core system, there is both a binary aspect (core or no core) and a variable aspect (differing levels of intrinsic magical potential between wizards).

And so a binary system can become a variable system, and a variable system can become a binary system. I fear, in Taure's attempt to avoid using terminology like 'magical cores' (presumably because of complaints about them being limiting, or due to the baggage that comes with them), we've ended up in a terminological soup which doesn't actually tell us anything about what people think.

Or maybe I've thought myself into a knot.

 

This is basically my argument. Those intelligences might be influenced by other factors too, but they're definitely there. Whatever natural affinities exist in a wizard are also probably amplified by their wand's specialisation, e.g., James has a natural affinity for transfiguration, picks up a wand that is good for casting transfiguration magic, likes his transfiguration teacher, and decides to independently study advanced transfiguration magic at a young age with his friends. Because of all of this, he's noted to be extremely talented at transfiguration by multiple characters.

If he'd had different friends, a different wand and a shite transfiguration teacher, he'd probably still be good at the subject without having to try all that much, but he'd never be excellent.