This comment has no relevance to anything. If it was trying to imply that Americans don’t avoid healthcare due to cost, in effect denying Americans healthcare, it’s totally inaccurate. There are thousands of American citizens all over the USA that cannot afford healthcare, and Americans routinely avoid getting needed healthcare just to make ends meet.

Even Americans with higher incomes avoid healthcare, and here is a link that mentions that specifically: https://www.cbsnews.com/news/health-care-costs-rising-americans/

While it’s true that linear algebra and vectors are used in learning models, they’re not using the term correctly in a way that says they know something about the subject (at least, the modern subject). Concepts aren’t embedded as vectors. In older models (before the craze), concepts were manually embedded as numbers or a collection of numbers, which could be a vector (but could be something else as well), and the machine would learn by modifying weights. However, in current models (and by current, I mean at least more than a couple years), concepts are learnt by the machine (weights are still modified by the machine as well) and the machine makes its own connections between features presented to it.

For example, you give it a dataset of 10x10 pixel images (with text descriptions) and it reads that as 100 pixels split into 3 numbers (RGB) and then looks for connections between those numbers and in which pixels. It’s not identifying what a boob is, but knows that when an image has ‘boob’ in the text description then there’s a very high likelihood that there will be a circular collection of pixels with lots of red somewhere in the image that are also connected to other pixels that are often also lots of red. That’s me breaking down what a human would think given the same task/information, but the reality is the machine will come up with its own connections/concepts which are both often far better than humans (when the model works, at least) and far more ineffable to humans.

At this point you’re just ignoring whatever I say and I see no point in continuing this discussion. You haven’t responded to what I’ve said, you’ve just stated I’m wrong and to trust you on that because somewhere prior you said so. Good luck with convincing anyone that way.

You didn’t have to go looking - you could’ve just accepted it at face-value like other people do.

I could also walk off a cliff, doesn’t mean I should. Sources are important not just for what they say but how they say it, where they say it, and why they say it.

But they’re not. The other side is contradicting the rules of Maths. In a Maths test it would be marked as wrong. You can’t go into a Maths test and write “this is ambiguous” as an answer to a question.

…amongst people who have forgotten the rules of Maths. The Maths itself is never ambiguous (which is the claim many of them are making - that the Maths expression itself is ambiguous. In fact the article under discussion here makes that exact claim - that it’s written in an ambiguous way. No it isn’t! It’s written in the standard mathematical way, as per what is taught from textbooks). It’s like saying “I’ve forgotten the combination to my safe, and I’ve been unable to work it out, therefore the combination must be ambiguous”.

The side which obeys the rules of Maths is correct and the side which disobeys the rules of Maths is incorrect. That’s why the rules of Maths exist in the first place - only 1 answer can be correct (“ambiguity” people also keep claiming “both answers are correct”. Nope, one is correct and one is wrong).

Yes, that is your claim which you have yet to prove. You keep reiterating your point as if it is established fact, but you haven’t established it. That’s the whole argument.

Twice I said things about it and you said you didn’t believe my interpretation is correct, so I asked you what you think he’s saying. I’m not going to go round in circles with you just disagreeing with everything I say about it - just say what YOU think he says.

Literally just give me a direct quote. If you’re using it as supporting evidence, tell me how it supports you. If you can’t even do that, it’s not supporting evidence. I don’t know why you want me to analyze it, you’re the one who presented it as evidence. My analysis is irrelevant.

Thank you. I just commented to someone else last night, who had noticed the same thing, I am so tired of people quoting University people - this topic is NOT TAUGHT at university! It’s taught by high school teachers (I’ve taught this topic many times - I’m tutoring a student in it right now). Paradoxically, the first Youtube I saw to get it correct (in fact still the only one I’ve seen get it correct) was by a gamer! 😂 He took the algebra approach. i.e. rewrite this as 6/2a where a=1+2 (which I’ve also used before too. In fact I did an algebraic proof of it).

I was being sarcastic. If you truly think highschool teachers who require almost no training in comparison to a Phd are more qualified… I have no interest in continuing this discussion. That’s simply absurd, professors study every part of mathematics (in aggregate), including the ‘highschool’ math, and are far more qualified than any highschool teacher who is not a Phd. This is true of any discipline taught in highschool, a physics professor is much better at understanding and detailing the minutiae of physics than a highschool physics teacher. To say a teacher knows more than someone who has literally spent years of their life studying and expanding the field when all the teacher has to do is teach the same (or similar) curriculum each and every year is… insane–especially when you’ve been holding up math textbooks as the ultimate solution and so, so many of them are written by professors.

I want to point out that your only two sources, both a screenshot of a textbook, (yes, those are your only sources. You’ve given 4, but one I’ve repeatedly asked about and you’ve refused to point out a direct quote that provides support for your argument, another I dismissed earlier and I assume you accepted that seeing as you did not respond to that point) does not state the reasoning behind its conclusion. To me that’s far worse than a professor who at least says why they’ve done something.

I’ve given 3 sources, all of which you dismiss simply because they’re not highschool textbooks… y’know, textbooks notorious for over-simplifying things and not giving the logic behind the answer. I could probably find some highschool textbooks that support weak juxtaposition if I searched, but again that’s a waste of money and time. You don’t seem keen on acknowledging any sort of ambiguity here and constantly state it goes against the rules of math, without ever providing a source that explains these rules and how they work so as to prove only strong juxtaposition makes sense/works. If you’re really so confident in strong juxtaposition being the only way mathematically, I expect you to have a mathematical proof for why weak juxtaposition would never work, one that has no flaws. Otherwise, at best you have a hypothesis.

I told you, in my thread - multiple ones. You haven’t provided any textbooks at all that have “weak juxtaposition”. i.e. you keep asking me for more evidence whilst never producing any of your own.

You seem to have missed the point. I’m holding you to your own standard, as you are the one that used evidence as an excuse for dismissal first without providing evidence for your own position.

I didn’t “just happen” to include the name of the textbook and page number - that was quite deliberate. Not sure why you don’t want to believe a screenshot, especially since you can’t quote any that have “weak juxtaposition” in the first place. BTW I just tried Googling it and it was the first hit. You’re welcome.

You seem to have missed the point. You’re providing a bad source and expecting the person you’re arguing against to do legwork. I never said I couldn’t find the source. I’m saying I shouldn’t have to go looking.

You don’t - the screenshots of the relevant pages are right there. You’re the one choosing not to believe what is there in black and white, in multiple textbooks.

You’ve provided a single textbook, first of all. Second of all, the argument is that both sides are valid and accepted depending on who you ask, even amongst educated echelons. The fact there exists textbooks that support strong juxtaposition does nothing to that argument.

But you want some evidence, so here’s an article from someone who writes textbooks speaking on the ambiguity. Again, the ambiguity exists and your claim that it doesn’t according to educated professors is unsubstantiated. There are of course professors who support strong juxtaposition, but there are also professors who support weak juxtaposition and professors that merely acknowledge the ambiguity exist. The rules of mathematics you claim are set in stone aren’t relevant (and aren’t as set in stone as you imagine) but that’s not entirely relevant. What is relevant is there is an argument and it’s not just uneducated folk mistaking the ‘truth’.

People who aren’t high school Maths teachers (the ones who actually teach this topic). Did you notice that neither The Distributive Law nor Terms are mentioned at any point whatsoever? That’s like saying “I don’t remember what I did at Xmas, so therefore it’s ambiguous whether Xmas ever happened at all, and anyone who says it definitely did is wrong”.

You are correct, I suppose a mathematics professor from Harvard (see my previous link for the relevant discussion of the ambiguity) isn’t at the high school level.

But wait, there’s more. Here’s another source from another mathematics professor. This one ‘supports’ weak juxtaposition but really mostly just points at the ambiguity. Which again, is what I’m going for, that the ambiguity exists and one side is not immediately justified/‘correct’.

So what do you think he is complaining about?

That’s a leading question and is completely unhelpful to the discussion. I asked you to point out where exactly, and with what wording, your position is supported in the provided text. Please do that.

So you think it’s ok to teach contradictory stuff to them in Maths? 🤣 Ok sure, fine, go ahead and find me a Maths textbook which has “weak juxtaposition” in it. I’ll wait.

You haven’t provided a textbook that has strong juxtaposition.

So you’re telling me you can’t see the Maths textbook screenshots/photo’s?

That’s not a source, that’s a screenshot. You can’t look up the screenshot, you can’t identify authors, you can’t check for bias. At best I can search the title of the file you’re in that you also happened to screenshot and hope that I find the right text. The fact that you think this is somehow sufficient makes me question your claims of an academic background, but that’s neither here nor there. What does matter is that I shouldn’t have to go treasure hunting for your sources.

And, to blatantly examine the photo, this specific text appears to be signifying brackets as their own syntactic item with differing rules. However, I want to note that the whole issue is that people don’t agree so you will find cases on both sides, textbook or no.

Lennes was complaining that literally no textbooks he mentioned were following “weak juxtaposition”, and you think that’s not relevant to establishing that no textbooks used “weak juxtaposition” 100 years ago?

You are welcome to cite the specific wording he uses to state this. As far as I can tell, at least in the excerpt linked, there is no such complaint.

Correct, but it can’t be something which would contradict what they do have to teach, which is what “weak juxtaposition” would do.

Citation needed.

I see you didn’t read the whole thread then. Keep going if you want more. Literally every Year 7-8 Maths textbook says the same thing. I’ve quoted multiple textbooks (and haven’t even covered all the ones I own).

If I have to search your ‘source’ for the actual source you’re trying to reference, it’s a very poor source. This is the thread I searched. Your comments only reference ‘math textbooks’, not anything specific, outside of this link which you reference twice in separate comments but again, it’s not evidence for your side, or against it, or even relevant. It gets real close to almost talking about what we want, but it never gets there.

But fine, you reference ‘multiple textbooks’ so after a bit of searching I find the only other reference you’ve made. In the very same comment you yourself state “he says that Stokes PROPOSED that /b+c be interpreted as /(b+c). He says nothing further about it, however it’s certainly not the way we interpret it now”, which is kind of what we want. We’re talking about x/y(b+c) and whether that should be x/(yb+yc) or x/y * 1/(b+c). However, there’s just one little issue. Your last part of that statement is entirely self-supported, meaning you have an uncited refutation of the side you’re arguing against, which funnily enough you did cite.

Now, maybe that latter textbook citation I found has some supporting evidence for yourself somewhere, but an additional point is that when providing evidence and a source to support your argument you should probably make it easy to find the evidence you speak of. I’m certainly not going to spend a great amount of effort trying to disprove myself over an anonymous internet argument, and I believe I’ve already done my due diligence.

Nope. Teachers can decide how they teach. They cannot decide what they teach. The have to teach whatever is in the curriculum for their region.

Yes, teachers have certain things they need to teach. That doesn’t prohibit them from teaching additional material.

That’s because neither of those is a rule of Maths. The Distributive Law and Terms are, and they are already taught (they are both forms of what you call “strong juxtaposition”, but note that they are 2 different rules, so you can’t cover them both with a single rule like “strong juxtaposition”. That’s where the people who say “implicit multiplication” are going astray - trying to cover 2 rules with one).

Yep, saw it, and weak juxtaposition would break the existing rules of Maths, such as The Distributive Law and Terms. (Re)learn the existing rules, that is the point of the argument.

Well that part’s easy - I guess you missed the other links I posted. Order of operations thread index Text book references, proofs, the works.

You argue about sources and then cite yourself as a source with a single reference that isn’t you buried in the thread on the Distributive Law? That single reference doesn’t even really touch the topic. Your only evidence in the entire thread relevant to the discussion is self-sourced. Citation still needed.

Maths isn’t a language. It’s a group of notation and rules. It has syntax, not grammar. The equation in question has used all the correct notation, and so when solving it you have to follow all the relevant rules.

You can argue semantics all you like. I would put forth that since you want sources so much, according to Merriam-Webster, grammar’s definitions include “the principles or rules of an art, science, or technique”, of which I think the syntax of mathematics qualifies, as it is a set of rules and mathematics is a science.

Except it breaks the rules which already are taught.

It isn’t, because the ‘currently taught rules’ are on a case-by-case basis and each teacher defines this area themselves. Strong juxtaposition isn’t already taught, and neither is weak juxtaposition. That’s the whole point of the argument.

But they’re not rules - it’s a mnemonic to help you remember the actual order of operations rules.

See this part of my comment: “To note, yes, PEMDAS is a teaching tool and yes there are obviously other ways of thinking of math. But do those matter? The mathematical system we currently use will work for any usecase it does currently regardless of the juxtaposition we pick, brackets/parentheses (as well as better ordering of operations when writing them down) can pick up any slack. Weak juxtaposition provides better benefits because it has less rules (and is thusly simpler).”

Juxtaposition - in either case - isn’t a rule to begin with (the 2 appropriate rules here are The Distributive Law and Terms), yet it refuses to die because of incorrect posts like this one (which fails to quote any Maths textbooks at all, which is because it’s not in any textbooks, which is because it’s wrong).

You’re claiming the post is wrong and saying it doesn’t have any textbook citation (which is erroneous in and of itself because textbooks are not the only valid source) but you yourself don’t put down a citation for your own claim so… citation needed.

In addition, this issue isn’t a mathematical one, but a grammatical one. It’s about how we write math, not how math is (and thus the rules you’re referring to such as the Distributive Law don’t apply, as they are mathematical rules and remain constant regardless of how we write math).

Yeah, the title of this post, the meme’s upper text, and the rest are all at odds and I’m just confused as to what OP is going for.

Is the point that consoles are the AAA industry and services normal people with normal needs? How does this mean we should boycott it?

Are we being tongue-in-cheek? Are we not supposed to boycott the AAA industry?

Why does this meme single out ‘console peasants’ as normal people? Is normal bad? Is irregular bad? Is PC bad? But PC gamers also care about gameplay and are regular people? How much sarcasm is supposed to be here?

OP, WHAT DO YOU MEAN?

This is a classic slippery slope fallacy. Millions of religious people exist from all sorts of ideological spectrums. The vast, vast majority are not evil and don’t do bad things.

The extremism present in religious people is also apparent and present in atheists, agnostics, or whatever generic belief system you can think of. Religion by itself doesn’t cause extremism: ad hominems, whataboutisms, and disinformation causes extremism. Constantly comparing yourself to an enemy and convincing yourself you are in the absolute right causes extremism. Sure, you see some ‘religious’ people going crazy and shooting up places. They also have manifestos that are completely detached from reality in a way that reeks of far-right propaganda and disinformation, and never any real coherence or thought given to the religious teachings they supposedly follow (if they mention their religious texts at all, it’s often cherry-picking or outright incorrect).

We should not try to fix the issues of mental health that plague a lot of countries by going after religion. If anything, that would only backfire by virtue of validating any persecution complex religious people might have. We should instead focus on providing affordable mental healthcare that is easily, immediately accessible and normalized for the wider population, as well as providing clear sources of valid information and having any questionable sources that construe facts and claim to not be news sources in lawsuits or elsewhere be forced to clearly denote themselves as not news regularly.

You’re thinking of collectivism, the actual opposite of individualism. Confucianism isn’t really related and is about finding meaning and cultivating the self, it’s a form of civil religion.

In fact, Confucianism is about self-cultivation and actualization, though in the context of society.

I don’t see why they can’t own the property and pay a property manager of sorts.

At the end of the day, it is the moderators who maintain and control the community. They control what users even see, so it’s not fair to say a community is made by the average user, the average user is completely silent. I would rather competing communities over every community being at the whim of the masses. The masses are easy to misguide.

The whole point of the Reddit-style was that subreddits could be controlled by moderators and prevented from slipping into the same old tired town square-esque mess that arrives with popularity. I guarantee a mechanism to remove moderators would result in niche communities that get a surge in popularity winding up with the original moderators ousted because all the newcomers don’t understand the community.

If you don’t like how a community is run, you can start your own for completely free. That’s how this works, you shouldn’t be able to commandeer a community from the people who started it. If there’s a truly problematic moderator, the new community will grow quickly.

But here’s the thing: they could easily say the method that led to the finding is wrong. It’s not a fact.

That’s not how American courts work? The upper court can find issue with practically anything it likes.

Having read your article, I contend it should be:
P(arentheses)
E(xponents)
M(ultiplication)D(ivision)
A(ddition)S(ubtraction)
and strong juxtaposition should be thrown out the window.

Why? Well, to be clear, I would prefer one of them die so we can get past this argument that pops up every few years so weak or strong doesn’t matter much to me, and I think weak juxtaposition is more easily taught and more easily supported by PEMDAS. I’m not saying it receives direct support, but rather the lack of instruction has us fall back on what we know as an overarching rule (multiplication and division are equal). Strong juxtaposition has an additional ruling to PEMDAS that specifies this specific case, whereas weak juxtaposition doesn’t need an additional ruling (and I would argue anyone who says otherwise isn’t logically extrapolating from the PEMDAS ruleset). I don’t think the sides are as equal as people pose.

To note, yes, PEMDAS is a teaching tool and yes there are obviously other ways of thinking of math. But do those matter? The mathematical system we currently use will work for any usecase it does currently regardless of the juxtaposition we pick, brackets/parentheses (as well as better ordering of operations when writing them down) can pick up any slack. Weak juxtaposition provides better benefits because it has less rules (and is thusly simpler).

But again, I really don’t care. Just let one die. Kill it, if you have to.

Sure. That doesn’t mean it’s right to do.

Good. Don’t ever invite me.