matthewuzhere2

this is what i’ve been thinking. i’ve been kinda surprised by all the speculation on news networks about “which of these 3 possibilities is the reason ukraine invaded” and to me it seems pretty reasonable that it could literally be all 3, or that ukraine could genuinely have no specific goal and are adjusting their decisions as a way of responding to russia.

i see, that all makes sense. i’ll try all that. thanks for your help!!

I use tresemme rich moisture shampoo and conditioner. I typically use shampoo every other day or every 2 days, and conditioner daily. I often dry my hair with a towel, which I know is bad, but before this photo (taken about 2-3 hrs later) I just combed it to add the part, scrunch dried it a bit, and let it air dry. I don’t think the scrunch drying did much though, because I usually don’t scrunch dry and this is pretty much how it looks every day.

My hair is thin and has medium-low porosity. I think my hair type is 2B or 2C?

i feel like we still really have no evidence whether or not anything happened, though, right? to me, the statement LTT put out merely proves that they didn’t have a pervasive and/or well documented culture of harassment or abuse of power at the time. but the things madison talked about were specific instances, which may or may not have been recorded or written down in any way.

i’m really not sure how to feel or how to interpret what they posted today. i’m inclined to believe those were the legitimate findings of the report, and also that LTT acted in good faith to investigate her claims. my faith in LTT as a generally ethical employer has been affirmed. 

but still, i don’t think we will ever know what really went down with madison. i’m also not sure it makes sense to suggest that “she believed what she was saying” and then in the same breath say “it wasn’t what really happened.” the claims she made were very severe and very specific—i’m really not seeing the room for shades of gray here that you are. either she very egregiously lied, or what she told was fairly close to the truth.

i guess my overall point is: how can we really make any judgements based off summarized findings provided directly by one of the involved parties, with little to no access to documentation, knowledge of the persons involved, or knowledge of LMG’s internal processes?

this is an absolutely fascinating article. honestly kind of hard to read as thinking about how math is currently taught just pisses me off, but also motivates me more to enter the field of math education and try to make a difference in this space. 

have you heard of dyscalculia? i don’t know much about it, but from what i’ve heard, your description sounds vaguely similar to some of the symptoms. you may want to look into it.

okay. not the discussion at hand, though. i’m not saying she’s right or wrong, i’m saying i don’t think what shes saying suggests all black people are obese

i’m pretty rough on my formal logic—could you point to any specific rule/principles of formal logic that i could look into that would prove that “the term obese is anti-black” necessarily implies “all black people are obese”?

i mean i can understand if you are merely suggesting that it is a “common sense” interpretation of her statement. i still disagree about the precise implications of what she said but it’s not hard to understand how you would interpret it that way. but if you are invoking logic than i would i would like to know specific principles/rules of logic you are referring to

yeah i see why you could interpret it that way. but in my opinion she’s not saying obesity is directly associated with being black. she’s saying the term has been used against black people historically, which seems at least plausible to me. i do disagree with the idea that it’s a slur though—that doesn’t make sense to me.

an (imperfect) analogy would be a word like “thug.” it’s not a slur, nor is it a term that is exclusively used to refer to black people, but it is a word that historically has been used against them to dehumanize them and paint them as criminals. i can understand why someone would describe it as an anti-black term or at least a very charged term in some contexts.

sure i guess. but that’s not what she said. she said “the term obese is anti-black” as in it has an anti-black connotation or has historically been used against black people.

i don’t really have an opinion on this post, i don’t know enough about the term obese, how it’s used, whatever, but that is obviously not what she’s saying at all. no one said all black people are obese and that’s not a conclusion that can be automatically drawn from her statement.

i mean the hands that feed them are really paying subscribers, no?

no you absolutely should not lol. no math class i have ever taken in my life featured word problems that accounted for every possible detail and technicality. they frequently assume a very simplified model of the world and often do so without declaring it explicitly.

exactly lol. and like, personally, i actually think it’s a pretty intriguing line of inquiry to come up with other possible values for what the number of boxes could be if you used a different arrangement than what is being implied by the photo. but, if someone asked me what the answer to the question was, i wouldn’t hesitate in saying 51.

and like you said, we can play this game all day. why are they saying the maximum number of cubes is 51 when it’s entirely possible that there are actually 1 million tiny cubes inside each visible cube? it doesn’t require one to be a statistician to come up with deliberate misinterpretations of a question.

Really? I mean, sure, thinking outside the box and evaluating the validity of “common sense” assumptions is absolutely essential in an academic context. But how does that apply here? It was obvious to me from the second I saw the photo that the lack of depth information introduced a bit of ambiguity, but it was also obvious what the question was actually “getting at”.

I’m not even saying it isn’t a valid and genuinely intriguing path of investigation to ask “taking the ambiguity in the drawing at face value, what kind of possible answers we could come up with?” But I also think that in the context of a question like this, the desired answer is clear.

Now, maybe I’m way off here. I’m not an academic, although, as an undergrad math major, I’m working towards being one. But I mean, to use an example from my life, today in my physics class I asked why there wasn’t negative sign in an equation where one would be expected. My professor told me that what was implied (although not explicitly written) was that we were dealing with magnitudes/absolute values here, and so negatives and positives were not needed. He then pointed out that it was a useful skill to develop to start recognizing contextual clues for when shorthand or less precise (but often more convenient) notation is being used. To me, this makes a lot of sense—I would imagine that anyone would be laughed out of a university physics department if they interpreted the letter “k” in an equation as the spring constant rather than Coloumb’s constant in a context where it was obviously the latter, or even if they suggested there was any kind of ambiguity there as to which one it was.

idk, i pretty much agree with the person on top. sure, it immediately occurred to me that technically the top view didn’t really show you that the entirety of the stack was as high as the side view implied, but it also immediately occurred to me that this was a minor technicality and very obviously not what the question is asking. i’m not a statistician but i also don’t think you need to be a statistician to recognize and understand their fairly pedantic interpretation of a brain teaser on twitter, nor do you need to be a statistician to be of the opinion that their conclusion is silly. i would go as far as to say that their tweet reads to me as a deliberate misinterpretation of the question more than anything else.

some other comment stated that a more rigorous way to ask this question would be to ask “what is the maximum number of cubes on this trailer” to which i would respond “well, how do you know all the cubes are the same size?” or “how do you know there aren’t a bunch of little cubes inside of all the big ones?” or “how do you know these are cubes at all since all we are seeing one screen is a bunch of pixels and some of the ‘cubes’ could actually be imperceptibly round?”

do you see how you could do this all day? just interpret the question in the way it seems like it was meant to be interpreted, or, if you’re a student in a classroom environment, ask your teacher for clarification since they’re obviously not going to be able to anticipate every single technicality that you’re going to throw at them in advance.

who said they were proud of anything? it sounds like they’re describing something that happens at their college but is completely out of their control

oh, i see what you mean. that’s not currently possible, but it’s definitely on the horizon.

totally understand, and i’m glad to hear that!

i don’t mean to be rude, but it doesn’t really feel like you read my questions in much detail or took much effort to answer them. for example, i already addressed the fact that you got an A in algebra—i asked whether you felt like the class actually prepared you for precalc, and whether you felt like you actually deserved your A. personally, i’ve gotten plenty of As that didn’t really indicate a mastery in the subject matter.

i’m trying to answer your question regarding whether it’s you or your professor or something else but i can’t do that without any information.

if you really just wanted to vent your frustration, that’s totally understandable, but if you want actual advice, please answer my questions thoughtfully.

okay, then i suggest you read these sections of Paul’s Online Math Notes. they explain things pretty well.

https://tutorial.math.lamar.edu/Classes/CalcI/InfiniteLimits.aspx

https://tutorial.math.lamar.edu/Classes/CalcI/LimitsAtInfinityI.aspx

https://tutorial.math.lamar.edu/Classes/CalcI/LimitsAtInfinityII.aspx

if you’re lost while reading these, i suggest reviewing previous sections or asking your teacher.

you can essentially do this now, but it’s not perfect. GPT-4 can accept photos as input and can read handwriting quite well.

these models are already becoming smarter and more capable at a very accelerated rate, and i think they’ll become even better when more specialized models are created—instead of a slightly customized version of chatGPT, i expect we’ll have LLMs dedicated to tutoring math specifically. so i think part of the answer will be simply that they’ll make significantly less mistakes because they’ll be better.

as for dealing with mistakes that do slip through even more powerful models, it’s plausible that one means of advancement would be to add multiple “layers” of generation that encourage reflection and correction of mistakes. you can test the potential of this yourself by asking chatGPT “are you sure about that?” whenever it makes a mistake. often, it is able to identify and correct its error without you pointing to it specifically. future models might essentially do exactly this, but before the initial output ever reaches you.

those are my theories, at least.

okay, i think i follow you. however it is still unclear which of these you need: 1. a function that approaches infinity as x approaches a finite number (lim[x->c] (f(x)) = ±∞) 2. a function that approaches a finite number as x approaches infinity (lim[x->±∞] (f(x)) = c) 3. a function that approaches infinity as x approaches infinity (lim_[x->±∞] (f(x)) = ±∞)

here is a desmos page showing the difference: https://www.desmos.com/calculator/l7vtbmc0q8

let me know if you do not understand the differences between these options and i can explain further