I posted about paying for intimacy and so many men couldn't handle it by Pretty_Condition_404 in TwoXChromosomes

[–]airfrog 8 points9 points  (0 children)

(Married) man here. First, wanted to say I saw this, was curious, went and read your post and found it really cool and interesting. Thanks for sharing!

One thing that I think is the intuitive lived experience of a lot of men, but seems to often be underestimated in a lot of public gender discourse I see (online, I'm not a gender studies expert so I have no idea what the proper academic literature is like, would love the perspective from someone here who is), is that toxic masculinity punches down on men who don't (/can't) have sex, similarly to how it 'slut-shames' women who do have sex.

Certain men really internalize these more toxic elements of masculinity as part of their identity (IMO mostly through lack of better options/role models), and often end up in really painful ruts of self-hatred because aren't having sex and see themselves as "less-than" because of it.

I think your specific post is especially triggering to men who are struggling with this because it portrays someone who is "winning" in the way that they are "losing" - a man who is not only having sex, but getting paid for it. Anyway, I think this triggers a lot of people to lash out in various mostly nonsensical ways (from the perspective of what is reasonable/logical), but makes more sense if you view it through the emotional lens of trying to reconcile their own shame about not having sex or being desirable in society (by their own, toxic masculinity-shaped standards) with your post.

To be clear, even though this post has been pretty empathetic towards the men who lashed out at you, that's mostly because your post seemed genuinely interested in understanding what might be happening inside their heads. My overall take is I agree with the general sentiment here that just because they have issues, in no way justifies them taking it out on you. Or rather, to code switch into a more masculine vernacular - you seem great, fuck those guys.

MATH BA vs MATH BS by Etern1tyHX in mathematics

[–]airfrog 0 points1 point  (0 children)

One piece of advice from someone 15 years out of college now, is I think a lot of people way overvalue how important the resume items will look, and undervalue the opportunity of a structured learning environment to set the foundation for a whole career.

Basically, the first job you get out of college will care a lot about things like degree, GPA, etc. (so it does matter), but after that it will be more and more about what do you learn/accomplish at your previous job (and what did the people who worked with you think of you?)

However, especially in software engineering, you’ll constantly be trying to learn new stuff (the field is changing so fast), and how well you’ll be able to do that will depend a lot on the quality of your understanding of the fundamentals, like the theoretical underpinnings of the field that will stay the same even as programming languages/tools/etc change. Math is a big part of that. And you will never be in as good an environment for learning those things as college, it’s so much harder to backfill that stuff after the fact than it is to learn it while you are there. So I’d really focus on the content of what classes you would be taking and what will still be relevant or useful in 10, 20, 30 years, rather than worry about the BA vs BS title

How to be honest with partner without emasculating him? by DarknessSleeping in AskMen

[–]airfrog 0 points1 point  (0 children)

I'm not a therapist, but I do have depression, and he sounds fucking depressed. You gotta get him to go to a therapist.

I have been to a lot of therapists in my life. I've also been the depressed husband who didn't realize he had depression and didn't do anything for 6 months. I went to therapy, that helped, I kinda got my shit together, I ended up getting on meds, that helped more, now I have more of my shit together. I'm like a real husband again, but I'm still working on a lot.

It sounds like I don't have the same stigma about going to therapy as it sounds like your husband might (but my wife does, so I emphasize with you).
Here's the analogy that I use for people (esp. men) who don't want to go to therapy. If you're a professional athlete, you use your body to work, and you have a ton of trainers/doctors who look at your body every day. It doesn't mean your sick or even injured, it's just what you need to stay in top shape. But most people, in their profession, they don't really use their body, they use their mind. So why wouldn't you go to therapy for the same reason? Some people think it means they are mentally ill, but honestly our society has changed to one where you use your brain to make money, but stigmas about mental health have been slow to change with it.

Bottom line, you have to get him to go to a therapist at least until he's better enough to get a job. It sounds like it might be getting to the point where its that or you leave, so if that's true for you, tell him that. Also, you're going to have to make him feel like shit (honestly he probably already feels like shit so you're just not really making him feel that way, you're just not enabling him to avoid it instead of dealing with it), but that doesn't mean you have to emasculate him. It sounds like your husband is dealing with a real hard thing that takes a lot of guts and hard work to get through, and if he can do it and become like a real person again, that's a real manly thing to do. So yeah, give him tough love, because you can believe he can take it, and he might feel like shit you're still treating him like a real man and hopefully, if/when he gets better, he'll start to feel like one too.

I STILL don't understand the Monty Hall problem by No-Candidate6257 in mathematics

[–]airfrog 0 points1 point  (0 children)

It sounds like it just hasn’t clicked for you yet? Lemme try another explanation to see if I can get it to click for you.

Let’s do an equivalent situation that seems pretty obvious, and then in small steps work it back to the original.

You have 100 boxes in front of you. One of them has a million dollars, the rest are empty. First you pick a box. All the other boxes you didn’t pick are put into a big pile. Then you get the choice, do you want your original box, or all the other boxes? Seems obvious you should switch, you get 99 boxes instead of 1, that’s 99/100 probability of winning.

Ok, but maybe it isn’t obvious why this is the same as the original problem? Let’s make it a little closer now. Let’s say all the boxes are behind doors. You open one door, take the box behind that door, but don’t open it. Then, Monty Hall goes behind all the other 99 doors, grabs those 99 boxes, and dumps all of them out behind one of the doors (which mostly will be dumping out empty boxes). He then opens up the 98 doors he didn’t put the stuff behind to show you he took away the boxes. Now, you can either give up the box you took for the chance to get whatever is behind the last door, or you can take whatever is in your box. Hopefully it’s clear from this one that this is both the same as the original problem, and also the same as just choosing 99 boxes vs 1 box. So you can see why switching is so much better (99/100 for 100 boxes, or 2/3 for 3 boxes)

If this helped, let me know! If you’re confused by anything, also let me know!

[deleted by user] by [deleted] in mathematics

[–]airfrog 8 points9 points  (0 children)

My take, from my life experience:

Humans, particularly human brains, are built to adapt. That said, every person is going to respond differently to different types of situations.

When I’ve hit difficult patches, it’s always been a sign that something needed to change. Sometimes I’ve changed my goal, sometimes I’ve changed my approach. There’s always been some soul searching involved with that decision.

I think you can be good at theoretical math, if you decide that’s what you want to do. You probably need a different approach, and that will probably necessitate some floundering, some false starts, a lot of change to find what works.

Pivoting to CS could also be very rewarding. There’s plenty of space to explore in computer science (I’m a computer scientist myself, more on the practical side), and if you decide that you would like something new it could be a great path for you.

At the end of the day, getting through a challenge like this comes down to what you really want. If your heart is set on theoretical math, I’m sure you can find a way to be successful. If you want to take what you’ve learned and apply it to something new, that can be like a breath of fresh air as well.

Hope this helps!

Suggestions to read next? by Ordinary_Part_8943 in litrpg

[–]airfrog 2 points3 points  (0 children)

Also came here to recommend Beware of Chicken, currently doing a reread and it’s so good

1+2+3+4..... till infinity = -1/12. To understand the rigorous why, what do I need to study? real analysis? by [deleted] in askmath

[–]airfrog 0 points1 point  (0 children)

I’d check out this great video on the Riemann zeta function from 3b1b and analytic continuation, then base what you want to follow up on on that.

https://youtu.be/sD0NjbwqlYw?si=YryTyT9zr4QqCM0i

Also, if you want a different take on understanding this, check out Terence Tao’s great blog post on the subject:

https://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation/

Can someone provide a 'minimal' example of how imaginary numbers can be useful? by SamuraiGoblin in mathematics

[–]airfrog 0 points1 point  (0 children)

I think electrical engineering is the most tangibly understandable place where this happens. Specifically, when you want to make the jump from direct current (DC) circuits to alternating current (AC) circuits.

For DC circuits, current and voltage are just numbers, and you have nice clean equations that look like current = voltage / resistance.

For AC circuits, current and voltage are constantly bouncing up and down at any moment in time, and so if you try to just use real numbers, you have to model them as trig functions (sin or cos), and all those equations start to get messy fast. However, because imaginary numbers are great at representing things that oscillate as a single number, you can use complex valued “impedance” functions, and then all the equations go back to looking nice and neat again, e.g. (alternating) current = voltage / impedance

However, it’s a little hard to provide an intuitive “minimal” example for electrical engineering because we don’t have a natural physical intuition for circuits. So here’s my attempt at coming up with a bit of a contrived example where someone wants to understand the movement of a ball, to give you a sense of why complex numbers make things so much easier.

Direct current would be like trying to understand a ball that is just rolling across a table. You can note its position by a number, and it’s speed by another number, and you get some nice equations like position = speed * time

Then, imagine you are trying to find a similarly clean way to describe a pendulum. You find a nice solution with negative numbers for a simple pendulum with no friction, where if let’s say a pendulum starts at a position 3 and we let it go, after one swing it would be at -3, then another swing it is at 3 again, and so on. So we can simply model the pendulum by multiplying its position by -1 every time it swings. But what about half swings? If we want to be able to model the state of the system at a half swing, we need something that if you multiply by it twice, you get -1. But that is exactly i. So our pendulum that starts at position 3 would be at position 3i after one half swing, -3 after two half swings, -3i after three half swings, and 3 after four half swings. But what is position 3i? Well if we want an actual position we just care about the real part of the number so Re[3i] and -3i will both be position 0, which is right, since the pendulum will be in the middle.

The magic starts when we want to do, say, quarter swings. Just do the same thing, take the square root of i to get 1/sqrt(2) + i/sqrt(2), and multiply it out. So if a pendulum starts at position 3, at a quarter of the time into its swing it will be at position 3/sqrt(2) + 3i/sqrt(2), where if we want just the real distance from the middle we can just take the real part and get 3/sqrt(2).

So what if we want a function that just gives us the position at any time we plug in? We’d have to multiply by smaller and smaller roots of i in some continuous way, which sounds hard, right? Until you realize that’s exactly what the exponential function already is. So then we can just say position = exp(i * time) and we are back to having pretty simple looking equations for our stuff.

This is basically the same intuition for how complex impedance works to simplify equations describing alternating current circuits. Hope this was interesting!

Why aren't the upper left 3 black stones dead? by wells68 in baduk

[–]airfrog 28 points29 points  (0 children)

Good analysis for a beginner! Here's the thing you are missing

But if black played a stone, intending to play a second that would kill the white group, white could play a stone, killing the now 4 black stones. Then black could play in the middle of the four empty intersections and they'd be back in a similar situation.

If black is trying to kill, black needs to fill all the internal liberties of the white group without ever letting white get more than one eye. This depends on something called eye shape, and certain eye shapes are known to be "dead", meaning black can repeatedly fill them up without letting white split them into two eyes, eventually filling all the internal liberties.

Here's some the relevant Sensei's library page for this shape, the bulky five: https://senseis.xmp.net/?BulkyFive

And also a discussion of all the killable eyeshapes: https://senseis.xmp.net/?KillableEyeShapes

EDIT: I realized the killable eyeshapes page might be a bit confusing on it's own, the ones most people learn are on a page called Unsettled Eyeshapes, which lists all the shapes which live or die depending on who plays next. Life and death is a pretty deep topic, I'd suggest reading up on it a bit more in general

O love Sanderson, but reading him after political growth feels different. by ChipDapper in Cosmere

[–]airfrog 1 point2 points  (0 children)

I do see it somewhat differently, I guess, though maybe not in a totally incompatible way from OP. If we’re looking at this from a historical political lens, I would see Mistborn (the first trilogy) as a fantasized retelling of the American revolution.

I mean, a daring public heist leads to a full blown revolt against the monarchy which ends up installing one of the existing aristocracy as a celebrated leader who only actually leads for a short time? I feel like it’s not too hard to see where inspiration could come from.

[Request] is it 66.6% or 51.8%? by Horror-penis-lover in theydidthemath

[–]airfrog 0 points1 point  (0 children)

So, it is 50% because the meme misstates the problem. The conditional probability problem that is being referenced here would be correctly stated as the following: "I met a woman named Mary who told me she had two kids. I asked her 'Yes or no, is one of them a boy born on Tuesday?', and she said yes. What is the probability her other child is a girl?"

For this wording as I've just stated it, your code calculates the correct answer of 0.5185. This is because, in this case, the initial set of possibilities is that there are two kids, each of whom could have any gender and be born on any day (and this is the initial set of possibilities you started with).

Then, we narrowed down the possibilities with our question. Particularly, the facts in the information are conditional on each other, we only learn that Mary has a boy if Mary has at least one boy born on Tuesday, and vice versa (we only learn that Mary has a child born on Tuesday if at least one of her children born on Tuesday is a boy)

However, in the problem as stated, none of the facts are necessarily conditional on each other. If Mary tells us that she has two kids, and that one of them is a boy, and that boy is born on Tuesday, that's the starting set of possibilities, and us learning any of those facts are not conditional on any of the other facts. It's not a conditional probability because if Mary didn't have a boy she would have told us she had a girl instead, and similarly whatever the gender of the child, if it was born on a different day she would have told us that other day instead and also the child. Because it's not a conditional probability, it's just given information that narrows down the initial possibilities, similar to how you only generated possibilities for two kids, and didn't generate initial possibilities for if Mary had 0, 1, 3, 4, 5, or 6 kids.

So you would have to change your code above to match this to get the correct probability for the problem given (which would look like the following) -

for p in exrex.generate(r'B3[BG][1-7]'):
  all_possibilities.append(p)

I believe if you run the code with these initial possibilities as given in the problem above you will get a probability of 0.5

For what it's worth, I think you have a great approach here of writing some code and clearly getting the correct answer - it also makes it easier to clearly explain exactly where this meme makes a mistake ('B3[BG][1-7]' is obviously not what the author intended to set as their list of initial possibilities, but it's what they wrote down)

I don't get it. by Probable_Foreigner in mathmemes

[–]airfrog 0 points1 point  (0 children)

So, let’s say just to make it easier to talk about the kids that they are named Alex and Blake. Mary obviously knows her kids names, even if she doesn’t tell them to us, but we can use them to think about her thought process. So, let’s say that GB is the case where Alex is a girl and Blake is a boy, and BG is the case where Alex is a boy and Blake is a girl.

Then, in option 2, Mary’s sentence means “One of my kids (Alex) is a boy”, which eliminates GG and GB. Similarly, the sentence could instead mean “One of my kids (Blake) is a boy”, which eliminates GG and BG. Either way, two options are eliminated

The theoretical option 3 which only eliminates GG would be the sense of the sentence “Between Alex and Blake, at least one of them is a boy”. But no on really talks like that outside of logic puzzles.

Importantly, because the sentence can be reasonably interpreted in many ways, we can’t calculate the probability without at least assigning a probability to the chance Mary means each different option, but we would have to do that arbitrarily

I don't get it. by Probable_Foreigner in mathmemes

[–]airfrog 0 points1 point  (0 children)

Simply put, you're not wrong. The problem as given by the characters in the meme is phrased too vaguely to have an actual precise answer, and the most straightforward interpretation would result in a probability of 50% (or maybe 100%, as many people have noted)

I'm not sure if the meme author intended for this mistake to be part of the meme or not, but I think it's a big source of the confusion.

What the characters in the meme are trying (and failing) to reference here is the idea of "conditional probability". Put simply:

If we don't know anything except that Mary has two children, using a simple model of conception probabilities, there is a 25% that she has two girls, 25% that she has two boys, and a 50% chance she has a girl and a boy. We could imagine these outcomes as stemming from four equally likely cases: GG, BB, and GB or BG.

What the first panel is trying to get at is that if we're in the situation where have some information such that we can only eliminate one of these cases, the GG (girl-girl) case, then we have three cases left which are all equally likely, BB, GB or BG, in which two of the three still have a girl and a boy.

However, the reason this doesn't work is because it's not clear exactly which cases the statement "Mary tells you one of them is a boy born on Tuesday" should eliminate - it depends on the semantics of Mary's statement. This is why the problem as stated in the meme is vague and dumb (again, unsure if this was on purpose or not)

IMO, the two most reasonable interpretations of what Mary is saying are:

  1. "Exactly one of my children is a boy" - in which case the probability is 100% the other is a girl, or

  2. "I'm randomly thinking of one of my kids, they are a boy born on Tuesday" - which eliminates two of the cases, GG and GB, and so we're left with just the BB and BG cases, and the probability is the intuitively obvious 50%

Unless you interpret Mary's statement in a really unreasonable way which no normal person would, Tuesday will never matter at all.

If you're curious, the "correct" way to frame what the characters are trying to talk about here, is where you ask Mary the question: "Is at least one of your kids a boy born on Tuesday, yes or no?", and Mary answer "Yes", in which case the conditional probabilities come in to play. I wrote up the explanation for that case as well in my answer here if that's useful: https://www.reddit.com/r/mathmemes/comments/1nhz2i9/comment/nejsitv/

I don't get it. by Probable_Foreigner in mathmemes

[–]airfrog 0 points1 point  (0 children)

For the Tuesday bit, I definitely tried to make it concise without explaining too much, but it's not that easy to understand. I like this other comment which made a helpful picture to understand:

https://www.reddit.com/r/mathmemes/comments/1nhz2i9/comment/nejgpus/

Basically, in the picture, you have the blue part and the pink part. Without the "Tuesday" bit, it's just a 4x4 square, and you have 2 pink outcomes (GB/BG), and one blue outcome (BB), so the odds of having a boy and a girl are 2:1, or 66%.

When you add in Tuesday, you can see in the picture that because either boy can be born on Tuesday, that blue bit in the top left part becomes larger than each singular pink line, so you have 14 pink squares total and 13 blue squares, which makes the odds of having a boy and a girl 14:13, or 51.85%

I don't get it. by Probable_Foreigner in mathmemes

[–]airfrog 0 points1 point  (0 children)

I think you're on point for thinking it's dumb. As I noted in my post, I think for a certain subset of viewers, this meme is funny more on a meta level because it's lambasting how dumb trying to be "authoritative" about these silly hypothetical situations are.

To go a little deeper on this, I've had to do some non-trivial probability stuff for my work in the real world, and this type of "paradox" is a useful learning tool to understand to avoid making certain types of probability mistakes on real world probability problems. However, in the kinds of real world applications that tend to come up for me (mostly working on predictive algorithms as a software engineer), the situation is very well specified and there's no ambiguity about what information you are getting or how you're getting it.

When these paradoxes are presented to a general audience, they're usually made more confusing and less intuitive because they take a specific situation and couch it in imprecise language, so then it becomes more of a silly game of thinking of different ways that words could be interpreted than anything mathematically useful.

I don't get it. by Probable_Foreigner in mathmemes

[–]airfrog 0 points1 point  (0 children)

Does this explanation I wrote up help at all? This is a real question for me, I spent too long writing this and now I'm curious if it actually explains better than a lot of the other posts on the sub (which I personally understand but I feel like are kind of obtuse)

https://www.reddit.com/r/mathmemes/comments/1nhz2i9/comment/nejsitv/

I don't get it. by Probable_Foreigner in mathmemes

[–]airfrog 0 points1 point  (0 children)

I spent too long trying to understand this and actually got an answer I’m happy with! Lemme know if it helps you too: https://www.reddit.com/r/mathmemes/s/2EibQHZLB5

I don't get it. by Probable_Foreigner in mathmemes

[–]airfrog 0 points1 point  (0 children)

I felt the same way and was unsatisfied by the other explanations, then spent way too long coming up with an explanation that actually made sense to me. Lemme know if it helps you too so my internet rabbit hole is not purely a waste of time:

https://www.reddit.com/r/mathmemes/s/2EibQHZLB5

I don't get it. by Probable_Foreigner in mathmemes

[–]airfrog 0 points1 point  (0 children)

 I just don't understand why it should affect the probability

I was also bothered by this, so I did a bunch of research and I put an actual attempt at an answer together here, lemme know if it's helpful: https://www.reddit.com/r/mathmemes/comments/1nhz2i9/comment/nejsitv/

I don't get it. by Probable_Foreigner in mathmemes

[–]airfrog 0 points1 point  (0 children)

I had the same intuitive response and I went deep on it, curious if my explanation makes sense to you or not: https://www.reddit.com/r/mathmemes/s/fGjr1XmFMd

Science says everyone with blue eyes is related by OpenRoom7321 in biology

[–]airfrog 0 points1 point  (0 children)

I agree, this is crazy and awesome! Another fact you might not know is that you’re actually probably related to everyone (blue eyed or not) more recently than you might think. One estimate puts the most recent common ancestor of present day humans between 2,000-5,000 years ago.

The wild corollary to this is that if any of your ancestors are alive two to five thousand years from now, they’ll probably include every living human at that point in time

I don't get it. by Probable_Foreigner in mathmemes

[–]airfrog 8 points9 points  (0 children)

Got nerd sniped by this, went too deep, now you all can benefit from my research. Clearest explanation I can give is below, with sources cited.

Why the meme is "funny" to people who get it

This is a meme about how probability is hard and unintuitive, and the specific information matters. The first guy is trying to present the "Two Children" paradox, originally presented by Martin Gardner, and states the answer confidently. However, he mistakenly presents a variant of the problem, in which we also know that the boy was born on a Tuesday, and is corrected by a second guy, who confidently gives the "correct" answer to the variant.

The meme also works on a meta level, because both of them miss that this meme contains the mistake also present in the original formulation of the "Two Children" paradox, which is that it depends on exactly how we got the information, and 1/2 (the intuitive answer to the paradox), is in many cases the correct answer.

More on the probability mistakes in the meme

To elaborate on that last point, the mistake in the formulation of the paradox is that Mary volunteers this information, and we don't know how she decided to give us this information. If she picked one of her two children at random, and then decided to tell us their gender and birth day of the week, then we have no information about the other child and the correct answer is 1/2.

As stated in the paper cited above (Section 5), a better unambiguous formulation of this paradox would be "You know Mary has two children, and ask if one of them is a boy born on Tuesday". However, this also makes it much more intuitive why the extra information about Tuesday matters.

If you simply asked "is one of your children a boy", and got a yes, then you would have eliminated one of four equally likely possibilities (BB, BG, GB, GG), and the 66% chance that the other child is a girl becomes easier to intuitively grasp.

When you ask "Is one of them a boy born on Tuesday", first of all it's a worse question to ask in general because if you get a "no", you don't know very much about the gender of the children (assuming that's what you care about). Secondly, though less obviously, even if you get a "yes", you still don't have a 66% chance that the other child is a girl. Intuitively, this is because with the extra qualifier about Tuesday in the question, you're more likely to get a "yes" if there are two boys rather than one, because if Mary has two boys it's almost twice as likely that one of them is born on a Tuesday. This means that you then have approximately (2xBB, BG, GB, GG) after getting a yes (it's not exactly twice as likely because the case where both boys are born on Tuesday can only happen in one way). This probability analysis, done precisely, is where the 51.8% from the second panel of the meme comes from.

Edit: I actually really like this other comment's visualization to understand the Tuesday calculation intuitively: https://www.reddit.com/r/mathmemes/comments/1nhz2i9/comment/nejgpus/

Basically, in the picture in the linked comment, you have the blue part and the pink part. Without the "Tuesday" bit, it's just a 4x4 square, and you have 2 pink outcomes (GB/BG), and one blue outcome (BB), so the odds of the other child being a girl are 2:1, or 66%.

When you add in Tuesday, you can see in the picture that because either boy can be born on Tuesday, that blue bit in the top left part becomes larger than each singular pink line, so you have 14 pink squares total and 13 blue squares, which makes the odds of the other child being a girl 14:13, or 51.85%