Research @ Aether
Did MATS (Fellow + Research Manager) + CS @ Cambridge
Dennis Akar
Karma: 54
Yay it’s back up again.
What is the exact formal difference/relation between probability distribution , random variable , and causal model ?
And you can’t just get that stuff by asking your mind to tell you that stuff; you have to let your mind do its thing sometimes, without requiring a legible justification.
I need to really internalize this. I tend to “rediscover” this and forget about it the moment things become more stressful.
Requiring that things be explicitly justified in terms of consequences forces a dichotomy: if you want to do something for reasons other than explicit justifications in terms of consequences, then you either have to lie about its explicit consequences, or you have to not do the thing. Both options are bad.
Unless one explicit justification is simply that “this is fun to do, which is Good™ in-and-of-itself, and also <insert this article here/>”?
Overall extremely good article and makes me less guilty about engaging in playful thinking (a frequent occurrence)
Typos:
using repetitive that hacks aren’t easy → using repetitive hacks that aren’t easy
expects to be given you → expects to be given to you
Testing Out Shortform and Comments
I really appreciate the existence of this functionality, since when it comes to trying to do something I either overdo or don’t do at all. Shortforms make it managable and still publicly shared, so I still have enough incentive to create something nice and understandable. A much much better Twitter, and allows everyone to glimpse into the “studio” of very good writers.
Oh wow I can include images like this! Very nice.
Kind of agree. What do you think is the most value you get from this? Was wondering about whether I should post accountability-related stuff here (e.g. by editing the post) but not sure if it makes sense.
I have been feeling extremely impostery lately and do agree on the critical self-evaluation tendency. For the last month or so I felt entirely stuck with even the idea of an application giving me severe anxiety. Have been overcoming this slightly lately but I think this post and the conversations it caused has made em feel better. Thank you.
Successful Work Analysis
Managed to end up submitting some applications to places I think I would like to work at. I think things that helped me do this (notwithstanding chance/luck) were (in descending order of perceived priority):
Preventing potentially “oppressive” silence by having an audiobook/chat in the background. Not necessarily white noise chat, which can feel just irritating (not usually) and I don’t tend to like music due to it influencing emotions too much. It also sometimes requires too much fiddling about with playlists etc. Examples:
At the time it was two friends discussing how they’re thinking about their lives and video making ideas.
Next time I did this by listening to Connor chatting about life and AI safety.
“Positively” working myself out / physically tiring myself. Went out to have long walk with a friend. Though I think physical activity is indeed important, it didn’t feel as impactful as the oppressive-silence-breaking.
The idea of being able to tell a friend, who is not that much invested in what I’m doing, that I did this and this cool thing.
These seem to somewhat lower my sense of anxiety both for applications/rejections and sending a message to people I should send a message to (e.g. job or someone I haven’t replied to in a very long time).
This feels like a mini-twitter. Interesting
colab notebook
this interactive notebook
check out the notebook
notebook
First link is not like the others.
I propose a compromise: 1.5 hoses. This will lead to greatness.
We might have missed it.
I am a bit confused here.
I responded—note that this was completely spontaneous—”What on Earth do you mean? You can’t avoid assigning a probability to the mathematician making one statement or another. You’re just assuming the probability is 1, and that’s unjustified.”
Is it? We have observed the mathematician making the statement. Assuming observation matches reality, and the statement is true, the probability of the mathematician having made the statement should be 1 or close to it because it has already happened. In every world, as long as the mathematician already makes this statement, the statement being something other is not possible. This eliminates the possibility of it being girl-girl and through orthodox statistics brings us to 1⁄3 yada yada. I’ve even run a small program to test it out, and it is very close to 1⁄3.
If the mathematician has one boy and one girl, then my prior probability for her saying ‘at least one of them is a boy’ is 1⁄2 and my prior probability for her saying ‘at least one of them is a girl’ is 1⁄2. There’s no reason to believe, a priori, that the mathematician will only mention a girl if there is no possible alternative.
I have been pondering about this statement for hours on end. Assume I accept that the prior probabilities still need to be substantially considered despite the evidence, I am still confused about how there is a prior probability of 1⁄2 each for the mathematician saying that “at least one of them is a girl” and “at least one of them is a boy” (if she has a boy and a girl). Does this not assume that she can only make two statements about her state and no other? Aren’t there many other ways she could have stated this such as “I have a boy and a girl” or simply “I have two girls” and “I have two boys”? Despite our prior probabilities for statements, the last two statements make the probability of both being boys 0 or 1. This is of course assuming the mathematician does not lie.
Finally, I’d like to understand how adding the possibility of the mathematician stating at least one girl increases the possibility of both being boys, rather than decrease it.
Wait.
The reason the probability increases is that since the mathematician chooses this statement despite having two options, it is now more likely there are two boys. I see. I got the intuition but I’d like this in mathematical notation. This still does not seem to fix the problem of already having many statements to choose from, making the assumption that the prior probability of her choosing to say at least one boy 1⁄2 dubious.
But I seem to now understand the reasoning behind it in the event that if the prior for making the statement is 1⁄2, the answer is indeed 1⁄2. Though this now seems to bring to forth how far back one needs to go to reach optimal probability and how there may be so many little subtle observations in real life which substantially impact the probability of events. Very exciting!
I’d very much like to see your work for the question! This is my first comment, I apologize for its length and any folly involved which is purely my own.
Cheers.
minor typo