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- Comment on we love those power laws 2 weeks ago:
what were they doing for all that time
- Comment on checkmate, big geology!! 2 weeks ago:
unfortunately this would only work on tanks that shoot lava
- Comment on party poopers 2 weeks ago:
the teacher is the one doing the real lab experiment here
- Comment on cowabunga 2 weeks ago:
but can he grind on the topologists sine curve:
- Comment on Physics 3 weeks ago:
under an appropriate level of abstraction you can make lots of types of cylinders. in topology you can define a cylinder of a (topological space) X to just be X × [0,1]. this kind of definition comes up pretty frequently, and is used to create mapping cylinders, which i suppose are another type of cylinder.
the “normal” kind of cylinder is then just (circle) × [0,1], or (filled in circle) × [0,1], depending on whether you want it to look like an empty paper towel roll or a (full) can of beans
- Comment on You are in this solar system, but we do not grant you the rank of planet 3 weeks ago:
this condition makes “planetness” into a local condition. so theoretically, we can throw enough junk into space and stop anything we want from being a planet.
pluto just got unlucky in terms of the amount of trash it has in its way. its not fair :(
- Comment on I am the thing that goes *thump* 'Fuck!' in the night 3 weeks ago:
most horrifying thing is the bathroom being at the top of a flight of (carpeted) stairs
- Comment on just say no!! 3 weeks ago:
what if it’s not euclidean but only locally euclidean?
- Comment on Tesla seeks to award Elon Musk $56bn pay package | BBC 4 weeks ago:
completely agree. and it’s even more insidious when you take into account how he’s spent the past 6 years bragging about how he has a salary of $0 because he’s “only working for the betterment of humanity” or some nonsense like that.
- Comment on Tesla seeks to award Elon Musk $56bn pay package | BBC 4 weeks ago:
Board chair Robyn Denholm wrote in a letter included in the regulatory filing: “Elon has not been paid for any of his work for Tesla for the past six years… That strikes us, and the many stockholders from whom we already have heard, as fundamentally unfair.”
Musk’s compensation for 2023 was $0, the filing showed, as the billionaire does not take a salary from the company and is compensated through stock options.
it’s so unfair that elon hasnt gotten a single pay check and has instead had to settle for making billions off of his stock options. think of all the mega yachts and social media companies he could’ve bought if only he had been paid a salary.
- Comment on teachings 4 weeks ago:
i think this is a really clean explanation of why (-3) * (-3) should equal
9
. i wanted to point out that with a little more work, it’s possible to see why (-3) * (-3) must equal 9. and this is basically a consequence of the distributive law:0 = 0 * (-3) = (3 + -3) * (-3) = 3 * (-3) + (-3) * (-3) = -9 + (-3) * (-3).
the first equality uses
0 * anything = 0
. the second equality uses(3 + -3) = 0
. the third equality uses the distribute law, and the fourth equality uses3 * (-3) = -9
, which was shown in the previous comment.so, by adding
9
to both sides, we get:9 = 9 - 9 + (-3) * (-3).
in other words,
9 = (-3) * (-3)
. this basically says that if we want the distribute law to be true, then we need to have (-3) * (-3) = 9.it’s also worth mentioning that this is a specific instance of a proof that shows
(-a) * (-b) = a * b
is true for arbitrary rings. (a ring is basically a fancy name for a structure with addition and distribute multiplication.) so, any time you want to have any kind of multiplication that satisfies the distribute law, you need (-a) * (-b) = a * b.in particular,
(-A) * (-B) = A * B
is also true whenA
andB
are matrices. and you can prove this using the same argument that was used above. - Comment on "Yeah, but what if we used AI?" 4 weeks ago:
they finally found a way to add a built in service fee to taxes. i just hope this new model is compatible with turbo tax premium
- Comment on YSK : Dark patterns among large companies are becoming more mainstream 4 weeks ago:
this reminds me of what happened to the instagram cofounders when zuckerberg asked to buy their company:
Systrom [cofounder] said he feared turning down an acquisition offer from Facebook would send Zuckerberg into “destroy mode” — a concern that Cohler [early investor] affirmed.
(source)
this stuff came up in a court hearing, and then nothing happened about it
- Comment on YSK : Dark patterns among large companies are becoming more mainstream 4 weeks ago:
one time i had to call a company during regular 9-5 business hours to cancel a subscription after starting a free trial.
that experience was so horrible ive since sworn off free trials altogether. nowadays, if i need a free trial to use an app or website for a couple days, then i will simply not use that app or website.
- Comment on So much for free speech on X; Musk confirms new users must soon pay to post 4 weeks ago:
Everybody knows what free speech means.
i really dont think so.
free speech is a pretty complicated thing and i feel like many people dont have a solid grasp on it. i think a good number of people think they know what free speech means because they know “it only applies to what the government can do to you”, but there’s quite a bit more to it than that. like how to deal with hate speech, threats, misinformation, disinformation, etc.
and this is directly related to the problems twitter is facing: elon musk started out by saying hes a “free speech absolutist”, but twitter has been slowly rediscovering why “free speech absolutism” doesnt work. and you can see those discoveries in real time with twitter reintroducing moderation policies (among other things)
- Comment on He has to be stopped 4 weeks ago:
i can get up to 3 million on a good day
- Comment on Chicago Gang Rise Up 4 weeks ago:
is apa the one that makes you cite things in parentheses? because that one gets a thumbs down from me
- Comment on Dad is so cool 4 weeks ago:
how are you typing the “p”?
- Comment on pluto 4 weeks ago:
mee vee eee mee jee see uee nee pee
- Comment on pluto 4 weeks ago:
the more the merrier
- Comment on space 4 weeks ago:
then you’re in for a fun surprise
- Comment on pluto 4 weeks ago:
new planet definition is dumb and i don’t subscribe to it. pluto is always a planet as far as im concerned
- Comment on space 4 weeks ago:
if you believe in the notion that the universe is cyclic then you can mimic time traveling backwards by traveling forwards, past the end of the universe, and stopping at just the right time in the new universe.
e.g., to get to 1700 you’d go (present time) -> (death of the universe) -> (1700 in next universe)
- Comment on Feels like Apple is more about fashion then tech IMO 5 weeks ago:
doesnt sound like it’s something that will be of much use to you, and thats fine. but i use it all the time to annotate textbooks and take notes when studying.
- Comment on Still wondering why people from Alaska didn't post about the eclipse 5 weeks ago:
trust me you dont want to know
- Comment on Feels like Apple is more about fashion then tech IMO 5 weeks ago:
i feel like it’s going to be another case of the ipad. i dont really remember anyone thinking the original ipad had a reason to exist when it came out (myself included). but after 8-10 years or so, it found a problem that it could solve (taking notes well, and being a general purpose school device). it’s not really necessary now, but it’s certainly way more useful than the original ipad was when it first came out.
i dont think the original vision pro will be that useful to anyone, but it might start a line of products that leads to something interesting in 8-10 years. or not, who knows.
- Comment on wat 5 weeks ago:
from a practical perspective, you can mostly think of integration and differentiation as inverse operations. (it works fine for most functions that come up in most applications.)
but this doesnt really hold true in general. a famous example is that the gaussian distribution (used to make bell curves) is an integral that cannot be solved by using differentiation to “undo” integration. the general problem is that its a lot easier for a function to be integrable than it is for a function to be differentiable. (all continuous functions are integrable, but not all continuous functions are differentiable. even more troubling, there are integrable functions that aren’t even continuous.)
- Comment on wat 5 weeks ago:
i think this a really nice way of thinking of things, especially for regular everyday life.
as a mathematician though, i wanted to mention how utterly and terribly cursed square roots are. (mainly just to share some of the horrors that lurk beneath the surface.) they’ve been a problem for quite some time. even in ancient greece, people were running into trouble with √2. it was only fairly recently (around the 17th century) that they started looking at complex numbers in order to get a handle on √-1. square roots led to the invention of two different “extensions” of the standard number systems: the real numbers (e.g. for √2), and later, the complex numbers (e.g. for √-1).
at the heart of it, the problem is that there’s a fairly straightforward way to define exponentiation by whole numbers: 3^n^ just means multiply 3 by itself a bunch of times. but square roots want us to exponentiate things by a fraction, and its not really clear what 3^1/2^ is supposed to mean. it ends up being that 3^1/2^ is just defined as 3^1/2^ = x, where x is "“the number that satisfies x^2^ = 3"”. and so we’re in this weird situation where exponentiating by a fraction is somehow defined differently than exponentiating by a whole number.
but this is similar to how multiplication is defined: when you multiply something by a whole number, you just add a number to itself a bunch of times; but if you want to multiply by a fraction, then you have to get a bit creative. and in a very real sense, multiplication “is the exponentiation of addition”.
- Comment on wat 5 weeks ago:
from a formal perspective, division is an “”abbreviation”” for multiplying by a reciprocal. for example, you first define what 1/3 is, and then 2/3 is shorthand for 2 * (1/3). so in this sense, multiplication and division are extremely similar.
same thing goes for subtraction, but now the analogy is even stronger since you can subtract any two numbers (whereas you “can’t” divide by 0). so x - y is shorthand for x + (-y). and -y is defined “to be the number such that y + (-y) = 0”.
- Comment on Still wondering why people from Alaska didn't post about the eclipse 5 weeks ago:
further evidence in favor of the theory that canada and mexico are new zealand territories