[Epistemic status: providing suggestions for how to think about something (or how to justify how you already think about something) based on my own experience.]
When deciding between various options under uncertainty, one attractive framework is to calculate the expected value of each option, then choose the option with the highest expected value.
(This post essentially agrees with Probability Is In The Mind. It differs in emphasis and style.)
[Epistemic status: clarifying language in the hope of helping people who were confused like me, not stating anything about what is or isn't the case in the world.]
Today I'll be analyzing the song A Car, A Torch, A Death by Twenty-One Pilots, from their 2009 self-titled album.
When you imagine how the world should be, imagine also what work needs to be done to get it there. But do not yet imagine yourself doing that work. To do so at this stage would be to invite excess complication. First imagine what someone will need to do. Then, in place of "someone" put "myself".
This is an experiment where I narrate my thought process as I solve a math problem. My goal: writeups of the solutions to math problems usually present a polished, streamlined version of the solver's thought process that omits errors, wrong turns, and heuristics. I wondered what it would be like to represent the thought process "warts and all."
[Epistemic status: working out a course of action for myself, based on somewhat commonsensical observations.]
(This post essentially agrees with Ends Don't Justify Means Among Humans and Making Exceptions to General Rules. It differs in emphasis and style. If you are reading this, please read them as well.)
From the warm and noisy dark I watch,
from within a gentle fuss of feet and squeaking,
the resolute stars. And I watch you.
In 2019 I could descend my porch steps
and hear three short utterances
like coughs, but mixed with ideas or words
from a homeless woman sitting there.
I saw a biker get hit a little
by a red car scooting forwards
as it tried to park.
Today I'll be analyzing the song The Bug Collector by Haley Heynderickx, from her 2018 album I Need To Start A Garden.
Most programming languages have a way to represent "no value" or "nothing". Python has None, Ruby has nil, Java and friends have null. Javascript has two ways to represent this concept -- undefined and null.
I bought a bottle of cranberry juice which said "100% juice" on the label. But, later, I found that the label said it included apple juice. I became confused and suspicious about fruit juice labels, a state which lasted many years.
But it turns out that fruit juice labels are pretty comprehensible. I learned this from user rumtscho's lovely post on this topic at cooking.stackexchange.com. The following is just a restatement of that post.
(I'm just writing this to help myself remember. YMMV.)
This Cambridge, MA Jeep's window presents a difficult case in bumper sticker analysis. What is the person like who would assemble such a collection?
Today I'll be analysing the song Autoclave, by The Mountain Goats, off their 2008 album Heretic Pride. You can see the lyrics I'll be referencing and listen to the song on Genius. Additionally, here's a video of John Darnielle performing the song live in front of a huge troll statue which I thoroughly recommend.
Drawn using MS Paint 3D, with the assistance and instruction of my friend Gaby Yeshua. Check out her Instagram for other lovely MS Paint 3D works!
The boy's like a banana in a hoodie.
Tall, but he spends his time lying curved on the couch,
playing Smash with tiny twitches,
or steadily typing
orderly paragraphs.
Sending Digital Information Over a Wire
One way to convey digital information across distances is through copper wire (Ethernet cable). Here we just vary the voltage in the wire between two states A and B. When we are at A, we are sending a 0, and when we are at B we are sending a 1.
What is voltage? Voltage is the delta between two points of an electrical field.
These states are called symbols.
Number of symbols / seconds is a unit called baud. If your symbol rate is 1 symbol per second, you are sending information at 1 baud.
(I'm just writing this to help myself remember. YMMV.)
Question: we can write down a general formula for the roots of a quadratic, cubic, or quartic polynomial in terms of the coefficients. Why can't we do it for a quintic polynomial?
Apparently this is a thing. Consider the function $f(x) = \frac{1}{1-x}$. Maybe you know that you can express $f(x)$ as an infinite polynomial:
$$\frac{1}{1 - x} = 1 + x + x^2 + x^3 + x^4 + ...$$
How easy is it to do a lot of good? Imagine that opportunities to improve the world were tangible and visible. Say they look like purple jelly beans. When you pick one up, bam! Someone's life is a little better.
In world A, jelly beans are plentiful. Maybe they rain down from the sky every week. Everywhere in the country, this is true. The sidewalks are covered in jelly beans. Everyone picks up a few just going to work every day.
The Feynman Lectures on Physics are calmly beautiful and I am reading them right now instead of going to bed, but what the hell is with this paragraph in the middle of chapter 3?
One of the most impressive discoveries was the origin of the energy of the stars, that makes them continue to burn. One of the men who discovered this was out with his girlfriend the night after he realized that nuclear reactions must be going on in the stars in order to make them shine. She said “Look at how pretty the stars shine!” He said “Yes, and right now I am the only man in the world who knows why they shine.” She merely laughed at him. She was not impressed with being out with the only man who, at that moment, knew why stars shine. Well, it is sad to be alone, but that is the way it is in this world.
Some subgroups of a group $G$ are normal, and some are not. It's not easy to get an intuition for what that means. A week or two after encountering the concept in my abstract algebra class, I knew the following:
The complex number $z = a + bi$ can be drawn. Plot the imaginary part on the $y$-axis, and the real part on the $x$-axis.
