https://reallyeli.comEli Rose's bloghttp://www.rssboard.org/rss-specificationenhttps://reallyeli.com/posts/i_dont_know_what_the_purpose_of_life_is_but_i_know_what_it_is_at_least<p>What is best in life?</p>Mon, 30 Nov 2020 00:00:00 UTChttps://reallyeli.com/posts/i_dont_know_what_the_purpose_of_life_is_but_i_know_what_it_is_at_leasthttps://reallyeli.com/posts/of_mice_and_means<p>The mean of a set of numbers $x_1, x_2 \ldots x_n$ is the unique value $\overline{x}$ which minimizes $\sum (\overline{x} - x_i)^2$, the sum of squared distances between it and the numbers. Why? The mean seems very natural — for example, it's related to intuitive ideas about fairness — but the sum of squares less so. For instance, what's so special about squaring? Why not the sum of fourth powers $\sum (\overline{x} - x_i)^4$ ? Or the sum of unsigned distances $\sum |\overline{x} - x_i|$ ?</p>Fri, 5 Jun 2020 00:00:00 UTChttps://reallyeli.com/posts/of_mice_and_meanshttps://reallyeli.com/posts/affine_spaces_in_ruby_on_rails<p>A great example of Ruby on Rails "magic" is this:</p>Thu, 7 May 2020 00:00:00 UTChttps://reallyeli.com/posts/affine_spaces_in_ruby_on_railshttps://reallyeli.com/posts/processed_by_the_boys<p><em>Processed By The Boys</em> by <a href="https://en.wikipedia.org/wiki/Protomartyr_(band)">Protomartyr</a> is a song about totalitarianism.</p>Sun, 26 Apr 2020 00:00:00 UTChttps://reallyeli.com/posts/processed_by_the_boyshttps://reallyeli.com/posts/the_derivative_of_a_matrix<p>Consider a matrix acting on a vector, $\mathbf{W}\mathbf{x}$. You can see this as function $f$ with type $\mathbb{R}^n \rightarrow \mathbb{R}^m$, where $\mathbf{W}$ is an $m \times n$ matrix, being applied to the vector $\mathbf{x}$. What is the derivative of $f$?</p>Tue, 21 Jan 2020 00:00:00 UTChttps://reallyeli.com/posts/the_derivative_of_a_matrixhttps://reallyeli.com/posts/total_derivative<p>The analogue of the derivative for functions whose inputs and outputs are vectors is called the <em>total derivative</em>. The total derivative of a function $f: \mathbb{R}^n \rightarrow \mathbb{R}^m$ is an object that gives you a function for each point in $\mathbb{R}^n$. In other words it is a function $\mathbb{R}^n \rightarrow \mathbb{R}^n \rightarrow \mathbb{R}^m$.</p>Mon, 20 Jan 2020 00:00:00 UTChttps://reallyeli.com/posts/total_derivativehttps://reallyeli.com/posts/formalizing_mesa_optimizers<p><em>[This post is likely only to be of interest to you if you've read the paper under discussion.]</em></p>Fri, 3 Jan 2020 00:00:00 UTChttps://reallyeli.com/posts/formalizing_mesa_optimizershttps://reallyeli.com/posts/why_do_less_dense_things_rise<p>Why do less dense things rise? Recently I was asked this as a puzzle. I had always taken it as a basic truth, but we should be able to explain it in terms of forces.</p>Tue, 17 Dec 2019 00:00:00 UTChttps://reallyeli.com/posts/why_do_less_dense_things_risehttps://reallyeli.com/posts/times_alignment_chart<p>Conceived on a long hike with Lucy.</p>Tue, 26 Nov 2019 00:00:00 UTChttps://reallyeli.com/posts/times_alignment_charthttps://reallyeli.com/posts/sapphire_alone<p>still knows fire. It's the stilling flame,</p>Tue, 26 Nov 2019 00:00:00 UTChttps://reallyeli.com/posts/sapphire_alonehttps://reallyeli.com/posts/poisoned_wine<p>This is a brain teaser I came across recently (<a href="http://thinkingcomplete.blogspot.com/2018/09/a-compendium-of-conundrums.html">original source</a>):</p>Mon, 28 Oct 2019 00:00:00 UTChttps://reallyeli.com/posts/poisoned_winehttps://reallyeli.com/posts/sierpinskis_triangle_and_fermat_numbers<p>I made a <a href="https://reallyeli.com/sierpinski_fermat">demo</a> of a cool math thing.</p>Thu, 24 Oct 2019 00:00:00 UTChttps://reallyeli.com/posts/sierpinskis_triangle_and_fermat_numbershttps://reallyeli.com/posts/the_competent_authorities<p>When I was a kid, I remember hearing about the various damages of the world. War, corruption, the mismanagement of countries, families starving below the poverty line. Like a lot of kids, I was disturbed at this news and concocted various kid schemes to make everything better. I designed a utopia in fifth grade where everything was solar-powered, so the environment wouldn't get damaged. (I really wanted blaster guns, so I also made solar-powered blaster guns. But I remembered that it was supposed to be a utopia without war. I compromised by deciding the blasters were used only for mining.)</p>Wed, 16 Oct 2019 00:00:00 UTChttps://reallyeli.com/posts/the_competent_authoritieshttps://reallyeli.com/posts/irrationality_of_sqrt_3<p>Lucy and I found this proof last night. I'm sure it is not new, but hadn't seen it before.</p>Tue, 8 Oct 2019 00:00:00 UTChttps://reallyeli.com/posts/irrationality_of_sqrt_3https://reallyeli.com/posts/undone<img style="width: 100%;" src="https://reallyeli.com/static/images/undone_screenshot.jpg">Thu, 3 Oct 2019 00:00:00 UTChttps://reallyeli.com/posts/undonehttps://reallyeli.com/posts/thor_ragnarok<p>I saw <em>Thor: Ragnarok</em> recently. It's trying to be an imaginative, comedic sci-fi adventure movie with a touch of soul, and it pretty much is. However, it seemed to me and my friend that we could strictly improve the movie with some small tweaks. (That is, these tweaks would have done better something the movie was trying to do already, without affecting much else.)</p>Mon, 23 Sep 2019 00:00:00 UTChttps://reallyeli.com/posts/thor_ragnarokhttps://reallyeli.com/posts/1_plus_1_equals_13<p>Today I'll be analyzing the song <em>1+1=13</em> by <a href="https://en.wikipedia.org/wiki/Aesop_Rock">Aesop Rock</a>.</p>Sun, 15 Sep 2019 00:00:00 UTChttps://reallyeli.com/posts/1_plus_1_equals_13https://reallyeli.com/posts/coriolis_effect<p>I know the Coriolis Effect from 9th-grade earth science as what causes hurricanes to spin; counterclockwise in the northern hemisphere, and clockwise in the southern. The idea is this: imagine teleporting a section of air from the Equator to the North Pole. An exceptionally violent wind would result, because the rotation of the earth means that air around the equator is moving at ~ 1000 miles/hour, while air around the North Pole is hardly moving at all.</p>Tue, 3 Sep 2019 00:00:00 UTChttps://reallyeli.com/posts/coriolis_effecthttps://reallyeli.com/posts/explicitly_include_gather_more_information_in_your_expected_value_calculations<p><em>[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.]</em></p>Thu, 15 Aug 2019 00:00:00 UTChttps://reallyeli.com/posts/explicitly_include_gather_more_information_in_your_expected_value_calculationshttps://reallyeli.com/posts/dont_say_what_is_the_probability<p><em>(This post essentially agrees with <a href="https://www.lesswrong.com/posts/f6ZLxEWaankRZ2Crv/probability-is-in-the-mind">Probability Is In The Mind</a>. It differs in emphasis and style.)</em></p>Sat, 10 Aug 2019 00:00:00 UTChttps://reallyeli.com/posts/dont_say_what_is_the_probabilityhttps://reallyeli.com/posts/a_car_a_torch_a_death_song_analysis<p>Today I'll be analyzing the song <em>A Car, A Torch, A Death</em> by <a href="https://en.wikipedia.org/wiki/Twenty_One_Pilots">Twenty-One Pilots</a>, from their 2009 self-titled album.</p>Sun, 4 Aug 2019 00:00:00 UTChttps://reallyeli.com/posts/a_car_a_torch_a_death_song_analysishttps://reallyeli.com/posts/tentative_maxim<p>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".</p>Tue, 16 Jul 2019 00:00:00 UTChttps://reallyeli.com/posts/tentative_maximhttps://reallyeli.com/posts/math_problem_liveblogging_1<p><em>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."</em></p>Tue, 2 Jul 2019 00:00:00 UTChttps://reallyeli.com/posts/math_problem_liveblogging_1https://reallyeli.com/posts/rules_within_consequentialism<p><em>[Epistemic status: working out a course of action for myself, based on somewhat commonsensical observations.]</em></p>Mon, 27 May 2019 00:00:00 UTChttps://reallyeli.com/posts/rules_within_consequentialismhttps://reallyeli.com/posts/inferior_in_wisdom_superior_in_force<p>From the warm and noisy dark I watch,</p>Sun, 19 May 2019 00:00:00 UTChttps://reallyeli.com/posts/inferior_in_wisdom_superior_in_forcehttps://reallyeli.com/posts/2019<p>In 2019 I could descend my porch steps</p>Sun, 14 Apr 2019 00:00:00 UTChttps://reallyeli.com/posts/2019https://reallyeli.com/posts/car_accident<p>I saw a biker get hit a little</p>Fri, 29 Mar 2019 00:00:00 UTChttps://reallyeli.com/posts/car_accidenthttps://reallyeli.com/posts/bug_collector_song_analysis<p>Today I'll be analyzing the song <em>The Bug Collector</em> by <a href="https://haleyheynderickx.bandcamp.com/">Haley Heynderickx</a>, from her 2018 album <em>I Need To Start A Garden</em>.</p>Sun, 24 Feb 2019 00:00:00 UTChttps://reallyeli.com/posts/bug_collector_song_analysishttps://reallyeli.com/posts/undefined_and_null<p>Most programming languages have a way to represent "no value" or "nothing". Python has <code>None</code>, Ruby has <code>nil</code>, Java and friends have <code>null</code>. Javascript has <em>two</em> ways to represent this concept -- <code>undefined</code> and <code>null</code>.</p>Sat, 2 Feb 2019 00:00:00 UTChttps://reallyeli.com/posts/undefined_and_nullhttps://reallyeli.com/posts/what_does_100_percent_juice_mean<p>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.</p>Sun, 20 Jan 2019 00:00:00 UTChttps://reallyeli.com/posts/what_does_100_percent_juice_meanhttps://reallyeli.com/posts/bells_theorem<p>(I'm just writing this to help myself remember. YMMV.)</p>Sun, 13 Jan 2019 00:00:00 UTChttps://reallyeli.com/posts/bells_theoremhttps://reallyeli.com/posts/bumper_stickers<img src="https://reallyeli.com/static/images/jeep_window.jpg" style="width: 100%;">Sun, 6 Jan 2019 00:00:00 UTChttps://reallyeli.com/posts/bumper_stickershttps://reallyeli.com/posts/autoclave<p>Today I'll be analysing the song <em>Autoclave</em>, by <a href="https://en.wikipedia.org/wiki/The_Mountain_Goats">The Mountain Goats</a>, off their 2008 album <em>Heretic Pride</em>. You can see the lyrics I'll be referencing and listen to the song on <a href="https://genius.com/The-mountain-goats-autoclave-lyrics">Genius</a>. Additionally, here's a video of <a href="https://www.youtube.com/watch?v=RZ-2kbculaI">John Darnielle performing the song live in front of a huge troll statue</a> which I thoroughly recommend.</p>Tue, 1 Jan 2019 00:00:00 UTChttps://reallyeli.com/posts/autoclavehttps://reallyeli.com/posts/worms<img class="centered" width="100%" src="https://reallyeli.com/static/images/worms.png">Sat, 29 Dec 2018 00:00:00 UTChttps://reallyeli.com/posts/wormshttps://reallyeli.com/posts/boy<p>The boy's like a banana in a hoodie.</p>Sat, 29 Dec 2018 00:00:00 UTChttps://reallyeli.com/posts/boyhttps://reallyeli.com/posts/learning_networking<p><strong><a href="https://www.youtube.com/watch?v=XaGXPObx2Gs">Sending Digital Information Over a Wire</a></strong></p>Sat, 13 Jan 2018 00:00:00 UTChttps://reallyeli.com/posts/learning_networkinghttps://reallyeli.com/posts/galois_theory_nutshell<p><em>[Epistemic Status: I'm just writing this to help myself remember. YMMV.]</em></p>Sat, 30 Sep 2017 00:00:00 UTChttps://reallyeli.com/posts/galois_theory_nutshellhttps://reallyeli.com/posts/laurent_series<p>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:</p>Mon, 5 Sep 2016 00:00:00 UTChttps://reallyeli.com/posts/laurent_serieshttps://reallyeli.com/posts/what_is_the_world_like<p>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.</p>Tue, 16 Aug 2016 00:00:00 UTChttps://reallyeli.com/posts/what_is_the_world_likehttps://reallyeli.com/posts/bitter_richard_feynman<p>The <a href="http://www.feynmanlectures.caltech.edu/">Feynman Lectures on Physics</a> 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 <a href="http://www.feynmanlectures.caltech.edu/I_03.html">chapter 3</a>?</p>Mon, 11 Apr 2016 00:00:00 UTChttps://reallyeli.com/posts/bitter_richard_feynmanhttps://reallyeli.com/posts/normal_subgroups_hold_things_constant<p>Some subgroups of a group $G$ are <a href="https://en.wikipedia.org/wiki/Normal_subgroup">normal</a>, 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:</p>Thu, 31 Mar 2016 00:00:00 UTChttps://reallyeli.com/posts/normal_subgroups_hold_things_constanthttps://reallyeli.com/posts/multiplying_complex_numbers<p>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.</p>Thu, 10 Mar 2016 00:00:00 UTChttps://reallyeli.com/posts/multiplying_complex_numbers