{"version": "https://jsonfeed.org/version/1", "title": "BiteofanApple", "home_page_url": "https://brianschrader.com", "feed_url": "https://brianschrader.com/feed.json", "description": "Thoughts, and ramblings about technology, programming, history,\n and whatever else I'm interested in.", "icon": "https://www.gravatar.com/avatar/11b074a636e00292c98e3e60f7e16595", "author": {"name": "Brian Schrader", "url": "https://brianschrader.com", "avatar": "https://www.gravatar.com/avatar/11b074a636e00292c98e3e60f7e16595"}, "items": [{"id": "https://brianschrader.com/archive/gatekeepers-are-dead-long-live-the-gatekeepers/", "url": "https://brianschrader.com/archive/gatekeepers-are-dead-long-live-the-gatekeepers/", "title": "Gatekeepers are Dead, Long Live the Gatekeepers", "date_published": "2026-08-24T16:09:00", "tags": ["essay", "internet", "ai", "social media"], "author": {"name": "Brian Schrader"}, "content_html": "<p>Before the Internet things were different; this was the First Age.</p>\n<p>If you wanted to get your message out there you needed either a lot of money, fame, or power. Usually you needed some combination of all three. Barring that you needed to find someone with money, fame, or power (or some combination) who was also willing to help you. These people were often elites of some kind. They could be professionals with an industry journal, the editor of a local magazine, a rich patron with connections, or even political party officials. These were the people who held the keys needed to pass into the public sphere: gatekeepers. Their job was to search out people of interest, people with something interesting to say, and promote them. Musicians needed talent scouts, authors needed agents, writers needed editors.</p>\n<div class=\"image-right\" style=\"width: 350px;\">\n  <a href=\"https://archive.org/details/sim_saturday-magazine_1836-03_8_240/mode/2up\">\n    <img style=\"max-width: 100%;\" src=\"/images/blog/some-account-of-bridges.jpg\">\n  </a>\n  <center><small style=\"display: block;\">\n    Guarding the entrance to the bridge.<br>\n    The Saturday Magazine, 1836&ndash;03: Vol 8 Iss 240\n  </small></center>\n</div>\n\n<p>Attention was infinite and quality content was scarce. Gatekeepers filtered through the trash and surfaced the gems. The public paid attention because that was all that could be done.</p>\n<p>The Internet broke this system; we entered the Second Age.</p>\n<p>Self-published books made it so anyone can get their book out there. Self-service distributors allow anyone to publish music, YouTubers to self manage, and blogs (and more importantly social media) give anyone a platform to speak. This system didn't replace the gatekeepers (traditional publishing and record labels still exist) but it broke open the floodgates. A lot of this new content was bad but some of it was amazing.</p>\n<p>Attention became the currency of the land, a finite resource sure but one similar to oil: plentiful enough to build entire industries on. Tools existed to help filter it all. They became our gatekeepers: the feeds, then the algorithms. At first it was easy to find good, new content. Over time that got harder, but the system seemed to be stabilizing.</p>\n<p><div class=\"midroll newsletter-callout\">\n  <div class=\"callout text-center\">\n    <div id=\"prompt\">\n      <noscript>\n        Enjoying this post?\n      </noscript>\n    </div>\n    <a\n      href=\"https://sendfox.com/brianschrader/\"\n      title=\"Subscribe to the newsletter\"\n      class=\"subscribe\"\n      target=\"_blank\"\n    >\n      ✉️&nbsp;Subscribe to the Newsletter!\n    </a>\n  </div>\n</div>\n<script>\n(() => {\n  const prompts = [\n    'Enjoying this post?',\n    'Like what you see?',\n    'Cough cough...',\n    'Posts like this, in your inbox!',\n    'Consider subscribing!',\n    'Support this blog!',\n    'Really appreciate it if you...'\n  ];\n  const el = document.getElementById('prompt');\n  el.textContent = prompts[Math.floor(Math.random(0) * prompts.length)];\n})();\n</script></p>\n<p>Large Language Models broke this system; we are now in the Third Age.</p>\n<p>Now the Web is flooded with text, images, video, and audio not made by any human. <a href=\"https://travel.yahoo.com/guides/italy/articles/italy-travel-guide-arrives-infuriating-123029797.html\">Books exist</a> now which no human (including its supposed author) has ever read. We have reached a breaking point. Where before there was always at least one person who'd seen every piece of content, now it seems likely most content will never be read except by the unsuspecting fool who mistakes it for real work.</p>\n<div class=\"image-right\" style=\"width: 330px;\">\n  <a href=\"https://archive.org/details/sim_saturday-magazine_1834-08-23_5_137/mode/2up\">\n    <img style=\"max-width: 100%;\" src=\"/images/blog/castles.jpg\">\n  </a>\n  <center><small style=\"display: block;\">\n    Will we build castles to save us?<br>\n    The Saturday Magazine, 1834&ndash;08-23: Vol 5 Iss 137\n  </small></center>\n</div>\n\n<p>Yet in this new age, where attention is a scarce resource compared with the glut of content to consume it, we have found ourselves bereft of those who can wade through the cruft and the noise and surface real wisdom. The legacy gatekeepers exist still, but they guard their own hoards. The feeds exist but few resort to them. Algorithms are still king, but will they be able to keep up with this barrage of meaninglessness?</p>\n<p>We humans want to be distracted, to be entertained. That is what modern social media does for us. Yet people seek meaning too, and wisdom. In the prior age (and still somewhat today) that wisdom lies hidden in the muck, surfaced by legacy gatekeepers and by algorithmic feeds. I only wonder if this dam will hold.</p>\n<p>For centuries, the Romans kept their enemies at bay. Cities that once needed walls abandoned them. The inner lands were safe. Then the institutions failed. Enemy armies roamed the heartland and nowhere was safe. The walls returned.</p>\n<p>Speaking for myself these days I seek brand name goods on Amazon where I can. I find myself scrutinizing labels and FCC approval stickers. I buy what WireCutter recommends because at least I know that the product actually exists and has seen human hands. I prefer books published by Penguin/Random House or others of the Old Guard. I discover YouTubers via recommendation from those I already trust and treat algorithmic recommendations as inherently suspect. In short: I seek gatekeepers, not to surface diamonds in the rough, but to hold back the oncoming tide.</p>\n<p>Am I alone in this?</p>"}, {"id": "https://brianschrader.com/archive/with-flying-pen-when-mortals-sleep/", "url": "https://brianschrader.com/archive/with-flying-pen-when-mortals-sleep/", "title": "With Flying Pen, When Mortals Sleep", "date_published": "2026-08-10T16:45:00", "tags": ["history", "alchemy", "essay"], "author": {"name": "Brian Schrader"}, "content_html": "<p>It was a sweltering August day. I made my way across the promenade, and through the bustling crowd, to a small line forming outside the Timkin Art Museum. Inside, I stumbled on <a href=\"https://en.wikipedia.org/wiki/Parable_of_the_Sower_(Bruegel)\">Pieter Bruegel</a> the Elder's <em>Parable of the Sower</em>, painted in 1557, nearly five centuries ago.</p>\n<div class=\"image-right\" style=\"width: 350px;\">\n  <img src=\"/images/blog/Pieter_Bruegel_Parable-of-the-Sower.webp\" style=\"max-width: 100%;\">\n  <center><small style=\"line-height: 1.2; margin-top: 4px; display: block;\">Photo: The Yorck Project (2002) <br>10.000 Meisterwerke der Malerei </small></center>\n</div>\n\n<p>When Bruegel took his brush to this canvas, the New World had just been found by Europeans, and the United States was still long into the future. Around me then were all those people, those wandering souls, who across those centuries stood before this same piece and idly mused at a thing made by the hands of a long-dead Flemish man.</p>\n<p>I thought about <em>him</em>. Not Bruegel&mdash;another man&mdash;one whom I've come to know these past few years. He does not know of me, yet we both could have seen this very painting. We were connected through the mists of time by this canvas portal to the past.</p>\n<p>It was October 10th, 2023 at about ten in the evening. I was crawling down a research rabbit hole, as I am wont to do. I wanted to know more about the history of alchemy. I knew the stereotypes, the modern myths, but I wanted to know what <em>real</em> alchemists were doing in their labs.</p>\n<p><div class=\"midroll newsletter-callout\">\n  <div class=\"callout text-center\">\n    <div id=\"prompt\">\n      <noscript>\n        Enjoying this post?\n      </noscript>\n    </div>\n    <a\n      href=\"https://sendfox.com/brianschrader/\"\n      title=\"Subscribe to the newsletter\"\n      class=\"subscribe\"\n      target=\"_blank\"\n    >\n      ✉️&nbsp;Subscribe to the Newsletter!\n    </a>\n  </div>\n</div>\n<script>\n(() => {\n  const prompts = [\n    'Enjoying this post?',\n    'Like what you see?',\n    'Cough cough...',\n    'Posts like this, in your inbox!',\n    'Consider subscribing!',\n    'Support this blog!',\n    'Really appreciate it if you...'\n  ];\n  const el = document.getElementById('prompt');\n  el.textContent = prompts[Math.floor(Math.random(0) * prompts.length)];\n})();\n</script></p>\n<div class=\"image-right\" style=\"width: 300px;\">\n  <img src=\"/images/blog/alchemy/book-stack.jpg\" style=\"max-width: 100%;\">\n  <center><small>Photo: mine</small></center>\n</div>\n\n<p><a href=\"https://bookshop.org/p/books/the-secrets-of-alchemy-lawrence-m-principe/3453\"><em>The Secrets of Alchemy</em></a> by Dr. Lawrence Principe purported to answer this exact question and so I tore through that wondrous book, my face lit by screenglow. When I finished it, I dove into the footnote trail, seeking answers to further questions.</p>\n<p>I've pored through a great number of books in the intervening years, and written a <a href=\"/archive/science-models-and-squeaking-lead/\">fair</a> <a href=\"/archive/an-age-of-promethean-ambitions/\">number</a> of different <a href=\"/archive/nothing-throughout-the-ages/\">blog</a> <a href=\"/archive/chemical-telescopes-and-the-process-of-science/\">posts</a> on the subjects I discovered there. I met an array of different names: Ripley, Helmont, and Lull, different characters whose stories intermingled and wove a grand tale between the centuries on worn and precious parchment.</p>\n<p>Did you know that the seventeenth century was the heyday for alchemy in Europe? Or that Isaac Newton was an alchemist. So was John Locke, in a way. The two were part of a circle of scientists, alchemists, doctors, and philosophers who would go on to found the <a href=\"https://royalsociety.org\">Royal Society of London</a>. So many famous names in history were there, bound up in the story of alchemy and its rise and fall from grace.</p>\n<p>London in particular was a hotbed of alchemical interest at the time, as Germany had been in the decades before. All of Europe was abuzz with it. Yet, in all my reading, had there been no mention of the New World?</p>\n<blockquote>\n<p>What about <em>American</em> Alchemists? Was there such a thing?</p>\n</blockquote>\n<div class=\"image-right\" style=\"width: 300px;\">\n  <img src=\"/images/blog/alchemy/starkeys-pill.webp\" style=\"max-width: 100%;\">\n  <center><small style=\"line-height: 1.2; margin-top: 4px; display: block;\">Library of Congress, Rare Book Room.<br>Photo: mine</small></center>\n</div>\n\n<p>That question would lead me right to him and to the realization that we'd already met. I'd forgotten his name, but Principe had introduced us and his colleague, Dr. William Newman, had penned the man's biography: George Starkey, a name that I will never forget again.</p>\n<p>Born in Bermuda and educated as a doctor at Harvard, George Starkey became interested in alchemy early in life and so moved to London in his twenties to practice medicine and alchemy with England's best. At the time, alchemy, which was more akin to pharmacology today, was all the rage among the eager classes. Science was blossoming and so much was open to discovery.</p>\n<p>It was with this understanding that Starkey came into the circle of Robert Boyle, John Locke, and Isaac Newton. Like Newton, Starkey is a rare breed among alchemists and among historical figures in general. You see, we have his personal notebooks, and so in addition to deciphering his published works, we get a glimpse behind the curtain into the sort of man he really was. Dr. Principe worked to translate those scribbled writings from their original Latin into English and in them we find a man working to untangle the mysteries of the universe, to puzzle out its causes and effects.</p>\n<div class=\"image-right\" style=\"width: 300px;\">\n  <img src=\"/images/blog/alchemy/philathelies.webp\" style=\"max-width: 100%;\">\n  <center><small style=\"line-height: 1.2; margin-top: 4px; display: block;\">Starkey's Pseudonym. Library of Congress, Rare Book Room. Photo: mine</small></center>\n</div>\n\n<p>At the dawn of the modern age, Starkey and his cabal of conspirators wrote to each other as they quested to remake human knowledge. Starkey spent most of his free time beside his furnace, distilling various substances and trying to piece together the makeup of creation. He calculated mass lost to volatile vapors, discovered all manner of variously useful materials, and kept diligent notes that revealed  a rather stubborn and quizzical nature. In a curious twist on the traditional method: rather than debate the nature of matter in the cloistered halls of the colleges, Starkey brought his inquiries directly to Nature herself,  occasionally asking questions only to be <q>refuted by the fire</q>.</p>\n<p>Aside from his successes making <a href=\"https://en.wikipedia.org/wiki/Salammoniac\">ice powder</a> and specialist oils, Starkey described a new kind of \"Philosophical Mercury\" which he claims will lead him to his ultimate goal of making the Liquor Alkahest, a precursor to the philosopher's stone. He struggles with his work and his increasingly meager finances for years until on one page he writes:</p>\n<blockquote>\n<p>Εύρηκα!</p>\n</blockquote>\n<p>I remember reading that word, strangely Greek instead of Latin, in a coffeeshop one night. Mathematics taught me a few Greek letters and so I sounded out the word, knowing vaguely how the letters sound like their names. <em>Eureka</em>!</p>\n<div class=\"image-right\" style=\"width: 300px;\">\n  <img src=\"/images/blog/alchemy/my-notes.jpeg\" style=\"max-width: 100%;\">\n  <center><small>Photo: mine</small></center>\n</div>\n\n<p>On the next page we see a letter to his friend, Robert Boyle, recounting this discovery.</p>\n<blockquote>\n<p>Now, to show you honor, [my friend] that I am an Englishman I will add a disaster.</p>\n</blockquote>\n<p>Unfortunately, Starkey lost the results of this experiment, as the glassware flask that contained it broke and spilt its precious liquor into the coals. Reading this, I deflated in my chair right alongside him. His accounting of his life and his work  is a baffling ride of success, of trial and error. It's all so very human.</p>\n<p>On one page, Starkey wrote a set of prayers to God, and beside them a note to his future self: a plea, a reminder, to never drink so much wine at the tavern again.</p>\n<blockquote>\n<p>[I swear,] I shall not game at any tavern for more than half a pint of wine at most nor be in the company of any gamester nor at play with any when I do play that I know to be a swearer or a vain person nor to stand by while they do play.</p>\n</blockquote>\n<p>He notes later that he broke this promise.</p>\n<div class=\"image-right\" style=\"width: 280px;\">\n  <img src=\"/images/blog/alchemy/starey-note-principe.webp\" style=\"max-width: 100%;\">\n  <center><small style=\"line-height: 1.2; margin-top: 4px; display: block;\">A page of Starkey's notes, via Principe.<br/>Photo: mine</small></center>\n</div>\n\n<p>It was through these pages, through the myriad descriptions of boiling and distilling this or that poisonous substance, through all the triumph and the failure, that I got to know Mr. Starkey not as a historical figure but as a man, a curious, insightful, and flawed man trying to understand the world.</p>\n<p>Many of Starkey's letters to Robert Boyle survive. The two were friends and, for a time, Boyle was Starkey's student and patient. It was there, amid the pages of a particular letter to Boyle, that I was again captured and enthralled. In it, Starkey provides an update to his patron on the status of his experiments. Here was a man trying against the odds to follow in the footsteps of the Adepts in the same way all modern chemists follow in his.</p>\n<p>It's in this letter that Starkey describes what would be, for him, a typical method of experiment.</p>\n<blockquote>\n<p>While I was distilling, I took a drop to taste and in an instant it penetrated my tongue and at once made it bloody; and when by chance during its rectification I moved the candle nearby so that I might see whether any vapor was exhaling, the very light vapor took fire and burned with a truly stupendous spectacle.</p>\n</blockquote>\n<p>Yet this experiment did more than burn his tongue and likely singe his eyebrows. Starkey truly believed that he was onto something momentous, although like many great discoveries, this one was accidental.</p>\n<blockquote>\n<p>So when I wanted to determine whether it was combustible in a spoon, I poured out the first few drops falling [into the receiver] (because they contained some impurity that adhered to the neck of the retort) but being called by someone, I left the laboratory, since I did not want anyone to visit me there...</p>\n<p>I left [the matter in] the spoon, and... left it alone until morning, by which time the liquor had exhaled, leaving behind a few drops of the greatest sweetness <em>and greenness</em> which evaporated when exposed to a moderate fire.</p>\n<p>Good God, how I was filled with joy!</p>\n</blockquote>\n<p>For me, the best part comes at the end. In a post-script, Starkey inquires about his friend's recent spat of bad health, but before that he closes with the following words. I've left the Latin in place this time because it's just as beautiful as the English translation.</p>\n<blockquote>\n<p>Dederam volitanti Calamo altâ nocte quâ horâ plerique mortales\ndormire absolent prope Athanar meum.<br>\nTuis studiosissimus, Georgius Stirke<br>\n♀ is Jan. ut puto 26, 1651</p>\n<hr />\n<p><small>[My friend], I give to you my flying pen in the depth of night, when most mortals are wont to sleep, at my furnace.</small><br>\n<small>Yours studiously, George Starkey</small><br>\n<small>Friday, I think, January 26th, 1651</small>*</p>\n</blockquote>\n<p>It was in that moment, reading those words, that I had a new quest. I needed to see this letter. Not a translation on a page, but the real thing.  There were no pictures of it in Principe's book, and so, armed with the manuscript number, I hurried to the Royal Society website, only to find that neither Starkey's notebooks nor this particular letter had been digitized. If I wanted to see them, I'd have to either go to London myself or work with the archivists to get them photographed.</p>\n<p>One day I hope to visit the archives, but for now the latter would have to do.</p>\n<p>I still visit the Timkin Museum, and the larger San Diego Art Museum right beside it, whenever I get the chance. When I do, I seek out works, like that of Mr. Bruegel, works old enough that it's possible Mr. Starkey would have seen them. We have no record that he ever did, of course, but to me that isn't really the point. What I feel, staring into those brush strokes is the same as when I read the pages of Starkey's letter: connection, with a history and with a man I've come to know.</p>\n<p>One of the goals of the alchemists was transmutation, of base metals into gold. Another was eternal life. No one lives forever, but we all die two deaths: the first of the body, and the second when your name is said for the last time. Starkey never achieved the former, but the latter is within our power.</p>\n<p>Thank you George Starkey. You have given me so much these past few years, and for that I am honored and so, here and now, I give to you my flying pen.</p>\n<div class=\"footnote\">\n<hr>\n<p>My thanks to Dr. Principe, Dr. Newman, and all the other authors I have read on this subject in recent years. It was you all who inspired me to dig deeper and eventually to inquire at the Royal Society. Thank you to the Royal Society, and to the hardworking archivists there who worked to preserve and image these letters, and to let me share them with the world.</p>\n<hr>\n</div>\n\n<div style=\"flex: 1; text-align: center; color: #333; line-height: 1.3;\">\n  <small>Starkey's Letter To Boyle January 26 1651/2.\nManuscript RB/3/5/70. Copyright: The Royal Society Of London</small>\n</div>\n<div style=\"display: flex; gap: 0.05rem; justify-content: space-between; overflow-x: scroll; background: #000; padding: 5px; border-radius: 3px;\">\n  <img src=\"/images/collections/starkey/starkey-pg-1.jpg\" style=\"flex: 1; max-width: 300px;\">\n  <img src=\"/images/collections/starkey/starkey-pg-2.jpg\" style=\"flex: 1; max-width: 300px;\">\n  <img src=\"/images/collections/starkey/starkey-pg-3.jpg\" style=\"flex: 1; max-width: 300px;\">\n  <img src=\"/images/collections/starkey/starkey-pg-cover.jpg\" style=\"flex: 1; max-width: 300px;\">\n</div>\n<div style=\"display: flex; flex-wrap: wrap; gap-0.05rem; justify-content:space-between\">\n  <div style=\"flex: 1;\" class=\"hide-on-mobile\">\n    &nbsp;\n  </div>\n  <div style=\"flex: 1; text-align: center; color: #999;\">\n    <small>← scroll to see more →</small>\n  </div>\n  <div style=\"flex: 1; text-align:right;\" class=\"hide-on-mobile\">\n    <a href=\"/other-projects/protected-gallery/starkey/\">\n      Full-size image gallery &#8594;\n    </a>\n  </div>\n</div>\n<div style=\"text-align: center;\">\n  <a href=\"/other-projects/protected-gallery/starkey/\" class=\"show-on-mobile\" >\n    Full-size image gallery &#8594;\n  </a>\n</div>\n\n<div class=\"footnote\">\nQuotes from: Alchemical Laboratory Notebooks and Correspondence. P 49, 71, 72, 124<br/>\n* This translation is my own.<br/>\n</div>"}, {"id": "https://brianschrader.com/archive/what-is-potential-energy-really/", "url": "https://brianschrader.com/archive/what-is-potential-energy-really/", "title": "What is Potential Energy, Really?", "date_published": "2026-07-27T16:23:00", "tags": ["math", "physics"], "author": {"name": "Brian Schrader"}, "content_html": "<p>As with seemingly every other man my age, I've taken up running to stay fit. Your metabolism slows as you age and what used to come for free with youth now takes time and deliberate effort to maintain. I don't care for the running, but it needs to be done.</p>\n<p>The thing is: it does give me lots of idle time to think, just like a long walk. Both have become for me a form of meditation, a way to de-stress and to mull over complex ideas. I find that I think better when I'm moving, regardless of precisely how. Yet, near the end of every run my thoughts inevitably return to the same idea:</p>\n<blockquote>\n<p>When will this be over? I want to be done.</p>\n</blockquote>\n<p>Of course I want to complete my run, to go the distance I set for myself, but I also want, very badly, to do it in the most efficient way possible.</p>\n<h2>The Optimal Route</h2>\n<p>To end where you started, any route must go south for just as long as it goes north and the same goes for east and west. If you know it's three blocks west to get home and two blocks north then, because you're confined to the city grid, it doesn't matter what order you take those steps in. It's a quirk of city blocks that there are <em>multiple</em> shortest paths, but we'll come to that.<sup>1</sup></p>\n<div class=\"image-center\">\n  <img src=\"/images/blog/city-block.jpg\" alt=\"\" style=\"padding: 0; max-width: 100%; border-radius: 5px;\">\n  <div style=\"display: flex; justify-content: center; gap: 4rem; flex-wrap: wrap; padding: 1rem;\">\n    <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mi>E</mi><mn>1</mn></msub><mo>=</mo><mn>2</mn><mi>U</mi><mo>+</mo><mn>3</mn><mi>L</mi></mrow></math>\n    <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mi>E</mi><mn>2</mn></msub><mo>=</mo><mn>2</mn><mi>U</mi><mo>+</mo><mn>3</mn><mi>L</mi></mrow></math>\n    <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mi>E</mi><mn>3</mn></msub><mo>=</mo><mn>3</mn><mi>U</mi><mo>+</mo><mn>3</mn><mi>L</mi><mo>+</mo><mn>1</mn><mi>D</mi></mrow></math>\n  </div>\n  <center><small>Paths (1) and (2) take different routes but have the same total \"effort\" required to complete them and cover the same amount of total distance. It's only path (3) that differs. Why?</small></center>\n</div>\n\n<p>If you find that you need to add distance to your run as you go then you'll have to deviate from these ideal paths. To do that you need to use energy, more so than you would need to accomplish the ideal route. Of course you need energy to move your body in general but so long as we assume that you always intend to <em>eventually</em> go back home, and that your speed is constant, the energy to go from here to there is fixed by your current position along the ideal path, and thus already accounted for. The energy required to traverse that path can't change because that would require the path to get longer, and that means it wouldn't be the ideal path anymore. Thus, what can change is the amount of energy you use to get home <em>beyond</em> that fixed amount.</p>\n<math style=\"text-align: center; display: block;\"  xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mi>E</mi><mrow><mi>t</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>l</mi></mrow></msub><mo>=</mo><msub><mi>E</mi><mrow><mi>i</mi><mi>d</mi><mi>e</mi><mi>a</mi><mi>l</mi></mrow></msub><mo>+</mo><msub><mi>E</mi><mrow><mi>a</mi><mi>d</mi><mi>d</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mrow></msub></mrow></math>\n\n<p>We can arrive at a formal definition by renaming a few things. If we call the shortest, ideal route a <em>geodesic</em>, then this added energy is defined as whatever energy is required to deviate from a geodesic. We call this \"potential energy\" (V). If we rename the energy required to move along the geodesic the \"kinetic energy\" (T) then what we have is the familiar equation from elementary physics.<sup>2</sup></p>\n<math style=\"text-align: center; display: block;\"  xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>E</mi><mo>=</mo><mi>T</mi><mo>+</mo><mi>V</mi></mrow></math>\n\n<p>Crucially this potential energy is only expended to deviate from the ideal path, not to relax back toward it&mdash;that's just the process of following the new shortest path. In the (1)/(3) split in our diagram above, the energy is expended along the path of the green arrow. From there the path back is fully determined. One consequence of this is that, in our example, added blocks always come in pairs. Whatever additional city blocks you traverse away from your destination must eventually be retraced if you are to get home.</p>\n<p>Now these are not the typical definitions of these terms that you find in elementary physics, because in that context, kinetic energy is the energy of motion. Here we've discussed it as simply the energy required to reach a given destination. However these are two sides of the same coin. Throwing a ball from A to B causes the ball to move. If we don't know where the ball will land (i.e. we don't know the value of B), then we can define the kinetic energy to be the energy of motion and use that to compute the value of B. If we know the values of A and B already, then the kinetic energy is just the energy required to reach B from A. These are the same argument given two different framings.</p>\n<div class=\"image-center\">\n  <img src=\"/images/blog/ball-trajectory.jpg\" alt=\"\" style=\"padding: 0; max-width: 100%; border-radius: 5px;\">\n  <center><small>Keep in mind it doesn't matter that a real ball won't <q>end</q> its journey mid-air, but it doesn't end it's journey when it hits the ground either. It's still riding on the moving Earth.</small></center>\n</div>\n\n<p><div class=\"midroll newsletter-callout\">\n  <div class=\"callout text-center\">\n    <div id=\"prompt\">\n      <noscript>\n        Enjoying this post?\n      </noscript>\n    </div>\n    <a\n      href=\"https://sendfox.com/brianschrader/\"\n      title=\"Subscribe to the newsletter\"\n      class=\"subscribe\"\n      target=\"_blank\"\n    >\n      ✉️&nbsp;Subscribe to the Newsletter!\n    </a>\n  </div>\n</div>\n<script>\n(() => {\n  const prompts = [\n    'Enjoying this post?',\n    'Like what you see?',\n    'Cough cough...',\n    'Posts like this, in your inbox!',\n    'Consider subscribing!',\n    'Support this blog!',\n    'Really appreciate it if you...'\n  ];\n  const el = document.getElementById('prompt');\n  el.textContent = prompts[Math.floor(Math.random(0) * prompts.length)];\n})();\n</script></p>\n<p>One obvious complaint you may have about my city-block example is that it's wrong. The ideal path between my starting point and ending point is a straight line! That's Euclid's first postulate from geometry! It's the very definition of what a straight line <a href=\"https://mathworld.wolfram.com/EuclidsPostulates.html\">even is</a>, right?</p>\n<div class=\"image-right\" style=\"max-width: 320px;\">\n  <img src=\"/images/blog/dummy-path.jpg\" alt=\"\" style=\"padding: 0; max-width: 100%; border-radius: 5px;\">\n  <center><small>Isn't all this just a bit silly?</small></center>\n</div>\n\n<p>And you'd be entirely correct, kind of.</p>\n<p>The thing is, you can't run <q>as the crow flies</q>, at least I can't. Confined to the ground, such a straight line path isn't an option. This is an important restriction because it allows us to redefine what the word <q>distance</q> even means. We will come out of that discussion with something much more powerful than we might first expect. To do that I have one question we must answer:</p>\n<p>What's the distance from Rome to Edinburgh?</p>\n<p>A clever reader might want to know which units I want them to use, but the cleverest of you might instead ask me, <q>for whom</q>? For a car the journey is about 1,545 miles; for a plane it's 1,002. For the Roman Emperor Hadrian it is, rather famously, undefined.</p>\n<style>\n.tab {\n  overflow: hidden;\n  border: 1px solid #ccc;\n  background-color: #f1f1f1;\n}\n.tab button {\n  background-color: inherit;\n  border: none;\n  outline: none;\n  cursor: pointer;\n  padding: 14px 16px;\n  transition: 0.3s;\n  flex: 1;\n}\n.tab button:hover {\n  background-color: #ddd;\n}\n.tab button.active {\n  background-color: #ccc;\n}\n.tabcontent {\n  display: none;\n  padding: 6px 12px;\n  border: 1px solid #ccc;\n  border-top: none;\n}\n</style>\n<script>\nfunction showCard(evt, name) {\n  // Declare all variables\n  var i, tabcontent, tablinks;\n\n  // Get all elements with class=\"tabcontent\" and hide them\n  tabcontent = document.getElementsByClassName(\"tabcontent\");\n  for (i = 0; i < tabcontent.length; i++) {\n    tabcontent[i].style.display = \"none\";\n  }\n\n  // Get all elements with class=\"tablinks\" and remove the class \"active\"\n  tablinks = document.getElementsByClassName(\"tablinks\");\n  for (i = 0; i < tablinks.length; i++) {\n    tablinks[i].className = tablinks[i].className.replace(\" active\", \"\");\n  }\n\n  // Show the current tab, and add an \"active\" class to the button that opened the tab\n  document.getElementById(name).style.display = \"block\";\n  evt.currentTarget.className += \" active\";\n}\n</script>\n<div class=\"tab\" style=\"display: flex; justify-content: space-between;\">\n  <button id=\"defaultOpen\" class=\"tablinks\" onclick=\"showCard(event, 'dist-by-car')\">Via Car</button>\n  <button class=\"tablinks\" onclick=\"showCard(event, 'dist-by-plane')\">Via Plane</button>\n  <button class=\"tablinks\" onclick=\"showCard(event, 'dist-by-hadrian')\">Via Hadrian</button>\n</div>\n\n<!-- Tab content -->\n<div id=\"dist-by-car\" class=\"tabcontent active text-center\">\n    <img src=\"/images/blog/rom-edi-map.jpg\" style=\"max-width: 100%; padding: 0; border-radius: 5px; width: 500px; margin-right: auto;margin-left:auto;\" name=\"car\">\n  <center><small>Image credit: Apple Maps</small></center>\n</div>\n\n<div id=\"dist-by-plane\" class=\"tabcontent text-center\">\n  <img src=\"/images/blog/rom-edi-arc.gif\" style=\"max-width: 100%; padding: 0; border-radius: 5px;width: 500px; margin-right: auto;margin-left:auto;\" class=\"hide\" name=\"plane\">\n  <center><small>Image credit: <a href=\"http://www.gcmap.com/mapui?P=ROM-EDI\">Great Circle Mapper</a></small></center>\n</div>\n\n<div id=\"dist-by-hadrian\" class=\"tabcontent text-center\">\n  <img src=\"https://upload.wikimedia.org/wikipedia/commons/c/ce/Hadrians_Wall_map.svg\" style=\"max-width: 100%; padding: 0; border-radius: 5px;width: 500px; margin-right: auto;margin-left:auto;\" class=\"hide\" name=\"hadrian\">\n  <center><small>Image credit: <a href=\"https://commons.wikimedia.org/wiki/File:Hadrians_Wall_map.svg\">Wikimedia Commons</a></small></center>\n\n</div>\n<script>\ndocument.getElementById(\"defaultOpen\").click();\n</script>\n\n<p>This is all to say that the concept of distance is not independent of the constraints of motion. If we define distance in this way, then we get something called <q>a metric</q> which is our ruler to measure space. Euclid gave us one kind of ruler: the Euclidean Metric defined by the familiar Pythagorean Theorem.</p>\n<math style=\"text-align: center; display: block;\"  xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>c</mi><mo>=</mo><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt></mrow></math>\n<center><small>The Euclidean Metric</small></center>\n\n<p>However we can also define a metric <a href=\"https://en.wikipedia.org/wiki/Taxicab_geometry\">that works</a> for our city blocks. This one looks quite different from the usual measure we use and it results in a radically different notion of length. In principle though, lots of functions can be used as metrics and each has its own consequences. The point is that there's no limit to how you define the idea of length.</p>\n<math style=\"text-align: center; display: block;\"  xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>c</mi><mo>=</mo><mi>|</mi><mi>a</mi><mo>&#x2212;</mo><mi>b</mi><mi>|</mi></mrow></math>\n<center><small>The Taxi Cab Metric</small></center>\n\n<p>Why are we talking about this though? What does any of this have to do with potential energy? That is where we arrive at one of the most important discoveries in all of physics.</p>\n<h2>Bending the Grid</h2>\n<p>Once you understand that the notion of distance depends on the properties of motion and how you draw your grid, you find yourself where Einstein was after 1905, after his first major breakthrough but before he reformulated gravity.</p>\n<p>Anyone who's taken high school or introductory college physics knows that Newton taught us that gravity is a force that pulls objects to the ground. That idea was later generalized to the idea that objects live in something called a gravitational field and that field imparts the object with gravitational potential energy.</p>\n<p>Einstein realized however that this idea was overbuilt. Instead, he found a different way to understand how gravity works. To see how let's take a step back. Imagine a grid, but a bent one, where the lines are warped. By definition, those lines mark out <q>equal distance</q> so even when they're warped we still say that they are the same distance apart. To see how this is possible, imagine that instead the paper itself is warped and the lines are straight along that warping. You can kind of see this if you squint at the image below.</p>\n<div class=\"image-center\">\n  <img src=\"/images/blog/wavy-grid.jpg\" alt=\"\" style=\"padding: 0; max-width: 100%; border-radius: 5px;\">\n  <center><small>Warped lines or warped paper? Is there a difference?</small></center>\n</div>\n\n<p>The ball in the image above has moved along the straightest possible path, it's just that the lines <em>defining straightness</em> are bent, so the ball seems to curve. This, in a nutshell, is gravity. Massive objects like the Earth and Sun bend the very grid of space and time. They, in a sense, redefine what it means to move in a straight line.</p>\n<p>Under this formulation, there was no need for gravitational potential energy at all. The Earth doesn't pull you down. You <em>want</em> to fall toward it because spacetime is curved. It's actually the opposite: the Earth is preventing you from falling!</p>\n<p>This wonderful lecture goes through an excellent derivation of this idea that <a href=\"https://www.youtube.com/watch?v=IBlCu1zgD4Y\">I encourage you to watch</a>. It opened my eyes to a lot of this. Consider Newton's First Law:</p>\n<blockquote>\n<p>A body remains at rest, or in motion at a constant speed in a straight line, unless it is acted upon by a force.</p>\n</blockquote>\n<p>The key insight for those of you still rightfully confused by all this is that usually we define what an object does (move in a line) and then say happens to it (it's acted on by a force). This is only possible because we arrive at the problem with a pre-formulated idea of what a straight line is. Instead we can flip it and then define what a straight line is by what an object does when there's no force on it! In the first instance we define straightness and derive forces. In the second, we eliminate the forces and define whatever happens next as a straight line. So, if the object seems to bend towards the Earth, then that's a straight line. It has to be!</p>\n<p>We've moved from imposing a definition to observing one. In a sense we take a step back and watch what nature does, rather than telling it what it <em>should</em> do. In doing so we package two concepts into one and gain predictive power.</p>\n<p>But enough about gravity. We were talking about running, right?</p>\n<h2>Closer to Home</h2>\n<p>If you follow the city grid on a run, then you're using some variant of the Taxi-Cab Metric to measure distance, and you're constrained by the physics of that metric. I've wondered why the path back home doesn't seem to matter, but it's because of the metric. In Taxi-Cab geometry there are multiple shortest paths. In Euclidean geometry there is only one. No path directly home will affect your total distance. And so, if you need that extra half-mile, you can only get it by running away from where you started, so long as the blocks are essentially the same size. So long as you are retracing blocks, you follow a straight line, a geodesic, back home. Use up some potential energy though, add a single block, and notice you'll actually have added two once you get back. Technically the second block was a geodesic though, but it all still counts.</p>\n<hr />\n<div class=\"footnote\">\n    <sup>1</sup> Assuming of course that the E/W and N/S blocks are of equal length. If they aren't then we actually fastrack to the discussion of curved coordinates in later sections.\n</div>\n<div class=\"footnote\">\n    <sup>2</sup> No I have no idea why T and V were the chosen names for these. Susskind in his class didn't either, but neither of us have looked it up.\n</div>"}, {"id": "https://brianschrader.com/archive/friendship-is-an-exponential-function/", "url": "https://brianschrader.com/archive/friendship-is-an-exponential-function/", "title": "Friendship is an Exponential Function", "date_published": "2026-07-13T16:02:00", "tags": ["essay", "personal"], "author": {"name": "Brian Schrader"}, "content_html": "<script src=\"/other-projects/plotFns.js\"></script>\n\n<p>What allows you to make friends and to keep them? Being a social person helps with making friends, surely. As does putting in the effort to be a good friend. But I'm sure we've all had the experience of wanting to become friends with someone, but yet it never really happens. Maybe there's never the time. Maybe you're too far apart, and I mean that literally.</p>\n<p>This is something I've observed over time, as friends move around and as people's lives grow, evolve, and change: the total friendship between two people evolves as a function of distance.</p>\n<div id=\"friend2-container\" class=\"image-right\" style=\"width: 300px;\">\n  <canvas id=\"friend2-canvas\"></canvas>\n  <small><center>\n    I think this is how we <i>want</i> or expect friendship to behave.\n  </center></small>\n</div>\n<script>plotFns({W: 300, H: 250, labels: ['Imagined'], xMin: 0, xMax: 2, yMin: 0, yMax: 1, showPlayButton: false}, 'friend2-canvas', (x, t) => 1-x/2);</script>\n\n<p>This means that two people, given the inclination to become friends, will see their friendship improve and decay based on their physical distance from each other&mdash;how far they live from each other. I think this makes intuitive sense. Two people who live together obviously see each other more than two people who live a continent apart. Yet what is surprising is that this function is not linear.</p>\n<p>Friendships, in my experience, are strengthened not by planned time together, but by <em>accidental</em> happenstance and the unplanned ability to simply spend time in the same place. If you live next door to a friend, spending time together is easy. Outside of your home, that friend is your <em>easiest</em> option for social interaction. You can share meals, woes, gossip, and even just yell over the fence to each other. That closeness is not a function of your effort to connect, but precisely because of the lack of effort you both needed to expend!</p>\n<p>Given suitable places to go, a coffee, dinner, or beer with friends nearby becomes a text message away.</p>\n<blockquote>\n<p>Beer at Ould Sod?</p>\n</blockquote>\n<div id=\"friend-container\" class=\"image-right\" style=\"width: 300px;\">\n  <canvas id=\"friend-canvas\"></canvas>\n  <small><center>\n    Friendship falls off quickly with distance, then that descent slows down.\n  </center></small>\n</div>\n<script>plotFns({W: 300, H: 250, labels: ['Friendship'], xMin: 0, xMax: 5, yMin: 0, yMax: 1, showPlayButton: false}, 'friend-canvas', (x, t) => Math.exp(-x));</script>\n\n<p>In business-speak: there is very little friction here. Again think of a friendship within a household. You don't schedule wine with dinner. You just see if your friend or partner wants some, then open the bottle. The need to schedule, especially with a calendar, is the sign of a friendship's formality. It's the sign that physical distance has intruded on your shared lives.</p>\n<p>Yet, I assume none of this is surprising. The important thing I've discovered is that this function of distance is <em>not linear</em> as I said. We expect that moving a <em>little</em> further away would have a proportional effect on the friendship.\nIn practice though, it's exponential.</p>\n<p>This means that friendship, given no additional effort, will decay much faster than you think. Moving a block away is worse than being next door by a surprising amount. Moving across town marks the end of an era. Sure, given time and deliberate effort (and lots of calendars) you can overcome the barrier of distance. The internet has helped here too, but scheduled time and video calls are no basis for the same friendships that occur naturally in backyards, on doorsteps, or at nearby restaurants, coffeeshops, and bar counters.</p>\n<p>There's an <a href=\"https://www.reddit.com/r/Urbanism/comments/mbl0es/half_the_reason_folks_romanticize_college_is/\">old meme</a>:</p>\n<div class=\"image-right\" style=\"width: 240px;\">\n  <img src=\"/images/blog/shared-coffee.jpg\" style=\"max-width: 100%;\">\n  <small><center>Photo: mine</center></small>\n</div>\n\n<blockquote>\n<p>Half the reason folks romanticize college is because it's the last time most folks lived in dense, walkable neighborhoods focused on providing community during plentiful off-hours.</p>\n</blockquote>\n<p>I've been lucky enough to be able to live in a vibrant, walkable, and <a href=\"https://en.wikipedia.org/wiki/Third_place\">third-place abundant</a> neighborhood for over a decade. What's more I've been luckier still in that many of my friends live within walking distance. I grew up in a small neighborhood with several kids down the street to play with. In a way I still have that, for now.</p>\n<p>What it means though is that to be nearby is to be part of a group of friends who are just simply closer than my other friends, even if we weren't all that close to begin with. It's just easier to hang out, easier to spend time, and friendship, if anything, is a function of time spent together. That time is a function of effort, of shared interest, and importantly the exponential of distance.</p>"}, {"id": "https://brianschrader.com/archive/because-it-speaks-in-words/", "url": "https://brianschrader.com/archive/because-it-speaks-in-words/", "title": "Because it Speaks in Words", "date_published": "2026-06-29T16:01:00", "tags": ["essay", "technology"], "author": {"name": "Brian Schrader"}, "content_html": "<p>There is a difference between knowing something, and truly understanding it. I think we've all had those moments, the ones where a truth you learned a long time ago really sits with you for the first time. It rests in your mind and stretches out, finally showing off the great expanse of nuance hidden deep within.</p>\n<div class=\"image-right\" style=\"width: 280px;\">\n  <img src=\"/images/blog/moon-venus-jupiter.jpeg\" style=\"max-width: 100%;\">\n  <center><small>Photo: mine.</small></center>\n</div>\n\n<p>Most nights when you happen to spy the Moon, Jupiter, and Venus sitting in a line in the sky, you see them as the dots beside a crescent that they are. Yet sometimes, when framed amid the sunset sky above the wisps of silver cloud, you see them differently. You realize in that moment that you, your great-grandparents, Julius Caesar, and Aristotle all saw this same sky. It has always been for us. We know so much about Jupiter and Venus today, yet no human eye has ever seen more than you're seeing now.</p>\n<p>I think we are all, in this time, realizing the true power of words and what they mean, not to those who speak, but to those who listen.</p>\n<h2>The Power of Stories</h2>\n<p>It was Eugene Wigner who famously wrote about the unreasonable effectiveness of mathematics in the Natural Sciences, the empirical fact that advanced math is eerily accurate at predicting the behavior of nature, so much so that, for me, it can seem like mathematics is perhaps the true language that nature speaks.</p>\n<p>However, as children, we do not grow up with an innate understanding of complex mathematics, of this foundational language of nature. Instead we are all born with the innate desire to hear and to tell stories, of ourselves, of others, and of the world around us. Our well-known cognitive biases push us to accept <a href=\"https://en.wikipedia.org/wiki/Rhyme_as_reason_effect\">stories that rhyme</a> over those that do not, and believe the <a href=\"https://en.wikipedia.org/wiki/Truth_bias\">people we speak to</a>. That last one is particularly important in this age because there are simply so many words out there ready to be believed.</p>\n<p>Stories are how we share information and how we've warned, cast out, and praised each other for millenia. We tell stories, to ourselves and to others, about why we are successful (or not) and why others might be (or not). We moralize disease, in part perhaps because a moral story is easier to bear than the sheer randomness of a chaotic world. Our minds work to make sense of the world by finding patterns. As those patterns interweave and become cohesive narratives, a story emerges to explain the where and why. These stories are so critical to our understanding of the world that we hold on to them, make them part of our selves, and when they break down they can break the self too. In the end, all we have of the world and the only truth we know first-hand, are the stories we tell ourselves.</p>\n<p>We communicate those stories, to ourselves and to others, with gestures, actions, and most importantly with words. That makes those words perhaps the most powerful force in human society. They are the fundamental interaction that holds our world together. It's the words from the past that we reach for as some justification or authority. It's words of the famous and the clever that we laud or reject. Even Mathematics, this jewel of the modern world, is communicated and taught in words. To our storied minds, these atoms of thought are everything.</p>\n<div class=\"image-right\" style=\"width: 330px;\">\n  <img src=\"/images/blog/ulysees-sirens.jpg\" style=\"max-width: 100%; padding: 0;\">\n  <center><small>Ulysses and the Sirens. John William Waterhouse<br> via Wikimedia Commons</small></center>\n</div>\n\n<p>Disinformation and misinformation have been rampant in the past, but never before has there been a world filled so chaotically with so many clamoring voices. The Ancient Greeks warned of Sirens and their terrible, entrancing songs, yet today sirens sound in our ears and on our eyes every moment of every single day.</p>\n<p>However today, we have also come into a new thing, a step function in our communication. In this time we humans are not the only one who is talking. This is not because we are some perfect specimen of wordcraft, or that another species could not do what we do, but because our chosen, crafted interlocutor is not a mind like ours. It is a device which has no notion of truth or of morality. It is a parrot, who imitates our speech but does not understand it. It does not learn, and it cannot. Yet we still can, and we will learn what it tells us, regardless of its truth.</p>\n<h2>Words Without a Mind</h2>\n<p>Support Vector Machines (SVMs) are a type of machine learning algorithm that have been around a long time. Random Forests are another. Both are very good at sifting through swaths of noise looking for the signal. SVMs and Random Forests help identify disease incidence in large populations, and find novel ways to identify genetic causes of complex conditions. Techniques like these were spreading in academia and industry a decade ago. I remember when Apple released a drag-and-drop app to help developers build simple models for recommendation systems! This stuff has been around for a long time.</p>\n<p>Yet, if that's true, why did it take Large Language Models (LLMs) to break into mainstream consciousness? People had been hammering on the idea of rebranding Machine Learning as Artificial Intelligence for years, but these days LLMs are synonymous with AI while other techniques aren't. True, modern LLMs are impressive technically, but is that the reason? Or is the reason totally distinct from technology? Perhaps we call LLMs intelligent, perhaps we adopted them in a frenetic rush, and perhaps we fear them most not because they are particularly good machine learning algorithms, but because, at long last, they do not speak in vectors or in numbers, but because they speak in words and words are our domain.</p>\n<div class=\"image-center\">\n  <img src=\"/images/blog/voice-without-mind.jpg\" style=\"max-width: 100%; padding: 0;\">\n  <center><small>Ulysses and the Sirens. John William Waterhouse<br> via Wikimedia Commons</small></center>\n</div>\n\n<p>I think back to a cognitive bias I listed above: that we tend to believe the people we are speaking to. No other machine learning technique, no other AI, has ever spoken to us, sounded so much like another mind. At every opportunity when technology has enabled new forms of communication: books, pamphlets, letters, emails, instant messenger, text messaging, we have always used those tools to seek out others like ourselves and to share and listen to new stories. Those stories used to correlate roughly with some level of truth about the world, if even about a single interpretation of it. Now we have language statistically built to sound genuine, and yet its speaker has no mind or experience to convey. Still, we believe so deeply in the power of words that many of us have preferred this plausible-sounding make-believe to reality.</p>\n<h2>Left Wanting</h2>\n<p>There is evidence that perhaps LLMs, unlike social media, will help push us to the center&mdash;to the statistical average&mdash;and if LLMs were somehow guaranteed to only be trained on human-generated data forever, perhaps this would be true. However as we further diverge the words we see from any objective meaning, both in human communication and in the words written by our new AI chatbots, this situation will not be stable for long.</p>\n<p>Ultimately though, what's important is not that we have built tools to generate digital text. What is important is that, like processed food and sugar, our long-ingrained biological need to share and hear stories is being hijacked and used by technology. Ascribe whatever values to that you wish, the morality is not my point. Humans have looked out at the stars and wondered why: why we live and die, and whether this universe was made for us, and whether we belong within it for millenia. Those questions remain, save now we have the ability to trust in a voice that tells us precisely what we want to hear. We filled a caloric need with cheap candy, shelf-stable cupcakes, and soda. These are convenient things, good in moderation, but still they can hurt us and we're still struggling to solve the problems they created. Today we may be filling an emotional need as well, functioning as the scheming court vizier that whispers sweet and comfortable truths. Yet unlike the stereotype, this vizier does not scheme. It has no mind and no goal save to please, yet we wish so deeply to be pleased.</p>\n<div class=\"image-right\" style=\"width: 280px;\">\n  <img src=\"/images/blog/Mori_Uncanny_Valley.png\" style=\"max-width: 100%;\">\n  <center style=\"line-height: 1.3;\"><small>The Uncanny Valley<br> Masahiro Mori and Karl MacDorman</small></center>\n</div>\n\n<p>This need comes deeply ingrained in us and will be impossible to fill. It is part of the Human Condition. Perhaps, given time, this new kind of statistically-driven language will find itself deep within the unforgiving well of the Uncanny Valley. We shall see. No doubt the Sirens seemed convincing for a time. As a gas-station pastry is no substitute for a good and hearty meal, the words of prediction engines are but vain and fickle things, lovely in the ear perhaps but hardly satisfying to the soul.</p>\n<p>For millenia words have been a proxy for connection with another mind, today that link is severed but the need in us remains and there is only so long that one can fill a void with empty calories. We retain our position as the only being in the Universe who can tell their own stories and who can be said to learn and share the truth. The Font of Knowledge still begins and ends with us and The Odessy of Finding Truth is a lonely one, cast as we are amid the stormy waters of the world, even as there are many clamorous, seductive voices calling to us from the distant shore.</p>"}, {"id": "https://brianschrader.com/archive/would-you-believe-that-this-is-it/", "url": "https://brianschrader.com/archive/would-you-believe-that-this-is-it/", "title": "Would You Believe that This is It?", "date_published": "2026-06-15T16:07:00", "tags": ["history", "politics", "essay"], "author": {"name": "Brian Schrader"}, "content_html": "<p>Last year I heard this song from a band called Loser Demon. The song is called <a href=\"https://loserdemon.bandcamp.com/track/holding-ground\">Holding Ground</a> and here's the chorus that has been stuck in my soul ever since (added words, mine):</p>\n<blockquote>\n<p>would you believe that this is it and it is good?<br>\ndoesn't surprise me and i hope that it never would<br>\n(I'm) holding ground</p>\n</blockquote>\n<p>I heard that phrase and was immediately repulsed the first time, yet something about it lingered in my heart. I think that reaction is likely the same for lots of people these days. I mean, look at the world? Look at the strife and the trouble and the heartache? How can <em>this</em> be good?</p>\n<div class=\"image-right\" style=\"width: 300px; margin-right: 0.5rem;\">\n<a href=\"https://loserdemon.bandcamp.com/track/holding-ground\">\n  <img src=\"/images/blog/holding-ground.jpg\" alt=\"Holding Ground\" style=\"max-width: 300px; padding: 0;\"></a>\n  <iframe style=\"border: 0; margin: 0; max-width: 100%; display: block; height: 42px;\" src=\"https://bandcamp.com/EmbeddedPlayer/album=328450788/size=small/bgcol=ffffff/linkcol=0687f5/track=16424282/transparent=true/\" seamless><a href=\"https://loserdemon.bandcamp.com/album/ep2\">EP2 by Loser Demon</a></iframe>\n</div>\n\n<p>I think for me the real wisdom in those lyrics is that it's not describing what ought to be, but what is. Can the world be better? You better believe it. In so, so many ways.</p>\n<p>Yet the first part of that line reminds me of something else: the feeling of growing up and seeing that the adults are just as scared and clueless as the other kids in your class. At that point I think we all have the moment of realization, the fear that surely <em>this</em> can't be how things work. We then spend the rest of our lives learning to cope, or deny. But it's true.</p>\n<p><em>This</em> is it.</p>\n<p>The second part of that line is even more difficult to bear. So this is it, this is what the world is, how can this horrid state be anything like <em>good</em>? The moral repulsion is valid and, for me, it's strong. Yet while the world continues to get worse in numerous ways, any <a href=\"/archive/the-long-view-of-history/\">reading of history</a> will tell you things are a whole lot better than they've been for 99.99% of human history. Not in all ways, sure, but in the vast majority of ways: yes. It's not a question and those who debate that question are ignorant of how it feels to bathe once a week in baths powered by slaves without soap, suffer from near constant famine and plague, or live in a world where <a href=\"https://ourworldindata.org/child-mortality-in-the-past\">50% of children died before the age of 15</a>. Today humanity has succeeded in fending off a great many of the curses of the natural world.</p>\n<p>Not only that, but this world we have made is one built on consistent improvement. We have built structures that are intended to continually improve themselves and the lives of those they serve. These systems are flawed, and indeed bogged down and slow, but this can and should be fixed. Yet still, the mission, to improve the world and the lives of all within it, is one we have continually worked to fulfill. In the past fifty years we have done so much together as a country and a world to make things right.</p>\n<p>In other words: <em>this</em> is good.</p>\n<p>Yes, we have a great deal to do and so much of that progress has not been equally distributed, nor has it been made without harm. That is part of the work we have left to do, but let's not lose sight of our progress. Our job now is to advance the rest of the way, and to hold the ground we've gained.</p>\n<p><div class=\"midroll newsletter-callout\">\n  <div class=\"callout text-center\">\n    <div id=\"prompt\">\n      <noscript>\n        Enjoying this post?\n      </noscript>\n    </div>\n    <a\n      href=\"https://sendfox.com/brianschrader/\"\n      title=\"Subscribe to the newsletter\"\n      class=\"subscribe\"\n      target=\"_blank\"\n    >\n      ✉️&nbsp;Subscribe to the Newsletter!\n    </a>\n  </div>\n</div>\n<script>\n(() => {\n  const prompts = [\n    'Enjoying this post?',\n    'Like what you see?',\n    'Cough cough...',\n    'Posts like this, in your inbox!',\n    'Consider subscribing!',\n    'Support this blog!',\n    'Really appreciate it if you...'\n  ];\n  const el = document.getElementById('prompt');\n  el.textContent = prompts[Math.floor(Math.random(0) * prompts.length)];\n})();\n</script></p>\n<h2>The Liberal Order</h2>\n<blockquote>\n<p>Liberalism starts with the assumption that it’s just human beings trying to do the best we can, and there will be mistakes, there will be errors, so we need strong self-correcting mechanisms.<br>\n&ndash; Yuval Noah Harari on the <a href=\"https://www.nytimes.com/2026/05/26/opinion/ezra-klein-podcast-yuval-noah-harari.html\"><em>Ezra Klein Show</em></a></p>\n</blockquote>\n<p>I idolize Congress, and always have. I dislike many of the people in it, but the institution itself makes me so damn proud to be an American.<sup>1</sup> The House and Senate, though born of terrible compromise and riddled with problems, are together the engine of our shared work and the flagship of liberal democracy. The workings of Congress are almost mythical to me, shrouded in a veneer of Roman-looking symbols, British traditions, and founded on a Declaration containing some of the most beautiful words humanity has ever written.</p>\n<p>Yet, I remember what it felt like when I discovered that a lot of the people in the House of Representatives are lawyers and farmers and business owners. A lot of them are career politicians, but even so, I remember thinking:</p>\n<blockquote>\n<p>Wait, those are just people. Flawed people. Like me. But if that's it, if <em>that's</em> who's in charge, who's looking out for us?</p>\n</blockquote>\n<p>And there's the rub. <em>This</em> is it. There is no one else. That's precisely why we've constructed institutions, to protect us from the failure that might come one day. The trouble is that One Day™ seems to be nearing and many of us see it coming. I am one of those people. Many see nothing at present to protect. I am not one of those people. As well, these day's it's trite to defend our current world, and so people tend not to do so. I do not want to be one of those people.</p>\n<p>So I'm not sure who this is for, perhaps it's only for me. But I needed to write it, because in my heart I believe in this world we have made, and I do not wish to see it burn. Leading up to a&mdash;shall we say <em>contravertial</em>&mdash;celebration of our country's 250<sup>th</sup> birthday, I figured I would try to make the best case that I can for the world as it could be, and for a more Perfect Union.</p>\n<h2>What <em>This</em> Is</h2>\n<blockquote>\n<p>When in the Course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.</p>\n<p>We hold these truths to be self-evident:</p>\n<ul>\n<li>that all men are created equal</li>\n<li>that they are endowed by their Creator with certain unalienable Rights</li>\n<li>that among these are Life, Liberty and the pursuit of Happiness.</li>\n<li>that to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed...</li>\n</ul>\n<p>&ndash;The <a href=\"https://www.archives.gov/founding-docs/declaration-transcript0\">Declaration of Independence</a> <em>(formatting mine)</em></p>\n</blockquote>\n<p>These words, along with the French <a href=\"https://en.wikipedia.org/wiki/Declaration_of_the_Rights_of_Man_and_of_the_Citizen\">Declaration of the Rights of Man and Citizen</a> are some of the most important words mankind has ever written. Read them again, really read them and take in their meaning. It's profound stuff, especially if you know how history has usually gone, and it forms the foundation on which this whole modern world has been built. Today you'll hear from many different voices that these words are a convenient lie, that even their authors did not truly believe them, but that is not true. Even if written by imperfect people, words can be meant sincerely. And besides, regardless of what those words meant to their authors, let it be said: they mean something to me.</p>\n<div class=\"image-center\">\n  <img src=\"/images/blog/bbttr.png\" alt=\"Books Belong to their Readers.\" style=\"max-width: 100%;\">\n  <center><small>Credit: <a href=\"https://youtu.be/MGn9x4-Y_7A?si=RR_fr4J_Qyp5WiLR&t=300\">Lindsay Ellis</a></small></center>\n</div>\n\n<p>Sure, the intent of the founders is important&mdash;as context&mdash;but it matters more what those words mean to us today. The present belongs to the living, as <a href=\"https://founders.archives.gov/documents/Madison/01-12-02-0248#:~:text=This%20principle%20that%20the%20earth%20belongs%20to%20the%20living%2C%20&amp;%20not%20to%20the%20dead\">Thomas Jefferson wrote</a>. Today we are mired in debates of who to honor, and who historically to believe, but that debate does not really matter. What matter's is not whether George Washington believed all people are equal, but if we believe it. Washington is dead. We are not, and it is our country that exists today, not his.<sup>2</sup></p>\n<p>Words have meaning both to those who write them and to their readers, but there are more of one than the other and once the author dies, their intent need no longer have sway over their words. Their words can grow beyond them and their intent. This is the beauty of words. Once they are set free, they become something more.</p>\n<p>The words written in the Declaration of Independence, or The Rights of Man and Citizen, or the U.N. General Charter, these words are born of the idea that the world is imperfect, and that it will always be so, yet also of the idea that <em>here</em>, in them, is a world worth chasing, a dream to which we can always aspire. I want that world, I believe in it, and I want that dream to come true. If that commitment to equality, liberty, justice, and the pursuit of happiness for all sounds trite, then let it be so. Regardless, it is true. And these days, it needs to be said.</p>\n<h2>Ceding Symbols</h2>\n<p>There is something to be said for the Roman practice of erecting statues to personified <em>virtues</em> instead of actual people. Today we go through a constant cycle of tearing down once-proud symbols after reevaluating their impact. This process, however painful, is good. Yet it also betrays the frailty of our veneration and pokes holes in the shared illusion we have of ourselves as a country and that's done profound damage to us.</p>\n<p>Yet we should celebrate ourselves, and the world we all have made together (obviously not just the U.S.). We should celebrate the virtues of Victory, Liberty, Equality, and Justice. We used to know how to do this. The Capitol building records that fact on its dome and in the Visitor's Center. It's striking and proud and we should do it more.</p>\n<div class=\"image-center\">\n  <img src=\"/images/blog/Emancipation-Hall_1.jpg\" alt=\"\" style=\"max-width: 100%;\">\n  <center><small>Credit: <a href=\"https://en.wikipedia.org/wiki/Statue_of_Freedom#/media/File:Emancipation-Hall_1.jpg\">Architect of the Capitol Photogr; Public Domain</a>.</small></center>\n</div>\n\n<p>I fear these days we would be caught in endless debate over the cost and location of such a statue, and whether it distresses the birds, yet such monuments to our shared triumph deserve to exist&mdash;else we risk erecting triumphs to a single man which is the very antithesis of what this country is.</p>\n<p>We should not be afraid to stand up, proud to be a citizen of a great country, of a vision of the world where people are free, and to be proud to defend that cause even when current events do not align with our shared vision of the world.</p>\n<blockquote>\n<p>As Rosenblatt writes, for almost 2,000 years, liberality meant “demonstrating the virtues of a citizen, showing devotion to the common good and respecting the importance of mutual connectedness.”</p>\n<p>Liberality was talked about everywhere. You can read about it in Cicero, in John Locke, in the letters of George Washington. And yet we never talk about it today. Liberalism as a political philosophy and movement completely elbowed out liberality as a virtue, as an ethic that citizens aspire to meet.<br>\n&ndash;Helena Rosenblatt via <a href=\"https://www.nytimes.com/2026/05/05/opinion/ezra-klein-podcast-helena-rosenblatt.html\">Ezra Klein </a></p>\n</blockquote>\n<p>I feel that ethic deep within my soul. In liberal (read: left-leaning) circles it's cringe to admit such things, instead we avoid celebrating an ideal for fear of celebrating violent nationalism. The end result of that has been to cede all ownership of the symbols of our shared greatness to the people who seek to destroy it. Yet we must hold within ourselves the greatness to which we aspire and the conflict and trouble it has wrought and be prepared to defend those values in spite of that previous failure. Doing otherwise is a failure of conviction, not one of intelligence.</p>\n<blockquote>\n<p>Before I go on with this short history let me make a general observation—<strong>the test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function</strong>. One should, for example, be able to see that things are hopeless and yet be determined to make them otherwise. This philosophy fitted on to my early adult life, when I saw the improbable, the implausible, often the <q>impossible</q> come true.<br>\n&ndash; F. Scott Fitzgerald, <em><a href=\"https://www.pbs.org/wnet/americanmasters/f-scott-fitzgerald-essay-the-crack-up/1028/#:~:text=Before%20I%20go%20on%20with%20this%20short%20history\">The Crack-Up</a></em>, February 1 1936</p>\n</blockquote>\n<h2>A More Perfect Union</h2>\n<p>To me, The Declaration of Independence is so much more beautiful than The Constitution, not just because it isn't so soured by the 3/5<sup>ths</sup> compromise, but because the language is grander and more profound. Still it is a beautiful document. Consider the 1<sup>st</sup>, 4<sup>th</sup>, 5<sup>th</sup>, 13<sup>th</sup>, 14<sup>th</sup>, 15<sup>th</sup>, and  19<sup>th</sup> amendments. The positive freedoms of speech, assembly, press, and equal protection along with the guarantee of a jury trial, the prohibition of slavery, establishment of birthright citizenship, and guarantee of suffrage to women sit right along side the negative freedoms from unreasonable search. Those amendments are this country's most profound admission of its belief in the goals laid out in the Declaration of Independence, and they are the reason the United States became the light of the world, a shining city on a hill.</p>\n<p>The Preamble to the Constitution echoes the Declaration of Independence directly (emphasis mine):</p>\n<blockquote>\n<p>We the People of the United States, in Order to form <strong>a more perfect Union</strong>, establish Justice, insure domestic Tranquility, provide for the common defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America.</p>\n</blockquote>\n<p>That call, to better ourselves and our country through continued improvement, through trial and error and relentless self-evaluation, is what it means to be an American. We don't talk about the obligations of citizens are in this time, it's cliché at best. Yet we are called to do this work as part of the duty we have to maintain this great state. We've fallen behind on our progress lately, and we have much to answer for, but perfect was never the end game.</p>\n<p>A friend of mine calls this philosophy the idea of <q>It Sucks Less</q>. If what you're doing now <q>sucks less</q> than it did before, you're making progress. That is what the Constitution calls for, and it's what we must continue to do.</p>\n<p>I refuse to let the great ideas on which this country was founded be torn down idly by corrupt and authoritarian fools beneath the dignity of recognition and I refuse to sit and let the dream of what it means to be an American, a fighter for liberty and justice, be corrupted and belittled. Those of us who feel the spirit of the cause should continue this fight, however hard it may still prove to become.</p>\n<p>Let's take this opportunity, as mired in conflict as it is, to recommit ourselves in this moment to what it truly means to uphold the values we have at our foundation, and to admit to ourselves that things can <em>and will</em> get worse if we do not. No one else is coming to save us.</p>\n<p>This is it. Hold this ground.</p>\n<div class=\"footnote\">\n<sup>1</sup> Nothing made me feel more repulsively proud to be an American than watching English members of parlament bow to the new king. I remember recoiling and saying aloud, <q>I am an American and I bow to no one.</q><br/>\n<sup>2</sup> I refuse to call the United States a Nation because it isn't one. The words country and nation are not synonyms. The U.S. is great precisely because it <i>isn't</i> a nation-state.<br/>\n</div>"}, {"id": "https://brianschrader.com/archive/the-true-expense-of-nature/", "url": "https://brianschrader.com/archive/the-true-expense-of-nature/", "title": "The True Expense of Nature", "date_published": "2026-06-01T16:36:00", "tags": ["physics", "essay", "history"], "author": {"name": "Brian Schrader"}, "content_html": "<style>code { font-size: 10pt; background: #ddd; border-radius: 3px; padding: 4px; }</style>\n\n<p>It's Saturday morning, and you have no plans. Perhaps your schedule happened to line up that way, perhaps the kids are gone, or maybe it's just luck. Regardless, it's glorious. You bask in the glow of a lazy morning while you decide just how you're going to spend today. In your mind you go over different ideas, considering each and its consequences.</p>\n<p>You could go to the beach! No, too much effort. You could stay in and read a book, but it's a nice day. You could read outside. Perhaps though it's better to go for a long walk first, grab a coffee maybe? You need to grab some things at the store, and that's on the way. Eventually you arrive at a plan: walk to get coffee, read for a while at the café, then stop by the store on the way home! An excellent plan&mdash;efficient and relaxing!</p>\n<p>What have you just done? How did you arrive at this decision? There were so many variables, a nearly infinite possibility space, yet you managed to make do. Perhaps Nature itself is not so dissimilar.</p>\n<h2>Making Decisions</h2>\n<p>When you make a decision like in the example above, you consider and explore the options you have. Implicitly you ignore certain possibilities&mdash;even with a totally free day, few people decide to spend it by committing a whimsical burglary. Instead you narrow down the options by what fits your typical habits and recent situations, and then you imagine how those possibilities might play out, weighing the consequences.</p>\n<div id=\"potential-well-container\" class=\"image-right\" style=\"width: 330px;\">\n  <canvas id=\"potential-well-canvas\" style=\"border-radius: 5px;\"></canvas>\n</div>\n<script>window.WELL_CONFIG = {\n    width:  330,\n    height: 220,\n    x0: 0.7,\n    friction: 0.8,\n    ballRadius: 10,\n    wellDepth: 0.75,\n    yLabel: 'Sum of all Costs',\n    minValueLabel: 'Ideal Solution',\n};</script>\n<script src=\"/other-projects/potential-well/potential-well.js\"></script>\n\n<p>Hopefully you don't get stuck in analysis paralysis, and so, when you finally come to a decision, it's fairly optimal: taking into account your responsibilities, preferences, financial capacity, and mood.</p>\n<p>This is a kind of optimization problem, a kind of problem that humans solve, repeatedly, every single day and similar to the kinds that are the subject of Classical Physics. In effect, you're trying to find a path through the world which minimizes the financial, personal, and societal cost. Preferred solutions are not the choices with <em>no</em> cost, as those are very rare, instead they're the solutions with the <em>least</em> cost.</p>\n<p>In any given situation, the least costly solution should be the one that's preferred, assuming you've accounted for and weighed every type of cost.<sup>1</sup> If we wanted to calculate the optimal solution, perhaps using some calculus, we'd need a single notion, a unit of measure, that could represent any kind of cost and then we'd need a description for how much each decision, each path you might take, might cost. But once we had that, in principle anyway, we could calculate the best option every time.</p>\n<p>Let's call this generalized, hypothetical cost Action.</p>\n<p><div class=\"midroll newsletter-callout\">\n  <div class=\"callout text-center\">\n    <div id=\"prompt\">\n      <noscript>\n        Enjoying this post?\n      </noscript>\n    </div>\n    <a\n      href=\"https://sendfox.com/brianschrader/\"\n      title=\"Subscribe to the newsletter\"\n      class=\"subscribe\"\n      target=\"_blank\"\n    >\n      ✉️&nbsp;Subscribe to the Newsletter!\n    </a>\n  </div>\n</div>\n<script>\n(() => {\n  const prompts = [\n    'Enjoying this post?',\n    'Like what you see?',\n    'Cough cough...',\n    'Posts like this, in your inbox!',\n    'Consider subscribing!',\n    'Support this blog!',\n    'Really appreciate it if you...'\n  ];\n  const el = document.getElementById('prompt');\n  el.textContent = prompts[Math.floor(Math.random(0) * prompts.length)];\n})();\n</script></p>\n<h2>The Principle of Least Action</h2>\n<p>The so called <em>Principle of Least Action</em> is a real thing and it's <a href=\"https://www.youtube.com/watch?v=qJZ1Ez28C-A\">perhaps the most foundational concept</a> in Physics. It's honestly a shame that it's not taught to most people who take physics in college because, while it does require some advanced mathematical techniques to actually use, the Principle of Least Action underlies all of modern Physics. It's not strictly a theory, it's an assumption: the assumption that <strong>nature always does the most optimal thing</strong>.</p>\n<p>The French physicist, Pierre Louis Maupertuis, was the first to propose action as the currency of nature in the eighteenth century.</p>\n<div id=\"plotting-canvas-container\" class=\"image-right\" style=\"width: 300px; padding: 0;\">\n  <canvas id=\"plotting-canvas\" style=\"border-radius: 5px;\"></canvas>\n  <center><small>The trajectory of a ball being thrown.</small></center>\n</div>\n<script src=\"/other-projects/plotFns.js\"></script>\n<script>plotFns(\n    { W:  300, H: 280, xMin: 0, xMax: 0.7, yMin: 0, yMax: 1.5, showPlayButton: false, xFilter: 'positive' },\n    'plotting-canvas',\n    (x, t) => (5 * x - 5 * x*x),\n);\n</script>\n\n<p>In the time since we've seen action be used to describe every level of physical theory from Einstein's Theory of General Relativity to the Standard Model of Particle Physics. Action is truly fundamental in ways Maupertuis could never have imagined.</p>\n<p>In truth, when considering optimal paths, action is not always minimized, but instead made <q>stationary</q>. Usually it is indeed a minimum, but sometimes it's more of a stable point, like the seat of a saddle or a pass between two mountains. More precisely, nature prefers paths on which the action doesn't change much in the vicinity.</p>\n<h2>Nature's Choice</h2>\n<p>In the 17th and 18th centuries nature was occasionally referred to as a proper noun. Nature was referred to, not as a phenomenon, but as a person or a god. In alchemical circles, and throughout medieval literature, Nature was sometimes depicted and referred to as a being who directly controlled the function of the natural world. In this depiction, rocks fell and water ran, not because of God's direct intervention in earthly affairs, but because he'd created Nature to do that work instead. Nature was subservient to the rules made by God, but ultimately she (and it was almost always a <em>she</em>) did what she could within the rules she was given.</p>\n<div class=\"image-right\" style=\"width: 300px;\">\n  <img src=\"/images/blog/the-mirror-of-the-whole-of-nature.jpg\" alt=\"The Mirror of the Whole of Nature and the Image of Art\" style=\"max-width: 100%; border-radius: 5px; padding: 0; margin-bottom: 6px;\">\n  <center><small style=\"line-height: 1.3; display: block;\">The Mirror of the Whole of Nature <br> and the Image of Art, Robert Fludd</small></center>\n</div>\n\n<p>In modern science, it's considered uncouth to refer to Nature in this way, to personify her, as we once did. But there is a loveliness to that way of writing, and a grandeur of the tone that we've lost and one that I find quite beautiful. So I'll be resurrecting this tradition for a time.</p>\n<p>In this mode, you could say that Nature is being lazy by relying so heavily on the Principle of Least Action. After all, given the expense of moving around all particles on the board of the universe, nature always chooses the least costly path. Maupertuis called this economical, another word could be thrifty. You could say that Nature chooses the best path, or perhaps that she makes the best use of the effort that she spends.</p>\n<p>To us, in our macroscopic world, Nature always does the best possible thing. Yet Quantum Mechanics gives us a different view, and one that perhaps shows us a little more of Nature's problem solving than she wanted us to know.</p>\n<h2>Exploring What's Possible</h2>\n<p>To understand a whole, you must understand it's parts. This is the Principle of Reductionism which underlies modern science. And so, in order to fully understand how a ball travels from point A to point B, we must understand the motion of its atoms. The trouble is that here in the quantum realm, the land of fundamental particles, the familiar laws of nature that we know from human experience break down entirely.</p>\n<p>However in <a href=\"https://faculty.washington.edu/seattle/physics541/2012-path-integrals/feynman-thesis.pdf\">his doctoral thesis</a>, Richard Feynman discovered that Nature may in fact only accomplish her goal of minimizing action in the aggregate. At the most fundamental layer, as Feynman showed, particles can be thought of as taking <a href=\"https://www.youtube.com/watch?v=Q10_srZ-pbs\">every possible path</a>. In this interpretation, Nature only appears to do what's best once she manages to cobble together an assemblage of particles moving in unison.</p>\n<p>Quantum Mechanics has a reputation for being difficult to interpret and understand, but Feynman's interpretation may not be so difficult to understand if we, again eschewing modern sensibilities, consider a more human-like example.</p>\n<div class=\"image-right\" style=\"width: 310px;\">\n  <img src=\"/images/blog/action/all-paths.jpg\" alt=\"Every possible path\" style=\"max-width: 100%; border-radius: 5px; padding: 0; margin-bottom: 6px;\">\n  <center><small style=\"line-height: 1.3; display: block;\">Image Credit: Veritasium</small></center>\n</div>\n\n<p>Consider again how you made your decision to read at the café. You mentally explored the possible paths you might take, weighing their consequences and cost, then acted on the one which made the most sense. Nature herself, seems not to have this separation between thought and action, and instead must perform both with the same pieces. At the most foundational levels, we can see then Nature imagining&mdash;in a way&mdash;each path, feeling out the possibilities, and arriving at an aggregate course of action. It's obvious that she wished to hide this procedure of hers well, or else it would be more easily visible to us, but by peering into the quantum nature of the world, we can see just how she arrives at her answers.</p>\n<p>Nature is not human, and so the discussion above is simply framing, but I think it's interesting how nature tends to reuse similar phenomena across scales and levels of complexity. Metaphor can be dangerous, as it often gives false impressions, but it can also be useful, helping to bridge the knowledge gap that lies before true understanding.</p>\n<p>However, this unorthodox discussion of the Principle of Least Action begs an interesting question: why should Nature be so thrifty with action? After all, it's not like we're running out of the stuff. Right?</p>\n<h2>Nature's Treasury</h2>\n<p>Leaving behind the anthropomorphized version of Nature for a moment, it's interesting to consider the idea that action is minimized in order to extend, for the longest period of time, the lifetime of the universe. Action is not Entropy, the more commonly discussed currency of chaos that will eventually cause the Heat Death of the Universe, but let's explore this idea anyway, in case there is something interesting hidden deep inside it.</p>\n<div class=\"image-right\" style=\"width: 310px;\">\n  <img src=\"/images/blog/gracchus-treasury.jpg\" alt=\"TIBERIUS GRACCHUS closes the Temple of Saturn - the Roman Treasury Date: 133 BC\" style=\"max-width: 100%; border-radius: 5px; padding: 0; margin-bottom: 6px;\">\n  <center><small style=\"line-height: 1.3; display: block;\">Nature may be like Tiberius Gracchus here, guarding the treasury.</small></center>\n</div>\n\n<p>Maupertuis called Action the <q>true expense</q> of nature, and minimizing expenses is something to do when there is a finite budget you wish to use effectively. That's not to say that minimizing action locally along a path actually requires a finite supply, however it can be an interesting, intuitive frame. If the universe were indeed attempting to maximize its useful life, excusing the personification again, it makes sense to minimize the expense of each interaction, each motion, that gets taken.</p>\n<p>But is there a finite amount of action?</p>\n<p>Well, if there is a finite amount of energy in the universe, and a finite amount of time over which that energy could be spent, then indeed the action of the universe is finite. We don't know this, of course, but <a href=\"https://www.nature.com/articles/331031a0\">it has been discussed</a> by serious physicists. If such a theory were true, then it might illuminate some answers as to why nature prefers the action of particles and objects to be optimized this way.</p>\n<p>As I said, it's wondrous that nature can so often be described by similar methods across a wide variety of scales. Balls roll down a hill by the same principle as do planets around a star and particles amidst the most fundamental quantum fields. In all these phenomena, action is the thing, the currency that is being optimized. It's also wondrous how such a thing as optimization problems can be so central to both the physical description of the natural world and to our human thought processes.</p>\n<p>Maupertuis, in his earliest writings on the subject said this about action, and  still today we wonder at the reasons why:</p>\n<blockquote>\n<p>It is this quantity of action which is here the true expense (dépense) of nature, and which she economizes as much as possible...<br/>\n- Pierre Louis Maupertuis (via <a href=\"https://books.google.com/books?id=y3UVAQAAIAAJ\">Philip Edward Bertrand Jourdain</a>)</p>\n</blockquote>\n<p>It may be that Nature doles out action from a finite treasury, where in she jealously hoards the coin which makes all things act&mdash;including spacetime itself. Perhaps Nature is lazy, or she's on a budget. Regardless, for whatever reason, she does what she can to get the biggest bang for her buck.</p>\n<div class=\"footnote\">\n<sup>1</sup> This is often the real hard part.<br/>\n</div>"}, {"id": "https://brianschrader.com/archive/a-field-guide-to-learning/", "url": "https://brianschrader.com/archive/a-field-guide-to-learning/", "title": "A Field Guide to Learning", "date_published": "2026-05-11T16:22:00", "tags": ["research", "writing", "essay"], "author": {"name": "Brian Schrader"}, "content_html": "<p>Let's say you're someone who wants to learn about an academic discipline. Perhaps advanced Physics, Sociology, Early-Modern History, or Cognition Science. Of course, there's YouTube pop-sci videos (which I love) and no shortage of products and services that purport to teach you the basics. But what do you do when you want to go beyond those basics?</p>\n<p>I'm not an expert, but I have been on a few of these journeys myself and so I want to lay out the paths I've taken and offer some advice to those who, like me starting out, had a very hazy view of the terrain and no idea who to trust with your education.</p>\n<h2>Starting Simple</h2>\n<div class=\"image-right\" style=\"width: 300px;\">\n  <img src=\"/images/blog/short-intro.jpg\" style=\"max-width: 100%;\">\n  <center><small>As you can see, I like this series quite a bit</small></center>\n</div>\n\n<p>For anything vaguely academic in nature, I highly recommend trying out one of the books in the <em><a href=\"https://www.amazon.com/very-short-introductions/s?k=very+short+introductions\">Very Short Introduction</a></em> series.</p>\n<p>The books are, as expected, very short (~100 pages) and cover a quick survey of the topic at hand and its various sub-disciplines. They're approachable, quick to read, and the chapters are organized by discipline. At the end, there's not only a bibliography of sources, but a section dedicated to <em>Further Reading</em>.</p>\n<div class=\"image-right\" style=\"width: 250px;\">\n  <img src=\"/images/blog/further-reading.jpg\" style=\"max-width: 100%;\">\n  <center><small>Search out directional guidance</small></center>\n</div>\n\n<p>That section is a gold mine. One of the biggest issues with independent learning is the lack of guidance. It's hard to know whether you're on the typical track or venturing off into treacherous woods. These books are written by long-time field experts, and in my experience have been invaluable for getting the basic lay of the land.</p>\n<p>Journey into the depths of those recommendations, then if you're ready dive into actual courseware.</p>\n<h2>Open Courseware</h2>\n<p>Universities are still the gatekeepers of advanced knowledge, and they've graciously published a wide swath of <a href=\"https://www.youtube.com/watch?v=7G4SqIboeig&amp;list=PLFeEvEPtX_0S6vxxiiNPrJbLu9aK1UVC_\">excellent course materials</a>. Universities like Stanford and MIT have made entire <a href=\"https://www.youtube.com/watch?v=SwhOffh0kEE&amp;list=PLpGHT1n4-mAvcXwzOIz3dHnGZaQP1LEib\">major tracks</a> available to anyone with an internet connection. If you can find the syllabus: grab it. Buy (or <a href=\"/archive/you-have-access-to-almost-any-book/\">rent</a>) the books, read them, and <a href=\"/archive/take-better-notes-by-hand/\">take notes</a>. These topics are difficult, and they take time to learn.</p>\n<details open>\n  <summary>💡 Tips for Finding Books &amp; Course Materials</summary>\n  <div>\n    <ul>\n      <li>Try to find the course syllabus</li>\n      <li>Like a specific professor? Check out their books</li>\n      <li>Some of those books are freely available</li>\n      <li>For Math &amp; Science: check out Dover series books</li>\n      <li>When in doubt, follow the footnotes</li>\n    </ul>\n  </div>\n</details>\n\n<p>For me, the first major challenge here is to find a professor who speaks your language. There are several methods and interpretations of the mathematics of something like General Relativity and there are a dozen different angles from which one could tackle the problem. Do you want \"Physics for Engineers\" or \"Physics for Mathematicians\"? Perhaps you need to start earlier with, \"Introduction to Kinematics\". Watch the first lecture on a topic you think you know. Does the professor explain it well? The first lectures are usually review and ground-laying. If you're lost at the start, it won't bode well.</p>\n<h2>Passive Learning</h2>\n<p><em>Crash Course</em>, <em>PBS SpaceTime</em>, <em>3Blue1Brown</em>, <em>Numberphile</em>, and <em>Veritasium</em> are some of the best question-prompting educational resources ever developed. Even comedic series like <em>MapMen</em> and <em>Half as Interesting</em> have their place in this new world of distributed learning.</p>\n<p>Learning is about prompting the viewer, the reader, (you) to ask questions. To do that, you need to not only be familiar with the material, but you need to approach if from multiple angles, to identify gaps, and to ponder the implications. Speaking for myself, funny and wondrous videos help me do that.</p>\n<p>They're also a form of entertaining, passive learning retention. Repetition helps cement knowledge. Watching college lectures is difficult. It's time-consuming and it's taxing. If a pop-sci or pop-history video helps you retain the material, then it's helping.</p>\n<h2>The Literature</h2>\n<p>Once you've garnered enough knowledge to be dangerous, it's time to dive into The Literature: the published research books and white-papers from academic institutions and experts.</p>\n<p>This is perhaps the most challenging part. I recommend you get yourself a notebook, some highlighters, and a printer. I prefer to scribble notes on the paper, and to read away from screens.</p>\n<div class=\"image-right\" style=\"width: 300px;\">\n  <img src=\"/images/blog/research-papers.jpg\" style=\"max-width: 100%;\">\n  <center><small>The forest of all knowledge</small></center>\n</div>\n\n<p>Whatever you do, do not just go to Google Scholar and start searching. You'll be completely overwhelmed (or maybe that was just me). To effectively use the literature you need two things:</p>\n<ol>\n<li>The Canonical Terminology</li>\n<li>A Picture of the Current State of Research</li>\n</ol>\n<p>The biggest issue with traditional web search is that you need to know the right words to use if you want your search to be effective. LLMs like Claude are very useful here. However the most useful tool is going to be a kind of paper called a Review or Survey paper. Here's <a href=\"https://link.springer.com/article/10.12942/lrr-2014-4\">an example</a>.</p>\n<p>These papers try to give an updated picture of the field and its current dilemmas, questions, and methods. The good news is that review papers are often Open Access and so are available for free to the general public. This means that they can give you answers to both questions (1) and (2). Armed with that knowledge, you'll be more suited to searching through the random papers and books you find in the footnotes and Google Scholar searches.</p>\n<p>When it comes to the literature however, there are a few very important caveats to keep in mind: pre-prints (like those on arXiv.org) are not peer-reviewed and are for Advanced Researchers only. To read those you need to be able to sus out what's signal from noise. The same goes for really any paper outside of the reviews mentioned above. Individual papers are the results of one experiment (or one meta-study). They're less likely to be readable by anyone outside of the particular niche of study and, depending on the journal, can be of dubious quality. Finally, AI-written garbage papers (from so called Paper Mills) are flooding the literature at present). Remember, you're in the woods now. Tread carefully.</p>\n<h2>Personalized Critique</h2>\n<div class=\"image-right\" style=\"width: 350px;\">\n  <img src=\"/images/blog/claude-critique.png\" style=\"max-width: 100%;\">\n  <center><small>The quality of output depends on the quality of the input</small></center>\n</div>\n\n<p>I think a lot these days about the old C.G.P. Grey video: <a href=\"https://www.cgpgrey.com/blog/digital-aristotle-thoughts-on-the-future-of-education.html\">Digital Aristotle</a>.</p>\n<p>I've found great success in having AI grade my homework and help explain the solutions to specific problems because it's there that I've been able to constrain my questions and their likely solutions in ways that I can more often tell when it's misleading me.</p>\n<p>This is helped by my asking it to <em>critique</em> my ideas, not simply tell me what's true. Critique flips the script and forces me to confront the ideas head on. I think a lot in analogies and having the ability to \"gut check\" those analogies has been hugely helpful, even when the technicalities of the comparison are slightly off.</p>\n<p>The framing of critique helps avoid the implicit confirmation of your bad ideas. It also helps to avoid a key subtlety of AI tools: a machine designed to always provide a plausible-sounding answer has the side-effect of inadvertently supporting the impression that we know more about the world than we actually do.</p>\n<h2>Learning is about Trust</h2>\n<p>As a newcomer to a field, you have very little intuition about what is the \"correct\" course of action or whether the thing you're reading is correct. Learning requires trust in the teacher. Part of self-directed learning is deciding who and what sources to trust with your education. Not doing so, trusting blindly, will veer you into incorrect or fringe ideas very quickly and you won't even know it's happening. Aside from the technical details of a given subject, you need to learn how to be a good judge of your sources and to extend trust only to sources that deserve it.</p>\n<p>All of this stuff takes time and significant effort.</p>\n<p>Don't be discouraged by the difficulty or time-commitment. A major track at a college takes years of full-time study. It's ok if it takes you a long time to make progress, learning is hard.</p>"}, {"id": "https://brianschrader.com/archive/why-you-cant-write-that-book/", "url": "https://brianschrader.com/archive/why-you-cant-write-that-book/", "title": "Why You Can't Write That Book", "date_published": "2026-04-27T16:37:00", "tags": ["essay"], "author": {"name": "Brian Schrader"}, "content_html": "<blockquote>\n<p>I could do that, I just need more time.</p>\n</blockquote>\n<p>In life we are constantly wishing we had more of something: time, money, friends, energy, etc., and we develop plans to try and meet these goals. We alter our diets, our schedules, we start exercising or reading more. Often times these changes result in significant improvements to our lives. Yet, we never have the energy, the time, or the money that we want. Even when we do succeed in making changes, something else comes up and blocks further progress.</p>\n<div class=\"image-right\" style=\"width: 300px;\">\n  <img src=\"/images/blog/book-blink.gif\" style=\"max-width: 100%;\">\n  <center><small>The eternal curse.</small></center>\n</div>\n\n<p>Let's say you want to write a book. You change your schedule to allow for dedicated writing time. However during that time, you're unmotivated. You diet and exercise and read interesting books, trying to kindle the enthusiasm you know you have, but now you have no energy left to write. You have the time, but only to spend staring at a blank page.</p>\n<p>Life is a constant balance of particular factors and it takes considerable skill to strike any balance at all for any length of time.</p>\n<p>Permit me, if you will, to remind you of your high-school Chemistry class. You probably learned about the concept of a limiting reagent.</p>\n<blockquote>\n<p>The limiting reagent (or limiting reactant or limiting agent) in a chemical reaction is a reactant that is totally consumed when the chemical reaction is completed.<br >\n- <a href=\"https://en.wikipedia.org/wiki/Limiting_reagent\">Wikipedia</a></p>\n</blockquote>\n<p>Let's say you have a reaction between two compounds (for simplicity let's call them A and B). It takes 2 units of A + 3 units of B to make 1 unit of C.</p>\n<center>2A + 3B = 1C</center>\n\n<p>Now let's say you have 10lbs. of A and 12lbs. of B. How much C can you make and what ingredient will you run out of first? That ingredient is your limiting reagent (answer: it's B).</p>\n<p>However, this formulation assumes that the amounts of A and B are constant over time. For example, let's say that we know that we need more of B and want to increase the amount of it we have. We go to the store and get 20lbs. of it! However we now find that, flush with one ingredient, we quickly run out of another. We get less of C than we planned.</p>\n<p>Perhaps a cooking example would have been better here (cups of flour vs number of eggs), but I digress.</p>\n<p><div class=\"midroll newsletter-callout\">\n  <div class=\"callout text-center\">\n    <div id=\"prompt\">\n      <noscript>\n        Enjoying this post?\n      </noscript>\n    </div>\n    <a\n      href=\"https://sendfox.com/brianschrader/\"\n      title=\"Subscribe to the newsletter\"\n      class=\"subscribe\"\n      target=\"_blank\"\n    >\n      ✉️&nbsp;Subscribe to the Newsletter!\n    </a>\n  </div>\n</div>\n<script>\n(() => {\n  const prompts = [\n    'Enjoying this post?',\n    'Like what you see?',\n    'Cough cough...',\n    'Posts like this, in your inbox!',\n    'Consider subscribing!',\n    'Support this blog!',\n    'Really appreciate it if you...'\n  ];\n  const el = document.getElementById('prompt');\n  el.textContent = prompts[Math.floor(Math.random(0) * prompts.length)];\n})();\n</script></p>\n<h2>Limits Abound</h2>\n<p>We see examples of this phenomenon everywhere in our society and lives. For a completely different example, consider the current phenomenon of AI coding agents on the productivity of software companies. Writing code used to be slow, now it is significantly faster. However, humans still need to understand, design, and approve that code. A 10x speed-up in the writing of code has not translated to a 10x speed-up in productivity overall because something else in the pipeline is too slow to keep up with this new glut of AI-generated code. We've found a limiting reagent: system design and code approval.</p>\n<p>The Economist <a href=\"https://en.wikiquote.org/wiki/John_Maynard_Keynes#:~:text=Anything%20we%20can%20actually%20do%20we%20can%20afford.\">John Maynard-Keynes once said</a>, \"We can afford whatever we can do.\" By this he meant that if we want to fund the building of more schools we can, assuming we have enough construction workers, lumber, etc. I've often heard of this quote being used to critique plans for single-payer healthcare in America. We can certainly afford to offer healthcare to all Americans. Most American's have health insurance already, just through a private carrier. However, there is considerable pressure on people not to use their healthcare because it's expensive.</p>\n<script src=\"/other-projects/plotFns.js\"></script>\n<div class=\"image-right\" style=\"width: 300px;\">\n  <canvas id=\"plots\"></canvas>\n  <center><small>A marked phase-change, where the limiting reagent changes.</small></center>\n</div>\n<script>\n  plotFns({ showIntersections: true , labels: ['Insured Patients', 'Doctors Available'], xMin: 0, xMax: 5, yMin: 0, yMax: 5, H: 300, W: 300, plotLabels: false, showPlayButton: false}, 'plots', (x, t) => 2*x-2, (x, t) => 0.25*x+2);\n</script>\n\n<p>If we make it cheaper (by subsidizing care) then we will run into another problem. We physically don't have enough doctors to see all those people. We cannot simply pay doctors more because, no matter how many times you double a person's salary, they cannot double their patient count. We've found another limiting reagent.</p>\n<p>The lesson in all this is that no matter how much you push on one factor, work to increase its capacity, there are hidden walls, hidden assumptions, that will become relevant only once the limit in your current focus is removed. This is  the curse of supposed panacea. A thing which looks to solve a problem \"for good\" does indeed remove one particular problem, only to reveal that it was concealing other problems in its shadow. I've heard people use the refrain that \"success hides problems\", but problems also hide problems.</p>\n<p>We can make progress, of course, and we often do. But the universe has a cruel sense of humor. Sometimes our solutions can summon problems of their own. Geopolitics is full of such scenarios. Countries look to electrify, to move away from the dangerous and fragile world of fossil fuels, only to become reliant on a <em>cartel nuovo</em> of battery manufacturers.</p>\n<p>As humans, we struggle to see beyond the first derivative. We can predict the response to our actions, but not the response to that response. As such, there will always be limiting reagents, always another reason why you're too tired to write that novel of yours.</p>"}, {"id": "https://brianschrader.com/archive/mailing-things-is-fun/", "url": "https://brianschrader.com/archive/mailing-things-is-fun/", "title": "Mailing things is Fun", "date_published": "2026-04-13T16:06:00", "tags": ["personal", "essay", "writing"], "author": {"name": "Brian Schrader"}, "content_html": "<p>Sometimes I can't tell if I'm discovering a cool new hobby, or just getting old. Regardless, today I come to you with a tale of a little endeavor of mine.</p>\n<p>In early 2020, a family member took a job far from home and, because of the nature of the work, would therefore be out of cell service for large swaths of time. As a gag, we decided to communicate via long-form letters over email as well as the occasional postcard. Later that year, in the grips of a pandemic, my D&amp;D group went virtual, but that came with several drawbacks&mdash;including the sudden lack of the ability to pawn chewing gum off of me during games.<sup>1</sup> So, before our first virtual game, I mailed every one a pack of gum, to be opened on the call.</p>\n<p>It was fun, a cheap little laugh. However in the time since, my occasional appreciation for the mail has become nothing short of a deep and profound predilection.</p>\n<h2>You Can Just Mail Things</h2>\n<p>Receiving postcards is fun. Mailing them is even more so.</p>\n<p>I figure most people out there have sent a postcard to a friend or family member when they're on vacation (or at least the occasional holiday card). But remember, you need no special occasion to use the mail. <em>You can just mail things</em>. Go somewhere fun, like maybe an art museum? You know, they have postcards there. Does a work of art remind you of an inside joke with an old friend? Send them the postcard of it. It's $1 (+stamps). In a world of free and ubiquitous instant messenger apps, a card in the mail has a truly special significance.</p>\n<div class=\"image-center\">\n  <img src=\"/images/blog/desk-cards.jpeg\" style=\"max-width: 100%;\">\n  <center><small>A few of the cards and letters I've received (or have still waiting in my stockpile) along with a notecard of how much postage is for domestic and international letters.</small></center>\n</div>\n\n<p>Personally, I like to collect postcards from cool places and send them out to friends I haven't seen in a while, or who live far away. I could text them, and I often do, but it's never as special. What's more, if you receive a postcard from a friend, mail one to them in return! They'll smile just as much as you did.</p>\n<p>If you get hooked, don't worry. There's a plenty-deep-enough rabbit hole to fall down. In that case, grab a pen and some nice paper. Write a letter. It's hard work, and will make you appreciate the ease and rapidity of text messaging. But a letter is more than a way to communicate. It's an art form.</p>\n<div class=\"image-right\" style=\"width: 300px;\">\n  <img src=\"/images/blog/template-letter.jpeg\" style=\"max-width: 100%;\">\n  <center><small>I <i>love</i> writing letters.</small></center>\n</div>\n\n<p>Read any old letters. <a href=\"https://news.lettersofnote.com/p/i-loathe-i-abhor-the-sea-and-all\">Try Charles Darwin's</a>. They're a mix of both personal correspondence and artful prose. A letter isn't a text; it isn't mechanical like that. Today we talk so much, yet we convey so little about ourselves with those words.</p>\n<p>My advice to folks out there is this: write, <a href=\"/archive/blogging-writing-musing-and-thinking/\">to yourself</a> or in letters to others. When you do so, try to be eloquent. Writing helps you practice thinking and doing so in lofty prose improves your vocabulary and your eloquence. Make a pen-pal. Write to them genuinely, honestly. Work to shed the carapace of cynicism and irony that encases each of us these days.</p>\n<p>It's an antiquarian practice, yes. It's slow and difficult and time-consuming. But it's also a lot of fun to give and to receive.</p>\n<div class=\"footnote\">\n<sup>1</sup> I am notorious for having a pack of gum on me.<br>\n</div>"}]}