Radimentary

"Everything can be made radically elementary." ~Steven Rudich

There are Symbols for This

In his first proof-based mathematics course, a student asks, “Is the identity element in a group unique? It’s not one of the axioms.”

I respond, “It’s not one of the axioms, but you can prove it from them. Try.”

As far as I can tell, what starts happening in the student’s mind is something along the lines of figuring out why having multiple identities would not be useful, or persuading himself that the word “identity” connotes uniqueness already, or being mystified by how even such a thing could be proved.

What is definitely NOT happening is a search for a symbolic proof such as e = ef = f.


I’ve been playing a game called Slay The Spire, the lovechild of FTL: Faster than Light and Hearthstone’s Arena Mode. The goal is to win a series of randomly-generated card-based combats, where the reward of each combat is a choice of one of three cards to add to your deck.

The random and single-player nature of the game allows the designers to print some truly preposterous cards, such as the card “Seek: 0 mana, draw two cards of your choice from your deck.” Note that one of those cards can be Seek. Note that there is no limit to the number of copies of a given card you can have. Anyway, the absurdity of Seek is a story for another post.

I had the following series of thoughts the other day after yet another aborted run.

I wish there was a tier list for Slay the Spire cards.

I bet there is a tier list online.

Maybe I can make a tier list.

I spent the next couple hours copy pasting data into a spreadsheet and making up fake conversion rates from every card effect to damage numbers: “1 block is worth about 1.2 damage, 1 mana is worth about 6 damage, card draw about 3.” After all, if it’s worth doing, it’s worth doing with made-up numbers.

The resulting sheet was extraordinarily enlightening. I learned that several common cards are truly overpowered. I learned that a number of the flashy rare cards are truly abysmal – at least two are worth negative points in my system. This exercise didn’t feel like making magic math and receiving new wisdom from on high. It felt more like synthesizing and explicitly stating knowledge my gut already knew.


The point of these two anecdotes, insofar as anecdotes have points (which they shouldn’t), is a sort of article of faith in the power of articulation, the ability to represent one’s fuzzy feelings as symbols: words or numbers.

I used to have an instinct that putting words or numbers to fuzzy intuitions would distort and flatten them. I think this instinct is essentially wrong, or at least incomplete. When one’s ideas are put forth onto the page, something is lost, but the clarity created in the process more than makes up for it.

So whatever illegible intuition you are currently gripped by, remember that there are symbols for it too.

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Timothy Chu Origins Chapter 1

They remember his ideas, and how they saved the world.
But I remember the man, and how he saved me.

A great deal of ink (though in my estimation as yet too little) has by now been spilled about the life and times of Timothy Chu; among the more readable volumes on the legend are The Age of Tim and Inadequate in the Presence of Timothy. Reading the exploits of Timothy in his prime, it might be hard to believe that he too once knew loss, suffering, and human weakness.

But few of his adoring fans and biographers have the privilege of knowing Tim as a friend, as I do. With this unique privilege, I aim to tell the hidden story about the young man who became the legend, a young man who – while already extraordinary – lived a comparatively modest and down-to-earth life.

Chapter 1: From Steppes to Steps

It is tradition to seek wisdom at the Shaolin Temple as the final step towards manhood. At the age of fourteen, Timothy Chu is already a man, but as a man he knows the importance of tradition.

Tim climbs the steps to the temple four at a time.

Three monks, clad in plain grey-blue habits, sweep the steps up Shaoshi mountain, covertly guarding the only path to the temple.

Tim approaches the first monk, a hunchbacked and scarred man who presses his hands together in greetings.

“Amituofo, traveller. What business have you with Shaolin?”

Tim’s voice is usually unbelievably deep, but he softens it out of respect, “I have come to learn the Way from the Master of the temple.”

“I am Qiang, thirteenth seat of the fifty-third generation. To pass me you must demonstrate strength of will and body.”

Monk Qiang extends a wiry hand in the style of a Western handshake. Tim grips it automatically. Qiang tests Tim’s grip, hunching forward and pressing the force of his entire body into the handshake. The stone steps under Tim’s feet shudder and crack under the enormous force, but Tim himself seems immovable, keeping his pleasant smile and easy posture.

After progressively increasing the pressure for nearly a minute, Qiang gives way before the entire mountainside collapses under his legendary strength. He bows welcome to Tim and shifts aside to let him pass, letting go of his hand.

Tim catches the monk’s hand before it escapes.

“It’s my turn, now.”

Qiang feels an incredible pressure travel through his body from the center of his palm. The force ripples through his body, knocking him to his knees and loudly cracking the joints of his body from his wiry wrinkled fingers to his crooked neck, through his hunched back, all the way down to his bowed legs.

Dismayed and angered at the sudden assault, Qiang pushes himself up to retaliate –

– only to find that his spine now stands upright, his bowed legs straight and graceful, and his once-wrinkled skin stretches taught as fresh canvas across his bones. Rolling his neck in wonder, Qiang looks a whole twenty years younger. He opens his mouth in shock but no words come out, only an expression of silent gratitude.


A thousand feet further, the second monk, a placid young man, presses his hands together to greet Tim.

“Amituofo, commoner. I am Yong, eighth seat of the fifty-fourth generation. To pass, you must demonstrate courage beyond your years.”

Expressionless, Monk Yong produces a thin white rope. He ties a loop in one end and throws it high into the air to hook onto a branch of a sturdy oak on the outside of the mountain path. The other end, he ties around a large boulder. The rope stretches taut, cutting a thin white line through the air from the base of the boulder to a height of almost twenty feet in the trees.

Yong tiptoes onto the tightrope, somehow gripping the silky surface of the rope with the edges of his cloth shoes. Step by step, he ascends to the highest point. Despite the gentle breeze, it seems as if Yong is one body with the rope, every muscle and sinew pulled taut in perfect harmony. Only a thin veneer of sweat belies his exertion.

It’s an eternity before he reaches the highest point. With a flourish, he swings around the rope and slides down smoothly.

“Show me your courage, commoner.”

Tim rolls and stretches his broad shoulders to prepare for the challenge.

“I learned this move on the streets of Ulan Bataar. I call it the Team-Building Exercise.”

He jumps onto the boulder around which the rope is tied and turns so that his back faces the white line in the air. He closes his eyes and falls backwards – to be caught by the rope. Lying straight against it, he kicks off the boulder with a single foot. The power of the kick is such that his body shoots up the length of the rope, stopping just short of hitting his head on wood. Tim’s balance is such that his body seems as securely attached to the white line as a ski lift is to its supporting cable. For a single moment at the peak of his ascent, he lies suspended in the air, as if supported by an invisible hammock.

Tim slides back down the line gracefully.

Master Yong bows, “You have shown courage and grace.”

“No, Master Yong. That was merely skill. This is courage.”

Yong’s eyes are suddenly drawn to the lines of Tim’s face, which soften dramatically. A myriad of emotions pour forth through these expressive lines, painting a picture of a grand fourteen years of life.

Adventure. Brotherhood. Heartbreak. Anguish.

The joy of mathematics.

The passion of StarCraft.

Pride and the fall.

All these and more are written plain as day on Timothy Chu’s cherubic cheeks.

Reverent tears spring to Yong’s normally emotionless eyes, and he bows deeply, pressing his hands together, “Amituofo, brother. Truly, vulnerability is the greatest form of courage. May you find what you are looking for.”


On the last step before the imposing gate of Shaolin temple sits an ancient monk holding a book. His eyes are cloudy and unseeing, and yet he seems to be entranced by the book, reading its passages aloud.

“Who goes there?” The blind monk rises to his feet at the sound of Tim’s footsteps.

“Dear elder, I am Timothy Chu. I come to seek wisdom at this venerable temple. May I pass through the gate?”

The blind monk fumbles towards Tim and runs his ancient hands across the young man’s visage.

“Amituofo. I am Zhi, third seat of the fifty-second generation. To seek wisdom, you must first have knowledge. Have you walked a thousand miles and read ten thousand books?”

Tim remains silent, lost in thought. After a time, he opens his wallet and pulls out an sleek, understated black card embossed with an inscrutable pattern, which he hands to Zhi.

“I may not have walked a thousand miles, but I have flown a thousand million,” 

The blind monk accepts the card and runs his hands over its engraved surface. His bushy greying eyebrows spring up in surprise.

“This … this is … it seems to be a Untied Airlines Global Premier membership card! But this level … I have never heard of. Is there truly a level above Gold Elite?”

Tim lets out a deep, warm laugh at the old man’s naiveté.

“Above Untied Gold Elite, there is a secret tier called Untied Platinum known only to Gold Elite members and above, which requires ten million miles to qualify. Above Platinum, there is another secret tier called Untied Diamond known only to Platinum members, which requires a hundred million miles to qualify.”

“So this is the Untied Diamond tier?”

“No. Above Diamond, there is yet another secret tier called Untied Black Diamond, which requires a thousand million miles to qualify. The existence of this last and highest level is known only to Black Diamond members, of whom there is only one.”

The monk sits down, as if shocked to his core. He whispers a mantra to calm his racing heart, “Beyond mountains, there are yet higher mountains. Above people, there are yet greater people. For such a young man as yourself to have ascended such heights! Tell me, Timothy Chu. Why does the Untied Black Diamond level exist if you are the only member?”

Tim sits down next to monk Zhi and puts an easy-going arm around his shoulder.

“Elder Zhi, if an MIT student puts on an MIT shirt in the morning, what is he after?”

After only a moment’s thought, monk Zhi replies, “He is signalling to the world, of course.”

“And if an MIT student puts on a Course 18 shirt, what is he after?”

“To signal to other MIT students.”

“And if instead he wears a Math Olympiad shirt?”

“To signal to other Course 18’s!”

Tim nods in approval, “As it is with MIT, so it is with Untied Premier levels. Gold Elite exists to impress the outside world. Platinum exists to impress Gold Elite flyers. Diamond exists to impress Platinum flyers. But if Black Diamond is only known of by Black Diamond members …”

Monk Zhi waits for Timothy to finish the train of thought, but Tim falls silent to allow Zhi to connect the dots.

Finally, after a long wait, Zhi finishes the sentence.

“… Black Diamond exists to impress Timothy Chu.”

And in that moment, monk Zhi was enlightened.


After many tears of jubilation and revelation, Zhi finally calms down from his cathartic moment of understanding. His left eye, once milky white and sightless, is now a deep smoky brown. With his vision partially returned to him, he grasps Tim in a deep hug.

“Thank you for returning my vision to me, young man. But I cannot yet let you pass into the temple. You have indeed traveled far and wide, but have you read ten thousand works of literature?”

Again Tim falls silent, lost in thought. After a time, he pulls out his laptop and opens a browser.

“I may not have read ten thousand works of literature, but I have written ten million fanfiction!”

Squinting with his single seeing eye, monk Zhi scans the titles that flit past:

… Alman the All-Man, The First Age of Alman, The Second Age of Alman, The Second-to-Last Age of Alman, Balman: Alman Next Generations …

… Trotsky and BackHo, Churchill and BackHo, Genghis and BackHo, Son Chan Woong and BackHo …

… Romance of the Red Azalea, Waiting for the Red Azalea, Making Tea with Red Azalea, The Red Azalea Under Floor Pi …

Decision Theory for Damien, Life without Damien, Life with too little Damien, Damien and the Nameless Noodle Dish, Damien Damien Damien …

Zhi clicks the link to Damien Damien Damien: An Eternal Golden Braid and begins reading with his newly granted vision.

After the first sentence, he begins to giggle. Two pages in, elder Zhi is laughing harder than he’s ever laughed in his entire life, shaking his head while burying it in his arms. In this state, he continues to read, finishing all seven hundred odd pages in the afternoon. The sun dips below the horizon, but Tim waits for him without complaint.

Finally, monk Zhi sets it aside, still laughing.

“This is the worst thing I’ve ever read! Absolutely tasteless and low-brow! Such a thing hardly counts as literature, my friend.”

“With respect, elder Zhi, if you had to choose between writing literature and writing that makes human beings laugh and cry and love life, what would you choose?”

At those words, monk Zhi was enlightened and sight returned to his right eye.

It was the first time in recorded history that one man achieved enlightenment twice in the same day.

HPMoE 3

HPMOE3

ROT13, you know the drill.

HPMoE 2

HPMOE2

As usual, post solutions in ROT13.

Harry Potter and the Method of Entropy

I did some Aversion Factoring and found that my main aversion to writing math is the terrible LaTeX support on WordPress. For now, I’ll try writing things up offline and posting PDFs.

HPMoE is a sequence on the entropy method in combinatorics. It should be fun to think about for anyone interested in information theory and probability as well.

HPMoE1

Please post solutions to the exercises in ROT13.

Hammertime Postmortem

Intro.

A bit less than two months ago, I set out to write about instrumental rationality every day for thirty days. In this post, I will quickly evaluate how well I felt I did along each of my four stated objectives. I will simultaneously evaluate all the Hammertime techniques and ideas by their effectiveness to my life.

This period was my deadline to 80/20 instrumental rationality. Thus, I do not plan to blog any more about it for a while. However, I do want to express my strong intent to write a fourth cycle of Hammertime in the early months of 2019, if only to check my long-term progress.

1. Hammertime Report Card

I will grade myself on the four goals I stated in the first Intermission thread:

My reasons for writing this sequence were, in clear order of importance: (a) to practice writing, (b) to review CFAR techniques for my own benefit, (c) to entertain, and (d) to teach instrumental rationality.

On reflection, these were equally important goals and I only listed them in that relative order because I believed the later ones would be harder to achieve. I will grade everything out of 100, counting up from zero. Only the relative sizes of the numbers mean anything.

Writing Practice: 90/100

This worked out quite well. I produce content about three times faster than I did at the beginning of Hammertime, with perhaps the slightest decrease in quality. Speed I value as much as strength, so this was an amazing improvement. There are things like organization and style I should have played around with more, and a Yoda Timer of copy-editing after each post would have benefited the writing quality greatly.

Personal CFAR Review: 95/100

Through this process I was forced to reflect on, try out, and push the boundaries of almost every single technique in the manual. Other than a handful of techniques that don’t click with me at all, this two-month period has been the perfect amount of time to throw at dedicated instrumental rationality practice. The long-term value of the learning I did at CFAR at least tripled because I did this.

Entertainment: 65/100

Hit or miss. Handful of posts that were really fun to write, and still look fun to read. I noticed a number of clear limitations in my writing toolkit that don’t seem to be fixable in a day or two (but might be if I actually tried). Despite my best efforts, I’m still not Eliezer or Scott.

What am I missing? I plan to experiment more with dialogue, which I’m awful at writing but seems to make some of Eliezer’s and Scott’s funniest stuff. Also, detailed and entertaining expositions of science are sorely missing in my writing – this seems like a gold mine as well.

Teach Instrumental Rationality: 50/100

Not sure this sequence is any better as pedagogical material than just the CFAR Handbook, which is a moderately dry reference manual. Perhaps that’s good enough. A handful of people seemed to benefit quite a bit, but my sense is that even among the people who read every post, few did any of the exercises or got any mileage out of this sequence over learning what the concept handles are. In the end, I always made decisions in favor of “write what’s interesting for me” rather than “write what I think would be most useful to the reader.”

Perhaps an interested reader would like to take a couple hours and reassemble the most useful parts of Hammertime into a cleaner subsequence. As a resource on instrumental rationality instruction at most half of the posts in Hammertime are of high value.

Overall: 75/100

Very impressed with myself that I followed through with this project with only minor delays. Everything went approximately as well as could be Outside-View expected.

My main takeaway is to continue throwing myself headlong into medium-term projects without thinking too much about them, and trust my instincts. It’s not obvious that more planning or structure would have helped in net – it may even have soured the whole Hammertime project and caused me not to finish at all.

2. Hammers by Power Level

I will go through the core techniques I covered in Hammertime, and grade them each based on effectiveness in my own life.

I’ll sort them into three tiers of awesome. Note that the techniques in Hammertime were already pre-selected from a larger pool of techniques based on how good they seemed to me just after CFAR.

S/A Tier

Focusing: 100/100

Doesn’t always work, but when it does … life-changing insights. Probably had three or four over the course of Hammertime. Would recommend.

Yoda Timers: 95/100

Timers and deadlines really up my game. I think I’ve always shied away from using them because “contest math,” “speed,” and “competitiveness” became low-status after high school, but man am I built for this. Sometimes I think that if grad school was structured as a serious of olympiads except with open problems, I would get a lot more work done.

Design: 90/100

Amazingly underrated technique. Amortizing everything, allowing myself to remove trivial inconveniences, spending time making my physical space better. Substantially improved my baseline quality of life: sleep quality, overall comfort, aesthetics. If I gave up actively using instrumental rationality right now, the effects of the Design choices I made in the last two months would still last for years.

B/C Tier

Bug Hunt: 80/100

Very useful to practice every so often. Ups your noticing game quite a bit for a long time.

CoZE: 80/100

Another solid technique. Gave me the tools to push through many minor unendorsed aversions and try things instinctively. Doesn’t work as well by itself on the bigger aversions – in my experience, these require the aid of Focusing and Focusing is the one doing the work.

Silence: 80/100

I feel as if combating the tendrils of nihilism in everyday life is one of the biggest problems to solve. Silence was my first attempt at framing the problem and offering a partial solution. As always, people need to allow themselves to babble more.

TDT for Humans: 75/100

Important principle that finally allowed me to understand the appeal and utility of virtue ethics/deontology. Requires more iteration and work to make it actionable.

Friendship: 75/100

Noticing the value of and setting up long-term iterated conversations with friends was extremely valuable. Experimenting with this also led me into a handful of awkward social situations and unproductive conversations. I’ve updated towards there existing even fewer people than I thought with whom I can have interesting conversations on a regular basis.

D/F Tier

Murphyjitsu: 65/100

It feels as painful and difficult to practice as reading ability in Go – life is too chaotic. For now, it’s only useful on the five-second level: what are the obvious things that will go wrong? Perhaps after I collect more data about common failure modes Murphyjitsu will be more useful. As of now, I feel woefully uncalibrated.

On the plus side, did inspire my longest work of fiction to date.

TAPs: 60/100

Weird and unnatural to practice. Handful of useful things I thought I installed rapidly faded with time. TAPs seem to last about a week for me without some other regular reinforcement mechanism.

Internal Double Crux: 50/100

Too many steps. The only real value seems to be as a method for generating Focusing targets. This is pretty valuable, but still.

Aversion/Goal Factoring: 30/100

Tried a few times, didn’t stick. Much weaker than Focusing. Usually, what I need to do is “find out my true main motive and aversion towards the thing,” and once that is done the path forward becomes clear.

Hammertime Final Exam

This is part 30 of 30 in the Hammertime Sequence. Click here for the intro.

One of the overarching themes from CFAR, related to The Strategic Level, is that what you learn at CFAR is not a specific technique or set of techniques, but the cognitive strategy that produced those techniques. It follows that if I learned the right lessons from CFAR, then I would be able to produce qualitatively similar – if not as well empirically tested – new principles and approaches to instrumental rationality.

After CFAR, I wanted to design a test to see if I had learned the right lessons. Hammertime was that sort of test for me. Now here’s that same test for you.

The Final Exam

I will give three essay prompts and three difficulty levels. Original ideas would be great, but shining a new light on old hammers is also welcome!

Prompts

  1. Design a instrumental rationality technique.
  2. Introduce a rationality principle or framework.
  3. Describe a cognitive defect, bias, or blindspot.

Difficulty Levels

Bronze Mace mode. Write one essay on one of the topics above.
Steel Cudgel of the Lion mode. Write two of three.
Vorpal Dragonscale Sledgehammer of the Whale mode. Write all three. For each essay, give yourself five minutes to brainstorm and five minutes to write.

Here are my answers.

1. Cooperate First

There’s an old story about a famous painter of the Realist school who spent a whole year of his training painting still lives of eggs. Each day, he would draw a single egg over and over. He must have produced thousands of sketches and paintings of eggs. His teacher knew exactly how important fundamentals are.

This same motif is deeply embedded in stories all over the world:

Return to fundamentals. Practice your fundamentals.

The iterated prisoner’s dilemma is one of the fundamental lessons of rationality. The world is more like a number of iterated prisoner’s dilemmas than you’d think. Human beings are more like tit-for-tat players than you’d think. It follows:

Cooperate First!

The first move you make in any interaction with a new acquaintance should be a cooperate, even if you expect them to defect. Perhaps even if you observe them defecting already.

Here’s a lesson I learned from meditating on the maxim Cooperate First:

Cooperating First feels like accepting an unfair game from the inside. There will be many situations in life where things are framed in a slightly but noticeably unfair way towards you initially. Err on the side of accepting these games anyway!

2. Below the Object Level

One of my main complaints about rationalists (myself included) is our tendency to escalate to the meta-level too often. For example, in any given discussion, arguments over general discussion norms get much more heated and lively than any discussion of the underlying subject matter. We need to spend more time at the object level, touching reality, making experiments, testing our hypotheses.

The move I use to combat the tendency to escalate meta, I call looking below the object level.

Looking below the object level is like the move HPMOR_Harry does to achieve partial transfiguration: continually upping the magnification on your mental microscope to actually stare at the detail in reality. Reality is so exorbitantly detailed it’s overwhelming to take it all in. Try.

Look at the folds in your clothes, the way light and shadow play off each other. The way threads interweave. Pinch the cloth and watch the creases reorganize under your fingers.

Now reflect on this fact: falling water is attracted to both positive and negative charges.

What.

There’s so much going on under what we think of as the object level.

3. Pre-Excuses

Pre-hindsight is a version of Murphyjitsu where you query your mind for what you will learn from an action in hindsight. Pre-excuses are an unproductive cousin that often derail my work.

As a serial procrastinator, I notice a fairly regular pattern of thinking that appears the couple days before I have to meet a professor, and especially before meeting my thesis adviser. My mind is already spinning excuses on overdrive. Here’s what my mind sounds like a full day before I have to meet my adviser, when I think about the meeting:

Sorry, this paper took longer than I expected to read.

Sorry, I was busy from other classes, so I didn’t do as much paper-writing as I’d planned to.

Sorry, I got sidetracked by this research problem, so I didn’t finish the homework.

That’s right, I’m having these thoughts about how to apologize for not doing work even though I still have plenty of time to do the work. Even worse, I have these pre-excuse thoughts regularly even if I’ve done the work expected of me – it feels something like cushioning the fall in case it turns out I did it poorly.

And they’re usually not even good excuses.