Moontower #206


Wednesday’s He Disrespected Me post got a lot of engagement. Not unsurprising. Divorce, culture, masculinity stuff. I shared that stuff because it was taking up some mind real estate but writing about it helps me flush it. Diagnosing and understanding that type of stuff has an irresistible allure but I think it’s also kind of corrosive — you probably aren’t going to find useful conclusions at the end of what is nothing-more-than-armchair exploration (on our part, not the scholars). I indulge it when it internal kettle starts steaming, but once I release the pressure, I want to go right back to focusing on more nutritious material.

[I also tend to avoid people whose personality is basically “sharing opinions on the latest culture war item”. Major NPC energy.

Egh, I take that back — NPC is very literally a dehumanizing insult — my wife just learned the term this week so I was just using it in a sentence in case she reads this. But really, I do avoid those people. They like to think of themselves as independent thinkers and somehow don’t quite notice the irony.]

Back to inspiration and learning.

Grant Sanderson is the mathematician and YouTuber behind the 3blue1brown channel about discovery and creativity in math. The about from his webpage:

My name is Grant Sanderson. These videos, and the animation engine behind them, began as side projects as I was wrapping up my time studying math and computer science at Stanford.

From there, I was fortunate enough to start forging a less traditional path into math outreach thanks to Khan Academy’s talent search, which led me to make videos and write articles about multivariable calculus and a few other miscellaneous topics for them until the end of 2016. Since then, my main focus has been on 3b1b.

The channel is amazing but he’s also one of my favorite people to hear interviewed. I recommend 2 podcasts.

🎙️Richard Rusczyk interviews Grant Sanderson (AoPS)

Rusczyk is the founder of Art of Problem Solving, a math education portal I’ve discussed before (my 5th grader takes Pre-Algebra online with them). I actually know of AoPS because its founding is connected to Rusczyk’s Math Olympian friend Sandor Lehoczky who is a top executive at Jane Street (he left SIG’s pioneering index desk to be an early employee at JS shortly after I joined SIG). In 1994, Rusczyk’ and Lehoczky self-published the seminal two-volume set The Art of Problem Solving, books that continue to have a revolutionary impact on math preparation for ambitious high school students.

🎙️Grant Sanderson on Dwarkesh Patel Lunar Society podcast (Moontower notes)

My full notes are linked above. Here are some of the excerpts I emphasized:


On the future of education 

[key ideas: reducing distance to students, educator’s role is not just explanation but more importantly “bring out knowledge” not put it in, the non-linear influence of a teacher on a student’s future, and the chaotic concept of “sensitivity to initial conditions”]

Grant: I think it’s not a bad thing for more educators who are good at what they’re doing to put their stuff online for sure. I highly encourage that even if it’s as simple as getting someone to put a camera in the back of the classroom. I don’t think it would be a good idea to get those people out of the classroom.

If anything I think one of the best things that I could do for my career would be to put myself into more classrooms…

One of the most valuable things that you can have if you’re trying to explain stuff online is a sense of empathy for what possible viewers that are out there. The more distance that you put between yourself and them in terms of life circumstances…

The other thing I might disagree with is the idea that the reach is lower. Yes, it’s a smaller number of people but you’re with them for much, much more time and you actually have the chance of influencing their trajectory through a social connection in a way that you just don’t over Youtube.

You’re using the word education in a way that I would maybe sub out for the word explanation…You want explanations to be online but the word education derives from the same root as the word educe, to bring out, and I really like that as a bit of etymology because it reminds you that the job of an educator is not to take their knowledge and shove it into the heads of someone else the job is to bring it out.

when people talk about online education as being valuable or revolutionary or anything like that, there’s a part of me that sort of rolls my eyes because it just doesn’t get at the truth that online explanations have nothing to do with all of that important stuff that’s actually happening

Putting in work with calculations

Grant: I think where a lot of self-learners shoot themselves in the foot is by skipping calculations by thinking that that’s incidental to the core understanding. But actually, I do think you build a lot of intuition just by putting in the reps of certain calculations. Some of them may turn out not to be all that important and in that case, so be it, but sometimes that’s what maybe shapes your sense of where the substance of a result really came from.

The “failure to disrupt”

[key ideas: learning is not bottlenecked by good explanations but by social incentives. I found this deeply resonant. Reading between the lines — we are aspirational and good at copying others or trying to impress them, so if we know that we should provide good models for learners to emulate — not to make any equivalence between what I try to do with Moontower and Grant but you can probably see why I’m such a fan of this guy]

Grant: I would reemphasize that what’s probably most important to getting people to actually learn something is not the explanation…but instead, it’s going to be the social factors. Are the five best friends you have also interested in this stuff and do they tend to push you up or they tend to pull you down when it comes to learning more things? Or do you have a reason to? There’s a job that you want to get or a domain that you want to enter where you just have to understand something or is there a personal project that you’re doing?

The existence of compelling personal projects and encouraging friend groups probably does way way more than the average quality of explanation online ever could because once you get someone motivated, they’re just they’re going to learn it and it maybe makes it a more fluid process if there’s good explanations versus bad ones and it keeps you from having some people drop out of that process,which is important.

There’s a lot more in my excerpts and of course the whole interview is worth a listen.

Money Angle

I added another post to my ongoing Money Wiki. A reminder that the wiki, found at, is a Moontower guide to personal investing. It’s broken into 3 main units:

  1. The Nature of Investing
  2. Risk Absorption
  3. Implementation

The new post:

🔗2 Sides Of Compounding (permalink)

(These posts are intended to be concise so this is the full body of it ⬇️)


A Famous Riddle

The lily pad doubles in size every day and after 365 days it completely covers the pond. On what day does the lily pad cover half the pond?


The 364th day

Compound Growth

Our minds struggle with geometric growth (ie x²) and exponential growth (ie 2ˣ). We extrapolate and interpolate linearly but the key observation is that these processes are multiplicative, not additive.

This is the same process that governs compounding investment returns. When you invest, it’s typical that you stay invested or re-invest. If you start with $100,000 and earn 10%, you now have $110,000 to reinvest.

The tricky bit about compounding is appreciating how small changes in the rate of growth have a disproportionate impact on final wealth.

If you start investing at age 30 with $100k, and compound growth at 8% per year instead of 7%, you will have 45% more wealth by age 70.

notion image

This is a cold splash of water when you consider how many forces conspire to knock at least 1-2% off your investment returns:

  • Financial advisory AUM fees
  • Mutual fund expense ratios
  • The difference between ordinary income taxes and long-term capital gains
  • State income taxes
  • Property taxes that revalue higher as your home appreciates
  • Inflation

Another significant observation is how compounding’s best friend is uninterrupted time. If we doubled the rates of return in the chart to Hall of Fame return levels of 16% and 14% CAGRs but cut the compounding time in half to 20 years, you end up a bit worse off than in the 40-year case.

Teach your kids about compounding early!

{🗨️“Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it.” — Albert Einstein

The power of time While Warren Buffet has been an above-average investor over his entire career, his status as one of the richest people in the world owes much to longevity. [He was stellar for several decades but as you might expect by the time he was managing tens of billions, the performance asymptotically reverted to just market-like returns.] He didn’t become a billionaire until he was about 60. He has since been compounding for 30+ years! Most people don’t even make it into their 90s let alone can say they’ve been investing since they were teens.}

The Compounding “Gotcha”

If you earn a 10% return, then lose 10% your average return is 0…but your realized return is -1%

$100 —> $110 —> $99

If you lose 50%, you need to make 100% to get back to even.

More generally:

If you lose X%, you must earn X/(1−X)% to return your money.

notion image

2 key things to note:

  1. Return math is asymmetric — the return required to recover is larger than the percentage loss
  1. This asymmetry gets worse with volatility. The larger the loss, the steeper the recovery function. If you lose 75% on an investment you need to triple your money to get back to even!

This property of compounding math is so fundamental to investing that it underpins everything from risk management to option pricing. If you are interested in learning more there are several useful links below but the main takeaways:

  • Investing is a multiplicative process so we want to look at compounded returns not simple returns.
  • Volatility is asymmetric — over time it pulls median returns (the returns you expect to see) lower than average returns.
  • Volatility has a non-linear relationship with expected returns — while you need some volatility (if there were no volatility you would not get anything more than a risk-free rate), some drawdowns are too steep to recover from.

📎Learn More

I’ve written a lot on this topic.


From Around the Web


From My Actual Life

Extra $25 bucks and a week wait and voila custom low Blazer 77s. Would have put a🌛 emoji on the black leather back tag if those were allowable characters.

Customize your own. It’s a pretty quick, fun process. You can customize many of the Nike styles. Could be the perfect gift idea with the holidays around the corner.


Stay groovy ☮️

Leave a Reply