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Rest

 I hope that everybody in the world gets their infinite moment of respite today. 

Tuesday, November 11, 2025

Future

It's a well known question: if all we know and are is *now*, what sense is there in preparing for the future?

In the late 1960s, a study was conducted in Stanford where a child was seated at a table with a marshmallow placed in front of them. The child could eat it now or wait until the researcher returned, at which point they would get a second marshmallow. These children were tracked throughout their adult lives, and those who were able to delay gratification tended to have "better" life outcomes -- better paying jobs, better health, etc. 

Some people moralize delay of gratification, talk highly of discipline and grit. Not everyone feels so strongly about it but I'm sure most agree future-thinking is better than living hedonistically or impulsively -- that it's far better to wait for the second marshmallow.

I question that, though. Only the present moment is certain -- and even if we model the future, the further out it gets the more uncertain it is. And a marshmallow in hand is worth two in the bush, no?

There is no real benefit to assigning a hierarchy to different parts of the brain -- the so-called "monkey brain" and the frontal lobe are all part of a singular reinforcement learning agent that seeks reward. For some, two marshmallows doesn't mean double the happiness and they'd rather have a certain marshmallow now. For others, maybe the waiting itself is the reward, as the promise of two is worth it. Or perhaps the reward is the the feeling that you're following the rules, that you're taking the "smarter" path, being a good boy like your parents taught you, or even avoiding punishment by doing the "right" thing. Maybe you even get to feel better than those undisciplined, uneducated folk who just can't wait. 

As it turns out, the latter is closer to the truth. Later replications of the marshmallow study found that family environment and socioeconomic status explained much of the difference in life outcomes. In other words, people who wait for two marshmallows do so mostly because their parents told them to. Then they grow up and tell their kids the same thing, that two is better than one, which conditions their kids to reward themselves while waiting for that marshmallow ("I'm a good kid"/"I'll get hit if I..."/"I'm better than them"), and hence the two-marshmallow faith self-perpetuates. 

Loneliness

There's a kind of loneliness that goes deeper than physical loneliness, emotional loneliness. It's the realization that no matter how close you are with someone, at the end of the day it is only your conscious experience that you have. It is the solipsistic reality that you only presume what others think and feel, *that* others think and feel. It's what I describe as the realization that you are an island in a dense, eternal fog, and there's no real evidence that there are other islands in the sea, only currents to suggest so. 

Even if they do, you communicate through such channels already so narrow and further hampered by societal, cultural, or emotional barriers. 

It's a feeling I want to investigate further. I don't think it's necessarily a bad feeling, this loneliness. I think that maybe it's not necessarily the stripping away of the physical, mental, emotional frameworks of our everyday life that gives it this "lonely" flavor -- in fact I think this ought to be liberating. Maybe it's the holding onto that last frame of "concept of self" -- the ego. If we rid ourselves of this, then what is left but simply a collection of experiences and memories? What is there to *be* lonely?


Thursday, November 6, 2025

Moderation

Centenarians often say their secret to longevity is "everything in moderation". But moderation means different things to different people. What is moderation, in a lifestyle where excess is normalized? Too much sugar, meat, caffeine, too much sitting, too much stress, loneliness, and too little sleep... Not to mention our baseline exposure to substances we are slowly learning are poisons: PFAs, xenoestrogens, and more recently microplastics. Our bodies no longer understand "moderation" as it once was known -- it is now considered normal to live out the end of our lives in poor health and isolation.

It is amazing to me that in 16th century Europe, sugar cost more than gold per ounce. It was sold by apothecaries and praised for its medicinal properties: energizing the body, curing melancholy, warding off disease... makes it sound like a drug.

What is the "optimal" use of rote learning in studying (pure) math?

I feel like I wrote a decent answer to the above-titled MSE question so I'm pasting it here. 

How do you solve a jigsaw puzzle? Do you take each piece and try to figure out exactly where it must go first, piece by piece? Or do you start sorting a bunch of pieces by color, texture, until the images start clicking into place? How much of both?

Like puzzle pieces, mathematical concepts gain clarity in context -- e.g. an isolated dark spot on a puzzle piece may be identified as a roof tile only when gathered with other "roof pieces". Or maybe you could have added it with the "skyline pieces" instead. In the same way, there is often more than one way to "understand" a mathematical concept, and each way admits a different set of relations to other concepts. Look up any "intuition" question on MSE and you'll see this at play in the various answers given. It follows that if you are struggling with a particular proof or concept, it's sometimes better to cast your net wide and focus on expanding your context -- that is to say, memorize and move on.

You will find people giving similar advice when reading papers -- skim first, several times if you need to, then drill down as needed. Unfortunately, I don't have anything more specific that can apply to a general case as it even depends on how something is meant to be read, and how well it is written. The best expositors (Halmos comes to mind) mitigate the need for jumping around to some extent and try to keep things linear, but there are still lots of variables like writing style, learning style, and compatibility of background knowledge which make it difficult to give a general solution. The best thing to do, like others have mentioned, is to do the exercises to constantly evaluate your understanding and see where you might need to drill down a bit.